Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1488 conjugacy classes of subgroups; only the 813 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 813 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D43 |
| commutator | C2×C43 | C24×C4 |
| Fitting | C43×#519 | C2 |
| socle | C22×C43 | C25 |
| hypercenter | #519 | D43 |
| hypocenter | C43 | C2×#519 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #519 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14583377 | C2 | semidirect |
| 3. #14583376 | C2 | semidirect |
| 4. #14583375 | C2 | semidirect |
| 5. C4×Q8×D43 | C2 | semidirect |
| 7. C43×#519 | C2 | semidirect |
| 9. C2×Q8×D43 | C4 | semidirect |
| 13. Q8×Dic43 | C22 | semidirect |
| 14. C4×Dic86 | C22 | semidirect |
| 15. #13063290 | C22 | semidirect |
| 24. C4×Q8×C43 | C22 | semidirect |
| 27. C2×Q8×C43 | C2×C4 | semidirect |
| 32. Q8×D43 | C2×C4 | semidirect |
| 37. C2×Dic86 | C2×C4 | semidirect |
| 81. D43 | #519 | direct (N × H) |
| 86. #519 | D43 | direct (N × H) |
| 89. C43 | C2×#519 | semidirect |
| 99. C4×Q8 | C2×D43 | semidirect |
| 113. C2×Q8 | C4×D43 | semidirect |