Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
948 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 948 conjugacy classes of subgroups — too many to draw. Only its 185 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 | C2×C11×#127 | C2 |
| hypercenter | C2×#127 | D11 |
| hypocenter | C11 | #2541 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C11×#127 | C2 | semidirect |
| 2. C2×#66993 | C2 | semidirect |
| 3. C2×#66993 | C2 | semidirect |
| 4. C2×#66992 | C2 | semidirect |
| 5. C2×D4×Dic11 | C2 | semidirect |
| 6. #10622836 | C2 | semidirect |
| 7. #10622834 | C2 | semidirect |
| 8. #10622552 | C2 | semidirect |
| 9. C4×Dic11⋊C4 | C2 | semidirect |
| 43. C2×D4×C11 | D4 | semidirect |
| 67. Dic11⋊C4 | D4 | semidirect |
| 69. C4×Dic11 | D4 | semidirect |
| 112. C2×#127 | D11 | semidirect |
| 140. C4×C11 | #121 | semidirect |
| 144. Dic11 | #127 | semidirect |
| 196. C2×D4 | C22⋊D11 | semidirect |
| 213. C11 | #2541 | semidirect |
| 278. C4 | #66992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C11×#127 | 2 |
| C2×#66993 | 2 |
| C2×#66992 | 2 |
| C2×D4×Dic11 | 2 |
| #10622836 | 2 |
| #10622834 | 2 |
| #10622552 | 2 |
| C4×Dic11⋊C4 | 2 |
| #2541 | 11 |