Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
852 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 197 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, cosocle | C23×C11 | C24 |
| Fitting | C23×Q8×C11 | C2 |
| prime radical | C2×#66983 | C2 |
| hypercenter | C23×Q8 | D11 |
| hypocenter | C11 | #2436 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Q8×C11 | C2 | semidirect |
| 2. C2×#67000 | C2 | semidirect |
| 4. #10622844 | C2 | semidirect |
| 5. #10622843 | C2 | semidirect |
| 6. #10622826 | C2 | semidirect |
| 7. C4×C22⋊Dic11 | C2 | semidirect |
| 32. C2×Q8×C11 | D4 | semidirect |
| 79. C23×Q8 | D11 | semidirect |
| 89. C22×C11 | #124 | semidirect |
| 133. C2×Q8 | C22⋊D11 | semidirect |
| 152. C11 | #2436 | semidirect |
| 187. C22 | #67000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×C11 | 2 |
| C2×#67000 | 2 |
| C2×#66983 | 2 |
| #10622844 | 2 |
| #10622843 | 2 |
| #10622826 | 2 |
| C4×C22⋊Dic11 | 2 |
| #2436 | 11 |