Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1224 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D43 |
| commutator | C22×C43 | C23×C4 |
| Frattini | C23 | C23×D43 |
| Fitting | C24×C4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | C4×#120 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×C22⋊D43 | C2 | semidirect |
| 3. #14582778 | C2 | semidirect |
| 4. #14582772 | C2 | semidirect |
| 5. #14582755 | C2 | semidirect |
| 6. C4×C22⋊Dic43 | C2 | semidirect |
| 7. C24×C4×C43 | C2 | semidirect |
| 9. C22×C4×D43 | C22 | semidirect |
| 10. #13063294 | C4 | direct (N × H) |
| 12. C2×Dic43⋊C4 | C22 | semidirect |
| 16. C2×(C2×D43)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic43 | C22 | semidirect |
| 18. C43⋊#95 | C22 | semidirect |
| 25. C24×C43 | C2×C4 | semidirect |
| 32. C22×C4×C43 | D4 | semidirect |
| 37. C2×C22⋊D43 | C2×C4 | semidirect |
| 44. C22⋊Dic43 | C2×C4 | semidirect |
| 59. C22×D43 | C22×C4 | semidirect |
| 71. C2×Dic43 | C22×C4 | semidirect |
| 78. C22×C43 | C4×D4 | semidirect |
| 86. C4×C43 | #120 | semidirect |
| 96. C24×C4 | D43 | semidirect |
| 103. C43 | C4×#120 | semidirect |
| 122. C24 | C4×D43 | semidirect |
| 135. C22×C4 | C22⋊D43 | semidirect |
| 177. C22 | C4×C22⋊D43 | semidirect |
| 185. C4 | #13063294 | direct (N × H) |