Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
432 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C11 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| socle | C23×C11 | C24 |
| prime radical | C24×C11 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#401 | C2 | semidirect |
| 2. C11×#400 | C2 | semidirect |
| 5. C4×C11×C4⋊C4 | C2 | semidirect |
| 7. C11×#376 | C2 | semidirect |
| 35. #2401 | C11 | direct (N × H) |
| 55. #401 | C2×C11 | semidirect |
| 56. #400 | C2×C11 | semidirect |
| 59. C4×C4⋊C4 | C2×C11 | semidirect |
| 61. #376 | C2×C11 | semidirect |
| 105. C11 | #2401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#401 | 2 |
| C11×#400 | 2 |
| C11×#397 | 2 |
| C11×#396 | 2 |
| C4×C11×C4⋊C4 | 2 |
| C4×C11×C22⋊C4 | 2 |
| C11×#376 | 2 |
| #2401 | 11 |