Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
258 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C4×C499 | C24 |
| commutator | C2 | C23×C4×C499 |
| Frattini, cosocle | C4 | C24×C499 |
| socle | C2×C499 | C23×C4 |
| prime radical | C2×#41×C499 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C499 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #131×C499 | C2 | semidirect |
| 3. C2×M16×C499 | C2 | semidirect |
| 10. M16×C499 | C22 | semidirect |
| 11. C2×C8×C499 | C22 | semidirect |
| 29. C499 | #568 | direct (N × H) |
| 30. #568 | C499 | direct (N × H) |
| 32. #131 | C2×C499 | semidirect |
| 33. C2×M16 | C2×C499 | semidirect |
| 40. M16 | C22×C499 | semidirect |
| 41. C2×C8 | C22×C499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C499 | 2 |
| #131×C499 | 2 |
| C2×M16×C499 | 2 |
| #568 | 499 |