Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
2528 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C22×C43 | C25 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C22⋊C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C22⋊C4 | D43 |
| hypocenter | C43 | C22×#121 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C22×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C23×C22⋊D43 | C2 | semidirect |
| 3. C23×C22⋊D43 | C2 | semidirect |
| 4. C23×C4×D43 | C2 | semidirect |
| 5. C2×#13063298 | C2 | direct (N × H) |
| 6. C22×Dic43⋊C4 | C2 | semidirect |
| 7. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 8. C22×C22⋊C4×C43 | C2 | semidirect |
| 12. C22×D172 | C22 | semidirect |
| 15. C22×C22⋊D43 | C22 | semidirect |
| 16. C22×C22⋊D43 | C22 | semidirect |
| 20. C22×C4×D43 | C22 | semidirect |
| 21. #13063298 | C22 | direct (N × H) |
| 22. C2×Dic43⋊C4 | C22 | semidirect |
| 23. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 27. C2×C22⋊C4×C43 | C22 | semidirect |
| 38. C23×D43 | D4 | semidirect |
| 47. C2×C22⋊D43 | C23 | semidirect |
| 48. C2×C22⋊D43 | C23 | semidirect |
| 50. C22×Dic43 | D4 | semidirect |
| 54. C2×D172 | C23 | semidirect |
| 56. C2×C4×D43 | C23 | semidirect |
| 57. C22⋊C4×C43 | C23 | semidirect |
| 58. (C2×D43)⋊C4 | C23 | semidirect |
| 59. Dic43⋊C4 | C23 | semidirect |
| 76. C22×D43 | C2×D4 | semidirect |
| 86. C2×Dic43 | C2×D4 | semidirect |
| 95. C22×C43 | #121 | semidirect |
| 107. C2×D43 | C22×D4 | semidirect |
| 111. Dic43 | C22×D4 | semidirect |
| 114. C2×C43 | C2×#121 | semidirect |
| 127. C22×C22⋊C4 | D43 | semidirect |
| 128. C43 | C22×#121 | semidirect |
| 147. C2×C22⋊C4 | C2×D43 | semidirect |
| 179. C22⋊C4 | C22×D43 | semidirect |
| 223. C22 | #13063298 | direct (N × H) |
| 235. C2 | C2×#13063298 | direct (N × H) |