Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
556 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 169 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×#382 | C2 |
| prime radical | C23×D11 | C23 |
| hypercenter | #382 | D11 |
| hypocenter | C11 | #2851 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#66923 | C2 | semidirect |
| 3. C11×#382 | C2 | semidirect |
| 5. #10622598 | C2 | semidirect |
| 7. #10622266 | C2 | semidirect |
| 76. #382 | D11 | semidirect |
| 87. C2×D11 | #125 | semidirect |
| 136. C11 | #2851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D11 | 2 |
| C2×#66923 | 2 |
| C11×#382 | 2 |
| #10622600 | 2 |
| #10622598 | 2 |
| #10622281 | 2 |
| #10622266 | 2 |
| #2851 | 11 |