Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
1422 conjugacy classes of subgroups; only the 555 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 555 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D11 |
| commutator | C23×C11 | C23×C4 |
| Fitting | C2×C43×C11 | C2 |
| socle, prime radical, cosocle | C24×C11 | C24 |
| hypercenter | C2×C43 | D11 |
| hypocenter | C11 | #14688 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C24 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C43×C11 | C4 | semidirect |
| 45. C42×C11 | C4⋊C4 | semidirect |
| 77. C43 | Dic11 | semidirect |
| 87. C4×C11 | #383 | semidirect |
| 126. C42 | C4⋊Dic11 | semidirect |
| 127. C11 | #14688 | semidirect |
| 157. C4 | #10622550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10622550 | 2 |
| #13066846 | 2 |
| #13066843 | 2 |
| C2×C43×C11 | 2 |
| #14688 | 11 |