Finite Group DatabasebetaFinite Group DatabasebetaOrder 34624.
218 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 218 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×D4×C541 | C2 |
| prime radical | #31772600 | C2 |
| hypercenter | C4×D4 | D541 |
| hypocenter | C541 | #539 |
| LCS | G ▷ C22×C541 ▷ C541 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #31772622 | C2 | semidirect |
| 2. #31772621 | C2 | semidirect |
| 3. #31772620 | C2 | semidirect |
| 4. #31772618 | C2 | semidirect |
| 5. #31772612 | C2 | semidirect |
| 6. #31772611 | C2 | semidirect |
| 7. #31772610 | C2 | semidirect |
| 8. #31772609 | C2 | semidirect |
| 9. #31772607 | C2 | semidirect |
| 10. #31772606 | C2 | semidirect |
| 11. #31772605 | C2 | semidirect |
| 13. C4×C22⋊D541 | C2 | semidirect |
| 14. C2×#22575815 | C2 | semidirect |
| 15. C4×D4×C541 | C2 | semidirect |
| 103. C541 | #539 | semidirect |
| 118. C4×D4 | D541 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31772622 | 2 |
| #31772621 | 2 |
| #31772620 | 2 |
| #31772618 | 2 |
| #31772612 | 2 |
| #31772611 | 2 |
| #31772610 | 2 |
| #31772609 | 2 |
| #31772607 | 2 |
| #31772606 | 2 |
| #31772605 | 2 |
| #31772600 | 2 |
| C4×C22⋊D541 | 2 |
| C2×#22575815 | 2 |
| C4×D4×C541 | 2 |
| #539 | 541 |