Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
448 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 115 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×#460 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #460 | D43 |
| hypocenter | C43 | #3324 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #460 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583622 | C2 | semidirect |
| 3. #14583245 | C2 | semidirect |
| 4. #14583221 | C2 | semidirect |
| 5. #14583180 | C2 | semidirect |
| 6. #14583142 | C2 | semidirect |
| 7. #14583048 | C2 | semidirect |
| 8. C4×#10621884 | C2 | semidirect |
| 9. #14582976 | C2 | semidirect |
| 10. #14582902 | C2 | semidirect |
| 11. C43×#460 | C2 | semidirect |
| 15. C2×#10621872 | C22 | semidirect |
| 16. #13063325 | C22 | semidirect |
| 19. #13063301 | C22 | semidirect |
| 26. #13063283 | C22 | semidirect |
| 27. #13063259 | C22 | semidirect |
| 28. #13063256 | C22 | semidirect |
| 29. #13063249 | C22 | semidirect |
| 31. #13063246 | C22 | semidirect |
| 32. #13063246 | C22 | semidirect |
| 34. (C2×D43)⋊C8 | C22 | semidirect |
| 35. C4×C43⋊C8 | C22 | semidirect |
| 36. C2×SD16×C43 | C22 | semidirect |
| 38. C4×Q8×C43 | C22 | semidirect |
| 39. C4⋊C8×C43 | C22 | semidirect |
| 40. #102×C43 | C22 | semidirect |
| 142. #460 | D43 | semidirect |
| 147. C43 | #3324 | semidirect |
| 151. C2×SD16 | C2×D43 | semidirect |
| 162. C4×Q8 | C2×D43 | semidirect |
| 168. C4⋊C8 | C2×D43 | semidirect |
| 174. #102 | C2×D43 | semidirect |