Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D172 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#405 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #405 | D43 |
| hypocenter | C43 | #3154 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063358 | C2 | semidirect |
| 2. C2×#13063353 | C2 | semidirect |
| 3. C2×#13063347 | C2 | semidirect |
| 4. C22×#10621873 | C2 | semidirect |
| 5. #14583475 | C2 | semidirect |
| 6. #14583468 | C2 | semidirect |
| 7. #14583293 | C2 | semidirect |
| 8. #14583288 | C2 | semidirect |
| 9. #14583283 | C2 | semidirect |
| 10. #14583272 | C2 | semidirect |
| 11. C43×#405 | C2 | semidirect |
| 19. C2×Dic172 | C22 | semidirect |
| 20. C2×Dic172 | C22 | semidirect |
| 25. C2×#10621873 | C22 | semidirect |
| 26. C2×#10621873 | C22 | semidirect |
| 27. C2×#10621873 | C22 | semidirect |
| 29. C2×D344 | C22 | semidirect |
| 30. #13063325 | C22 | semidirect |
| 33. #13063313 | C22 | semidirect |
| 41. #97×C43 | C22 | semidirect |
| 42. C4×C8×C43 | C22 | semidirect |
| 67. M16×C43 | D4 | semidirect |
| 68. C2×C8×C43 | D4 | semidirect |
| 159. #405 | D43 | semidirect |
| 160. C43 | #3154 | semidirect |
| 190. #97 | C2×D43 | semidirect |
| 191. C4×C8 | C2×D43 | semidirect |
| 226. M16 | D172 | semidirect |
| 227. C2×C8 | D172 | semidirect |