Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
338 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#595 |
| commutator, socle | C2×C17 | C23×C4 |
| Fitting | C2×D4×C17 | C4 |
| prime radical | C2×D4×D17 | C2 |
| cosocle | C2×D17 | C24 |
| hypercenter | C2×D4 | #595 |
| hypocenter | C17 | #518 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C22⋊#595 | C2 | semidirect |
| 3. D4×#595 | C2 | semidirect |
| 4. #10587677 | C2 | semidirect |
| 6. C22×#595 | C22 | semidirect |
| 7. C2×D4×C17 | C4 | semidirect |
| 8. C2×C22⋊D17 | C4 | semidirect |
| 9. D4×D17 | C4 | semidirect |
| 11. C2×D68 | C4 | semidirect |
| 14. C22⋊#595 | C22 | semidirect |
| 15. C4⋊#595 | C22 | semidirect |
| 16. C4×#595 | C22 | semidirect |
| 17. C23×C17 | C2×C4 | semidirect |
| 19. C22×D17 | C2×C4 | semidirect |
| 20. C22×D17 | C2×C4 | semidirect |
| 25. D4×C17 | C2×C4 | semidirect |
| 26. C2×C4×C17 | C2×C4 | semidirect |
| 27. C22⋊D17 | C2×C4 | semidirect |
| 28. C2×Dic17 | C2×C4 | semidirect |
| 29. D68 | C2×C4 | semidirect |
| 30. C4×D17 | C2×C4 | semidirect |
| 56. C17 | #518 | semidirect |
| 62. C2×D4 | #595 | semidirect |
| 74. C23 | C2×#595 | semidirect |
| 77. D4 | C2×#595 | semidirect |
| 83. C2×C4 | C2×#595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D17 | 2 |
| C2×C22⋊#595 | 2 |
| D4×#595 | 2 |
| #10587677 | 2 |
| #518 | 17 |