Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
138 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C42×D17 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | (C2×#595)⋊C4 | C2 | 1 | 6 | yes | maximal |
| 3 | C22×#595 | C22 | 1 | 4 | yes | — |
| 4 | C2×C4×D17 | C22 | 1 | 3 | yes | — |
| 5 | C42×C17 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C4×Dic17 | C4 | 1 | 3 | yes | complemented |
| 7 | C22×D17 | C23 | 1 | 1 | yes | characteristic |
| 8 | C2×#595 | — | 2 | 12 | no | — |
| 9 | C2×C4×C17 | C2×C4 | 1 | 3 | yes | — |
| 10 | C2×Dic17 | C2×C4 | 1 | 3 | yes | — |
| 11 | C4×D17 | — | 2 | 6 | no | — |
| 12 | C22×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 13 | C2×D17 | #41 | 1 | 6 | yes | — |
| 14 | #595 | — | 4 | 4 | no | — |
| 15 | C4×C17 | — | 2 | 3 | no | — |
| 16 | Dic17 | — | 2 | 3 | no | — |
| 17 | #383 | — | 17 | 1 | no | maximal, Sylow |
| 18 | C2×C17 | #117 | 1 | 3 | yes | — |
| 19 | D17 | #126 | 1 | 4 | yes | — |
| 20 | C2×C42 | — | 17 | 1 | no | — |
| 21 | #95 | — | 17 | 6 | no | — |
| 22 | C17 | #383 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 23 | C22×C4 | — | 17 | 3 | no | — |
| 24 | C22×C4 | — | 17 | 4 | no | — |
| 25 | C42 | — | 17 | 3 | no | — |
| 26 | C42 | #595 | 1 | 1 | yes | characteristic, complemented |
| 27 | C23 | — | 17 | 1 | no | — |
| 28 | C2×C4 | — | 17 | 3 | no | — |
| 29 | C2×C4 | — | 34 | 6 | no | — |
| 30 | C2×C4 | — | 34 | 12 | no | — |
| 31 | C2×C4 | C2×#595 | 1 | 3 | yes | — |
| 32 | C22 | — | 17 | 6 | no | — |
| 33 | C22 | C22×#595 | 1 | 1 | yes | characteristic |
| 34 | C4 | — | 2 | 3 | no | — |
| 35 | C4 | — | 34 | 3 | no | — |
| 36 | C4 | — | 68 | 4 | no | — |
| 37 | C2 | — | 17 | 4 | no | — |
| 38 | C2 | #10587677 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#595 |
| commutator, socle | C22×C17 | C22×C4 |
| Fitting | C42×C17 | C4 |
| prime radical, cosocle | C22×D17 | C23 |
| hypercenter | C42 | #595 |
| hypocenter | C17 | #383 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C42×C17 | C4 | semidirect |
| 6. C4×Dic17 | C4 | semidirect |
| 22. C17 | #383 | semidirect |
| 26. C42 | #595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×D17 | 2 |
| (C2×#595)⋊C4 | 2 |
| #383 | 17 |