Finite Group DatabasebetaFinite Group DatabasebetaOrder 1408.
840 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 189 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×#380 | C2 |
| prime radical | C22×C22⋊D11 | C22 |
| hypercenter | #380 | D11 |
| hypocenter | C11 | #2409 |
| LCS | G ▷ C23×C11 ▷ C11 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×Dic22 | C2 | semidirect |
| 3. C2×#66950 | C2 | semidirect |
| 4. C11×#380 | C2 | semidirect |
| 5. #10622587 | C2 | semidirect |
| 7. #10622563 | C2 | semidirect |
| 8. #10622286 | C2 | semidirect |
| 9. #10622269 | C2 | semidirect |
| 40. C2×C22⋊D11 | Q8 | semidirect |
| 54. C2×Dic22 | D4 | semidirect |
| 74. C22×D11 | C2×Q8 | semidirect |
| 94. C2×Dic11 | C2×Q8 | semidirect |
| 106. #380 | D11 | semidirect |
| 111. C22×C11 | C22⋊Q8 | semidirect |
| 189. C11 | #2409 | semidirect |
| 233. C22 | #66950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic22 | 2 |
| C2×C4×C22⋊D11 | 2 |
| C2×#66950 | 2 |
| C11×#380 | 2 |
| #10622587 | 2 |
| #10622571 | 2 |
| #10622563 | 2 |
| #10622286 | 2 |
| #10622269 | 2 |
| #2409 | 11 |