| 1 | C7×#1010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10621551 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10621433 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#6514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10621082 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | D3×#1144 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10621057 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #10621048 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10620883 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#66569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10620850 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #90529 | — | 3 | 1 | no | maximal, Hall |
| 13 | C3×C7×#41 | C22 | 1 | 1 | yes | characteristic |
| 14 | #66728 | C22 | 1 | 1 | yes | characteristic |
| 15 | D3×C7×Q8 | C22 | 1 | 2 | yes | — |
| 16 | C7×#237 | — | 2 | 2 | no | — |
| 17 | C7×#237 | C22 | 1 | 2 | yes | — |
| 18 | C7×#235 | — | 2 | 1 | no | — |
| 19 | C7×#235 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C7×Dic6 | — | 2 | 1 | no | — |
| 21 | C2×C7×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C3×Dic14 | C22 | 1 | 1 | yes | characteristic |
| 23 | #66686 | — | 2 | 2 | no | — |
| 24 | D21⋊Q8 | — | 2 | 1 | no | — |
| 25 | #66673 | C22 | 1 | 2 | yes | — |
| 26 | #66672 | — | 2 | 1 | no | — |
| 27 | D3×Dic14 | C22 | 1 | 2 | yes | — |
| 28 | #66635 | C22 | 1 | 1 | yes | characteristic |
| 29 | #66634 | C22 | 1 | 1 | yes | characteristic |
| 30 | #66633 | C22 | 1 | 1 | yes | characteristic |
| 31 | #66632 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×C3⋊(C7⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 33 | C3×#1144 | C22 | 1 | 2 | yes | — |
| 34 | C3×#1142 | C22 | 1 | 2 | yes | — |
| 35 | C3×#1136 | C22 | 1 | 1 | yes | characteristic |
| 36 | #66571 | C22 | 1 | 2 | yes | — |
| 37 | #66569 | C22 | 1 | 2 | yes | — |
| 38 | #66569 | C22 | 1 | 2 | yes | — |
| 39 | #66568 | C22 | 1 | 2 | yes | — |
| 40 | #66558 | C22 | 1 | 2 | yes | — |
| 41 | D3×C7⋊C8 | C22 | 1 | 2 | yes | — |
| 42 | C7×2−1+4 | — | 3 | 1 | no | — |
| 43 | #6554 | — | 3 | 1 | no | — |
| 44 | #6514 | — | 3 | 2 | no | — |
| 45 | #6514 | D3 | 1 | 1 | yes | characteristic, complemented |
| 46 | #6513 | — | 3 | 1 | no | — |
| 47 | #6513 | — | 3 | 2 | no | — |
| 48 | #6511 | — | 3 | 1 | no | — |
| 49 | C2×#1144 | — | 3 | 1 | no | — |
| 50 | C2×#1144 | — | 3 | 2 | no | — |
| 51 | #6505 | — | 3 | 2 | no | — |
| 52 | #6505 | — | 3 | 1 | no | — |
| 53 | #5779 | — | 7 | 1 | no | maximal, Hall |
| 54 | C3×C7×Q8 | C23 | 1 | 1 | yes | characteristic |
| 55 | C3×C7×D4 | — | 2 | 1 | no | — |
| 56 | C3×C7×D4 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×C4×C7 | — | 2 | 1 | no | — |
| 58 | C2×C3×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 59 | #4268 | — | 2 | 1 | no | — |
| 60 | D84 | C23 | 1 | 1 | yes | characteristic |
| 61 | C4×D21 | — | 2 | 1 | no | — |
| 62 | Dic42 | C23 | 1 | 1 | yes | characteristic |
| 63 | C7×#67 | — | 2 | 2 | no | — |
| 64 | C7×#67 | D4 | 1 | 2 | yes | — |
| 65 | C2×C7×Dic3 | — | 2 | 1 | no | — |
| 66 | C2×C7×Dic3 | — | 2 | 2 | no | — |
| 67 | C7×D12 | D4 | 1 | 1 | yes | characteristic |
| 68 | C4×D3×C7 | — | 2 | 2 | no | — |
| 69 | C4×D3×C7 | C23 | 1 | 2 | yes | — |
| 70 | C7×Dic6 | — | 2 | 1 | no | — |
| 71 | C7×Dic6 | — | 2 | 2 | no | — |
| 72 | C7×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 73 | C7×Dic6 | C23 | 1 | 2 | yes | — |
| 74 | C2×C3×Dic7 | — | 2 | 1 | no | — |
| 75 | C3×Dic14 | — | 2 | 1 | no | — |
| 76 | C3×Dic14 | C23 | 1 | 2 | yes | — |
| 77 | #4248 | — | 2 | 2 | no | — |
| 78 | #4247 | — | 2 | 2 | no | — |
| 79 | D21⋊C4 | — | 2 | 2 | no | — |
| 80 | D3×Dic7 | — | 2 | 2 | no | — |
| 81 | C3⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 82 | C3⋊(C7⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 83 | C3×C7⋊C8 | C23 | 1 | 2 | yes | — |
| 84 | C7×#41 | — | 3 | 1 | no | — |
| 85 | C7×#41 | — | 3 | 2 | no | — |
| 86 | C7×#41 | — | 6 | 1 | no | — |
| 87 | C7×#41 | — | 6 | 2 | no | — |
| 88 | C7×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 89 | C2×C7×Q8 | — | 3 | 2 | no | — |
| 90 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 91 | C2×C7×Q8 | — | 6 | 1 | no | — |
| 92 | Q8×D7 | — | 6 | 1 | no | — |
| 93 | #1159 | — | 6 | 1 | no | — |
| 94 | #1159 | — | 6 | 2 | no | — |
| 95 | #1157 | — | 3 | 1 | no | — |
| 96 | #1157 | — | 3 | 2 | no | — |
| 97 | C2×Dic14 | — | 3 | 2 | no | — |
| 98 | C2×Dic14 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | #1144 | — | 3 | 1 | no | — |
| 100 | #1144 | — | 3 | 2 | no | — |
| 101 | #1144 | — | 3 | 2 | no | — |
| 102 | #1144 | — | 3 | 2 | no | — |
| 103 | #1144 | C2×D3 | 1 | 2 | yes | — |
| 104 | #1143 | — | 3 | 1 | no | — |
| 105 | #1143 | — | 3 | 2 | no | — |
| 106 | #1142 | — | 3 | 1 | no | — |
| 107 | #1142 | C2×D3 | 1 | 2 | yes | — |
| 108 | #1141 | — | 3 | 1 | no | — |
| 109 | #1136 | — | 3 | 2 | no | — |
| 110 | #1136 | C2×D3 | 1 | 1 | yes | characteristic |
| 111 | C2×C7⋊C8 | — | 3 | 1 | no | — |
| 112 | C2×C7⋊C8 | — | 3 | 2 | no | — |
| 113 | #1010 | D7 | 1 | 1 | yes | characteristic, complemented |
| 114 | #1007 | — | 7 | 1 | no | — |
| 115 | C3×#137 | — | 7 | 1 | no | — |
| 116 | #950 | — | 7 | 1 | no | — |
| 117 | C2×#216 | — | 7 | 1 | no | — |
| 118 | #918 | — | 7 | 2 | no | — |
| 119 | D3×Q16 | — | 7 | 2 | no | — |
| 120 | #916 | — | 7 | 2 | no | — |
| 121 | #915 | — | 7 | 2 | no | — |
| 122 | #909 | — | 7 | 1 | no | — |
| 123 | #907 | — | 7 | 1 | no | — |
| 124 | C22×C3×C7 | — | 2 | 1 | no | — |
| 125 | C22×C3×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×D21 | — | 2 | 1 | no | — |
| 127 | C2×D3×C7 | C2×D4 | 1 | 2 | yes | — |
| 128 | C3×C4×C7 | — | 2 | 1 | no | — |
| 129 | C3×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C3×C4×C7 | C24 | 1 | 1 | yes | characteristic |
| 131 | Dic21 | — | 2 | 1 | no | — |
| 132 | C3×Dic7 | — | 2 | 2 | no | — |
| 133 | C7×Dic3 | — | 2 | 2 | no | — |
| 134 | C7×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 135 | #578 | — | 21 | 1 | no | Sylow |
| 136 | C7×Q8 | — | 3 | 1 | no | — |
| 137 | C7×Q8 | — | 3 | 2 | no | — |
| 138 | C7×Q8 | — | 6 | 2 | no | — |
| 139 | C7×Q8 | — | 6 | 1 | no | — |
| 140 | C7×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 141 | C7×D4 | — | 2 | 1 | no | — |
| 142 | C7×D4 | — | 3 | 2 | no | — |
| 143 | C7×D4 | — | 3 | 1 | no | — |
| 144 | C7×D4 | — | 6 | 2 | no | — |
| 145 | C7×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C7 | — | 2 | 1 | no | — |
| 147 | C2×C4×C7 | — | 3 | 2 | no | — |
| 148 | C2×C4×C7 | — | 6 | 2 | no | — |
| 149 | C2×C4×C7 | — | 6 | 2 | no | — |
| 150 | C2×C4×C7 | — | 6 | 1 | no | — |
| 151 | C2×C4×C7 | C22×D3 | 1 | 1 | yes | characteristic |
| 152 | C22⋊D7 | — | 6 | 2 | no | — |
| 153 | C22⋊D7 | — | 6 | 1 | no | — |
| 154 | C2×Dic7 | — | 2 | 1 | no | — |
| 155 | C2×Dic7 | — | 6 | 2 | no | — |
| 156 | D28 | — | 3 | 1 | no | — |
| 157 | C4×D7 | — | 6 | 2 | no | — |
| 158 | C4×D7 | — | 6 | 1 | no | — |
| 159 | Dic14 | — | 2 | 1 | no | — |
| 160 | Dic14 | — | 3 | 1 | no | — |
| 161 | Dic14 | — | 6 | 2 | no | — |
| 162 | Dic14 | C22×D3 | 1 | 2 | yes | — |
| 163 | C7⋊C8 | — | 3 | 1 | no | — |
| 164 | C7⋊C8 | — | 3 | 1 | no | — |
| 165 | C7⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 166 | C3×#41 | C2×D7 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 168 | #239 | — | 7 | 2 | no | — |
| 169 | #239 | — | 14 | 1 | no | — |
| 170 | D3×Q8 | — | 7 | 2 | no | — |
| 171 | D3×Q8 | — | 14 | 1 | no | — |
| 172 | D3×Q8 | C2×D7 | 1 | 2 | yes | — |
| 173 | #237 | — | 2 | 2 | no | — |
| 174 | #237 | C2×D7 | 1 | 2 | yes | — |
| 175 | #235 | — | 2 | 1 | no | — |
| 176 | #235 | — | 7 | 1 | no | — |
| 177 | #235 | — | 14 | 2 | no | — |
| 178 | #235 | C2×D7 | 1 | 1 | yes | characteristic |
| 179 | C2×Dic6 | — | 2 | 1 | no | — |
| 180 | C2×Dic6 | C2×D7 | 1 | 1 | yes | characteristic |
| 181 | C3×Q16 | — | 7 | 2 | no | — |
| 182 | C3×SD16 | — | 7 | 2 | no | — |
| 183 | C3×M16 | — | 7 | 1 | no | — |
| 184 | #216 | — | 7 | 1 | no | — |
| 185 | #216 | — | 7 | 2 | no | — |
| 186 | #216 | — | 7 | 2 | no | — |
| 187 | #215 | — | 7 | 1 | no | — |
| 188 | #214 | — | 7 | 1 | no | — |
| 189 | #213 | — | 7 | 1 | no | — |
| 190 | C2×C3⋊C8 | — | 7 | 1 | no | — |
| 191 | Dic12 | — | 7 | 2 | no | — |
| 192 | #204 | — | 7 | 2 | no | — |
| 193 | ΓL(1,𝔽25) | — | 7 | 2 | no | — |
| 194 | D3×C8 | — | 7 | 2 | no | — |
| 195 | C2×C3×C7 | — | 2 | 1 | no | — |
| 196 | C2×C3×C7 | — | 4 | 1 | no | — |
| 197 | C2×C3×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 198 | D21 | — | 4 | 1 | no | — |
| 199 | D3×C7 | — | 2 | 2 | no | — |
| 200 | 2−1+4 | — | 3 | 1 | no | — |
| 201 | 2−1+4 | — | 21 | 1 | no | — |
| 202 | #137 | — | 7 | 1 | no | — |
| 203 | #137 | — | 21 | 1 | no | — |
| 204 | #137 | — | 21 | 2 | no | — |
| 205 | #137 | — | 21 | 2 | no | — |
| 206 | #135 | — | 21 | 2 | no | — |
| 207 | #135 | — | 21 | 1 | no | — |
| 208 | C2×Q16 | — | 21 | 2 | no | — |
| 209 | C2×Q16 | — | 21 | 1 | no | — |
| 210 | #131 | — | 21 | 1 | no | — |
| 211 | C22×C7 | — | 2 | 1 | no | — |
| 212 | C22×C7 | — | 3 | 2 | no | — |
| 213 | C22×C7 | D3×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×D7 | — | 6 | 1 | no | — |
| 215 | C4×C7 | — | 2 | 1 | no | — |
| 216 | C4×C7 | — | 3 | 2 | no | — |
| 217 | C4×C7 | — | 6 | 2 | no | — |
| 218 | C4×C7 | D3×D4 | 1 | 1 | yes | characteristic |
| 219 | C4×C7 | C23×D3 | 1 | 1 | yes | characteristic |
| 220 | Dic7 | — | 2 | 2 | no | — |
| 221 | Dic7 | — | 6 | 1 | no | — |
| 222 | C3×Q8 | — | 7 | 2 | no | — |
| 223 | C3×Q8 | — | 14 | 1 | no | — |
| 224 | C3×Q8 | C22×D7 | 1 | 1 | yes | characteristic |
| 225 | C3×D4 | — | 2 | 1 | no | — |
| 226 | C3×D4 | C22×D7 | 1 | 1 | yes | characteristic |
| 227 | C2×C3×C4 | — | 2 | 1 | no | — |
| 228 | C2×C3×C4 | — | 14 | 1 | no | — |
| 229 | C2×C3×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 230 | #67 | — | 2 | 2 | no | — |
| 231 | #67 | — | 14 | 1 | no | — |
| 232 | #67 | C22⋊D7 | 1 | 2 | yes | — |
| 233 | C2×Dic3 | — | 2 | 1 | no | — |
| 234 | C2×Dic3 | — | 2 | 2 | no | — |
| 235 | D12 | — | 7 | 1 | no | — |
| 236 | D12 | — | 14 | 2 | no | — |
| 237 | D12 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 238 | C4×D3 | — | 2 | 2 | no | — |
| 239 | C4×D3 | — | 14 | 2 | no | — |
| 240 | C4×D3 | — | 14 | 1 | no | — |
| 241 | C4×D3 | — | 14 | 2 | no | — |
| 242 | C4×D3 | C22×D7 | 1 | 2 | yes | — |
| 243 | Dic6 | — | 2 | 1 | no | — |
| 244 | Dic6 | — | 2 | 2 | no | — |
| 245 | Dic6 | — | 7 | 1 | no | — |
| 246 | Dic6 | — | 14 | 2 | no | — |
| 247 | Dic6 | C22⋊D7 | 1 | 1 | yes | characteristic |
| 248 | Dic6 | C22×D7 | 1 | 2 | yes | — |
| 249 | C3×C8 | — | 7 | 2 | no | — |
| 250 | C3⋊C8 | — | 7 | 1 | no | — |
| 251 | C3⋊C8 | — | 7 | 1 | no | — |
| 252 | C3×C7 | #578 | 1 | 1 | yes | characteristic, complemented, Hall |
| 253 | #41 | — | 3 | 1 | no | — |
| 254 | #41 | — | 3 | 2 | no | — |
| 255 | #41 | — | 6 | 1 | no | — |
| 256 | #41 | — | 6 | 2 | no | — |
| 257 | #41 | — | 21 | 2 | no | — |
| 258 | #41 | — | 21 | 1 | no | — |
| 259 | #41 | — | 42 | 2 | no | — |
| 260 | #41 | — | 42 | 1 | no | — |
| 261 | #41 | D3×D7 | 1 | 1 | yes | characteristic |
| 262 | C2×Q8 | — | 3 | 2 | no | — |
| 263 | C2×Q8 | — | 3 | 1 | no | — |
| 264 | C2×Q8 | — | 6 | 1 | no | — |
| 265 | C2×Q8 | — | 7 | 1 | no | — |
| 266 | C2×Q8 | — | 21 | 2 | no | — |
| 267 | C2×Q8 | — | 42 | 1 | no | — |
| 268 | Q16 | — | 7 | 2 | no | — |
| 269 | Q16 | — | 21 | 2 | no | — |
| 270 | Q16 | — | 21 | 2 | no | — |
| 271 | Q16 | — | 21 | 2 | no | — |
| 272 | Q16 | — | 21 | 1 | no | — |
| 273 | SD16 | — | 7 | 2 | no | — |
| 274 | SD16 | — | 21 | 2 | no | — |
| 275 | SD16 | — | 21 | 1 | no | — |
| 276 | SD16 | — | 21 | 1 | no | — |
| 277 | D8 | — | 21 | 1 | no | — |
| 278 | M16 | — | 7 | 1 | no | — |
| 279 | M16 | — | 21 | 2 | no | — |
| 280 | C2×C8 | — | 21 | 2 | no | — |
| 281 | C2×C8 | — | 21 | 1 | no | — |
| 282 | C2×C7 | — | 2 | 1 | no | — |
| 283 | C2×C7 | — | 4 | 1 | no | — |
| 284 | C2×C7 | — | 6 | 2 | no | — |
| 285 | C2×C7 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 286 | D7 | — | 12 | 1 | no | — |
| 287 | C22×C3 | — | 2 | 1 | no | — |
| 288 | C22×C3 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 289 | C2×D3 | — | 14 | 1 | no | — |
| 290 | C2×D3 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 291 | C3×C4 | — | 2 | 1 | no | — |
| 292 | C3×C4 | — | 14 | 2 | no | — |
| 293 | C3×C4 | C2×C22⋊D7 | 1 | 1 | yes | characteristic |
| 294 | C3×C4 | C23×D7 | 1 | 1 | yes | characteristic |
| 295 | Dic3 | — | 2 | 2 | no | — |
| 296 | Dic3 | — | 14 | 1 | no | — |
| 297 | Dic3 | C2×C22⋊D7 | 1 | 2 | yes | — |
| 298 | Q8 | — | 3 | 1 | no | — |
| 299 | Q8 | — | 3 | 2 | no | — |
| 300 | Q8 | — | 6 | 2 | no | — |
| 301 | Q8 | — | 6 | 1 | no | — |
| 302 | Q8 | — | 7 | 2 | no | — |
| 303 | Q8 | — | 14 | 1 | no | — |
| 304 | Q8 | — | 21 | 1 | no | — |
| 305 | Q8 | — | 42 | 2 | no | — |
| 306 | Q8 | C2×D3×D7 | 1 | 1 | yes | characteristic |
| 307 | D4 | — | 2 | 1 | no | — |
| 308 | D4 | — | 3 | 2 | no | — |
| 309 | D4 | — | 3 | 1 | no | — |
| 310 | D4 | — | 6 | 2 | no | — |
| 311 | D4 | — | 21 | 1 | no | — |
| 312 | D4 | — | 42 | 2 | no | — |
| 313 | D4 | — | 42 | 1 | no | — |
| 314 | D4 | C2×D3×D7 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 3 | 2 | no | — |
| 317 | C2×C4 | — | 6 | 2 | no | — |
| 318 | C2×C4 | — | 6 | 2 | no | — |
| 319 | C2×C4 | — | 6 | 1 | no | — |
| 320 | C2×C4 | — | 14 | 1 | no | — |
| 321 | C2×C4 | — | 42 | 2 | no | — |
| 322 | C2×C4 | — | 42 | 2 | no | — |
| 323 | C2×C4 | — | 42 | 1 | no | — |
| 324 | C2×C4 | C2×D3×D7 | 1 | 1 | yes | characteristic |
| 325 | C8 | — | 7 | 2 | no | — |
| 326 | C8 | — | 21 | 1 | no | — |
| 327 | C8 | — | 21 | 1 | no | — |
| 328 | C7 | #5779 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 329 | C2×C3 | — | 2 | 1 | no | — |
| 330 | C2×C3 | — | 4 | 1 | no | — |
| 331 | C2×C3 | C22×C22⋊D7 | 1 | 1 | yes | characteristic |
| 332 | D3 | — | 2 | 2 | no | — |
| 333 | D3 | — | 28 | 1 | no | — |
| 334 | C22 | — | 2 | 1 | no | — |
| 335 | C22 | — | 3 | 2 | no | — |
| 336 | C22 | — | 42 | 1 | no | — |
| 337 | C22 | D3×C22⋊D7 | 1 | 1 | yes | characteristic |
| 338 | C4 | — | 2 | 1 | no | — |
| 339 | C4 | — | 3 | 2 | no | — |
| 340 | C4 | — | 6 | 2 | no | — |
| 341 | C4 | — | 14 | 2 | no | — |
| 342 | C4 | — | 42 | 1 | no | — |
| 343 | C4 | D3×C22⋊D7 | 1 | 1 | yes | characteristic |
| 344 | C4 | C22×D3×D7 | 1 | 1 | yes | characteristic |
| 345 | C3 | #90529 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 346 | C2 | — | 2 | 1 | no | — |
| 347 | C2 | — | 4 | 1 | no | — |
| 348 | C2 | — | 6 | 2 | no | — |
| 349 | C2 | — | 84 | 1 | no | — |
| 350 | C2 | C2×D3×C22⋊D7 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta