Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D11 |
| commutator, cosocle | C23×C11 | C24 |
| Frattini | C23 | C23×D11 |
| Fitting | C2×C11×#95 | C2 |
| socle | C24×C11 | C23 |
| hypercenter | C2×#95 | D11 |
| hypocenter | C11 | C2×#392 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D44 | C2 | semidirect |
| 2. C22×(C2×D11)⋊C4 | C2 | semidirect |
| 3. C2×C11×#95 | C2 | semidirect |
| 4. #10622284 | C2 | direct (N × H) |
| 10. C22×D44 | C22 | semidirect |
| 12. C2×(C2×D11)⋊C4 | C22 | semidirect |
| 13. C11×#95 | C22 | semidirect |
| 19. C23×D11 | D4 | semidirect |
| 22. C22×C4×C11 | D4 | semidirect |
| 44. C22×D11 | C2×D4 | semidirect |
| 47. C2×C4×C11 | C2×D4 | semidirect |
| 54. C2×#95 | D11 | semidirect |
| 77. #95 | C2×D11 | semidirect |
| 78. C2×C11 | #392 | semidirect |
| 96. C22×C4 | D44 | semidirect |
| 99. C11 | C2×#392 | semidirect |
| 119. C2×C4 | C2×D44 | semidirect |
| 135. C2 | #10622284 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D44 | 2 |
| C22×(C2×D11)⋊C4 | 2 |
| C2×C11×#95 | 2 |
| #10622284 | 2 |
| C2×#392 | 11 |