Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
444 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 111 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×#496 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #496 | D43 |
| hypocenter | C43 | #3213 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583447 | C2 | semidirect |
| 2. #124×D43 | C2 | semidirect |
| 3. #14583286 | C2 | semidirect |
| 4. #14583259 | C2 | semidirect |
| 5. #14583258 | C2 | semidirect |
| 6. #14583116 | C2 | semidirect |
| 7. #14583112 | C2 | semidirect |
| 8. #14583036 | C2 | semidirect |
| 9. #14583031 | C2 | semidirect |
| 10. #14582954 | C2 | semidirect |
| 11. C43×#496 | C2 | semidirect |
| 15. C2×#10621883 | C22 | semidirect |
| 17. #13063325 | C22 | semidirect |
| 27. D4×Dic43 | C22 | semidirect |
| 31. Dic43⋊C8 | C22 | semidirect |
| 32. #13063250 | C22 | semidirect |
| 33. #13063249 | C22 | semidirect |
| 37. #13063236 | C22 | semidirect |
| 38. C2×SD16×C43 | C22 | semidirect |
| 40. #127×C43 | C22 | semidirect |
| 42. #97×C43 | C22 | semidirect |
| 154. #496 | D43 | semidirect |
| 162. C43 | #3213 | semidirect |
| 167. C2×SD16 | C2×D43 | semidirect |
| 171. #127 | C2×D43 | semidirect |
| 193. #97 | C2×D43 | semidirect |