Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 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×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Fitting | C31×#124 | C2 |
| prime radical | #11758517 | C2 |
| hypercenter | #124 | D31 |
| hypocenter | C31 | #559 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#124 | C2 | semidirect |
| 2. #11758524 | C2 | semidirect |
| 3. Q8×Dic31 | C2 | semidirect |
| 5. D4×Dic31 | C2 | semidirect |
| 6. #11758463 | C2 | semidirect |
| 7. #11758462 | C2 | semidirect |
| 8. #11758460 | C2 | semidirect |
| 9. (C22⋊D31)⋊C4 | C2 | semidirect |
| 10. C4×D124 | C2 | semidirect |
| 11. C4×Dic62 | C2 | semidirect |
| 79. #124 | D31 | semidirect |
| 87. C31 | #559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#124 | 2 |
| #11758524 | 2 |
| Q8×Dic31 | 2 |
| #11758517 | 2 |
| D4×Dic31 | 2 |
| #11758463 | 2 |
| #11758462 | 2 |
| #11758460 | 2 |
| (C22⋊D31)⋊C4 | 2 |
| C4×D124 | 2 |
| C4×Dic62 | 2 |
| #559 | 31 |