Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 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, prime radical, cosocle | C23×C11 | C24 |
| Fitting | C2×C4×Q8×C11 | C2 |
| hypercenter | C2×C4×Q8 | D11 |
| hypocenter | C11 | #2567 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 25. C2×Q8×C11 | Q8 | semidirect |
| 41. C4⋊Dic11 | Q8 | semidirect |
| 108. C2×Q8 | Dic22 | semidirect |
| 125. C11 | #2567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C11 | 2 |
| C2×#66922 | 2 |
| #10622843 | 2 |
| #10622592 | 2 |
| #10622589 | 2 |
| C4×C4⋊Dic11 | 2 |
| #10622541 | 2 |
| #2567 | 11 |