| 1 | C7×#120 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#99 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C24×C7 | C4 | 1 | 1 | yes | characteristic, complemented |
| 5 | C2×C7×D4 | — | 2 | 1 | no | — |
| 6 | C2×C7×D4 | C22 | 1 | 1 | yes | characteristic |
| 7 | C7×M16 | — | 2 | 1 | no | — |
| 8 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 9 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 10 | C7×C22⋊C4 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | AΣL(1,𝔽16) | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 12 | C23×C7 | — | 2 | 1 | no | — |
| 13 | C23×C7 | — | 4 | 2 | no | — |
| 14 | C23×C7 | — | 4 | 1 | no | — |
| 15 | C23×C7 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C23×C7 | D4 | 1 | 1 | yes | characteristic |
| 17 | C7×D4 | — | 4 | 1 | no | — |
| 18 | C7×D4 | — | 4 | 2 | no | — |
| 19 | C2×C4×C7 | — | 2 | 1 | no | — |
| 20 | C2×C4×C7 | — | 4 | 1 | no | — |
| 21 | C2×C4×C7 | D4 | 1 | 1 | yes | characteristic |
| 22 | C7×C8 | — | 4 | 1 | no | — |
| 23 | #120 | C2×C7 | 1 | 1 | yes | characteristic |
| 24 | #100 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 25 | #99 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 26 | C22×C7 | — | 2 | 2 | no | — |
| 27 | C22×C7 | — | 2 | 1 | no | — |
| 28 | C22×C7 | — | 2 | 1 | no | — |
| 29 | C22×C7 | — | 4 | 1 | no | — |
| 30 | C22×C7 | — | 4 | 1 | no | — |
| 31 | C22×C7 | — | 4 | 1 | no | — |
| 32 | C22×C7 | — | 4 | 2 | no | — |
| 33 | C22×C7 | — | 4 | 2 | no | — |
| 34 | C22×C7 | — | 4 | 1 | no | — |
| 35 | C22×C7 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 36 | C4×C7 | — | 2 | 1 | no | — |
| 37 | C4×C7 | — | 4 | 1 | no | — |
| 38 | C4×C7 | — | 8 | 1 | no | — |
| 39 | C24 | C4×C7 | 1 | 1 | yes | characteristic, complemented |
| 40 | C2×D4 | — | 2 | 1 | no | — |
| 41 | C2×D4 | C22×C7 | 1 | 1 | yes | characteristic |
| 42 | M16 | — | 2 | 1 | no | — |
| 43 | C22⋊C4 | — | 2 | 1 | no | — |
| 44 | C22⋊C4 | — | 2 | 1 | no | — |
| 45 | C22⋊C4 | C4×C7 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C7 | — | 2 | 1 | no | — |
| 47 | C2×C7 | — | 4 | 1 | no | — |
| 48 | C2×C7 | — | 4 | 2 | no | — |
| 49 | C2×C7 | — | 4 | 1 | no | — |
| 50 | C2×C7 | #99 | 1 | 1 | yes | characteristic |
| 51 | C23 | — | 2 | 1 | no | — |
| 52 | C23 | — | 4 | 2 | no | — |
| 53 | C23 | — | 4 | 1 | no | — |
| 54 | C23 | C2×C4×C7 | 1 | 1 | yes | characteristic |
| 55 | C23 | C7×D4 | 1 | 1 | yes | characteristic |
| 56 | D4 | — | 4 | 1 | no | — |
| 57 | D4 | — | 4 | 2 | no | — |
| 58 | C2×C4 | — | 2 | 1 | no | — |
| 59 | C2×C4 | — | 4 | 1 | no | — |
| 60 | C2×C4 | C7×D4 | 1 | 1 | yes | characteristic |
| 61 | C8 | — | 4 | 1 | no | — |
| 62 | C7 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 63 | C22 | — | 2 | 2 | no | — |
| 64 | C22 | — | 2 | 1 | no | — |
| 65 | C22 | — | 2 | 1 | no | — |
| 66 | C22 | — | 4 | 1 | no | — |
| 67 | C22 | — | 4 | 1 | no | — |
| 68 | C22 | — | 4 | 1 | no | — |
| 69 | C22 | — | 4 | 2 | no | — |
| 70 | C22 | — | 4 | 2 | no | — |
| 71 | C22 | — | 4 | 1 | no | — |
| 72 | C22 | C7×C22⋊C4 | 1 | 1 | yes | characteristic |
| 73 | C4 | — | 2 | 1 | no | — |
| 74 | C4 | — | 4 | 1 | no | — |
| 75 | C4 | — | 8 | 1 | no | — |
| 76 | C2 | — | 2 | 1 | no | — |
| 77 | C2 | — | 4 | 1 | no | — |
| 78 | C2 | — | 4 | 2 | no | — |
| 79 | C2 | — | 4 | 1 | no | — |
| 80 | C2 | C7×#99 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta