Finite Group DatabasebetaFinite Group DatabasebetaOrder 31936.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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×D499 |
| commutator, socle, cosocle | C22×C499 | C24 |
| Fitting | C4×D4×C499 | C2 |
| hypercenter | C4×D4 | D499 |
| hypocenter | C499 | #538 |
| LCS | G ▷ C22×C499 ▷ C499 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30630346 | C2 | semidirect |
| 2. #30630345 | C2 | semidirect |
| 3. #30630339 | C2 | semidirect |
| 4. #30630337 | C2 | semidirect |
| 5. #30630336 | C2 | semidirect |
| 6. #30630334 | C2 | semidirect |
| 7. #30630328 | C2 | semidirect |
| 8. #30630325 | C2 | semidirect |
| 9. #30630324 | C2 | semidirect |
| 10. #30630323 | C2 | semidirect |
| 11. #30630321 | C2 | semidirect |
| 12. #30630319 | C2 | semidirect |
| 13. C4×C22⋊D499 | C2 | semidirect |
| 14. C2×(C2×D499)⋊C4 | C2 | semidirect |
| 15. C4×D4×C499 | C2 | semidirect |
| 17. C2×Dic998 | C22 | semidirect |
| 23. C2×C22⋊D499 | C22 | semidirect |
| 25. C2×C4×D499 | C22 | semidirect |
| 26. C4⋊Dic499 | C22 | semidirect |
| 27. Dic499⋊C4 | C22 | semidirect |
| 28. Dic499⋊C4 | C22 | semidirect |
| 29. Dic499⋊C4 | C22 | semidirect |
| 30. Dic499⋊C4 | C22 | semidirect |
| 32. C22⋊Dic499 | C22 | semidirect |
| 41. (C2×D499)⋊C4 | C22 | semidirect |
| 42. (C2×D499)⋊C4 | C22 | semidirect |
| 43. C4×Dic499 | C22 | semidirect |
| 46. C22×C4×C499 | C22 | semidirect |
| 47. C4⋊C4×C499 | C22 | semidirect |
| 49. C22⋊C4×C499 | C22 | semidirect |
| 50. C42×C499 | C22 | semidirect |
| 116. C499 | #538 | semidirect |
| 131. C4×D4 | D499 | semidirect |
| 145. C22×C4 | C2×D499 | semidirect |
| 151. C4⋊C4 | C2×D499 | semidirect |
| 165. C22⋊C4 | C2×D499 | semidirect |
| 167. C42 | C2×D499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30630346 | 2 |
| #30630345 | 2 |
| #30630339 | 2 |
| #30630337 | 2 |
| #30630336 | 2 |
| #30630334 | 2 |
| #30630328 | 2 |
| #30630325 | 2 |
| #30630324 | 2 |
| #30630323 | 2 |
| #30630321 | 2 |
| #30630319 | 2 |
| C4×C22⋊D499 | 2 |
| C2×(C2×D499)⋊C4 | 2 |
| C4×D4×C499 | 2 |
| #538 | 499 |