| 1 | #33610 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #33607 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13713 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13711 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13699 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13696 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #13694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #13664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #13663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #13663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #13661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #13554 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#508 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C22×D16 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3061 | — | 2 | 1 | no | — |
| 20 | #3058 | — | 2 | 1 | no | — |
| 21 | C2×SD64 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×SD64 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×D32 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×D32 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×M64 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C22×C32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #2220 | — | 2 | 1 | no | — |
| 28 | #2220 | — | 2 | 1 | no | — |
| 29 | #2218 | — | 2 | 1 | no | — |
| 30 | #2218 | — | 2 | 1 | no | — |
| 31 | #2216 | C22 | 1 | 1 | yes | characteristic |
| 32 | #2216 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #2215 | C22 | 1 | 1 | yes | characteristic |
| 34 | #2215 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2215 | C22 | 1 | 1 | yes | characteristic |
| 36 | #2215 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2215 | C22 | 1 | 1 | yes | characteristic |
| 38 | #2215 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #2158 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#366 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #2140 | — | 2 | 1 | no | — |
| 42 | #2139 | — | 2 | 1 | no | — |
| 43 | #1424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #1424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #1423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #1423 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #1416 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #1416 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #1415 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1415 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1415 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1415 | C22 | 1 | 1 | yes | characteristic |
| 53 | #1415 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #1415 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C22⋊C32 | C22 | 1 | 1 | yes | characteristic |
| 56 | C22⋊C32 | C22 | 1 | 1 | yes | characteristic |
| 57 | C22⋊C32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C22⋊C32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C2×#135 | — | 2 | 1 | no | — |
| 60 | C22×D8 | — | 2 | 1 | no | — |
| 61 | C2×#131 | D4 | 1 | 1 | yes | characteristic |
| 62 | #537 | — | 4 | 1 | no | — |
| 63 | #535 | — | 4 | 1 | no | — |
| 64 | #508 | — | 4 | 1 | no | — |
| 65 | #508 | — | 4 | 1 | no | — |
| 66 | C2×Q32 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×SD32 | — | 2 | 1 | no | — |
| 68 | C2×D16 | — | 2 | 1 | no | — |
| 69 | C2×D16 | — | 4 | 1 | no | — |
| 70 | C2×D16 | — | 4 | 1 | no | — |
| 71 | C2×D16 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×D16 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×D16 | C23 | 1 | 1 | yes | characteristic |
| 74 | #504 | — | 4 | 1 | no | — |
| 75 | #504 | — | 4 | 1 | no | — |
| 76 | C2×M32 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×M32 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×M32 | D4 | 1 | 1 | yes | characteristic |
| 79 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 82 | #469 | — | 4 | 1 | no | — |
| 83 | #469 | — | 4 | 1 | no | — |
| 84 | #468 | — | 4 | 1 | no | — |
| 85 | #468 | — | 4 | 1 | no | — |
| 86 | #467 | — | 2 | 1 | no | — |
| 87 | #467 | — | 2 | 1 | no | — |
| 88 | #466 | — | 2 | 1 | no | — |
| 89 | #466 | — | 2 | 1 | no | — |
| 90 | #466 | — | 2 | 1 | no | — |
| 91 | #466 | — | 2 | 1 | no | — |
| 92 | #466 | — | 2 | 1 | no | — |
| 93 | #466 | — | 2 | 1 | no | — |
| 94 | #427 | — | 2 | 1 | no | — |
| 95 | C2×#107 | — | 2 | 1 | no | — |
| 96 | #418 | — | 4 | 1 | no | — |
| 97 | #417 | — | 4 | 1 | no | — |
| 98 | SD64 | — | 4 | 1 | no | — |
| 99 | SD64 | — | 4 | 1 | no | — |
| 100 | D32 | — | 4 | 1 | no | — |
| 101 | D32 | — | 4 | 1 | no | — |
| 102 | M64 | — | 4 | 1 | no | — |
| 103 | C2×C32 | — | 4 | 1 | no | — |
| 104 | C2×C32 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C32 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C32 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×C32 | C23 | 1 | 1 | yes | characteristic |
| 108 | #367 | — | 2 | 1 | no | — |
| 109 | #366 | — | 2 | 1 | no | — |
| 110 | #366 | C23 | 1 | 1 | yes | characteristic |
| 111 | #366 | C23 | 1 | 1 | yes | characteristic |
| 112 | #366 | C23 | 1 | 1 | yes | characteristic |
| 113 | #366 | C23 | 1 | 1 | yes | characteristic |
| 114 | #358 | — | 2 | 1 | no | — |
| 115 | #358 | — | 2 | 1 | no | — |
| 116 | #357 | — | 2 | 1 | no | — |
| 117 | #357 | — | 2 | 1 | no | — |
| 118 | #357 | — | 2 | 1 | no | — |
| 119 | #357 | — | 2 | 1 | no | — |
| 120 | #357 | — | 2 | 1 | no | — |
| 121 | #357 | — | 2 | 1 | no | — |
| 122 | C2×#41 | — | 4 | 1 | no | — |
| 123 | C2×#41 | D8 | 1 | 1 | yes | characteristic |
| 124 | C22×D4 | — | 4 | 1 | no | — |
| 125 | #135 | — | 4 | 2 | no | — |
| 126 | #135 | — | 4 | 2 | no | — |
| 127 | C2×Q16 | — | 2 | 1 | no | — |
| 128 | C2×SD16 | — | 4 | 1 | no | — |
| 129 | C2×D8 | — | 2 | 1 | no | — |
| 130 | C2×D8 | — | 2 | 1 | no | — |
| 131 | C2×D8 | — | 2 | 1 | no | — |
| 132 | C2×D8 | — | 4 | 2 | no | — |
| 133 | C2×D8 | — | 4 | 2 | no | — |
| 134 | C2×D8 | — | 4 | 1 | no | — |
| 135 | #131 | — | 4 | 1 | no | — |
| 136 | #131 | — | 4 | 1 | no | — |
| 137 | C2×M16 | D8 | 1 | 1 | yes | characteristic |
| 138 | C2×M16 | D8 | 1 | 1 | yes | characteristic |
| 139 | C2×M16 | D8 | 1 | 1 | yes | characteristic |
| 140 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 142 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | #127 | — | 8 | 1 | no | — |
| 144 | #124 | — | 8 | 1 | no | — |
| 145 | C22⋊Q8 | — | 4 | 1 | no | — |
| 146 | C22⋊Q8 | — | 4 | 1 | no | — |
| 147 | C22⋊Q8 | — | 8 | 1 | no | — |
| 148 | #121 | — | 4 | 1 | no | — |
| 149 | #121 | — | 4 | 1 | no | — |
| 150 | #121 | — | 4 | 1 | no | — |
| 151 | #121 | — | 4 | 1 | no | — |
| 152 | #121 | — | 4 | 1 | no | — |
| 153 | #121 | — | 4 | 1 | no | — |
| 154 | #121 | — | 8 | 1 | no | — |
| 155 | #121 | — | 8 | 1 | no | — |
| 156 | #121 | — | 8 | 1 | no | — |
| 157 | #120 | — | 8 | 1 | no | — |
| 158 | #120 | — | 8 | 1 | no | — |
| 159 | #117 | — | 4 | 1 | no | — |
| 160 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 161 | Q32 | — | 2 | 1 | no | — |
| 162 | Q32 | — | 2 | 1 | no | — |
| 163 | SD32 | — | 4 | 2 | no | — |
| 164 | D16 | — | 2 | 1 | no | — |
| 165 | D16 | — | 2 | 1 | no | — |
| 166 | D16 | — | 2 | 1 | no | — |
| 167 | D16 | — | 2 | 1 | no | — |
| 168 | D16 | — | 2 | 1 | no | — |
| 169 | D16 | — | 2 | 1 | no | — |
| 170 | D16 | — | 4 | 2 | no | — |
| 171 | M32 | — | 4 | 1 | no | — |
| 172 | M32 | — | 4 | 1 | no | — |
| 173 | M32 | — | 4 | 1 | no | — |
| 174 | C2×C16 | — | 2 | 1 | no | — |
| 175 | C2×C16 | — | 2 | 1 | no | — |
| 176 | C2×C16 | — | 2 | 1 | no | — |
| 177 | C2×C16 | — | 2 | 1 | no | — |
| 178 | C2×C16 | — | 2 | 1 | no | — |
| 179 | C2×C16 | — | 2 | 1 | no | — |
| 180 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 184 | #107 | — | 2 | 1 | no | — |
| 185 | #107 | — | 2 | 1 | no | — |
| 186 | #107 | — | 2 | 1 | no | — |
| 187 | #107 | — | 2 | 1 | no | — |
| 188 | #107 | — | 4 | 1 | no | — |
| 189 | #106 | — | 4 | 1 | no | — |
| 190 | #103 | — | 4 | 1 | no | — |
| 191 | #103 | — | 4 | 1 | no | — |
| 192 | #102 | — | 4 | 1 | no | — |
| 193 | #102 | — | 4 | 1 | no | — |
| 194 | #102 | — | 4 | 1 | no | — |
| 195 | #102 | — | 4 | 1 | no | — |
| 196 | #102 | — | 4 | 1 | no | — |
| 197 | #102 | — | 4 | 1 | no | — |
| 198 | C32 | — | 2 | 1 | no | — |
| 199 | C32 | — | 2 | 1 | no | — |
| 200 | C32 | — | 2 | 1 | no | — |
| 201 | C32 | — | 2 | 1 | no | — |
| 202 | C24 | — | 8 | 1 | no | — |
| 203 | #41 | — | 4 | 1 | no | — |
| 204 | #41 | — | 4 | 1 | no | — |
| 205 | #41 | — | 8 | 2 | no | — |
| 206 | #41 | — | 8 | 2 | no | — |
| 207 | C2×Q8 | — | 4 | 1 | no | — |
| 208 | C2×Q8 | D16 | 1 | 1 | yes | characteristic |
| 209 | C2×D4 | — | 4 | 1 | no | — |
| 210 | C2×D4 | — | 4 | 1 | no | — |
| 211 | C2×D4 | — | 4 | 1 | no | — |
| 212 | C2×D4 | — | 8 | 2 | no | — |
| 213 | C2×D4 | — | 8 | 2 | no | — |
| 214 | C2×D4 | — | 8 | 1 | no | — |
| 215 | C2×D4 | — | 8 | 1 | no | — |
| 216 | C2×D4 | — | 8 | 1 | no | — |
| 217 | C2×D4 | — | 8 | 1 | no | — |
| 218 | C2×D4 | — | 8 | 1 | no | — |
| 219 | C2×D4 | — | 8 | 1 | no | — |
| 220 | C2×D4 | — | 8 | 1 | no | — |
| 221 | C2×D4 | — | 8 | 1 | no | — |
| 222 | C2×D4 | D16 | 1 | 1 | yes | characteristic |
| 223 | C2×D4 | D16 | 1 | 1 | yes | characteristic |
| 224 | C2×D4 | D16 | 1 | 1 | yes | characteristic |
| 225 | C22×C4 | — | 8 | 1 | no | — |
| 226 | C22×C4 | — | 8 | 1 | no | — |
| 227 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 228 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 229 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 230 | Q16 | — | 4 | 1 | no | — |
| 231 | Q16 | — | 4 | 1 | no | — |
| 232 | SD16 | — | 8 | 2 | no | — |
| 233 | D8 | — | 4 | 1 | no | — |
| 234 | D8 | — | 4 | 1 | no | — |
| 235 | D8 | — | 4 | 1 | no | — |
| 236 | D8 | — | 4 | 1 | no | — |
| 237 | D8 | — | 4 | 1 | no | — |
| 238 | D8 | — | 4 | 1 | no | — |
| 239 | D8 | — | 8 | 2 | no | — |
| 240 | M16 | — | 4 | 1 | no | — |
| 241 | M16 | — | 4 | 1 | no | — |
| 242 | M16 | — | 4 | 1 | no | — |
| 243 | C2×C8 | — | 2 | 1 | no | — |
| 244 | C2×C8 | — | 2 | 1 | no | — |
| 245 | C2×C8 | — | 2 | 1 | no | — |
| 246 | C2×C8 | — | 2 | 1 | no | — |
| 247 | C2×C8 | — | 2 | 1 | no | — |
| 248 | C2×C8 | — | 2 | 1 | no | — |
| 249 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 250 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 251 | C2×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 252 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 253 | C4⋊C4 | — | 4 | 1 | no | — |
| 254 | C4⋊C4 | — | 4 | 1 | no | — |
| 255 | C4⋊C4 | — | 4 | 1 | no | — |
| 256 | C4⋊C4 | — | 4 | 1 | no | — |
| 257 | C4⋊C4 | — | 8 | 1 | no | — |
| 258 | C4⋊C4 | — | 8 | 1 | no | — |
| 259 | C4⋊C4 | — | 8 | 1 | no | — |
| 260 | C22⋊C4 | — | 8 | 1 | no | — |
| 261 | C22⋊C4 | — | 8 | 1 | no | — |
| 262 | C22⋊C4 | — | 8 | 1 | no | — |
| 263 | C22⋊C4 | — | 8 | 1 | no | — |
| 264 | C22⋊C4 | — | 8 | 1 | no | — |
| 265 | C22⋊C4 | — | 8 | 1 | no | — |
| 266 | C22⋊C4 | — | 8 | 1 | no | — |
| 267 | C22⋊C4 | — | 8 | 1 | no | — |
| 268 | C22⋊C4 | — | 8 | 1 | no | — |
| 269 | C42 | — | 8 | 1 | no | — |
| 270 | C16 | — | 2 | 1 | no | — |
| 271 | C16 | — | 2 | 1 | no | — |
| 272 | C16 | — | 2 | 1 | no | — |
| 273 | C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 274 | C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 275 | C23 | — | 8 | 1 | no | — |
| 276 | C23 | — | 8 | 1 | no | — |
| 277 | C23 | — | 8 | 1 | no | — |
| 278 | C23 | — | 16 | 2 | no | — |
| 279 | C23 | — | 32 | 1 | no | — |
| 280 | C23 | — | 32 | 1 | no | — |
| 281 | C23 | C2×D16 | 1 | 1 | yes | characteristic |
| 282 | C23 | C2×D16 | 1 | 1 | yes | characteristic |
| 283 | C23 | C2×D16 | 1 | 1 | yes | characteristic |
| 284 | Q8 | — | 4 | 1 | no | — |
| 285 | Q8 | — | 8 | 1 | no | — |
| 286 | Q8 | — | 8 | 1 | no | — |
| 287 | D4 | — | 4 | 1 | no | — |
| 288 | D4 | — | 4 | 1 | no | — |
| 289 | D4 | — | 4 | 1 | no | — |
| 290 | D4 | — | 8 | 1 | no | — |
| 291 | D4 | — | 8 | 1 | no | — |
| 292 | D4 | — | 8 | 1 | no | — |
| 293 | D4 | — | 8 | 1 | no | — |
| 294 | D4 | — | 8 | 1 | no | — |
| 295 | D4 | — | 8 | 1 | no | — |
| 296 | D4 | — | 16 | 2 | no | — |
| 297 | D4 | — | 16 | 2 | no | — |
| 298 | D4 | — | 32 | 1 | no | — |
| 299 | D4 | — | 32 | 1 | no | — |
| 300 | D4 | — | 32 | 1 | no | — |
| 301 | D4 | — | 32 | 1 | no | — |
| 302 | D4 | — | 32 | 1 | no | — |
| 303 | D4 | — | 32 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 2 | 1 | no | — |
| 306 | C2×C4 | — | 2 | 1 | no | — |
| 307 | C2×C4 | — | 2 | 1 | no | — |
| 308 | C2×C4 | — | 2 | 1 | no | — |
| 309 | C2×C4 | — | 2 | 1 | no | — |
| 310 | C2×C4 | — | 8 | 1 | no | — |
| 311 | C2×C4 | — | 8 | 1 | no | — |
| 312 | C2×C4 | — | 8 | 1 | no | — |
| 313 | C2×C4 | — | 8 | 1 | no | — |
| 314 | C2×C4 | — | 8 | 1 | no | — |
| 315 | C2×C4 | — | 16 | 2 | no | — |
| 316 | C2×C4 | — | 32 | 1 | no | — |
| 317 | C2×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 318 | C2×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 320 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 321 | C8 | — | 2 | 1 | no | — |
| 322 | C8 | — | 2 | 1 | no | — |
| 323 | C8 | — | 2 | 1 | no | — |
| 324 | C8 | #534 | 1 | 1 | yes | characteristic |
| 325 | C8 | #575 | 1 | 1 | yes | characteristic |
| 326 | C22 | — | 2 | 1 | no | — |
| 327 | C22 | — | 2 | 1 | no | — |
| 328 | C22 | — | 2 | 1 | no | — |
| 329 | C22 | — | 2 | 1 | no | — |
| 330 | C22 | — | 2 | 1 | no | — |
| 331 | C22 | — | 2 | 1 | no | — |
| 332 | C22 | — | 2 | 1 | no | — |
| 333 | C22 | — | 2 | 1 | no | — |
| 334 | C22 | — | 2 | 1 | no | — |
| 335 | C22 | — | 16 | 1 | no | — |
| 336 | C22 | — | 16 | 1 | no | — |
| 337 | C22 | — | 16 | 1 | no | — |
| 338 | C22 | — | 16 | 1 | no | — |
| 339 | C22 | — | 16 | 1 | no | — |
| 340 | C22 | — | 16 | 1 | no | — |
| 341 | C22 | — | 16 | 1 | no | — |
| 342 | C22 | — | 16 | 1 | no | — |
| 343 | C22 | — | 16 | 1 | no | — |
| 344 | C22 | — | 32 | 4 | no | — |
| 345 | C22 | C22×D16 | 1 | 1 | yes | characteristic |
| 346 | C4 | — | 2 | 1 | no | — |
| 347 | C4 | — | 2 | 1 | no | — |
| 348 | C4 | — | 2 | 1 | no | — |
| 349 | C4 | — | 16 | 1 | no | — |
| 350 | C4 | — | 16 | 1 | no | — |
| 351 | C4 | — | 16 | 1 | no | — |
| 352 | C4 | — | 16 | 1 | no | — |
| 353 | C4 | — | 16 | 1 | no | — |
| 354 | C4 | #3186 | 1 | 1 | yes | characteristic |
| 355 | C4 | #3414 | 1 | 1 | yes | characteristic |
| 356 | C2 | — | 4 | 1 | no | — |
| 357 | C2 | — | 4 | 1 | no | — |
| 358 | C2 | — | 4 | 1 | no | — |
| 359 | C2 | — | 32 | 1 | no | — |
| 360 | C2 | — | 32 | 1 | no | — |
| 361 | C2 | — | 32 | 1 | no | — |
| 362 | C2 | #33752 | 1 | 1 | yes | characteristic |
| 363 | C2 | #33982 | 1 | 1 | yes | characteristic |
| 364 | C2 | #33983 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta