← ΓL(1,𝔽8)×GL(3,𝔽2) #72209940
Order 3528.
74 conjugacy classes of subgroups.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C7×GL(3,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | ΓL(1,𝔽8)×S4 | — | 7 | 2 | no | maximal |
| 3 | C3×GL(3,𝔽2) | — | 7 | 1 | no | maximal |
| 4 | ΓL(1,𝔽8)2 | — | 8 | 1 | no | maximal, Hall |
| 5 | A4×ΓL(1,𝔽8) | — | 7 | 2 | no | — |
| 6 | C7×S4 | — | 7 | 2 | no | — |
| 7 | GL(3,𝔽2) | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 8 | D4×ΓL(1,𝔽8) | — | 21 | 1 | no | — |
| 9 | #3862 | — | 8 | 1 | no | — |
| 10 | #3861 | — | 8 | 1 | no | — |
| 11 | C7×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 12 | C7×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 13 | D3×ΓL(1,𝔽8) | — | 28 | 1 | no | — |
| 14 | C22⋊ΓL(1,𝔽8) | — | 14 | 2 | no | — |
| 15 | C7×A4 | — | 7 | 2 | no | — |
| 16 | C22×ΓL(1,𝔽8) | — | 7 | 2 | no | — |
| 17 | C4×ΓL(1,𝔽8) | — | 21 | 1 | no | — |
| 18 | C3×S4 | — | 49 | 2 | no | Hall |
| 19 | C3×ΓL(1,𝔽8) | — | 28 | 1 | no | — |
| 20 | C3×ΓL(1,𝔽8) | — | 56 | 1 | no | — |
| 21 | C7×D4 | — | 21 | 1 | no | — |
| 22 | C72 | — | 8 | 1 | no | Sylow |
| 23 | D3×C7 | — | 28 | 1 | no | — |
| 24 | C2×ΓL(1,𝔽8) | — | 21 | 1 | no | — |
| 25 | C3×A4 | — | 49 | 2 | no | — |
| 26 | C22×C7 | — | 7 | 2 | no | — |
| 27 | C4×C7 | — | 21 | 1 | no | — |
| 28 | S4 | — | 7 | 2 | no | — |
| 29 | C3×D4 | — | 147 | 1 | no | — |
| 30 | C3×C7 | — | 28 | 1 | no | — |
| 31 | C3×C7 | — | 56 | 1 | no | — |
| 32 | ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 33 | ΓL(1,𝔽8) | — | 56 | 1 | no | — |
| 34 | ΓL(1,𝔽8) | — | 56 | 1 | no | — |
| 35 | ΓL(1,𝔽8) | — | 56 | 1 | no | — |
| 36 | ΓL(1,𝔽8) | — | 168 | 2 | no | — |
| 37 | ΓL(1,𝔽8) | GL(3,𝔽2) | 1 | 1 | yes | maximal normal, characteristic, direct product factor |
| 38 | C3×D3 | — | 196 | 1 | no | — |
| 39 | C2×C7 | — | 21 | 1 | no | — |
| 40 | C22×C3 | — | 49 | 2 | no | — |
| 41 | A4 | — | 7 | 2 | no | — |
| 42 | A4 | — | 98 | 2 | no | — |
| 43 | C3×C4 | — | 147 | 1 | no | — |
| 44 | C32 | — | 196 | 1 | no | Sylow |
| 45 | D4 | — | 21 | 1 | no | Sylow |
| 46 | C7 | — | 8 | 1 | no | — |
| 47 | C7 | — | 24 | 2 | no | — |
| 48 | C7 | C3×GL(3,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 49 | C2×C3 | — | 147 | 1 | no | — |
| 50 | D3 | — | 28 | 1 | no | — |
| 51 | C22 | — | 7 | 2 | no | — |
| 52 | C4 | — | 21 | 1 | no | — |
| 53 | C3 | — | 7 | 1 | no | — |
| 54 | C3 | — | 28 | 1 | no | — |
| 55 | C3 | — | 392 | 1 | no | — |
| 56 | C2 | — | 21 | 1 | no | — |
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