Finite Group DatabasebetaFinite Group DatabasebetaOrder 30656.
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×D479 |
| commutator, socle, cosocle | C22×C479 | C24 |
| Fitting | C4⋊Q8×C479 | C2 |
| prime radical | #29506357 | C2 |
| hypercenter | C4⋊Q8 | D479 |
| hypocenter | C479 | #542 |
| LCS | G ▷ C22×C479 ▷ C479 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #29506377 | C2 | semidirect |
| 2. #29506371 | C2 | semidirect |
| 3. #29506370 | C2 | semidirect |
| 4. #29506367 | C2 | semidirect |
| 5. #29506362 | C2 | semidirect |
| 6. #29506358 | C2 | semidirect |
| 8. #29506347 | C2 | semidirect |
| 9. #29506344 | C2 | semidirect |
| 10. #29506339 | C2 | semidirect |
| 11. C4⋊Q8×C479 | C2 | semidirect |
| 73. C479 | #542 | semidirect |
| 75. C4⋊Q8 | D479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #29506377 | 2 |
| #29506371 | 2 |
| #29506370 | 2 |
| #29506367 | 2 |
| #29506362 | 2 |
| #29506358 | 2 |
| #29506357 | 2 |
| #29506347 | 2 |
| #29506344 | 2 |
| #29506339 | 2 |
| C4⋊Q8×C479 | 2 |
| #542 | 479 |