Finite Group DatabasebetaFinite Group DatabasebetaOrder 6208.
258 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C4×#87604 | C2 | 1 | 6 | yes | maximal |
| 2 | C42×D97 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C22×#87604 | C22 | 1 | 4 | yes | — |
| 4 | C4×#87604 | C4 | 1 | 24 | yes | direct product factor |
| 5 | C2×C4×D97 | C22 | 1 | 3 | yes | — |
| 6 | C4×Dic97 | C4 | 1 | 3 | yes | complemented |
| 7 | C42×C97 | C4 | 1 | 1 | yes | characteristic, complemented |
| 8 | C22×D97 | C23 | 1 | 1 | yes | characteristic |
| 9 | C2×#87604 | C2×C4 | 1 | 24 | yes | — |
| 10 | C2×C4×C97 | C2×C4 | 1 | 3 | yes | — |
| 11 | C2×Dic97 | C2×C4 | 1 | 3 | yes | — |
| 12 | C4×D97 | C2×C4 | 1 | 12 | yes | — |
| 13 | C22×C97 | C22×C4 | 1 | 1 | yes | characteristic |
| 14 | C2×D97 | C22×C4 | 1 | 6 | yes | — |
| 15 | #87604 | C42 | 1 | 16 | yes | direct product factor |
| 16 | C4×C97 | C42 | 1 | 6 | yes | complemented |
| 17 | Dic97 | C42 | 1 | 6 | yes | complemented |
| 18 | C2×C97 | C2×C42 | 1 | 3 | yes | — |
| 19 | D97 | C2×C42 | 1 | 4 | yes | — |
| 20 | C97 | C43 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 21 | C43 | — | 97 | 1 | no | maximal, Sylow |
| 22 | C2×C42 | — | 97 | 6 | no | — |
| 23 | C2×C42 | — | 97 | 1 | no | — |
| 24 | C22×C4 | — | 97 | 4 | no | — |
| 25 | C22×C4 | — | 97 | 3 | no | — |
| 26 | C42 | — | 97 | 24 | no | — |
| 27 | C42 | — | 97 | 3 | no | — |
| 28 | C42 | #87604 | 1 | 1 | yes | characteristic, direct product factor |
| 29 | C23 | — | 97 | 1 | no | — |
| 30 | C2×C4 | — | 97 | 24 | no | — |
| 31 | C2×C4 | — | 97 | 3 | no | — |
| 32 | C2×C4 | — | 97 | 12 | no | — |
| 33 | C2×C4 | C2×#87604 | 1 | 3 | yes | — |
| 34 | C22 | — | 97 | 6 | no | — |
| 35 | C22 | C22×#87604 | 1 | 1 | yes | characteristic |
| 36 | C4 | — | 97 | 16 | no | — |
| 37 | C4 | — | 97 | 6 | no | — |
| 38 | C4 | C4×#87604 | 1 | 6 | yes | direct product factor |
| 39 | C2 | — | 97 | 4 | no | — |
| 40 | C2 | C2×C4×#87604 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #87604 |
| commutator, hypocenter | C97 | C43 |
| Frattini | C22 | C22×#87604 |
| Fitting | C42×C97 | C4 |
| socle | C22×C97 | C22×C4 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×#87604 | C4 | direct (N × H) |
| 6. C4×Dic97 | C4 | semidirect |
| 7. C42×C97 | C4 | semidirect |
| 15. #87604 | C42 | direct (N × H) |
| 16. C4×C97 | C42 | semidirect |
| 17. Dic97 | C42 | semidirect |
| 20. C97 | C43 | semidirect |
| 28. C42 | #87604 | direct (N × H) |
| 38. C4 | C4×#87604 | direct (N × H) |