| 1 | C3×C5×C7×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×D60 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C7×C3⋊#168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7×#688 | — | 3 | 1 | no | maximal, Hall |
| 5 | C2×C7×D15 | — | 2 | 1 | no | — |
| 6 | C3×C4×C5×C7 | — | 2 | 1 | no | — |
| 7 | C3×C4×C5×C7 | C22 | 1 | 1 | yes | characteristic |
| 8 | C7×#215 | — | 5 | 1 | no | maximal, Hall |
| 9 | C5×C7×Q8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C7×D20 | — | 3 | 1 | no | — |
| 11 | C7×#168 | — | 3 | 1 | no | — |
| 12 | #6717 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 13 | C2×C3×C5×C7 | D4 | 1 | 1 | yes | characteristic |
| 14 | C7×D15 | — | 4 | 1 | no | — |
| 15 | C3×C7×Q8 | D5 | 1 | 1 | yes | characteristic, complemented |
| 16 | C7×D12 | — | 5 | 1 | no | — |
| 17 | C7×C3⋊C8 | — | 5 | 1 | no | — |
| 18 | C2×C7×D5 | — | 6 | 1 | no | — |
| 19 | C4×C5×C7 | — | 2 | 1 | no | — |
| 20 | C4×C5×C7 | C2×D3 | 1 | 1 | yes | characteristic |
| 21 | C3×C5×Q8 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 22 | D60 | C2×C7 | 1 | 1 | yes | characteristic |
| 23 | C3⋊#168 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 24 | C7×SD16 | — | 15 | 1 | no | Hall |
| 25 | C3×C5×C7 | SD16 | 1 | 1 | yes | characteristic, complemented, Hall |
| 26 | C2×D3×C7 | — | 10 | 1 | no | — |
| 27 | C3×C4×C7 | — | 2 | 1 | no | — |
| 28 | C3×C4×C7 | C2×D5 | 1 | 1 | yes | characteristic |
| 29 | #688 | — | 3 | 1 | no | Hall |
| 30 | C2×C5×C7 | #67 | 1 | 1 | yes | characteristic |
| 31 | C7×D5 | — | 12 | 1 | no | — |
| 32 | C2×D15 | — | 2 | 1 | no | — |
| 33 | C3×C4×C5 | — | 2 | 1 | no | — |
| 34 | C3×C4×C5 | C22×C7 | 1 | 1 | yes | characteristic |
| 35 | C7×Q8 | D15 | 1 | 1 | yes | characteristic, complemented |
| 36 | C7×D4 | — | 15 | 1 | no | — |
| 37 | C7×C8 | — | 15 | 1 | no | — |
| 38 | #215 | — | 5 | 1 | no | Hall |
| 39 | C2×C3×C7 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 40 | D3×C7 | — | 20 | 1 | no | — |
| 41 | C5×Q8 | D3×C7 | 1 | 1 | yes | characteristic, complemented |
| 42 | D20 | — | 3 | 1 | no | — |
| 43 | #168 | — | 3 | 1 | no | — |
| 44 | C5×C7 | #215 | 1 | 1 | yes | characteristic, complemented, Hall |
| 45 | C2×C3×C5 | C7×D4 | 1 | 1 | yes | characteristic |
| 46 | D15 | — | 4 | 1 | no | — |
| 47 | C22×C7 | — | 30 | 1 | no | — |
| 48 | C4×C7 | — | 2 | 1 | no | — |
| 49 | C4×C7 | C2×D15 | 1 | 1 | yes | characteristic |
| 50 | C3×Q8 | C7×D5 | 1 | 1 | yes | characteristic, complemented |
| 51 | D12 | — | 5 | 1 | no | — |
| 52 | C3⋊C8 | — | 5 | 1 | no | — |
| 53 | C3×C7 | #688 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | C2×D5 | — | 6 | 1 | no | — |
| 55 | C4×C5 | — | 2 | 1 | no | — |
| 56 | C4×C5 | C2×D3×C7 | 1 | 1 | yes | characteristic |
| 57 | SD16 | — | 15 | 1 | no | Sylow |
| 58 | C3×C5 | C7×SD16 | 1 | 1 | yes | characteristic, complemented, Hall |
| 59 | C2×C7 | — | 60 | 1 | no | — |
| 60 | C2×C7 | #1220 | 1 | 1 | yes | characteristic |
| 61 | C2×D3 | — | 10 | 1 | no | — |
| 62 | C3×C4 | — | 2 | 1 | no | — |
| 63 | C3×C4 | C2×C7×D5 | 1 | 1 | yes | characteristic |
| 64 | C2×C5 | C7×#67 | 1 | 1 | yes | characteristic |
| 65 | D5 | — | 12 | 1 | no | — |
| 66 | Q8 | C7×D15 | 1 | 1 | yes | characteristic, complemented |
| 67 | D4 | — | 15 | 1 | no | — |
| 68 | C8 | — | 15 | 1 | no | — |
| 69 | C7 | #6717 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 70 | C2×C3 | C7×C22⋊D5 | 1 | 1 | yes | characteristic |
| 71 | D3 | — | 20 | 1 | no | — |
| 72 | C5 | C7×#215 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 73 | C22 | — | 30 | 1 | no | — |
| 74 | C4 | — | 2 | 1 | no | — |
| 75 | C4 | C2×C7×D15 | 1 | 1 | yes | characteristic |
| 76 | C3 | C7×#688 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 77 | C2 | — | 60 | 1 | no | — |
| 78 | C2 | C7×#1220 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta