Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
270 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D11 |
| commutator, hypocenter | C11 | C2×C4×C32 |
| Frattini | C2×C16 | C22×D11 |
| Fitting | C22×C11×C32 | C2 |
| socle, prime radical | C23×C11 | C2×C16 |
| cosocle | C2×C11×C16 | C23 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C22×C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C32×Dic11 | C2 | direct (N × H) |
| 8. C2×C11×C32 | C4 | semidirect |
| 12. C2×C11⋊C32 | C4 | semidirect |
| 25. C11×C32 | C2×C4 | semidirect |
| 26. C11⋊C32 | C2×C4 | semidirect |
| 51. C2×Dic11 | C32 | direct (N × H) |
| 62. C2×C32 | Dic11 | direct (N × H) |
| 72. Dic11 | C2×C32 | direct (N × H) |
| 85. C32 | C2×Dic11 | direct (N × H) |
| 86. C2×C11 | C4×C32 | semidirect |
| 103. C11 | C2×C4×C32 | semidirect |
| 122. C2 | C32×Dic11 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11⋊C32 | 2 |
| C2×C16×Dic11 | 2 |
| C32×Dic11 | 2 |
| C22×C11×C32 | 2 |
| C2×C4×C32 | 11 |