Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
150 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C11 |
| prime radical | C11×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C22×C4×C11 ◁ C22×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C11×#107 | C2 | semidirect |
| 3. C11×#366 | C2 | semidirect |
| 4. C11×#357 | C2 | semidirect |
| 5. C11×C22⋊C16 | C2 | semidirect |
| 28. #2232 | C11 | direct (N × H) |
| 44. C2×#107 | C2×C11 | semidirect |
| 45. #366 | C2×C11 | semidirect |
| 46. #357 | C2×C11 | semidirect |
| 47. C22⋊C16 | C2×C11 | semidirect |
| 87. C11 | #2232 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#466 | 2 |
| C2×C11×#107 | 2 |
| C11×#366 | 2 |
| C11×#357 | 2 |
| C11×C22⋊C16 | 2 |
| #2232 | 11 |