Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
484 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C11 |
| prime radical | C2×C11×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ C2×C42×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2844 | C2 | semidirect |
| 3. C11×#1295 | C2 | semidirect |
| 15. C11×#127 | Q8 | semidirect |
| 26. #10358 | C11 | direct (N × H) |
| 46. #2844 | C2×C11 | semidirect |
| 48. #1295 | C2×C11 | semidirect |
| 88. #127 | Q8×C11 | semidirect |
| 122. C11 | #10358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2844 | 2 |
| C11×#1961 | 2 |
| C11×#1295 | 2 |
| #10358 | 11 |