Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
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×D487 |
| commutator, socle, cosocle | C22×C487 | C24 |
| Fitting | C4×D4×C487 | C2 |
| prime radical | #29510183 | C2 |
| hypercenter | C4×D4 | D487 |
| hypocenter | C487 | #551 |
| LCS | G ▷ C22×C487 ▷ C487 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29510210 | C2 | semidirect |
| 2. #29510209 | C2 | semidirect |
| 3. #29510201 | C2 | semidirect |
| 4. #29510198 | C2 | semidirect |
| 5. #29510197 | C2 | semidirect |
| 6. #29510196 | C2 | semidirect |
| 7. #29510194 | C2 | semidirect |
| 8. #29510193 | C2 | semidirect |
| 10. C4×C22⋊D487 | C2 | semidirect |
| 11. #29510172 | C2 | semidirect |
| 12. #29510171 | C2 | semidirect |
| 13. C2×(C2×D487)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D487 | C2 | semidirect |
| 15. C4×D4×C487 | C2 | semidirect |
| 17. C2×Dic974 | C22 | semidirect |
| 23. C4⋊Dic487 | C22 | semidirect |
| 24. Dic487⋊C4 | C22 | semidirect |
| 25. Dic487⋊C4 | C22 | semidirect |
| 26. Dic487⋊C4 | C22 | semidirect |
| 27. Dic487⋊C4 | C22 | semidirect |
| 28. Dic487⋊C4 | C22 | semidirect |
| 29. Dic487⋊C4 | C22 | semidirect |
| 32. C22⋊Dic487 | C22 | semidirect |
| 33. C22⋊Dic487 | C22 | semidirect |
| 42. C4×Dic487 | C22 | semidirect |
| 43. C4×Dic487 | C22 | semidirect |
| 46. C22×C4×C487 | C22 | semidirect |
| 47. C4⋊C4×C487 | C22 | semidirect |
| 49. C22⋊C4×C487 | C22 | semidirect |
| 50. C42×C487 | C22 | semidirect |
| 110. C487 | #551 | semidirect |
| 122. C4×D4 | D487 | semidirect |
| 136. C22×C4 | C2×D487 | semidirect |
| 144. C4⋊C4 | C2×D487 | semidirect |
| 158. C22⋊C4 | C2×D487 | semidirect |
| 161. C42 | C2×D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510210 | 2 |
| #29510209 | 2 |
| #29510201 | 2 |
| #29510198 | 2 |
| #29510197 | 2 |
| #29510196 | 2 |
| #29510194 | 2 |
| #29510193 | 2 |
| #29510183 | 2 |
| C4×C22⋊D487 | 2 |
| #29510172 | 2 |
| #29510171 | 2 |
| C2×(C2×D487)⋊C4 | 2 |
| C22⋊C4×D487 | 2 |
| C4×D4×C487 | 2 |
| #551 | 487 |