Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1295 conjugacy classes of subgroups.
The subgroup lattice has 999 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6345864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #489285 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #483992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #483881 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #211864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #137499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #137060 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #137036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #136569 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #136481 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #136463 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #131813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #129029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #128691 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #128636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #61436 | C22 | 1 | 1 | yes | characteristic |
| 17 | #60308 | — | 2 | 1 | no | — |
| 18 | #33748 | C22 | 1 | 1 | yes | characteristic |
| 19 | #33675 | C22 | 1 | 1 | yes | characteristic |
| 20 | #21517 | — | 2 | 1 | no | — |
| 21 | #19125 | C22 | 1 | 1 | yes | characteristic |
| 22 | #18091 | — | 2 | 1 | no | — |
| 23 | #18091 | C22 | 1 | 1 | yes | characteristic |
| 24 | #18063 | — | 2 | 1 | no | — |
| 25 | #18063 | C22 | 1 | 1 | yes | characteristic |
| 26 | #18025 | — | 2 | 1 | no | — |
| 27 | #18025 | — | 2 | 2 | no | — |
| 28 | #17962 | — | 2 | 1 | no | — |
| 29 | #17962 | C22 | 1 | 1 | yes | characteristic |
| 30 | #17962 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17917 | — | 2 | 1 | no | — |
| 32 | #17917 | — | 2 | 2 | no | — |
| 33 | #17849 | — | 2 | 1 | no | — |
| 34 | #17849 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17835 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17520 | — | 2 | 1 | no | — |
| 37 | #17320 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×#360 | C22 | 1 | 1 | yes | characteristic |
| 39 | #12406 | C4 | 1 | 1 | yes | characteristic, complemented |
| 40 | #12395 | C4 | 1 | 1 | yes | characteristic, complemented |
| 41 | #12380 | C4 | 1 | 1 | yes | characteristic, complemented |
| 42 | #12369 | C4 | 1 | 1 | yes | characteristic, complemented |
| 43 | #12354 | C4 | 1 | 1 | yes | characteristic, complemented |
| 44 | #12343 | C4 | 1 | 1 | yes | characteristic, complemented |
| 45 | #12328 | C4 | 1 | 1 | yes | characteristic, complemented |
| 46 | #12317 | C4 | 1 | 1 | yes | characteristic, complemented |
| 47 | #12080 | — | 2 | 1 | no | — |
| 48 | #12078 | — | 2 | 2 | no | — |
| 49 | #12078 | — | 2 | 1 | no | — |
| 50 | #12078 | — | 2 | 2 | no | — |
| 51 | #12067 | — | 2 | 1 | no | — |
| 52 | #12065 | — | 2 | 1 | no | — |
| 53 | #12029 | C22 | 1 | 1 | yes | characteristic |
| 54 | #12020 | C22 | 1 | 1 | yes | characteristic |
| 55 | #11952 | C22 | 1 | 1 | yes | characteristic |
| 56 | #11744 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11680 | C22 | 1 | 1 | yes | characteristic |
| 58 | #11680 | C22 | 1 | 1 | yes | characteristic |
| 59 | #11666 | C22 | 1 | 1 | yes | characteristic |
| 60 | #11652 | C22 | 1 | 1 | yes | characteristic |
| 61 | #11615 | C22 | 1 | 1 | yes | characteristic |
| 62 | #11615 | C22 | 1 | 1 | yes | characteristic |
| 63 | #11592 | C22 | 1 | 1 | yes | characteristic |
| 64 | #11415 | C22 | 1 | 1 | yes | characteristic |
| 65 | #11404 | C22 | 1 | 1 | yes | characteristic |
| 66 | #9721 | C22 | 1 | 1 | yes | characteristic |
| 67 | #9625 | C22 | 1 | 1 | yes | characteristic |
| 68 | #9592 | — | 2 | 1 | no | — |
| 69 | #9208 | — | 2 | 1 | no | — |
| 70 | #8666 | C22 | 1 | 1 | yes | characteristic |
| 71 | #8285 | C22 | 1 | 1 | yes | characteristic |
| 72 | #8257 | — | 2 | 1 | no | — |
| 73 | #7302 | C22 | 1 | 1 | yes | characteristic |
| 74 | #7292 | C22 | 1 | 1 | yes | characteristic |
| 75 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 76 | #7164 | C22 | 1 | 1 | yes | characteristic |
| 77 | #7164 | C22 | 1 | 1 | yes | characteristic |
| 78 | #7159 | C22 | 1 | 1 | yes | characteristic |
| 79 | #3483 | — | 2 | 1 | no | — |
| 80 | #3391 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | Q8×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | #3362 | — | 2 | 1 | no | — |
| 83 | #3341 | — | 2 | 1 | no | — |
| 84 | #3341 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #3305 | — | 2 | 2 | no | — |
| 86 | #3305 | — | 2 | 1 | no | — |
| 87 | #3287 | — | 2 | 1 | no | — |
| 88 | #3287 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | #3169 | — | 2 | 1 | no | — |
| 90 | #3169 | C23 | 1 | 1 | yes | characteristic |
| 91 | #3169 | C23 | 1 | 1 | yes | characteristic |
| 92 | #3106 | — | 2 | 2 | no | — |
| 93 | #3106 | — | 2 | 1 | no | — |
| 94 | #3035 | — | 2 | 1 | no | — |
| 95 | #2991 | — | 2 | 2 | no | — |
| 96 | #2991 | — | 2 | 1 | no | — |
| 97 | #2991 | — | 2 | 1 | no | — |
| 98 | #2991 | — | 4 | 1 | no | — |
| 99 | #2979 | — | 2 | 2 | no | — |
| 100 | #2979 | — | 2 | 1 | no | — |
| 101 | #2979 | — | 4 | 2 | no | — |
| 102 | #2979 | — | 4 | 1 | no | — |
| 103 | C8×#41 | — | 2 | 2 | no | — |
| 104 | C8×#41 | — | 2 | 1 | no | — |
| 105 | C8×#41 | — | 4 | 1 | no | — |
| 106 | C8×#41 | D4 | 1 | 1 | yes | characteristic |
| 107 | C8×#41 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×#443 | — | 4 | 1 | no | — |
| 109 | C4×#135 | — | 2 | 1 | no | — |
| 110 | C4×#135 | C23 | 1 | 1 | yes | characteristic |
| 111 | #2931 | — | 2 | 2 | no | — |
| 112 | #2931 | — | 2 | 1 | no | — |
| 113 | #2931 | — | 2 | 1 | no | — |
| 114 | #2931 | — | 4 | 2 | no | — |
| 115 | #2931 | — | 4 | 1 | no | — |
| 116 | C4×#131 | D4 | 1 | 1 | yes | characteristic |
| 117 | #2254 | C2×C4 | 1 | 1 | yes | characteristic |
| 118 | #2246 | C2×C4 | 1 | 1 | yes | characteristic |
| 119 | #2240 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | #2240 | C2×C4 | 1 | 1 | yes | characteristic |
| 121 | #2234 | — | 2 | 1 | no | — |
| 122 | #2225 | C2×C4 | 1 | 1 | yes | characteristic |
| 123 | #2224 | C2×C4 | 1 | 1 | yes | characteristic |
| 124 | #2218 | — | 2 | 2 | no | — |
| 125 | #2207 | C2×C4 | 1 | 1 | yes | characteristic |
| 126 | #2206 | C2×C4 | 1 | 1 | yes | characteristic |
| 127 | #2186 | — | 2 | 1 | no | — |
| 128 | #2177 | — | 2 | 1 | no | — |
| 129 | #2177 | — | 2 | 2 | no | — |
| 130 | #2175 | — | 2 | 1 | no | — |
| 131 | #2163 | C23 | 1 | 1 | yes | characteristic |
| 132 | #2163 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×#360 | — | 2 | 1 | no | — |
| 134 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 135 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 136 | #1980 | — | 2 | 1 | no | — |
| 137 | #1950 | — | 2 | 1 | no | — |
| 138 | #1929 | — | 4 | 1 | no | — |
| 139 | #1876 | — | 4 | 1 | no | — |
| 140 | #1806 | — | 2 | 1 | no | — |
| 141 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 142 | C8×C4⋊C4 | — | 2 | 1 | no | — |
| 143 | #1764 | — | 4 | 1 | no | — |
| 144 | #1682 | — | 2 | 1 | no | — |
| 145 | #1681 | — | 2 | 1 | no | — |
| 146 | #1674 | C2×C4 | 1 | 1 | yes | characteristic |
| 147 | #1673 | C2×C4 | 1 | 1 | yes | characteristic |
| 148 | #1668 | C2×C4 | 1 | 1 | yes | characteristic |
| 149 | #1667 | C2×C4 | 1 | 1 | yes | characteristic |
| 150 | #1594 | — | 2 | 2 | no | — |
| 151 | #1594 | — | 2 | 1 | no | — |
| 152 | #1594 | — | 2 | 1 | no | — |
| 153 | #1594 | — | 2 | 1 | no | — |
| 154 | #1594 | — | 2 | 1 | no | — |
| 155 | #1594 | — | 2 | 1 | no | — |
| 156 | #1594 | D4 | 1 | 2 | yes | — |
| 157 | #1583 | — | 2 | 2 | no | — |
| 158 | #1583 | — | 2 | 2 | no | — |
| 159 | #1583 | — | 2 | 2 | no | — |
| 160 | #1581 | — | 2 | 2 | no | — |
| 161 | #1581 | — | 2 | 2 | no | — |
| 162 | #1581 | — | 2 | 2 | no | — |
| 163 | #1580 | — | 2 | 2 | no | — |
| 164 | #1580 | — | 2 | 1 | no | — |
| 165 | #1580 | — | 2 | 1 | no | — |
| 166 | #1580 | — | 2 | 1 | no | — |
| 167 | #1580 | — | 2 | 1 | no | — |
| 168 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 169 | #1580 | D4 | 1 | 2 | yes | — |
| 170 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 171 | #1579 | — | 2 | 1 | no | — |
| 172 | #1579 | D4 | 1 | 1 | yes | characteristic |
| 173 | #1579 | D4 | 1 | 1 | yes | characteristic |
| 174 | SD16⋊C8 | — | 2 | 2 | no | — |
| 175 | SD16⋊C8 | — | 2 | 2 | no | — |
| 176 | SD16⋊C8 | — | 2 | 1 | no | — |
| 177 | SD16⋊C8 | — | 2 | 1 | no | — |
| 178 | #1574 | — | 2 | 1 | no | — |
| 179 | #1574 | — | 2 | 2 | no | — |
| 180 | #1566 | — | 2 | 1 | no | — |
| 181 | #1566 | C23 | 1 | 1 | yes | characteristic |
| 182 | #1566 | C23 | 1 | 1 | yes | characteristic |
| 183 | #1564 | — | 2 | 1 | no | — |
| 184 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 185 | C2×#335 | C23 | 1 | 1 | yes | characteristic |
| 186 | #1540 | — | 2 | 1 | no | — |
| 187 | #1502 | — | 2 | 1 | no | — |
| 188 | #1492 | — | 2 | 2 | no | — |
| 189 | #1492 | — | 2 | 1 | no | — |
| 190 | #1492 | — | 2 | 1 | no | — |
| 191 | #1489 | — | 2 | 2 | no | — |
| 192 | #1489 | — | 2 | 1 | no | — |
| 193 | #1484 | — | 2 | 2 | no | — |
| 194 | #1484 | — | 2 | 1 | no | — |
| 195 | #1476 | — | 2 | 2 | no | — |
| 196 | #1476 | — | 2 | 1 | no | — |
| 197 | #1452 | — | 2 | 1 | no | — |
| 198 | #1452 | D4 | 1 | 1 | yes | characteristic |
| 199 | #1451 | — | 2 | 1 | no | — |
| 200 | #1451 | — | 2 | 1 | no | — |
| 201 | #1451 | D4 | 1 | 1 | yes | characteristic |
| 202 | #1451 | C23 | 1 | 1 | yes | characteristic |
| 203 | C2×#322 | — | 2 | 1 | no | — |
| 204 | C2×#322 | C23 | 1 | 1 | yes | characteristic |
| 205 | #1386 | — | 2 | 1 | no | — |
| 206 | #1368 | — | 2 | 1 | no | — |
| 207 | #1368 | — | 2 | 1 | no | — |
| 208 | #1368 | — | 2 | 2 | no | — |
| 209 | #1365 | C2×C4 | 1 | 1 | yes | characteristic |
| 210 | #1365 | C2×C4 | 1 | 1 | yes | characteristic |
| 211 | #1361 | C2×C4 | 1 | 1 | yes | characteristic |
| 212 | #1361 | C2×C4 | 1 | 1 | yes | characteristic |
| 213 | #1347 | — | 2 | 2 | no | — |
| 214 | Q8⋊C16 | — | 2 | 1 | no | — |
| 215 | Q8⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 216 | Q8⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 217 | #1334 | — | 2 | 1 | no | — |
| 218 | #1333 | — | 2 | 1 | no | — |
| 219 | #1333 | — | 2 | 2 | no | — |
| 220 | #1333 | — | 2 | 1 | no | — |
| 221 | #1333 | — | 2 | 1 | no | — |
| 222 | #1333 | — | 2 | 2 | no | — |
| 223 | #1332 | C2×C4 | 1 | 1 | yes | characteristic |
| 224 | #1332 | C2×C4 | 1 | 1 | yes | characteristic |
| 225 | #1331 | C2×C4 | 1 | 1 | yes | characteristic |
| 226 | #1331 | C2×C4 | 1 | 1 | yes | characteristic |
| 227 | D4⋊C16 | — | 2 | 1 | no | — |
| 228 | D4⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 229 | D4⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 230 | #1313 | — | 2 | 1 | no | — |
| 231 | #1313 | — | 2 | 1 | no | — |
| 232 | #1313 | — | 2 | 1 | no | — |
| 233 | #1313 | — | 2 | 1 | no | — |
| 234 | #1303 | — | 2 | 1 | no | — |
| 235 | #1301 | — | 2 | 1 | no | — |
| 236 | #1279 | — | 2 | 1 | no | — |
| 237 | C2×#135 | — | 2 | 1 | no | — |
| 238 | C2×#135 | — | 4 | 1 | no | — |
| 239 | C2×#135 | #41 | 1 | 1 | yes | characteristic |
| 240 | C2×#131 | — | 2 | 1 | no | — |
| 241 | C2×#131 | — | 4 | 2 | no | — |
| 242 | C2×#131 | — | 4 | 1 | no | — |
| 243 | C2×#131 | — | 4 | 1 | no | — |
| 244 | Q82 | — | 2 | 1 | no | — |
| 245 | #555 | — | 2 | 2 | no | — |
| 246 | #555 | — | 2 | 1 | no | — |
| 247 | #555 | — | 4 | 2 | no | — |
| 248 | #555 | — | 4 | 1 | no | — |
| 249 | #550 | — | 2 | 1 | no | — |
| 250 | #550 | — | 2 | 2 | no | — |
| 251 | #550 | — | 2 | 1 | no | — |
| 252 | #550 | — | 4 | 1 | no | — |
| 253 | #532 | — | 2 | 2 | no | — |
| 254 | #532 | — | 2 | 1 | no | — |
| 255 | #532 | — | 2 | 1 | no | — |
| 256 | #532 | — | 4 | 2 | no | — |
| 257 | #532 | — | 4 | 1 | no | — |
| 258 | C4×#41 | — | 2 | 2 | no | — |
| 259 | C4×#41 | — | 2 | 1 | no | — |
| 260 | C4×#41 | — | 4 | 1 | no | — |
| 261 | C4×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 262 | C2×SD32 | — | 2 | 1 | no | — |
| 263 | C2×D16 | — | 2 | 1 | no | — |
| 264 | C2×D16 | — | 2 | 2 | no | — |
| 265 | C2×M32 | — | 2 | 1 | no | — |
| 266 | C2×M32 | — | 2 | 1 | no | — |
| 267 | #500 | — | 2 | 1 | no | — |
| 268 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 269 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 270 | #493 | — | 2 | 1 | no | — |
| 271 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 272 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 273 | #486 | — | 2 | 2 | no | — |
| 274 | #486 | — | 2 | 1 | no | — |
| 275 | #486 | — | 2 | 1 | no | — |
| 276 | #482 | — | 2 | 2 | no | — |
| 277 | #482 | — | 2 | 2 | no | — |
| 278 | #482 | — | 2 | 2 | no | — |
| 279 | #477 | — | 2 | 2 | no | — |
| 280 | #477 | — | 2 | 1 | no | — |
| 281 | #476 | — | 2 | 2 | no | — |
| 282 | #476 | — | 2 | 1 | no | — |
| 283 | #466 | — | 2 | 2 | no | — |
| 284 | #466 | — | 2 | 1 | no | — |
| 285 | #466 | — | 2 | 1 | no | — |
| 286 | #466 | — | 2 | 1 | no | — |
| 287 | #466 | — | 2 | 1 | no | — |
| 288 | #466 | — | 2 | 1 | no | — |
| 289 | #466 | #41 | 1 | 2 | yes | — |
| 290 | #464 | — | 4 | 1 | no | — |
| 291 | #463 | — | 4 | 1 | no | — |
| 292 | #462 | — | 2 | 1 | no | — |
| 293 | #461 | — | 2 | 1 | no | — |
| 294 | #460 | — | 2 | 2 | no | — |
| 295 | #460 | — | 2 | 1 | no | — |
| 296 | #460 | — | 2 | 1 | no | — |
| 297 | #459 | — | 2 | 2 | no | — |
| 298 | #459 | — | 2 | 1 | no | — |
| 299 | #459 | — | 2 | 1 | no | — |
| 300 | #449 | — | 2 | 2 | no | — |
| 301 | #449 | — | 2 | 2 | no | — |
| 302 | #449 | — | 2 | 2 | no | — |
| 303 | C8×Q8 | — | 2 | 1 | no | — |
| 304 | C8×Q8 | — | 2 | 2 | no | — |
| 305 | C8×Q8 | — | 2 | 1 | no | — |
| 306 | C8×Q8 | — | 2 | 1 | no | — |
| 307 | C8×Q8 | — | 4 | 1 | no | — |
| 308 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 309 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 310 | #443 | — | 8 | 4 | no | — |
| 311 | C4×Q16 | — | 2 | 1 | no | — |
| 312 | C4×Q16 | C22×C4 | 1 | 1 | yes | characteristic |
| 313 | C4×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 314 | C4×SD16 | — | 2 | 2 | no | — |
| 315 | C4×SD16 | — | 2 | 2 | no | — |
| 316 | C4×SD16 | — | 2 | 1 | no | — |
| 317 | C4×SD16 | — | 2 | 1 | no | — |
| 318 | C4×D8 | — | 2 | 2 | no | — |
| 319 | C4×D8 | — | 2 | 1 | no | — |
| 320 | C4×D8 | — | 2 | 1 | no | — |
| 321 | C4×D8 | — | 2 | 1 | no | — |
| 322 | C4×D8 | — | 2 | 1 | no | — |
| 323 | C4×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 324 | C4×D8 | C2×D4 | 1 | 2 | yes | — |
| 325 | C4×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 326 | #436 | — | 2 | 2 | no | — |
| 327 | #436 | — | 2 | 2 | no | — |
| 328 | #436 | — | 2 | 2 | no | — |
| 329 | #436 | — | 4 | 2 | no | — |
| 330 | #436 | — | 4 | 1 | no | — |
| 331 | #436 | — | 4 | 1 | no | — |
| 332 | #436 | — | 4 | 2 | no | — |
| 333 | #436 | — | 4 | 2 | no | — |
| 334 | #436 | — | 4 | 2 | no | — |
| 335 | #436 | — | 4 | 1 | no | — |
| 336 | #436 | — | 4 | 2 | no | — |
| 337 | #436 | — | 4 | 1 | no | — |
| 338 | #436 | — | 4 | 2 | no | — |
| 339 | #436 | — | 4 | 1 | no | — |
| 340 | C8×D4 | — | 2 | 1 | no | — |
| 341 | C8×D4 | — | 2 | 1 | no | — |
| 342 | C8×D4 | — | 2 | 1 | no | — |
| 343 | C8×D4 | — | 2 | 2 | no | — |
| 344 | C8×D4 | — | 2 | 2 | no | — |
| 345 | C8×D4 | — | 2 | 2 | no | — |
| 346 | C8×D4 | — | 2 | 1 | no | — |
| 347 | C8×D4 | — | 2 | 1 | no | — |
| 348 | C8×D4 | — | 4 | 2 | no | — |
| 349 | C8×D4 | — | 4 | 1 | no | — |
| 350 | C8×D4 | — | 4 | 1 | no | — |
| 351 | C8×D4 | — | 4 | 2 | no | — |
| 352 | C8×D4 | — | 4 | 1 | no | — |
| 353 | C8×D4 | — | 4 | 2 | no | — |
| 354 | C8×D4 | — | 4 | 1 | no | — |
| 355 | C8×D4 | — | 4 | 2 | no | — |
| 356 | C8×D4 | — | 4 | 1 | no | — |
| 357 | C8×D4 | — | 4 | 1 | no | — |
| 358 | C8×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 359 | C8×D4 | #41 | 1 | 1 | yes | characteristic |
| 360 | #431 | — | 2 | 1 | no | — |
| 361 | #431 | — | 2 | 1 | no | — |
| 362 | #431 | — | 2 | 2 | no | — |
| 363 | #431 | — | 2 | 1 | no | — |
| 364 | #431 | — | 4 | 2 | no | — |
| 365 | #431 | — | 4 | 1 | no | — |
| 366 | #431 | — | 4 | 2 | no | — |
| 367 | #431 | — | 4 | 1 | no | — |
| 368 | #431 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | #431 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | C2×#108 | — | 4 | 1 | no | — |
| 371 | #427 | — | 2 | 1 | no | — |
| 372 | #427 | #41 | 1 | 1 | yes | characteristic |
| 373 | C2×#106 | — | 2 | 1 | no | — |
| 374 | #423 | — | 2 | 2 | no | — |
| 375 | #423 | — | 2 | 1 | no | — |
| 376 | #423 | — | 2 | 1 | no | — |
| 377 | #423 | — | 4 | 2 | no | — |
| 378 | #423 | — | 4 | 1 | no | — |
| 379 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 380 | C2×#104 | — | 4 | 1 | no | — |
| 381 | C2×#104 | — | 4 | 1 | no | — |
| 382 | C2×#104 | — | 4 | 1 | no | — |
| 383 | #416 | — | 2 | 2 | no | — |
| 384 | #416 | — | 2 | 1 | no | — |
| 385 | #416 | — | 4 | 1 | no | — |
| 386 | #408 | — | 4 | 2 | no | — |
| 387 | #408 | — | 4 | 2 | no | — |
| 388 | #408 | — | 4 | 2 | no | — |
| 389 | #408 | — | 4 | 1 | no | — |
| 390 | #408 | — | 4 | 2 | no | — |
| 391 | #408 | — | 4 | 1 | no | — |
| 392 | #405 | — | 2 | 1 | no | — |
| 393 | #405 | — | 4 | 1 | no | — |
| 394 | C4×M16 | — | 2 | 1 | no | — |
| 395 | C4×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 396 | C2×C4×C8 | — | 2 | 1 | no | — |
| 397 | C2×C4×C8 | — | 2 | 1 | no | — |
| 398 | C2×C4×C8 | — | 2 | 1 | no | — |
| 399 | C2×C4×C8 | — | 4 | 2 | no | — |
| 400 | C2×C4×C8 | — | 4 | 1 | no | — |
| 401 | C2×C4×C8 | — | 4 | 1 | no | — |
| 402 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 403 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 404 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 405 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 406 | #367 | — | 2 | 2 | no | — |
| 407 | #367 | — | 2 | 1 | no | — |
| 408 | #366 | — | 2 | 1 | no | — |
| 409 | C4⋊C16 | — | 2 | 1 | no | — |
| 410 | C4⋊C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 411 | C4⋊C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 412 | #360 | — | 2 | 4 | no | — |
| 413 | #358 | — | 2 | 1 | no | — |
| 414 | #357 | — | 2 | 1 | no | — |
| 415 | #357 | — | 2 | 2 | no | — |
| 416 | #357 | — | 2 | 1 | no | — |
| 417 | #357 | — | 2 | 1 | no | — |
| 418 | #357 | — | 2 | 2 | no | — |
| 419 | C22⋊C16 | — | 2 | 1 | no | — |
| 420 | C22⋊C16 | — | 2 | 1 | no | — |
| 421 | #346 | — | 2 | 1 | no | — |
| 422 | #346 | — | 2 | 1 | no | — |
| 423 | #346 | — | 2 | 1 | no | — |
| 424 | #346 | — | 2 | 1 | no | — |
| 425 | C4×C16 | — | 2 | 1 | no | — |
| 426 | C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 427 | C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 428 | #341 | — | 4 | 1 | no | — |
| 429 | #340 | — | 2 | 1 | no | — |
| 430 | #339 | — | 4 | 1 | no | — |
| 431 | #336 | — | 4 | 1 | no | — |
| 432 | #335 | — | 2 | 2 | no | — |
| 433 | #335 | — | 2 | 1 | no | — |
| 434 | #335 | — | 2 | 1 | no | — |
| 435 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 436 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 437 | #334 | — | 2 | 2 | no | — |
| 438 | #334 | — | 2 | 1 | no | — |
| 439 | #334 | — | 2 | 1 | no | — |
| 440 | #334 | — | 2 | 1 | no | — |
| 441 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 442 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 443 | #334 | C2×D4 | 1 | 2 | yes | — |
| 444 | #332 | — | 2 | 1 | no | — |
| 445 | #332 | — | 2 | 1 | no | — |
| 446 | #331 | — | 2 | 1 | no | — |
| 447 | #331 | — | 2 | 1 | no | — |
| 448 | #327 | — | 4 | 2 | no | — |
| 449 | Q8⋊C8 | — | 2 | 2 | no | — |
| 450 | Q8⋊C8 | — | 2 | 1 | no | — |
| 451 | Q8⋊C8 | — | 2 | 1 | no | — |
| 452 | D4⋊C8 | — | 2 | 2 | no | — |
| 453 | D4⋊C8 | — | 2 | 2 | no | — |
| 454 | D4⋊C8 | — | 2 | 2 | no | — |
| 455 | D4⋊C8 | — | 2 | 2 | no | — |
| 456 | D4⋊C8 | — | 2 | 1 | no | — |
| 457 | D4⋊C8 | — | 2 | 1 | no | — |
| 458 | D4⋊C8 | — | 2 | 2 | no | — |
| 459 | D4⋊C8 | — | 4 | 1 | no | — |
| 460 | D4⋊C8 | — | 4 | 1 | no | — |
| 461 | #322 | — | 2 | 1 | no | — |
| 462 | #322 | — | 2 | 1 | no | — |
| 463 | #322 | — | 2 | 1 | no | — |
| 464 | #322 | — | 2 | 1 | no | — |
| 465 | #322 | — | 2 | 1 | no | — |
| 466 | #322 | — | 2 | 1 | no | — |
| 467 | #322 | C2×D4 | 1 | 1 | yes | characteristic |
| 468 | #322 | C2×D4 | 1 | 1 | yes | characteristic |
| 469 | #322 | C2×D4 | 1 | 1 | yes | characteristic |
| 470 | #322 | C2×D4 | 1 | 1 | yes | characteristic |
| 471 | C2×#41 | — | 2 | 2 | no | — |
| 472 | C2×#41 | — | 2 | 1 | no | — |
| 473 | C2×#41 | — | 4 | 2 | no | — |
| 474 | C2×#41 | — | 4 | 1 | no | — |
| 475 | C2×#41 | — | 4 | 1 | no | — |
| 476 | C2×#41 | — | 4 | 1 | no | — |
| 477 | C2×#41 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 478 | #135 | — | 2 | 2 | no | — |
| 479 | #135 | — | 4 | 1 | no | — |
| 480 | #135 | — | 4 | 2 | no | — |
| 481 | #135 | — | 4 | 2 | no | — |
| 482 | #135 | — | 8 | 2 | no | — |
| 483 | #135 | — | 8 | 2 | no | — |
| 484 | C2×Q16 | — | 4 | 1 | no | — |
| 485 | C2×Q16 | C4×D4 | 1 | 1 | yes | characteristic |
| 486 | C2×SD16 | — | 2 | 2 | no | — |
| 487 | C2×SD16 | — | 2 | 1 | no | — |
| 488 | C2×SD16 | — | 4 | 1 | no | — |
| 489 | C2×SD16 | — | 4 | 1 | no | — |
| 490 | C2×D8 | — | 2 | 2 | no | — |
| 491 | C2×D8 | — | 2 | 1 | no | — |
| 492 | C2×D8 | — | 2 | 1 | no | — |
| 493 | C2×D8 | — | 2 | 1 | no | — |
| 494 | C2×D8 | — | 4 | 1 | no | — |
| 495 | C2×D8 | C4×D4 | 1 | 1 | yes | characteristic |
| 496 | C2×D8 | C4×D4 | 1 | 2 | yes | — |
| 497 | #131 | — | 4 | 2 | no | — |
| 498 | #131 | — | 8 | 1 | no | — |
| 499 | #131 | — | 8 | 2 | no | — |
| 500 | #131 | — | 8 | 2 | no | — |
| 501 | #131 | — | 16 | 2 | no | — |
| 502 | #131 | — | 16 | 4 | no | — |
| 503 | C2×M16 | — | 2 | 1 | no | — |
| 504 | C2×M16 | — | 4 | 1 | no | — |
| 505 | C2×M16 | — | 4 | 2 | no | — |
| 506 | C2×M16 | — | 4 | 2 | no | — |
| 507 | C2×M16 | — | 4 | 2 | no | — |
| 508 | C2×M16 | — | 4 | 2 | no | — |
| 509 | C2×M16 | — | 4 | 1 | no | — |
| 510 | C2×M16 | — | 4 | 1 | no | — |
| 511 | C2×M16 | — | 8 | 1 | no | — |
| 512 | C22×C8 | — | 2 | 1 | no | — |
| 513 | C22×C8 | — | 2 | 2 | no | — |
| 514 | C22×C8 | — | 2 | 1 | no | — |
| 515 | C22×C8 | — | 2 | 1 | no | — |
| 516 | C22×C8 | — | 2 | 1 | no | — |
| 517 | C22×C8 | — | 4 | 1 | no | — |
| 518 | C22×C8 | — | 4 | 2 | no | — |
| 519 | C22×C8 | — | 4 | 1 | no | — |
| 520 | C22×C8 | — | 4 | 2 | no | — |
| 521 | C22×C8 | — | 4 | 1 | no | — |
| 522 | C22×C8 | — | 4 | 1 | no | — |
| 523 | C22×C8 | — | 8 | 1 | no | — |
| 524 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 525 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 526 | C4⋊Q8 | — | 2 | 2 | no | — |
| 527 | C4⋊Q8 | — | 2 | 1 | no | — |
| 528 | C4⋊Q8 | — | 2 | 1 | no | — |
| 529 | C4⋊Q8 | — | 4 | 2 | no | — |
| 530 | C4⋊Q8 | — | 4 | 1 | no | — |
| 531 | #127 | — | 2 | 2 | no | — |
| 532 | #127 | — | 2 | 1 | no | — |
| 533 | #127 | — | 2 | 1 | no | — |
| 534 | #127 | — | 4 | 2 | no | — |
| 535 | #127 | — | 4 | 1 | no | — |
| 536 | #124 | — | 4 | 2 | no | — |
| 537 | #124 | — | 4 | 2 | no | — |
| 538 | #124 | — | 4 | 2 | no | — |
| 539 | #124 | — | 4 | 2 | no | — |
| 540 | #124 | — | 4 | 1 | no | — |
| 541 | #124 | — | 4 | 1 | no | — |
| 542 | #121 | — | 2 | 2 | no | — |
| 543 | #121 | — | 2 | 2 | no | — |
| 544 | #121 | — | 2 | 2 | no | — |
| 545 | #121 | — | 4 | 2 | no | — |
| 546 | #121 | — | 4 | 2 | no | — |
| 547 | #121 | — | 4 | 2 | no | — |
| 548 | #121 | — | 4 | 2 | no | — |
| 549 | #121 | — | 4 | 2 | no | — |
| 550 | #121 | — | 4 | 2 | no | — |
| 551 | #121 | — | 4 | 1 | no | — |
| 552 | #121 | — | 4 | 1 | no | — |
| 553 | #121 | — | 4 | 1 | no | — |
| 554 | #121 | — | 4 | 1 | no | — |
| 555 | #121 | — | 4 | 1 | no | — |
| 556 | C4×Q8 | — | 2 | 2 | no | — |
| 557 | C4×Q8 | — | 2 | 1 | no | — |
| 558 | C4×Q8 | — | 2 | 1 | no | — |
| 559 | C4×Q8 | — | 4 | 1 | no | — |
| 560 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 561 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 562 | C4×D4 | — | 2 | 1 | no | — |
| 563 | C4×D4 | — | 2 | 1 | no | — |
| 564 | C4×D4 | — | 2 | 2 | no | — |
| 565 | C4×D4 | — | 2 | 1 | no | — |
| 566 | C4×D4 | — | 2 | 2 | no | — |
| 567 | C4×D4 | — | 2 | 1 | no | — |
| 568 | C4×D4 | — | 4 | 2 | no | — |
| 569 | C4×D4 | — | 4 | 2 | no | — |
| 570 | C4×D4 | — | 4 | 2 | no | — |
| 571 | C4×D4 | — | 4 | 2 | no | — |
| 572 | C4×D4 | — | 4 | 1 | no | — |
| 573 | C4×D4 | — | 4 | 1 | no | — |
| 574 | C4×D4 | — | 4 | 1 | no | — |
| 575 | C4×D4 | — | 4 | 1 | no | — |
| 576 | C4×D4 | — | 4 | 1 | no | — |
| 577 | C4×D4 | — | 4 | 1 | no | — |
| 578 | C4×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 579 | C4×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 580 | #117 | — | 2 | 1 | no | — |
| 581 | #117 | — | 2 | 2 | no | — |
| 582 | #117 | — | 2 | 1 | no | — |
| 583 | #117 | — | 4 | 2 | no | — |
| 584 | #117 | — | 4 | 2 | no | — |
| 585 | #117 | — | 4 | 1 | no | — |
| 586 | #117 | — | 4 | 1 | no | — |
| 587 | #117 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 588 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 589 | C2×C42 | — | 2 | 1 | no | — |
| 590 | C2×C42 | — | 4 | 2 | no | — |
| 591 | C2×C42 | — | 4 | 1 | no | — |
| 592 | C2×C42 | — | 4 | 1 | no | — |
| 593 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 594 | SD32 | — | 4 | 2 | no | — |
| 595 | D16 | — | 4 | 2 | no | — |
| 596 | D16 | — | 8 | 2 | no | — |
| 597 | M32 | — | 2 | 2 | no | — |
| 598 | M32 | — | 4 | 1 | no | — |
| 599 | M32 | — | 8 | 1 | no | — |
| 600 | C2×C16 | — | 2 | 1 | no | — |
| 601 | C2×C16 | — | 2 | 1 | no | — |
| 602 | C2×C16 | — | 2 | 1 | no | — |
| 603 | C2×C16 | — | 2 | 1 | no | — |
| 604 | C2×C16 | — | 4 | 1 | no | — |
| 605 | C2×C16 | — | 4 | 1 | no | — |
| 606 | #108 | — | 8 | 2 | no | — |
| 607 | #107 | — | 2 | 2 | no | — |
| 608 | #107 | — | 2 | 1 | no | — |
| 609 | #107 | — | 2 | 1 | no | — |
| 610 | #107 | — | 2 | 1 | no | — |
| 611 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 612 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 613 | #107 | C4×D4 | 1 | 2 | yes | — |
| 614 | #106 | — | 2 | 2 | no | — |
| 615 | #106 | — | 2 | 1 | no | — |
| 616 | #106 | — | 2 | 2 | no | — |
| 617 | #106 | — | 4 | 1 | no | — |
| 618 | C4⋊C8 | — | 2 | 2 | no | — |
| 619 | C4⋊C8 | — | 2 | 1 | no | — |
| 620 | C4⋊C8 | — | 2 | 1 | no | — |
| 621 | C4⋊C8 | — | 2 | 1 | no | — |
| 622 | C4⋊C8 | — | 2 | 1 | no | — |
| 623 | C4⋊C8 | — | 2 | 1 | no | — |
| 624 | C4⋊C8 | — | 2 | 2 | no | — |
| 625 | C4⋊C8 | — | 2 | 1 | no | — |
| 626 | C4⋊C8 | — | 2 | 1 | no | — |
| 627 | C4⋊C8 | — | 4 | 2 | no | — |
| 628 | C4⋊C8 | — | 4 | 2 | no | — |
| 629 | C4⋊C8 | — | 4 | 1 | no | — |
| 630 | C4⋊C8 | — | 4 | 1 | no | — |
| 631 | C4⋊C8 | — | 4 | 1 | no | — |
| 632 | C4⋊C8 | — | 4 | 1 | no | — |
| 633 | C4⋊C8 | — | 4 | 1 | no | — |
| 634 | C4⋊C8 | — | 4 | 1 | no | — |
| 635 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 636 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 637 | #104 | — | 8 | 2 | no | — |
| 638 | #104 | — | 8 | 2 | no | — |
| 639 | #104 | — | 8 | 2 | no | — |
| 640 | #103 | — | 2 | 2 | no | — |
| 641 | #103 | — | 2 | 1 | no | — |
| 642 | #103 | — | 2 | 1 | no | — |
| 643 | #103 | — | 4 | 1 | no | — |
| 644 | #103 | — | 4 | 1 | no | — |
| 645 | #102 | — | 2 | 2 | no | — |
| 646 | #102 | — | 2 | 2 | no | — |
| 647 | #102 | — | 2 | 2 | no | — |
| 648 | #102 | — | 2 | 1 | no | — |
| 649 | #102 | — | 2 | 2 | no | — |
| 650 | #102 | — | 2 | 1 | no | — |
| 651 | #102 | — | 2 | 2 | no | — |
| 652 | #102 | — | 4 | 1 | no | — |
| 653 | #102 | — | 4 | 1 | no | — |
| 654 | #102 | — | 4 | 1 | no | — |
| 655 | #102 | — | 4 | 1 | no | — |
| 656 | C22⋊C8 | — | 2 | 2 | no | — |
| 657 | C22⋊C8 | — | 2 | 1 | no | — |
| 658 | C22⋊C8 | — | 2 | 1 | no | — |
| 659 | C22⋊C8 | — | 2 | 1 | no | — |
| 660 | C22⋊C8 | — | 4 | 2 | no | — |
| 661 | C22⋊C8 | — | 4 | 1 | no | — |
| 662 | C22⋊C8 | — | 4 | 2 | no | — |
| 663 | C22⋊C8 | — | 4 | 1 | no | — |
| 664 | C22⋊C8 | — | 4 | 2 | no | — |
| 665 | C22⋊C8 | — | 4 | 2 | no | — |
| 666 | C22⋊C8 | — | 4 | 2 | no | — |
| 667 | C22⋊C8 | — | 4 | 2 | no | — |
| 668 | C22⋊C8 | — | 4 | 1 | no | — |
| 669 | C22⋊C8 | — | 8 | 1 | no | — |
| 670 | C22⋊C8 | — | 8 | 1 | no | — |
| 671 | C22⋊C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 672 | #97 | — | 2 | 1 | no | — |
| 673 | #97 | — | 4 | 1 | no | — |
| 674 | C4×C8 | — | 2 | 2 | no | — |
| 675 | C4×C8 | — | 2 | 1 | no | — |
| 676 | C4×C8 | — | 2 | 1 | no | — |
| 677 | C4×C8 | — | 2 | 1 | no | — |
| 678 | C4×C8 | — | 2 | 1 | no | — |
| 679 | C4×C8 | — | 2 | 1 | no | — |
| 680 | C4×C8 | — | 2 | 1 | no | — |
| 681 | C4×C8 | — | 2 | 1 | no | — |
| 682 | C4×C8 | — | 4 | 1 | no | — |
| 683 | C4×C8 | — | 4 | 2 | no | — |
| 684 | C4×C8 | — | 4 | 1 | no | — |
| 685 | C4×C8 | — | 4 | 2 | no | — |
| 686 | C4×C8 | — | 4 | 1 | no | — |
| 687 | C4×C8 | — | 4 | 1 | no | — |
| 688 | C4×C8 | — | 8 | 2 | no | — |
| 689 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 690 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 691 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 692 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 693 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 694 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 695 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 696 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 697 | #95 | — | 4 | 1 | no | — |
| 698 | #41 | — | 2 | 2 | no | — |
| 699 | #41 | — | 4 | 1 | no | — |
| 700 | #41 | — | 4 | 2 | no | — |
| 701 | #41 | — | 4 | 4 | no | — |
| 702 | #41 | — | 8 | 1 | no | — |
| 703 | #41 | — | 8 | 1 | no | — |
| 704 | #41 | — | 8 | 1 | no | — |
| 705 | #41 | — | 8 | 1 | no | — |
| 706 | #41 | — | 8 | 1 | no | — |
| 707 | #41 | — | 8 | 2 | no | — |
| 708 | #41 | — | 8 | 2 | no | — |
| 709 | #41 | — | 8 | 2 | no | — |
| 710 | #41 | — | 16 | 1 | no | — |
| 711 | #41 | — | 16 | 2 | no | — |
| 712 | #41 | — | 16 | 1 | no | — |
| 713 | #41 | — | 16 | 2 | no | — |
| 714 | C2×Q8 | — | 2 | 1 | no | — |
| 715 | C2×Q8 | — | 4 | 2 | no | — |
| 716 | C2×Q8 | — | 4 | 1 | no | — |
| 717 | C2×Q8 | — | 4 | 1 | no | — |
| 718 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 719 | C2×D4 | — | 2 | 1 | no | — |
| 720 | C2×D4 | — | 2 | 1 | no | — |
| 721 | C2×D4 | — | 2 | 2 | no | — |
| 722 | C2×D4 | — | 4 | 2 | no | — |
| 723 | C2×D4 | — | 4 | 2 | no | — |
| 724 | C2×D4 | — | 4 | 2 | no | — |
| 725 | C2×D4 | — | 4 | 1 | no | — |
| 726 | C2×D4 | — | 4 | 2 | no | — |
| 727 | C2×D4 | — | 4 | 2 | no | — |
| 728 | C2×D4 | — | 4 | 2 | no | — |
| 729 | C2×D4 | — | 4 | 1 | no | — |
| 730 | C2×D4 | — | 4 | 1 | no | — |
| 731 | C2×D4 | — | 4 | 1 | no | — |
| 732 | C2×D4 | — | 4 | 1 | no | — |
| 733 | C2×D4 | — | 4 | 1 | no | — |
| 734 | C2×D4 | — | 8 | 1 | no | — |
| 735 | C2×D4 | #442 | 1 | 1 | yes | characteristic |
| 736 | C22×C4 | — | 2 | 1 | no | — |
| 737 | C22×C4 | — | 2 | 1 | no | — |
| 738 | C22×C4 | — | 2 | 1 | no | — |
| 739 | C22×C4 | — | 4 | 2 | no | — |
| 740 | C22×C4 | — | 4 | 2 | no | — |
| 741 | C22×C4 | — | 4 | 1 | no | — |
| 742 | C22×C4 | — | 4 | 1 | no | — |
| 743 | C22×C4 | — | 4 | 2 | no | — |
| 744 | C22×C4 | — | 4 | 1 | no | — |
| 745 | C22×C4 | — | 8 | 1 | no | — |
| 746 | C22×C4 | — | 8 | 1 | no | — |
| 747 | C22×C4 | #525 | 1 | 1 | yes | characteristic |
| 748 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 749 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 750 | Q16 | — | 2 | 1 | no | — |
| 751 | Q16 | — | 8 | 2 | no | — |
| 752 | Q16 | #443 | 1 | 2 | yes | complemented |
| 753 | SD16 | — | 4 | 2 | no | — |
| 754 | SD16 | — | 4 | 4 | no | — |
| 755 | SD16 | — | 8 | 2 | no | — |
| 756 | SD16 | — | 8 | 2 | no | — |
| 757 | D8 | — | 2 | 1 | no | — |
| 758 | D8 | — | 2 | 1 | no | — |
| 759 | D8 | — | 4 | 2 | no | — |
| 760 | D8 | — | 4 | 2 | no | — |
| 761 | D8 | — | 4 | 1 | no | — |
| 762 | D8 | — | 4 | 1 | no | — |
| 763 | D8 | — | 4 | 1 | no | — |
| 764 | D8 | — | 4 | 1 | no | — |
| 765 | D8 | — | 8 | 2 | no | — |
| 766 | D8 | — | 8 | 2 | no | — |
| 767 | M16 | — | 4 | 1 | no | — |
| 768 | M16 | — | 4 | 1 | no | — |
| 769 | M16 | — | 8 | 2 | no | — |
| 770 | M16 | — | 8 | 1 | no | — |
| 771 | M16 | — | 8 | 1 | no | — |
| 772 | M16 | — | 16 | 2 | no | — |
| 773 | M16 | — | 16 | 2 | no | — |
| 774 | M16 | — | 16 | 2 | no | — |
| 775 | M16 | — | 16 | 2 | no | — |
| 776 | M16 | — | 16 | 1 | no | — |
| 777 | M16 | — | 16 | 2 | no | — |
| 778 | C2×C8 | — | 2 | 1 | no | — |
| 779 | C2×C8 | — | 2 | 1 | no | — |
| 780 | C2×C8 | — | 2 | 1 | no | — |
| 781 | C2×C8 | — | 2 | 2 | no | — |
| 782 | C2×C8 | — | 2 | 1 | no | — |
| 783 | C2×C8 | — | 2 | 1 | no | — |
| 784 | C2×C8 | — | 2 | 1 | no | — |
| 785 | C2×C8 | — | 2 | 1 | no | — |
| 786 | C2×C8 | — | 2 | 1 | no | — |
| 787 | C2×C8 | — | 4 | 1 | no | — |
| 788 | C2×C8 | — | 4 | 1 | no | — |
| 789 | C2×C8 | — | 4 | 1 | no | — |
| 790 | C2×C8 | — | 4 | 1 | no | — |
| 791 | C2×C8 | — | 4 | 1 | no | — |
| 792 | C2×C8 | — | 4 | 1 | no | — |
| 793 | C2×C8 | — | 4 | 1 | no | — |
| 794 | C2×C8 | — | 4 | 1 | no | — |
| 795 | C2×C8 | — | 4 | 2 | no | — |
| 796 | C2×C8 | — | 4 | 1 | no | — |
| 797 | C2×C8 | — | 4 | 1 | no | — |
| 798 | C2×C8 | — | 8 | 1 | no | — |
| 799 | C2×C8 | — | 8 | 1 | no | — |
| 800 | C2×C8 | — | 8 | 2 | no | — |
| 801 | C2×C8 | — | 8 | 2 | no | — |
| 802 | C2×C8 | — | 8 | 4 | no | — |
| 803 | C2×C8 | — | 8 | 2 | no | — |
| 804 | C2×C8 | — | 8 | 1 | no | — |
| 805 | C2×C8 | — | 8 | 1 | no | — |
| 806 | C2×C8 | — | 8 | 1 | no | — |
| 807 | C2×C8 | — | 16 | 2 | no | — |
| 808 | C2×C8 | — | 16 | 1 | no | — |
| 809 | C2×C8 | — | 16 | 2 | no | — |
| 810 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 811 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 812 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 813 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 814 | C4⋊C4 | — | 2 | 1 | no | — |
| 815 | C4⋊C4 | — | 2 | 1 | no | — |
| 816 | C4⋊C4 | — | 2 | 1 | no | — |
| 817 | C4⋊C4 | — | 2 | 1 | no | — |
| 818 | C4⋊C4 | — | 2 | 2 | no | — |
| 819 | C4⋊C4 | — | 4 | 2 | no | — |
| 820 | C4⋊C4 | — | 4 | 2 | no | — |
| 821 | C4⋊C4 | — | 4 | 2 | no | — |
| 822 | C4⋊C4 | — | 4 | 1 | no | — |
| 823 | C4⋊C4 | — | 4 | 1 | no | — |
| 824 | C4⋊C4 | — | 4 | 1 | no | — |
| 825 | C4⋊C4 | — | 4 | 1 | no | — |
| 826 | C4⋊C4 | — | 4 | 1 | no | — |
| 827 | C4⋊C4 | — | 8 | 1 | no | — |
| 828 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 829 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 830 | C22⋊C4 | — | 2 | 1 | no | — |
| 831 | C22⋊C4 | — | 2 | 1 | no | — |
| 832 | C22⋊C4 | — | 2 | 1 | no | — |
| 833 | C22⋊C4 | — | 4 | 2 | no | — |
| 834 | C22⋊C4 | — | 4 | 2 | no | — |
| 835 | C22⋊C4 | — | 4 | 2 | no | — |
| 836 | C22⋊C4 | — | 4 | 2 | no | — |
| 837 | C22⋊C4 | — | 4 | 1 | no | — |
| 838 | C22⋊C4 | — | 4 | 2 | no | — |
| 839 | C22⋊C4 | — | 4 | 1 | no | — |
| 840 | C22⋊C4 | — | 4 | 2 | no | — |
| 841 | C22⋊C4 | — | 4 | 1 | no | — |
| 842 | C22⋊C4 | — | 8 | 1 | no | — |
| 843 | C22⋊C4 | — | 8 | 1 | no | — |
| 844 | C42 | — | 2 | 1 | no | — |
| 845 | C42 | — | 2 | 1 | no | — |
| 846 | C42 | — | 2 | 1 | no | — |
| 847 | C42 | — | 4 | 2 | no | — |
| 848 | C42 | — | 4 | 2 | no | — |
| 849 | C42 | — | 4 | 1 | no | — |
| 850 | C42 | — | 4 | 1 | no | — |
| 851 | C42 | — | 4 | 1 | no | — |
| 852 | C42 | — | 8 | 1 | no | — |
| 853 | C42 | — | 8 | 1 | no | — |
| 854 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 855 | C42 | C2×#120 | 1 | 1 | yes | characteristic |
| 856 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 857 | C42 | #575 | 1 | 1 | yes | characteristic |
| 858 | C16 | — | 4 | 1 | no | — |
| 859 | C16 | — | 4 | 1 | no | — |
| 860 | C16 | — | 4 | 2 | no | — |
| 861 | C16 | — | 4 | 1 | no | — |
| 862 | C16 | — | 4 | 1 | no | — |
| 863 | C16 | — | 8 | 1 | no | — |
| 864 | C23 | — | 2 | 1 | no | — |
| 865 | C23 | — | 4 | 2 | no | — |
| 866 | C23 | — | 4 | 1 | no | — |
| 867 | C23 | — | 8 | 1 | no | — |
| 868 | C23 | #3109 | 1 | 1 | yes | characteristic |
| 869 | Q8 | — | 2 | 1 | no | — |
| 870 | Q8 | — | 2 | 2 | no | — |
| 871 | Q8 | — | 4 | 1 | no | — |
| 872 | Q8 | — | 8 | 1 | no | — |
| 873 | Q8 | — | 8 | 1 | no | — |
| 874 | Q8 | — | 16 | 1 | no | — |
| 875 | Q8 | — | 16 | 2 | no | — |
| 876 | Q8 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 877 | D4 | — | 2 | 1 | no | — |
| 878 | D4 | — | 2 | 1 | no | — |
| 879 | D4 | — | 4 | 2 | no | — |
| 880 | D4 | — | 4 | 1 | no | — |
| 881 | D4 | — | 4 | 2 | no | — |
| 882 | D4 | — | 4 | 2 | no | — |
| 883 | D4 | — | 4 | 1 | no | — |
| 884 | D4 | — | 8 | 4 | no | — |
| 885 | D4 | — | 8 | 2 | no | — |
| 886 | D4 | — | 8 | 4 | no | — |
| 887 | D4 | — | 8 | 1 | no | — |
| 888 | D4 | — | 8 | 1 | no | — |
| 889 | D4 | — | 8 | 1 | no | — |
| 890 | D4 | — | 8 | 1 | no | — |
| 891 | D4 | — | 8 | 1 | no | — |
| 892 | D4 | — | 8 | 1 | no | — |
| 893 | D4 | — | 16 | 1 | no | — |
| 894 | D4 | — | 16 | 1 | no | — |
| 895 | D4 | — | 16 | 2 | no | — |
| 896 | D4 | — | 16 | 2 | no | — |
| 897 | D4 | — | 16 | 2 | no | — |
| 898 | D4 | — | 16 | 2 | no | — |
| 899 | D4 | — | 16 | 1 | no | — |
| 900 | D4 | — | 16 | 1 | no | — |
| 901 | C2×C4 | — | 2 | 1 | no | — |
| 902 | C2×C4 | — | 2 | 1 | no | — |
| 903 | C2×C4 | — | 2 | 1 | no | — |
| 904 | C2×C4 | — | 2 | 1 | no | — |
| 905 | C2×C4 | — | 2 | 1 | no | — |
| 906 | C2×C4 | — | 2 | 1 | no | — |
| 907 | C2×C4 | — | 2 | 1 | no | — |
| 908 | C2×C4 | — | 4 | 1 | no | — |
| 909 | C2×C4 | — | 4 | 2 | no | — |
| 910 | C2×C4 | — | 4 | 2 | no | — |
| 911 | C2×C4 | — | 4 | 1 | no | — |
| 912 | C2×C4 | — | 4 | 1 | no | — |
| 913 | C2×C4 | — | 4 | 1 | no | — |
| 914 | C2×C4 | — | 4 | 1 | no | — |
| 915 | C2×C4 | — | 4 | 2 | no | — |
| 916 | C2×C4 | — | 4 | 1 | no | — |
| 917 | C2×C4 | — | 8 | 2 | no | — |
| 918 | C2×C4 | — | 8 | 2 | no | — |
| 919 | C2×C4 | — | 8 | 1 | no | — |
| 920 | C2×C4 | — | 8 | 2 | no | — |
| 921 | C2×C4 | — | 8 | 1 | no | — |
| 922 | C2×C4 | — | 8 | 4 | no | — |
| 923 | C2×C4 | — | 8 | 4 | no | — |
| 924 | C2×C4 | — | 8 | 1 | no | — |
| 925 | C2×C4 | — | 8 | 1 | no | — |
| 926 | C2×C4 | — | 8 | 2 | no | — |
| 927 | C2×C4 | — | 8 | 1 | no | — |
| 928 | C2×C4 | — | 16 | 1 | no | — |
| 929 | C2×C4 | — | 16 | 1 | no | — |
| 930 | C2×C4 | — | 16 | 1 | no | — |
| 931 | C2×C4 | — | 16 | 1 | no | — |
| 932 | C2×C4 | C4×#120 | 1 | 1 | yes | characteristic |
| 933 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 934 | C2×C4 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 935 | C2×C4 | #3003 | 1 | 1 | yes | characteristic |
| 936 | C2×C4 | #3006 | 1 | 1 | yes | characteristic |
| 937 | C2×C4 | #3114 | 1 | 1 | yes | characteristic |
| 938 | C8 | — | 2 | 1 | no | — |
| 939 | C8 | — | 2 | 1 | no | — |
| 940 | C8 | — | 2 | 1 | no | — |
| 941 | C8 | — | 4 | 1 | no | — |
| 942 | C8 | — | 4 | 1 | no | — |
| 943 | C8 | — | 4 | 1 | no | — |
| 944 | C8 | — | 4 | 2 | no | — |
| 945 | C8 | — | 4 | 1 | no | — |
| 946 | C8 | — | 4 | 1 | no | — |
| 947 | C8 | — | 4 | 1 | no | — |
| 948 | C8 | — | 8 | 1 | no | — |
| 949 | C8 | — | 8 | 2 | no | — |
| 950 | C8 | — | 8 | 1 | no | — |
| 951 | C8 | — | 8 | 1 | no | — |
| 952 | C8 | — | 8 | 1 | no | — |
| 953 | C8 | — | 8 | 1 | no | — |
| 954 | C8 | — | 16 | 1 | no | — |
| 955 | C8 | C2×#443 | 1 | 1 | yes | characteristic |
| 956 | C8 | #2955 | 1 | 1 | yes | characteristic |
| 957 | C22 | — | 2 | 1 | no | — |
| 958 | C22 | — | 2 | 1 | no | — |
| 959 | C22 | — | 2 | 1 | no | — |
| 960 | C22 | — | 4 | 1 | no | — |
| 961 | C22 | — | 4 | 1 | no | — |
| 962 | C22 | — | 4 | 1 | no | — |
| 963 | C22 | — | 8 | 2 | no | — |
| 964 | C22 | — | 8 | 1 | no | — |
| 965 | C22 | — | 8 | 2 | no | — |
| 966 | C22 | — | 8 | 1 | no | — |
| 967 | C22 | — | 8 | 1 | no | — |
| 968 | C22 | — | 8 | 2 | no | — |
| 969 | C22 | — | 16 | 1 | no | — |
| 970 | C22 | — | 16 | 1 | no | — |
| 971 | C22 | — | 16 | 1 | no | — |
| 972 | C22 | #21452 | 1 | 1 | yes | characteristic |
| 973 | C4 | — | 2 | 1 | no | — |
| 974 | C4 | — | 2 | 2 | no | — |
| 975 | C4 | — | 2 | 1 | no | — |
| 976 | C4 | — | 2 | 1 | no | — |
| 977 | C4 | — | 2 | 1 | no | — |
| 978 | C4 | — | 4 | 1 | no | — |
| 979 | C4 | — | 4 | 1 | no | — |
| 980 | C4 | — | 4 | 2 | no | — |
| 981 | C4 | — | 8 | 1 | no | — |
| 982 | C4 | — | 8 | 2 | no | — |
| 983 | C4 | — | 8 | 1 | no | — |
| 984 | C4 | — | 16 | 2 | no | — |
| 985 | C4 | — | 16 | 1 | no | — |
| 986 | C4 | #21466 | 1 | 1 | yes | characteristic |
| 987 | C4 | #21478 | 1 | 1 | yes | characteristic |
| 988 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 989 | C4 | #33468 | 1 | 1 | yes | characteristic |
| 990 | C2 | — | 4 | 1 | no | — |
| 991 | C2 | — | 8 | 1 | no | — |
| 992 | C2 | — | 16 | 2 | no | — |
| 993 | C2 | — | 16 | 1 | no | — |
| 994 | C2 | — | 32 | 1 | no | — |
| 995 | C2 | #210356 | 1 | 1 | yes | characteristic |
| 996 | C2 | #495721 | 1 | 1 | yes | characteristic |
| 997 | C2 | #495739 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #21452 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #489285 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #17320 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6345864 | C2 | semidirect |
| 3. #483992 | C2 | semidirect |
| 4. #483881 | C2 | semidirect |
| 5. #211864 | C2 | semidirect |
| 6. #137499 | C2 | semidirect |
| 7. #137060 | C2 | semidirect |
| 8. #137036 | C2 | semidirect |
| 9. #136569 | C2 | semidirect |
| 10. #136481 | C2 | semidirect |
| 11. #136463 | C2 | semidirect |
| 12. #131813 | C2 | semidirect |
| 13. #129029 | C2 | semidirect |
| 14. #128691 | C2 | semidirect |
| 15. #128636 | C2 | semidirect |
| 39. #12406 | C4 | semidirect |
| 40. #12395 | C4 | semidirect |
| 41. #12380 | C4 | semidirect |
| 42. #12369 | C4 | semidirect |
| 43. #12354 | C4 | semidirect |
| 44. #12343 | C4 | semidirect |
| 45. #12328 | C4 | semidirect |
| 46. #12317 | C4 | semidirect |
| 752. Q16 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6345864 | 2 |
| #489285 | 2 |
| #483992 | 2 |
| #483881 | 2 |
| #211864 | 2 |
| #137499 | 2 |
| #137060 | 2 |
| #137036 | 2 |
| #136569 | 2 |
| #136481 | 2 |
| #136463 | 2 |
| #131813 | 2 |
| #129029 | 2 |
| #128691 | 2 |
| #128636 | 2 |