| 1 | #10588045 | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 2 | C2×C7×3−1+2 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C7⋊H(3,𝔽3) | C3 | 1 | 1 | yes | maximal, characteristic |
| 4 | C2×#4430 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C3×C7⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×3−1+2 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C7⋊H(3,𝔽3) | C2×C3 | 1 | 1 | yes | characteristic |
| 8 | #4430 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 9 | C3×C7⋊C9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×#731 | — | 7 | 1 | no | maximal, Hall |
| 11 | C2×C32×C7 | C32 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 13 | C2×C7×C9 | — | 3 | 1 | no | — |
| 14 | C2×C7⋊C9 | — | 3 | 1 | no | — |
| 15 | C2×C7⋊C9 | — | 3 | 1 | no | — |
| 16 | #731 | — | 7 | 1 | no | Sylow |
| 17 | C32×C7 | C2×C32 | 1 | 1 | yes | characteristic |
| 18 | C3×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 19 | C7×C9 | — | 3 | 1 | no | — |
| 20 | C7⋊C9 | — | 3 | 1 | no | — |
| 21 | C7⋊C9 | — | 3 | 1 | no | — |
| 22 | C2×3−1+2 | — | 7 | 1 | no | — |
| 23 | C2×3−1+2 | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×H(3,𝔽3) | — | 7 | 1 | no | — |
| 25 | C2×C3×C9 | — | 7 | 1 | no | — |
| 26 | C2×C3×C7 | — | 3 | 1 | no | — |
| 27 | C2×C3×C7 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 28 | C2×ΓL(1,𝔽8) | — | 9 | 1 | no | — |
| 29 | 3−1+2 | — | 7 | 1 | no | — |
| 30 | 3−1+2 | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 31 | H(3,𝔽3) | — | 7 | 1 | no | — |
| 32 | C3×C9 | — | 7 | 1 | no | — |
| 33 | C3×C7 | — | 3 | 1 | no | — |
| 34 | C3×C7 | C2×H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 35 | ΓL(1,𝔽8) | — | 9 | 1 | no | — |
| 36 | C2×C32 | — | 21 | 1 | no | — |
| 37 | C2×C32 | C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 38 | C2×C9 | — | 3 | 1 | no | — |
| 39 | C2×C9 | — | 21 | 1 | no | — |
| 40 | C2×C9 | — | 21 | 1 | no | — |
| 41 | C2×C7 | #731 | 1 | 1 | yes | characteristic, complemented, Hall |
| 42 | C32 | — | 21 | 1 | no | — |
| 43 | C32 | C2×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic |
| 44 | C9 | — | 3 | 1 | no | — |
| 45 | C9 | — | 21 | 1 | no | — |
| 46 | C9 | — | 21 | 1 | no | — |
| 47 | C7 | C2×#731 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 48 | C2×C3 | — | 3 | 1 | no | — |
| 49 | C2×C3 | — | 63 | 1 | no | — |
| 50 | C2×C3 | C7⋊H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 51 | C3 | — | 3 | 1 | no | — |
| 52 | C3 | — | 63 | 1 | no | — |
| 53 | C3 | C2×C7⋊H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 54 | C2 | #10588045 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
Finite Group Databasebeta