Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
564 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 564 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×#497 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #497 | D43 |
| hypocenter | C43 | C2×#497 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q16×D43 | C2 | semidirect |
| 3. C4⋊Q8×D43 | C2 | semidirect |
| 5. #14583294 | C2 | semidirect |
| 6. #14583293 | C2 | semidirect |
| 7. #14583292 | C2 | semidirect |
| 8. #14583291 | C2 | semidirect |
| 9. #14583290 | C2 | semidirect |
| 10. #97×D43 | C2 | semidirect |
| 11. C43×#497 | C2 | semidirect |
| 15. C2×Dic172 | C22 | semidirect |
| 16. C2×#10621885 | C22 | semidirect |
| 17. C2×#10621885 | C22 | semidirect |
| 24. #13063325 | C22 | semidirect |
| 26. #13063323 | C22 | semidirect |
| 34. #13063236 | C22 | semidirect |
| 35. #13063235 | C22 | semidirect |
| 36. C2×Q16×C43 | C22 | semidirect |
| 38. C4⋊Q8×C43 | C22 | semidirect |
| 40. #97×C43 | C22 | semidirect |
| 131. D43 | #497 | direct (N × H) |
| 141. #497 | D43 | direct (N × H) |
| 143. C43 | C2×#497 | semidirect |
| 151. C2×Q16 | C2×D43 | semidirect |
| 161. C4⋊Q8 | C2×D43 | semidirect |
| 172. #97 | C2×D43 | semidirect |