Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1452 conjugacy classes of subgroups.
The subgroup lattice has 1040 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6345807 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #489284 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #483992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #483875 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #211944 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #137501 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #137055 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #137039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #136567 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #136482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #136464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #131816 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #129033 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #128692 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #128636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | D8×#41 | C22 | 1 | 1 | yes | characteristic |
| 17 | D4×#131 | — | 2 | 1 | no | — |
| 18 | #33748 | C22 | 1 | 1 | yes | characteristic |
| 19 | #33669 | C22 | 1 | 1 | yes | characteristic |
| 20 | #19128 | C22 | 1 | 1 | yes | characteristic |
| 21 | #18073 | — | 2 | 1 | no | — |
| 22 | #18073 | C22 | 1 | 1 | yes | characteristic |
| 23 | #18044 | — | 2 | 1 | no | — |
| 24 | #18044 | C22 | 1 | 1 | yes | characteristic |
| 25 | #18001 | — | 2 | 1 | no | — |
| 26 | #18001 | — | 2 | 2 | no | — |
| 27 | #17962 | — | 2 | 1 | no | — |
| 28 | #17962 | C22 | 1 | 1 | yes | characteristic |
| 29 | #17962 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | #17912 | — | 2 | 1 | no | — |
| 31 | #17907 | — | 2 | 1 | no | — |
| 32 | #17907 | — | 2 | 2 | no | — |
| 33 | C2×#1580 | — | 2 | 1 | no | — |
| 34 | C2×#1580 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17826 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17507 | — | 2 | 1 | no | — |
| 37 | #17320 | C22 | 1 | 1 | yes | characteristic |
| 38 | C4×#361 | C22 | 1 | 1 | yes | characteristic |
| 39 | #12408 | C4 | 1 | 1 | yes | characteristic |
| 40 | #12396 | C4 | 1 | 1 | yes | characteristic |
| 41 | #12384 | C4 | 1 | 1 | yes | characteristic |
| 42 | #12372 | C4 | 1 | 1 | yes | characteristic |
| 43 | #12352 | C4 | 1 | 1 | yes | characteristic |
| 44 | #12340 | C4 | 1 | 1 | yes | characteristic |
| 45 | #12328 | C4 | 1 | 1 | yes | characteristic |
| 46 | #12316 | C4 | 1 | 1 | yes | characteristic |
| 47 | #12078 | — | 2 | 2 | no | — |
| 48 | #12078 | — | 2 | 1 | no | — |
| 49 | #12078 | — | 2 | 1 | no | — |
| 50 | #12078 | — | 2 | 2 | no | — |
| 51 | #12067 | — | 2 | 1 | no | — |
| 52 | #12067 | — | 2 | 1 | no | — |
| 53 | #12030 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #12020 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #11951 | C22 | 1 | 1 | yes | characteristic |
| 56 | #11751 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11680 | C22 | 1 | 1 | yes | characteristic |
| 58 | #11680 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #11663 | C22 | 1 | 1 | yes | characteristic |
| 60 | #11654 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #11615 | C22 | 1 | 1 | yes | characteristic |
| 62 | #11615 | C22 | 1 | 1 | yes | characteristic |
| 63 | #11593 | C22 | 1 | 1 | yes | characteristic |
| 64 | #11415 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #11404 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #9726 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | #9635 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | #9588 | — | 2 | 1 | no | — |
| 69 | #9211 | — | 2 | 1 | no | — |
| 70 | #8670 | C22 | 1 | 1 | yes | characteristic |
| 71 | #8294 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | #8245 | — | 2 | 1 | no | — |
| 73 | #7300 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #7295 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | #7173 | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #7164 | C22 | 1 | 1 | yes | characteristic, complemented |
| 77 | #7164 | C22 | 1 | 1 | yes | characteristic, complemented |
| 78 | #7158 | C22 | 1 | 1 | yes | characteristic, complemented |
| 79 | C22×#131 | — | 4 | 1 | no | — |
| 80 | D4×#41 | — | 2 | 1 | no | — |
| 81 | #3391 | C2×C4 | 1 | 1 | yes | characteristic |
| 82 | Q8×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | #3358 | — | 2 | 1 | no | — |
| 84 | #3334 | — | 2 | 1 | no | — |
| 85 | #3334 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #3294 | — | 2 | 2 | no | — |
| 87 | #3294 | — | 2 | 1 | no | — |
| 88 | D4×D8 | — | 2 | 1 | no | — |
| 89 | D4×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 90 | #3169 | — | 2 | 1 | no | — |
| 91 | #3169 | C23 | 1 | 1 | yes | characteristic |
| 92 | #3169 | C23 | 1 | 1 | yes | characteristic |
| 93 | #3106 | — | 2 | 1 | no | — |
| 94 | #3100 | — | 2 | 2 | no | — |
| 95 | #3100 | — | 2 | 1 | no | — |
| 96 | C8×#41 | D4 | 1 | 1 | yes | characteristic |
| 97 | C8×#41 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×D8 | — | 2 | 1 | no | — |
| 99 | C2×C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 100 | #2935 | — | 2 | 2 | no | — |
| 101 | #2935 | — | 2 | 1 | no | — |
| 102 | D4×M16 | — | 2 | 2 | no | — |
| 103 | D4×M16 | — | 2 | 1 | no | — |
| 104 | #2933 | — | 4 | 2 | no | — |
| 105 | #2933 | — | 4 | 1 | no | — |
| 106 | #2931 | — | 2 | 2 | no | — |
| 107 | #2931 | — | 2 | 1 | no | — |
| 108 | #2931 | — | 2 | 1 | no | — |
| 109 | #2929 | — | 4 | 2 | no | — |
| 110 | #2929 | — | 4 | 1 | no | — |
| 111 | C2×C8×D4 | — | 2 | 2 | no | — |
| 112 | C2×C8×D4 | — | 2 | 1 | no | — |
| 113 | #2906 | — | 2 | 1 | no | — |
| 114 | #2880 | — | 4 | 1 | no | — |
| 115 | C4×#131 | D4 | 1 | 1 | yes | characteristic |
| 116 | #2254 | C2×C4 | 1 | 1 | yes | characteristic |
| 117 | #2246 | C2×C4 | 1 | 1 | yes | characteristic |
| 118 | #2240 | C2×C4 | 1 | 1 | yes | characteristic |
| 119 | #2240 | C2×C4 | 1 | 1 | yes | characteristic |
| 120 | #2233 | — | 2 | 1 | no | — |
| 121 | #2226 | C2×C4 | 1 | 1 | yes | characteristic |
| 122 | #2226 | C2×C4 | 1 | 1 | yes | characteristic |
| 123 | #2218 | — | 2 | 2 | no | — |
| 124 | #2206 | C2×C4 | 1 | 1 | yes | characteristic |
| 125 | #2206 | C2×C4 | 1 | 1 | yes | characteristic |
| 126 | #2184 | — | 2 | 1 | no | — |
| 127 | #2177 | — | 2 | 1 | no | — |
| 128 | #2177 | — | 2 | 1 | no | — |
| 129 | #2177 | — | 2 | 2 | no | — |
| 130 | #2163 | C23 | 1 | 1 | yes | characteristic |
| 131 | #2163 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×#361 | — | 2 | 1 | no | — |
| 133 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 134 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 135 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 136 | #1678 | — | 2 | 1 | no | — |
| 137 | #1677 | — | 2 | 1 | no | — |
| 138 | #1676 | C2×C4 | 1 | 1 | yes | characteristic |
| 139 | #1675 | C2×C4 | 1 | 1 | yes | characteristic |
| 140 | #1668 | C2×C4 | 1 | 1 | yes | characteristic |
| 141 | #1667 | C2×C4 | 1 | 1 | yes | characteristic |
| 142 | #1594 | — | 2 | 2 | no | — |
| 143 | #1594 | — | 2 | 1 | no | — |
| 144 | #1594 | — | 2 | 1 | no | — |
| 145 | #1594 | — | 2 | 1 | no | — |
| 146 | #1594 | — | 2 | 1 | no | — |
| 147 | #1594 | — | 2 | 1 | no | — |
| 148 | #1594 | D4 | 1 | 2 | yes | — |
| 149 | #1588 | — | 4 | 1 | no | — |
| 150 | #1586 | — | 2 | 2 | no | — |
| 151 | #1586 | — | 2 | 2 | no | — |
| 152 | #1586 | — | 2 | 2 | no | — |
| 153 | #1586 | — | 2 | 2 | no | — |
| 154 | #1586 | — | 2 | 2 | no | — |
| 155 | #1586 | — | 2 | 2 | no | — |
| 156 | #1586 | — | 4 | 1 | no | — |
| 157 | #1580 | — | 2 | 2 | no | — |
| 158 | #1580 | — | 2 | 2 | no | — |
| 159 | #1580 | — | 2 | 2 | no | — |
| 160 | #1580 | — | 2 | 1 | no | — |
| 161 | #1580 | — | 2 | 1 | no | — |
| 162 | #1580 | — | 2 | 1 | no | — |
| 163 | #1580 | — | 2 | 1 | no | — |
| 164 | #1580 | — | 2 | 1 | no | — |
| 165 | #1580 | — | 2 | 1 | no | — |
| 166 | #1580 | — | 2 | 1 | no | — |
| 167 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 168 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 169 | #1580 | D4 | 1 | 2 | yes | — |
| 170 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 171 | #1580 | D4 | 1 | 1 | yes | characteristic |
| 172 | C8×SD16 | — | 4 | 1 | no | — |
| 173 | C8×D8 | — | 4 | 1 | no | — |
| 174 | #1574 | — | 2 | 1 | no | — |
| 175 | #1570 | — | 2 | 1 | no | — |
| 176 | #1570 | — | 2 | 2 | no | — |
| 177 | #1566 | — | 2 | 1 | no | — |
| 178 | #1566 | C23 | 1 | 1 | yes | characteristic |
| 179 | #1566 | C23 | 1 | 1 | yes | characteristic |
| 180 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 181 | C2×#334 | — | 2 | 1 | no | — |
| 182 | C2×#334 | C23 | 1 | 1 | yes | characteristic |
| 183 | #1543 | — | 2 | 1 | no | — |
| 184 | #1525 | — | 2 | 1 | no | — |
| 185 | #1492 | — | 2 | 2 | no | — |
| 186 | #1492 | — | 2 | 1 | no | — |
| 187 | #1492 | — | 2 | 1 | no | — |
| 188 | #1489 | — | 2 | 1 | no | — |
| 189 | #1486 | — | 2 | 2 | no | — |
| 190 | #1486 | — | 2 | 1 | no | — |
| 191 | #1484 | — | 2 | 1 | no | — |
| 192 | #1480 | — | 2 | 2 | no | — |
| 193 | #1480 | — | 2 | 1 | no | — |
| 194 | C2×D4⋊C8 | — | 2 | 2 | no | — |
| 195 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 196 | #1452 | — | 2 | 1 | no | — |
| 197 | #1452 | D4 | 1 | 1 | yes | characteristic |
| 198 | #1451 | — | 2 | 1 | no | — |
| 199 | #1451 | — | 2 | 1 | no | — |
| 200 | #1451 | D4 | 1 | 1 | yes | characteristic |
| 201 | #1451 | C23 | 1 | 1 | yes | characteristic |
| 202 | C8×M16 | — | 2 | 1 | no | — |
| 203 | C2×#322 | — | 2 | 1 | no | — |
| 204 | C2×#322 | C23 | 1 | 1 | yes | characteristic |
| 205 | #1387 | — | 2 | 1 | no | — |
| 206 | #1368 | — | 2 | 1 | no | — |
| 207 | #1368 | — | 2 | 1 | no | — |
| 208 | #1368 | — | 2 | 2 | no | — |
| 209 | #1364 | C2×C4 | 1 | 1 | yes | characteristic |
| 210 | #1364 | C2×C4 | 1 | 1 | yes | characteristic |
| 211 | #1361 | C2×C4 | 1 | 1 | yes | characteristic |
| 212 | #1361 | C2×C4 | 1 | 1 | yes | characteristic |
| 213 | #1349 | — | 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 | #1333 | — | 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 | #1331 | C2×C4 | 1 | 1 | yes | characteristic |
| 224 | #1331 | 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 | #1299 | — | 2 | 1 | no | — |
| 235 | #1299 | — | 2 | 1 | no | — |
| 236 | #1278 | — | 2 | 1 | no | — |
| 237 | C22×#41 | — | 4 | 1 | no | — |
| 238 | C22×D8 | — | 2 | 1 | no | — |
| 239 | C22×D8 | #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 | C2×#131 | — | 4 | 2 | no | — |
| 245 | C2×#131 | — | 4 | 1 | no | — |
| 246 | C2×#131 | — | 4 | 1 | no | — |
| 247 | C2×#131 | — | 8 | 4 | no | — |
| 248 | C2×#131 | — | 8 | 4 | no | — |
| 249 | C22×M16 | — | 4 | 2 | no | — |
| 250 | C22×M16 | — | 4 | 1 | no | — |
| 251 | C23×C8 | — | 4 | 2 | no | — |
| 252 | C23×C8 | — | 4 | 1 | no | — |
| 253 | #550 | — | 2 | 1 | no | — |
| 254 | D4×Q8 | — | 2 | 1 | no | — |
| 255 | #548 | — | 4 | 1 | no | — |
| 256 | #547 | — | 2 | 2 | no | — |
| 257 | #547 | — | 2 | 1 | no | — |
| 258 | #546 | — | 4 | 2 | no | — |
| 259 | #546 | — | 4 | 1 | no | — |
| 260 | D42 | — | 2 | 2 | no | — |
| 261 | D42 | — | 2 | 1 | no | — |
| 262 | #532 | — | 2 | 2 | no | — |
| 263 | #532 | — | 2 | 1 | no | — |
| 264 | #532 | — | 2 | 1 | no | — |
| 265 | #525 | — | 4 | 2 | no | — |
| 266 | #525 | — | 4 | 1 | no | — |
| 267 | C4×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×D4 | — | 2 | 2 | no | — |
| 269 | C2×C4×D4 | — | 2 | 1 | no | — |
| 270 | C2×D16 | — | 2 | 1 | no | — |
| 271 | C2×D16 | — | 2 | 1 | no | — |
| 272 | C2×D16 | — | 2 | 2 | no | — |
| 273 | C2×M32 | — | 2 | 1 | no | — |
| 274 | C2×M32 | — | 2 | 1 | no | — |
| 275 | #500 | — | 2 | 1 | no | — |
| 276 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 277 | #500 | C22×C4 | 1 | 1 | yes | characteristic |
| 278 | #493 | — | 2 | 1 | no | — |
| 279 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 280 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 281 | #486 | — | 2 | 2 | no | — |
| 282 | #486 | — | 2 | 1 | no | — |
| 283 | #486 | — | 2 | 1 | no | — |
| 284 | #482 | — | 4 | 1 | no | — |
| 285 | #480 | — | 2 | 2 | no | — |
| 286 | #480 | — | 2 | 2 | no | — |
| 287 | #480 | — | 2 | 2 | no | — |
| 288 | #477 | — | 2 | 1 | no | — |
| 289 | #476 | — | 2 | 1 | no | — |
| 290 | #474 | — | 2 | 2 | no | — |
| 291 | #474 | — | 2 | 2 | no | — |
| 292 | #474 | — | 2 | 1 | no | — |
| 293 | #474 | — | 2 | 1 | no | — |
| 294 | #466 | — | 2 | 2 | no | — |
| 295 | #466 | — | 2 | 1 | no | — |
| 296 | #466 | — | 2 | 1 | no | — |
| 297 | #466 | — | 2 | 1 | no | — |
| 298 | #466 | — | 2 | 1 | no | — |
| 299 | #466 | — | 2 | 1 | no | — |
| 300 | #466 | #41 | 1 | 2 | yes | — |
| 301 | #460 | — | 2 | 1 | no | — |
| 302 | #459 | — | 2 | 2 | no | — |
| 303 | #459 | — | 2 | 2 | no | — |
| 304 | #459 | — | 2 | 1 | no | — |
| 305 | #459 | — | 2 | 1 | no | — |
| 306 | #459 | — | 2 | 1 | no | — |
| 307 | #449 | — | 4 | 1 | no | — |
| 308 | #447 | — | 2 | 2 | no | — |
| 309 | #447 | — | 2 | 2 | no | — |
| 310 | #447 | — | 2 | 2 | no | — |
| 311 | C8×Q8 | — | 2 | 1 | no | — |
| 312 | C8×Q8 | C22×C4 | 1 | 1 | yes | characteristic |
| 313 | C8×Q8 | #41 | 1 | 1 | yes | characteristic |
| 314 | C4×SD16 | — | 4 | 1 | no | — |
| 315 | C4×D8 | — | 2 | 2 | no | — |
| 316 | C4×D8 | — | 2 | 2 | no | — |
| 317 | C4×D8 | — | 2 | 2 | no | — |
| 318 | C4×D8 | — | 2 | 1 | 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 | — | 2 | 1 | no | — |
| 324 | C4×D8 | — | 2 | 1 | no | — |
| 325 | C4×D8 | — | 4 | 1 | no | — |
| 326 | C4×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 327 | C4×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 328 | C4×D8 | C2×D4 | 1 | 2 | yes | — |
| 329 | C4×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | C4×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | #436 | — | 2 | 2 | no | — |
| 332 | #436 | — | 2 | 2 | no | — |
| 333 | #436 | — | 2 | 2 | no | — |
| 334 | #436 | — | 4 | 2 | no | — |
| 335 | #436 | — | 4 | 1 | no | — |
| 336 | #436 | — | 4 | 1 | no | — |
| 337 | #436 | — | 4 | 1 | no | — |
| 338 | #435 | — | 4 | 2 | no | — |
| 339 | #435 | — | 4 | 2 | no | — |
| 340 | #435 | — | 4 | 2 | no | — |
| 341 | #435 | — | 4 | 2 | no | — |
| 342 | #435 | — | 4 | 2 | no | — |
| 343 | #435 | — | 4 | 2 | no | — |
| 344 | C8×D4 | — | 2 | 1 | no | — |
| 345 | C8×D4 | — | 2 | 1 | no | — |
| 346 | C8×D4 | — | 2 | 2 | no | — |
| 347 | C8×D4 | — | 2 | 2 | no | — |
| 348 | C8×D4 | — | 2 | 1 | no | — |
| 349 | C8×D4 | — | 2 | 1 | no | — |
| 350 | C8×D4 | — | 2 | 1 | no | — |
| 351 | C8×D4 | — | 2 | 2 | no | — |
| 352 | C8×D4 | — | 2 | 1 | no | — |
| 353 | C8×D4 | — | 2 | 1 | no | — |
| 354 | C8×D4 | — | 4 | 2 | no | — |
| 355 | C8×D4 | — | 4 | 1 | no | — |
| 356 | C8×D4 | — | 4 | 2 | no | — |
| 357 | C8×D4 | — | 4 | 1 | no | — |
| 358 | C8×D4 | — | 4 | 2 | no | — |
| 359 | C8×D4 | — | 4 | 1 | no | — |
| 360 | C8×D4 | — | 4 | 1 | no | — |
| 361 | C8×D4 | — | 4 | 1 | no | — |
| 362 | C8×D4 | — | 4 | 1 | no | — |
| 363 | C8×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 364 | C8×D4 | #41 | 1 | 1 | yes | characteristic |
| 365 | #431 | — | 2 | 1 | no | — |
| 366 | #431 | — | 2 | 1 | no | — |
| 367 | #431 | — | 2 | 1 | no | — |
| 368 | #431 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | #431 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | C2×#108 | — | 2 | 1 | no | — |
| 371 | C2×#107 | — | 2 | 1 | no | — |
| 372 | C2×#107 | #41 | 1 | 1 | yes | characteristic |
| 373 | #424 | — | 4 | 2 | no | — |
| 374 | #424 | — | 4 | 1 | no | — |
| 375 | #423 | — | 2 | 2 | no | — |
| 376 | #423 | — | 2 | 1 | no | — |
| 377 | #423 | — | 2 | 1 | no | — |
| 378 | C2×C4⋊C8 | — | 2 | 2 | no | — |
| 379 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 380 | C2×#102 | — | 2 | 2 | no | — |
| 381 | C2×#102 | — | 2 | 1 | no | — |
| 382 | #408 | — | 4 | 2 | no | — |
| 383 | #408 | — | 4 | 1 | no | — |
| 384 | #408 | — | 4 | 2 | no | — |
| 385 | #408 | — | 4 | 1 | no | — |
| 386 | #408 | — | 4 | 1 | no | — |
| 387 | #407 | — | 4 | 2 | no | — |
| 388 | #407 | — | 4 | 1 | no | — |
| 389 | C2×C22⋊C8 | — | 4 | 2 | no | — |
| 390 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 391 | #405 | — | 2 | 1 | no | — |
| 392 | #405 | — | 2 | 2 | no | — |
| 393 | C4×M16 | — | 2 | 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 | C2×D4 | 1 | 1 | yes | characteristic |
| 400 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 401 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 402 | #367 | — | 2 | 2 | no | — |
| 403 | #367 | — | 2 | 1 | no | — |
| 404 | #367 | — | 2 | 1 | no | — |
| 405 | C4⋊C16 | — | 2 | 1 | no | — |
| 406 | C4⋊C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 407 | C4⋊C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 408 | #361 | — | 2 | 4 | no | — |
| 409 | #357 | — | 2 | 1 | no | — |
| 410 | #357 | — | 2 | 1 | no | — |
| 411 | #357 | — | 2 | 2 | no | — |
| 412 | #357 | — | 2 | 1 | no | — |
| 413 | #357 | — | 2 | 1 | no | — |
| 414 | #357 | — | 2 | 2 | no | — |
| 415 | C22⋊C16 | — | 2 | 1 | no | — |
| 416 | C22⋊C16 | — | 2 | 1 | no | — |
| 417 | #346 | — | 2 | 1 | no | — |
| 418 | #346 | — | 2 | 1 | no | — |
| 419 | #346 | — | 2 | 1 | no | — |
| 420 | #346 | — | 2 | 1 | no | — |
| 421 | C4×C16 | — | 2 | 1 | no | — |
| 422 | C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 423 | C4×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 424 | #341 | — | 2 | 1 | no | — |
| 425 | #335 | — | 4 | 1 | no | — |
| 426 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 427 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 428 | #334 | — | 2 | 2 | no | — |
| 429 | #334 | — | 2 | 2 | no | — |
| 430 | #334 | — | 2 | 1 | no | — |
| 431 | #334 | — | 2 | 1 | no | — |
| 432 | #334 | — | 2 | 1 | no | — |
| 433 | #334 | — | 2 | 1 | no | — |
| 434 | #334 | — | 2 | 1 | no | — |
| 435 | #334 | — | 4 | 1 | no | — |
| 436 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 437 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 438 | #334 | C2×D4 | 1 | 2 | yes | — |
| 439 | #333 | — | 2 | 1 | no | — |
| 440 | #333 | — | 2 | 1 | no | — |
| 441 | #331 | — | 2 | 1 | no | — |
| 442 | #331 | — | 2 | 1 | no | — |
| 443 | #329 | — | 4 | 2 | no | — |
| 444 | Q8⋊C8 | — | 4 | 1 | no | — |
| 445 | D4⋊C8 | — | 2 | 2 | no | — |
| 446 | D4⋊C8 | — | 2 | 2 | no | — |
| 447 | D4⋊C8 | — | 2 | 2 | no | — |
| 448 | D4⋊C8 | — | 2 | 2 | no | — |
| 449 | D4⋊C8 | — | 2 | 1 | no | — |
| 450 | D4⋊C8 | — | 2 | 2 | no | — |
| 451 | D4⋊C8 | — | 2 | 1 | no | — |
| 452 | D4⋊C8 | — | 2 | 1 | no | — |
| 453 | D4⋊C8 | — | 2 | 1 | no | — |
| 454 | D4⋊C8 | — | 2 | 2 | no | — |
| 455 | D4⋊C8 | — | 4 | 1 | no | — |
| 456 | D4⋊C8 | — | 4 | 1 | no | — |
| 457 | D4⋊C8 | — | 4 | 1 | no | — |
| 458 | D4⋊C8 | — | 4 | 1 | no | — |
| 459 | D4⋊C8 | — | 4 | 1 | no | — |
| 460 | #322 | — | 2 | 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 | — | 4 | 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 | C82 | — | 4 | 1 | no | — |
| 472 | C2×#41 | — | 4 | 2 | 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 | — | 4 | 1 | no | — |
| 478 | C2×#41 | — | 8 | 2 | no | — |
| 479 | C2×#41 | — | 8 | 2 | no | — |
| 480 | C2×#41 | — | 8 | 2 | no | — |
| 481 | C2×#41 | — | 8 | 2 | no | — |
| 482 | C2×#41 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 483 | C22×Q8 | — | 4 | 1 | no | — |
| 484 | C22×D4 | — | 2 | 2 | no | — |
| 485 | C22×D4 | — | 2 | 1 | no | — |
| 486 | C22×D4 | — | 4 | 2 | no | — |
| 487 | C22×D4 | — | 4 | 1 | no | — |
| 488 | C23×C4 | — | 4 | 2 | no | — |
| 489 | C23×C4 | — | 4 | 1 | no | — |
| 490 | C2×SD16 | — | 4 | 1 | no | — |
| 491 | C2×D8 | — | 2 | 2 | no | — |
| 492 | C2×D8 | — | 2 | 2 | no | — |
| 493 | C2×D8 | — | 2 | 2 | no | — |
| 494 | C2×D8 | — | 2 | 1 | no | — |
| 495 | C2×D8 | — | 2 | 1 | no | — |
| 496 | C2×D8 | — | 2 | 1 | no | — |
| 497 | C2×D8 | — | 2 | 1 | no | — |
| 498 | C2×D8 | — | 4 | 1 | no | — |
| 499 | C2×D8 | — | 4 | 2 | no | — |
| 500 | C2×D8 | — | 4 | 2 | no | — |
| 501 | C2×D8 | — | 4 | 1 | no | — |
| 502 | C2×D8 | C4×D4 | 1 | 1 | yes | characteristic |
| 503 | C2×D8 | C4×D4 | 1 | 1 | yes | characteristic |
| 504 | C2×D8 | C4×D4 | 1 | 2 | yes | — |
| 505 | #131 | — | 4 | 2 | no | — |
| 506 | #131 | — | 4 | 2 | no | — |
| 507 | #131 | — | 8 | 8 | no | — |
| 508 | #131 | — | 8 | 2 | no | — |
| 509 | #131 | — | 8 | 2 | no | — |
| 510 | #131 | — | 8 | 8 | no | — |
| 511 | #131 | — | 8 | 2 | no | — |
| 512 | #131 | — | 8 | 2 | no | — |
| 513 | #131 | — | 8 | 2 | no | — |
| 514 | #131 | — | 8 | 2 | no | — |
| 515 | #131 | — | 16 | 2 | no | — |
| 516 | C2×M16 | — | 2 | 2 | no | — |
| 517 | C2×M16 | — | 2 | 1 | no | — |
| 518 | C2×M16 | — | 4 | 2 | no | — |
| 519 | C2×M16 | — | 4 | 2 | no | — |
| 520 | C2×M16 | — | 4 | 2 | no | — |
| 521 | C2×M16 | — | 4 | 2 | no | — |
| 522 | C2×M16 | — | 4 | 1 | no | — |
| 523 | C2×M16 | — | 4 | 1 | no | — |
| 524 | C2×M16 | — | 4 | 1 | no | — |
| 525 | C2×M16 | — | 8 | 1 | no | — |
| 526 | C2×M16 | — | 8 | 8 | no | — |
| 527 | C2×M16 | — | 8 | 2 | no | — |
| 528 | C2×M16 | — | 8 | 2 | no | — |
| 529 | C22×C8 | — | 2 | 2 | no | — |
| 530 | C22×C8 | — | 2 | 1 | no | — |
| 531 | C22×C8 | — | 2 | 1 | no | — |
| 532 | C22×C8 | — | 2 | 1 | no | — |
| 533 | C22×C8 | — | 2 | 1 | no | — |
| 534 | C22×C8 | — | 4 | 1 | no | — |
| 535 | C22×C8 | — | 4 | 2 | no | — |
| 536 | C22×C8 | — | 4 | 1 | no | — |
| 537 | C22×C8 | — | 4 | 2 | no | — |
| 538 | C22×C8 | — | 4 | 1 | no | — |
| 539 | C22×C8 | — | 4 | 2 | no | — |
| 540 | C22×C8 | — | 4 | 1 | no | — |
| 541 | C22×C8 | — | 4 | 1 | no | — |
| 542 | C22×C8 | — | 4 | 2 | no | — |
| 543 | C22×C8 | — | 4 | 1 | no | — |
| 544 | C22×C8 | — | 8 | 1 | no | — |
| 545 | C22×C8 | — | 8 | 8 | no | — |
| 546 | C22×C8 | — | 8 | 2 | no | — |
| 547 | C22×C8 | — | 8 | 2 | no | — |
| 548 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 549 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 550 | C4⋊Q8 | — | 2 | 2 | no | — |
| 551 | C4⋊Q8 | — | 2 | 1 | no | — |
| 552 | C4⋊Q8 | — | 2 | 1 | no | — |
| 553 | #127 | — | 2 | 2 | no | — |
| 554 | #127 | — | 2 | 1 | no | — |
| 555 | #127 | — | 2 | 1 | no | — |
| 556 | #124 | — | 4 | 2 | no | — |
| 557 | #124 | — | 4 | 1 | no | — |
| 558 | #124 | — | 4 | 1 | no | — |
| 559 | #123 | — | 4 | 2 | no | — |
| 560 | #123 | — | 4 | 2 | no | — |
| 561 | #123 | — | 4 | 2 | no | — |
| 562 | C22⋊Q8 | — | 4 | 2 | no | — |
| 563 | C22⋊Q8 | — | 4 | 2 | no | — |
| 564 | C22⋊Q8 | — | 4 | 1 | no | — |
| 565 | C22⋊Q8 | — | 4 | 1 | no | — |
| 566 | #121 | — | 2 | 2 | no | — |
| 567 | #121 | — | 2 | 2 | no | — |
| 568 | #121 | — | 2 | 2 | no | — |
| 569 | #121 | — | 4 | 2 | no | — |
| 570 | #121 | — | 4 | 2 | no | — |
| 571 | #121 | — | 4 | 2 | no | — |
| 572 | #121 | — | 4 | 1 | no | — |
| 573 | #121 | — | 4 | 1 | no | — |
| 574 | #121 | — | 4 | 1 | no | — |
| 575 | #121 | — | 4 | 1 | no | — |
| 576 | #121 | — | 4 | 1 | no | — |
| 577 | #120 | — | 4 | 2 | no | — |
| 578 | #120 | — | 4 | 2 | no | — |
| 579 | #120 | — | 4 | 2 | no | — |
| 580 | C4×Q8 | C4×D4 | 1 | 1 | yes | characteristic |
| 581 | C4×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 582 | C4×D4 | — | 2 | 1 | no | — |
| 583 | C4×D4 | — | 2 | 1 | no | — |
| 584 | C4×D4 | — | 2 | 2 | no | — |
| 585 | C4×D4 | — | 2 | 2 | no | — |
| 586 | C4×D4 | — | 2 | 1 | no | — |
| 587 | C4×D4 | — | 2 | 1 | no | — |
| 588 | C4×D4 | — | 2 | 1 | no | — |
| 589 | C4×D4 | — | 2 | 2 | no | — |
| 590 | C4×D4 | — | 2 | 1 | no | — |
| 591 | C4×D4 | — | 4 | 2 | no | — |
| 592 | C4×D4 | — | 4 | 2 | no | — |
| 593 | C4×D4 | — | 4 | 2 | no | — |
| 594 | C4×D4 | — | 4 | 1 | no | — |
| 595 | C4×D4 | — | 4 | 1 | no | — |
| 596 | C4×D4 | — | 4 | 1 | no | — |
| 597 | C4×D4 | — | 4 | 1 | no | — |
| 598 | C4×D4 | — | 4 | 1 | no | — |
| 599 | C4×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 600 | C4×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 601 | #117 | — | 2 | 1 | no | — |
| 602 | #117 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 603 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 604 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 605 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 606 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 607 | C2×C42 | — | 2 | 1 | no | — |
| 608 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 609 | D16 | — | 4 | 2 | no | — |
| 610 | D16 | — | 4 | 2 | no | — |
| 611 | D16 | — | 8 | 2 | no | — |
| 612 | M32 | — | 2 | 2 | no | — |
| 613 | M32 | — | 4 | 1 | no | — |
| 614 | M32 | — | 8 | 1 | no | — |
| 615 | C2×C16 | — | 2 | 1 | no | — |
| 616 | C2×C16 | — | 2 | 1 | no | — |
| 617 | C2×C16 | — | 2 | 1 | no | — |
| 618 | C2×C16 | — | 2 | 1 | no | — |
| 619 | C2×C16 | — | 4 | 1 | no | — |
| 620 | C2×C16 | — | 4 | 1 | no | — |
| 621 | #108 | — | 2 | 2 | no | — |
| 622 | #108 | — | 4 | 1 | no | — |
| 623 | #107 | — | 2 | 2 | no | — |
| 624 | #107 | — | 2 | 2 | no | — |
| 625 | #107 | — | 2 | 1 | no | — |
| 626 | #107 | — | 2 | 1 | no | — |
| 627 | #107 | — | 2 | 1 | no | — |
| 628 | #107 | — | 2 | 1 | no | — |
| 629 | #107 | — | 4 | 1 | no | — |
| 630 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 631 | #107 | C4×D4 | 1 | 1 | yes | characteristic |
| 632 | #107 | C4×D4 | 1 | 2 | yes | — |
| 633 | #106 | — | 4 | 1 | no | — |
| 634 | C4⋊C8 | — | 2 | 1 | no | — |
| 635 | C4⋊C8 | — | 2 | 1 | no | — |
| 636 | C4⋊C8 | — | 2 | 1 | no | — |
| 637 | C4⋊C8 | — | 2 | 1 | no | — |
| 638 | C4⋊C8 | — | 2 | 1 | no | — |
| 639 | C4⋊C8 | — | 2 | 2 | no | — |
| 640 | C4⋊C8 | — | 2 | 1 | no | — |
| 641 | C4⋊C8 | — | 2 | 1 | no | — |
| 642 | C4⋊C8 | — | 4 | 1 | no | — |
| 643 | C4⋊C8 | — | 4 | 2 | no | — |
| 644 | C4⋊C8 | — | 4 | 2 | no | — |
| 645 | C4⋊C8 | — | 4 | 1 | no | — |
| 646 | C4⋊C8 | — | 4 | 1 | no | — |
| 647 | C4⋊C8 | — | 4 | 1 | no | — |
| 648 | C4⋊C8 | — | 4 | 1 | no | — |
| 649 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 650 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 651 | #103 | — | 4 | 1 | no | — |
| 652 | #102 | — | 2 | 2 | no | — |
| 653 | #102 | — | 2 | 2 | no | — |
| 654 | #102 | — | 2 | 2 | no | — |
| 655 | #102 | — | 2 | 2 | no | — |
| 656 | #102 | — | 2 | 1 | no | — |
| 657 | #102 | — | 2 | 1 | no | — |
| 658 | #102 | — | 2 | 1 | no | — |
| 659 | #102 | — | 2 | 2 | no | — |
| 660 | #102 | — | 2 | 1 | no | — |
| 661 | #102 | — | 2 | 2 | no | — |
| 662 | #102 | — | 4 | 1 | no | — |
| 663 | #102 | — | 4 | 1 | no | — |
| 664 | #102 | — | 4 | 1 | no | — |
| 665 | #102 | — | 4 | 1 | no | — |
| 666 | #102 | — | 4 | 1 | no | — |
| 667 | C22⋊C8 | — | 2 | 1 | no | — |
| 668 | C22⋊C8 | — | 2 | 1 | no | — |
| 669 | C22⋊C8 | — | 2 | 1 | no | — |
| 670 | C22⋊C8 | — | 2 | 1 | no | — |
| 671 | C22⋊C8 | — | 4 | 1 | no | — |
| 672 | C22⋊C8 | — | 4 | 1 | no | — |
| 673 | C22⋊C8 | — | 4 | 2 | no | — |
| 674 | C22⋊C8 | — | 4 | 1 | no | — |
| 675 | C22⋊C8 | — | 4 | 2 | no | — |
| 676 | C22⋊C8 | — | 4 | 1 | no | — |
| 677 | C22⋊C8 | — | 4 | 2 | no | — |
| 678 | C22⋊C8 | — | 4 | 1 | no | — |
| 679 | C22⋊C8 | — | 4 | 2 | no | — |
| 680 | C22⋊C8 | — | 4 | 2 | no | — |
| 681 | C22⋊C8 | — | 4 | 2 | no | — |
| 682 | C22⋊C8 | — | 4 | 1 | no | — |
| 683 | C22⋊C8 | — | 8 | 1 | no | — |
| 684 | C22⋊C8 | — | 8 | 1 | no | — |
| 685 | #97 | — | 2 | 2 | no | — |
| 686 | #97 | — | 4 | 1 | no | — |
| 687 | #97 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 688 | C4×C8 | — | 2 | 2 | no | — |
| 689 | C4×C8 | — | 2 | 1 | no | — |
| 690 | C4×C8 | — | 2 | 1 | no | — |
| 691 | C4×C8 | — | 2 | 1 | no | — |
| 692 | C4×C8 | — | 2 | 1 | no | — |
| 693 | C4×C8 | — | 2 | 1 | no | — |
| 694 | C4×C8 | — | 2 | 1 | no | — |
| 695 | C4×C8 | — | 2 | 1 | no | — |
| 696 | C4×C8 | — | 4 | 1 | no | — |
| 697 | C4×C8 | — | 4 | 1 | no | — |
| 698 | C4×C8 | — | 4 | 1 | no | — |
| 699 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 700 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 701 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 702 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 703 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 704 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 705 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 706 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 707 | C24 | — | 4 | 2 | no | — |
| 708 | C24 | — | 4 | 1 | no | — |
| 709 | #41 | — | 2 | 2 | no | — |
| 710 | #41 | — | 2 | 2 | no | — |
| 711 | #41 | — | 8 | 4 | no | — |
| 712 | #41 | — | 8 | 1 | no | — |
| 713 | #41 | — | 8 | 1 | no | — |
| 714 | #41 | — | 8 | 4 | no | — |
| 715 | #41 | — | 8 | 1 | no | — |
| 716 | #41 | — | 8 | 1 | no | — |
| 717 | #41 | — | 8 | 4 | no | — |
| 718 | #41 | — | 8 | 4 | no | — |
| 719 | #41 | — | 8 | 2 | no | — |
| 720 | #41 | — | 8 | 2 | no | — |
| 721 | #41 | — | 8 | 2 | no | — |
| 722 | #41 | — | 8 | 2 | no | — |
| 723 | #41 | — | 16 | 1 | no | — |
| 724 | #41 | — | 16 | 1 | no | — |
| 725 | C2×Q8 | — | 4 | 2 | no | — |
| 726 | C2×Q8 | — | 4 | 1 | no | — |
| 727 | C2×Q8 | — | 4 | 1 | no | — |
| 728 | C2×Q8 | — | 8 | 2 | no | — |
| 729 | C2×Q8 | — | 8 | 2 | no | — |
| 730 | C2×Q8 | #442 | 1 | 1 | yes | characteristic |
| 731 | C2×D4 | — | 2 | 1 | no | — |
| 732 | C2×D4 | — | 2 | 1 | no | — |
| 733 | C2×D4 | — | 2 | 1 | no | — |
| 734 | C2×D4 | — | 2 | 2 | no | — |
| 735 | C2×D4 | — | 4 | 2 | no | — |
| 736 | C2×D4 | — | 4 | 2 | no | — |
| 737 | C2×D4 | — | 4 | 2 | no | — |
| 738 | C2×D4 | — | 4 | 2 | no | — |
| 739 | C2×D4 | — | 4 | 4 | no | — |
| 740 | C2×D4 | — | 4 | 2 | no | — |
| 741 | C2×D4 | — | 4 | 2 | no | — |
| 742 | C2×D4 | — | 4 | 2 | no | — |
| 743 | C2×D4 | — | 4 | 1 | no | — |
| 744 | C2×D4 | — | 4 | 1 | no | — |
| 745 | C2×D4 | — | 4 | 1 | no | — |
| 746 | C2×D4 | — | 4 | 1 | no | — |
| 747 | C2×D4 | — | 4 | 1 | no | — |
| 748 | C2×D4 | — | 4 | 1 | no | — |
| 749 | C2×D4 | — | 8 | 1 | no | — |
| 750 | C2×D4 | — | 8 | 2 | no | — |
| 751 | C2×D4 | — | 8 | 4 | no | — |
| 752 | C2×D4 | — | 8 | 4 | no | — |
| 753 | C2×D4 | — | 8 | 2 | no | — |
| 754 | C2×D4 | — | 8 | 2 | no | — |
| 755 | C2×D4 | — | 8 | 1 | no | — |
| 756 | C2×D4 | #442 | 1 | 1 | yes | characteristic |
| 757 | C22×C4 | — | 2 | 1 | no | — |
| 758 | C22×C4 | — | 2 | 1 | no | — |
| 759 | C22×C4 | — | 2 | 1 | no | — |
| 760 | C22×C4 | — | 4 | 2 | no | — |
| 761 | C22×C4 | — | 4 | 2 | no | — |
| 762 | C22×C4 | — | 4 | 2 | no | — |
| 763 | C22×C4 | — | 4 | 1 | no | — |
| 764 | C22×C4 | — | 4 | 1 | no | — |
| 765 | C22×C4 | — | 4 | 1 | no | — |
| 766 | C22×C4 | — | 4 | 1 | no | — |
| 767 | C22×C4 | — | 4 | 2 | no | — |
| 768 | C22×C4 | — | 4 | 1 | no | — |
| 769 | C22×C4 | — | 8 | 4 | no | — |
| 770 | C22×C4 | — | 8 | 1 | no | — |
| 771 | C22×C4 | — | 8 | 1 | no | — |
| 772 | C22×C4 | — | 8 | 4 | no | — |
| 773 | C22×C4 | — | 8 | 1 | no | — |
| 774 | C22×C4 | — | 8 | 1 | no | — |
| 775 | C22×C4 | — | 8 | 1 | no | — |
| 776 | C22×C4 | #525 | 1 | 1 | yes | characteristic |
| 777 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 778 | C22×C4 | #575 | 1 | 1 | yes | characteristic |
| 779 | SD16 | — | 8 | 2 | no | — |
| 780 | D8 | — | 2 | 1 | no | — |
| 781 | D8 | — | 2 | 1 | no | — |
| 782 | D8 | — | 2 | 1 | no | — |
| 783 | D8 | — | 4 | 2 | no | — |
| 784 | D8 | — | 4 | 2 | no | — |
| 785 | D8 | — | 4 | 2 | no | — |
| 786 | D8 | — | 4 | 4 | no | — |
| 787 | D8 | — | 4 | 1 | no | — |
| 788 | D8 | — | 4 | 1 | no | — |
| 789 | D8 | — | 4 | 1 | no | — |
| 790 | D8 | — | 4 | 1 | no | — |
| 791 | D8 | — | 8 | 2 | no | — |
| 792 | D8 | — | 8 | 2 | no | — |
| 793 | D8 | #443 | 1 | 2 | yes | — |
| 794 | M16 | — | 4 | 4 | no | — |
| 795 | M16 | — | 4 | 1 | no | — |
| 796 | M16 | — | 4 | 1 | no | — |
| 797 | M16 | — | 4 | 2 | no | — |
| 798 | M16 | — | 8 | 4 | no | — |
| 799 | M16 | — | 8 | 4 | no | — |
| 800 | M16 | — | 8 | 4 | no | — |
| 801 | M16 | — | 8 | 1 | no | — |
| 802 | M16 | — | 8 | 4 | no | — |
| 803 | M16 | — | 8 | 1 | no | — |
| 804 | M16 | — | 8 | 1 | no | — |
| 805 | M16 | — | 16 | 2 | no | — |
| 806 | M16 | — | 16 | 1 | no | — |
| 807 | C2×C8 | — | 2 | 1 | no | — |
| 808 | C2×C8 | — | 2 | 1 | no | — |
| 809 | C2×C8 | — | 2 | 1 | no | — |
| 810 | C2×C8 | — | 2 | 2 | no | — |
| 811 | C2×C8 | — | 2 | 1 | no | — |
| 812 | C2×C8 | — | 2 | 1 | no | — |
| 813 | C2×C8 | — | 2 | 1 | no | — |
| 814 | C2×C8 | — | 2 | 1 | no | — |
| 815 | C2×C8 | — | 2 | 1 | no | — |
| 816 | C2×C8 | — | 4 | 1 | no | — |
| 817 | C2×C8 | — | 4 | 4 | no | — |
| 818 | C2×C8 | — | 4 | 1 | no | — |
| 819 | C2×C8 | — | 4 | 1 | no | — |
| 820 | C2×C8 | — | 4 | 1 | no | — |
| 821 | C2×C8 | — | 4 | 1 | no | — |
| 822 | C2×C8 | — | 4 | 1 | no | — |
| 823 | C2×C8 | — | 4 | 1 | no | — |
| 824 | C2×C8 | — | 4 | 1 | no | — |
| 825 | C2×C8 | — | 4 | 2 | no | — |
| 826 | C2×C8 | — | 4 | 1 | no | — |
| 827 | C2×C8 | — | 4 | 1 | no | — |
| 828 | C2×C8 | — | 8 | 1 | no | — |
| 829 | C2×C8 | — | 8 | 1 | no | — |
| 830 | C2×C8 | — | 8 | 2 | no | — |
| 831 | C2×C8 | — | 8 | 4 | no | — |
| 832 | C2×C8 | — | 8 | 2 | no | — |
| 833 | C2×C8 | — | 8 | 4 | no | — |
| 834 | C2×C8 | — | 8 | 2 | no | — |
| 835 | C2×C8 | — | 8 | 4 | no | — |
| 836 | C2×C8 | — | 8 | 2 | no | — |
| 837 | C2×C8 | — | 8 | 4 | no | — |
| 838 | C2×C8 | — | 8 | 1 | no | — |
| 839 | C2×C8 | — | 8 | 1 | no | — |
| 840 | C2×C8 | — | 8 | 1 | no | — |
| 841 | C2×C8 | — | 8 | 1 | no | — |
| 842 | C2×C8 | — | 16 | 1 | no | — |
| 843 | C2×C8 | — | 16 | 2 | no | — |
| 844 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 845 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 846 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 847 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 848 | C4⋊C4 | — | 2 | 1 | no | — |
| 849 | C4⋊C4 | — | 2 | 1 | no | — |
| 850 | C4⋊C4 | — | 2 | 1 | no | — |
| 851 | C4⋊C4 | — | 2 | 2 | no | — |
| 852 | C4⋊C4 | — | 2 | 1 | no | — |
| 853 | C4⋊C4 | — | 4 | 2 | no | — |
| 854 | C4⋊C4 | — | 4 | 2 | no | — |
| 855 | C4⋊C4 | — | 4 | 1 | no | — |
| 856 | C4⋊C4 | — | 4 | 1 | no | — |
| 857 | C4⋊C4 | — | 4 | 1 | no | — |
| 858 | C4⋊C4 | — | 4 | 1 | no | — |
| 859 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 860 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 861 | C22⋊C4 | — | 2 | 1 | no | — |
| 862 | C22⋊C4 | — | 2 | 1 | no | — |
| 863 | C22⋊C4 | — | 2 | 1 | no | — |
| 864 | C22⋊C4 | — | 4 | 2 | no | — |
| 865 | C22⋊C4 | — | 4 | 2 | no | — |
| 866 | C22⋊C4 | — | 4 | 2 | no | — |
| 867 | C22⋊C4 | — | 4 | 2 | no | — |
| 868 | C22⋊C4 | — | 4 | 2 | no | — |
| 869 | C22⋊C4 | — | 4 | 1 | no | — |
| 870 | C22⋊C4 | — | 4 | 1 | no | — |
| 871 | C22⋊C4 | — | 4 | 1 | no | — |
| 872 | C22⋊C4 | — | 4 | 2 | no | — |
| 873 | C22⋊C4 | — | 4 | 1 | no | — |
| 874 | C22⋊C4 | — | 8 | 1 | no | — |
| 875 | C22⋊C4 | — | 8 | 1 | no | — |
| 876 | C42 | — | 2 | 1 | no | — |
| 877 | C42 | — | 2 | 1 | no | — |
| 878 | C42 | — | 2 | 1 | no | — |
| 879 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 880 | C42 | C2×#120 | 1 | 1 | yes | characteristic |
| 881 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 882 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 883 | C16 | — | 4 | 1 | no | — |
| 884 | C16 | — | 4 | 1 | no | — |
| 885 | C16 | — | 4 | 2 | no | — |
| 886 | C16 | — | 4 | 1 | no | — |
| 887 | C16 | — | 4 | 1 | no | — |
| 888 | C16 | — | 8 | 1 | no | — |
| 889 | C23 | — | 2 | 1 | no | — |
| 890 | C23 | — | 4 | 1 | no | — |
| 891 | C23 | — | 4 | 2 | no | — |
| 892 | C23 | — | 4 | 1 | no | — |
| 893 | C23 | — | 8 | 2 | no | — |
| 894 | C23 | — | 8 | 1 | no | — |
| 895 | C23 | — | 8 | 1 | no | — |
| 896 | C23 | — | 8 | 4 | no | — |
| 897 | C23 | — | 8 | 4 | no | — |
| 898 | C23 | — | 8 | 1 | no | — |
| 899 | C23 | — | 16 | 1 | no | — |
| 900 | C23 | — | 16 | 2 | no | — |
| 901 | C23 | #3114 | 1 | 1 | yes | characteristic |
| 902 | Q8 | — | 2 | 1 | no | — |
| 903 | Q8 | — | 8 | 4 | no | — |
| 904 | Q8 | — | 8 | 1 | no | — |
| 905 | Q8 | — | 8 | 1 | no | — |
| 906 | Q8 | — | 16 | 1 | no | — |
| 907 | Q8 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 908 | D4 | — | 2 | 4 | no | — |
| 909 | D4 | — | 2 | 1 | no | — |
| 910 | D4 | — | 2 | 2 | no | — |
| 911 | D4 | — | 4 | 1 | no | — |
| 912 | D4 | — | 4 | 2 | no | — |
| 913 | D4 | — | 4 | 1 | no | — |
| 914 | D4 | — | 4 | 2 | no | — |
| 915 | D4 | — | 4 | 1 | no | — |
| 916 | D4 | — | 8 | 2 | no | — |
| 917 | D4 | — | 8 | 4 | no | — |
| 918 | D4 | — | 8 | 4 | no | — |
| 919 | D4 | — | 8 | 2 | no | — |
| 920 | D4 | — | 8 | 2 | no | — |
| 921 | D4 | — | 8 | 4 | no | — |
| 922 | D4 | — | 8 | 4 | no | — |
| 923 | D4 | — | 8 | 1 | no | — |
| 924 | D4 | — | 8 | 1 | no | — |
| 925 | D4 | — | 8 | 1 | no | — |
| 926 | D4 | — | 8 | 1 | no | — |
| 927 | D4 | — | 8 | 1 | no | — |
| 928 | D4 | — | 8 | 1 | no | — |
| 929 | D4 | — | 16 | 1 | no | — |
| 930 | D4 | — | 16 | 1 | no | — |
| 931 | D4 | — | 16 | 2 | no | — |
| 932 | D4 | — | 16 | 2 | no | — |
| 933 | D4 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 934 | C2×C4 | — | 2 | 4 | no | — |
| 935 | C2×C4 | — | 2 | 1 | no | — |
| 936 | C2×C4 | — | 2 | 1 | no | — |
| 937 | C2×C4 | — | 2 | 1 | no | — |
| 938 | C2×C4 | — | 2 | 1 | no | — |
| 939 | C2×C4 | — | 2 | 1 | no | — |
| 940 | C2×C4 | — | 2 | 1 | no | — |
| 941 | C2×C4 | — | 2 | 1 | no | — |
| 942 | C2×C4 | — | 4 | 1 | no | — |
| 943 | C2×C4 | — | 4 | 1 | no | — |
| 944 | C2×C4 | — | 4 | 1 | no | — |
| 945 | C2×C4 | — | 4 | 1 | no | — |
| 946 | C2×C4 | — | 4 | 2 | no | — |
| 947 | C2×C4 | — | 4 | 1 | no | — |
| 948 | C2×C4 | — | 8 | 1 | no | — |
| 949 | C2×C4 | — | 8 | 1 | no | — |
| 950 | C2×C4 | — | 8 | 2 | no | — |
| 951 | C2×C4 | — | 8 | 1 | no | — |
| 952 | C2×C4 | — | 8 | 1 | no | — |
| 953 | C2×C4 | — | 8 | 4 | no | — |
| 954 | C2×C4 | — | 8 | 2 | no | — |
| 955 | C2×C4 | — | 8 | 1 | no | — |
| 956 | C2×C4 | — | 8 | 4 | no | — |
| 957 | C2×C4 | — | 8 | 1 | no | — |
| 958 | C2×C4 | — | 8 | 1 | no | — |
| 959 | C2×C4 | — | 8 | 4 | no | — |
| 960 | C2×C4 | — | 8 | 1 | no | — |
| 961 | C2×C4 | — | 8 | 1 | no | — |
| 962 | C2×C4 | — | 8 | 1 | no | — |
| 963 | C2×C4 | — | 8 | 1 | no | — |
| 964 | C2×C4 | — | 8 | 1 | no | — |
| 965 | C2×C4 | — | 16 | 1 | no | — |
| 966 | C2×C4 | — | 16 | 1 | no | — |
| 967 | C2×C4 | C4×#120 | 1 | 1 | yes | characteristic |
| 968 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 969 | C2×C4 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 970 | C2×C4 | #3003 | 1 | 1 | yes | characteristic |
| 971 | C2×C4 | #3006 | 1 | 1 | yes | characteristic |
| 972 | C2×C4 | #3109 | 1 | 1 | yes | characteristic |
| 973 | C8 | — | 2 | 1 | no | — |
| 974 | C8 | — | 2 | 1 | no | — |
| 975 | C8 | — | 2 | 1 | no | — |
| 976 | C8 | — | 4 | 1 | no | — |
| 977 | C8 | — | 4 | 2 | no | — |
| 978 | C8 | — | 4 | 1 | no | — |
| 979 | C8 | — | 4 | 1 | no | — |
| 980 | C8 | — | 4 | 1 | no | — |
| 981 | C8 | — | 4 | 1 | no | — |
| 982 | C8 | — | 4 | 1 | no | — |
| 983 | C8 | — | 8 | 1 | no | — |
| 984 | C8 | — | 8 | 2 | no | — |
| 985 | C8 | — | 8 | 1 | no | — |
| 986 | C8 | — | 8 | 1 | no | — |
| 987 | C8 | — | 8 | 2 | no | — |
| 988 | C8 | — | 8 | 1 | no | — |
| 989 | C8 | — | 8 | 1 | no | — |
| 990 | C8 | — | 16 | 1 | no | — |
| 991 | C8 | C2×#443 | 1 | 1 | yes | characteristic |
| 992 | C8 | #2955 | 1 | 1 | yes | characteristic |
| 993 | C22 | — | 2 | 1 | no | — |
| 994 | C22 | — | 2 | 2 | no | — |
| 995 | C22 | — | 2 | 1 | no | — |
| 996 | C22 | — | 2 | 1 | no | — |
| 997 | C22 | — | 4 | 1 | no | — |
| 998 | C22 | — | 4 | 1 | no | — |
| 999 | C22 | — | 4 | 2 | no | — |
| 1000 | C22 | — | 8 | 1 | no | — |
| 1001 | C22 | — | 8 | 1 | no | — |
| 1002 | C22 | — | 8 | 2 | no | — |
| 1003 | C22 | — | 8 | 1 | no | — |
| 1004 | C22 | — | 8 | 2 | no | — |
| 1005 | C22 | — | 8 | 1 | no | — |
| 1006 | C22 | — | 8 | 1 | no | — |
| 1007 | C22 | — | 8 | 2 | no | — |
| 1008 | C22 | — | 16 | 2 | no | — |
| 1009 | C22 | — | 16 | 2 | no | — |
| 1010 | C22 | — | 16 | 8 | no | — |
| 1011 | C22 | — | 16 | 1 | no | — |
| 1012 | C22 | — | 16 | 1 | no | — |
| 1013 | C22 | — | 16 | 1 | no | — |
| 1014 | C22 | #21452 | 1 | 1 | yes | characteristic |
| 1015 | C4 | — | 2 | 1 | no | — |
| 1016 | C4 | — | 2 | 2 | no | — |
| 1017 | C4 | — | 2 | 1 | no | — |
| 1018 | C4 | — | 2 | 1 | no | — |
| 1019 | C4 | — | 2 | 1 | no | — |
| 1020 | C4 | — | 4 | 1 | no | — |
| 1021 | C4 | — | 4 | 1 | no | — |
| 1022 | C4 | — | 8 | 1 | no | — |
| 1023 | C4 | — | 8 | 2 | no | — |
| 1024 | C4 | — | 8 | 1 | no | — |
| 1025 | C4 | — | 16 | 1 | no | — |
| 1026 | C4 | #21466 | 1 | 1 | yes | characteristic |
| 1027 | C4 | #21478 | 1 | 1 | yes | characteristic |
| 1028 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 1029 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 1030 | C2 | — | 4 | 1 | no | — |
| 1031 | C2 | — | 4 | 2 | no | — |
| 1032 | C2 | — | 8 | 2 | no | — |
| 1033 | C2 | — | 16 | 2 | no | — |
| 1034 | C2 | — | 16 | 1 | no | — |
| 1035 | C2 | — | 32 | 1 | no | — |
| 1036 | C2 | #210356 | 1 | 1 | yes | characteristic |
| 1037 | C2 | #495725 | 1 | 1 | yes | characteristic |
| 1038 | C2 | #495737 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #21452 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #489284 | 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. #6345807 | C2 | semidirect |
| 3. #483992 | C2 | semidirect |
| 4. #483875 | C2 | semidirect |
| 5. #211944 | C2 | semidirect |
| 6. #137501 | C2 | semidirect |
| 7. #137055 | C2 | semidirect |
| 8. #137039 | C2 | semidirect |
| 9. #136567 | C2 | semidirect |
| 10. #136482 | C2 | semidirect |
| 11. #136464 | C2 | semidirect |
| 12. #131816 | C2 | semidirect |
| 13. #129033 | C2 | semidirect |
| 14. #128692 | C2 | semidirect |
| 15. #128636 | C2 | semidirect |
| 29. #17962 | C22 | semidirect |
| 53. #12030 | C22 | semidirect |
| 54. #12020 | C22 | semidirect |
| 58. #11680 | C22 | semidirect |
| 60. #11654 | C22 | semidirect |
| 64. #11415 | C22 | semidirect |
| 65. #11404 | C22 | semidirect |
| 66. #9726 | C22 | semidirect |
| 67. #9635 | C22 | semidirect |
| 71. #8294 | C22 | semidirect |
| 73. #7300 | C22 | semidirect |
| 74. #7295 | C22 | semidirect |
| 75. #7173 | C22 | semidirect |
| 76. #7164 | C22 | semidirect |
| 77. #7164 | C22 | semidirect |
| 78. #7158 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6345807 | 2 |
| #489284 | 2 |
| #483992 | 2 |
| #483875 | 2 |
| #211944 | 2 |
| #137501 | 2 |
| #137055 | 2 |
| #137039 | 2 |
| #136567 | 2 |
| #136482 | 2 |
| #136464 | 2 |
| #131816 | 2 |
| #129033 | 2 |
| #128692 | 2 |
| #128636 | 2 |