Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 137 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×#493 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #493 | D43 |
| hypocenter | C43 | #3155 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063349 | C2 | semidirect |
| 2. C2×#13063344 | C2 | semidirect |
| 3. C2×D8×D43 | C2 | semidirect |
| 4. #14583462 | C2 | semidirect |
| 5. #14583287 | C2 | semidirect |
| 6. #14583286 | C2 | semidirect |
| 7. #14583283 | C2 | semidirect |
| 8. #14583282 | C2 | semidirect |
| 9. #14583274 | C2 | semidirect |
| 10. #14582853 | C2 | semidirect |
| 11. C43×#493 | C2 | semidirect |
| 16. C2×Dic172 | C22 | semidirect |
| 17. C2×#10621873 | C22 | semidirect |
| 18. C2×#10621883 | C22 | semidirect |
| 19. C2×#10621883 | C22 | semidirect |
| 22. C2×#10621882 | C22 | semidirect |
| 26. #13063321 | C22 | semidirect |
| 27. #13063313 | C22 | semidirect |
| 28. #13063312 | C22 | semidirect |
| 32. #13063236 | C22 | semidirect |
| 33. #13063235 | C22 | semidirect |
| 34. C8×Dic43 | C22 | semidirect |
| 36. C2×D8×C43 | C22 | semidirect |
| 37. C2×D8×C43 | C22 | semidirect |
| 38. #127×C43 | C22 | semidirect |
| 39. C4×C8×C43 | C22 | semidirect |
| 75. #10621872 | D4 | semidirect |
| 76. C8×D43 | D4 | semidirect |
| 139. #493 | D43 | semidirect |
| 141. C43 | #3155 | semidirect |
| 155. C2×D8 | C2×D43 | semidirect |
| 156. C2×D8 | C2×D43 | semidirect |
| 160. #127 | C2×D43 | semidirect |
| 169. C4×C8 | C2×D43 | semidirect |