I41md No. 109 C4v11

 Axes Coordinates Wyckoff positions 4a 8b 16c I Maximal translationengleiche subgroups [2] I41 (80) 4a 8b 2 × 8b [2] Imm2 (44) 2a; 2b 4c; 4d 2 × 8e [2] Fdd2 (43) a + b, -a + b, c (1/2)(x + y), (1/2)(-x + y), z 8a 16b 2 × 16b II Maximal klassengleiche subgroups Enlarged unit cell, isomorphic [3] I41md b, -a, 3c y, -x, (1/3)z; ±(0, 0, (1/3)) 3 × 4a 3 × 8b 3 × 16c [p] I41md b, -a, pc y, -x, (1/p)z; +(0, 0, (u/p)) p × 4a p × 8b p × 16c p = prime = 4n - 1; u = 1, . . ., p - 1 [5] I41md a, b, 5c x, y, (1/5)z; ±(0, 0, (1/5)); ±(0, 0, (2/5)) 5 × 4a 5 × 8b 5 × 16c [p] I41md a, b, pc x, y, (1/p)z; +(0, 0, (u/p)) p × 4a p × 8b p × 16c p = prime = 4n + 1; u = 1, . . ., p - 1 [9] I41md 3a, 3b, c (1/3)x, (1/3)y, z; ±((1/3), 0, 0); 4a; 2 × 8b; 16c 3 × 8b; 3 × 16c 9 × 16c ±(0, (1/3), 0); ±((1/3), (1/3), 0); ±((1/3), (2/3), 0) [p2] I41md pa, pb, c (1/p)x, (1/p)y, z; +((u/p), (v/p), 0) 4a; (p - 1) × 8b; p × 8b; p2 × 16c p = prime > 2; u, v = 1, . . ., p - 1 (1/4)(p - 1)2 × 16c (1/2)p(p - 1) × 16c