Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
452 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 268 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C24 |
| commutator | C22 | C23×C4×C11 |
| Frattini, cosocle | C2×C4 | C24×C11 |
| socle | C22×C11 | C23×C4 |
| prime radical | C22×D4×C11 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#436 | C2 | semidirect |
| 3. C11×#431 | C2 | semidirect |
| 4. C11×#407 | C2 | semidirect |
| 7. C2×C11×M16 | C22 | semidirect |
| 13. C11×C4⋊C8 | C22 | semidirect |
| 15. C11×C22⋊C8 | C22 | semidirect |
| 16. C4×C8×C11 | C22 | semidirect |
| 33. #2975 | C11 | direct (N × H) |
| 45. C2×C4×C11 | M16 | semidirect |
| 53. #436 | C2×C11 | semidirect |
| 54. #431 | C2×C11 | semidirect |
| 55. #407 | C2×C11 | semidirect |
| 71. C2×M16 | C22×C11 | semidirect |
| 77. C4⋊C8 | C22×C11 | semidirect |
| 79. C22⋊C8 | C22×C11 | semidirect |
| 80. C4×C8 | C22×C11 | semidirect |
| 102. C11 | #2975 | direct (N × H) |
| 114. C2×C4 | C11×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D4×C11 | 2 |
| C11×#436 | 2 |
| C11×#431 | 2 |
| C11×#407 | 2 |
| #2975 | 11 |