Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | #66993 |
| commutator, cosocle | C42×C11 | C23 |
| Frattini | C42 | C22×D11 |
| Fitting | C11×#492 | C2 |
| socle | C22×C11 | #127 |
| hypercenter | #492 | D11 |
| hypocenter | C11 | #1721 |
| LCS | G ▷ C42×C11 ▷ C22×C11 ▷ C11 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #492 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#492 | C2 | semidirect |
| 2. #10622701 | C2 | semidirect |
| 3. #10622686 | C2 | semidirect |
| 4. #10622308 | C2 | semidirect |
| 5. #10622093 | C2 | semidirect |
| 40. C8×C11 | D8 | semidirect |
| 44. #492 | D11 | semidirect |
| 82. C11 | #1721 | semidirect |
| 95. C8 | #4323 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#492 | 2 |
| #10622701 | 2 |
| #10622686 | 2 |
| #10622308 | 2 |
| #10622093 | 2 |
| #1721 | 11 |