Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 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×#494 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #494 | D43 |
| hypocenter | C43 | #3276 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #494 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063357 | C2 | semidirect |
| 2. #14583564 | C2 | semidirect |
| 4. #14583154 | C2 | semidirect |
| 5. #14583106 | C2 | semidirect |
| 6. #14583101 | C2 | semidirect |
| 7. #14583060 | C2 | semidirect |
| 8. #14583053 | C2 | semidirect |
| 9. C4×#10621873 | C2 | semidirect |
| 10. #14582978 | C2 | semidirect |
| 11. C43×#494 | C2 | semidirect |
| 80. #10621873 | D4 | semidirect |
| 122. C4×C43 | #137 | semidirect |
| 138. #494 | D43 | semidirect |
| 146. C43 | #3276 | semidirect |
| 261. C4 | #13063357 | semidirect |