Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
2176 conjugacy classes of subgroups.
The subgroup lattice has 953 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72226930 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #72226915 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72226888 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72226887 | — | 2 | 2 | no | — |
| 5 | #72226886 | — | 2 | 2 | no | — |
| 6 | #72226885 | — | 2 | 2 | no | — |
| 7 | #72226878 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72226876 | — | 2 | 2 | no | — |
| 9 | #72226875 | — | 2 | 2 | no | — |
| 10 | #72226874 | — | 2 | 2 | no | — |
| 11 | #72226855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #72226852 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #72225587 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #72225586 | C4 | 1 | 2 | yes | complemented |
| 15 | #72225585 | C4 | 1 | 2 | yes | complemented |
| 16 | #72225584 | C4 | 1 | 2 | yes | complemented |
| 17 | #72225579 | C22 | 1 | 1 | yes | characteristic |
| 18 | #72225560 | — | 2 | 2 | no | — |
| 19 | #72225558 | — | 2 | 2 | no | — |
| 20 | #72225406 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #72225394 | C22 | 1 | 1 | yes | characteristic |
| 22 | #72225385 | C2 | 1 | 2 | yes | maximal, complemented |
| 23 | #72225373 | C22 | 1 | 2 | yes | complemented |
| 24 | #72225363 | C22 | 1 | 2 | yes | complemented |
| 25 | #72225353 | C22 | 1 | 2 | yes | — |
| 26 | #72225344 | C22 | 1 | 2 | yes | — |
| 27 | #72225339 | C22 | 1 | 2 | yes | — |
| 28 | #72225311 | C22 | 1 | 2 | yes | — |
| 29 | #72225194 | C2 | 1 | 2 | yes | maximal, complemented |
| 30 | #72216560 | C22 | 1 | 2 | yes | complemented |
| 31 | #72216534 | C22 | 1 | 2 | yes | complemented |
| 32 | C2×#93751 | C22 | 1 | 2 | yes | — |
| 33 | #72216413 | C22 | 1 | 2 | yes | — |
| 34 | #72216382 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 35 | #72216290 | C22 | 1 | 2 | yes | — |
| 36 | #72216290 | C22 | 1 | 2 | yes | complemented |
| 37 | #72216273 | C22 | 1 | 2 | yes | complemented |
| 38 | #72216267 | C22 | 1 | 2 | yes | — |
| 39 | #72216236 | C22 | 1 | 1 | yes | characteristic |
| 40 | #72216220 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #72216197 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #72214187 | C4 | 1 | 2 | yes | complemented |
| 43 | #7623661 | — | 2 | 2 | no | — |
| 44 | #512928 | — | 2 | 2 | no | — |
| 45 | #512779 | — | 4 | 2 | no | — |
| 46 | #512751 | — | 2 | 2 | no | — |
| 47 | #512698 | — | 4 | 2 | no | — |
| 48 | #498569 | — | 2 | 2 | no | — |
| 49 | #497891 | — | 2 | 2 | no | — |
| 50 | #497855 | — | 2 | 2 | no | — |
| 51 | #492533 | C2×C4 | 1 | 2 | yes | — |
| 52 | #492532 | C2×C4 | 1 | 2 | yes | — |
| 53 | #492531 | — | 4 | 1 | no | — |
| 54 | #492530 | — | 2 | 4 | no | — |
| 55 | #491485 | — | 4 | 1 | no | — |
| 56 | #491465 | C23 | 1 | 1 | yes | characteristic |
| 57 | #491465 | C23 | 1 | 1 | yes | characteristic |
| 58 | #490484 | — | 2 | 2 | no | — |
| 59 | #488869 | — | 4 | 1 | no | — |
| 60 | C2×#12046 | C23 | 1 | 2 | yes | — |
| 61 | #152996 | — | 2 | 2 | no | — |
| 62 | #152896 | — | 2 | 2 | no | — |
| 63 | #152896 | — | 2 | 2 | no | — |
| 64 | #152896 | — | 2 | 2 | no | — |
| 65 | #152896 | — | 2 | 2 | no | — |
| 66 | #152873 | — | 2 | 2 | no | — |
| 67 | #152839 | — | 4 | 2 | no | — |
| 68 | #152640 | — | 4 | 2 | no | — |
| 69 | #152542 | — | 4 | 2 | no | — |
| 70 | #152517 | — | 4 | 2 | no | — |
| 71 | #152450 | — | 4 | 2 | no | — |
| 72 | #152282 | — | 2 | 2 | no | — |
| 73 | #152178 | — | 4 | 2 | no | — |
| 74 | #151989 | — | 2 | 2 | no | — |
| 75 | #151968 | D4 | 1 | 2 | yes | — |
| 76 | #151636 | — | 2 | 4 | no | — |
| 77 | #151635 | C2×C4 | 1 | 4 | yes | complemented |
| 78 | #151634 | C2×C4 | 1 | 4 | yes | complemented |
| 79 | #151073 | — | 2 | 4 | no | — |
| 80 | #151072 | — | 4 | 2 | no | — |
| 81 | C2×#7459 | C23 | 1 | 2 | yes | — |
| 82 | C2×#7459 | C23 | 1 | 2 | yes | — |
| 83 | #150950 | — | 2 | 2 | no | — |
| 84 | #150947 | — | 2 | 2 | no | — |
| 85 | #150069 | D4 | 1 | 2 | yes | — |
| 86 | #150051 | — | 2 | 2 | no | — |
| 87 | C8×M64 | C23 | 1 | 2 | yes | — |
| 88 | #141262 | — | 2 | 2 | no | — |
| 89 | #140437 | — | 2 | 2 | no | — |
| 90 | #137550 | — | 4 | 1 | no | — |
| 91 | #136324 | — | 4 | 2 | no | — |
| 92 | #135778 | — | 4 | 1 | no | — |
| 93 | #135778 | C23 | 1 | 2 | yes | — |
| 94 | #134970 | — | 2 | 2 | no | — |
| 95 | #129142 | C23 | 1 | 2 | yes | — |
| 96 | #123406 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 97 | #123406 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 98 | #123405 | — | 4 | 1 | no | — |
| 99 | #123404 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 100 | #123403 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 101 | C2×C162 | C23 | 1 | 1 | yes | characteristic |
| 102 | #94364 | — | 2 | 2 | no | — |
| 103 | #94364 | — | 2 | 2 | no | — |
| 104 | #94054 | D4 | 1 | 2 | yes | — |
| 105 | #94041 | — | 2 | 2 | no | — |
| 106 | #94029 | D4 | 1 | 2 | yes | — |
| 107 | #93868 | — | 4 | 1 | no | — |
| 108 | #93867 | C2×C4 | 1 | 2 | yes | complemented |
| 109 | #93866 | C2×C4 | 1 | 2 | yes | complemented |
| 110 | #93751 | C2×C4 | 1 | 4 | yes | complemented |
| 111 | #93751 | C2×C4 | 1 | 4 | yes | complemented |
| 112 | #93665 | — | 4 | 1 | no | — |
| 113 | #62635 | — | 4 | 2 | no | — |
| 114 | #61105 | — | 4 | 1 | no | — |
| 115 | #33981 | — | 4 | 2 | no | — |
| 116 | #33974 | — | 4 | 2 | no | — |
| 117 | #33860 | — | 2 | 4 | no | — |
| 118 | #33859 | — | 4 | 4 | no | — |
| 119 | #33858 | — | 2 | 4 | no | — |
| 120 | #33857 | — | 8 | 2 | no | — |
| 121 | #33856 | — | 4 | 4 | no | — |
| 122 | #33733 | — | 8 | 2 | no | — |
| 123 | #33713 | — | 2 | 2 | no | — |
| 124 | #33713 | — | 2 | 2 | no | — |
| 125 | #33617 | — | 4 | 2 | no | — |
| 126 | #33594 | — | 4 | 2 | no | — |
| 127 | #33538 | — | 8 | 2 | no | — |
| 128 | #33465 | — | 4 | 2 | no | — |
| 129 | C2×#2178 | C2×D4 | 1 | 2 | yes | — |
| 130 | #33460 | — | 4 | 2 | no | — |
| 131 | C2×#2170 | — | 2 | 2 | no | — |
| 132 | #33411 | — | 4 | 2 | no | — |
| 133 | #23196 | — | 4 | 1 | no | — |
| 134 | #22692 | — | 4 | 2 | no | — |
| 135 | #19603 | — | 2 | 1 | no | — |
| 136 | #19603 | — | 2 | 1 | no | — |
| 137 | #13693 | — | 2 | 4 | no | — |
| 138 | #13692 | — | 2 | 4 | no | — |
| 139 | #13691 | — | 4 | 4 | no | — |
| 140 | #13658 | — | 8 | 4 | no | — |
| 141 | #13657 | — | 8 | 4 | no | — |
| 142 | #13648 | — | 8 | 2 | no | — |
| 143 | #13647 | — | 4 | 4 | no | — |
| 144 | C2×#1426 | — | 4 | 2 | no | — |
| 145 | C2×#1422 | — | 2 | 2 | no | — |
| 146 | C2×#1422 | — | 2 | 2 | no | — |
| 147 | #13625 | — | 4 | 2 | no | — |
| 148 | #13625 | D8 | 1 | 2 | yes | — |
| 149 | #13622 | — | 4 | 2 | no | — |
| 150 | #13622 | — | 8 | 4 | no | — |
| 151 | #13622 | D8 | 1 | 2 | yes | — |
| 152 | C2×#1418 | — | 4 | 2 | no | — |
| 153 | C2×#1418 | — | 4 | 2 | no | — |
| 154 | C2×#1418 | — | 4 | 2 | no | — |
| 155 | C2×#1418 | — | 4 | 2 | no | — |
| 156 | C2×#1418 | — | 4 | 2 | no | — |
| 157 | C2×#1418 | — | 8 | 2 | no | — |
| 158 | C2×#1418 | — | 8 | 2 | no | — |
| 159 | C2×#1418 | — | 8 | 4 | no | — |
| 160 | #13620 | — | 4 | 2 | no | — |
| 161 | #13558 | — | 4 | 2 | no | — |
| 162 | #13551 | — | 4 | 2 | no | — |
| 163 | C4×M64 | C2×D4 | 1 | 2 | yes | — |
| 164 | C4×M64 | C2×D4 | 1 | 2 | yes | — |
| 165 | #13259 | — | 4 | 2 | no | — |
| 166 | #13243 | — | 4 | 2 | no | — |
| 167 | #13181 | — | 4 | 2 | no | — |
| 168 | #13172 | — | 4 | 2 | no | — |
| 169 | #13016 | — | 8 | 2 | no | — |
| 170 | #12946 | — | 8 | 2 | no | — |
| 171 | #12926 | — | 8 | 2 | no | — |
| 172 | #12906 | — | 2 | 2 | no | — |
| 173 | #12906 | — | 2 | 2 | no | — |
| 174 | #12906 | — | 8 | 2 | no | — |
| 175 | #12843 | — | 4 | 2 | no | — |
| 176 | #12821 | — | 4 | 2 | no | — |
| 177 | #12670 | C2×D4 | 1 | 2 | yes | — |
| 178 | #12664 | — | 2 | 2 | no | — |
| 179 | #12521 | — | 4 | 1 | no | — |
| 180 | #12518 | — | 2 | 2 | no | — |
| 181 | #12518 | — | 2 | 2 | no | — |
| 182 | #12517 | — | 2 | 1 | no | — |
| 183 | #12517 | — | 2 | 1 | no | — |
| 184 | #12516 | C22×C4 | 1 | 1 | yes | characteristic |
| 185 | #12516 | C22×C4 | 1 | 1 | yes | characteristic |
| 186 | #12515 | — | 4 | 1 | no | — |
| 187 | #12515 | C22×C4 | 1 | 1 | yes | characteristic |
| 188 | #12515 | C22×C4 | 1 | 1 | yes | characteristic |
| 189 | #12509 | — | 4 | 1 | no | — |
| 190 | #12509 | — | 4 | 1 | no | — |
| 191 | #12503 | — | 8 | 2 | no | — |
| 192 | #12438 | — | 4 | 4 | no | — |
| 193 | #12437 | — | 2 | 4 | no | — |
| 194 | #12436 | — | 2 | 4 | no | — |
| 195 | #12313 | — | 4 | 2 | no | — |
| 196 | #12312 | — | 4 | 2 | no | — |
| 197 | #12311 | — | 4 | 2 | no | — |
| 198 | #12310 | — | 4 | 2 | no | — |
| 199 | #12046 | — | 2 | 2 | no | — |
| 200 | #12046 | — | 2 | 2 | no | — |
| 201 | #12046 | C22×C4 | 1 | 4 | yes | — |
| 202 | #12046 | #41 | 1 | 4 | yes | — |
| 203 | C2×#1373 | C2×D4 | 1 | 2 | yes | — |
| 204 | C2×#1373 | C2×D4 | 1 | 2 | yes | — |
| 205 | #11922 | — | 4 | 1 | no | — |
| 206 | #11920 | — | 4 | 1 | no | — |
| 207 | C2×#1335 | — | 2 | 2 | no | — |
| 208 | C2×C8×C16 | — | 2 | 1 | no | — |
| 209 | C2×C8×C16 | C24 | 1 | 1 | yes | characteristic |
| 210 | #8818 | — | 2 | 2 | no | — |
| 211 | #7480 | D8 | 1 | 2 | yes | — |
| 212 | #7479 | D8 | 1 | 2 | yes | — |
| 213 | #7477 | — | 4 | 2 | no | — |
| 214 | #7474 | — | 4 | 2 | no | — |
| 215 | #7469 | — | 4 | 2 | no | — |
| 216 | #7459 | — | 2 | 2 | no | — |
| 217 | #7459 | — | 2 | 2 | no | — |
| 218 | #7459 | — | 2 | 2 | no | — |
| 219 | #7459 | C22×C4 | 1 | 4 | yes | — |
| 220 | #7449 | — | 2 | 4 | no | — |
| 221 | #7448 | — | 2 | 4 | no | — |
| 222 | #7447 | — | 8 | 2 | no | — |
| 223 | #7388 | — | 2 | 4 | no | — |
| 224 | #7381 | — | 4 | 4 | no | — |
| 225 | #7329 | — | 2 | 2 | no | — |
| 226 | C8×C32 | — | 2 | 2 | no | — |
| 227 | #7269 | — | 4 | 2 | no | — |
| 228 | #7179 | — | 2 | 2 | no | — |
| 229 | C162 | — | 2 | 1 | no | — |
| 230 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 231 | C162 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | #3584 | — | 8 | 2 | no | — |
| 233 | #3417 | — | 4 | 4 | no | — |
| 234 | #3417 | — | 8 | 2 | no | — |
| 235 | #3416 | — | 8 | 4 | no | — |
| 236 | #3416 | — | 16 | 2 | no | — |
| 237 | #3415 | — | 4 | 4 | no | — |
| 238 | #3415 | — | 8 | 2 | no | — |
| 239 | #3414 | — | 8 | 2 | no | — |
| 240 | #3414 | — | 16 | 2 | no | — |
| 241 | C2×#508 | — | 4 | 2 | no | — |
| 242 | C2×#508 | — | 4 | 2 | no | — |
| 243 | C2×#508 | — | 4 | 2 | no | — |
| 244 | C2×#508 | — | 4 | 2 | no | — |
| 245 | C2×#508 | — | 8 | 4 | no | — |
| 246 | C2×#508 | C2×D8 | 1 | 2 | yes | — |
| 247 | C2×#504 | — | 4 | 2 | no | — |
| 248 | #3293 | — | 4 | 2 | no | — |
| 249 | #3292 | — | 4 | 2 | no | — |
| 250 | #3291 | — | 16 | 1 | no | — |
| 251 | #3290 | — | 8 | 4 | no | — |
| 252 | #3169 | — | 8 | 1 | no | — |
| 253 | #3169 | — | 8 | 1 | no | — |
| 254 | #3147 | — | 4 | 1 | no | — |
| 255 | #3147 | — | 4 | 1 | no | — |
| 256 | #3067 | — | 8 | 2 | no | — |
| 257 | #3018 | — | 16 | 1 | no | — |
| 258 | #2957 | — | 8 | 2 | no | — |
| 259 | C2×#443 | — | 2 | 2 | no | — |
| 260 | #2951 | — | 8 | 2 | no | — |
| 261 | #2913 | — | 8 | 2 | no | — |
| 262 | #2264 | — | 4 | 4 | no | — |
| 263 | #2264 | — | 8 | 2 | no | — |
| 264 | #2263 | — | 4 | 4 | no | — |
| 265 | #2263 | — | 8 | 2 | no | — |
| 266 | #2262 | — | 8 | 4 | no | — |
| 267 | #2258 | — | 8 | 4 | no | — |
| 268 | #2258 | — | 16 | 2 | no | — |
| 269 | C2×M64 | — | 2 | 2 | no | — |
| 270 | C2×M64 | — | 4 | 2 | no | — |
| 271 | C2×M64 | — | 4 | 2 | no | — |
| 272 | C2×M64 | — | 8 | 4 | no | — |
| 273 | C2×M64 | C2×D8 | 1 | 2 | yes | — |
| 274 | C2×M64 | C2×D8 | 1 | 2 | yes | — |
| 275 | #2252 | — | 8 | 2 | no | — |
| 276 | #2249 | — | 4 | 2 | no | — |
| 277 | #2249 | — | 4 | 2 | no | — |
| 278 | #2249 | — | 4 | 2 | no | — |
| 279 | #2249 | — | 4 | 2 | no | — |
| 280 | #2248 | — | 4 | 2 | no | — |
| 281 | #2248 | — | 4 | 2 | no | — |
| 282 | #2247 | — | 2 | 2 | no | — |
| 283 | #2247 | — | 2 | 2 | no | — |
| 284 | #2246 | — | 2 | 2 | no | — |
| 285 | #2246 | — | 2 | 2 | no | — |
| 286 | #2246 | — | 8 | 2 | no | — |
| 287 | #2240 | — | 8 | 2 | no | — |
| 288 | #2240 | — | 8 | 2 | no | — |
| 289 | #2223 | — | 8 | 4 | no | — |
| 290 | #2222 | — | 4 | 4 | no | — |
| 291 | #2221 | — | 4 | 4 | no | — |
| 292 | #2215 | — | 16 | 4 | no | — |
| 293 | #2214 | — | 4 | 4 | no | — |
| 294 | #2213 | — | 4 | 4 | no | — |
| 295 | #2212 | — | 8 | 4 | no | — |
| 296 | #2195 | — | 8 | 4 | no | — |
| 297 | #2194 | — | 8 | 4 | no | — |
| 298 | #2193 | — | 8 | 4 | no | — |
| 299 | #2192 | — | 8 | 4 | no | — |
| 300 | #2179 | — | 8 | 4 | no | — |
| 301 | #2178 | — | 2 | 2 | no | — |
| 302 | #2178 | — | 2 | 2 | no | — |
| 303 | #2178 | — | 16 | 2 | no | — |
| 304 | #2178 | C4×D4 | 1 | 4 | yes | — |
| 305 | #2178 | #135 | 1 | 4 | yes | — |
| 306 | #2177 | — | 8 | 2 | no | — |
| 307 | #2176 | — | 8 | 2 | no | — |
| 308 | C4×SD32 | — | 16 | 2 | no | — |
| 309 | C4×D16 | — | 16 | 4 | no | — |
| 310 | #2170 | — | 2 | 4 | no | — |
| 311 | #2170 | — | 2 | 4 | no | — |
| 312 | #2170 | — | 4 | 2 | no | — |
| 313 | #2170 | — | 4 | 2 | no | — |
| 314 | C2×#368 | C2×D8 | 1 | 2 | yes | — |
| 315 | C2×#368 | C2×D8 | 1 | 2 | yes | — |
| 316 | #2159 | — | 8 | 2 | no | — |
| 317 | #2159 | — | 16 | 2 | no | — |
| 318 | #2158 | — | 8 | 2 | no | — |
| 319 | #2158 | C2×D8 | 1 | 2 | yes | — |
| 320 | C2×#367 | — | 4 | 2 | no | — |
| 321 | C2×#367 | — | 4 | 2 | no | — |
| 322 | C2×#367 | — | 4 | 2 | no | — |
| 323 | C2×#367 | — | 4 | 2 | no | — |
| 324 | C2×#367 | — | 8 | 2 | no | — |
| 325 | C2×#367 | — | 16 | 4 | no | — |
| 326 | C2×#364 | — | 2 | 2 | no | — |
| 327 | C2×#364 | — | 2 | 2 | no | — |
| 328 | #2148 | — | 8 | 2 | no | — |
| 329 | #2145 | — | 8 | 2 | no | — |
| 330 | #2143 | — | 8 | 2 | no | — |
| 331 | C2×#359 | — | 2 | 2 | no | — |
| 332 | #2139 | — | 8 | 2 | no | — |
| 333 | C2×#350 | — | 4 | 2 | no | — |
| 334 | #2108 | — | 4 | 2 | no | — |
| 335 | C2×C4×C16 | — | 2 | 2 | no | — |
| 336 | C2×C4×C16 | C22×D4 | 1 | 2 | yes | — |
| 337 | #1976 | — | 8 | 2 | no | — |
| 338 | #1952 | — | 8 | 2 | no | — |
| 339 | #1884 | — | 16 | 1 | no | — |
| 340 | #1859 | — | 16 | 2 | no | — |
| 341 | #1845 | — | 4 | 2 | no | — |
| 342 | #1845 | — | 8 | 2 | no | — |
| 343 | #1816 | — | 8 | 2 | no | — |
| 344 | #1772 | — | 2 | 2 | no | — |
| 345 | #1713 | — | 2 | 1 | no | — |
| 346 | #1713 | — | 2 | 1 | no | — |
| 347 | #1712 | — | 2 | 1 | no | — |
| 348 | #1712 | — | 2 | 1 | no | — |
| 349 | #1709 | — | 4 | 1 | no | — |
| 350 | #1709 | — | 4 | 1 | no | — |
| 351 | #1706 | — | 8 | 1 | no | — |
| 352 | #1706 | — | 8 | 1 | no | — |
| 353 | C2×C82 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 354 | #1426 | — | 8 | 4 | no | — |
| 355 | #1422 | — | 2 | 4 | no | — |
| 356 | #1422 | — | 4 | 2 | no | — |
| 357 | #1422 | — | 4 | 2 | no | — |
| 358 | #1422 | — | 4 | 2 | no | — |
| 359 | #1420 | — | 2 | 2 | no | — |
| 360 | #1420 | — | 4 | 4 | no | — |
| 361 | #1419 | — | 2 | 2 | no | — |
| 362 | #1419 | — | 4 | 4 | no | — |
| 363 | #1418 | — | 2 | 4 | no | — |
| 364 | #1418 | — | 8 | 2 | no | — |
| 365 | #1418 | — | 8 | 2 | no | — |
| 366 | #1418 | — | 8 | 4 | no | — |
| 367 | #1418 | — | 8 | 4 | no | — |
| 368 | #1418 | — | 8 | 4 | no | — |
| 369 | #1418 | — | 16 | 2 | no | — |
| 370 | #1418 | — | 16 | 2 | no | — |
| 371 | #1418 | — | 16 | 4 | no | — |
| 372 | #1418 | — | 16 | 4 | no | — |
| 373 | #1417 | — | 16 | 2 | no | — |
| 374 | #1401 | — | 8 | 4 | no | — |
| 375 | #1398 | — | 8 | 4 | no | — |
| 376 | #1397 | — | 2 | 2 | no | — |
| 377 | #1397 | — | 2 | 2 | no | — |
| 378 | C4×C32 | — | 2 | 2 | no | — |
| 379 | C4×C32 | — | 2 | 2 | no | — |
| 380 | #1387 | — | 8 | 2 | no | — |
| 381 | #1387 | — | 8 | 2 | no | — |
| 382 | #1382 | — | 2 | 2 | no | — |
| 383 | #1379 | — | 4 | 2 | no | — |
| 384 | #1373 | — | 2 | 2 | no | — |
| 385 | #1373 | — | 2 | 2 | no | — |
| 386 | #1373 | — | 2 | 2 | no | — |
| 387 | #1373 | C4×D4 | 1 | 4 | yes | — |
| 388 | #1359 | — | 16 | 1 | no | — |
| 389 | #1358 | — | 4 | 2 | no | — |
| 390 | #1357 | — | 4 | 2 | no | — |
| 391 | #1335 | — | 2 | 4 | no | — |
| 392 | #1335 | — | 2 | 4 | no | — |
| 393 | C8×C16 | — | 2 | 2 | no | — |
| 394 | C8×C16 | — | 2 | 1 | no | — |
| 395 | C8×C16 | — | 2 | 1 | no | — |
| 396 | C8×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 397 | C8×C16 | C2×#41 | 1 | 2 | yes | — |
| 398 | C8×C16 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 399 | #585 | — | 16 | 1 | no | — |
| 400 | #578 | — | 8 | 4 | no | — |
| 401 | #578 | — | 16 | 2 | no | — |
| 402 | #577 | — | 16 | 4 | no | — |
| 403 | #577 | — | 32 | 2 | no | — |
| 404 | #576 | — | 8 | 4 | no | — |
| 405 | #576 | — | 16 | 2 | no | — |
| 406 | #575 | — | 16 | 2 | no | — |
| 407 | #575 | — | 32 | 2 | no | — |
| 408 | C2×#135 | — | 2 | 2 | no | — |
| 409 | C2×#135 | — | 8 | 2 | no | — |
| 410 | C2×#135 | — | 8 | 2 | no | — |
| 411 | C2×#135 | — | 16 | 4 | no | — |
| 412 | #568 | — | 16 | 1 | no | — |
| 413 | C2×#131 | — | 4 | 2 | no | — |
| 414 | #532 | — | 8 | 1 | no | — |
| 415 | #532 | — | 8 | 1 | no | — |
| 416 | #520 | — | 16 | 2 | no | — |
| 417 | #510 | — | 8 | 4 | no | — |
| 418 | #510 | — | 16 | 4 | no | — |
| 419 | #510 | — | 16 | 4 | no | — |
| 420 | #510 | — | 16 | 2 | no | — |
| 421 | #509 | — | 8 | 4 | no | — |
| 422 | #509 | — | 16 | 4 | no | — |
| 423 | #509 | — | 16 | 4 | no | — |
| 424 | #509 | — | 16 | 2 | no | — |
| 425 | #508 | — | 2 | 2 | no | — |
| 426 | #508 | — | 2 | 2 | no | — |
| 427 | #508 | — | 8 | 4 | no | — |
| 428 | #508 | — | 8 | 4 | no | — |
| 429 | #508 | — | 8 | 2 | no | — |
| 430 | #508 | — | 8 | 2 | no | — |
| 431 | #508 | — | 8 | 2 | no | — |
| 432 | #508 | — | 8 | 2 | no | — |
| 433 | #508 | — | 8 | 2 | no | — |
| 434 | #508 | — | 8 | 2 | no | — |
| 435 | #508 | — | 8 | 2 | no | — |
| 436 | #508 | — | 8 | 2 | no | — |
| 437 | #508 | — | 16 | 2 | no | — |
| 438 | #508 | — | 16 | 2 | no | — |
| 439 | #508 | — | 16 | 2 | no | — |
| 440 | #508 | — | 16 | 2 | no | — |
| 441 | #508 | — | 16 | 4 | no | — |
| 442 | #508 | — | 16 | 4 | no | — |
| 443 | #508 | C4×D8 | 1 | 4 | yes | — |
| 444 | #508 | #509 | 1 | 4 | yes | — |
| 445 | C2×Q32 | — | 4 | 2 | no | — |
| 446 | C2×Q32 | — | 4 | 2 | no | — |
| 447 | C2×Q32 | — | 4 | 2 | no | — |
| 448 | C2×Q32 | — | 4 | 2 | no | — |
| 449 | C2×Q32 | — | 8 | 4 | no | — |
| 450 | C2×Q32 | #509 | 1 | 2 | yes | — |
| 451 | C2×SD32 | — | 2 | 2 | no | — |
| 452 | C2×SD32 | — | 8 | 2 | no | — |
| 453 | C2×SD32 | — | 8 | 2 | no | — |
| 454 | C2×SD32 | — | 8 | 2 | no | — |
| 455 | C2×SD32 | — | 8 | 2 | no | — |
| 456 | C2×SD32 | — | 16 | 4 | no | — |
| 457 | C2×D16 | — | 4 | 2 | no | — |
| 458 | C2×D16 | — | 4 | 2 | no | — |
| 459 | C2×D16 | — | 4 | 2 | no | — |
| 460 | C2×D16 | — | 4 | 2 | no | — |
| 461 | C2×D16 | — | 8 | 4 | no | — |
| 462 | C2×D16 | — | 16 | 4 | no | — |
| 463 | C2×D16 | #509 | 1 | 2 | yes | — |
| 464 | #504 | — | 4 | 4 | no | — |
| 465 | #504 | — | 4 | 4 | no | — |
| 466 | #504 | — | 8 | 2 | no | — |
| 467 | #504 | — | 8 | 2 | no | — |
| 468 | C2×M32 | — | 4 | 2 | no | — |
| 469 | C2×M32 | — | 4 | 2 | no | — |
| 470 | C2×M32 | — | 8 | 2 | no | — |
| 471 | C22×C16 | — | 2 | 4 | no | — |
| 472 | C22×C16 | — | 8 | 2 | no | — |
| 473 | C22×C16 | C22×D8 | 1 | 2 | yes | — |
| 474 | C22×C16 | #576 | 1 | 2 | yes | — |
| 475 | #500 | — | 8 | 1 | no | — |
| 476 | #500 | — | 8 | 1 | no | — |
| 477 | #495 | — | 8 | 2 | no | — |
| 478 | #495 | — | 8 | 2 | no | — |
| 479 | #494 | — | 4 | 1 | no | — |
| 480 | #494 | — | 4 | 1 | no | — |
| 481 | #493 | — | 4 | 1 | no | — |
| 482 | #493 | — | 4 | 1 | no | — |
| 483 | #493 | — | 8 | 1 | no | — |
| 484 | #493 | — | 8 | 1 | no | — |
| 485 | #492 | — | 8 | 1 | no | — |
| 486 | #492 | — | 8 | 1 | no | — |
| 487 | #486 | — | 16 | 1 | no | — |
| 488 | #486 | — | 16 | 1 | no | — |
| 489 | #473 | — | 8 | 4 | no | — |
| 490 | #472 | — | 8 | 4 | no | — |
| 491 | #471 | — | 16 | 4 | no | — |
| 492 | #466 | — | 16 | 2 | no | — |
| 493 | #466 | — | 16 | 2 | no | — |
| 494 | #456 | — | 16 | 2 | no | — |
| 495 | #455 | — | 16 | 2 | no | — |
| 496 | #454 | — | 16 | 2 | no | — |
| 497 | #453 | — | 16 | 2 | no | — |
| 498 | #444 | — | 32 | 2 | no | — |
| 499 | #443 | — | 2 | 4 | no | — |
| 500 | #443 | — | 2 | 4 | no | — |
| 501 | #443 | — | 4 | 2 | no | — |
| 502 | #443 | — | 4 | 2 | no | — |
| 503 | #443 | — | 16 | 4 | no | — |
| 504 | #440 | — | 32 | 2 | no | — |
| 505 | C4×Q16 | — | 16 | 2 | no | — |
| 506 | C4×D8 | — | 16 | 2 | no | — |
| 507 | C4×D8 | — | 16 | 2 | no | — |
| 508 | C4×D8 | — | 16 | 2 | no | — |
| 509 | C2×#108 | — | 2 | 2 | no | — |
| 510 | C2×#108 | — | 2 | 2 | no | — |
| 511 | #428 | — | 16 | 2 | no | — |
| 512 | #428 | — | 32 | 2 | no | — |
| 513 | #427 | — | 2 | 2 | no | — |
| 514 | #427 | — | 16 | 2 | no | — |
| 515 | C2×#107 | — | 8 | 2 | no | — |
| 516 | C2×#107 | — | 8 | 2 | no | — |
| 517 | C2×#107 | — | 16 | 2 | no | — |
| 518 | C2×#107 | — | 16 | 4 | no | — |
| 519 | #421 | — | 16 | 2 | no | — |
| 520 | C2×#104 | — | 4 | 2 | no | — |
| 521 | #417 | — | 16 | 2 | no | — |
| 522 | #413 | — | 16 | 1 | no | — |
| 523 | #410 | — | 16 | 1 | no | — |
| 524 | #405 | — | 4 | 2 | no | — |
| 525 | C2×C4×C8 | — | 2 | 1 | no | — |
| 526 | C2×C4×C8 | D42 | 1 | 1 | yes | characteristic |
| 527 | #384 | — | 8 | 2 | no | — |
| 528 | Q64 | — | 8 | 4 | no | — |
| 529 | SD64 | — | 8 | 4 | no | — |
| 530 | SD64 | — | 8 | 4 | no | — |
| 531 | D32 | — | 8 | 4 | no | — |
| 532 | M64 | — | 2 | 2 | no | — |
| 533 | M64 | — | 2 | 2 | no | — |
| 534 | M64 | — | 2 | 2 | no | — |
| 535 | M64 | — | 2 | 2 | no | — |
| 536 | M64 | — | 4 | 2 | no | — |
| 537 | M64 | — | 4 | 2 | no | — |
| 538 | M64 | — | 4 | 4 | no | — |
| 539 | M64 | — | 8 | 2 | no | — |
| 540 | M64 | — | 8 | 2 | no | — |
| 541 | M64 | — | 8 | 2 | no | — |
| 542 | M64 | — | 16 | 4 | no | — |
| 543 | C2×C32 | — | 2 | 2 | no | — |
| 544 | C2×C32 | — | 2 | 2 | no | — |
| 545 | C2×C32 | — | 4 | 2 | no | — |
| 546 | C2×C32 | — | 8 | 2 | no | — |
| 547 | C2×C32 | — | 8 | 2 | no | — |
| 548 | C2×C32 | — | 16 | 4 | no | — |
| 549 | #368 | — | 2 | 2 | no | — |
| 550 | #368 | — | 2 | 2 | no | — |
| 551 | #368 | — | 2 | 2 | no | — |
| 552 | #368 | C4×D8 | 1 | 4 | yes | — |
| 553 | #367 | — | 2 | 2 | no | — |
| 554 | #367 | — | 8 | 2 | no | — |
| 555 | #367 | — | 8 | 2 | no | — |
| 556 | #367 | — | 8 | 2 | no | — |
| 557 | #367 | — | 8 | 2 | no | — |
| 558 | #367 | — | 16 | 2 | no | — |
| 559 | #367 | — | 16 | 2 | no | — |
| 560 | #367 | — | 16 | 2 | no | — |
| 561 | #367 | — | 32 | 8 | no | — |
| 562 | #366 | — | 2 | 2 | no | — |
| 563 | #366 | — | 16 | 2 | no | — |
| 564 | #366 | — | 16 | 4 | no | — |
| 565 | #364 | — | 2 | 4 | no | — |
| 566 | #364 | — | 4 | 2 | no | — |
| 567 | #364 | — | 4 | 2 | no | — |
| 568 | #364 | — | 4 | 2 | no | — |
| 569 | #362 | — | 8 | 4 | no | — |
| 570 | #361 | — | 8 | 4 | no | — |
| 571 | #360 | — | 32 | 2 | no | — |
| 572 | #359 | — | 2 | 4 | no | — |
| 573 | #359 | — | 2 | 4 | no | — |
| 574 | #359 | — | 16 | 4 | no | — |
| 575 | #358 | — | 16 | 2 | no | — |
| 576 | #357 | — | 16 | 4 | no | — |
| 577 | #357 | — | 16 | 4 | no | — |
| 578 | #357 | — | 16 | 2 | no | — |
| 579 | #350 | — | 4 | 4 | no | — |
| 580 | #350 | — | 4 | 4 | no | — |
| 581 | #346 | — | 8 | 2 | no | — |
| 582 | C4×C16 | — | 2 | 2 | no | — |
| 583 | C4×C16 | — | 2 | 2 | no | — |
| 584 | C4×C16 | — | 2 | 4 | no | — |
| 585 | C4×C16 | — | 8 | 2 | no | — |
| 586 | C4×C16 | C2×C4×D4 | 1 | 2 | yes | — |
| 587 | C4×C16 | #546 | 1 | 2 | yes | — |
| 588 | C4×C16 | C2×#135 | 1 | 2 | yes | — |
| 589 | C4×C16 | #577 | 1 | 2 | yes | — |
| 590 | #343 | — | 16 | 2 | no | — |
| 591 | #339 | — | 4 | 2 | no | — |
| 592 | C82 | — | 2 | 1 | no | — |
| 593 | C82 | #518 | 1 | 1 | yes | characteristic |
| 594 | C82 | #551 | 1 | 1 | yes | characteristic |
| 595 | 2−1+4 | — | 16 | 2 | no | — |
| 596 | 2−1+4 | — | 32 | 2 | no | — |
| 597 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 598 | H(5,𝔽2) | — | 32 | 2 | no | — |
| 599 | H(5,𝔽2) | — | 64 | 1 | no | — |
| 600 | C2×#41 | — | 4 | 2 | no | — |
| 601 | C2×#41 | — | 16 | 1 | no | — |
| 602 | C2×#41 | — | 16 | 1 | no | — |
| 603 | C2×#41 | — | 32 | 4 | no | — |
| 604 | C2×#41 | — | 64 | 1 | no | — |
| 605 | #137 | — | 16 | 4 | no | — |
| 606 | #137 | — | 32 | 4 | no | — |
| 607 | #137 | — | 32 | 4 | no | — |
| 608 | #137 | — | 32 | 2 | no | — |
| 609 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 610 | AGL(1,ℤ/8) | — | 32 | 4 | no | — |
| 611 | AGL(1,ℤ/8) | — | 32 | 4 | no | — |
| 612 | AGL(1,ℤ/8) | — | 32 | 2 | no | — |
| 613 | #135 | — | 2 | 4 | no | — |
| 614 | #135 | — | 2 | 4 | no | — |
| 615 | #135 | — | 4 | 2 | no | — |
| 616 | #135 | — | 4 | 2 | no | — |
| 617 | #135 | — | 16 | 4 | no | — |
| 618 | #135 | — | 16 | 4 | no | — |
| 619 | #135 | — | 16 | 2 | no | — |
| 620 | #135 | — | 16 | 2 | no | — |
| 621 | #135 | — | 16 | 2 | no | — |
| 622 | #135 | — | 16 | 2 | no | — |
| 623 | #135 | — | 16 | 2 | no | — |
| 624 | #135 | — | 16 | 2 | no | — |
| 625 | #135 | — | 16 | 2 | no | — |
| 626 | #135 | — | 16 | 2 | no | — |
| 627 | #135 | — | 32 | 4 | no | — |
| 628 | #135 | — | 32 | 4 | no | — |
| 629 | C2×Q16 | — | 2 | 2 | no | — |
| 630 | C2×Q16 | — | 8 | 2 | no | — |
| 631 | C2×Q16 | — | 8 | 2 | no | — |
| 632 | C2×Q16 | — | 16 | 4 | no | — |
| 633 | C2×SD16 | — | 4 | 2 | no | — |
| 634 | C2×SD16 | — | 16 | 2 | no | — |
| 635 | C2×SD16 | — | 16 | 2 | no | — |
| 636 | C2×SD16 | — | 32 | 4 | no | — |
| 637 | C2×D8 | — | 2 | 2 | no | — |
| 638 | C2×D8 | — | 8 | 2 | no | — |
| 639 | C2×D8 | — | 8 | 2 | no | — |
| 640 | C2×D8 | — | 16 | 2 | no | — |
| 641 | C2×D8 | — | 16 | 2 | no | — |
| 642 | C2×D8 | — | 16 | 4 | no | — |
| 643 | #131 | — | 4 | 4 | no | — |
| 644 | #131 | — | 4 | 4 | no | — |
| 645 | #131 | — | 8 | 2 | no | — |
| 646 | #131 | — | 8 | 2 | no | — |
| 647 | #131 | — | 32 | 4 | no | — |
| 648 | C2×M16 | — | 4 | 2 | no | — |
| 649 | C2×M16 | — | 4 | 2 | no | — |
| 650 | C2×M16 | — | 8 | 2 | no | — |
| 651 | C2×M16 | — | 64 | 1 | no | — |
| 652 | C22×C8 | — | 2 | 2 | no | — |
| 653 | C22×C8 | — | 8 | 2 | no | — |
| 654 | C22×C8 | D4×D8 | 1 | 2 | yes | — |
| 655 | C4⋊Q8 | — | 8 | 1 | no | — |
| 656 | C4⋊Q8 | — | 8 | 1 | no | — |
| 657 | #127 | — | 8 | 1 | no | — |
| 658 | #127 | — | 8 | 1 | no | — |
| 659 | #124 | — | 16 | 1 | no | — |
| 660 | #124 | — | 16 | 1 | no | — |
| 661 | #121 | — | 32 | 1 | no | — |
| 662 | #121 | — | 32 | 1 | no | — |
| 663 | C4×Q8 | — | 32 | 2 | no | — |
| 664 | C4×D4 | — | 32 | 1 | no | — |
| 665 | C4×D4 | — | 32 | 1 | no | — |
| 666 | C4×D4 | — | 32 | 2 | no | — |
| 667 | C4×D4 | — | 64 | 2 | no | — |
| 668 | #117 | — | 4 | 2 | no | — |
| 669 | #117 | — | 32 | 2 | no | — |
| 670 | C2×C4⋊C4 | — | 16 | 2 | no | — |
| 671 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 672 | C2×C4⋊C4 | — | 32 | 2 | no | — |
| 673 | C2×C42 | #3292 | 1 | 1 | yes | characteristic |
| 674 | Q32 | — | 2 | 2 | no | — |
| 675 | Q32 | — | 8 | 2 | no | — |
| 676 | Q32 | — | 8 | 2 | no | — |
| 677 | Q32 | — | 8 | 2 | no | — |
| 678 | Q32 | — | 8 | 2 | no | — |
| 679 | Q32 | — | 16 | 2 | no | — |
| 680 | Q32 | — | 16 | 2 | no | — |
| 681 | Q32 | — | 16 | 4 | no | — |
| 682 | Q32 | #2177 | 1 | 4 | yes | — |
| 683 | SD32 | — | 2 | 4 | no | — |
| 684 | SD32 | — | 2 | 4 | no | — |
| 685 | SD32 | — | 16 | 4 | no | — |
| 686 | SD32 | — | 16 | 4 | no | — |
| 687 | SD32 | — | 16 | 2 | no | — |
| 688 | SD32 | — | 16 | 2 | no | — |
| 689 | SD32 | — | 16 | 2 | no | — |
| 690 | SD32 | — | 16 | 2 | no | — |
| 691 | SD32 | — | 32 | 2 | no | — |
| 692 | SD32 | — | 32 | 2 | no | — |
| 693 | D16 | — | 2 | 2 | no | — |
| 694 | D16 | — | 8 | 2 | no | — |
| 695 | D16 | — | 8 | 2 | no | — |
| 696 | D16 | — | 8 | 2 | no | — |
| 697 | D16 | — | 8 | 2 | no | — |
| 698 | D16 | — | 16 | 2 | no | — |
| 699 | D16 | — | 16 | 2 | no | — |
| 700 | D16 | — | 16 | 4 | no | — |
| 701 | D16 | — | 32 | 8 | no | — |
| 702 | D16 | #2177 | 1 | 4 | yes | — |
| 703 | M32 | — | 4 | 4 | no | — |
| 704 | M32 | — | 8 | 2 | no | — |
| 705 | M32 | — | 8 | 4 | no | — |
| 706 | M32 | — | 8 | 4 | no | — |
| 707 | M32 | — | 8 | 2 | no | — |
| 708 | M32 | — | 8 | 2 | no | — |
| 709 | C2×C16 | — | 2 | 4 | no | — |
| 710 | C2×C16 | — | 2 | 2 | no | — |
| 711 | C2×C16 | — | 2 | 2 | no | — |
| 712 | C2×C16 | — | 2 | 4 | no | — |
| 713 | C2×C16 | — | 4 | 8 | no | — |
| 714 | C2×C16 | — | 8 | 2 | no | — |
| 715 | C2×C16 | — | 8 | 4 | no | — |
| 716 | C2×C16 | — | 8 | 4 | no | — |
| 717 | C2×C16 | — | 8 | 2 | no | — |
| 718 | C2×C16 | C2×C4×D8 | 1 | 2 | yes | — |
| 719 | C2×C16 | #2946 | 1 | 2 | yes | — |
| 720 | C2×C16 | #3294 | 1 | 2 | yes | — |
| 721 | C2×C16 | #3297 | 1 | 2 | yes | — |
| 722 | C2×C16 | C2×#509 | 1 | 2 | yes | — |
| 723 | C2×C16 | C2×#509 | 1 | 2 | yes | — |
| 724 | C2×C16 | #3415 | 1 | 2 | yes | — |
| 725 | C2×C16 | #3416 | 1 | 2 | yes | — |
| 726 | #108 | — | 2 | 4 | no | — |
| 727 | #108 | — | 4 | 2 | no | — |
| 728 | #108 | — | 4 | 2 | no | — |
| 729 | #108 | — | 4 | 2 | no | — |
| 730 | #107 | — | 4 | 2 | no | — |
| 731 | #107 | — | 16 | 2 | no | — |
| 732 | #107 | — | 16 | 2 | no | — |
| 733 | #107 | — | 16 | 2 | no | — |
| 734 | #107 | — | 16 | 2 | no | — |
| 735 | #107 | — | 16 | 2 | no | — |
| 736 | #107 | — | 16 | 2 | no | — |
| 737 | #107 | — | 32 | 2 | no | — |
| 738 | #107 | — | 32 | 8 | no | — |
| 739 | #106 | — | 4 | 2 | no | — |
| 740 | #106 | — | 32 | 2 | no | — |
| 741 | #104 | — | 4 | 4 | no | — |
| 742 | #104 | — | 4 | 4 | no | — |
| 743 | #104 | — | 32 | 4 | no | — |
| 744 | #103 | — | 32 | 2 | no | — |
| 745 | #102 | — | 32 | 2 | no | — |
| 746 | #102 | — | 32 | 2 | no | — |
| 747 | #102 | — | 32 | 2 | no | — |
| 748 | #101 | — | 16 | 2 | no | — |
| 749 | #100 | — | 16 | 2 | no | — |
| 750 | #99 | — | 64 | 1 | no | — |
| 751 | #97 | — | 8 | 2 | no | — |
| 752 | C4×C8 | — | 2 | 2 | no | — |
| 753 | C4×C8 | — | 2 | 1 | no | — |
| 754 | C4×C8 | — | 2 | 1 | no | — |
| 755 | C4×C8 | — | 8 | 2 | no | — |
| 756 | C4×C8 | #2358 | 1 | 1 | yes | characteristic |
| 757 | C4×C8 | #3282 | 1 | 2 | yes | — |
| 758 | C4×C8 | #3291 | 1 | 1 | yes | characteristic |
| 759 | C32 | — | 4 | 2 | no | — |
| 760 | C32 | — | 4 | 2 | no | — |
| 761 | C32 | — | 8 | 2 | no | — |
| 762 | C32 | — | 8 | 4 | no | — |
| 763 | C32 | — | 16 | 2 | no | — |
| 764 | #41 | — | 4 | 4 | no | — |
| 765 | #41 | — | 4 | 4 | no | — |
| 766 | #41 | — | 8 | 2 | no | — |
| 767 | #41 | — | 8 | 2 | no | — |
| 768 | #41 | — | 32 | 4 | no | — |
| 769 | #41 | — | 32 | 4 | no | — |
| 770 | #41 | — | 32 | 2 | no | — |
| 771 | #41 | — | 32 | 2 | no | — |
| 772 | #41 | — | 32 | 2 | no | — |
| 773 | #41 | — | 32 | 2 | no | — |
| 774 | #41 | — | 64 | 2 | no | — |
| 775 | #41 | — | 64 | 4 | no | — |
| 776 | #41 | — | 64 | 2 | no | — |
| 777 | #41 | — | 64 | 2 | no | — |
| 778 | C2×Q8 | — | 4 | 2 | no | — |
| 779 | C2×Q8 | — | 16 | 1 | no | — |
| 780 | C2×Q8 | — | 16 | 1 | no | — |
| 781 | C2×Q8 | — | 32 | 4 | no | — |
| 782 | C2×Q8 | — | 64 | 1 | no | — |
| 783 | C2×D4 | — | 4 | 2 | no | — |
| 784 | C2×D4 | — | 8 | 2 | no | — |
| 785 | C2×D4 | — | 16 | 1 | no | — |
| 786 | C2×D4 | — | 16 | 1 | no | — |
| 787 | C2×D4 | — | 32 | 1 | no | — |
| 788 | C2×D4 | — | 32 | 1 | no | — |
| 789 | C2×D4 | — | 32 | 4 | no | — |
| 790 | C2×D4 | — | 32 | 1 | no | — |
| 791 | C2×D4 | — | 32 | 1 | no | — |
| 792 | C2×D4 | — | 64 | 2 | no | — |
| 793 | C2×D4 | — | 64 | 1 | no | — |
| 794 | C2×D4 | — | 64 | 4 | no | — |
| 795 | C22×C4 | — | 2 | 1 | no | — |
| 796 | C22×C4 | — | 8 | 2 | no | — |
| 797 | C22×C4 | — | 32 | 1 | no | — |
| 798 | C22×C4 | — | 32 | 1 | no | — |
| 799 | C22×C4 | — | 32 | 2 | no | — |
| 800 | C22×C4 | — | 64 | 2 | no | — |
| 801 | C22×C4 | — | 64 | 2 | no | — |
| 802 | C22×C4 | D82 | 1 | 1 | yes | characteristic |
| 803 | Q16 | — | 2 | 4 | no | — |
| 804 | Q16 | — | 4 | 2 | no | — |
| 805 | Q16 | — | 16 | 2 | no | — |
| 806 | Q16 | — | 16 | 2 | no | — |
| 807 | Q16 | — | 16 | 2 | no | — |
| 808 | Q16 | — | 16 | 2 | no | — |
| 809 | Q16 | — | 32 | 4 | no | — |
| 810 | SD16 | — | 4 | 4 | no | — |
| 811 | SD16 | — | 4 | 4 | no | — |
| 812 | SD16 | — | 32 | 4 | no | — |
| 813 | SD16 | — | 32 | 4 | no | — |
| 814 | SD16 | — | 32 | 2 | no | — |
| 815 | SD16 | — | 32 | 2 | no | — |
| 816 | SD16 | — | 32 | 2 | no | — |
| 817 | SD16 | — | 32 | 2 | no | — |
| 818 | D8 | — | 2 | 4 | no | — |
| 819 | D8 | — | 4 | 2 | no | — |
| 820 | D8 | — | 16 | 2 | no | — |
| 821 | D8 | — | 16 | 2 | no | — |
| 822 | D8 | — | 16 | 2 | no | — |
| 823 | D8 | — | 16 | 2 | no | — |
| 824 | D8 | — | 32 | 4 | no | — |
| 825 | D8 | — | 32 | 4 | no | — |
| 826 | D8 | — | 32 | 4 | no | — |
| 827 | M16 | — | 4 | 4 | no | — |
| 828 | M16 | — | 8 | 2 | no | — |
| 829 | M16 | — | 8 | 4 | no | — |
| 830 | M16 | — | 8 | 4 | no | — |
| 831 | M16 | — | 8 | 2 | no | — |
| 832 | M16 | — | 8 | 2 | no | — |
| 833 | M16 | — | 64 | 2 | no | — |
| 834 | C2×C8 | — | 2 | 2 | no | — |
| 835 | C2×C8 | — | 2 | 2 | no | — |
| 836 | C2×C8 | — | 4 | 4 | no | — |
| 837 | C2×C8 | — | 8 | 2 | no | — |
| 838 | C2×C8 | — | 8 | 4 | no | — |
| 839 | C2×C8 | — | 8 | 4 | no | — |
| 840 | C2×C8 | — | 8 | 2 | no | — |
| 841 | C2×C8 | — | 64 | 2 | no | — |
| 842 | C2×C8 | #19970 | 1 | 2 | yes | — |
| 843 | C2×C8 | #22870 | 1 | 2 | yes | — |
| 844 | C2×C8 | #33830 | 1 | 2 | yes | — |
| 845 | C2×C8 | #33831 | 1 | 2 | yes | — |
| 846 | C2×C8 | #33854 | 1 | 2 | yes | — |
| 847 | C2×C8 | #33854 | 1 | 2 | yes | — |
| 848 | C4⋊C4 | — | 8 | 2 | no | — |
| 849 | C4⋊C4 | — | 32 | 1 | no | — |
| 850 | C4⋊C4 | — | 32 | 1 | no | — |
| 851 | C4⋊C4 | — | 32 | 2 | no | — |
| 852 | C4⋊C4 | — | 32 | 2 | no | — |
| 853 | C4⋊C4 | — | 64 | 4 | no | — |
| 854 | C4⋊C4 | — | 64 | 2 | no | — |
| 855 | C22⋊C4 | — | 8 | 2 | no | — |
| 856 | C22⋊C4 | — | 64 | 1 | no | — |
| 857 | C22⋊C4 | — | 64 | 1 | no | — |
| 858 | C22⋊C4 | — | 64 | 2 | no | — |
| 859 | C42 | — | 2 | 1 | no | — |
| 860 | C42 | — | 8 | 2 | no | — |
| 861 | C42 | — | 64 | 2 | no | — |
| 862 | C42 | #19996 | 1 | 1 | yes | characteristic |
| 863 | C42 | #22897 | 1 | 1 | yes | characteristic |
| 864 | C16 | — | 2 | 8 | no | — |
| 865 | C16 | — | 2 | 2 | no | — |
| 866 | C16 | — | 2 | 2 | no | — |
| 867 | C16 | — | 4 | 4 | no | — |
| 868 | C16 | — | 8 | 4 | no | — |
| 869 | C16 | — | 16 | 2 | no | — |
| 870 | C16 | C2×#2177 | 1 | 2 | yes | — |
| 871 | C16 | #33454 | 1 | 2 | yes | — |
| 872 | C16 | #33873 | 1 | 2 | yes | — |
| 873 | C16 | #33885 | 1 | 2 | yes | — |
| 874 | C23 | — | 8 | 2 | no | — |
| 875 | C23 | — | 32 | 1 | no | — |
| 876 | C23 | — | 32 | 1 | no | — |
| 877 | C23 | — | 64 | 2 | no | — |
| 878 | C23 | #492532 | 1 | 1 | yes | characteristic |
| 879 | Q8 | — | 4 | 4 | no | — |
| 880 | Q8 | — | 8 | 2 | no | — |
| 881 | Q8 | — | 32 | 2 | no | — |
| 882 | Q8 | — | 32 | 2 | no | — |
| 883 | Q8 | — | 64 | 2 | no | — |
| 884 | D4 | — | 4 | 4 | no | — |
| 885 | D4 | — | 8 | 4 | no | — |
| 886 | D4 | — | 8 | 4 | no | — |
| 887 | D4 | — | 8 | 2 | no | — |
| 888 | D4 | — | 32 | 2 | no | — |
| 889 | D4 | — | 32 | 2 | no | — |
| 890 | D4 | — | 64 | 2 | no | — |
| 891 | D4 | — | 64 | 2 | no | — |
| 892 | D4 | — | 64 | 4 | no | — |
| 893 | D4 | — | 64 | 2 | no | — |
| 894 | D4 | — | 64 | 2 | no | — |
| 895 | D4 | — | 64 | 2 | no | — |
| 896 | C2×C4 | — | 256 | 2 | no | — |
| 897 | C2×C4 | — | 2 | 1 | no | — |
| 898 | C2×C4 | — | 2 | 1 | no | — |
| 899 | C2×C4 | — | 4 | 2 | no | — |
| 900 | C2×C4 | — | 8 | 2 | no | — |
| 901 | C2×C4 | — | 8 | 4 | no | — |
| 902 | C2×C4 | — | 8 | 4 | no | — |
| 903 | C2×C4 | — | 16 | 2 | no | — |
| 904 | C2×C4 | — | 32 | 1 | no | — |
| 905 | C2×C4 | — | 32 | 1 | no | — |
| 906 | C2×C4 | — | 64 | 2 | no | — |
| 907 | C2×C4 | — | 64 | 4 | no | — |
| 908 | C2×C4 | — | 64 | 1 | no | — |
| 909 | C2×C4 | — | 64 | 1 | no | — |
| 910 | C2×C4 | — | 64 | 1 | no | — |
| 911 | C2×C4 | — | 64 | 1 | no | — |
| 912 | C2×C4 | — | 64 | 2 | no | — |
| 913 | C2×C4 | — | 128 | 2 | no | — |
| 914 | C2×C4 | #226998 | 1 | 1 | yes | characteristic |
| 915 | C2×C4 | #492504 | 1 | 2 | yes | — |
| 916 | C2×C4 | #492505 | 1 | 2 | yes | — |
| 917 | C2×C4 | #492531 | 1 | 1 | yes | characteristic |
| 918 | C8 | — | 2 | 4 | no | — |
| 919 | C8 | — | 4 | 2 | no | — |
| 920 | C8 | — | 8 | 4 | no | — |
| 921 | C8 | — | 16 | 2 | no | — |
| 922 | C8 | #492646 | 1 | 2 | yes | — |
| 923 | C8 | #492650 | 1 | 2 | yes | — |
| 924 | C8 | #498148 | 1 | 2 | yes | — |
| 925 | C8 | #498170 | 1 | 2 | yes | — |
| 926 | C22 | — | 256 | 2 | no | — |
| 927 | C22 | — | 4 | 1 | no | — |
| 928 | C22 | — | 8 | 4 | no | — |
| 929 | C22 | — | 32 | 2 | no | — |
| 930 | C22 | — | 64 | 1 | no | — |
| 931 | C22 | — | 64 | 1 | no | — |
| 932 | C22 | — | 128 | 1 | no | — |
| 933 | C22 | — | 128 | 1 | no | — |
| 934 | C22 | #72216411 | 1 | 1 | yes | characteristic |
| 935 | C22 | #72226954 | 1 | 2 | yes | — |
| 936 | C4 | — | 2 | 2 | no | — |
| 937 | C4 | — | 4 | 1 | no | — |
| 938 | C4 | — | 8 | 4 | no | — |
| 939 | C4 | — | 32 | 2 | no | — |
| 940 | C4 | — | 64 | 1 | no | — |
| 941 | C4 | — | 64 | 1 | no | — |
| 942 | C4 | — | 128 | 2 | no | — |
| 943 | C4 | #72226892 | 1 | 2 | yes | — |
| 944 | C4 | #72226955 | 1 | 1 | yes | characteristic |
| 945 | C4 | #72226956 | 1 | 1 | yes | characteristic |
| 946 | C2 | — | 2 | 1 | no | — |
| 947 | C2 | — | 2 | 2 | no | — |
| 948 | C2 | — | 16 | 4 | no | — |
| 949 | C2 | — | 128 | 1 | no | — |
| 950 | C2 | — | 128 | 1 | no | — |
| 951 | C2 | #72226957 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72226957 |
| commutator | C8×C16 | C23×C4 |
| Frattini, cosocle | C2×C8×C16 | C24 |
| prime radical | #72225587 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72226930 | C2 | semidirect |
| 2. #72226915 | C2 | semidirect |
| 3. #72226888 | C2 | semidirect |
| 7. #72226878 | C2 | semidirect |
| 11. #72226855 | C2 | semidirect |
| 12. #72226852 | C22 | semidirect |
| 14. #72225586 | C4 | semidirect |
| 15. #72225585 | C4 | semidirect |
| 16. #72225584 | C4 | semidirect |
| 20. #72225406 | C22 | semidirect |
| 22. #72225385 | C2 | semidirect |
| 23. #72225373 | C22 | semidirect |
| 24. #72225363 | C22 | semidirect |
| 29. #72225194 | C2 | semidirect |
| 30. #72216560 | C22 | semidirect |
| 31. #72216534 | C22 | semidirect |
| 34. #72216382 | C2 | semidirect |
| 36. #72216290 | C22 | semidirect |
| 37. #72216273 | C22 | semidirect |
| 40. #72216220 | C22 | semidirect |
| 41. #72216197 | C22 | semidirect |
| 42. #72214187 | C4 | semidirect |
| 77. #151635 | C2×C4 | semidirect |
| 78. #151634 | C2×C4 | semidirect |
| 96. #123406 | C2×C4 | semidirect |
| 97. #123406 | C2×C4 | semidirect |
| 99. #123404 | C2×C4 | semidirect |
| 100. #123403 | C2×C4 | semidirect |
| 108. #93867 | C2×C4 | semidirect |
| 109. #93866 | C2×C4 | semidirect |
| 110. #93751 | C2×C4 | semidirect |
| 111. #93751 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72226930 | 2 |
| #72226915 | 2 |
| #72226888 | 2 |
| #72226878 | 2 |
| #72226855 | 2 |
| #72225587 | 2 |
| #72225385 | 2 |
| #72225194 | 2 |
| #72216382 | 2 |