Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
220 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 91 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 | C22⋊Q8×C487 | C2 |
| hypercenter | C22⋊Q8 | D487 |
| hypocenter | C487 | #562 |
| LCS | G ▷ C22×C487 ▷ C487 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29510205 | C2 | semidirect |
| 2. #29510204 | C2 | semidirect |
| 3. #29510201 | C2 | semidirect |
| 4. #29510200 | C2 | semidirect |
| 5. #29510200 | C2 | semidirect |
| 6. #29510198 | C2 | semidirect |
| 7. #29510197 | C2 | semidirect |
| 8. #29510195 | C2 | semidirect |
| 9. #29510193 | C2 | semidirect |
| 10. #29510191 | C2 | semidirect |
| 11. #29510190 | C2 | semidirect |
| 12. #29510189 | C2 | semidirect |
| 13. #29510188 | C2 | semidirect |
| 14. #29510188 | C2 | semidirect |
| 15. C22⋊Q8×C487 | C2 | semidirect |
| 109. C487 | #562 | semidirect |
| 121. C22⋊Q8 | D487 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29510205 | 2 |
| #29510204 | 2 |
| #29510201 | 2 |
| #29510200 | 2 |
| #29510198 | 2 |
| #29510197 | 2 |
| #29510195 | 2 |
| #29510193 | 2 |
| #29510191 | 2 |
| #29510190 | 2 |
| #29510189 | 2 |
| #29510188 | 2 |
| C22⋊Q8×C487 | 2 |
| #562 | 487 |