Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
334 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 111 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×D509 |
| commutator, socle, cosocle | C22×C509 | C24 |
| Fitting | C2×#41×C509 | C2 |
| hypercenter | C2×#41 | D509 |
| hypocenter | C509 | #535 |
| LCS | G ▷ C22×C509 ▷ C509 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D2036 | C2 | semidirect |
| 2. #30654211 | C2 | semidirect |
| 3. #30654204 | C2 | semidirect |
| 4. #30654189 | C2 | semidirect |
| 5. #30654183 | C2 | semidirect |
| 6. #30654174 | C2 | semidirect |
| 7. C2×#41×C509 | C2 | semidirect |
| 12. C2×C22⋊D509 | C22 | semidirect |
| 13. C4⋊Dic509 | C22 | semidirect |
| 15. #22550838 | C22 | semidirect |
| 16. C4×Dic509 | C22 | semidirect |
| 18. C2×Q8×C509 | C22 | semidirect |
| 20. C2×D4×C509 | C22 | semidirect |
| 22. C22×C4×C509 | C22 | semidirect |
| 36. C2×C4×C509 | D4 | semidirect |
| 57. C509 | #535 | semidirect |
| 59. C2×#41 | D509 | semidirect |
| 68. C2×Q8 | C2×D509 | semidirect |
| 74. C2×D4 | C2×D509 | semidirect |
| 76. C22×C4 | C2×D509 | semidirect |
| 94. C2×C4 | C22⋊D509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D2036 | 2 |
| #30654211 | 2 |
| #30654204 | 2 |
| #30654189 | 2 |
| #30654183 | 2 |
| #30654174 | 2 |
| C2×#41×C509 | 2 |
| #535 | 509 |