Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1102 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C11×#379 | C2 |
| prime radical | C2×#67006 | C2 |
| hypercenter | #379 | D11 |
| hypocenter | C11 | #2849 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic11 | C2 | semidirect |
| 3. C2×#66939 | C2 | semidirect |
| 4. C11×#379 | C2 | semidirect |
| 5. #10622571 | C2 | semidirect |
| 6. #10622563 | C2 | semidirect |
| 7. #10622556 | C2 | semidirect |
| 20. C2×(C2×D11)⋊C4 | C22 | semidirect |
| 21. C2×C4⋊Dic11 | C22 | semidirect |
| 23. C11⋊#95 | C22 | semidirect |
| 40. C22×Dic11 | D4 | semidirect |
| 84. #379 | D11 | semidirect |
| 92. C22×C11 | #123 | semidirect |
| 151. C11 | #2849 | semidirect |
| 189. C22 | #66939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic11 | 2 |
| C2×#67006 | 2 |
| C2×#66939 | 2 |
| C11×#379 | 2 |
| #10622571 | 2 |
| #10622563 | 2 |
| #10622556 | 2 |
| #2849 | 11 |