Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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×#436 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #436 | D43 |
| hypocenter | C43 | #3325 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ #436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583614 | C2 | semidirect |
| 2. D4×D172 | C2 | semidirect |
| 3. #14583246 | C2 | semidirect |
| 4. #14583224 | C2 | semidirect |
| 5. #14583190 | C2 | semidirect |
| 6. #14583152 | C2 | semidirect |
| 7. #14583095 | C2 | semidirect |
| 8. #14583035 | C2 | semidirect |
| 9. C4×D344 | C2 | semidirect |
| 10. #14582905 | C2 | semidirect |
| 11. C43×#436 | C2 | semidirect |
| 15. C2×D344 | C22 | semidirect |
| 16. #13063325 | C22 | semidirect |
| 21. #13063299 | C22 | semidirect |
| 25. C4×D172 | C22 | semidirect |
| 26. #13063284 | C22 | semidirect |
| 28. #13063259 | C22 | semidirect |
| 29. #13063257 | C22 | semidirect |
| 32. #13063247 | C22 | semidirect |
| 33. #13063247 | C22 | semidirect |
| 34. #13063247 | C22 | semidirect |
| 35. #13063247 | C22 | semidirect |
| 36. C2×M16×C43 | C22 | semidirect |
| 38. C4⋊C8×C43 | C22 | semidirect |
| 39. C22⋊C8×C43 | C22 | semidirect |
| 40. C4×C8×C43 | C22 | semidirect |
| 150. #436 | D43 | semidirect |
| 152. C43 | #3325 | semidirect |
| 157. C2×M16 | C2×D43 | semidirect |
| 173. C4⋊C8 | C2×D43 | semidirect |
| 180. C22⋊C8 | C2×D43 | semidirect |
| 181. C4×C8 | C2×D43 | semidirect |