← C2×C3×GL(3,𝔽2) #11759713
Order 1008.
90 conjugacy classes of subgroups.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×GL(3,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 2 | C2×GL(3,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | GL(3,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, direct product factor |
| 4 | C2×C3×S4 | — | 7 | 2 | no | maximal, Hall |
| 5 | C2×C3×ΓL(1,𝔽8) | — | 8 | 1 | no | maximal |
| 6 | C2×C3×A4 | — | 7 | 2 | no | — |
| 7 | C3×S4 | — | 7 | 2 | no | — |
| 8 | C3×S4 | — | 7 | 2 | no | — |
| 9 | C3×ΓL(1,𝔽8) | — | 8 | 1 | no | Hall |
| 10 | C2×S4 | — | 7 | 2 | no | — |
| 11 | C2×C3×D4 | — | 21 | 1 | no | — |
| 12 | C2×C3×C7 | — | 8 | 1 | no | — |
| 13 | C2×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 14 | C2×ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 15 | C2×C3×D3 | — | 28 | 1 | no | — |
| 16 | C3×A4 | — | 7 | 2 | no | — |
| 17 | C23×C3 | — | 7 | 2 | no | — |
| 18 | C2×A4 | — | 7 | 2 | no | — |
| 19 | C2×A4 | — | 14 | 2 | no | — |
| 20 | S4 | — | 7 | 2 | no | — |
| 21 | S4 | — | 7 | 2 | no | — |
| 22 | C3×D4 | — | 21 | 1 | no | — |
| 23 | C3×D4 | — | 21 | 2 | no | — |
| 24 | C3×D4 | — | 21 | 1 | no | — |
| 25 | C2×C3×C4 | — | 21 | 1 | no | — |
| 26 | C3×C7 | — | 8 | 1 | no | — |
| 27 | ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 28 | ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 29 | C2×C32 | — | 28 | 1 | no | — |
| 30 | C3×D3 | — | 28 | 1 | no | — |
| 31 | C3×D3 | — | 28 | 1 | no | — |
| 32 | C2×D4 | — | 21 | 1 | no | Sylow |
| 33 | C2×C7 | — | 8 | 1 | no | — |
| 34 | C22×C3 | — | 7 | 2 | no | — |
| 35 | C22×C3 | — | 21 | 2 | no | — |
| 36 | C22×C3 | — | 21 | 1 | no | — |
| 37 | C2×D3 | — | 28 | 1 | no | — |
| 38 | A4 | — | 7 | 2 | no | — |
| 39 | A4 | — | 14 | 2 | no | — |
| 40 | C3×C4 | — | 21 | 1 | no | — |
| 41 | C3×C4 | — | 21 | 1 | no | — |
| 42 | C32 | — | 28 | 1 | no | Sylow |
| 43 | C23 | — | 7 | 2 | no | — |
| 44 | D4 | — | 21 | 1 | no | — |
| 45 | D4 | — | 21 | 2 | no | — |
| 46 | D4 | — | 21 | 1 | no | — |
| 47 | C2×C4 | — | 21 | 1 | no | — |
| 48 | C7 | — | 8 | 1 | no | Sylow |
| 49 | C2×C3 | — | 21 | 1 | no | — |
| 50 | C2×C3 | — | 21 | 1 | no | — |
| 51 | C2×C3 | — | 28 | 1 | no | — |
| 52 | C2×C3 | — | 56 | 1 | no | — |
| 53 | C2×C3 | GL(3,𝔽2) | 1 | 1 | yes | maximal normal, characteristic, direct product factor |
| 54 | D3 | — | 28 | 1 | no | — |
| 55 | D3 | — | 28 | 1 | no | — |
| 56 | C22 | — | 7 | 2 | no | — |
| 57 | C22 | — | 21 | 2 | no | — |
| 58 | C22 | — | 21 | 1 | no | — |
| 59 | C4 | — | 21 | 1 | no | — |
| 60 | C4 | — | 21 | 1 | no | — |
| 61 | C3 | — | 28 | 1 | no | — |
| 62 | C3 | — | 56 | 1 | no | — |
| 63 | C3 | C2×GL(3,𝔽2) | 1 | 1 | yes | characteristic, direct product factor |
| 64 | C2 | — | 21 | 1 | no | — |
| 65 | C2 | — | 21 | 1 | no | — |
| 66 | C2 | C3×GL(3,𝔽2) | 1 | 1 | yes | characteristic, direct product factor |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta