Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1072 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 230 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×#3152 | C2 | semidirect |
| 3. C11×#3141 | C2 | semidirect |
| 4. C11×#1659 | C2 | semidirect |
| 5. C11×#1525 | C2 | semidirect |
| 6. C11×#1525 | C2 | semidirect |
| 17. C2×C11×C4⋊Q8 | C22 | semidirect |
| 18. C11×#497 | C22 | semidirect |
| 21. C11×#489 | C22 | semidirect |
| 25. C4×C11×M16 | C22 | semidirect |
| 26. C4×C11×M16 | C22 | semidirect |
| 27. C11×#329 | C22 | semidirect |
| 28. C11×#329 | C22 | semidirect |
| 73. #19074 | C11 | direct (N × H) |
| 119. #3152 | C2×C11 | semidirect |
| 120. #3141 | C2×C11 | semidirect |
| 121. #1659 | C2×C11 | semidirect |
| 122. #1525 | C2×C11 | semidirect |
| 123. #1525 | C2×C11 | semidirect |
| 166. C2×C4⋊Q8 | C22×C11 | semidirect |
| 167. #497 | C22×C11 | semidirect |
| 170. #489 | C22×C11 | semidirect |
| 174. C4×M16 | C22×C11 | semidirect |
| 175. C4×M16 | C22×C11 | semidirect |
| 176. #329 | C22×C11 | semidirect |
| 177. #329 | C22×C11 | semidirect |
| 287. C11 | #19074 | 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×#3152 | 2 |
| C11×#3141 | 2 |
| C11×#1659 | 2 |
| C11×#1525 | 2 |
| #19074 | 11 |