Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1220 conjugacy classes of subgroups.
The subgroup lattice has 766 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72322761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72322725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72322624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72322440 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72322053 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #72321831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72321622 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72321409 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72321207 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72320880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72286849 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #7623817 | — | 2 | 1 | no | — |
| 13 | #513308 | C22 | 1 | 1 | yes | characteristic |
| 14 | #513246 | — | 2 | 2 | no | — |
| 15 | #513245 | — | 2 | 2 | no | — |
| 16 | #513238 | — | 2 | 2 | no | — |
| 17 | #513236 | — | 2 | 2 | no | — |
| 18 | #513064 | C22 | 1 | 1 | yes | characteristic |
| 19 | #512987 | — | 2 | 1 | no | — |
| 20 | #512980 | — | 2 | 1 | no | — |
| 21 | #512968 | — | 2 | 1 | no | — |
| 22 | #512945 | C22 | 1 | 1 | yes | characteristic |
| 23 | #512934 | C22 | 1 | 1 | yes | characteristic |
| 24 | #512770 | C22 | 1 | 1 | yes | characteristic |
| 25 | #512742 | C22 | 1 | 1 | yes | characteristic |
| 26 | #512721 | C22 | 1 | 1 | yes | characteristic |
| 27 | #512720 | C22 | 1 | 1 | yes | characteristic |
| 28 | C22×#1424 | C22 | 1 | 1 | yes | characteristic |
| 29 | #505704 | — | 2 | 1 | no | — |
| 30 | #153682 | — | 2 | 2 | no | — |
| 31 | #153681 | — | 2 | 2 | no | — |
| 32 | #153578 | — | 2 | 2 | no | — |
| 33 | #153578 | C22 | 1 | 2 | yes | — |
| 34 | C2×#7548 | — | 2 | 2 | no | — |
| 35 | C2×#7548 | C22 | 1 | 2 | yes | — |
| 36 | C2×#7548 | C22 | 1 | 2 | yes | — |
| 37 | #153565 | C22 | 1 | 2 | yes | — |
| 38 | #153560 | C22 | 1 | 2 | yes | — |
| 39 | #153430 | C22 | 1 | 1 | yes | characteristic |
| 40 | #153427 | C22 | 1 | 2 | yes | — |
| 41 | #153394 | — | 2 | 1 | no | — |
| 42 | #153372 | — | 2 | 1 | no | — |
| 43 | #152859 | C22 | 1 | 2 | yes | — |
| 44 | #152376 | — | 2 | 1 | no | — |
| 45 | #152295 | C22 | 1 | 1 | yes | characteristic |
| 46 | #152292 | C22 | 1 | 2 | yes | — |
| 47 | #94770 | C22 | 1 | 2 | yes | — |
| 48 | #94764 | C22 | 1 | 2 | yes | — |
| 49 | #94764 | C22 | 1 | 2 | yes | — |
| 50 | #94759 | C22 | 1 | 2 | yes | — |
| 51 | #61258 | — | 4 | 1 | no | — |
| 52 | C2×#2262 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×#2258 | C23 | 1 | 1 | yes | characteristic |
| 54 | C23×C32 | C23 | 1 | 1 | yes | characteristic |
| 55 | #33913 | — | 4 | 2 | no | — |
| 56 | #33910 | — | 4 | 2 | no | — |
| 57 | #33906 | — | 2 | 2 | no | — |
| 58 | #33905 | — | 2 | 2 | no | — |
| 59 | #33903 | — | 2 | 2 | no | — |
| 60 | #33901 | — | 2 | 2 | no | — |
| 61 | #33729 | — | 2 | 1 | no | — |
| 62 | #33652 | — | 4 | 1 | no | — |
| 63 | #33646 | — | 4 | 1 | no | — |
| 64 | #33633 | — | 4 | 1 | no | — |
| 65 | #33610 | — | 2 | 1 | no | — |
| 66 | #33600 | — | 2 | 1 | no | — |
| 67 | #33459 | — | 2 | 1 | no | — |
| 68 | #33432 | D4 | 1 | 1 | yes | characteristic |
| 69 | #33414 | — | 2 | 1 | no | — |
| 70 | #33410 | — | 2 | 1 | no | — |
| 71 | C22×#366 | — | 2 | 1 | no | — |
| 72 | #27691 | — | 4 | 1 | no | — |
| 73 | #13737 | — | 2 | 4 | no | — |
| 74 | C2×M128 | — | 2 | 2 | no | — |
| 75 | C2×M128 | C23 | 1 | 2 | yes | — |
| 76 | C2×M128 | C23 | 1 | 2 | yes | — |
| 77 | #13734 | — | 2 | 2 | no | — |
| 78 | #13733 | — | 2 | 1 | no | — |
| 79 | #13732 | — | 2 | 1 | no | — |
| 80 | #13716 | — | 2 | 2 | no | — |
| 81 | #13715 | — | 2 | 2 | no | — |
| 82 | #13714 | — | 2 | 2 | no | — |
| 83 | #13714 | — | 2 | 2 | no | — |
| 84 | #13713 | — | 2 | 2 | no | — |
| 85 | #13712 | — | 2 | 2 | no | — |
| 86 | #13712 | — | 2 | 2 | no | — |
| 87 | #13711 | — | 2 | 2 | no | — |
| 88 | #13708 | — | 2 | 2 | no | — |
| 89 | #13707 | — | 2 | 2 | no | — |
| 90 | #13705 | — | 2 | 2 | no | — |
| 91 | #13704 | — | 2 | 2 | no | — |
| 92 | #13698 | D4 | 1 | 2 | yes | — |
| 93 | #13697 | D4 | 1 | 2 | yes | — |
| 94 | #13696 | — | 2 | 2 | no | — |
| 95 | #13696 | — | 2 | 1 | no | — |
| 96 | #13696 | — | 2 | 1 | no | — |
| 97 | #13695 | — | 2 | 1 | no | — |
| 98 | #13694 | — | 2 | 1 | no | — |
| 99 | #13654 | — | 2 | 1 | no | — |
| 100 | #13653 | — | 2 | 1 | no | — |
| 101 | C4×SD64 | — | 2 | 2 | no | — |
| 102 | #13645 | — | 2 | 2 | no | — |
| 103 | D4×C32 | — | 2 | 2 | no | — |
| 104 | #13636 | — | 2 | 1 | no | — |
| 105 | #13636 | — | 2 | 2 | no | — |
| 106 | C2×#1425 | — | 2 | 2 | no | — |
| 107 | C2×#1425 | C23 | 1 | 2 | yes | — |
| 108 | C2×#1425 | C23 | 1 | 2 | yes | — |
| 109 | #13634 | — | 2 | 1 | no | — |
| 110 | #13634 | — | 2 | 1 | no | — |
| 111 | #13634 | — | 2 | 2 | no | — |
| 112 | #13633 | D4 | 1 | 2 | yes | — |
| 113 | #13633 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×#1424 | — | 2 | 1 | no | — |
| 115 | C2×#1424 | — | 2 | 2 | no | — |
| 116 | C2×#1424 | — | 2 | 2 | no | — |
| 117 | C2×#1424 | D4 | 1 | 2 | yes | — |
| 118 | C2×#1424 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#1424 | C23 | 1 | 1 | yes | characteristic |
| 120 | #13628 | D4 | 1 | 1 | yes | characteristic |
| 121 | #13616 | — | 2 | 1 | no | — |
| 122 | #13616 | — | 2 | 1 | no | — |
| 123 | #13615 | — | 2 | 1 | no | — |
| 124 | #13554 | D4 | 1 | 1 | yes | characteristic |
| 125 | #13553 | D4 | 1 | 1 | yes | characteristic |
| 126 | #13549 | C23 | 1 | 1 | yes | characteristic |
| 127 | #13520 | — | 4 | 1 | no | — |
| 128 | #13498 | — | 4 | 1 | no | — |
| 129 | #13173 | — | 2 | 2 | no | — |
| 130 | #12878 | — | 4 | 1 | no | — |
| 131 | #12840 | — | 2 | 1 | no | — |
| 132 | #12837 | — | 2 | 2 | no | — |
| 133 | #7548 | — | 2 | 4 | no | — |
| 134 | #7548 | — | 2 | 2 | no | — |
| 135 | #7548 | — | 2 | 4 | no | — |
| 136 | #7548 | — | 2 | 2 | no | — |
| 137 | #7542 | — | 2 | 2 | no | — |
| 138 | #7541 | — | 2 | 2 | no | — |
| 139 | #7539 | — | 2 | 4 | no | — |
| 140 | #7513 | — | 2 | 2 | no | — |
| 141 | C22⋊C64 | — | 2 | 4 | no | — |
| 142 | #7479 | — | 2 | 2 | no | — |
| 143 | #7476 | — | 2 | 1 | no | — |
| 144 | #7472 | — | 2 | 2 | no | — |
| 145 | #3492 | — | 8 | 1 | no | — |
| 146 | C2×#508 | — | 2 | 1 | no | — |
| 147 | C2×#504 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C23×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | #3346 | — | 8 | 2 | no | — |
| 150 | #3343 | — | 8 | 2 | no | — |
| 151 | #3339 | — | 4 | 2 | no | — |
| 152 | #3338 | — | 4 | 2 | no | — |
| 153 | #3336 | — | 4 | 2 | no | — |
| 154 | #3334 | — | 4 | 2 | no | — |
| 155 | #3164 | — | 4 | 1 | no | — |
| 156 | #3098 | — | 8 | 1 | no | — |
| 157 | #3092 | — | 8 | 1 | no | — |
| 158 | #3083 | — | 8 | 1 | no | — |
| 159 | #3061 | — | 4 | 1 | no | — |
| 160 | #3050 | — | 4 | 1 | no | — |
| 161 | #2951 | — | 4 | 1 | no | — |
| 162 | #2929 | D8 | 1 | 1 | yes | characteristic |
| 163 | #2916 | — | 4 | 1 | no | — |
| 164 | #2913 | — | 4 | 1 | no | — |
| 165 | C22×#107 | — | 4 | 1 | no | — |
| 166 | #2262 | — | 2 | 2 | no | — |
| 167 | #2262 | — | 2 | 2 | no | — |
| 168 | C2×Q64 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×SD64 | — | 2 | 1 | no | — |
| 170 | C2×D32 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | #2258 | — | 2 | 2 | no | — |
| 172 | #2258 | — | 2 | 2 | no | — |
| 173 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×M64 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×M64 | C2×D4 | 1 | 2 | yes | — |
| 176 | C22×C32 | — | 2 | 1 | no | — |
| 177 | C22×C32 | — | 2 | 1 | no | — |
| 178 | C22×C32 | — | 2 | 2 | no | — |
| 179 | C22×C32 | — | 2 | 2 | no | — |
| 180 | C22×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C32 | C2×D4 | 1 | 2 | yes | — |
| 182 | C22×C32 | C24 | 1 | 1 | yes | characteristic |
| 183 | #2255 | — | 4 | 2 | no | — |
| 184 | #2253 | — | 2 | 2 | no | — |
| 185 | #2252 | — | 2 | 2 | no | — |
| 186 | #2237 | — | 4 | 2 | no | — |
| 187 | #2236 | — | 4 | 2 | no | — |
| 188 | #2236 | — | 4 | 2 | no | — |
| 189 | #2235 | — | 4 | 2 | no | — |
| 190 | #2234 | — | 4 | 2 | no | — |
| 191 | #2233 | — | 4 | 2 | no | — |
| 192 | #2232 | — | 4 | 2 | no | — |
| 193 | #2232 | — | 4 | 2 | no | — |
| 194 | #2229 | — | 4 | 2 | no | — |
| 195 | #2228 | — | 4 | 2 | no | — |
| 196 | #2227 | — | 4 | 2 | no | — |
| 197 | #2224 | — | 4 | 2 | no | — |
| 198 | #2220 | — | 4 | 2 | no | — |
| 199 | #2217 | — | 4 | 1 | no | — |
| 200 | #2217 | — | 4 | 1 | no | — |
| 201 | #2216 | — | 2 | 1 | no | — |
| 202 | #2216 | — | 2 | 1 | no | — |
| 203 | #2216 | — | 2 | 2 | no | — |
| 204 | #2215 | — | 2 | 1 | no | — |
| 205 | #2215 | — | 2 | 1 | no | — |
| 206 | #2215 | — | 2 | 2 | no | — |
| 207 | #2175 | — | 4 | 2 | no | — |
| 208 | C4×Q32 | — | 2 | 2 | no | — |
| 209 | C4×D16 | — | 2 | 2 | no | — |
| 210 | #2168 | — | 2 | 2 | no | — |
| 211 | D4×C16 | — | 2 | 2 | no | — |
| 212 | #2161 | — | 4 | 2 | no | — |
| 213 | #2161 | — | 4 | 1 | no | — |
| 214 | C2×#368 | — | 2 | 2 | no | — |
| 215 | C2×#368 | — | 2 | 2 | no | — |
| 216 | C2×#368 | — | 4 | 2 | no | — |
| 217 | #2159 | — | 4 | 1 | no | — |
| 218 | #2159 | — | 4 | 1 | no | — |
| 219 | #2159 | — | 4 | 2 | no | — |
| 220 | #2158 | — | 2 | 2 | no | — |
| 221 | #2158 | — | 2 | 1 | no | — |
| 222 | C2×#366 | — | 2 | 2 | no | — |
| 223 | C2×#366 | — | 2 | 2 | no | — |
| 224 | C2×#366 | — | 2 | 2 | no | — |
| 225 | C2×#366 | — | 2 | 1 | no | — |
| 226 | C2×#366 | — | 2 | 1 | no | — |
| 227 | C2×#366 | — | 4 | 1 | no | — |
| 228 | C2×#366 | — | 4 | 1 | no | — |
| 229 | C2×#366 | — | 4 | 1 | no | — |
| 230 | #2151 | D8 | 1 | 1 | yes | characteristic |
| 231 | #2139 | — | 4 | 1 | no | — |
| 232 | #2139 | — | 4 | 1 | no | — |
| 233 | #2138 | — | 4 | 1 | no | — |
| 234 | #2113 | D8 | 1 | 1 | yes | characteristic |
| 235 | #2112 | D8 | 1 | 1 | yes | characteristic |
| 236 | #2108 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | #2103 | — | 8 | 1 | no | — |
| 238 | #2091 | — | 8 | 1 | no | — |
| 239 | #1953 | — | 4 | 2 | no | — |
| 240 | #1891 | — | 8 | 1 | no | — |
| 241 | #1858 | — | 8 | 1 | no | — |
| 242 | #1813 | — | 4 | 1 | no | — |
| 243 | #1810 | — | 4 | 2 | no | — |
| 244 | M128 | — | 2 | 4 | no | — |
| 245 | M128 | — | 2 | 2 | no | — |
| 246 | M128 | — | 2 | 2 | no | — |
| 247 | M128 | — | 2 | 2 | no | — |
| 248 | M128 | — | 2 | 2 | no | — |
| 249 | C2×C64 | — | 2 | 4 | no | — |
| 250 | C2×C64 | — | 2 | 2 | no | — |
| 251 | C2×C64 | #41 | 1 | 4 | yes | complemented |
| 252 | #1425 | — | 2 | 2 | no | — |
| 253 | #1425 | — | 2 | 2 | no | — |
| 254 | #1425 | — | 2 | 2 | no | — |
| 255 | #1425 | — | 2 | 2 | no | — |
| 256 | #1425 | — | 4 | 2 | no | — |
| 257 | #1424 | — | 2 | 2 | no | — |
| 258 | #1424 | — | 2 | 2 | no | — |
| 259 | #1424 | — | 2 | 2 | no | — |
| 260 | #1424 | — | 2 | 2 | no | — |
| 261 | #1424 | — | 2 | 1 | no | — |
| 262 | #1424 | — | 2 | 1 | no | — |
| 263 | #1424 | C2×D4 | 1 | 2 | yes | — |
| 264 | #1424 | C2×D4 | 1 | 2 | yes | — |
| 265 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | #1424 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | #1423 | — | 2 | 2 | no | — |
| 268 | #1423 | — | 2 | 2 | no | — |
| 269 | #1423 | — | 2 | 1 | no | — |
| 270 | C4⋊C32 | — | 2 | 2 | no | — |
| 271 | #1416 | — | 2 | 1 | no | — |
| 272 | #1416 | — | 2 | 1 | no | — |
| 273 | #1416 | — | 2 | 2 | no | — |
| 274 | #1416 | — | 2 | 2 | no | — |
| 275 | #1415 | — | 2 | 1 | no | — |
| 276 | #1415 | — | 2 | 1 | no | — |
| 277 | #1415 | — | 2 | 2 | no | — |
| 278 | #1415 | — | 2 | 2 | no | — |
| 279 | C22⋊C32 | — | 2 | 2 | no | — |
| 280 | C22⋊C32 | — | 2 | 2 | no | — |
| 281 | #1397 | — | 2 | 1 | no | — |
| 282 | C4×C32 | — | 2 | 1 | no | — |
| 283 | #1388 | — | 4 | 2 | no | — |
| 284 | #1385 | — | 4 | 1 | no | — |
| 285 | #1381 | — | 4 | 2 | no | — |
| 286 | C2×#135 | — | 4 | 1 | no | — |
| 287 | #568 | — | 8 | 1 | no | — |
| 288 | C2×#131 | C2×D8 | 1 | 1 | yes | characteristic |
| 289 | C23×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 290 | #554 | — | 8 | 2 | no | — |
| 291 | #554 | — | 16 | 1 | no | — |
| 292 | #553 | — | 8 | 2 | no | — |
| 293 | #553 | — | 16 | 1 | no | — |
| 294 | #552 | — | 8 | 2 | no | — |
| 295 | #552 | — | 16 | 1 | no | — |
| 296 | #547 | — | 8 | 2 | no | — |
| 297 | #547 | — | 16 | 1 | no | — |
| 298 | #544 | — | 8 | 1 | no | — |
| 299 | #539 | — | 16 | 2 | no | — |
| 300 | #537 | — | 8 | 1 | no | — |
| 301 | #525 | — | 8 | 1 | no | — |
| 302 | #525 | — | 16 | 2 | no | — |
| 303 | #525 | D16 | 1 | 1 | yes | characteristic |
| 304 | #520 | — | 8 | 1 | no | — |
| 305 | #520 | — | 8 | 1 | no | — |
| 306 | C22×C4⋊C4 | — | 8 | 1 | no | — |
| 307 | #508 | — | 4 | 2 | no | — |
| 308 | #508 | — | 4 | 2 | no | — |
| 309 | C2×Q32 | — | 2 | 1 | no | — |
| 310 | C2×SD32 | — | 4 | 1 | no | — |
| 311 | C2×D16 | — | 2 | 1 | no | — |
| 312 | #504 | — | 2 | 2 | no | — |
| 313 | #504 | — | 2 | 2 | no | — |
| 314 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 315 | C2×M32 | C2×D8 | 1 | 1 | yes | characteristic |
| 316 | C2×M32 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 317 | C22×C16 | — | 2 | 1 | no | — |
| 318 | C22×C16 | — | 2 | 2 | no | — |
| 319 | C22×C16 | — | 2 | 1 | no | — |
| 320 | C22×C16 | — | 2 | 2 | no | — |
| 321 | C22×C16 | #120 | 1 | 2 | yes | — |
| 322 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 323 | C22×C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 324 | #501 | — | 8 | 2 | no | — |
| 325 | #500 | — | 4 | 2 | no | — |
| 326 | #499 | — | 4 | 2 | no | — |
| 327 | #485 | — | 8 | 2 | no | — |
| 328 | #484 | — | 8 | 2 | no | — |
| 329 | #484 | — | 8 | 2 | no | — |
| 330 | #483 | — | 8 | 2 | no | — |
| 331 | #482 | — | 8 | 2 | no | — |
| 332 | #481 | — | 8 | 2 | no | — |
| 333 | #480 | — | 8 | 2 | no | — |
| 334 | #480 | — | 8 | 2 | no | — |
| 335 | #479 | — | 8 | 2 | no | — |
| 336 | #478 | — | 8 | 2 | no | — |
| 337 | #477 | — | 8 | 2 | no | — |
| 338 | #474 | — | 8 | 2 | no | — |
| 339 | #468 | — | 8 | 2 | no | — |
| 340 | #467 | — | 4 | 1 | no | — |
| 341 | #467 | — | 4 | 1 | no | — |
| 342 | #467 | — | 4 | 2 | no | — |
| 343 | #466 | — | 4 | 1 | no | — |
| 344 | #466 | — | 4 | 1 | no | — |
| 345 | #466 | — | 4 | 2 | no | — |
| 346 | #465 | — | 8 | 1 | no | — |
| 347 | #465 | — | 8 | 1 | no | — |
| 348 | #440 | — | 8 | 2 | no | — |
| 349 | C4×Q16 | — | 4 | 2 | no | — |
| 350 | C4×D8 | — | 4 | 2 | no | — |
| 351 | #435 | — | 2 | 2 | no | — |
| 352 | C8×D4 | — | 2 | 2 | no | — |
| 353 | #430 | — | 8 | 2 | no | — |
| 354 | #430 | — | 8 | 1 | no | — |
| 355 | #430 | — | 8 | 2 | no | — |
| 356 | C2×#108 | — | 4 | 2 | no | — |
| 357 | C2×#108 | — | 4 | 2 | no | — |
| 358 | C2×#108 | — | 8 | 2 | no | — |
| 359 | #428 | — | 8 | 1 | no | — |
| 360 | #428 | — | 8 | 1 | no | — |
| 361 | #428 | — | 8 | 2 | no | — |
| 362 | #427 | — | 4 | 1 | no | — |
| 363 | #427 | — | 4 | 2 | no | — |
| 364 | C2×#107 | — | 4 | 2 | no | — |
| 365 | C2×#107 | — | 4 | 2 | no | — |
| 366 | C2×#107 | — | 4 | 1 | no | — |
| 367 | C2×#107 | — | 4 | 1 | no | — |
| 368 | C2×#107 | — | 4 | 2 | no | — |
| 369 | C2×#107 | — | 8 | 1 | no | — |
| 370 | C2×#107 | — | 8 | 1 | no | — |
| 371 | C2×#107 | — | 8 | 1 | no | — |
| 372 | #424 | D16 | 1 | 1 | yes | characteristic |
| 373 | #417 | — | 8 | 1 | no | — |
| 374 | #417 | — | 8 | 1 | no | — |
| 375 | #416 | — | 8 | 1 | no | — |
| 376 | #413 | — | 8 | 1 | no | — |
| 377 | #408 | D16 | 1 | 1 | yes | characteristic |
| 378 | #407 | — | 8 | 2 | no | — |
| 379 | #407 | D16 | 1 | 1 | yes | characteristic |
| 380 | #405 | C2×D8 | 1 | 1 | yes | characteristic |
| 381 | Q64 | — | 2 | 2 | no | — |
| 382 | SD64 | — | 4 | 1 | no | — |
| 383 | SD64 | — | 4 | 1 | no | — |
| 384 | D32 | — | 2 | 2 | no | — |
| 385 | M64 | — | 2 | 2 | no | — |
| 386 | M64 | — | 2 | 4 | no | — |
| 387 | M64 | — | 2 | 2 | no | — |
| 388 | C2×C32 | — | 2 | 2 | no | — |
| 389 | C2×C32 | — | 2 | 2 | no | — |
| 390 | C2×C32 | — | 2 | 1 | no | — |
| 391 | C2×C32 | — | 2 | 1 | no | — |
| 392 | C2×C32 | — | 2 | 2 | no | — |
| 393 | C2×C32 | — | 4 | 1 | no | — |
| 394 | C2×C32 | — | 4 | 1 | no | — |
| 395 | C2×C32 | — | 4 | 2 | no | — |
| 396 | C2×C32 | #120 | 1 | 2 | yes | — |
| 397 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 398 | C2×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×C32 | C2×#41 | 1 | 2 | yes | — |
| 400 | C2×C32 | 2−1+4 | 1 | 2 | yes | — |
| 401 | #368 | — | 4 | 2 | no | — |
| 402 | #368 | — | 4 | 2 | no | — |
| 403 | #368 | — | 4 | 2 | no | — |
| 404 | #368 | — | 4 | 2 | no | — |
| 405 | #368 | — | 8 | 2 | no | — |
| 406 | #367 | — | 4 | 2 | no | — |
| 407 | #367 | — | 4 | 1 | no | — |
| 408 | #367 | — | 4 | 2 | no | — |
| 409 | #366 | — | 2 | 2 | no | — |
| 410 | #366 | — | 2 | 2 | no | — |
| 411 | #366 | — | 2 | 1 | no | — |
| 412 | #366 | — | 2 | 1 | no | — |
| 413 | #366 | — | 4 | 2 | no | — |
| 414 | #366 | — | 4 | 2 | no | — |
| 415 | #366 | — | 4 | 2 | no | — |
| 416 | #366 | — | 4 | 1 | no | — |
| 417 | #366 | — | 4 | 1 | no | — |
| 418 | #366 | — | 4 | 2 | no | — |
| 419 | C4⋊C16 | — | 2 | 2 | no | — |
| 420 | #358 | — | 4 | 1 | no | — |
| 421 | #358 | — | 4 | 1 | no | — |
| 422 | #358 | — | 4 | 2 | no | — |
| 423 | #358 | — | 4 | 2 | no | — |
| 424 | #357 | — | 4 | 1 | no | — |
| 425 | #357 | — | 4 | 1 | no | — |
| 426 | #357 | — | 4 | 2 | no | — |
| 427 | #357 | — | 4 | 2 | no | — |
| 428 | C22⋊C16 | — | 2 | 2 | no | — |
| 429 | C22⋊C16 | — | 2 | 2 | no | — |
| 430 | #346 | — | 2 | 1 | no | — |
| 431 | C4×C16 | — | 2 | 1 | no | — |
| 432 | #344 | — | 8 | 2 | no | — |
| 433 | #341 | — | 8 | 2 | no | — |
| 434 | #338 | — | 8 | 1 | no | — |
| 435 | C64 | — | 2 | 4 | no | — |
| 436 | C64 | — | 4 | 2 | no | — |
| 437 | C2×#41 | — | 8 | 1 | no | — |
| 438 | C2×#41 | — | 16 | 2 | no | — |
| 439 | C2×#41 | C2×D16 | 1 | 1 | yes | characteristic |
| 440 | C23×C4 | — | 16 | 1 | no | — |
| 441 | C23×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 442 | #135 | — | 8 | 2 | no | — |
| 443 | #135 | — | 8 | 2 | no | — |
| 444 | C2×Q16 | — | 4 | 1 | no | — |
| 445 | C2×SD16 | — | 8 | 1 | no | — |
| 446 | C2×D8 | — | 4 | 1 | no | — |
| 447 | #131 | — | 2 | 2 | no | — |
| 448 | #131 | — | 2 | 2 | no | — |
| 449 | #131 | — | 32 | 2 | no | — |
| 450 | C2×M16 | — | 8 | 2 | no | — |
| 451 | C2×M16 | — | 8 | 2 | no | — |
| 452 | C2×M16 | — | 16 | 2 | no | — |
| 453 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 454 | C2×M16 | C2×D16 | 1 | 1 | yes | characteristic |
| 455 | C2×M16 | #509 | 1 | 2 | yes | — |
| 456 | C22×C8 | — | 2 | 2 | no | — |
| 457 | C22×C8 | — | 2 | 1 | no | — |
| 458 | C22×C8 | — | 2 | 2 | no | — |
| 459 | C22×C8 | — | 2 | 1 | no | — |
| 460 | C22×C8 | #447 | 1 | 2 | yes | — |
| 461 | C22×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 462 | C22×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 463 | C4⋊Q8 | — | 8 | 2 | no | — |
| 464 | C4⋊Q8 | — | 16 | 1 | no | — |
| 465 | #126 | — | 16 | 2 | no | — |
| 466 | #126 | — | 16 | 2 | no | — |
| 467 | #125 | — | 8 | 2 | no | — |
| 468 | #125 | — | 16 | 2 | no | — |
| 469 | #125 | — | 16 | 2 | no | — |
| 470 | #125 | — | 16 | 1 | no | — |
| 471 | #123 | — | 16 | 2 | no | — |
| 472 | #123 | — | 16 | 2 | no | — |
| 473 | #123 | — | 16 | 2 | no | — |
| 474 | #123 | — | 16 | 2 | no | — |
| 475 | #123 | — | 16 | 1 | no | — |
| 476 | #123 | SD64 | 1 | 2 | yes | — |
| 477 | C22⋊Q8 | — | 2 | 1 | no | — |
| 478 | C22⋊Q8 | — | 8 | 1 | no | — |
| 479 | C22⋊Q8 | — | 8 | 1 | no | — |
| 480 | C22⋊Q8 | — | 8 | 2 | no | — |
| 481 | C22⋊Q8 | — | 16 | 2 | no | — |
| 482 | C22⋊Q8 | — | 16 | 2 | no | — |
| 483 | C22⋊Q8 | — | 16 | 2 | no | — |
| 484 | C22⋊Q8 | — | 16 | 1 | no | — |
| 485 | C22⋊Q8 | — | 16 | 2 | no | — |
| 486 | #121 | — | 2 | 1 | no | — |
| 487 | #121 | — | 8 | 1 | no | — |
| 488 | #121 | — | 8 | 1 | no | — |
| 489 | #121 | — | 8 | 2 | no | — |
| 490 | #121 | — | 16 | 2 | no | — |
| 491 | #121 | — | 16 | 2 | no | — |
| 492 | #121 | — | 16 | 1 | no | — |
| 493 | #120 | — | 16 | 1 | no | — |
| 494 | #120 | SD64 | 1 | 2 | yes | — |
| 495 | C4×Q8 | — | 8 | 2 | no | — |
| 496 | C4×Q8 | — | 16 | 1 | no | — |
| 497 | C4×D4 | — | 2 | 2 | no | — |
| 498 | C4×D4 | — | 8 | 2 | no | — |
| 499 | C4×D4 | — | 16 | 2 | no | — |
| 500 | C4×D4 | — | 16 | 1 | no | — |
| 501 | C4×D4 | — | 16 | 1 | no | — |
| 502 | C4×D4 | — | 16 | 2 | no | — |
| 503 | C4×D4 | — | 16 | 2 | no | — |
| 504 | C4×D4 | — | 16 | 1 | no | — |
| 505 | C4×D4 | — | 16 | 2 | no | — |
| 506 | #117 | — | 8 | 1 | no | — |
| 507 | #117 | — | 8 | 2 | no | — |
| 508 | #117 | — | 16 | 2 | no | — |
| 509 | #117 | — | 16 | 1 | no | — |
| 510 | #117 | C2×D16 | 1 | 1 | yes | characteristic |
| 511 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 512 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 513 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 514 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 515 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 516 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 517 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 518 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 519 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 520 | Q32 | — | 4 | 1 | no | — |
| 521 | Q32 | — | 4 | 1 | no | — |
| 522 | SD32 | — | 8 | 2 | no | — |
| 523 | D16 | — | 4 | 1 | no | — |
| 524 | D16 | — | 4 | 1 | no | — |
| 525 | M32 | — | 2 | 2 | no | — |
| 526 | M32 | — | 2 | 4 | no | — |
| 527 | M32 | — | 2 | 2 | no | — |
| 528 | C2×C16 | — | 2 | 2 | no | — |
| 529 | C2×C16 | — | 2 | 2 | no | — |
| 530 | C2×C16 | — | 2 | 2 | no | — |
| 531 | C2×C16 | — | 2 | 1 | no | — |
| 532 | C2×C16 | — | 2 | 1 | no | — |
| 533 | C2×C16 | — | 4 | 2 | no | — |
| 534 | C2×C16 | — | 4 | 1 | no | — |
| 535 | C2×C16 | — | 4 | 1 | no | — |
| 536 | C2×C16 | #447 | 1 | 2 | yes | — |
| 537 | C2×C16 | C2×#120 | 1 | 1 | yes | characteristic |
| 538 | C2×C16 | #547 | 1 | 2 | yes | — |
| 539 | C2×C16 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 540 | C2×C16 | #578 | 1 | 2 | yes | — |
| 541 | #108 | — | 8 | 2 | no | — |
| 542 | #108 | — | 8 | 2 | no | — |
| 543 | #108 | — | 8 | 2 | no | — |
| 544 | #108 | — | 8 | 2 | no | — |
| 545 | #108 | — | 16 | 2 | no | — |
| 546 | #108 | — | 32 | 2 | no | — |
| 547 | #107 | — | 4 | 2 | no | — |
| 548 | #107 | — | 4 | 2 | no | — |
| 549 | #107 | — | 4 | 1 | no | — |
| 550 | #107 | — | 4 | 1 | no | — |
| 551 | #107 | — | 8 | 2 | no | — |
| 552 | #107 | — | 8 | 2 | no | — |
| 553 | #107 | — | 8 | 2 | no | — |
| 554 | #107 | — | 8 | 1 | no | — |
| 555 | #107 | — | 8 | 1 | no | — |
| 556 | #107 | — | 8 | 2 | no | — |
| 557 | #106 | — | 8 | 2 | no | — |
| 558 | #106 | — | 8 | 1 | no | — |
| 559 | #106 | — | 8 | 2 | no | — |
| 560 | C4⋊C8 | — | 2 | 2 | no | — |
| 561 | #103 | — | 8 | 1 | no | — |
| 562 | #103 | — | 8 | 1 | no | — |
| 563 | #103 | — | 8 | 2 | no | — |
| 564 | #103 | — | 8 | 2 | no | — |
| 565 | #102 | — | 8 | 1 | no | — |
| 566 | #102 | — | 8 | 1 | no | — |
| 567 | #102 | — | 8 | 2 | no | — |
| 568 | #102 | — | 8 | 2 | no | — |
| 569 | #101 | — | 16 | 1 | no | — |
| 570 | #100 | — | 16 | 1 | no | — |
| 571 | C22⋊C8 | — | 2 | 2 | no | — |
| 572 | C22⋊C8 | — | 2 | 2 | no | — |
| 573 | C22⋊C8 | — | 32 | 2 | no | — |
| 574 | #97 | — | 2 | 1 | no | — |
| 575 | C4×C8 | — | 2 | 1 | no | — |
| 576 | C32 | — | 2 | 2 | no | — |
| 577 | C32 | — | 4 | 1 | no | — |
| 578 | C32 | — | 4 | 1 | no | — |
| 579 | C32 | #525 | 1 | 1 | yes | characteristic |
| 580 | C32 | #536 | 1 | 1 | yes | characteristic |
| 581 | C32 | #547 | 1 | 2 | yes | — |
| 582 | C24 | C2×SD64 | 1 | 1 | yes | characteristic |
| 583 | #41 | — | 2 | 2 | no | — |
| 584 | #41 | — | 2 | 2 | no | — |
| 585 | #41 | — | 16 | 2 | no | — |
| 586 | #41 | — | 16 | 2 | no | — |
| 587 | #41 | — | 64 | 4 | no | — |
| 588 | C2×Q8 | — | 8 | 1 | no | — |
| 589 | C2×Q8 | — | 16 | 2 | no | — |
| 590 | C2×Q8 | #2263 | 1 | 1 | yes | characteristic |
| 591 | C2×D4 | — | 2 | 2 | no | — |
| 592 | C2×D4 | — | 8 | 1 | no | — |
| 593 | C2×D4 | — | 16 | 1 | no | — |
| 594 | C2×D4 | — | 16 | 1 | no | — |
| 595 | C2×D4 | — | 16 | 1 | no | — |
| 596 | C2×D4 | — | 16 | 2 | no | — |
| 597 | C2×D4 | C2×SD64 | 1 | 2 | yes | — |
| 598 | C2×D4 | #2263 | 1 | 1 | yes | characteristic |
| 599 | C22×C4 | — | 2 | 2 | no | — |
| 600 | C22×C4 | — | 2 | 1 | no | — |
| 601 | C22×C4 | — | 2 | 2 | no | — |
| 602 | C22×C4 | — | 2 | 1 | no | — |
| 603 | C22×C4 | — | 16 | 2 | no | — |
| 604 | C22×C4 | — | 16 | 2 | no | — |
| 605 | C22×C4 | — | 16 | 2 | no | — |
| 606 | C22×C4 | — | 16 | 2 | no | — |
| 607 | C22×C4 | — | 16 | 1 | no | — |
| 608 | C22×C4 | — | 16 | 1 | no | — |
| 609 | C22×C4 | — | 16 | 1 | no | — |
| 610 | C22×C4 | — | 64 | 2 | no | — |
| 611 | C22×C4 | #2184 | 1 | 2 | yes | — |
| 612 | C22×C4 | C2×SD64 | 1 | 1 | yes | characteristic |
| 613 | C22×C4 | C22×D16 | 1 | 1 | yes | characteristic |
| 614 | Q16 | — | 8 | 1 | no | — |
| 615 | Q16 | — | 8 | 1 | no | — |
| 616 | SD16 | — | 16 | 2 | no | — |
| 617 | D8 | — | 8 | 1 | no | — |
| 618 | D8 | — | 8 | 1 | no | — |
| 619 | M16 | — | 2 | 2 | no | — |
| 620 | M16 | — | 2 | 4 | no | — |
| 621 | M16 | — | 2 | 2 | no | — |
| 622 | M16 | — | 16 | 2 | no | — |
| 623 | M16 | — | 16 | 2 | no | — |
| 624 | M16 | — | 16 | 2 | no | — |
| 625 | M16 | — | 16 | 2 | no | — |
| 626 | M16 | — | 32 | 2 | no | — |
| 627 | C2×C8 | — | 2 | 2 | no | — |
| 628 | C2×C8 | — | 2 | 2 | no | — |
| 629 | C2×C8 | — | 2 | 2 | no | — |
| 630 | C2×C8 | — | 2 | 1 | no | — |
| 631 | C2×C8 | — | 2 | 1 | no | — |
| 632 | C2×C8 | — | 4 | 1 | no | — |
| 633 | C2×C8 | — | 4 | 2 | no | — |
| 634 | C2×C8 | — | 4 | 1 | no | — |
| 635 | C2×C8 | — | 16 | 2 | no | — |
| 636 | C2×C8 | — | 16 | 2 | no | — |
| 637 | C2×C8 | — | 32 | 2 | no | — |
| 638 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 639 | C2×C8 | C2×#447 | 1 | 1 | yes | characteristic |
| 640 | C2×C8 | #3334 | 1 | 2 | yes | — |
| 641 | C2×C8 | C2×#509 | 1 | 1 | yes | characteristic |
| 642 | C2×C8 | #3417 | 1 | 2 | yes | — |
| 643 | C4⋊C4 | — | 2 | 2 | no | — |
| 644 | C4⋊C4 | — | 2 | 1 | no | — |
| 645 | C4⋊C4 | — | 8 | 1 | no | — |
| 646 | C4⋊C4 | — | 8 | 2 | no | — |
| 647 | C4⋊C4 | — | 8 | 2 | no | — |
| 648 | C4⋊C4 | — | 8 | 1 | no | — |
| 649 | C4⋊C4 | — | 16 | 2 | no | — |
| 650 | C4⋊C4 | — | 16 | 2 | no | — |
| 651 | C4⋊C4 | — | 16 | 2 | no | — |
| 652 | C4⋊C4 | — | 16 | 2 | no | — |
| 653 | C4⋊C4 | — | 16 | 1 | no | — |
| 654 | C4⋊C4 | — | 16 | 1 | no | — |
| 655 | C4⋊C4 | — | 16 | 2 | no | — |
| 656 | C4⋊C4 | — | 16 | 2 | no | — |
| 657 | C4⋊C4 | — | 16 | 2 | no | — |
| 658 | C4⋊C4 | — | 16 | 2 | no | — |
| 659 | C4⋊C4 | — | 16 | 1 | no | — |
| 660 | C4⋊C4 | — | 16 | 1 | no | — |
| 661 | C22⋊C4 | — | 2 | 2 | no | — |
| 662 | C22⋊C4 | — | 2 | 2 | no | — |
| 663 | C22⋊C4 | — | 16 | 2 | no | — |
| 664 | C22⋊C4 | — | 16 | 1 | no | — |
| 665 | C22⋊C4 | — | 16 | 1 | no | — |
| 666 | C22⋊C4 | — | 16 | 1 | no | — |
| 667 | C22⋊C4 | — | 16 | 1 | no | — |
| 668 | C22⋊C4 | — | 16 | 2 | no | — |
| 669 | C22⋊C4 | — | 16 | 2 | no | — |
| 670 | C22⋊C4 | — | 16 | 1 | no | — |
| 671 | C22⋊C4 | — | 16 | 2 | no | — |
| 672 | C22⋊C4 | C2×SD64 | 1 | 2 | yes | — |
| 673 | C42 | — | 2 | 1 | no | — |
| 674 | C42 | — | 16 | 2 | no | — |
| 675 | C42 | — | 16 | 2 | no | — |
| 676 | C42 | — | 16 | 1 | no | — |
| 677 | C16 | — | 2 | 2 | no | — |
| 678 | C16 | — | 4 | 1 | no | — |
| 679 | C16 | — | 4 | 1 | no | — |
| 680 | C16 | #2406 | 1 | 1 | yes | characteristic |
| 681 | C16 | #3011 | 1 | 1 | yes | characteristic |
| 682 | C16 | #3343 | 1 | 2 | yes | — |
| 683 | C23 | — | 2 | 1 | no | — |
| 684 | C23 | — | 2 | 2 | no | — |
| 685 | C23 | — | 4 | 2 | no | — |
| 686 | C23 | — | 16 | 1 | no | — |
| 687 | C23 | #13664 | 1 | 2 | yes | — |
| 688 | C23 | C22×SD64 | 1 | 1 | yes | characteristic |
| 689 | Q8 | — | 2 | 2 | no | — |
| 690 | Q8 | — | 16 | 1 | no | — |
| 691 | Q8 | — | 16 | 1 | no | — |
| 692 | Q8 | — | 64 | 2 | no | — |
| 693 | D4 | — | 2 | 4 | no | — |
| 694 | D4 | — | 2 | 2 | no | — |
| 695 | D4 | — | 4 | 4 | no | — |
| 696 | D4 | — | 16 | 1 | no | — |
| 697 | D4 | — | 16 | 1 | no | — |
| 698 | D4 | — | 32 | 2 | no | — |
| 699 | D4 | — | 32 | 2 | no | — |
| 700 | D4 | — | 32 | 2 | no | — |
| 701 | D4 | — | 64 | 2 | no | — |
| 702 | C2×C4 | — | 2 | 2 | no | — |
| 703 | C2×C4 | — | 2 | 2 | no | — |
| 704 | C2×C4 | — | 2 | 2 | no | — |
| 705 | C2×C4 | — | 2 | 1 | no | — |
| 706 | C2×C4 | — | 2 | 2 | no | — |
| 707 | C2×C4 | — | 4 | 1 | no | — |
| 708 | C2×C4 | — | 4 | 1 | no | — |
| 709 | C2×C4 | — | 4 | 2 | no | — |
| 710 | C2×C4 | — | 16 | 1 | no | — |
| 711 | C2×C4 | — | 16 | 1 | no | — |
| 712 | C2×C4 | — | 16 | 2 | no | — |
| 713 | C2×C4 | — | 16 | 1 | no | — |
| 714 | C2×C4 | — | 16 | 2 | no | — |
| 715 | C2×C4 | — | 32 | 4 | no | — |
| 716 | C2×C4 | — | 32 | 2 | no | — |
| 717 | C2×C4 | — | 64 | 2 | no | — |
| 718 | C2×C4 | — | 64 | 1 | no | — |
| 719 | C2×C4 | — | 64 | 2 | no | — |
| 720 | C2×C4 | — | 64 | 1 | no | — |
| 721 | C2×C4 | — | 64 | 2 | no | — |
| 722 | C2×C4 | #13664 | 1 | 2 | yes | — |
| 723 | C2×C4 | C2×#2184 | 1 | 1 | yes | characteristic |
| 724 | C2×C4 | #33901 | 1 | 2 | yes | — |
| 725 | C2×C4 | C2×#2263 | 1 | 1 | yes | characteristic |
| 726 | C2×C4 | #33983 | 1 | 2 | yes | — |
| 727 | C8 | — | 2 | 2 | no | — |
| 728 | C8 | — | 4 | 1 | no | — |
| 729 | C8 | — | 4 | 1 | no | — |
| 730 | C8 | — | 32 | 2 | no | — |
| 731 | C8 | — | 32 | 2 | no | — |
| 732 | C8 | #24088 | 1 | 1 | yes | characteristic |
| 733 | C8 | #33525 | 1 | 1 | yes | characteristic |
| 734 | C8 | #33910 | 1 | 2 | yes | — |
| 735 | C22 | — | 2 | 2 | no | — |
| 736 | C22 | — | 2 | 4 | no | — |
| 737 | C22 | — | 2 | 2 | no | — |
| 738 | C22 | — | 4 | 1 | no | — |
| 739 | C22 | — | 4 | 2 | no | — |
| 740 | C22 | — | 4 | 1 | no | — |
| 741 | C22 | — | 4 | 2 | no | — |
| 742 | C22 | — | 4 | 1 | no | — |
| 743 | C22 | — | 32 | 1 | no | — |
| 744 | C22 | — | 32 | 1 | no | — |
| 745 | C22 | — | 32 | 1 | no | — |
| 746 | C22 | C2×#13664 | 1 | 1 | yes | characteristic |
| 747 | C22 | #513236 | 1 | 2 | yes | — |
| 748 | C4 | — | 2 | 2 | no | — |
| 749 | C4 | — | 4 | 2 | no | — |
| 750 | C4 | — | 4 | 1 | no | — |
| 751 | C4 | — | 32 | 2 | no | — |
| 752 | C4 | — | 32 | 2 | no | — |
| 753 | C4 | — | 32 | 1 | no | — |
| 754 | C4 | — | 32 | 1 | no | — |
| 755 | C4 | — | 32 | 1 | no | — |
| 756 | C4 | #500310 | 1 | 1 | yes | characteristic |
| 757 | C4 | #512834 | 1 | 1 | yes | characteristic |
| 758 | C4 | #513246 | 1 | 2 | yes | — |
| 759 | C2 | — | 2 | 1 | no | — |
| 760 | C2 | — | 2 | 2 | no | — |
| 761 | C2 | — | 4 | 2 | no | — |
| 762 | C2 | — | 4 | 2 | no | — |
| 763 | C2 | — | 64 | 1 | no | — |
| 764 | C2 | #72322878 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #72322878 |
| commutator, Frattini, cosocle | C22×C32 | C24 |
| prime radical | #72322440 | C2 |
| LCS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #2929 ◁ #33432 ◁ #512742 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72322761 | C2 | semidirect |
| 2. #72322725 | C2 | semidirect |
| 3. #72322624 | C2 | semidirect |
| 5. #72322053 | C2 | semidirect |
| 6. #72321831 | C2 | semidirect |
| 7. #72321622 | C2 | semidirect |
| 8. #72321409 | C2 | semidirect |
| 9. #72321207 | C2 | semidirect |
| 10. #72320880 | C2 | semidirect |
| 11. #72286849 | C2 | semidirect |
| 251. C2×C64 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72322761 | 2 |
| #72322725 | 2 |
| #72322624 | 2 |
| #72322440 | 2 |
| #72322053 | 2 |
| #72321831 | 2 |
| #72321622 | 2 |
| #72321409 | 2 |
| #72321207 | 2 |
| #72320880 | 2 |
| #72286849 | 2 |