Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#476 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #476 | D43 |
| hypocenter | C43 | #3325 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #476 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583615 | C2 | semidirect |
| 2. D4×D172 | C2 | semidirect |
| 3. #14583247 | C2 | semidirect |
| 4. #14583225 | C2 | semidirect |
| 5. #14583153 | C2 | semidirect |
| 6. #14583095 | C2 | semidirect |
| 7. #14583034 | C2 | semidirect |
| 8. C4×#10621882 | C2 | semidirect |
| 9. #14582976 | C2 | semidirect |
| 10. #14582902 | C2 | semidirect |
| 11. C43×#476 | C2 | semidirect |
| 14. C2×D344 | C22 | semidirect |
| 16. C2×#10621872 | C22 | semidirect |
| 21. #13063300 | C22 | semidirect |
| 25. C4×D172 | C22 | semidirect |
| 27. #13063283 | C22 | semidirect |
| 28. #13063258 | C22 | semidirect |
| 29. #13063247 | C22 | semidirect |
| 31. #13063245 | C22 | semidirect |
| 32. #13063245 | C22 | semidirect |
| 33. #13063245 | C22 | semidirect |
| 34. (C2×D43)⋊C8 | C22 | semidirect |
| 35. C4×C43⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C43 | C22 | semidirect |
| 38. #106×C43 | C22 | semidirect |
| 39. C4⋊C8×C43 | C22 | semidirect |
| 145. #476 | D43 | semidirect |
| 152. C43 | #3325 | semidirect |
| 158. C4⋊Q8 | C2×D43 | semidirect |
| 172. #106 | C2×D43 | semidirect |
| 173. C4⋊C8 | C2×D43 | semidirect |