Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
482 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 270 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C11 |
| socle | C22×C11 | C22×D8 |
| prime radical | C23×C11 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ C2×C42×C11 ◁ C2×C4×C8×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C11×#2255 | C2 | semidirect |
| 25. C2×C11×C16 | Q8 | semidirect |
| 33. #33728 | C11 | direct (N × H) |
| 51. #2255 | C2×C11 | semidirect |
| 94. C2×C16 | Q8×C11 | semidirect |
| 121. C11 | #33728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#3160 | 2 |
| C11×#2255 | 2 |
| C11×#2158 | 2 |
| C2×C11×#346 | 2 |
| #33728 | 11 |