| 1 | C7×#237 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3×C7×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#214 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C7×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×C7×C8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#135 | — | 3 | 1 | no | maximal, Hall |
| 7 | C3×C7×D4 | C22 | 1 | 2 | yes | — |
| 8 | C7×#67 | — | 2 | 2 | no | — |
| 9 | C2×C7×Dic3 | — | 2 | 2 | no | — |
| 10 | C4×D3×C7 | C22 | 1 | 1 | yes | characteristic |
| 11 | C7×Dic6 | C22 | 1 | 2 | yes | — |
| 12 | C3×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C7×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7×#41 | — | 3 | 2 | no | — |
| 15 | C7×Q16 | — | 3 | 1 | no | — |
| 16 | C7×SD16 | — | 3 | 2 | no | — |
| 17 | C7×D8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C7×C8 | — | 3 | 1 | no | — |
| 19 | #912 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 20 | C22×C3×C7 | — | 2 | 2 | no | — |
| 21 | C2×D3×C7 | D4 | 1 | 1 | yes | characteristic |
| 22 | C3×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 23 | C7×Dic3 | — | 2 | 2 | no | — |
| 24 | C7×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 25 | C7×Q8 | — | 3 | 2 | no | — |
| 26 | C7×D4 | — | 6 | 2 | no | — |
| 27 | C7×D4 | C2×D3 | 1 | 2 | yes | — |
| 28 | C2×C4×C7 | — | 3 | 1 | no | — |
| 29 | C2×C4×C7 | — | 6 | 2 | no | — |
| 30 | C7×C8 | — | 3 | 1 | no | — |
| 31 | C7×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 32 | #237 | C2×C7 | 1 | 2 | yes | complemented |
| 33 | C3×D8 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 34 | #214 | C2×C7 | 1 | 2 | yes | complemented |
| 35 | Dic12 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 36 | D3×C8 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×C3×C7 | — | 4 | 2 | no | — |
| 38 | C2×C3×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 39 | D3×C7 | — | 2 | 1 | no | — |
| 40 | #135 | — | 3 | 1 | no | Sylow |
| 41 | C22×C7 | — | 2 | 2 | no | — |
| 42 | C22×C7 | — | 3 | 1 | no | — |
| 43 | C4×C7 | — | 3 | 1 | no | — |
| 44 | C4×C7 | — | 6 | 2 | no | — |
| 45 | C4×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 46 | C3×D4 | C22×C7 | 1 | 2 | yes | — |
| 47 | #67 | — | 2 | 2 | no | — |
| 48 | C2×Dic3 | — | 2 | 2 | no | — |
| 49 | C4×D3 | C22×C7 | 1 | 1 | yes | characteristic |
| 50 | Dic6 | C22×C7 | 1 | 2 | yes | — |
| 51 | C3×C8 | C22×C7 | 1 | 1 | yes | characteristic |
| 52 | C3⋊C8 | C22×C7 | 1 | 1 | yes | characteristic |
| 53 | C3×C7 | #135 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | #41 | — | 3 | 2 | no | — |
| 55 | Q16 | — | 3 | 1 | no | — |
| 56 | SD16 | — | 3 | 2 | no | — |
| 57 | D8 | D3×C7 | 1 | 1 | yes | characteristic, complemented |
| 58 | C2×C8 | — | 3 | 1 | no | — |
| 59 | C2×C7 | — | 4 | 2 | no | — |
| 60 | C2×C7 | — | 6 | 1 | no | — |
| 61 | C2×C7 | D3×D4 | 1 | 1 | yes | characteristic |
| 62 | C22×C3 | — | 2 | 2 | no | — |
| 63 | C2×D3 | C7×D4 | 1 | 1 | yes | characteristic |
| 64 | C3×C4 | C23×C7 | 1 | 1 | yes | characteristic |
| 65 | Dic3 | — | 2 | 2 | no | — |
| 66 | Dic3 | C7×D4 | 1 | 1 | yes | characteristic |
| 67 | Q8 | — | 3 | 2 | no | — |
| 68 | D4 | — | 6 | 2 | no | — |
| 69 | D4 | C2×D3×C7 | 1 | 2 | yes | — |
| 70 | C2×C4 | — | 3 | 1 | no | — |
| 71 | C2×C4 | — | 6 | 2 | no | — |
| 72 | C8 | — | 3 | 1 | no | — |
| 73 | C8 | C2×D3×C7 | 1 | 1 | yes | characteristic |
| 74 | C7 | #912 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 75 | C2×C3 | — | 4 | 2 | no | — |
| 76 | C2×C3 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 77 | D3 | — | 2 | 1 | no | — |
| 78 | C22 | — | 2 | 2 | no | — |
| 79 | C22 | — | 3 | 1 | no | — |
| 80 | C4 | — | 3 | 1 | no | — |
| 81 | C4 | — | 6 | 2 | no | — |
| 82 | C4 | C22×D3×C7 | 1 | 1 | yes | characteristic |
| 83 | C3 | C7×#135 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 84 | C2 | — | 4 | 2 | no | — |
| 85 | C2 | — | 6 | 1 | no | — |
| 86 | C2 | D3×C7×D4 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta