Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
992 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C11 |
| prime radical | C11×#3549 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#3216 | C2 | semidirect |
| 3. C11×#3135 | C2 | semidirect |
| 4. C11×#1659 | C2 | semidirect |
| 5. C11×#1536 | C2 | semidirect |
| 6. C11×#1530 | C2 | semidirect |
| 14. C11×#533 | C22 | semidirect |
| 17. C11×#497 | C22 | semidirect |
| 20. C11×#489 | C22 | semidirect |
| 21. C11×#489 | C22 | semidirect |
| 25. C11×#432 | C22 | semidirect |
| 27. C2×C11×#97 | C22 | semidirect |
| 28. C11×#329 | C22 | semidirect |
| 29. C11×#329 | C22 | semidirect |
| 75. #19056 | C11 | direct (N × H) |
| 120. #3216 | C2×C11 | semidirect |
| 121. #3135 | C2×C11 | semidirect |
| 122. #1659 | C2×C11 | semidirect |
| 123. #1536 | C2×C11 | semidirect |
| 124. #1530 | C2×C11 | semidirect |
| 163. #533 | C22×C11 | semidirect |
| 166. #497 | C22×C11 | semidirect |
| 169. #489 | C22×C11 | semidirect |
| 170. #489 | C22×C11 | semidirect |
| 174. #432 | C22×C11 | semidirect |
| 176. C2×#97 | C22×C11 | semidirect |
| 177. #329 | C22×C11 | semidirect |
| 178. #329 | C22×C11 | semidirect |
| 288. C11 | #19056 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3549 | 2 |
| C11×#3216 | 2 |
| C11×#3135 | 2 |
| C11×#1659 | 2 |
| C11×#1536 | 2 |
| C11×#1530 | 2 |
| #19056 | 11 |