| 1 | Q8×H(3,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C4⋊((C3⋊D3)⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | (C3⋊(C3⋊C8))⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #3755 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#215 | — | 3 | 1 | no | maximal |
| 6 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 7 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 8 | C4×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 9 | C32×Q8 | — | 2 | 1 | no | — |
| 10 | C32×Q8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C32×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C4⋊(C3⋊D3) | C2×C3 | 1 | 1 | yes | characteristic |
| 13 | C3×D12 | — | 3 | 1 | no | — |
| 14 | C3⋊(C3⋊C8) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 16 | C2×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 17 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 18 | C3×SD16 | — | 9 | 1 | no | — |
| 19 | #215 | — | 3 | 1 | no | — |
| 20 | #215 | — | 9 | 1 | no | — |
| 21 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 22 | C2×C3×D3 | — | 6 | 1 | no | — |
| 23 | C32×C4 | — | 2 | 2 | no | — |
| 24 | C32×C4 | — | 2 | 1 | no | — |
| 25 | C32×C4 | — | 2 | 1 | no | — |
| 26 | C32×C4 | — | 2 | 1 | no | — |
| 27 | C32×C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 28 | C32×C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 29 | H(3,𝔽3) | SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 30 | C3×Q8 | — | 3 | 1 | no | — |
| 31 | C3×Q8 | — | 6 | 1 | no | — |
| 32 | C3×Q8 | — | 6 | 1 | no | — |
| 33 | C3×Q8 | C3×D3 | 1 | 1 | yes | characteristic |
| 34 | C3×D4 | — | 9 | 1 | no | — |
| 35 | D12 | — | 3 | 1 | no | — |
| 36 | D12 | — | 9 | 1 | no | — |
| 37 | C3×C8 | — | 9 | 1 | no | — |
| 38 | C3⋊C8 | — | 3 | 1 | no | — |
| 39 | C3⋊C8 | — | 9 | 1 | no | — |
| 40 | C2×C32 | — | 2 | 1 | no | — |
| 41 | C2×C32 | #67 | 1 | 1 | yes | characteristic |
| 42 | C2×C32 | C3×D4 | 1 | 1 | yes | characteristic |
| 43 | C3⋊D3 | — | 4 | 1 | no | — |
| 44 | C3×D3 | — | 12 | 1 | no | — |
| 45 | SD16 | — | 9 | 1 | no | Sylow |
| 46 | C22×C3 | — | 18 | 1 | no | — |
| 47 | C2×D3 | — | 6 | 1 | no | — |
| 48 | C2×D3 | — | 18 | 1 | no | — |
| 49 | C3×C4 | — | 2 | 1 | no | — |
| 50 | C3×C4 | — | 3 | 1 | no | — |
| 51 | C3×C4 | — | 6 | 1 | no | — |
| 52 | C3×C4 | — | 6 | 2 | no | — |
| 53 | C3×C4 | — | 6 | 1 | no | — |
| 54 | C3×C4 | — | 6 | 1 | no | — |
| 55 | C3×C4 | — | 6 | 1 | no | — |
| 56 | C3×C4 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 57 | C32 | — | 2 | 1 | no | — |
| 58 | C32 | #215 | 1 | 1 | yes | characteristic, complemented |
| 59 | C32 | C3×SD16 | 1 | 1 | yes | characteristic, complemented |
| 60 | Q8 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 61 | D4 | — | 9 | 1 | no | — |
| 62 | C8 | — | 9 | 1 | no | — |
| 63 | C2×C3 | — | 3 | 1 | no | — |
| 64 | C2×C3 | — | 6 | 1 | no | — |
| 65 | C2×C3 | — | 6 | 1 | no | — |
| 66 | C2×C3 | — | 36 | 1 | no | — |
| 67 | C2×C3 | C3×#67 | 1 | 1 | yes | characteristic |
| 68 | D3 | — | 12 | 1 | no | — |
| 69 | D3 | — | 36 | 1 | no | — |
| 70 | C22 | — | 18 | 1 | no | — |
| 71 | C4 | — | 2 | 1 | no | — |
| 72 | C4 | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 73 | C3 | — | 3 | 1 | no | — |
| 74 | C3 | — | 6 | 1 | no | — |
| 75 | C3 | — | 6 | 1 | no | — |
| 76 | C3 | C3×#215 | 1 | 1 | yes | characteristic |
| 77 | C2 | — | 36 | 1 | no | — |
| 78 | C2 | #638⋊C3 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta