Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 103 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×C22⋊Q8 | C2 |
| prime radical | C2×#92495 | C2 |
| hypercenter | C22⋊Q8 | D31 |
| hypocenter | C31 | #536 |
| LCS | G ▷ C22×C31 ▷ C31 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D31 | C2 | semidirect |
| 3. C31×C22⋊Q8 | C2 | semidirect |
| 4. #11758523 | C2 | semidirect |
| 5. #11758501 | C2 | semidirect |
| 6. #11758474 | C2 | semidirect |
| 7. #11758471 | C2 | semidirect |
| 8. #11758469 | C2 | semidirect |
| 9. #11758465 | C2 | semidirect |
| 10. #11758462 | C2 | semidirect |
| 11. #11758460 | C2 | semidirect |
| 93. C22⋊Q8 | D31 | semidirect |
| 95. C31 | #536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D31 | 2 |
| C2×#92495 | 2 |
| C31×C22⋊Q8 | 2 |
| #11758523 | 2 |
| #11758501 | 2 |
| #11758474 | 2 |
| #11758471 | 2 |
| #11758469 | 2 |
| #11758465 | 2 |
| #11758462 | 2 |
| #11758460 | 2 |
| #536 | 31 |