Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
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×D541 |
| commutator, socle, cosocle | C22×C541 | C24 |
| Fitting | C4⋊Q8×C541 | C2 |
| prime radical | #31772603 | C2 |
| hypercenter | C4⋊Q8 | D541 |
| hypocenter | C541 | #542 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ C4⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31772623 | C2 | semidirect |
| 2. #31772617 | C2 | semidirect |
| 3. #31772616 | C2 | semidirect |
| 4. #31772613 | C2 | semidirect |
| 5. #31772608 | C2 | semidirect |
| 6. #31772604 | C2 | semidirect |
| 8. #31772593 | C2 | semidirect |
| 9. #31772590 | C2 | semidirect |
| 10. #31772585 | C2 | semidirect |
| 11. C4⋊Q8×C541 | C2 | semidirect |
| 73. C541 | #542 | semidirect |
| 75. C4⋊Q8 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772623 | 2 |
| #31772617 | 2 |
| #31772616 | 2 |
| #31772613 | 2 |
| #31772608 | 2 |
| #31772604 | 2 |
| #31772603 | 2 |
| #31772593 | 2 |
| #31772590 | 2 |
| #31772585 | 2 |
| C4⋊Q8×C541 | 2 |
| #542 | 541 |