Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
2938 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 2938 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C43 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C43 |
| prime radical | C26×C43 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#126×C43 | C2 | semidirect |
| 3. C43×#1440 | C2 | semidirect |
| 4. C43×#1439 | C2 | semidirect |
| 5. C43×#1437 | C2 | semidirect |
| 8. C22×C4⋊C4×C43 | C22 | semidirect |
| 13. C22×C42×C43 | C22 | semidirect |
| 15. C2×#95×C43 | C22 | semidirect |
| 16. C2×#95×C43 | C22 | semidirect |
| 110. C23×C43 | #126 | semidirect |
| 131. #15986 | C43 | direct (N × H) |
| 153. C22×#126 | C2×C43 | semidirect |
| 155. #1440 | C2×C43 | semidirect |
| 156. #1439 | C2×C43 | semidirect |
| 157. #1437 | C2×C43 | semidirect |
| 165. C22×C4⋊C4 | C22×C43 | semidirect |
| 170. C22×C42 | C22×C43 | semidirect |
| 172. C2×#95 | C22×C43 | semidirect |
| 173. C2×#95 | C22×C43 | semidirect |
| 174. C43 | #15986 | direct (N × H) |
| 268. C23 | #126×C43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#126×C43 | 2 |
| C2×C43×#379 | 2 |
| C43×#1440 | 2 |
| C43×#1439 | 2 |
| C43×#1437 | 2 |
| #15986 | 43 |