Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D509 |
| commutator, socle, cosocle | C22×C509 | C24 |
| Frattini | C22 | C23×D509 |
| Fitting | C23×C4×C509 | C2 |
| hypercenter | C23×C4 | D509 |
| hypocenter | C509 | #525 |
| LCS | G ▷ C22×C509 ▷ C509 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22550861 | C2 | semidirect |
| 2. #30654198 | C2 | semidirect |
| 3. #30654194 | C2 | semidirect |
| 4. #30654189 | C2 | semidirect |
| 5. #30654184 | C2 | semidirect |
| 6. C4×C22⋊D509 | C2 | semidirect |
| 7. #30654174 | C2 | semidirect |
| 8. C23×C4×C509 | C2 | semidirect |
| 10. C2×Dic1018 | C22 | semidirect |
| 11. C2×D2036 | C22 | semidirect |
| 14. C2×C4×D509 | C22 | semidirect |
| 15. C4⋊Dic509 | C22 | semidirect |
| 16. #22550840 | C22 | semidirect |
| 19. #22550838 | C22 | semidirect |
| 20. C4×Dic509 | C22 | semidirect |
| 42. C2×C4×C509 | D4 | semidirect |
| 51. C22×C509 | #41 | semidirect |
| 65. C509 | #525 | semidirect |
| 68. C23×C4 | D509 | semidirect |
| 108. C2×C4 | C22⋊D509 | semidirect |
| 119. C22 | #22550861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550861 | 2 |
| #30654198 | 2 |
| #30654194 | 2 |
| #30654189 | 2 |
| #30654184 | 2 |
| C4×C22⋊D509 | 2 |
| #30654174 | 2 |
| C23×C4×C509 | 2 |
| #525 | 509 |