| 1 | C7×#135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #6467 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #6402 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #6401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #6400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C7⋊C16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×#41 | — | 2 | 1 | no | — |
| 9 | #1157 | — | 2 | 1 | no | — |
| 10 | C7×Q16 | C22 | 1 | 1 | yes | characteristic |
| 11 | C7×SD16 | — | 2 | 1 | no | — |
| 12 | C7×D8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C7×C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | Dic28 | C22 | 1 | 1 | yes | characteristic |
| 15 | D56 | C22 | 1 | 1 | yes | characteristic |
| 16 | #1132 | — | 2 | 1 | no | — |
| 17 | C7⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C7⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 19 | #508 | — | 7 | 1 | no | maximal, Sylow |
| 20 | C7×Q8 | — | 2 | 1 | no | — |
| 21 | C7×D4 | — | 2 | 1 | no | — |
| 22 | C7×D4 | — | 4 | 1 | no | — |
| 23 | C2×C4×C7 | — | 4 | 1 | no | — |
| 24 | C2×C4×C7 | D4 | 1 | 1 | yes | characteristic |
| 25 | C22⋊D7 | — | 4 | 1 | no | — |
| 26 | D28 | — | 2 | 1 | no | — |
| 27 | C4×D7 | — | 4 | 1 | no | — |
| 28 | Dic14 | — | 2 | 1 | no | — |
| 29 | C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 30 | C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 31 | #135 | — | 7 | 1 | no | — |
| 32 | #135 | D7 | 1 | 1 | yes | characteristic, complemented |
| 33 | Q32 | — | 7 | 1 | no | — |
| 34 | SD32 | — | 7 | 1 | no | — |
| 35 | SD32 | — | 7 | 1 | no | — |
| 36 | D16 | — | 7 | 1 | no | — |
| 37 | C2×C16 | — | 7 | 1 | no | — |
| 38 | C22×C7 | — | 4 | 1 | no | — |
| 39 | C22×C7 | D8 | 1 | 1 | yes | characteristic |
| 40 | C2×D7 | — | 4 | 1 | no | — |
| 41 | C4×C7 | — | 4 | 1 | no | — |
| 42 | C4×C7 | D8 | 1 | 1 | yes | characteristic |
| 43 | C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 44 | Dic7 | — | 4 | 1 | no | — |
| 45 | #41 | — | 2 | 1 | no | — |
| 46 | #41 | — | 14 | 1 | no | — |
| 47 | Q16 | — | 7 | 1 | no | — |
| 48 | Q16 | C2×D7 | 1 | 1 | yes | characteristic |
| 49 | SD16 | — | 2 | 1 | no | — |
| 50 | SD16 | — | 14 | 1 | no | — |
| 51 | D8 | — | 7 | 1 | no | — |
| 52 | D8 | C2×D7 | 1 | 1 | yes | characteristic |
| 53 | C2×C8 | C2×D7 | 1 | 1 | yes | characteristic |
| 54 | C16 | — | 7 | 1 | no | — |
| 55 | C16 | — | 7 | 1 | no | — |
| 56 | C2×C7 | — | 2 | 1 | no | — |
| 57 | C2×C7 | — | 8 | 1 | no | — |
| 58 | C2×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 59 | D7 | — | 8 | 1 | no | — |
| 60 | Q8 | — | 2 | 1 | no | — |
| 61 | Q8 | — | 14 | 1 | no | — |
| 62 | D4 | — | 2 | 1 | no | — |
| 63 | D4 | — | 4 | 1 | no | — |
| 64 | D4 | — | 14 | 1 | no | — |
| 65 | D4 | — | 28 | 1 | no | — |
| 66 | C2×C4 | — | 4 | 1 | no | — |
| 67 | C2×C4 | — | 28 | 1 | no | — |
| 68 | C2×C4 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 69 | C8 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 70 | C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 71 | C7 | #508 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 72 | C22 | — | 4 | 1 | no | — |
| 73 | C22 | — | 28 | 1 | no | — |
| 74 | C22 | #1141 | 1 | 1 | yes | characteristic |
| 75 | C4 | — | 4 | 1 | no | — |
| 76 | C4 | — | 28 | 1 | no | — |
| 77 | C4 | #1141 | 1 | 1 | yes | characteristic |
| 78 | C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 79 | C2 | — | 2 | 1 | no | — |
| 80 | C2 | — | 8 | 1 | no | — |
| 81 | C2 | — | 56 | 1 | no | — |
| 82 | C2 | C2×#1141 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta