Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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×#495 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #495 | D43 |
| hypocenter | C43 | C2×#495 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #495 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×D43 | C2 | semidirect |
| 2. C2×SD16×D43 | C2 | semidirect |
| 4. #124×D43 | C2 | semidirect |
| 5. #14583284 | C2 | semidirect |
| 6. #14583283 | C2 | semidirect |
| 7. #14583282 | C2 | semidirect |
| 8. #14583281 | C2 | semidirect |
| 9. #14583280 | C2 | semidirect |
| 10. C4×C8×D43 | C2 | semidirect |
| 11. C43×#495 | C2 | semidirect |
| 14. C2×Dic172 | C22 | semidirect |
| 15. C2×#10621885 | C22 | semidirect |
| 17. C2×#10621873 | C22 | semidirect |
| 18. C2×#10621883 | C22 | semidirect |
| 19. C2×#10621884 | C22 | semidirect |
| 26. #13063314 | C22 | semidirect |
| 27. #13063313 | C22 | semidirect |
| 28. #13063312 | C22 | semidirect |
| 32. C4×C43⋊C8 | C22 | semidirect |
| 33. C8×Dic43 | C22 | semidirect |
| 34. C8×Dic43 | C22 | semidirect |
| 35. C2×Q16×C43 | C22 | semidirect |
| 36. C2×SD16×C43 | C22 | semidirect |
| 38. #124×C43 | C22 | semidirect |
| 39. C4×C8×C43 | C22 | semidirect |
| 126. D43 | #495 | direct (N × H) |
| 136. #495 | D43 | direct (N × H) |
| 138. C43 | C2×#495 | semidirect |
| 144. C2×Q16 | C2×D43 | semidirect |
| 149. C2×SD16 | C2×D43 | semidirect |
| 160. #124 | C2×D43 | semidirect |
| 166. C4×C8 | C2×D43 | semidirect |