| 1 | C22×C3×C7×Q8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C7×#239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×#947 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C7×#946 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C7×Q8×Dic3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#930 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C4×C7×#67 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C7×#548 | — | 3 | 1 | no | maximal, Hall |
| 9 | C2×C3×C7×Q8 | — | 2 | 4 | no | — |
| 10 | C2×C3×C7×Q8 | C22 | 1 | 3 | yes | — |
| 11 | C2×C3×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C3×C4×C7 | C22 | 1 | 3 | yes | — |
| 13 | C2×C7×#67 | C22 | 1 | 3 | yes | — |
| 14 | C7×#239 | — | 2 | 4 | no | — |
| 15 | C2×C7×D12 | C22 | 1 | 3 | yes | — |
| 16 | C2×C4×D3×C7 | C22 | 1 | 3 | yes | — |
| 17 | C7×#217 | C22 | 1 | 1 | yes | characteristic |
| 18 | C7×(C2×D3)⋊C4 | C22 | 1 | 3 | yes | — |
| 19 | C7×(C2×D3)⋊C4 | C22 | 1 | 6 | yes | — |
| 20 | C7×C4⋊Dic3 | C22 | 1 | 3 | yes | — |
| 21 | C7×Dic3⋊C4 | C22 | 1 | 3 | yes | — |
| 22 | C4×C7×Dic3 | C22 | 1 | 3 | yes | — |
| 23 | C2×C7×#41 | — | 3 | 1 | no | — |
| 24 | C22×C7×Q8 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C7×#124 | — | 3 | 3 | no | — |
| 26 | C7×C22⋊Q8 | — | 3 | 3 | no | — |
| 27 | C7×#121 | — | 3 | 3 | no | — |
| 28 | C4×C7×Q8 | — | 3 | 1 | no | — |
| 29 | C4×C7×D4 | — | 3 | 3 | no | — |
| 30 | #5817 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 31 | C23×C3×C7 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×D3×C7 | C23 | 1 | 3 | yes | — |
| 33 | C3×C7×Q8 | — | 2 | 6 | no | — |
| 34 | C3×C7×Q8 | D4 | 1 | 4 | yes | complemented |
| 35 | C2×C3×C4×C7 | — | 2 | 6 | no | — |
| 36 | C2×C3×C4×C7 | C23 | 1 | 3 | yes | — |
| 37 | C2×C3×C4×C7 | C23 | 1 | 3 | yes | — |
| 38 | C7×#67 | — | 2 | 6 | no | — |
| 39 | C2×C7×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 40 | C2×C7×Dic3 | C23 | 1 | 3 | yes | — |
| 41 | C2×C7×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 42 | C7×D12 | — | 2 | 6 | no | — |
| 43 | C4×D3×C7 | — | 2 | 6 | no | — |
| 44 | C7×#41 | — | 6 | 4 | no | — |
| 45 | C2×C7×Q8 | — | 2 | 4 | no | — |
| 46 | C2×C7×Q8 | C2×D3 | 1 | 3 | yes | — |
| 47 | C2×C7×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 48 | C2×C7×D4 | — | 3 | 3 | no | — |
| 49 | C2×C7×D4 | — | 3 | 3 | no | — |
| 50 | C22×C4×C7 | — | 3 | 3 | no | — |
| 51 | C22×C4×C7 | C2×D3 | 1 | 3 | yes | — |
| 52 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 53 | C7×C4⋊C4 | — | 3 | 3 | no | — |
| 54 | C7×C22⋊C4 | — | 3 | 1 | no | — |
| 55 | C7×C22⋊C4 | — | 3 | 3 | no | — |
| 56 | C7×C22⋊C4 | — | 3 | 6 | no | — |
| 57 | C42×C7 | — | 3 | 3 | no | — |
| 58 | C22×C3×Q8 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×#239 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 60 | #947 | C2×C7 | 1 | 3 | yes | complemented |
| 61 | #946 | C2×C7 | 1 | 3 | yes | complemented |
| 62 | Q8×Dic3 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 63 | #930 | C2×C7 | 1 | 3 | yes | complemented |
| 64 | C4×#67 | C2×C7 | 1 | 3 | yes | complemented |
| 65 | C22×C3×C7 | — | 2 | 1 | no | — |
| 66 | C22×C3×C7 | — | 2 | 1 | no | — |
| 67 | C22×C3×C7 | #41 | 1 | 2 | yes | complemented |
| 68 | C22×C3×C7 | C24 | 1 | 1 | yes | characteristic |
| 69 | C2×D3×C7 | — | 2 | 3 | no | — |
| 70 | C2×D3×C7 | — | 2 | 3 | no | — |
| 71 | C2×D3×C7 | — | 2 | 3 | no | — |
| 72 | C3×C4×C7 | — | 2 | 3 | no | — |
| 73 | C3×C4×C7 | C2×D4 | 1 | 6 | yes | — |
| 74 | C7×Dic3 | — | 2 | 1 | no | — |
| 75 | C7×Dic3 | — | 2 | 3 | no | — |
| 76 | C7×Dic3 | — | 2 | 1 | no | — |
| 77 | #548 | — | 3 | 1 | no | Sylow |
| 78 | C23×C7 | — | 3 | 3 | no | — |
| 79 | C23×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 80 | C7×Q8 | — | 2 | 6 | no | — |
| 81 | C7×Q8 | #67 | 1 | 4 | yes | complemented |
| 82 | C7×D4 | — | 6 | 6 | no | — |
| 83 | C7×D4 | — | 6 | 6 | no | — |
| 84 | C2×C4×C7 | — | 2 | 6 | no | — |
| 85 | C2×C4×C7 | — | 3 | 1 | no | — |
| 86 | C2×C4×C7 | — | 3 | 3 | no | — |
| 87 | C2×C4×C7 | — | 3 | 1 | no | — |
| 88 | C2×C4×C7 | — | 6 | 6 | no | — |
| 89 | C2×C4×C7 | C22×D3 | 1 | 3 | yes | — |
| 90 | C2×C4×C7 | C22×D3 | 1 | 3 | yes | — |
| 91 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 92 | C2×C3×Q8 | C22×C7 | 1 | 3 | yes | — |
| 93 | C2×C3×Q8 | C22×C7 | 1 | 1 | yes | characteristic |
| 94 | C22×C3×C4 | C22×C7 | 1 | 3 | yes | — |
| 95 | C2×#67 | C22×C7 | 1 | 3 | yes | — |
| 96 | #239 | — | 2 | 4 | no | — |
| 97 | C2×D12 | C22×C7 | 1 | 3 | yes | — |
| 98 | C2×C4×D3 | C22×C7 | 1 | 3 | yes | — |
| 99 | #217 | C22×C7 | 1 | 1 | yes | characteristic |
| 100 | (C2×D3)⋊C4 | C22×C7 | 1 | 3 | yes | — |
| 101 | (C2×D3)⋊C4 | C22×C7 | 1 | 6 | yes | — |
| 102 | C4⋊Dic3 | C22×C7 | 1 | 3 | yes | — |
| 103 | Dic3⋊C4 | C22×C7 | 1 | 3 | yes | — |
| 104 | C4×Dic3 | C22×C7 | 1 | 3 | yes | — |
| 105 | C2×C3×C7 | — | 2 | 2 | no | — |
| 106 | C2×C3×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C3×C7 | C2×#41 | 1 | 1 | yes | characteristic |
| 108 | C2×C3×C7 | 2−1+4 | 1 | 1 | yes | characteristic |
| 109 | D3×C7 | — | 4 | 3 | no | — |
| 110 | C2×#41 | — | 3 | 1 | no | — |
| 111 | C22×Q8 | D3×C7 | 1 | 1 | yes | characteristic, complemented |
| 112 | #124 | — | 3 | 3 | no | — |
| 113 | C22⋊Q8 | — | 3 | 3 | no | — |
| 114 | #121 | — | 3 | 3 | no | — |
| 115 | C4×Q8 | — | 3 | 1 | no | — |
| 116 | C4×D4 | — | 3 | 3 | no | — |
| 117 | C22×C7 | — | 2 | 1 | no | — |
| 118 | C22×C7 | — | 2 | 1 | no | — |
| 119 | C22×C7 | — | 6 | 3 | no | — |
| 120 | C22×C7 | — | 6 | 3 | no | — |
| 121 | C22×C7 | — | 6 | 3 | no | — |
| 122 | C22×C7 | #239 | 1 | 2 | yes | complemented |
| 123 | C22×C7 | C23×D3 | 1 | 1 | yes | characteristic |
| 124 | C4×C7 | — | 2 | 3 | no | — |
| 125 | C4×C7 | — | 6 | 3 | no | — |
| 126 | C4×C7 | — | 6 | 1 | no | — |
| 127 | C4×C7 | — | 6 | 1 | no | — |
| 128 | C4×C7 | C2×#67 | 1 | 6 | yes | — |
| 129 | C23×C3 | C23×C7 | 1 | 1 | yes | characteristic |
| 130 | C22×D3 | C23×C7 | 1 | 3 | yes | — |
| 131 | C3×Q8 | — | 2 | 6 | no | — |
| 132 | C3×Q8 | C7×D4 | 1 | 4 | yes | complemented |
| 133 | C2×C3×C4 | — | 2 | 6 | no | — |
| 134 | C2×C3×C4 | C23×C7 | 1 | 3 | yes | — |
| 135 | C2×C3×C4 | C23×C7 | 1 | 3 | yes | — |
| 136 | #67 | — | 2 | 6 | no | — |
| 137 | C2×Dic3 | C23×C7 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic3 | C23×C7 | 1 | 3 | yes | — |
| 139 | C2×Dic3 | C23×C7 | 1 | 1 | yes | characteristic |
| 140 | D12 | — | 2 | 6 | no | — |
| 141 | C4×D3 | — | 2 | 6 | no | — |
| 142 | C3×C7 | #548 | 1 | 1 | yes | characteristic, complemented, Hall |
| 143 | #41 | — | 6 | 4 | no | — |
| 144 | C2×Q8 | — | 2 | 4 | no | — |
| 145 | C2×Q8 | C2×D3×C7 | 1 | 3 | yes | — |
| 146 | C2×Q8 | C2×D3×C7 | 1 | 1 | yes | characteristic |
| 147 | C2×D4 | — | 3 | 3 | no | — |
| 148 | C2×D4 | — | 3 | 3 | no | — |
| 149 | C22×C4 | — | 3 | 3 | no | — |
| 150 | C22×C4 | C2×D3×C7 | 1 | 3 | yes | — |
| 151 | C4⋊C4 | — | 3 | 3 | no | — |
| 152 | C4⋊C4 | — | 3 | 3 | no | — |
| 153 | C22⋊C4 | — | 3 | 1 | no | — |
| 154 | C22⋊C4 | — | 3 | 3 | no | — |
| 155 | C22⋊C4 | — | 3 | 6 | no | — |
| 156 | C42 | — | 3 | 3 | no | — |
| 157 | C2×C7 | — | 2 | 2 | no | — |
| 158 | C2×C7 | — | 12 | 3 | no | — |
| 159 | C2×C7 | C2×#239 | 1 | 1 | yes | characteristic |
| 160 | C2×C7 | #1007 | 1 | 1 | yes | characteristic |
| 161 | C2×C7 | C22×#67 | 1 | 1 | yes | characteristic |
| 162 | C22×C3 | — | 2 | 1 | no | — |
| 163 | C22×C3 | — | 2 | 1 | no | — |
| 164 | C22×C3 | C7×#41 | 1 | 2 | yes | complemented |
| 165 | C22×C3 | C24×C7 | 1 | 1 | yes | characteristic |
| 166 | C2×D3 | — | 2 | 3 | no | — |
| 167 | C2×D3 | — | 2 | 3 | no | — |
| 168 | C2×D3 | — | 2 | 3 | no | — |
| 169 | C3×C4 | — | 2 | 3 | no | — |
| 170 | C3×C4 | C2×C7×D4 | 1 | 6 | yes | — |
| 171 | Dic3 | — | 2 | 1 | no | — |
| 172 | Dic3 | — | 2 | 3 | no | — |
| 173 | Dic3 | — | 2 | 1 | no | — |
| 174 | C23 | — | 3 | 3 | no | — |
| 175 | C23 | C22×D3×C7 | 1 | 1 | yes | characteristic |
| 176 | Q8 | — | 2 | 6 | no | — |
| 177 | Q8 | C7×#67 | 1 | 4 | yes | complemented |
| 178 | D4 | — | 6 | 6 | no | — |
| 179 | D4 | — | 6 | 6 | no | — |
| 180 | C2×C4 | — | 2 | 6 | no | — |
| 181 | C2×C4 | — | 3 | 1 | no | — |
| 182 | C2×C4 | — | 3 | 3 | no | — |
| 183 | C2×C4 | — | 3 | 1 | no | — |
| 184 | C2×C4 | — | 6 | 6 | no | — |
| 185 | C2×C4 | C22×D3×C7 | 1 | 3 | yes | — |
| 186 | C2×C4 | C22×D3×C7 | 1 | 3 | yes | — |
| 187 | C7 | #5817 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 188 | C2×C3 | — | 2 | 2 | no | — |
| 189 | C2×C3 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C3 | C2×C7×#41 | 1 | 1 | yes | characteristic |
| 191 | C2×C3 | C7×2−1+4 | 1 | 1 | yes | characteristic |
| 192 | D3 | — | 4 | 3 | no | — |
| 193 | C22 | — | 2 | 1 | no | — |
| 194 | C22 | — | 2 | 1 | no | — |
| 195 | C22 | — | 6 | 3 | no | — |
| 196 | C22 | — | 6 | 3 | no | — |
| 197 | C22 | — | 6 | 3 | no | — |
| 198 | C22 | C7×#239 | 1 | 2 | yes | complemented |
| 199 | C22 | C23×D3×C7 | 1 | 1 | yes | characteristic |
| 200 | C4 | — | 2 | 3 | no | — |
| 201 | C4 | — | 6 | 3 | no | — |
| 202 | C4 | — | 6 | 1 | no | — |
| 203 | C4 | — | 6 | 1 | no | — |
| 204 | C4 | C2×C7×#67 | 1 | 6 | yes | — |
| 205 | C3 | C7×#548 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 206 | C2 | — | 2 | 2 | no | — |
| 207 | C2 | — | 12 | 3 | no | — |
| 208 | C2 | C2×C7×#239 | 1 | 1 | yes | characteristic |
| 209 | C2 | C7×#1007 | 1 | 1 | yes | characteristic |
| 210 | C2 | C22×C7×#67 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta