Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D17 |
| commutator, socle, cosocle | C22×C17 | C24 |
| Fitting | C17×C22⋊Q8 | C2 |
| prime radical | C2×C22⋊D17 | C22 |
| hypercenter | C22⋊Q8 | D17 |
| hypocenter | C17 | #554 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C17×C22⋊Q8 | C2 | semidirect |
| 2. #10587632 | C2 | semidirect |
| 3. #10587630 | C2 | semidirect |
| 5. C2×#63225 | C2 | semidirect |
| 6. #10587582 | C2 | semidirect |
| 7. #10587582 | C2 | semidirect |
| 8. C4⋊C4×D17 | C2 | semidirect |
| 9. #10587575 | C2 | semidirect |
| 10. #10587575 | C2 | semidirect |
| 11. #10587573 | C2 | semidirect |
| 14. #10587564 | C2 | semidirect |
| 15. #10587564 | C2 | semidirect |
| 61. C22⋊D17 | Q8 | semidirect |
| 110. C22⋊Q8 | D17 | semidirect |
| 117. C17 | #554 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C17×C22⋊Q8 | 2 |
| #10587632 | 2 |
| #10587630 | 2 |
| C4×C22⋊D17 | 2 |
| C2×#63225 | 2 |
| #10587582 | 2 |
| C4⋊C4×D17 | 2 |
| #10587575 | 2 |
| #10587573 | 2 |
| #10587567 | 2 |
| #10587564 | 2 |
| #554 | 17 |