Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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×#497 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #497 | D43 |
| hypocenter | C43 | #3218 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×D43 | C2 | semidirect |
| 3. #14583294 | C2 | semidirect |
| 4. #14583268 | C2 | semidirect |
| 5. #14583267 | C2 | semidirect |
| 6. #14583107 | C2 | semidirect |
| 7. #14583102 | C2 | semidirect |
| 8. #14583053 | C2 | semidirect |
| 10. #14582954 | C2 | semidirect |
| 11. C43×#497 | C2 | semidirect |
| 139. #497 | D43 | semidirect |
| 147. C43 | #3218 | semidirect |