Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
4544 conjugacy classes of subgroups; only the 725 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 725 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×#120 |
| 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. C25×D43 | C2 | semidirect |
| 2. C23×D172 | C2 | semidirect |
| 3. C23×C22⋊D43 | C2 | semidirect |
| 4. C2×#13063295 | C2 | direct (N × H) |
| 5. C22×(C2×D43)⋊C4 | C2 | semidirect |
| 6. C22×C22⋊C4×C43 | C2 | semidirect |
| 10. C24×D43 | C22 | semidirect |
| 11. C24×D43 | C22 | semidirect |
| 13. C22×D172 | C22 | semidirect |
| 15. C22×C22⋊D43 | C22 | semidirect |
| 16. C23×Dic43 | C22 | semidirect |
| 17. #13063295 | C22 | direct (N × H) |
| 18. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 20. C23×C4×C43 | C22 | semidirect |
| 21. C2×C22⋊C4×C43 | C22 | semidirect |
| 23. C24×C43 | D4 | semidirect |
| 33. C23×D43 | D4 | semidirect |
| 35. C23×D43 | C23 | semidirect |
| 36. C23×D43 | C23 | semidirect |
| 38. C22×C4×C43 | C23 | semidirect |
| 40. C2×C22⋊D43 | C23 | semidirect |
| 42. C22×Dic43 | C23 | semidirect |
| 44. C2×D172 | C23 | semidirect |
| 45. C22⋊C4×C43 | C23 | semidirect |
| 46. (C2×D43)⋊C4 | C23 | semidirect |
| 51. C23×C43 | C2×D4 | semidirect |
| 63. C22×D43 | C2×D4 | semidirect |
| 65. C22×D43 | C24 | semidirect |
| 67. C2×C4×C43 | C24 | semidirect |
| 70. C2×Dic43 | C24 | semidirect |
| 74. C22×C43 | #120 | semidirect |
| 77. C22×C43 | C22×D4 | semidirect |
| 86. C2×D43 | C22×D4 | semidirect |
| 91. C2×C43 | C2×#120 | semidirect |
| 101. C22×C22⋊C4 | D43 | semidirect |
| 102. C43 | C22×#120 | semidirect |
| 114. C23×C4 | C2×D43 | semidirect |
| 117. C2×C22⋊C4 | C2×D43 | semidirect |
| 130. C24 | D172 | semidirect |
| 140. C22×C4 | C22×D43 | semidirect |
| 142. C22⋊C4 | C22×D43 | semidirect |
| 158. C23 | C2×D172 | semidirect |
| 167. C2×C4 | C23×D43 | semidirect |
| 178. C22 | #13063295 | direct (N × H) |
| 181. C22 | C22×D172 | semidirect |
| 188. C2 | C2×#13063295 | direct (N × H) |