Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C11×#3213 | C2 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. C11×#3216 | C2 | semidirect |
| 3. C11×#3140 | C2 | semidirect |
| 4. C11×#1497 | C2 | semidirect |
| 5. C11×#1484 | C2 | semidirect |
| 6. C11×#1469 | C2 | semidirect |
| 7. C11×#1291 | C2 | semidirect |
| 82. #10124 | C11 | direct (N × H) |
| 132. #3216 | C2×C11 | semidirect |
| 134. #3140 | C2×C11 | semidirect |
| 135. #1497 | C2×C11 | semidirect |
| 136. #1484 | C2×C11 | semidirect |
| 137. #1469 | C2×C11 | semidirect |
| 138. #1291 | C2×C11 | semidirect |
| 326. C11 | #10124 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3216 | 2 |
| C11×#3213 | 2 |
| C11×#3140 | 2 |
| C11×#1497 | 2 |
| C11×#1484 | 2 |
| C11×#1469 | 2 |
| C11×#1291 | 2 |
| #10124 | 11 |