Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 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×#459 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #459 | D43 |
| hypocenter | C43 | #3284 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #459 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063344 | C2 | semidirect |
| 2. #14583569 | C2 | semidirect |
| 3. #14583553 | C2 | semidirect |
| 4. #14583271 | C2 | semidirect |
| 5. #14583127 | C2 | semidirect |
| 6. #14583110 | C2 | semidirect |
| 7. #14583062 | C2 | semidirect |
| 8. #14583041 | C2 | semidirect |
| 9. C4×#10621883 | C2 | semidirect |
| 10. #14582964 | C2 | semidirect |
| 11. C43×#459 | C2 | semidirect |
| 68. #10621883 | D4 | semidirect |
| 127. C4×C43 | #135 | semidirect |
| 147. #459 | D43 | semidirect |
| 152. C43 | #3284 | semidirect |
| 272. C4 | #13063344 | semidirect |