Finite Group DatabasebetaFinite Group DatabasebetaOrder 6368.
70 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C4⋊Dic199 | C2 | 1 | 3 | yes | maximal |
| 2 | C4×Dic199 | C2 | 1 | 3 | yes | maximal |
| 3 | C2×Q8×C199 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×Dic199 | C22 | 1 | 3 | yes | — |
| 5 | C2×Dic199 | C22 | 1 | 1 | yes | characteristic |
| 6 | Q8×C199 | C4 | 1 | 4 | yes | complemented |
| 7 | C2×C4×C199 | C22 | 1 | 3 | yes | — |
| 8 | C22×C199 | C23 | 1 | 1 | yes | characteristic |
| 9 | C4×C199 | C2×C4 | 1 | 6 | yes | — |
| 10 | Dic199 | — | 2 | 3 | no | — |
| 11 | Dic199 | Q8 | 1 | 2 | yes | direct product factor |
| 12 | C2×C199 | C22×C4 | 1 | 1 | yes | characteristic |
| 13 | C2×C199 | C2×Q8 | 1 | 1 | yes | characteristic |
| 14 | C2×C199 | #41 | 1 | 1 | yes | characteristic |
| 15 | C199 | C4×Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | C4×Q8 | — | 199 | 1 | no | maximal, Sylow |
| 17 | C2×Q8 | D199 | 1 | 1 | yes | characteristic |
| 18 | C4⋊C4 | — | 199 | 3 | no | — |
| 19 | C42 | — | 199 | 3 | no | — |
| 20 | Q8 | Dic199 | 1 | 4 | yes | direct product factor |
| 21 | C2×C4 | — | 199 | 3 | no | — |
| 22 | C2×C4 | — | 199 | 1 | no | — |
| 23 | C2×C4 | C2×D199 | 1 | 3 | yes | — |
| 24 | C22 | C22×D199 | 1 | 1 | yes | characteristic |
| 25 | C4 | — | 398 | 3 | no | — |
| 26 | C4 | — | 199 | 2 | no | — |
| 27 | C4 | C2×Dic199 | 1 | 6 | yes | — |
| 28 | C2 | C22×Dic199 | 1 | 1 | yes | characteristic |
| 29 | C2 | Q8×D199 | 1 | 1 | yes | characteristic |
| 30 | C2 | #15691887 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D199 |
| commutator | C2×C199 | C22×C4 |
| Fitting | C2×Q8×C199 | C2 |
| socle | C22×C199 | C23 |
| hypercenter | C2×Q8 | D199 |
| hypocenter | C199 | C4×Q8 |
| LCS | G ▷ C2×C199 ▷ C199 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. Q8×C199 | C4 | semidirect |
| 11. Dic199 | Q8 | direct (N × H) |
| 15. C199 | C4×Q8 | semidirect |
| 20. Q8 | Dic199 | direct (N × H) |