Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
64 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10587561 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10587545 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×D68 | C4 | 1 | 1 | yes | characteristic |
| 4 | C2×Dic34 | C22 | 1 | 1 | yes | characteristic |
| 5 | #63247 | — | 2 | 2 | no | — |
| 6 | C42×C17 | C4 | 1 | 1 | yes | characteristic |
| 7 | #63227 | — | 2 | 2 | no | — |
| 8 | C22×D17 | — | 2 | 1 | no | — |
| 9 | C2×C4×C17 | — | 2 | 1 | no | — |
| 10 | C2×C4×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 11 | C2×Dic17 | D4 | 1 | 2 | yes | — |
| 12 | D68 | — | 4 | 1 | no | — |
| 13 | Dic34 | — | 4 | 1 | no | — |
| 14 | #3624 | — | 4 | 2 | no | — |
| 15 | C22×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 16 | C2×D17 | — | 4 | 2 | no | — |
| 17 | C2×D17 | — | 4 | 1 | no | — |
| 18 | C4×C17 | — | 2 | 1 | no | — |
| 19 | C4×C17 | — | 4 | 1 | no | — |
| 20 | Dic17 | — | 2 | 2 | no | — |
| 21 | #355 | — | 17 | 1 | no | maximal, Sylow |
| 22 | C2×C17 | — | 2 | 1 | no | — |
| 23 | C2×C17 | #99 | 1 | 1 | yes | characteristic |
| 24 | D17 | — | 8 | 1 | no | — |
| 25 | #124 | — | 17 | 1 | no | — |
| 26 | #101 | — | 17 | 2 | no | — |
| 27 | C17 | #355 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 28 | C2×Q8 | — | 17 | 1 | no | — |
| 29 | C2×D4 | — | 17 | 1 | no | — |
| 30 | M16 | — | 34 | 2 | no | — |
| 31 | C22⋊C4 | — | 34 | 2 | no | — |
| 32 | C42 | #595 | 1 | 1 | yes | characteristic |
| 33 | C23 | — | 34 | 1 | no | — |
| 34 | Q8 | — | 68 | 1 | no | — |
| 35 | D4 | — | 68 | 1 | no | — |
| 36 | C2×C4 | — | 2 | 1 | no | — |
| 37 | C2×C4 | — | 17 | 2 | no | — |
| 38 | C2×C4 | C2×#595 | 1 | 1 | yes | characteristic |
| 39 | C8 | — | 68 | 2 | no | — |
| 40 | C22 | — | 68 | 2 | no | — |
| 41 | C22 | — | 68 | 1 | no | — |
| 42 | C22 | C22⋊#595 | 1 | 1 | yes | characteristic |
| 43 | C4 | — | 2 | 1 | no | — |
| 44 | C4 | — | 4 | 1 | no | — |
| 45 | C4 | — | 34 | 2 | no | — |
| 46 | C2 | — | 2 | 1 | no | — |
| 47 | C2 | — | 136 | 1 | no | — |
| 48 | C2 | #10587539 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #10587545 | C2 | semidirect |
| 27. C17 | #355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10587561 | 2 |
| #10587545 | 2 |
| #355 | 17 |