Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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 | C2×C4×Q8×C11 | C2 |
| prime radical | C22×D44 | C22 |
| hypercenter | C2×C4×Q8 | D11 |
| hypocenter | C11 | #2632 |
| 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 |
|---|---|---|
| 1. C2×C4×Q8×C11 | C2 | semidirect |
| 3. #10622844 | C2 | semidirect |
| 4. #10622605 | C2 | semidirect |
| 6. #10622592 | C2 | semidirect |
| 7. #10622553 | C2 | semidirect |
| 8. #10622550 | C2 | semidirect |
| 76. C2×C4×Q8 | D11 | semidirect |
| 144. C11 | #2632 | 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×#66928 | 2 |
| #10622844 | 2 |
| #10622605 | 2 |
| #10622604 | 2 |
| #10622592 | 2 |
| #10622553 | 2 |
| #10622550 | 2 |
| #2632 | 11 |