Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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 | C4×D4×C509 | C2 |
| hypercenter | C4×D4 | D509 |
| hypocenter | C509 | #525 |
| LCS | G ▷ C22×C509 ▷ C509 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#22550861 | C2 | semidirect |
| 2. C22×C4×D509 | C2 | semidirect |
| 3. #30654200 | C2 | semidirect |
| 4. #30654197 | C2 | semidirect |
| 5. #30654193 | C2 | semidirect |
| 6. #30654192 | C2 | semidirect |
| 7. #30654188 | C2 | semidirect |
| 8. #30654187 | C2 | semidirect |
| 9. #30654185 | C2 | semidirect |
| 10. #30654183 | C2 | semidirect |
| 11. C4×D2036 | C2 | semidirect |
| 12. C4×C22⋊D509 | C2 | semidirect |
| 13. C4×C22⋊D509 | C2 | semidirect |
| 14. #30654172 | C2 | semidirect |
| 15. C4×D4×C509 | C2 | semidirect |
| 18. C2×Dic1018 | C22 | semidirect |
| 24. C2×C22⋊D509 | C22 | semidirect |
| 31. C2×C4×D509 | C22 | semidirect |
| 32. C4⋊Dic509 | C22 | semidirect |
| 33. #22550840 | C22 | semidirect |
| 34. #22550840 | C22 | semidirect |
| 35. #22550840 | C22 | semidirect |
| 36. #22550840 | C22 | semidirect |
| 38. C22⋊Dic509 | C22 | semidirect |
| 43. #22550838 | C22 | semidirect |
| 44. #22550838 | C22 | semidirect |
| 45. C4×Dic509 | C22 | semidirect |
| 48. C22×C4×C509 | C22 | semidirect |
| 49. C4⋊C4×C509 | C22 | semidirect |
| 51. C22⋊C4×C509 | C22 | semidirect |
| 52. C42×C509 | C22 | semidirect |
| 76. C4×D509 | D4 | semidirect |
| 92. C22×C509 | #41 | semidirect |
| 103. C2×D509 | #41 | semidirect |
| 122. C509 | #525 | semidirect |
| 137. C4×D4 | D509 | semidirect |
| 157. C22×C4 | C2×D509 | semidirect |
| 163. C4⋊C4 | C2×D509 | semidirect |
| 173. C22⋊C4 | C2×D509 | semidirect |
| 175. C42 | C2×D509 | semidirect |
| 225. 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 |
| C22×C4×D509 | 2 |
| #30654200 | 2 |
| #30654197 | 2 |
| #30654193 | 2 |
| #30654192 | 2 |
| #30654188 | 2 |
| #30654187 | 2 |
| #30654185 | 2 |
| #30654183 | 2 |
| C4×D2036 | 2 |
| C4×C22⋊D509 | 2 |
| #30654172 | 2 |
| C4×D4×C509 | 2 |
| #525 | 509 |