Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
444 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 121 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×#461 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #461 | D43 |
| hypocenter | C43 | #3110 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583454 | C2 | semidirect |
| 3. #14583233 | C2 | semidirect |
| 4. #14583180 | C2 | semidirect |
| 5. #14583179 | C2 | semidirect |
| 6. #14583101 | C2 | semidirect |
| 8. #14583002 | C2 | semidirect |
| 9. #14583000 | C2 | semidirect |
| 10. #14582955 | C2 | semidirect |
| 11. C43×#461 | C2 | semidirect |
| 15. #13063325 | C22 | semidirect |
| 19. Q8×Dic43 | C22 | semidirect |
| 30. #13063259 | C22 | semidirect |
| 31. #13063258 | C22 | semidirect |
| 32. C4⋊(C43⋊C8) | C22 | semidirect |
| 33. #13063249 | C22 | semidirect |
| 37. #13063235 | C22 | semidirect |
| 39. C4⋊Q8×C43 | C22 | semidirect |
| 41. C4⋊C8×C43 | C22 | semidirect |
| 42. #103×C43 | C22 | semidirect |
| 153. #461 | D43 | semidirect |
| 158. C43 | #3110 | semidirect |
| 164. C4⋊Q8 | C2×D43 | semidirect |
| 183. C4⋊C8 | C2×D43 | semidirect |
| 185. #103 | C2×D43 | semidirect |