Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
836 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 173 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 | C11×#390 | C2 |
| prime radical | C22×#4341 | C2 |
| hypercenter | #390 | D11 |
| hypocenter | C11 | #2432 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#66989 | C2 | semidirect |
| 3. C2×#66950 | C2 | semidirect |
| 4. C2×#66922 | C2 | semidirect |
| 5. C11×#390 | C2 | semidirect |
| 6. #10622587 | C2 | semidirect |
| 7. #10622574 | C2 | semidirect |
| 8. #10622563 | C2 | semidirect |
| 9. C4×(C2×D11)⋊C4 | C2 | semidirect |
| 90. C2×C4×C11 | #41 | semidirect |
| 114. #390 | D11 | semidirect |
| 206. C11 | #2432 | semidirect |
| 243. C2×C4 | #4341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#4341 | 2 |
| C2×#66989 | 2 |
| C2×#66950 | 2 |
| C2×#66922 | 2 |
| C11×#390 | 2 |
| #10622587 | 2 |
| #10622574 | 2 |
| #10622563 | 2 |
| C4×(C2×D11)⋊C4 | 2 |
| #2432 | 11 |