Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D461 |
| commutator, socle, cosocle | C22×C461 | C24 |
| Fitting | #126×C461 | C2 |
| prime radical | C2×C22⋊D461 | C22 |
| hypercenter | #126 | D461 |
| hypocenter | C461 | #563 |
| LCS | G ▷ C22×C461 ▷ C461 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28414118 | C2 | semidirect |
| 2. #28414117 | C2 | semidirect |
| 3. #28414113 | C2 | semidirect |
| 4. #28414112 | C2 | semidirect |
| 5. #28414111 | C2 | semidirect |
| 6. #28414109 | C2 | semidirect |
| 7. #28414108 | C2 | semidirect |
| 11. #28414098 | C2 | semidirect |
| 12. #28414096 | C2 | semidirect |
| 13. #28414095 | C2 | semidirect |
| 14. #28414095 | C2 | semidirect |
| 15. #126×C461 | C2 | semidirect |
| 97. C461 | #563 | semidirect |
| 104. #126 | D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414118 | 2 |
| #28414117 | 2 |
| #28414113 | 2 |
| #28414112 | 2 |
| #28414111 | 2 |
| #28414109 | 2 |
| #28414108 | 2 |
| #28414104 | 2 |
| #28414102 | 2 |
| #28414100 | 2 |
| #28414098 | 2 |
| #28414096 | 2 |
| #28414095 | 2 |
| #126×C461 | 2 |
| #563 | 461 |