Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
644 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 237 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 | C22×C42×C11 | C2 |
| prime radical | C24×C11 | C23 |
| hypercenter | C22×C42 | D11 |
| hypocenter | C11 | #2857 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#66922 | C2 | semidirect |
| 5. #10622548 | C2 | semidirect |
| 6. #10622542 | C2 | semidirect |
| 7. #10622541 | C2 | semidirect |
| 29. C22×C4×C11 | Q8 | semidirect |
| 85. C22×C11 | C4⋊Q8 | semidirect |
| 94. C4×C11 | C22⋊Q8 | semidirect |
| 128. C22×C4 | Dic22 | semidirect |
| 142. C11 | #2857 | semidirect |
| 173. C22 | #66922 | semidirect |
| 183. C4 | #66977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C42×C11 | 2 |
| C2×#66977 | 2 |
| C2×#66922 | 2 |
| #10622825 | 2 |
| #10622548 | 2 |
| #10622542 | 2 |
| #10622541 | 2 |
| #2857 | 11 |