Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
528 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 189 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 | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#518 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #518 | D43 |
| hypocenter | C43 | #2948 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #518 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583373 | C2 | semidirect |
| 3. #14583009 | C2 | semidirect |
| 4. C4×#10621882 | C2 | semidirect |
| 5. #14582935 | C2 | semidirect |
| 6. #14582904 | C2 | semidirect |
| 7. #14582903 | C2 | semidirect |
| 8. #14582855 | C2 | semidirect |
| 9. C43×#518 | C2 | semidirect |
| 11. C2×#10621882 | C4 | semidirect |
| 16. C4×D172 | C22 | semidirect |
| 20. #13063258 | C22 | semidirect |
| 21. #13063256 | C22 | semidirect |
| 22. #13063246 | C22 | semidirect |
| 23. #13063245 | C22 | semidirect |
| 24. #13063236 | C22 | semidirect |
| 25. C4×C43⋊C8 | C22 | semidirect |
| 28. C4×D4×C43 | C22 | semidirect |
| 36. C2×D4×C43 | C2×C4 | semidirect |
| 42. C2×D172 | C2×C4 | semidirect |
| 53. #10621882 | C2×C4 | semidirect |
| 54. #10621882 | C2×C4 | semidirect |
| 59. C2×C43⋊C8 | C2×C4 | semidirect |
| 111. #518 | D43 | semidirect |
| 118. C43 | #2948 | semidirect |
| 129. C4×D4 | C2×D43 | semidirect |
| 149. C2×D4 | C4×D43 | semidirect |