Finite Group DatabasebetaFinite Group DatabasebetaOrder 31424.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×D491 |
| commutator, socle, cosocle | C22×C491 | C24 |
| Fitting | C4×D4×C491 | C2 |
| prime radical | #30628305 | C2 |
| hypercenter | C4×D4 | D491 |
| hypocenter | C491 | #551 |
| LCS | G ▷ C22×C491 ▷ C491 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #30628332 | C2 | semidirect |
| 2. #30628331 | C2 | semidirect |
| 3. #30628323 | C2 | semidirect |
| 4. #30628320 | C2 | semidirect |
| 5. #30628319 | C2 | semidirect |
| 6. #30628318 | C2 | semidirect |
| 7. #30628316 | C2 | semidirect |
| 8. #30628315 | C2 | semidirect |
| 10. C4×C22⋊D491 | C2 | semidirect |
| 11. #30628294 | C2 | semidirect |
| 12. #30628293 | C2 | semidirect |
| 13. C2×(C2×D491)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D491 | C2 | semidirect |
| 15. C4×D4×C491 | C2 | semidirect |
| 17. C2×Dic982 | C22 | semidirect |
| 23. C4⋊Dic491 | C22 | semidirect |
| 24. Dic491⋊C4 | C22 | semidirect |
| 25. Dic491⋊C4 | C22 | semidirect |
| 26. Dic491⋊C4 | C22 | semidirect |
| 27. Dic491⋊C4 | C22 | semidirect |
| 28. Dic491⋊C4 | C22 | semidirect |
| 29. Dic491⋊C4 | C22 | semidirect |
| 32. C22⋊Dic491 | C22 | semidirect |
| 33. C22⋊Dic491 | C22 | semidirect |
| 42. C4×Dic491 | C22 | semidirect |
| 43. C4×Dic491 | C22 | semidirect |
| 46. C22×C4×C491 | C22 | semidirect |
| 47. C4⋊C4×C491 | C22 | semidirect |
| 49. C22⋊C4×C491 | C22 | semidirect |
| 50. C42×C491 | C22 | semidirect |
| 110. C491 | #551 | semidirect |
| 122. C4×D4 | D491 | semidirect |
| 136. C22×C4 | C2×D491 | semidirect |
| 144. C4⋊C4 | C2×D491 | semidirect |
| 158. C22⋊C4 | C2×D491 | semidirect |
| 161. C42 | C2×D491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30628332 | 2 |
| #30628331 | 2 |
| #30628323 | 2 |
| #30628320 | 2 |
| #30628319 | 2 |
| #30628318 | 2 |
| #30628316 | 2 |
| #30628315 | 2 |
| #30628305 | 2 |
| C4×C22⋊D491 | 2 |
| #30628294 | 2 |
| #30628293 | 2 |
| C2×(C2×D491)⋊C4 | 2 |
| C22⋊C4×D491 | 2 |
| C4×D4×C491 | 2 |
| #551 | 491 |