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 | C4×D4×C487 | C2 |
| hypercenter | C4×D4 | D487 |
| hypocenter | C487 | #548 |
| 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. C2×#21441261 | C2 | semidirect |
| 2. C22×Dic974 | C2 | semidirect |
| 3. #29510203 | C2 | semidirect |
| 4. #29510201 | C2 | semidirect |
| 5. #29510194 | C2 | semidirect |
| 6. #29510193 | C2 | semidirect |
| 7. #29510189 | C2 | semidirect |
| 8. #29510187 | C2 | semidirect |
| 9. C4×Dic974 | C2 | semidirect |
| 10. (C22⋊D487)⋊C4 | C2 | semidirect |
| 11. C4×D4×C487 | C2 | semidirect |
| 40. Dic974 | D4 | semidirect |
| 64. C22×C487 | #41 | semidirect |
| 83. C487 | #548 | semidirect |
| 95. C4×D4 | D487 | semidirect |
| 151. C22 | #21441261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#21441261 | 2 |
| C22×Dic974 | 2 |
| #29510203 | 2 |
| #29510201 | 2 |
| #29510194 | 2 |
| #29510193 | 2 |
| #29510189 | 2 |
| #29510187 | 2 |
| C4×Dic974 | 2 |
| (C22⋊D487)⋊C4 | 2 |
| C4×D4×C487 | 2 |
| #548 | 487 |