Finite Group DatabasebetaFinite Group DatabasebetaOrder 31168.
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 107 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 | #121×C487 | C2 |
| hypercenter | #121 | D487 |
| hypocenter | C487 | #548 |
| LCS | G ▷ C22×C487 ▷ C487 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#21441260 | C2 | semidirect |
| 2. C22×Dic974 | C2 | semidirect |
| 3. #29510202 | C2 | semidirect |
| 4. #29510201 | C2 | semidirect |
| 5. #29510195 | C2 | semidirect |
| 6. #29510192 | C2 | semidirect |
| 7. #29510187 | C2 | semidirect |
| 8. #29510180 | C2 | semidirect |
| 9. D4×Dic487 | C2 | semidirect |
| 10. C4×C22⋊D487 | C2 | semidirect |
| 11. #121×C487 | C2 | semidirect |
| 40. Dic974 | D4 | semidirect |
| 64. C22×C487 | #41 | semidirect |
| 83. C487 | #548 | semidirect |
| 92. #121 | D487 | semidirect |
| 151. C22 | #21441260 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21441260 | 2 |
| C22×Dic974 | 2 |
| #29510202 | 2 |
| #29510201 | 2 |
| #29510195 | 2 |
| #29510192 | 2 |
| #29510187 | 2 |
| #29510180 | 2 |
| D4×Dic487 | 2 |
| C4×C22⋊D487 | 2 |
| #121×C487 | 2 |
| #548 | 487 |