Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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 | #3280 |
| 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×#13063348 | C2 | semidirect |
| 2. C2×D8×D43 | C2 | semidirect |
| 3. #14583542 | C2 | semidirect |
| 4. #14583137 | C2 | semidirect |
| 5. #14583132 | C2 | semidirect |
| 6. #14583111 | C2 | semidirect |
| 7. #14583048 | C2 | semidirect |
| 8. #14583043 | C2 | semidirect |
| 9. C4×D344 | C2 | semidirect |
| 10. C8×D172 | C2 | semidirect |
| 11. C43×#495 | C2 | semidirect |
| 12. C2×#10621902 | C22 | semidirect |
| 15. C2×#10621884 | C22 | semidirect |
| 20. C2×C8×D43 | C22 | semidirect |
| 24. #13063296 | C22 | semidirect |
| 27. C4×D172 | C22 | semidirect |
| 29. #13063259 | C22 | semidirect |
| 30. C4⋊(C43⋊C8) | C22 | semidirect |
| 31. #13063249 | C22 | semidirect |
| 32. #13063247 | C22 | semidirect |
| 33. #13063246 | C22 | semidirect |
| 35. (C2×D43)⋊C8 | C22 | semidirect |
| 36. C2×Q16×C43 | C22 | semidirect |
| 37. C2×SD16×C43 | C22 | semidirect |
| 39. #124×C43 | C22 | semidirect |
| 40. C4×C8×C43 | C22 | semidirect |
| 77. D344 | D4 | semidirect |
| 127. C2×D43 | #135 | semidirect |
| 147. #495 | D43 | semidirect |
| 155. C43 | #3280 | semidirect |
| 159. C2×Q16 | C2×D43 | semidirect |
| 161. C2×SD16 | C2×D43 | semidirect |
| 168. #124 | C2×D43 | semidirect |
| 184. C4×C8 | C2×D43 | semidirect |