| 1 | #121×C397 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C22⋊C8×C397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #95×C397 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×D4×C397 | — | 2 | 1 | no | — |
| 5 | C2×D4×C397 | C4 | 1 | 1 | yes | characteristic, complemented |
| 6 | C22×C4×C397 | — | 2 | 1 | no | — |
| 7 | C22×C4×C397 | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×C8×C397 | — | 2 | 1 | no | — |
| 9 | C4⋊C4×C397 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | C22⋊C4×C397 | — | 2 | 1 | no | — |
| 11 | C23×C397 | — | 2 | 1 | no | — |
| 12 | C23×C397 | D4 | 1 | 1 | yes | characteristic |
| 13 | D4×C397 | — | 4 | 1 | no | — |
| 14 | D4×C397 | — | 4 | 1 | no | — |
| 15 | D4×C397 | — | 4 | 1 | no | — |
| 16 | C2×C4×C397 | — | 2 | 2 | no | — |
| 17 | C2×C4×C397 | — | 2 | 1 | no | — |
| 18 | C2×C4×C397 | — | 4 | 1 | no | — |
| 19 | C2×C4×C397 | — | 4 | 1 | no | — |
| 20 | C2×C4×C397 | — | 4 | 1 | no | — |
| 21 | C2×C4×C397 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×C397 | D4 | 1 | 1 | yes | characteristic |
| 23 | C8×C397 | — | 4 | 1 | no | — |
| 24 | C22×C397 | — | 2 | 1 | no | — |
| 25 | C22×C397 | — | 2 | 1 | no | — |
| 26 | C22×C397 | — | 4 | 1 | no | — |
| 27 | C22×C397 | — | 4 | 1 | no | — |
| 28 | C22×C397 | — | 4 | 1 | no | — |
| 29 | C22×C397 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 30 | C22×C397 | D8 | 1 | 1 | yes | characteristic |
| 31 | C22×C397 | SD16 | 1 | 1 | yes | characteristic |
| 32 | C4×C397 | — | 2 | 1 | no | — |
| 33 | C4×C397 | — | 2 | 1 | no | — |
| 34 | C4×C397 | — | 4 | 2 | no | — |
| 35 | C4×C397 | — | 4 | 1 | no | — |
| 36 | C2×C397 | — | 2 | 1 | no | — |
| 37 | C2×C397 | — | 2 | 1 | no | — |
| 38 | C2×C397 | — | 8 | 1 | no | — |
| 39 | C2×C397 | #99 | 1 | 1 | yes | characteristic |
| 40 | C2×C397 | #102 | 1 | 1 | yes | characteristic |
| 41 | C2×C397 | #104 | 1 | 1 | yes | characteristic |
| 42 | C397 | #327 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 43 | #327 | C397 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 44 | #121 | C2×C397 | 1 | 1 | yes | characteristic |
| 45 | C22⋊C8 | C2×C397 | 1 | 1 | yes | characteristic, complemented |
| 46 | #95 | C2×C397 | 1 | 1 | yes | characteristic, complemented |
| 47 | C2×D4 | — | 2 | 1 | no | — |
| 48 | C2×D4 | C4×C397 | 1 | 1 | yes | characteristic, complemented |
| 49 | C22×C4 | — | 2 | 1 | no | — |
| 50 | C22×C4 | C22×C397 | 1 | 1 | yes | characteristic |
| 51 | C2×C8 | — | 2 | 1 | no | — |
| 52 | C4⋊C4 | C4×C397 | 1 | 1 | yes | characteristic, complemented |
| 53 | C22⋊C4 | — | 2 | 1 | no | — |
| 54 | C23 | — | 2 | 1 | no | — |
| 55 | C23 | D4×C397 | 1 | 1 | yes | characteristic |
| 56 | D4 | — | 4 | 1 | no | — |
| 57 | D4 | — | 4 | 1 | no | — |
| 58 | D4 | — | 4 | 1 | no | — |
| 59 | C2×C4 | — | 2 | 2 | no | — |
| 60 | C2×C4 | — | 2 | 1 | no | — |
| 61 | C2×C4 | — | 4 | 1 | no | — |
| 62 | C2×C4 | — | 4 | 1 | no | — |
| 63 | C2×C4 | — | 4 | 1 | no | — |
| 64 | C2×C4 | C2×C4×C397 | 1 | 1 | yes | characteristic |
| 65 | C2×C4 | D4×C397 | 1 | 1 | yes | characteristic |
| 66 | C8 | — | 4 | 1 | no | — |
| 67 | C22 | — | 2 | 1 | no | — |
| 68 | C22 | — | 2 | 1 | no | — |
| 69 | C22 | — | 4 | 1 | no | — |
| 70 | C22 | — | 4 | 1 | no | — |
| 71 | C22 | — | 4 | 1 | no | — |
| 72 | C22 | C22⋊C4×C397 | 1 | 1 | yes | characteristic |
| 73 | C22 | D8×C397 | 1 | 1 | yes | characteristic |
| 74 | C22 | SD16×C397 | 1 | 1 | yes | characteristic |
| 75 | C4 | — | 2 | 1 | no | — |
| 76 | C4 | — | 2 | 1 | no | — |
| 77 | C4 | — | 4 | 2 | no | — |
| 78 | C4 | — | 4 | 1 | no | — |
| 79 | C2 | — | 2 | 1 | no | — |
| 80 | C2 | — | 2 | 1 | no | — |
| 81 | C2 | — | 8 | 1 | no | — |
| 82 | C2 | #99×C397 | 1 | 1 | yes | characteristic |
| 83 | C2 | #102×C397 | 1 | 1 | yes | characteristic |
| 84 | C2 | #104×C397 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta