Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
568 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 568 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 | C22×C11 | C23×C4 |
| Fitting | C11×#383 | C2 |
| socle, cosocle | C23×C11 | C24 |
| prime radical | C23×D11 | C23 |
| hypercenter | #383 | D11 |
| hypocenter | C11 | #2283 |
| LCS | G ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#383 | C2 | semidirect |
| 3. #10622550 | C2 | semidirect |
| 7. #10622263 | C2 | semidirect |
| 8. #10622262 | C2 | semidirect |
| 9. #10622261 | C2 | semidirect |
| 20. C42×D11 | C4 | semidirect |
| 79. #383 | D11 | semidirect |
| 147. C11 | #2283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D11 | 2 |
| C11×#383 | 2 |
| #10622550 | 2 |
| #10622280 | 2 |
| #10622279 | 2 |
| #10622277 | 2 |
| #10622263 | 2 |
| #10622262 | 2 |
| #10622261 | 2 |
| #2283 | 11 |