| 1 | C7×C22⋊Q8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C7×#117 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C7×#107 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7×#106 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#103 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C7×C22⋊C8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×C4×C7 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 13 | C7×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C7×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 15 | C7×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 16 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 17 | C7×C22⋊C4 | — | 2 | 1 | no | — |
| 18 | C42×C7 | — | 2 | 1 | no | — |
| 19 | #485 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 20 | C23×C7 | D4 | 1 | 1 | yes | characteristic |
| 21 | C7×Q8 | — | 2 | 1 | no | — |
| 22 | C7×Q8 | — | 2 | 1 | no | — |
| 23 | C2×C4×C7 | — | 2 | 1 | no | — |
| 24 | C2×C4×C7 | — | 2 | 1 | no | — |
| 25 | C2×C4×C7 | — | 2 | 1 | no | — |
| 26 | C2×C4×C7 | — | 2 | 1 | no | — |
| 27 | C2×C4×C7 | — | 2 | 1 | no | — |
| 28 | C2×C4×C7 | — | 2 | 1 | no | — |
| 29 | C2×C4×C7 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 31 | C7×C8 | — | 2 | 1 | no | — |
| 32 | C7×C8 | — | 2 | 1 | no | — |
| 33 | C22⋊Q8 | C2×C7 | 1 | 1 | yes | characteristic |
| 34 | #117 | C2×C7 | 1 | 1 | yes | characteristic |
| 35 | #107 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 36 | #106 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 37 | #103 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 38 | #103 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 39 | C22⋊C8 | C2×C7 | 1 | 1 | yes | characteristic |
| 40 | C22×C7 | — | 2 | 1 | no | — |
| 41 | C22×C7 | — | 2 | 1 | no | — |
| 42 | C22×C7 | — | 2 | 1 | no | — |
| 43 | C22×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 44 | C4×C7 | — | 2 | 1 | no | — |
| 45 | C4×C7 | — | 4 | 1 | no | — |
| 46 | C4×C7 | — | 4 | 1 | no | — |
| 47 | C4×C7 | — | 4 | 1 | no | — |
| 48 | C4×C7 | — | 4 | 1 | no | — |
| 49 | C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 50 | C4×C7 | #41 | 1 | 1 | yes | characteristic |
| 51 | C2×Q8 | C22×C7 | 1 | 1 | yes | characteristic |
| 52 | C22×C4 | C22×C7 | 1 | 1 | yes | characteristic |
| 53 | C2×C8 | C22×C7 | 1 | 1 | yes | characteristic |
| 54 | C2×C8 | C22×C7 | 1 | 1 | yes | characteristic |
| 55 | C4⋊C4 | — | 2 | 1 | no | — |
| 56 | C4⋊C4 | C22×C7 | 1 | 1 | yes | characteristic |
| 57 | C4⋊C4 | C22×C7 | 1 | 1 | yes | characteristic |
| 58 | C4⋊C4 | C22×C7 | 1 | 1 | yes | characteristic |
| 59 | C22⋊C4 | — | 2 | 1 | no | — |
| 60 | C22⋊C4 | — | 2 | 1 | no | — |
| 61 | C42 | — | 2 | 1 | no | — |
| 62 | C2×C7 | — | 4 | 1 | no | — |
| 63 | C2×C7 | #123 | 1 | 1 | yes | characteristic |
| 64 | C2×C7 | #135 | 1 | 1 | yes | characteristic |
| 65 | C2×C7 | #137 | 1 | 1 | yes | characteristic |
| 66 | C23 | C7×D4 | 1 | 1 | yes | characteristic |
| 67 | Q8 | — | 2 | 1 | no | — |
| 68 | Q8 | — | 2 | 1 | no | — |
| 69 | C2×C4 | — | 2 | 1 | no | — |
| 70 | C2×C4 | — | 2 | 1 | no | — |
| 71 | C2×C4 | — | 2 | 1 | no | — |
| 72 | C2×C4 | — | 2 | 1 | no | — |
| 73 | C2×C4 | — | 2 | 1 | no | — |
| 74 | C2×C4 | — | 2 | 1 | no | — |
| 75 | C2×C4 | C7×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C4 | C23×C7 | 1 | 1 | yes | characteristic |
| 77 | C8 | — | 2 | 1 | no | — |
| 78 | C8 | — | 2 | 1 | no | — |
| 79 | C7 | #485 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 80 | C22 | — | 2 | 1 | no | — |
| 81 | C22 | — | 2 | 1 | no | — |
| 82 | C22 | — | 2 | 1 | no | — |
| 83 | C22 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 84 | C4 | — | 2 | 1 | no | — |
| 85 | C4 | — | 4 | 1 | no | — |
| 86 | C4 | — | 4 | 1 | no | — |
| 87 | C4 | — | 4 | 1 | no | — |
| 88 | C4 | — | 4 | 1 | no | — |
| 89 | C4 | C7×#41 | 1 | 1 | yes | characteristic |
| 90 | C4 | C7×#41 | 1 | 1 | yes | characteristic |
| 91 | C2 | — | 4 | 1 | no | — |
| 92 | C2 | C7×#123 | 1 | 1 | yes | characteristic |
| 93 | C2 | C7×#135 | 1 | 1 | yes | characteristic |
| 94 | C2 | C7×#137 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta