| 1 | C2×ΓL(1,𝔽8)×C97⋊C3 | C2 | 1 | 3 | yes | maximal, direct product factor |
| 2 | C22×C7×C97⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×ΓL(1,𝔽8)×C97 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#14523272 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C22×#14523271 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | ΓL(1,𝔽8)×C97⋊C3 | C22 | 1 | 1 | yes | characteristic, direct product factor, Hall |
| 7 | C2×#14523272 | C2×C3 | 1 | 3 | yes | complemented |
| 8 | C2×#14523271 | C2×C3 | 1 | 3 | yes | complemented |
| 9 | C2×ΓL(1,𝔽8)×C97 | C2×C3 | 1 | 3 | yes | complemented |
| 10 | C2×C7×C97⋊C3 | C2×C3 | 1 | 3 | yes | complemented |
| 11 | C22×C3×C97⋊C3 | — | 7 | 1 | no | maximal, Hall |
| 12 | C22×C7×C97 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 13 | #14523272 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #14523271 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C7×C97⋊C3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | ΓL(1,𝔽8)×C97 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×C3×C97⋊C3 | — | 7 | 3 | no | — |
| 18 | C2×C7×C97 | C2×C32 | 1 | 3 | yes | complemented |
| 19 | C22×C3×C97 | — | 7 | 1 | no | — |
| 20 | C22×C97⋊C3 | — | 7 | 1 | no | — |
| 21 | C22×C97⋊C3 | — | 7 | 1 | no | — |
| 22 | C22×C97⋊C3 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 23 | C3×C97⋊C3 | — | 7 | 1 | no | Hall |
| 24 | C7×C97 | C22×C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 25 | C2×C3×C97 | — | 7 | 3 | no | — |
| 26 | C2×C97⋊C3 | — | 7 | 3 | no | — |
| 27 | C2×C97⋊C3 | — | 7 | 3 | no | — |
| 28 | C2×C97⋊C3 | C2×ΓL(1,𝔽8) | 1 | 3 | yes | direct product factor |
| 29 | C22×C97 | C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented, Hall |
| 30 | C3×C97 | — | 7 | 1 | no | — |
| 31 | C97⋊C3 | — | 7 | 1 | no | — |
| 32 | C97⋊C3 | — | 7 | 1 | no | — |
| 33 | C97⋊C3 | C22×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 34 | C22×C3×ΓL(1,𝔽8) | — | 97 | 1 | no | maximal, Hall |
| 35 | C2×C97 | C2×C3×ΓL(1,𝔽8) | 1 | 3 | yes | complemented |
| 36 | C2×C3×ΓL(1,𝔽8) | — | 97 | 3 | no | — |
| 37 | C97 | C22×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 38 | C22×C3×C7 | — | 97 | 1 | no | — |
| 39 | C22×ΓL(1,𝔽8) | — | 97 | 1 | no | — |
| 40 | C22×ΓL(1,𝔽8) | — | 97 | 1 | no | — |
| 41 | C22×ΓL(1,𝔽8) | C97⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 42 | C3×ΓL(1,𝔽8) | — | 97 | 1 | no | Hall |
| 43 | C2×C3×C7 | — | 97 | 3 | no | — |
| 44 | C2×ΓL(1,𝔽8) | — | 97 | 3 | no | — |
| 45 | C2×ΓL(1,𝔽8) | — | 97 | 3 | no | — |
| 46 | C2×ΓL(1,𝔽8) | C2×C97⋊C3 | 1 | 3 | yes | direct product factor |
| 47 | C22×C32 | — | 679 | 1 | no | Hall |
| 48 | C22×C7 | C3×C97⋊C3 | 1 | 1 | yes | characteristic, complemented, Hall |
| 49 | C3×C7 | — | 97 | 1 | no | — |
| 50 | ΓL(1,𝔽8) | — | 97 | 1 | no | — |
| 51 | ΓL(1,𝔽8) | — | 97 | 1 | no | — |
| 52 | ΓL(1,𝔽8) | C22×C97⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 53 | C2×C32 | — | 679 | 3 | no | — |
| 54 | C2×C7 | C2×C3×C97⋊C3 | 1 | 3 | yes | complemented |
| 55 | C22×C3 | — | 7 | 1 | no | — |
| 56 | C22×C3 | — | 97 | 1 | no | — |
| 57 | C22×C3 | — | 679 | 1 | no | — |
| 58 | C22×C3 | — | 679 | 1 | no | — |
| 59 | C32 | — | 679 | 1 | no | Sylow |
| 60 | C7 | C22×C3×C97⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 61 | C2×C3 | — | 7 | 3 | no | — |
| 62 | C2×C3 | — | 97 | 3 | no | — |
| 63 | C2×C3 | — | 679 | 3 | no | — |
| 64 | C2×C3 | — | 679 | 3 | no | — |
| 65 | C22 | ΓL(1,𝔽8)×C97⋊C3 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 66 | C3 | — | 7 | 1 | no | — |
| 67 | C3 | — | 97 | 1 | no | — |
| 68 | C3 | — | 679 | 1 | no | — |
| 69 | C3 | — | 679 | 1 | no | — |
| 70 | C2 | C2×ΓL(1,𝔽8)×C97⋊C3 | 1 | 3 | yes | direct product factor |
Finite Group Databasebeta