P4/nbm No. 125 P4/n2/b2/m D4h3


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 2c 2d 4e 4f 4g 4h 8i 8j 8k
8l 8m 16n
I Maximal translationengleiche subgroups
[2] P-4b2 (117) x + (1/2), y, z x + (1/4), y - (1/4), z 2c 2d 2a 2b 4g 4h 4f 4e 2 × 4g 2 × 4h 8i
8i 8i 2 × 8i
[2] P-42m (111) x + (1/2), y, z x + (1/4), y - (1/4), z 2e 2f 1a; 1d 1b; 1c 4n 4n 4m 2g; 2h 8o 8o 4i; 4l
4j; 4k 2 × 4n 2 × 8o
[2] P4bm (100) x + (1/4), y + (1/4), z 2a 2a 2b 2b 4c 4c 2 × 2a 2 × 2b 8d 8d 8d
8d 2 × 4c 2 × 8d
[2] P422 (89) x + (1/4), y + (1/4), z 1a; 1c 1b; 1d 2e 2f 4j 4k 2g; 2h 4i 2 × 4j 2 × 4k 4l; 4o
4m; 4n 8p 2 × 8p
[2] P4/n (85) x + (1/2), y, z 2c 2c 2a 2b 4d 4e 2 × 2c 4f 8g 8g 8g
8g 8g 2 × 8g
[2] Pban (50) 2a 2d 2b 2c 4e 4f 4k 4l 8m 8m 4g; 4i
4h; 4j 8m 2 × 8m
[2] Cmme (67) a + b, (1/2)(x + y) + (1/4), (1/2)(x + y), 4a 4b 4g 4g 4c; 4e 4d; 4f 8l 2 × 4g 8h; 8j 8i; 8k 16o
-a + b, c (1/2)(-x + y), z (1/2)(-x + y), z 16o 8m; 8n 2 × 16o
II Maximal klassengleiche subgroups
   Enlarged unit cell, non-isomorphic
[2] P42/nnm a, b, 2c x + (1/2), y, (1/2)z + (1/4) x, y, (1/2)z 4d 4c 4g 2a; 2b 4e; 4f 8m 8h 2 × 4g 8k; 8l 16n 16n
(134) 8i; 8j 2 × 8m 2 × 16n
[2] P42/nnm a, b, 2c x + (1/2), y, (1/2)z x, y, (1/2)z + (1/4) 4c 4d 2a; 2b 4g 8m 4e; 4f 8h 2 × 4g 16n 8k; 8l 8i; 8j
(134) 16n 2 × 8m 2 × 16n
[2] P42/nbc a, b, 2c x + (1/2), y, (1/2)z + (1/4) x, y, (1/2)z 4a 4c 4b 4d 8e 8j 8f 8g 16k 2 × 8j 8h; 8i
(133) 16k 16k 2 × 16k
[2] P42/nbc a, b, 2c x + (1/2), y, (1/2)z x, y, (1/2)z + (1/4) 4c 4a 4d 4b 8j 8e 8f 8g 2 × 8j 16k 16k
(133) 8h; 8i 16k 2 × 16k
[2] P4/nnc a, b, 2c x, y, (1/2)z + (1/4) x, y, (1/2)z 4e 2a; 2b 4d 4c 8f 8h 2 × 4e 8g 16k 2 × 8h 16k
(126) 8i; 8j 16k 2 × 16k
[2] P4/nnc a, b, 2c x, y, (1/2)z x, y, (1/2)z + (1/4) 2a; 2b 4e 4c 4d 8h 8f 2 × 4e 8g 2 × 8h 16k 8i; 8j
(126) 16k 16k 2 × 16k


Axes Coordinates Wyckoff positions
origin 1 origin 2 2a 2b 2c 2d 4e
4f 4g 4h 8i 8j
8k 8l 8m 16n
   Enlarged unit cell, isomorphic
[2] P4/nbm a, b, 2c x, y, (1/2)z; x, y, (1/2)z; 2a; 2b 4g 2c; 2d 4h 4e; 4f
±(0, 0, (1/2)) ±(0, 0, (1/2)) 8m 2 × 4g 2 × 4h 8i; 8j 16n
8k; 8l 16n 2 × 8m 2 × 16n
[2] P4/nbm a, b, 2c x, y, (1/2)z + (1/4); x, y, (1/2)z + (1/4); 4g 2a; 2b 4h 2c; 2d 8m
±(0, 0, (1/2)) ±(0, 0, (1/2)) 4e; 4f 2 × 4g 2 × 4h 16n 8i; 8j
16n 8k; 8l 2 × 8m 2 × 16n
[3] P4/nbm a, b, 3c x, y, (1/3)z; x, y, (1/3)z; 2a; 4g 2b; 4g 2c; 4h 2d; 4h 4e; 8m
±(0, 0, (1/3)) ±(0, 0, (1/3)) 4f; 8m 3 × 4g 3 × 4h 8i; 16n 8j; 16n
8k; 16n 8l; 16n 3 × 8m 3 × 16n
[p] P4/nbm a, b, pc x, y, (1/p)z; x, y, (1/p)z; 2a; ((p - 1)/2) × 4g 2b; ((p - 1)/2) × 4g 2c; ((p - 1)/2) × 4h 2d; ((p - 1)/2) × 4h 4e; ((p - 1)/2) × 8m
+(0, 0, (u/p)) +(0, 0, (u/p)) 4f; ((p - 1)/2) × 8m p × 4g p × 4h 8i; ((p - 1)/2) × 16n 8j; ((p - 1)/2) × 16n
p = prime > 2; u = 1, . . ., p - 1 8k; ((p - 1)/2) × 16n 8l; ((p - 1)/2) × 16n p × 8m p × 16n
[9] P4/nbm 3a, 3b, c (1/3)x, (1/3)y, z; (1/3)x, (1/3)y, z; 2a; 8i; 8k; 2b; 8j; 8l 2c; 8k; 8m 2d; 8l; 8m 4e; 8i; 8m; 16n
±((1/3), 0, 0); ±(0, (1/3), 0); 4f; 8j; 8m; 16n 4g; 2 × 16n 4h; 2 × 8m; 16n 3 × 8i; 3 × 16n 3 × 8j; 3 × 16n
±((1/3), (1/3), 0); ±((1/3), (2/3), 0) 3 × 8k; 3 × 16n 3 × 8l; 3 × 16n 3 × 8m; 3 × 16n 9 × 16n
[p2] P4/nbm pa, pb, c (1/p)x, (1/p)y, z; (1/p)x, (1/p)y, z; 2a; ((p - 1)/2) × 8i; 2b; ((p - 1)/2) × 8j; 2c; ((p - 1)/2) × 8k; 2d; ((p - 1)/2) × 8l; 4e; ((p - 1)/2) × 8i;
+((u/p), (v/p), 0) +((u/p), (v/p), 0) ((p - 1)/2) × 8k; ((p - 1)/2) × 8l; ((p - 1)/2) × 8m; ((p - 1)/2) × 8m; ((p - 1)/2) × 8m;
p = prime > 2; (((p - 1)(p - 3))/8) × 16n (((p - 1)(p - 3))/8) × 16n (((p - 1)(p - 3))/8) × 16n (((p - 1)(p - 3))/8) × 16n (((p - 1)2)/4) × 16n
u, v = 1, . . ., p - 1 4f; ((p - 1)/2) × 8j; 4g; ((p2 - 1)/4) × 16n 4h; (p - 1) × 8m; p × 8i; p × 8j;
((p - 1)/2) × 8m; (((p - 1)2)/4) × 16n ((p(p - 1))/2) × 16n ((p(p - 1))/2) × 16n
(((p - 1)2)/4) × 16n
p × 8k; p × 8l; p × 8m; p2 × 16n
((p(p - 1))/2) × 16n ((p(p - 1))/2) × 16n ((p(p - 1))/2) × 16n









































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