Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C22×C11 | C23×C4 |
| Fitting | C11×#380 | C2 |
| socle, cosocle | C23×C11 | C24 |
| prime radical | C24×C11 | C23 |
| hypercenter | #380 | D11 |
| hypocenter | C11 | #2316 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10622585 | C2 | semidirect |
| 7. #10622260 | C2 | semidirect |
| 15. C2×Dic11⋊C4 | C4 | semidirect |
| 68. C2×Dic11 | C4⋊C4 | semidirect |
| 142. C11 | #2316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic11⋊C4 | 2 |
| C2×#66930 | 2 |
| C11×#380 | 2 |
| #10622825 | 2 |
| #10622585 | 2 |
| #10622555 | 2 |
| #10622260 | 2 |
| #2316 | 11 |