Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
234 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8×C11 | #124 |
| commutator | C22×C4 | C22×C4×C11 |
| Frattini, cosocle | C22×C8 | C23×C11 |
| socle | C2×C11 | #1832 |
| prime radical | C23×C11 | #131 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C11 ◁ C22×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 32. #12885 | C11 | direct (N × H) |
| 125. C11 | #12885 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2153 | 2 |
| C11×#2151 | 2 |
| C11×#1747 | 2 |
| C11×#1379 | 2 |
| C11×#1378 | 2 |
| #12885 | 11 |