Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
248 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 248 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 | C2 | C22×C22⋊D31 |
| commutator, cosocle | C4×C31 | C24 |
| Frattini | C4 | C23×D31 |
| Fitting | C31×2−1+4 | C2 |
| socle | C2×C31 | C22×D4 |
| hypercenter | 2−1+4 | D31 |
| hypocenter | C31 | #578 |
| LCS | G ▷ C4×C31 ▷ C2×C31 ▷ C31 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ 2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×2−1+4 | C2 | semidirect |
| 2. #11758567 | C2 | semidirect |
| 3. #11758528 | C2 | semidirect |
| 4. #11758527 | C2 | semidirect |
| 5. #11758525 | C2 | semidirect |
| 6. C2×#92482 | C2 | semidirect |
| 7. #11758519 | C2 | semidirect |
| 54. 2−1+4 | D31 | semidirect |
| 60. C31 | #578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×2−1+4 | 2 |
| #11758567 | 2 |
| #11758528 | 2 |
| #11758527 | 2 |
| #11758525 | 2 |
| C2×#92482 | 2 |
| #11758519 | 2 |
| #578 | 31 |