Finite Group DatabasebetaFinite Group DatabasebetaOrder 32576.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 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 | #532 |
| 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. #30654214 | C2 | semidirect |
| 3. #30654211 | C2 | semidirect |
| 4. #30654201 | C2 | semidirect |
| 5. #30654190 | C2 | semidirect |
| 6. #30654188 | C2 | semidirect |
| 7. #30654186 | C2 | semidirect |
| 8. C4×D2036 | C2 | semidirect |
| 9. C4×C22⋊D509 | C2 | semidirect |
| 10. C42×D509 | C2 | semidirect |
| 11. C4×D4×C509 | C2 | semidirect |
| 51. C4×D509 | D4 | semidirect |
| 72. C4×C509 | #41 | semidirect |
| 76. Dic509 | #41 | semidirect |
| 83. C509 | #532 | semidirect |
| 94. C4×D4 | D509 | semidirect |
| 160. C4 | #22550861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22550861 | 2 |
| #30654214 | 2 |
| #30654211 | 2 |
| #30654201 | 2 |
| #30654190 | 2 |
| #30654188 | 2 |
| #30654186 | 2 |
| C4×D2036 | 2 |
| C4×C22⋊D509 | 2 |
| C42×D509 | 2 |
| C4×D4×C509 | 2 |
| #532 | 509 |