| 1 | C3×#4427 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 2 | C3×C3⋊AGL(1,𝔽7) | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C9×D21 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3⋊(D7⋊C9) | C3 | 1 | 2 | yes | maximal, complemented |
| 5 | #67356 | — | 3 | 1 | no | maximal |
| 6 | C32×ΓL(1,𝔽8) | C2×C3 | 1 | 1 | yes | characteristic |
| 7 | C3×C7×C9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | C3×C7⋊C9 | C2×C3 | 1 | 2 | yes | complemented |
| 9 | #4427 | — | 2 | 1 | no | — |
| 10 | #4427 | — | 2 | 1 | no | — |
| 11 | #4427 | — | 2 | 2 | no | — |
| 12 | #4427 | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | D3×3−1+2 | — | 7 | 1 | no | maximal, Hall |
| 14 | C3×D21 | C32 | 1 | 1 | yes | characteristic |
| 15 | C3⋊AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 16 | C3×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 17 | C9×D7 | — | 3 | 1 | no | — |
| 18 | D7⋊C9 | — | 3 | 2 | no | — |
| 19 | C3×3−1+2 | — | 7 | 1 | no | Sylow |
| 20 | C32×C7 | C2×C32 | 1 | 1 | yes | characteristic |
| 21 | C3×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 22 | C3×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 23 | C3×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 24 | C3×ΓL(1,𝔽8) | C3×D3 | 1 | 1 | yes | characteristic |
| 25 | C7×C9 | — | 2 | 1 | no | — |
| 26 | C7×C9 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C7⋊C9 | — | 2 | 2 | no | — |
| 28 | C7⋊C9 | C3×D3 | 1 | 2 | yes | complemented |
| 29 | C32×D3 | — | 7 | 1 | no | — |
| 30 | C2×3−1+2 | — | 21 | 1 | no | — |
| 31 | D3×C9 | — | 7 | 2 | no | — |
| 32 | D3×C9 | — | 7 | 1 | no | — |
| 33 | D21 | 3−1+2 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×D7 | — | 3 | 1 | no | — |
| 35 | AGL(1,𝔽7) | — | 9 | 1 | no | — |
| 36 | C33 | — | 7 | 1 | no | — |
| 37 | 3−1+2 | — | 7 | 1 | no | — |
| 38 | 3−1+2 | — | 14 | 2 | no | — |
| 39 | 3−1+2 | — | 14 | 1 | no | — |
| 40 | 3−1+2 | — | 14 | 1 | no | — |
| 41 | C3×C9 | — | 7 | 2 | no | — |
| 42 | C3×C9 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×C7 | — | 2 | 1 | no | — |
| 44 | C3×C7 | C2×3−1+2 | 1 | 1 | yes | characteristic, complemented |
| 45 | C3×C7 | C32×D3 | 1 | 1 | yes | characteristic |
| 46 | ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 47 | ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 48 | C2×C32 | — | 21 | 1 | no | — |
| 49 | C3×D3 | — | 7 | 1 | no | — |
| 50 | C3×D3 | — | 21 | 1 | no | — |
| 51 | C2×C9 | — | 21 | 2 | no | — |
| 52 | C2×C9 | — | 21 | 1 | no | — |
| 53 | D7 | — | 3 | 1 | no | Hall |
| 54 | C32 | — | 7 | 1 | no | — |
| 55 | C32 | — | 14 | 1 | no | — |
| 56 | C32 | — | 21 | 1 | no | — |
| 57 | C32 | — | 42 | 1 | no | — |
| 58 | C32 | C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 59 | C9 | — | 2 | 1 | no | — |
| 60 | C9 | — | 7 | 2 | no | — |
| 61 | C9 | — | 14 | 2 | no | — |
| 62 | C9 | C3⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 63 | C7 | D3×3−1+2 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 64 | C2×C3 | — | 21 | 1 | no | — |
| 65 | C2×C3 | — | 63 | 1 | no | — |
| 66 | D3 | — | 7 | 1 | no | — |
| 67 | C3 | — | 2 | 1 | no | — |
| 68 | C3 | — | 21 | 1 | no | — |
| 69 | C3 | — | 42 | 1 | no | — |
| 70 | C3 | #67356 | 1 | 1 | yes | characteristic, complemented |
| 71 | C3 | C3×C3⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 72 | C2 | — | 21 | 1 | no | Sylow |
Finite Group Databasebeta