Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 125 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×C22⋊D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | D42×C43 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | D42 | D43 |
| hypocenter | C43 | #3325 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C4×D4 ◁ D42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583614 | C2 | semidirect |
| 2. #14583245 | C2 | semidirect |
| 3. #14583220 | C2 | semidirect |
| 4. #14583189 | C2 | semidirect |
| 5. #14583150 | C2 | semidirect |
| 6. #14583091 | C2 | semidirect |
| 7. #14583033 | C2 | semidirect |
| 8. C4×#10621882 | C2 | semidirect |
| 9. #14582977 | C2 | semidirect |
| 10. #14582904 | C2 | semidirect |
| 11. D42×C43 | C2 | semidirect |
| 13. C2×#10621882 | C22 | semidirect |
| 14. C2×#10621877 | C22 | semidirect |
| 15. #13063325 | C22 | semidirect |
| 17. #13063299 | C22 | semidirect |
| 19. C4×D172 | C22 | semidirect |
| 20. #13063284 | C22 | semidirect |
| 22. #13063258 | C22 | semidirect |
| 23. #13063256 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 27. #13063246 | C22 | semidirect |
| 28. #13063246 | C22 | semidirect |
| 29. #13063246 | C22 | semidirect |
| 30. #13063245 | C22 | semidirect |
| 31. C22⋊(C43⋊C8) | C22 | semidirect |
| 32. C4×C43⋊C8 | C22 | semidirect |
| 142. D42 | D43 | semidirect |
| 152. C43 | #3325 | semidirect |