Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D11 |
| commutator, socle, prime radical, cosocle | C23×C11 | C24 |
| Fitting | C11×#389 | C2 |
| hypercenter | #389 | D11 |
| hypocenter | C11 | #2734 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #389 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 49. C11×C4⋊C4 | Q8 | semidirect |
| 54. C4⋊Dic11 | Q8 | semidirect |
| 168. C4⋊C4 | Dic22 | semidirect |
| 171. C11 | #2734 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#66941 | 2 |
| C11×#389 | 2 |
| #10622597 | 2 |
| #10622594 | 2 |
| #10622592 | 2 |
| #10622542 | 2 |
| #10622541 | 2 |
| #10622269 | 2 |
| #10622267 | 2 |
| #2734 | 11 |