| 1 | Q16×D353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D8×D353 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #26014937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26014936 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26014935 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C16×D353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | SD32×C353 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | Q8×D353 | — | 2 | 1 | no | — |
| 9 | D4×D353 | — | 2 | 1 | no | — |
| 10 | Dic1412 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #19150727 | — | 2 | 1 | no | — |
| 12 | D2824 | C22 | 1 | 1 | yes | characteristic |
| 13 | #19150722 | — | 2 | 1 | no | — |
| 14 | C8×D353 | C22 | 1 | 1 | yes | characteristic |
| 15 | #19150712 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | Q16×C353 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | D8×C353 | C22 | 1 | 1 | yes | characteristic |
| 18 | C16×C353 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C22×D353 | — | 4 | 1 | no | — |
| 20 | Dic706 | — | 2 | 1 | no | — |
| 21 | Dic706 | — | 4 | 1 | no | — |
| 22 | D1412 | — | 2 | 1 | no | — |
| 23 | C22⋊D353 | — | 4 | 1 | no | — |
| 24 | C4×D353 | — | 4 | 1 | no | — |
| 25 | C4×D353 | D4 | 1 | 1 | yes | characteristic |
| 26 | #15667725 | D4 | 1 | 1 | yes | characteristic |
| 27 | Q8×C353 | — | 2 | 1 | no | — |
| 28 | D4×C353 | — | 2 | 1 | no | — |
| 29 | C8×C353 | C23 | 1 | 1 | yes | characteristic |
| 30 | C22×C353 | — | 4 | 1 | no | — |
| 31 | C2×D353 | — | 4 | 1 | no | — |
| 32 | C2×D353 | — | 8 | 2 | no | — |
| 33 | C2×D353 | D8 | 1 | 1 | yes | characteristic |
| 34 | C4×C353 | — | 4 | 1 | no | — |
| 35 | C4×C353 | C2×D4 | 1 | 1 | yes | characteristic |
| 36 | Dic353 | — | 4 | 1 | no | — |
| 37 | Dic353 | D8 | 1 | 1 | yes | characteristic |
| 38 | C2×C353 | — | 8 | 1 | no | — |
| 39 | C2×C353 | C2×D8 | 1 | 1 | yes | characteristic |
| 40 | D353 | — | 8 | 1 | no | — |
| 41 | D353 | SD32 | 1 | 2 | yes | direct product factor |
| 42 | C353 | C2×SD32 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 43 | C2×SD32 | — | 353 | 1 | no | maximal, Sylow |
| 44 | C2×Q16 | — | 353 | 1 | no | — |
| 45 | C2×D8 | — | 353 | 1 | no | — |
| 46 | SD32 | — | 353 | 1 | no | — |
| 47 | SD32 | — | 353 | 1 | no | — |
| 48 | SD32 | — | 353 | 1 | no | — |
| 49 | SD32 | D353 | 1 | 1 | yes | characteristic, direct product factor |
| 50 | C2×C16 | — | 353 | 1 | no | — |
| 51 | C2×Q8 | — | 706 | 1 | no | — |
| 52 | C2×D4 | — | 706 | 1 | no | — |
| 53 | Q16 | — | 353 | 1 | no | — |
| 54 | Q16 | — | 706 | 1 | no | — |
| 55 | Q16 | C2×D353 | 1 | 1 | yes | characteristic, complemented |
| 56 | D8 | — | 353 | 1 | no | — |
| 57 | D8 | — | 706 | 1 | no | — |
| 58 | D8 | C2×D353 | 1 | 1 | yes | characteristic |
| 59 | C2×C8 | — | 353 | 1 | no | — |
| 60 | C16 | — | 353 | 1 | no | — |
| 61 | C16 | C2×D353 | 1 | 1 | yes | characteristic, complemented |
| 62 | C23 | — | 1412 | 1 | no | — |
| 63 | Q8 | — | 2 | 1 | no | — |
| 64 | Q8 | — | 1412 | 1 | no | — |
| 65 | Q8 | — | 706 | 1 | no | — |
| 66 | D4 | — | 2 | 1 | no | — |
| 67 | D4 | — | 1412 | 1 | no | — |
| 68 | D4 | — | 706 | 1 | no | — |
| 69 | C2×C4 | — | 353 | 1 | no | — |
| 70 | C2×C4 | — | 1412 | 1 | no | — |
| 71 | C8 | — | 353 | 1 | no | — |
| 72 | C8 | C22×D353 | 1 | 1 | yes | characteristic |
| 73 | C22 | — | 4 | 1 | no | — |
| 74 | C22 | — | 2824 | 2 | no | — |
| 75 | C22 | — | 353 | 1 | no | — |
| 76 | C22 | — | 1412 | 1 | no | — |
| 77 | C4 | — | 4 | 1 | no | — |
| 78 | C4 | — | 353 | 1 | no | — |
| 79 | C4 | — | 1412 | 1 | no | — |
| 80 | C4 | D4×D353 | 1 | 1 | yes | characteristic |
| 81 | C2 | — | 8 | 1 | no | — |
| 82 | C2 | — | 2824 | 1 | no | — |
| 83 | C2 | — | 353 | 2 | no | — |
| 84 | C2 | D8×D353 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta