Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D31 |
| commutator, socle, cosocle | C22×C31 | C24 |
| Frattini | C22 | C23×D31 |
| Fitting | C31×#117 | C2 |
| prime radical | #11758461 | C2 |
| hypercenter | #117 | D31 |
| hypocenter | C31 | #529 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×#117 | C2 | semidirect |
| 2. C4×C22⋊D31 | C2 | semidirect |
| 3. C4×C22⋊D31 | C2 | semidirect |
| 4. #11758475 | C2 | semidirect |
| 5. #11758473 | C2 | semidirect |
| 6. #11758471 | C2 | semidirect |
| 7. #11758466 | C2 | semidirect |
| 8. #11758462 | C2 | semidirect |
| 10. #11758460 | C2 | semidirect |
| 11. #11758456 | C2 | semidirect |
| 12. C4×D124 | C2 | semidirect |
| 13. #11758449 | C2 | semidirect |
| 14. C42×D31 | C2 | semidirect |
| 15. C4×Dic62 | C2 | semidirect |
| 117. #117 | D31 | semidirect |
| 119. C31 | #529 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×#117 | 2 |
| C4×C22⋊D31 | 2 |
| #11758475 | 2 |
| #11758473 | 2 |
| #11758471 | 2 |
| #11758466 | 2 |
| #11758462 | 2 |
| #11758461 | 2 |
| #11758460 | 2 |
| #11758456 | 2 |
| C4×D124 | 2 |
| #11758449 | 2 |
| C42×D31 | 2 |
| C4×Dic62 | 2 |
| #529 | 31 |