Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
240 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C11 |
| prime radical | C11×#493 | C22 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ C82×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2227 | C2 | semidirect |
| 4. C8×C11×Q16 | C2 | semidirect |
| 5. C11×#1367 | C2 | semidirect |
| 6. C11×#1365 | C2 | semidirect |
| 45. #12419 | C11 | direct (N × H) |
| 52. C11×Q16 | SD16 | semidirect |
| 71. #2227 | C2×C11 | semidirect |
| 74. C8×Q16 | C2×C11 | semidirect |
| 75. #1367 | C2×C11 | semidirect |
| 76. #1365 | C2×C11 | semidirect |
| 159. Q16 | C11×SD16 | semidirect |
| 178. C11 | #12419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2227 | 2 |
| C11×#2207 | 2 |
| C11×#1706 | 2 |
| C8×C11×Q16 | 2 |
| C11×#1367 | 2 |
| C11×#1365 | 2 |
| C11×#1361 | 2 |
| #12419 | 11 |