Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
1348 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 1348 conjugacy classes of subgroups — too many to draw. Only its 213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, cosocle | C23×C11 | C24 |
| Fitting | C23×D4×C11 | C2 |
| hypercenter | C23×D4 | D11 |
| hypocenter | C11 | #2433 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D4×C11 | C2 | semidirect |
| 2. C2×#67006 | C2 | semidirect |
| 3. C2×#66993 | C2 | semidirect |
| 4. C2×#66983 | C2 | semidirect |
| 5. #10622836 | C2 | semidirect |
| 6. #10622834 | C2 | semidirect |
| 7. C4×C22⋊Dic11 | C2 | semidirect |
| 15. C22×C22⋊D11 | C22 | semidirect |
| 16. C22×D44 | C22 | semidirect |
| 19. C2×C22⋊Dic11 | C22 | semidirect |
| 22. C2×(C2×D11)⋊C4 | C22 | semidirect |
| 23. C2×C4⋊Dic11 | C22 | semidirect |
| 24. C2×C4×Dic11 | C22 | semidirect |
| 25. C11⋊#95 | C22 | semidirect |
| 38. C2×D4×C11 | D4 | semidirect |
| 40. C22×C4×C11 | D4 | semidirect |
| 53. C22⋊Dic11 | D4 | semidirect |
| 89. C2×Dic11 | C2×D4 | semidirect |
| 91. C23×D4 | D11 | semidirect |
| 107. C22×C11 | #127 | semidirect |
| 117. C4×C11 | #120 | semidirect |
| 164. C2×D4 | C22⋊D11 | semidirect |
| 168. C22×C4 | C22⋊D11 | semidirect |
| 176. C11 | #2433 | semidirect |
| 223. C22 | #66993 | semidirect |
| 231. C4 | #67006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C11 | 2 |
| C2×#67006 | 2 |
| C2×#66993 | 2 |
| C2×#66983 | 2 |
| #10622836 | 2 |
| #10622834 | 2 |
| C4×C22⋊Dic11 | 2 |
| #2433 | 11 |