Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
154 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C22×#595 |
| commutator, socle | C22×C17 | C22×C4 |
| Fitting | C4⋊C4×C17 | C4 |
| prime radical, cosocle | C22×D17 | C23 |
| hypercenter | C4⋊C4 | #595 |
| hypocenter | C17 | #387 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 17. C4⋊C4×C17 | C4 | semidirect |
| 18. C4⋊Dic17 | C4 | semidirect |
| 19. #63225 | C4 | semidirect |
| 20. #63225 | C4 | semidirect |
| 78. C17 | #387 | semidirect |
| 90. C4⋊C4 | #595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#595 | 2 |
| C2×C4×#595 | 2 |
| C4⋊C4×D17 | 2 |
| (C2×#595)⋊C4 | 2 |
| #387 | 17 |