Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3); (5); (9)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ |
| | (1) x, y, z | (2) -x, -y, z | (3) -y, x, z | (4) y, -x, z | | (5) -x, y, -z | (6) x, -y, -z | (7) y, x, -z | (8) -y, -x, -z | | (9) -x, -y, -z | (10) x, y, -z | (11) y, -x, -z | (12) -y, x, -z | | (13) x, -y, z | (14) -x, y, z | (15) -y, -x, z | (16) y, x, z |
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I Maximal translationengleiche subgroups
| [2] I-42m (121) | (1; 2; 5; 6; 11; 12; 15; 16)+ |
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| [2] I-4m2 (119) | (1; 2; 7; 8; 11; 12; 13; 14)+ |
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| [2] I4mm (107) | (1; 2; 3; 4; 13; 14; 15; 16)+ |
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| [2] I422 (97) | (1; 2; 3; 4; 5; 6; 7; 8)+ |
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| [2] I4/m11 (87, I4/m) | (1; 2; 3; 4; 9; 10; 11; 12)+ |
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| [2] I2/m2/m1 (71, Immm) | (1; 2; 5; 6; 9; 10; 13; 14)+ |
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| [2] I2/m12/m (69, Fmmm) | (1; 2; 7; 8; 9; 10; 15; 16)+ | a - b, a + b, c
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II Maximal klassengleiche subgroups
- Loss of centring translations
| [2] P42/nmc (137) | 1; 2; 7; 8; 11; 12; 13; 14; (3; 4; 5; 6; 9; 10; 15; 16) + (1/2, 1/2, 1/2) | | 1/4, 3/4, 1/4 |
| [2] P42/mnm (136) | 1; 2; 7; 8; 9; 10; 15; 16; (3; 4; 5; 6; 11; 12; 13; 14) + (1/2, 1/2, 1/2) | | |
| [2] P42/nnm (134) | 1; 2; 5; 6; 11; 12; 15; 16; (3; 4; 7; 8; 9; 10; 13; 14) + (1/2, 1/2, 1/2) | | 1/4, 3/4, 1/4 |
| [2] P42/mmc (131) | 1; 2; 5; 6; 9; 10; 13; 14; (3; 4; 7; 8; 11; 12; 15; 16) + (1/2, 1/2, 1/2) | | 0, 1/2, 0 |
| [2] P4/nmm (129) | 1; 2; 3; 4; 13; 14; 15; 16; (5; 6; 7; 8; 9; 10; 11; 12) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] P4/mnc (128) | 1; 2; 3; 4; 9; 10; 11; 12; (5; 6; 7; 8; 13; 14; 15; 16) + (1/2, 1/2, 1/2) | | |
| [2] P4/nnc (126) | 1; 2; 3; 4; 5; 6; 7; 8; (9; 10; 11; 12; 13; 14; 15; 16) + (1/2, 1/2, 1/2) | | 1/4, 1/4, 1/4 |
| [2] P4/mmm (123) | 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16 | | |
[3] c' = 3c
 | I4/mmm (139) | <2; 3; 5; 9> | a, b, 3c | | | I4/mmm (139) | <2; 3; (5; 9) + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | I4/mmm (139) | <2; 3; (5; 9) + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] c' = pc
| I4/mmm (139) | <2; 3; (5; 9) + (0, 0, 2u)> | a, b, pc | 0, 0, u | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p2] a' = pa, b' = pb
| I4/mmm (139) | <(2; 9) + (2u, 2v, 0); 3 + (u + v, -u + v, 0); 5 + (2u, 0, 0)> | pa, pb, c | u, v, 0 | | | p > 2; 0 ≤ u < p; 0 ≤ v < p
p2 conjugate subgroups for the prime p |
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I Minimal translationengleiche supergroups
| [3] Fm-3m (225); [3] Im-3m (229) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] c' = 1/2c C4/mmm (123, P4/mmm) |
