Finite Group DatabasebetaFinite Group DatabasebetaOrder 8224.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #16861627 | C2 | 1 | 2 | yes | maximal |
| 2 | C2×Dic514 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14523346 | — | 2 | 2 | no | — |
| 4 | Dic514 | — | 2 | 2 | no | — |
| 5 | C2×Dic257 | C4 | 1 | 1 | yes | characteristic |
| 6 | C2×Dic257 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×C257 | C4 | 1 | 1 | yes | characteristic |
| 8 | C22×C257 | C2×C4 | 1 | 1 | yes | characteristic |
| 9 | C4×C257 | — | 2 | 1 | no | — |
| 10 | Dic257 | — | 2 | 1 | no | — |
| 11 | Dic257 | D4 | 1 | 2 | yes | — |
| 12 | C2×C257 | — | 2 | 1 | no | — |
| 13 | C2×C257 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 14 | C257 | #101 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 15 | #101 | — | 257 | 1 | no | maximal, Sylow |
| 16 | C2×Q8 | — | 257 | 1 | no | — |
| 17 | M16 | — | 257 | 2 | no | — |
| 18 | Q8 | — | 514 | 2 | no | — |
| 19 | C2×C4 | — | 257 | 1 | no | — |
| 20 | C2×C4 | — | 257 | 1 | no | — |
| 21 | C2×C4 | #11759967 | 1 | 1 | yes | characteristic |
| 22 | C8 | — | 514 | 2 | no | — |
| 23 | C22 | C2×#11759967 | 1 | 1 | yes | characteristic |
| 24 | C4 | — | 257 | 2 | no | — |
| 25 | C4 | — | 2 | 1 | no | — |
| 26 | C4 | — | 514 | 1 | no | — |
| 27 | C2 | — | 2 | 1 | no | — |
| 28 | C2 | C22⋊#11759967 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. C257 | #101 | semidirect |