Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
216 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 95 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×C4⋊Q8 | C2 |
| prime radical | #11758472 | C2 |
| hypercenter | C4⋊Q8 | D31 |
| hypocenter | C31 | #542 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C31×C4⋊Q8 | C2 | semidirect |
| 2. #11758524 | C2 | semidirect |
| 3. #11758523 | C2 | semidirect |
| 4. #11758475 | C2 | semidirect |
| 5. #11758474 | C2 | semidirect |
| 7. #11758471 | C2 | semidirect |
| 8. #11758470 | C2 | semidirect |
| 9. #11758464 | C2 | semidirect |
| 10. #11758452 | C2 | semidirect |
| 11. #11758449 | C2 | semidirect |
| 74. C4⋊Q8 | D31 | semidirect |
| 85. C31 | #542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×C4⋊Q8 | 2 |
| #11758524 | 2 |
| #11758523 | 2 |
| #11758475 | 2 |
| #11758474 | 2 |
| #11758472 | 2 |
| #11758471 | 2 |
| #11758470 | 2 |
| #11758464 | 2 |
| #11758452 | 2 |
| #11758449 | 2 |
| #542 | 31 |