P2/c No. 13 C2h4


P 1 2/c 1

UNIQUE AXIS b

CELL CHOICE 1
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
[2] P1c1 (7) 2a 2a 2a 2a 2a 2a 2 × 2a
[2] P121 (3) x, y, z + (1/4) 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
[2] P-1 (2) 1a; 1b 1e; 1h 1c; 1g 1d; 1f 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] C12/c1 (15) 2a, 2b, c (1/2)x, (1/2)y, z; +(0, (1/2), 0) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
[2] C12/c1 (15) 2a, 2b, c (1/2)x + (1/4), (1/2)y, z; +(0, (1/2), 0) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
[2] C12/c1 (15) 2a, 2b, c (1/2)x, (1/2)y + (1/4), z; +(0, (1/2), 0) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
[2] C12/c1 (15) 2a, 2b, c (1/2)x + (1/4), (1/2)y + (1/4), z; +(0, (1/2), 0) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
[2] P121/c1 (14) a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
[2] P121/c1 (14) a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
[2] P12/c1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
[2] P12/c1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
[3] P12/c1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
[p] P12/c1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
[2] P12/c1 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
[2] P12/c1 2a, b, c (1/2)x + (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
[2] P12/n1 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
[2] P12/n1 2a, b, c (1/2)x + (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
[3] P12/c1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P12/c1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
[3] P12/c1 a - c, b, 3c x, y, (1/3)(x + z); ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P12/c1 a + c, b, 3c x, y, (1/3)(-x + z); ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[p] P12/c1 pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
[p] P12/c1 a + qc, b, pc x, y, (1/p)(-qx + z); +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q≤ (1/2)(p - 1)
* cell choice 2 (P12/n1)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3



P12/n1

UNIQUE AXIS b

CELL CHOICE 2
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
[2] P1n1 2a 2a 2a 2a 2a 2a 2 × 2a
[2] P121 x - (1/4), y, z - (1/4) 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
[2] P-1 1a; 1f 1e; 1g 1c; 1h 1b; 1d 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] A12/n1 a - c, 2b, 2c x, (1/2)y, (1/2)(x + z); +(0, (1/2), 0) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
[2] A12/n1 a - c, 2b, 2c x, (1/2)y, (1/2)(x + z) + (1/4); +(0, (1/2), 0) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
[2] A12/n1 a - c, 2b, 2c x, (1/2)y + (1/4), (1/2)(x + z); +(0, (1/2), 0) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
[2] A12/n1 a - c, 2b, 2c x, (1/2)y + (1/4), (1/2)(x + z) + (1/4); +(0, (1/2), 0) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
[2] P121/n1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
[2] P121/n1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
[2] P12/n1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
[2] P12/n1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
[3] P12/n1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
[p] P12/n1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
[2] P12/n1 a - c, b, 2c x, y, (1/2)(x + z); +(0, 0, (1/2)) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
[2] P12/n1 a - c, b, 2c x, y, (1/2)(x + z) + (1/4); +(0, 0, (1/2)) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
[2] P12/a1 a - c, b, 2c x, y, (1/2)(x + z); +(0, 0, (1/2)) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
[2] P12/a1 a - c, b, 2c x, y, (1/2)(x + z) + (1/4); +(0, 0, (1/2)) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
[3] P12/n1 a - 2c, b, 3c x, y, (1/3)(2x + z); ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P12/n1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
[3] P12/n1 2a + c, b, a + 2c (1/3)(2x - z), y, (1/3)(-x + 2z); ±((1/3), 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P12/n1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[p] P12/n1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
[p] P12/n1 pa, b, 2qa + c (1/p)(x - 2qz), y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* cell choice 2 (P12/n1)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3



P12/a1

UNIQUE AXIS b

CELL CHOICE 3
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
P11a 2a 2a 2a 2a 2a 2a 2 × 2a
P121 x + (1/4), y, z 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
P-1 1a; 1d 1g; 1h 1c; 1e 1b; 1f 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
I12/a1 a, 2b, a + 2c x - (1/2)z, (1/2)y, (1/2)z; +(0, (1/2), 0) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
I12/a1 a, 2b, a + 2c x - (1/2)z - (1/4), (1/2)y, (1/2)z - (1/4); +(0, (1/2), 0) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
I12/a1 a, 2b, a + 2c x - (1/2)z, (1/2)y + (1/4), (1/2)z; +(0, (1/2), 0) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
I12/a1 a, 2b, a + 2c x - (1/2)z - (1/4), (1/2)y + (1/4), (1/2)z - (1/4); +(0, (1/2), 0) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
P121/a1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
P121/a1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
P12/a1 a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
P12/a1 a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
P12/a1 a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
P12/a1 a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
P12/a1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
P12/a1 a, b, 2c x, y, (1/2)z - (1/4); +(0, 0, (1/2)) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
P12/n1 a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
P12/n1 a, b, 2c x, y, (1/2)z - (1/4); +(0, 0, (1/2)) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
P12/a1 a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P12/a1 3a, b, a + c (1/3)(x - z), y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
P12/a1 3a, b, -a + c (1/3)(x + z), y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P12/a1 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P12/a1 a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
P12/a1 pa, b, qa + c (1/p)(x - qz), y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* cell choice 2 (P12/n1)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3



P112/a

UNIQUE AXIS c

CELL CHOICE 1
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
[2] P11a (7) 2a 2a 2a 2a 2a 2a 2 × 2a
[2] P112 (3) x + (1/4), y, z 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
[2] P-1 (2) 1a; 1d 1g; 1h 1b; 1f 1c; 1e 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] A112/a (15) a, 2b, 2c x, (1/2)y, (1/2)z; +(0, 0, (1/2)) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
[2] A112/a (15) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z; +(0, 0, (1/2)) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
[2] A112/a (15) a, 2b, 2c x, (1/2)y, (1/2)z + (1/4); +(0, 0, (1/2)) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
[2] A112/a (15) a, 2b, 2c x, (1/2)y + (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
[2] P1121/a (14) a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
[2] P1121/a (14) a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
[2] P112/a a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
[2] P112/a a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
[3] P112/a a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
[p] P112/a a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
[2] P112/a a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
[2] P112/a a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
[2] P112/n a, 2b, c x, (1/2)y, z; +(0, (1/2), 0) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
[2] P112/n a, 2b, c x, (1/2)y + (1/4), z; +(0, (1/2), 0) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
[3] P112/a a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P112/a 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
[3] P112/a 3a, -a + b, c (1/3)(x + y), y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P112/a 3a, a + b, c (1/3)(x - y), y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[p] P112/a a, pb, c x, (1/p)y, z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
[p] P112/a pa, qa + b, c (1/p)(x - qy), y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q≤ (1/2)(p - 1)
* cell choice 2 (P112/n)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3



P112/n

UNIQUE AXIS c

CELL CHOICE 2
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
[2] P11n 2a 2a 2a 2a 2a 2a 2 × 2a
[2] P112 x - (1/4), y - (1/4), z 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
[2] P-1 1a; 1e 1f; 1g 1b; 1h 1c; 1d 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] B112/n 2a, -a + b, 2c (1/2)(x + y), y, (1/2)z,; +(0, 0, (1/2)) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
[2] B112/n 2a, -a + b, 2c (1/2)(x + y) + (1/4), y, (1/2)z,; +(0, 0, (1/2)) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
[2] B112/n 2a, -a + b, 2c (1/2)(x + y), y, (1/2)z + (1/4); +(0, 0, (1/2)) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
[2] B112/n 2a, -a + b, 2c (1/2)(x + y) + (1/4), y, (1/2)z + (1/4); +(0, 0, (1/2)) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
[2] P1121/n a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
[2] P1121/n a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
[2] P112/n a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
[2] P112/n a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
[3] P112/n a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
[p] P112/n a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
[2] P112/n 2a, -a + b, c (1/2)(x + y), y, z,; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
[2] P112/n 2a, -a + b, c (1/2)(x + y) + (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
[2] P112/b 2a, -a + b, c (1/2)(x + y), y, z; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
[2] P112/b 2a, -a + b, c (1/2)(x + y) + (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
[3] P112/n 3a, -2a + b, c (1/3)(x + 2y), y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P112/n a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
[3] P112/n 2a + b, a + 2b, c (1/3)(2x - y), (1/3)(-x + 2y), z; ±((1/3), (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[3] P112/n 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
[p] P112/n pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
[p] P112/n a + 2qb, pb, c x, (1/p)(-2qx + y), z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* cell choice 2 (P112/n)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3



P112/b

UNIQUE AXIS c

CELL CHOICE 3
Axes Coordinates Wyckoff positions
2a 2b 2c 2d 2e 2f 4g
I Maximal translationengleiche subgroups
P11b 2a 2a 2a 2a 2a 2a 2 × 2a
P112 x, y + (1/4), z 2e 2e 2e 2e 1a; 1b 1c; 1d 2 × 2e
P-1 1a; 1c 1f; 1h 1b; 1g 1d; 1e 2i 2i 2 × 2i
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
I112/b 2a + b, b, 2c (1/2)x, -(1/2)x + y, (1/2)z; +(0, 0, (1/2)) 4a; 4b 4c; 4d 8f 8f 2 × 4e 8f 2 × 8f
I112/b 2a + b, b, 2c (1/2)x - (1/4), -(1/2)x + y - (1/4), (1/2)z; +(0, 0, (1/2)) 8f 8f 4c; 4d 4a; 4b 8f 2 × 4e 2 × 8f
I112/b 2a + b, b, 2c (1/2)x, -(1/2)x + y, (1/2)z + (1/4); +(0, 0, (1/2)) 8f 8f 4a; 4b 4c; 4d 2 × 4e 8f 2 × 8f
I112/b 2a + b, b, 2c (1/2)x - (1/4), -(1/2)x + y - (1/4), (1/2)z + (1/4); +(0, 0, (1/2)) 4c; 4d 4a; 4b 8f 8f 8f 2 × 4e 2 × 8f
P1121/b a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4e 4e 2b; 2d 4e 4e 2 × 4e
P1121/b a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4e 2b; 2d 2a; 2c 4e 4e 4e 2 × 4e
   Enlarged unit cell, isomorphic
P112/b a, b, 2c x, y, (1/2)z; +(0, 0, (1/2)) 2a; 2c 4g 4g 2b; 2d 2 × 2e 2 × 2f 2 × 4g
P112/b a, b, 2c x, y, (1/2)z + (1/4); +(0, 0, (1/2)) 4g 2b; 2d 2a; 2c 4g 2 × 2e 2 × 2f 2 × 4g
P112/b a, b, 3c x, y, (1/3)z; ±(0, 0, (1/3)) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 3 × 2e 3 × 2f 3 × 4g
P112/b a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × p × 2e p × 2f p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g
P112/b 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 2e; 2f 4g 2 × 4g
P112/b 2a, b, c (1/2)x - (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 4g 2e; 2f 2 × 4g
P112/n 2a, b, c (1/2)x, y, z; +((1/2), 0, 0) 2a; 2d 4g 2b; 2c 4g 4g 2e; 2f 2 × 4g
P112/n 2a, b, c (1/2)x - (1/4), y, z; +((1/2), 0, 0) 4g 2b; 2c 4g 2a; 2d 2e; 2f 4g 2 × 4g
P112/b 3a, b, c (1/3)x, y, z; ±((1/3), 0, 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P112/b a + b, 3b, c x, (1/3)(-x + y), z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e(f*); 4g 2f(e*); 4g 3 × 4g
P112/b a - b, 3b, c x, (1/3)(x + y), z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P112/b a, 3b, c x, (1/3)y, z; ±(0, (1/3), 0) 2a; 4g 2b; 4g 2c; 4g 2d; 4g 2e; 4g 2f; 4g 3 × 4g
P112/b pa, b, c (1/p)x, y, z; +((u/p), 0, 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1 4g 4g 4g 4g 4g 4g
P112/b a + qb, pb, c x, (1/p)(-qx + y), z; +(0, (u/p), 0) 2a; ((p - 1)/2) × 2b; ((p - 1)/2) × 2c; ((p - 1)/2) × 2d; ((p - 1)/2) × 2e; ((p - 1)/2) × 2f; ((p - 1)/2) × p × 4g
p = prime > 2; u = 1, . . ., p - 1; 4g 4g 4g 4g 4g 4g
-(1/2)(p - 1)≤ q ≤ (1/2)(p - 1)
* cell choice 2 (P112/n)

Space groups of the series of isomorphic subgroups appear in different sequences for cell choices 1, 2 and 3










































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