Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #14583533 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#472 | C2 |
| socle | C2×C43 | D42 |
| hypercenter | #472 | D43 |
| hypocenter | C43 | #3290 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583716 | C2 | semidirect |
| 2. #14583709 | C2 | semidirect |
| 3. #14583700 | C2 | semidirect |
| 4. #14583282 | C2 | semidirect |
| 5. #14583175 | C2 | semidirect |
| 6. #14583161 | C2 | semidirect |
| 7. #14583079 | C2 | semidirect |
| 8. #14583070 | C2 | semidirect |
| 9. #14583015 | C2 | semidirect |
| 10. #14583014 | C2 | semidirect |
| 11. C43×#472 | C2 | semidirect |
| 12. #13063372 | C22 | semidirect |
| 16. #13063358 | C22 | semidirect |
| 27. C2×Dic172 | C22 | semidirect |
| 28. C2×#10621883 | C22 | semidirect |
| 31. #13063333 | C22 | semidirect |
| 33. #13063312 | C22 | semidirect |
| 34. #13063260 | C22 | semidirect |
| 35. #13063252 | C22 | semidirect |
| 37. #13063251 | C22 | semidirect |
| 38. #13063243 | C22 | semidirect |
| 39. C8×Dic43 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C43 | C22 | semidirect |
| 42. #131×C43 | C22 | semidirect |
| 43. #108×C43 | C22 | semidirect |
| 44. #100×C43 | C22 | semidirect |
| 155. #472 | D43 | semidirect |
| 161. C43 | #3290 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D43 | semidirect |
| 185. #131 | C2×D43 | semidirect |
| 188. #108 | C2×D43 | semidirect |
| 193. #100 | C2×D43 | semidirect |