Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
488 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 125 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×#492 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #492 | D43 |
| hypocenter | C43 | #3208 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #492 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583454 | C2 | semidirect |
| 3. #14583273 | C2 | semidirect |
| 4. #14583246 | C2 | semidirect |
| 5. #14583245 | C2 | semidirect |
| 6. #14583097 | C2 | semidirect |
| 7. #14583048 | C2 | semidirect |
| 8. #14582950 | C2 | semidirect |
| 9. C43×#492 | C2 | semidirect |
| 13. C2×#10621884 | C22 | semidirect |
| 14. #13063325 | C22 | semidirect |
| 22. Q8×Dic43 | C22 | semidirect |
| 26. Dic43⋊C8 | C22 | semidirect |
| 27. #13063247 | C22 | semidirect |
| 28. #13063246 | C22 | semidirect |
| 30. C4×C43⋊C8 | C22 | semidirect |
| 31. C2×SD16×C43 | C22 | semidirect |
| 32. C4⋊Q8×C43 | C22 | semidirect |
| 34. C4×C8×C43 | C22 | semidirect |
| 95. C4×D43 | SD16 | semidirect |
| 128. #492 | D43 | semidirect |
| 134. C43 | #3208 | semidirect |
| 139. C2×SD16 | C2×D43 | semidirect |
| 141. C4⋊Q8 | C2×D43 | semidirect |
| 159. C4×C8 | C2×D43 | semidirect |