Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
564 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #3150 |
| 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. C2×#13063346 | C2 | semidirect |
| 2. C2×#13063344 | C2 | semidirect |
| 3. #14583448 | C2 | semidirect |
| 4. #14583447 | C2 | semidirect |
| 5. #14583294 | C2 | semidirect |
| 6. #14583293 | C2 | semidirect |
| 7. #14583290 | C2 | semidirect |
| 8. #14583287 | C2 | semidirect |
| 9. #14583286 | C2 | semidirect |
| 10. #97×D43 | C2 | semidirect |
| 11. C43×#496 | C2 | semidirect |
| 79. C8×D43 | D4 | semidirect |
| 143. #496 | D43 | semidirect |
| 145. C43 | #3150 | semidirect |