| 1 | C3×#508 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×M64 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #1418 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 5 | C3×#135 | — | 2 | 1 | no | — |
| 6 | C3×Q32 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C3×SD32 | — | 2 | 1 | no | — |
| 8 | C3×D16 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | C2×C3×C16 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#107 | — | 2 | 1 | no | — |
| 11 | C3×C32 | — | 2 | 1 | no | — |
| 12 | #508 | C2×C3 | 1 | 1 | yes | characteristic |
| 13 | M64 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #367 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#41 | — | 4 | 1 | no | — |
| 16 | C3×Q16 | — | 2 | 1 | no | — |
| 17 | C3×SD16 | — | 4 | 1 | no | — |
| 18 | C3×D8 | — | 2 | 1 | no | — |
| 19 | C2×C3×C8 | D4 | 1 | 1 | yes | characteristic |
| 20 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 21 | C3×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C3×C16 | D4 | 1 | 1 | yes | characteristic |
| 23 | #135 | — | 2 | 1 | no | — |
| 24 | Q32 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | SD32 | — | 2 | 1 | no | — |
| 26 | D16 | C3×C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×C16 | C22×C3 | 1 | 1 | yes | characteristic |
| 28 | #107 | — | 2 | 1 | no | — |
| 29 | C32 | — | 2 | 1 | no | — |
| 30 | C3×Q8 | — | 4 | 1 | no | — |
| 31 | C3×D4 | — | 4 | 1 | no | — |
| 32 | C3×D4 | — | 8 | 1 | no | — |
| 33 | C2×C3×C4 | — | 8 | 1 | no | — |
| 34 | C2×C3×C4 | — | 8 | 1 | no | — |
| 35 | C2×C3×C4 | D8 | 1 | 1 | yes | characteristic |
| 36 | C3×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 37 | C3×C8 | SD16 | 1 | 1 | yes | characteristic |
| 38 | #41 | — | 4 | 1 | no | — |
| 39 | Q16 | — | 2 | 1 | no | — |
| 40 | SD16 | — | 4 | 1 | no | — |
| 41 | D8 | — | 2 | 1 | no | — |
| 42 | C2×C8 | C3×D4 | 1 | 1 | yes | characteristic |
| 43 | C4⋊C4 | — | 4 | 1 | no | — |
| 44 | C16 | C2×C3×C4 | 1 | 1 | yes | characteristic |
| 45 | C16 | C3×D4 | 1 | 1 | yes | characteristic |
| 46 | C22×C3 | — | 8 | 1 | no | — |
| 47 | C22×C3 | D16 | 1 | 1 | yes | characteristic |
| 48 | C3×C4 | — | 8 | 1 | no | — |
| 49 | C3×C4 | — | 16 | 1 | no | — |
| 50 | C3×C4 | #102 | 1 | 1 | yes | characteristic |
| 51 | C3×C4 | SD32 | 1 | 1 | yes | characteristic |
| 52 | Q8 | — | 4 | 1 | no | — |
| 53 | D4 | — | 4 | 1 | no | — |
| 54 | D4 | — | 8 | 1 | no | — |
| 55 | C2×C4 | — | 8 | 1 | no | — |
| 56 | C2×C4 | — | 8 | 1 | no | — |
| 57 | C2×C4 | C3×D8 | 1 | 1 | yes | characteristic |
| 58 | C8 | C3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 59 | C8 | C3×SD16 | 1 | 1 | yes | characteristic |
| 60 | C2×C3 | — | 2 | 1 | no | — |
| 61 | C2×C3 | — | 16 | 1 | no | — |
| 62 | C2×C3 | #357 | 1 | 1 | yes | characteristic |
| 63 | C22 | — | 8 | 1 | no | — |
| 64 | C22 | C3×D16 | 1 | 1 | yes | characteristic |
| 65 | C4 | — | 8 | 1 | no | — |
| 66 | C4 | — | 16 | 1 | no | — |
| 67 | C4 | C3×#102 | 1 | 1 | yes | characteristic |
| 68 | C4 | C3×SD32 | 1 | 1 | yes | characteristic |
| 69 | C3 | #1418 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 70 | C2 | — | 2 | 1 | no | — |
| 71 | C2 | — | 16 | 1 | no | — |
| 72 | C2 | C3×#357 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta