Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates |
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| | (1) x, y, z | (2) -x, -y, z | (3) -x, y, -z | (4) x, -y, -z |
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I Maximal translationengleiche subgroups
| [2] P112 (3) | 1; 2 |
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| [2] P121 (3) | 1; 3 |
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| [2] P211 (3, P121) | 1; 4 | c, a, b
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II Maximal klassengleiche subgroups
[2] a' = 2a
| P2122 (17, P2221) | <3; 2 + (1, 0, 0)> | b, c, 2a | |
| P2122 (17, P2221) | <2; 3 + (1, 0, 0)> | b, c, 2a | 1/2, 0, 0 |
| P222 (16) | <2; 3> | 2a, b, c | |
| P222 (16) | <(2; 3) + (1, 0, 0)> | 2a, b, c | 1/2, 0, 0 |
[2] b' = 2b
| P2212 (17, P2221) | <2; 3 + (0, 1, 0)> | c, a, 2b | |
| P2212 (17, P2221) | <(2; 3) + (0, 1, 0)> | c, a, 2b | 0, 1/2, 0 |
| P222 (16) | <2; 3> | a, 2b, c | |
| P222 (16) | <3; 2 + (0, 1, 0)> | a, 2b, c | 0, 1/2, 0 |
[2] c' = 2c
| P2221 (17) | <3; 2 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
| P2221 (17) | <(2; 3) + (0, 0, 1)> | a, b, 2c | |
| P222 (16) | <2; 3> | a, b, 2c | |
| P222 (16) | <2; 3 + (0, 0, 1)> | a, b, 2c | 0, 0, 1/2 |
[2] b' = 2b, c' = 2c
| A222 (21, C222) | <2; 3> | 2b, 2c, a | |
| A222 (21, C222) | <3; 2 + (0, 1, 0)> | 2b, 2c, a | 0, 1/2, 0 |
| A222 (21, C222) | <2; 3 + (0, 0, 1)> | 2b, 2c, a | 0, 0, 1/2 |
| A222 (21, C222) | <2 + (0, 1, 0); 3 + (0, 0, 1)> | 2b, 2c, a | 0, 1/2, 1/2 |
[2] a' = 2a, c' = 2c
| B222 (21, C222) | <2; 3> | 2c, 2a, b | |
| B222 (21, C222) | <2; 3 + (0, 0, 1)> | 2c, 2a, b | 0, 0, 1/2 |
| B222 (21, C222) | <(2; 3) + (1, 0, 0)> | 2c, 2a, b | 1/2, 0, 0 |
| B222 (21, C222) | <2 + (1, 0, 0); 3 + (1, 0, 1)> | 2c, 2a, b | 1/2, 0, 1/2 |
[2] a' = 2a, b' = 2b
| C222 (21) | <2; 3> | 2a, 2b, c | |
| C222 (21) | <(2; 3) + (1, 0, 0)> | 2a, 2b, c | 1/2, 0, 0 |
| C222 (21) | <3; 2 + (0, 1, 0)> | 2a, 2b, c | 0, 1/2, 0 |
| C222 (21) | <2 + (1, 1, 0); 3 + (1, 0, 0)> | 2a, 2b, c | 1/2, 1/2, 0 |
[2] a' = 2a, b' = 2b, c' = 2c
| F222 (22) | <2; 3> | 2a, 2b, 2c | |
| F222 (22) | <3; 2 + (0, 1, 0)> | 2a, 2b, 2c | 0, 1/2, 0 |
| F222 (22) | <2; 3 + (0, 0, 1)> | 2a, 2b, 2c | 0, 0, 1/2 |
| F222 (22) | <(2; 3) + (1, 0, 0)> | 2a, 2b, 2c | 1/2, 0, 0 |
[3] a' = 3a
 | P222 (16) | <2; 3> | 3a, b, c | | | P222 (16) | <(2; 3) + (2, 0, 0)> | 3a, b, c | 1, 0, 0 | | P222 (16) | <(2; 3) + (4, 0, 0)> | 3a, b, c | 2, 0, 0 |
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[3] b' = 3b
| P222 (16) | <2; 3> | a, 3b, c | | | P222 (16) | <3; 2 + (0, 2, 0)> | a, 3b, c | 0, 1, 0 | | P222 (16) | <3; 2 + (0, 4, 0)> | a, 3b, c | 0, 2, 0 |
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[3] c' = 3c
| P222 (16) | <2; 3> | a, b, 3c | | | P222 (16) | <2; 3 + (0, 0, 2)> | a, b, 3c | 0, 0, 1 | | P222 (16) | <2; 3 + (0, 0, 4)> | a, b, 3c | 0, 0, 2 |
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- Series of maximal isomorphic subgroups
[p] a' = pa
| P222 (16) | <(2; 3) + (2u, 0, 0)> | pa, b, c | u, 0, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] b' = pb
| P222 (16) | <3; 2 + (0, 2u, 0)> | a, pb, c | 0, u, 0 | | | p > 2; 0 ≤ u < p
p conjugate subgroups for the prime p |
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[p] c' = pc
| P222 (16) | <2; 3 + (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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I Minimal translationengleiche supergroups
| [2] Pmmm (47); [2] Pnnn (48); [2] Pccm (49); [2] Pban (50); [2] P422 (89); [2] P4222 (93); [2] P-42c (112); [2] P-42m (111); [3] P23 (195) |
II Minimal non-isomorphic klassengleiche supergroups
- Additional centring translations
| [2] A222 (21, C222); [2] B222 (21, C222); [2] C222 (21); [2] I222 (23) |
