Finite Group DatabasebetaFinite Group DatabasebetaOrder 10784.
70 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4⋊#13062438 | C2 | 1 | 3 | yes | maximal |
| 2 | C4×#13062438 | C2 | 1 | 3 | yes | maximal |
| 3 | Q8×D337 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#13062438 | C22 | 1 | 3 | yes | — |
| 5 | C2×#13062438 | C22 | 1 | 1 | yes | characteristic |
| 6 | Dic674 | C4 | 1 | 3 | yes | complemented |
| 7 | C4×D337 | C22 | 1 | 3 | yes | — |
| 8 | Q8×C337 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×D337 | C23 | 1 | 1 | yes | characteristic |
| 10 | #13062438 | — | 2 | 3 | no | — |
| 11 | #13062438 | Q8 | 1 | 2 | yes | direct product factor |
| 12 | C4×C337 | C2×C4 | 1 | 3 | yes | — |
| 13 | Dic337 | C2×C4 | 1 | 3 | yes | — |
| 14 | C2×C337 | C22×C4 | 1 | 1 | yes | characteristic |
| 15 | D337 | C2×Q8 | 1 | 1 | yes | characteristic |
| 16 | D337 | #41 | 1 | 1 | yes | characteristic |
| 17 | C337 | C4×Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | C4×Q8 | — | 337 | 1 | no | maximal, Sylow |
| 19 | C2×Q8 | — | 337 | 1 | no | — |
| 20 | C4⋊C4 | — | 337 | 3 | no | — |
| 21 | C42 | — | 337 | 3 | no | — |
| 22 | Q8 | — | 337 | 3 | no | — |
| 23 | Q8 | #13062438 | 1 | 1 | yes | characteristic, direct product factor |
| 24 | C2×C4 | — | 337 | 1 | no | — |
| 25 | C2×C4 | — | 337 | 3 | no | — |
| 26 | C2×C4 | — | 337 | 3 | no | — |
| 27 | C22 | — | 337 | 1 | no | — |
| 28 | C4 | — | 337 | 2 | no | — |
| 29 | C4 | — | 337 | 3 | no | — |
| 30 | C4 | — | 674 | 3 | no | — |
| 31 | C4 | C2×#13062438 | 1 | 3 | yes | — |
| 32 | C2 | — | 337 | 1 | no | — |
| 33 | C2 | — | 337 | 1 | no | — |
| 34 | C2 | C22×#13062438 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#13062438 |
| commutator, socle | C2×C337 | C22×C4 |
| Fitting | Q8×C337 | C4 |
| prime radical, cosocle | C2×D337 | C23 |
| hypercenter | Q8 | #13062438 |
| hypocenter | C337 | C4×Q8 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. Dic674 | C4 | semidirect |
| 8. Q8×C337 | C4 | semidirect |
| 11. #13062438 | Q8 | direct (N × H) |
| 17. C337 | C4×Q8 | semidirect |
| 23. Q8 | #13062438 | direct (N × H) |