Finite Group DatabasebetaFinite Group DatabasebetaOrder 32192.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C23×D503 |
| commutator, socle, cosocle | C22×C503 | C24 |
| Fitting | #123×C503 | C2 |
| prime radical | #30632836 | C2 |
| hypercenter | #123 | D503 |
| hypocenter | C503 | #529 |
| LCS | G ▷ C22×C503 ▷ C503 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30632859 | C2 | semidirect |
| 2. #30632857 | C2 | semidirect |
| 3. #30632854 | C2 | semidirect |
| 4. #30632850 | C2 | semidirect |
| 5. #30632847 | C2 | semidirect |
| 6. #30632841 | C2 | semidirect |
| 8. #30632829 | C2 | semidirect |
| 9. D4×Dic503 | C2 | semidirect |
| 10. (C22⋊D503)⋊C4 | C2 | semidirect |
| 11. (C22⋊D503)⋊C4 | C2 | semidirect |
| 12. #30632822 | C2 | semidirect |
| 13. #30632820 | C2 | semidirect |
| 14. C2×C4×Dic503 | C2 | semidirect |
| 15. #123×C503 | C2 | semidirect |
| 103. C503 | #529 | semidirect |
| 110. #123 | D503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30632859 | 2 |
| #30632857 | 2 |
| #30632854 | 2 |
| #30632850 | 2 |
| #30632847 | 2 |
| #30632841 | 2 |
| #30632836 | 2 |
| #30632829 | 2 |
| D4×Dic503 | 2 |
| (C22⋊D503)⋊C4 | 2 |
| #30632822 | 2 |
| #30632820 | 2 |
| C2×C4×Dic503 | 2 |
| #123×C503 | 2 |
| #529 | 503 |