Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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×#474 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #474 | D43 |
| hypocenter | C43 | #3100 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583450 | C2 | semidirect |
| 2. C4×D4×D43 | C2 | semidirect |
| 3. #14583214 | C2 | semidirect |
| 4. #14583176 | C2 | semidirect |
| 5. #14583095 | C2 | semidirect |
| 6. #14583094 | C2 | semidirect |
| 7. #14583034 | C2 | semidirect |
| 8. #14582981 | C2 | semidirect |
| 9. #14582979 | C2 | semidirect |
| 10. #14582951 | C2 | semidirect |
| 11. C43×#474 | C2 | semidirect |
| 17. #13063322 | C22 | semidirect |
| 25. #13063287 | C22 | semidirect |
| 31. #13063258 | C22 | semidirect |
| 32. C4⋊(C43⋊C8) | C22 | semidirect |
| 33. #13063247 | C22 | semidirect |
| 35. #13063245 | C22 | semidirect |
| 37. C8×Dic43 | C22 | semidirect |
| 38. C4⋊Q8×C43 | C22 | semidirect |
| 40. #107×C43 | C22 | semidirect |
| 41. C4⋊C8×C43 | C22 | semidirect |
| 93. D4×C43 | #41 | semidirect |
| 112. D172 | #41 | semidirect |
| 120. C4×D43 | D8 | semidirect |
| 159. #474 | D43 | semidirect |
| 166. C43 | #3100 | semidirect |
| 172. C4⋊Q8 | C2×D43 | semidirect |
| 189. #107 | C2×D43 | semidirect |
| 191. C4⋊C8 | C2×D43 | semidirect |
| 256. D4 | #10621902 | semidirect |