Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
790 conjugacy classes of subgroups.
The subgroup lattice has 773 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7623826 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #152372 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #152371 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #150881 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #150879 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #149670 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #134774 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #61262 | — | 2 | 1 | no | — |
| 9 | #33922 | — | 2 | 1 | no | — |
| 10 | #33922 | — | 2 | 1 | no | — |
| 11 | #33921 | — | 2 | 1 | no | — |
| 12 | #33921 | — | 2 | 1 | no | — |
| 13 | #33914 | — | 2 | 1 | no | — |
| 14 | #33914 | — | 2 | 1 | no | — |
| 15 | #33912 | — | 2 | 1 | no | — |
| 16 | #33912 | — | 2 | 1 | no | — |
| 17 | #33730 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #33650 | — | 2 | 1 | no | — |
| 19 | #33648 | — | 2 | 1 | no | — |
| 20 | #33631 | — | 2 | 1 | no | — |
| 21 | #33607 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#2218 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #33456 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #33433 | C22 | 1 | 1 | yes | characteristic |
| 25 | #33411 | C22 | 1 | 1 | yes | characteristic |
| 26 | #33409 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #13556 | C22 | 1 | 1 | yes | characteristic |
| 28 | #13556 | C22 | 1 | 1 | yes | characteristic |
| 29 | #12840 | C22 | 1 | 1 | yes | characteristic |
| 30 | #12839 | C22 | 1 | 1 | yes | characteristic |
| 31 | #12805 | — | 2 | 1 | no | — |
| 32 | #7480 | — | 2 | 1 | no | — |
| 33 | #7477 | — | 2 | 1 | no | — |
| 34 | #7475 | — | 2 | 1 | no | — |
| 35 | #7474 | — | 2 | 1 | no | — |
| 36 | #7424 | — | 2 | 1 | no | — |
| 37 | #7424 | — | 2 | 1 | no | — |
| 38 | #7422 | — | 2 | 1 | no | — |
| 39 | #7422 | — | 2 | 1 | no | — |
| 40 | #7365 | — | 2 | 1 | no | — |
| 41 | #7336 | — | 2 | 1 | no | — |
| 42 | #7227 | — | 2 | 1 | no | — |
| 43 | #3494 | — | 4 | 1 | no | — |
| 44 | C22×D16 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 46 | C22×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | #3347 | — | 4 | 1 | no | — |
| 48 | #3347 | — | 4 | 1 | no | — |
| 49 | #3345 | — | 4 | 1 | no | — |
| 50 | #3345 | — | 4 | 1 | no | — |
| 51 | #3341 | — | 2 | 1 | no | — |
| 52 | #3341 | — | 2 | 1 | no | — |
| 53 | #3339 | — | 2 | 1 | no | — |
| 54 | #3339 | — | 2 | 1 | no | — |
| 55 | #3339 | — | 2 | 1 | no | — |
| 56 | #3339 | — | 2 | 1 | no | — |
| 57 | #3334 | — | 2 | 1 | no | — |
| 58 | #3334 | — | 2 | 1 | no | — |
| 59 | #3164 | — | 2 | 1 | no | — |
| 60 | #3096 | — | 4 | 1 | no | — |
| 61 | #3094 | — | 4 | 1 | no | — |
| 62 | #3081 | — | 4 | 1 | no | — |
| 63 | #3058 | — | 2 | 1 | no | — |
| 64 | C2×#466 | — | 2 | 1 | no | — |
| 65 | #2948 | — | 2 | 1 | no | — |
| 66 | #2929 | D4 | 1 | 1 | yes | characteristic |
| 67 | #2913 | — | 2 | 1 | no | — |
| 68 | C2×#427 | — | 2 | 1 | no | — |
| 69 | C2×M64 | — | 2 | 1 | no | — |
| 70 | C2×M64 | — | 2 | 1 | no | — |
| 71 | #2255 | — | 2 | 1 | no | — |
| 72 | #2255 | — | 2 | 1 | no | — |
| 73 | #2254 | — | 2 | 1 | no | — |
| 74 | #2253 | — | 2 | 1 | no | — |
| 75 | #2234 | — | 2 | 1 | no | — |
| 76 | #2234 | — | 2 | 1 | no | — |
| 77 | #2234 | — | 2 | 1 | no | — |
| 78 | #2234 | — | 2 | 1 | no | — |
| 79 | #2234 | — | 2 | 1 | no | — |
| 80 | #2234 | — | 2 | 1 | no | — |
| 81 | #2234 | — | 2 | 1 | no | — |
| 82 | #2234 | — | 2 | 1 | no | — |
| 83 | #2233 | — | 2 | 1 | no | — |
| 84 | #2233 | — | 2 | 1 | no | — |
| 85 | #2233 | — | 2 | 1 | no | — |
| 86 | #2233 | — | 2 | 1 | no | — |
| 87 | #2232 | — | 2 | 1 | no | — |
| 88 | #2232 | — | 2 | 1 | no | — |
| 89 | #2232 | — | 2 | 1 | no | — |
| 90 | #2232 | — | 2 | 1 | no | — |
| 91 | #2228 | — | 2 | 1 | no | — |
| 92 | #2228 | — | 2 | 1 | no | — |
| 93 | #2228 | — | 2 | 1 | no | — |
| 94 | #2228 | — | 2 | 1 | no | — |
| 95 | #2226 | — | 2 | 1 | no | — |
| 96 | #2226 | — | 2 | 1 | no | — |
| 97 | #2224 | — | 2 | 1 | no | — |
| 98 | #2224 | — | 2 | 1 | no | — |
| 99 | #2218 | — | 2 | 1 | no | — |
| 100 | #2218 | — | 2 | 1 | no | — |
| 101 | #2218 | — | 2 | 1 | no | — |
| 102 | #2218 | — | 2 | 1 | no | — |
| 103 | #2218 | D4 | 1 | 1 | yes | characteristic |
| 104 | #2218 | D4 | 1 | 1 | yes | characteristic |
| 105 | #2218 | D4 | 1 | 1 | yes | characteristic |
| 106 | #2218 | D4 | 1 | 1 | yes | characteristic |
| 107 | #2215 | — | 2 | 1 | no | — |
| 108 | #2215 | — | 2 | 1 | no | — |
| 109 | #2177 | — | 2 | 1 | no | — |
| 110 | #2177 | — | 2 | 1 | no | — |
| 111 | C4×D16 | — | 2 | 1 | no | — |
| 112 | C4×D16 | — | 2 | 1 | no | — |
| 113 | #2169 | — | 2 | 1 | no | — |
| 114 | #2169 | — | 2 | 1 | no | — |
| 115 | #2168 | — | 2 | 1 | no | — |
| 116 | #2168 | — | 2 | 1 | no | — |
| 117 | C2×#368 | — | 2 | 1 | no | — |
| 118 | #2159 | — | 2 | 1 | no | — |
| 119 | #2159 | — | 2 | 1 | no | — |
| 120 | #2159 | — | 2 | 1 | no | — |
| 121 | #2159 | — | 2 | 1 | no | — |
| 122 | #2159 | — | 2 | 1 | no | — |
| 123 | #2159 | — | 2 | 1 | no | — |
| 124 | #2159 | — | 2 | 1 | no | — |
| 125 | #2159 | — | 2 | 1 | no | — |
| 126 | #2158 | — | 2 | 1 | no | — |
| 127 | #2158 | — | 2 | 1 | no | — |
| 128 | #2158 | C2×C4 | 1 | 1 | yes | characteristic |
| 129 | #2158 | C2×C4 | 1 | 1 | yes | characteristic |
| 130 | #2158 | D4 | 1 | 1 | yes | characteristic |
| 131 | #2158 | D4 | 1 | 1 | yes | characteristic |
| 132 | C2×#367 | C2×C4 | 1 | 1 | yes | characteristic |
| 133 | C2×#367 | D4 | 1 | 1 | yes | characteristic |
| 134 | C2×#367 | D4 | 1 | 1 | yes | characteristic |
| 135 | #2151 | D4 | 1 | 1 | yes | characteristic |
| 136 | #2140 | — | 2 | 1 | no | — |
| 137 | #2140 | — | 2 | 1 | no | — |
| 138 | C2×#357 | — | 2 | 1 | no | — |
| 139 | #2120 | — | 4 | 1 | no | — |
| 140 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 141 | #2112 | D4 | 1 | 1 | yes | characteristic |
| 142 | #2108 | C2×C4 | 1 | 1 | yes | characteristic |
| 143 | #1813 | — | 2 | 1 | no | — |
| 144 | #1812 | — | 2 | 1 | no | — |
| 145 | #1400 | — | 2 | 1 | no | — |
| 146 | #1400 | — | 2 | 1 | no | — |
| 147 | #1400 | — | 2 | 1 | no | — |
| 148 | #1400 | — | 2 | 1 | no | — |
| 149 | #1395 | — | 4 | 1 | no | — |
| 150 | #1385 | — | 2 | 1 | no | — |
| 151 | #1384 | — | 2 | 1 | no | — |
| 152 | C22×D8 | — | 2 | 1 | no | — |
| 153 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C23×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 155 | #555 | — | 4 | 1 | no | — |
| 156 | #555 | — | 4 | 1 | no | — |
| 157 | #553 | — | 4 | 1 | no | — |
| 158 | #553 | — | 4 | 1 | no | — |
| 159 | #553 | — | 4 | 1 | no | — |
| 160 | #553 | — | 4 | 1 | no | — |
| 161 | #551 | — | 8 | 1 | no | — |
| 162 | #551 | — | 8 | 1 | no | — |
| 163 | #547 | — | 4 | 1 | no | — |
| 164 | #547 | — | 4 | 1 | no | — |
| 165 | #546 | — | 8 | 1 | no | — |
| 166 | #546 | — | 8 | 1 | no | — |
| 167 | #544 | — | 4 | 1 | no | — |
| 168 | #542 | — | 8 | 1 | no | — |
| 169 | #540 | — | 8 | 1 | no | — |
| 170 | #535 | — | 4 | 1 | no | — |
| 171 | #532 | — | 8 | 1 | no | — |
| 172 | #529 | — | 8 | 1 | no | — |
| 173 | #525 | D8 | 1 | 1 | yes | characteristic |
| 174 | C2×#121 | — | 4 | 1 | no | — |
| 175 | #520 | — | 4 | 1 | no | — |
| 176 | #518 | — | 4 | 1 | no | — |
| 177 | C2×#117 | — | 4 | 1 | no | — |
| 178 | C2×D16 | — | 2 | 1 | no | — |
| 179 | C2×D16 | — | 4 | 1 | no | — |
| 180 | C2×D16 | — | 4 | 1 | no | — |
| 181 | C2×D16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×D16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 183 | #504 | — | 4 | 1 | no | — |
| 184 | #504 | — | 4 | 1 | no | — |
| 185 | C2×M32 | — | 2 | 1 | no | — |
| 186 | C2×M32 | — | 2 | 1 | no | — |
| 187 | C2×M32 | — | 4 | 1 | no | — |
| 188 | C2×M32 | — | 4 | 1 | no | — |
| 189 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 190 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C22×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | #501 | — | 4 | 1 | no | — |
| 198 | #501 | — | 4 | 1 | no | — |
| 199 | #500 | — | 2 | 1 | no | — |
| 200 | #500 | — | 2 | 1 | no | — |
| 201 | #499 | — | 2 | 1 | no | — |
| 202 | #499 | — | 2 | 1 | no | — |
| 203 | #482 | — | 4 | 1 | no | — |
| 204 | #482 | — | 4 | 1 | no | — |
| 205 | #482 | — | 4 | 1 | no | — |
| 206 | #482 | — | 4 | 1 | no | — |
| 207 | #482 | — | 4 | 1 | no | — |
| 208 | #482 | — | 4 | 1 | no | — |
| 209 | #482 | — | 4 | 1 | no | — |
| 210 | #482 | — | 4 | 1 | no | — |
| 211 | #481 | — | 4 | 1 | no | — |
| 212 | #481 | — | 4 | 1 | no | — |
| 213 | #481 | — | 4 | 1 | no | — |
| 214 | #481 | — | 4 | 1 | no | — |
| 215 | #480 | — | 4 | 1 | no | — |
| 216 | #480 | — | 4 | 1 | no | — |
| 217 | #480 | — | 4 | 1 | no | — |
| 218 | #480 | — | 4 | 1 | no | — |
| 219 | #478 | — | 4 | 1 | no | — |
| 220 | #478 | — | 4 | 1 | no | — |
| 221 | #478 | — | 4 | 1 | no | — |
| 222 | #478 | — | 4 | 1 | no | — |
| 223 | #476 | — | 4 | 1 | no | — |
| 224 | #476 | — | 4 | 1 | no | — |
| 225 | #474 | — | 4 | 1 | no | — |
| 226 | #474 | — | 4 | 1 | no | — |
| 227 | #469 | — | 4 | 1 | no | — |
| 228 | #469 | — | 4 | 1 | no | — |
| 229 | #466 | — | 2 | 1 | no | — |
| 230 | #466 | — | 2 | 1 | no | — |
| 231 | #466 | — | 2 | 1 | no | — |
| 232 | #466 | — | 2 | 1 | no | — |
| 233 | #466 | — | 2 | 1 | no | — |
| 234 | #466 | — | 2 | 1 | no | — |
| 235 | #466 | — | 2 | 1 | no | — |
| 236 | #466 | — | 2 | 1 | no | — |
| 237 | #466 | — | 4 | 1 | no | — |
| 238 | #466 | — | 4 | 1 | no | — |
| 239 | #442 | — | 4 | 1 | no | — |
| 240 | #442 | — | 4 | 1 | no | — |
| 241 | C4×D8 | — | 2 | 1 | no | — |
| 242 | C4×D8 | — | 2 | 1 | no | — |
| 243 | C4×D8 | — | 2 | 1 | no | — |
| 244 | C4×D8 | — | 2 | 1 | no | — |
| 245 | #435 | — | 2 | 1 | no | — |
| 246 | #435 | — | 2 | 1 | no | — |
| 247 | C8×D4 | — | 2 | 1 | no | — |
| 248 | C8×D4 | — | 2 | 1 | no | — |
| 249 | C2×#108 | — | 4 | 1 | no | — |
| 250 | #428 | — | 4 | 1 | no | — |
| 251 | #428 | — | 4 | 1 | no | — |
| 252 | #428 | — | 4 | 1 | no | — |
| 253 | #428 | — | 4 | 1 | no | — |
| 254 | #427 | — | 2 | 1 | no | — |
| 255 | #427 | — | 2 | 1 | no | — |
| 256 | #427 | — | 2 | 1 | no | — |
| 257 | #427 | — | 2 | 1 | no | — |
| 258 | #427 | — | 2 | 1 | no | — |
| 259 | #427 | — | 2 | 1 | no | — |
| 260 | #427 | — | 4 | 1 | no | — |
| 261 | #427 | — | 4 | 1 | no | — |
| 262 | #427 | — | 4 | 1 | no | — |
| 263 | C2×#107 | — | 2 | 1 | no | — |
| 264 | C2×#107 | — | 2 | 1 | no | — |
| 265 | C2×#107 | — | 2 | 1 | no | — |
| 266 | C2×#107 | — | 2 | 1 | no | — |
| 267 | C2×#107 | — | 2 | 1 | no | — |
| 268 | C2×#106 | — | 4 | 1 | no | — |
| 269 | #424 | SD16 | 1 | 1 | yes | characteristic |
| 270 | #418 | — | 4 | 1 | no | — |
| 271 | #418 | — | 4 | 1 | no | — |
| 272 | C2×#102 | — | 4 | 1 | no | — |
| 273 | #413 | — | 4 | 1 | no | — |
| 274 | #410 | — | 4 | 1 | no | — |
| 275 | #408 | D8 | 1 | 1 | yes | characteristic |
| 276 | #407 | SD16 | 1 | 1 | yes | characteristic |
| 277 | #405 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 278 | M64 | — | 4 | 1 | no | — |
| 279 | M64 | — | 4 | 1 | no | — |
| 280 | M64 | — | 4 | 1 | no | — |
| 281 | M64 | — | 4 | 1 | no | — |
| 282 | C2×C32 | — | 4 | 1 | no | — |
| 283 | C2×C32 | — | 4 | 1 | no | — |
| 284 | #368 | — | 4 | 1 | no | — |
| 285 | #368 | — | 4 | 1 | no | — |
| 286 | #367 | — | 2 | 1 | no | — |
| 287 | #367 | — | 2 | 1 | no | — |
| 288 | #367 | — | 2 | 1 | no | — |
| 289 | #367 | — | 2 | 1 | no | — |
| 290 | #367 | — | 2 | 1 | no | — |
| 291 | #367 | — | 2 | 1 | no | — |
| 292 | #367 | — | 2 | 1 | no | — |
| 293 | #367 | — | 4 | 1 | no | — |
| 294 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 295 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 296 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 297 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 298 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 299 | #367 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 300 | #366 | — | 2 | 1 | no | — |
| 301 | #366 | — | 2 | 1 | no | — |
| 302 | #366 | — | 2 | 1 | no | — |
| 303 | #366 | — | 2 | 1 | no | — |
| 304 | #366 | — | 2 | 1 | no | — |
| 305 | #366 | — | 2 | 1 | no | — |
| 306 | #366 | — | 2 | 1 | no | — |
| 307 | #366 | — | 2 | 1 | no | — |
| 308 | #366 | — | 4 | 1 | no | — |
| 309 | C4⋊C16 | — | 2 | 1 | no | — |
| 310 | C4⋊C16 | — | 2 | 1 | no | — |
| 311 | #357 | — | 2 | 1 | no | — |
| 312 | #357 | — | 2 | 1 | no | — |
| 313 | #357 | — | 2 | 1 | no | — |
| 314 | #357 | — | 2 | 1 | no | — |
| 315 | #357 | — | 2 | 1 | no | — |
| 316 | #357 | — | 2 | 1 | no | — |
| 317 | #357 | — | 2 | 1 | no | — |
| 318 | #357 | — | 2 | 1 | no | — |
| 319 | #357 | — | 2 | 1 | no | — |
| 320 | #357 | — | 2 | 1 | no | — |
| 321 | #357 | — | 2 | 1 | no | — |
| 322 | #357 | — | 2 | 1 | no | — |
| 323 | #352 | — | 8 | 1 | no | — |
| 324 | AΣL(1,𝔽16) | — | 8 | 1 | no | — |
| 325 | C22⋊C16 | — | 2 | 1 | no | — |
| 326 | C22⋊C16 | — | 2 | 1 | no | — |
| 327 | C22⋊C16 | — | 2 | 1 | no | — |
| 328 | C22⋊C16 | — | 2 | 1 | no | — |
| 329 | #346 | — | 2 | 1 | no | — |
| 330 | C4×C16 | — | 2 | 1 | no | — |
| 331 | #338 | — | 4 | 1 | no | — |
| 332 | H(3,ℤ/4) | — | 4 | 1 | no | — |
| 333 | C2×#41 | — | 8 | 1 | no | — |
| 334 | C2×#41 | — | 8 | 1 | no | — |
| 335 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 336 | C22×D4 | — | 4 | 1 | no | — |
| 337 | C22×D4 | — | 8 | 1 | no | — |
| 338 | C23×C4 | #102 | 1 | 1 | yes | characteristic |
| 339 | C2×D8 | — | 2 | 1 | no | — |
| 340 | C2×D8 | — | 2 | 1 | no | — |
| 341 | C2×D8 | — | 4 | 2 | no | — |
| 342 | C2×D8 | — | 4 | 2 | no | — |
| 343 | C2×D8 | — | 4 | 1 | no | — |
| 344 | #131 | — | 4 | 1 | no | — |
| 345 | #131 | — | 4 | 1 | no | — |
| 346 | C2×M16 | — | 8 | 1 | no | — |
| 347 | C2×M16 | #102 | 1 | 1 | yes | characteristic |
| 348 | C2×M16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 349 | C2×M16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 350 | C2×M16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 351 | C22×C8 | — | 2 | 1 | no | — |
| 352 | C22×C8 | — | 2 | 1 | no | — |
| 353 | C22×C8 | — | 4 | 1 | no | — |
| 354 | C22×C8 | — | 4 | 1 | no | — |
| 355 | C22×C8 | #102 | 1 | 1 | yes | characteristic |
| 356 | C22×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 357 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 358 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 359 | C4⋊Q8 | — | 4 | 1 | no | — |
| 360 | C4⋊Q8 | — | 4 | 1 | no | — |
| 361 | C4⋊Q8 | — | 8 | 1 | no | — |
| 362 | #127 | — | 8 | 1 | no | — |
| 363 | #126 | — | 8 | 1 | no | — |
| 364 | #126 | — | 8 | 1 | no | — |
| 365 | #126 | — | 8 | 1 | no | — |
| 366 | #126 | — | 8 | 1 | no | — |
| 367 | #125 | — | 4 | 1 | no | — |
| 368 | #125 | — | 4 | 1 | no | — |
| 369 | #125 | — | 8 | 1 | no | — |
| 370 | #124 | — | 8 | 1 | no | — |
| 371 | #124 | — | 8 | 1 | no | — |
| 372 | #124 | — | 8 | 1 | no | — |
| 373 | #124 | — | 8 | 1 | no | — |
| 374 | #124 | — | 8 | 1 | no | — |
| 375 | #123 | — | 8 | 1 | no | — |
| 376 | #123 | — | 8 | 1 | no | — |
| 377 | #123 | — | 8 | 1 | no | — |
| 378 | #123 | — | 8 | 1 | no | — |
| 379 | #123 | — | 8 | 1 | no | — |
| 380 | #123 | — | 8 | 1 | no | — |
| 381 | #123 | — | 8 | 1 | no | — |
| 382 | #123 | — | 8 | 1 | no | — |
| 383 | #123 | D16 | 1 | 1 | yes | characteristic |
| 384 | #123 | SD32 | 1 | 1 | yes | characteristic |
| 385 | C22⋊Q8 | — | 2 | 1 | no | — |
| 386 | C22⋊Q8 | — | 8 | 1 | no | — |
| 387 | C22⋊Q8 | — | 8 | 1 | no | — |
| 388 | C22⋊Q8 | — | 8 | 1 | no | — |
| 389 | C22⋊Q8 | — | 8 | 1 | no | — |
| 390 | #121 | — | 2 | 1 | no | — |
| 391 | #121 | — | 4 | 1 | no | — |
| 392 | #121 | — | 4 | 1 | no | — |
| 393 | #121 | — | 4 | 1 | no | — |
| 394 | #121 | — | 4 | 1 | no | — |
| 395 | #121 | — | 4 | 1 | no | — |
| 396 | #121 | — | 4 | 1 | no | — |
| 397 | #121 | — | 4 | 1 | no | — |
| 398 | #121 | — | 4 | 1 | no | — |
| 399 | #121 | — | 8 | 1 | no | — |
| 400 | #121 | — | 8 | 1 | no | — |
| 401 | #121 | — | 8 | 1 | no | — |
| 402 | #121 | — | 8 | 1 | no | — |
| 403 | #121 | — | 8 | 1 | no | — |
| 404 | #121 | — | 8 | 1 | no | — |
| 405 | #121 | — | 8 | 1 | no | — |
| 406 | #121 | — | 8 | 1 | no | — |
| 407 | #120 | — | 8 | 1 | no | — |
| 408 | #120 | — | 8 | 1 | no | — |
| 409 | #120 | D16 | 1 | 1 | yes | characteristic |
| 410 | #120 | SD32 | 1 | 1 | yes | characteristic |
| 411 | C4×Q8 | — | 8 | 1 | no | — |
| 412 | C4×D4 | — | 2 | 1 | no | — |
| 413 | C4×D4 | — | 2 | 1 | no | — |
| 414 | C4×D4 | — | 4 | 1 | no | — |
| 415 | C4×D4 | — | 4 | 1 | no | — |
| 416 | C4×D4 | — | 4 | 1 | no | — |
| 417 | C4×D4 | — | 4 | 1 | no | — |
| 418 | C4×D4 | — | 8 | 1 | no | — |
| 419 | C4×D4 | — | 8 | 1 | no | — |
| 420 | C4×D4 | — | 8 | 1 | no | — |
| 421 | C4×D4 | — | 8 | 1 | no | — |
| 422 | C4×D4 | — | 8 | 1 | no | — |
| 423 | C4×D4 | — | 8 | 1 | no | — |
| 424 | C4×D4 | — | 8 | 1 | no | — |
| 425 | C4×D4 | — | 8 | 1 | no | — |
| 426 | C4×D4 | — | 8 | 1 | no | — |
| 427 | #117 | — | 4 | 1 | no | — |
| 428 | #117 | — | 4 | 1 | no | — |
| 429 | #117 | — | 4 | 1 | no | — |
| 430 | #117 | — | 4 | 1 | no | — |
| 431 | #117 | — | 4 | 1 | no | — |
| 432 | #117 | — | 4 | 1 | no | — |
| 433 | #117 | — | 8 | 1 | no | — |
| 434 | #117 | — | 8 | 1 | no | — |
| 435 | #117 | — | 8 | 1 | no | — |
| 436 | #117 | — | 8 | 1 | no | — |
| 437 | #117 | — | 8 | 1 | no | — |
| 438 | #117 | #102 | 1 | 1 | yes | characteristic |
| 439 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 440 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 441 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 443 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 444 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 445 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 446 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 447 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 448 | C2×C42 | — | 8 | 1 | no | — |
| 449 | D16 | — | 4 | 1 | no | — |
| 450 | D16 | — | 4 | 1 | no | — |
| 451 | D16 | — | 4 | 1 | no | — |
| 452 | D16 | — | 4 | 1 | no | — |
| 453 | M32 | — | 4 | 1 | no | — |
| 454 | M32 | — | 4 | 1 | no | — |
| 455 | M32 | — | 4 | 1 | no | — |
| 456 | M32 | — | 4 | 2 | no | — |
| 457 | M32 | — | 4 | 1 | no | — |
| 458 | M32 | — | 4 | 1 | no | — |
| 459 | M32 | — | 4 | 1 | no | — |
| 460 | C2×C16 | — | 2 | 1 | no | — |
| 461 | C2×C16 | — | 2 | 1 | no | — |
| 462 | C2×C16 | — | 2 | 1 | no | — |
| 463 | C2×C16 | — | 2 | 1 | no | — |
| 464 | C2×C16 | — | 2 | 1 | no | — |
| 465 | C2×C16 | — | 2 | 1 | no | — |
| 466 | C2×C16 | — | 2 | 1 | no | — |
| 467 | C2×C16 | — | 2 | 1 | no | — |
| 468 | C2×C16 | — | 4 | 1 | no | — |
| 469 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 470 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 471 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 472 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 473 | #108 | — | 8 | 1 | no | — |
| 474 | #108 | — | 8 | 1 | no | — |
| 475 | #107 | — | 2 | 1 | no | — |
| 476 | #107 | — | 2 | 1 | no | — |
| 477 | #107 | — | 2 | 1 | no | — |
| 478 | #107 | — | 2 | 1 | no | — |
| 479 | #107 | — | 2 | 1 | no | — |
| 480 | #107 | — | 2 | 1 | no | — |
| 481 | #107 | — | 4 | 1 | no | — |
| 482 | #107 | — | 4 | 1 | no | — |
| 483 | #107 | — | 4 | 1 | no | — |
| 484 | #107 | — | 4 | 1 | no | — |
| 485 | #107 | — | 4 | 1 | no | — |
| 486 | #107 | — | 4 | 1 | no | — |
| 487 | #107 | — | 4 | 1 | no | — |
| 488 | #107 | — | 8 | 1 | no | — |
| 489 | #106 | — | 4 | 1 | no | — |
| 490 | #106 | — | 4 | 1 | no | — |
| 491 | #106 | — | 4 | 1 | no | — |
| 492 | #106 | — | 4 | 1 | no | — |
| 493 | #106 | — | 4 | 1 | no | — |
| 494 | #106 | — | 4 | 1 | no | — |
| 495 | #106 | — | 4 | 1 | no | — |
| 496 | #106 | — | 4 | 1 | no | — |
| 497 | #106 | — | 8 | 1 | no | — |
| 498 | C4⋊C8 | — | 2 | 1 | no | — |
| 499 | C4⋊C8 | — | 2 | 1 | no | — |
| 500 | #102 | — | 4 | 1 | no | — |
| 501 | #102 | — | 4 | 1 | no | — |
| 502 | #102 | — | 4 | 1 | no | — |
| 503 | #102 | — | 4 | 1 | no | — |
| 504 | #102 | — | 4 | 1 | no | — |
| 505 | #102 | — | 4 | 1 | no | — |
| 506 | #102 | — | 4 | 1 | no | — |
| 507 | #102 | — | 4 | 1 | no | — |
| 508 | #102 | — | 4 | 1 | no | — |
| 509 | #102 | — | 4 | 1 | no | — |
| 510 | #102 | — | 4 | 1 | no | — |
| 511 | #102 | — | 4 | 1 | no | — |
| 512 | #101 | — | 8 | 1 | no | — |
| 513 | #100 | — | 8 | 1 | no | — |
| 514 | #99 | — | 8 | 1 | no | — |
| 515 | #99 | — | 8 | 1 | no | — |
| 516 | C22⋊C8 | — | 2 | 1 | no | — |
| 517 | C22⋊C8 | — | 2 | 1 | no | — |
| 518 | C22⋊C8 | — | 2 | 1 | no | — |
| 519 | C22⋊C8 | — | 2 | 1 | no | — |
| 520 | #97 | — | 2 | 1 | no | — |
| 521 | C4×C8 | — | 2 | 1 | no | — |
| 522 | C32 | — | 8 | 1 | no | — |
| 523 | C32 | — | 8 | 1 | no | — |
| 524 | C24 | — | 8 | 1 | no | — |
| 525 | C24 | #357 | 1 | 1 | yes | characteristic |
| 526 | #41 | — | 4 | 1 | no | — |
| 527 | #41 | — | 4 | 1 | no | — |
| 528 | #41 | — | 32 | 2 | no | — |
| 529 | #41 | — | 32 | 2 | no | — |
| 530 | C2×Q8 | — | 8 | 1 | no | — |
| 531 | C2×Q8 | — | 8 | 1 | no | — |
| 532 | C2×Q8 | #509 | 1 | 1 | yes | characteristic |
| 533 | C2×D4 | — | 2 | 1 | no | — |
| 534 | C2×D4 | — | 2 | 1 | no | — |
| 535 | C2×D4 | — | 4 | 1 | no | — |
| 536 | C2×D4 | — | 4 | 1 | no | — |
| 537 | C2×D4 | — | 8 | 2 | no | — |
| 538 | C2×D4 | — | 8 | 2 | no | — |
| 539 | C2×D4 | — | 8 | 1 | no | — |
| 540 | C2×D4 | — | 8 | 1 | no | — |
| 541 | C2×D4 | — | 8 | 1 | no | — |
| 542 | C2×D4 | — | 8 | 1 | no | — |
| 543 | C2×D4 | — | 8 | 1 | no | — |
| 544 | C2×D4 | — | 8 | 1 | no | — |
| 545 | C2×D4 | — | 8 | 1 | no | — |
| 546 | C2×D4 | — | 8 | 1 | no | — |
| 547 | C2×D4 | — | 8 | 1 | no | — |
| 548 | C2×D4 | — | 32 | 2 | no | — |
| 549 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 550 | C2×D4 | C2×SD32 | 1 | 1 | yes | characteristic |
| 551 | C2×D4 | #509 | 1 | 1 | yes | characteristic |
| 552 | C22×C4 | — | 2 | 1 | no | — |
| 553 | C22×C4 | — | 2 | 1 | no | — |
| 554 | C22×C4 | — | 4 | 1 | no | — |
| 555 | C22×C4 | — | 4 | 1 | no | — |
| 556 | C22×C4 | — | 8 | 1 | no | — |
| 557 | C22×C4 | — | 8 | 1 | no | — |
| 558 | C22×C4 | — | 8 | 1 | no | — |
| 559 | C22×C4 | — | 8 | 1 | no | — |
| 560 | C22×C4 | — | 8 | 1 | no | — |
| 561 | C22×C4 | — | 8 | 1 | no | — |
| 562 | C22×C4 | — | 8 | 1 | no | — |
| 563 | C22×C4 | — | 8 | 1 | no | — |
| 564 | C22×C4 | — | 8 | 1 | no | — |
| 565 | C22×C4 | #357 | 1 | 1 | yes | characteristic |
| 566 | C22×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 567 | C22×C4 | #447 | 1 | 1 | yes | characteristic |
| 568 | C22×C4 | #447 | 1 | 1 | yes | characteristic |
| 569 | D8 | — | 4 | 1 | no | — |
| 570 | D8 | — | 4 | 1 | no | — |
| 571 | D8 | — | 4 | 1 | no | — |
| 572 | D8 | — | 4 | 1 | no | — |
| 573 | D8 | — | 8 | 2 | no | — |
| 574 | M16 | — | 4 | 1 | no | — |
| 575 | M16 | — | 4 | 1 | no | — |
| 576 | M16 | — | 4 | 1 | no | — |
| 577 | M16 | — | 4 | 1 | no | — |
| 578 | M16 | — | 16 | 1 | no | — |
| 579 | M16 | — | 16 | 1 | no | — |
| 580 | C2×C8 | — | 2 | 1 | no | — |
| 581 | C2×C8 | — | 2 | 1 | no | — |
| 582 | C2×C8 | — | 2 | 1 | no | — |
| 583 | C2×C8 | — | 2 | 1 | no | — |
| 584 | C2×C8 | — | 2 | 1 | no | — |
| 585 | C2×C8 | — | 2 | 1 | no | — |
| 586 | C2×C8 | — | 2 | 1 | no | — |
| 587 | C2×C8 | — | 2 | 1 | no | — |
| 588 | C2×C8 | — | 4 | 2 | no | — |
| 589 | C2×C8 | — | 4 | 1 | no | — |
| 590 | C2×C8 | — | 4 | 1 | no | — |
| 591 | C2×C8 | — | 4 | 1 | no | — |
| 592 | C2×C8 | — | 16 | 1 | no | — |
| 593 | C2×C8 | #379 | 1 | 1 | yes | characteristic |
| 594 | C2×C8 | #418 | 1 | 1 | yes | characteristic |
| 595 | C2×C8 | #450 | 1 | 1 | yes | characteristic |
| 596 | C2×C8 | #450 | 1 | 1 | yes | characteristic |
| 597 | C4⋊C4 | — | 2 | 1 | no | — |
| 598 | C4⋊C4 | — | 2 | 1 | no | — |
| 599 | C4⋊C4 | — | 2 | 1 | no | — |
| 600 | C4⋊C4 | — | 4 | 1 | no | — |
| 601 | C4⋊C4 | — | 4 | 1 | no | — |
| 602 | C4⋊C4 | — | 4 | 1 | no | — |
| 603 | C4⋊C4 | — | 4 | 1 | no | — |
| 604 | C4⋊C4 | — | 4 | 1 | no | — |
| 605 | C4⋊C4 | — | 4 | 1 | no | — |
| 606 | C4⋊C4 | — | 8 | 1 | no | — |
| 607 | C4⋊C4 | — | 8 | 1 | no | — |
| 608 | C4⋊C4 | — | 8 | 1 | no | — |
| 609 | C4⋊C4 | — | 8 | 1 | no | — |
| 610 | C4⋊C4 | — | 8 | 1 | no | — |
| 611 | C4⋊C4 | — | 8 | 1 | no | — |
| 612 | C4⋊C4 | — | 8 | 1 | no | — |
| 613 | C4⋊C4 | — | 8 | 1 | no | — |
| 614 | C4⋊C4 | — | 8 | 1 | no | — |
| 615 | C4⋊C4 | — | 8 | 1 | no | — |
| 616 | C4⋊C4 | — | 8 | 1 | no | — |
| 617 | C4⋊C4 | — | 16 | 1 | no | — |
| 618 | C22⋊C4 | — | 2 | 1 | no | — |
| 619 | C22⋊C4 | — | 2 | 1 | no | — |
| 620 | C22⋊C4 | — | 2 | 1 | no | — |
| 621 | C22⋊C4 | — | 2 | 1 | no | — |
| 622 | C22⋊C4 | — | 8 | 1 | no | — |
| 623 | C22⋊C4 | — | 8 | 1 | no | — |
| 624 | C22⋊C4 | — | 8 | 1 | no | — |
| 625 | C22⋊C4 | — | 8 | 1 | no | — |
| 626 | C22⋊C4 | — | 8 | 1 | no | — |
| 627 | C22⋊C4 | — | 8 | 1 | no | — |
| 628 | C22⋊C4 | — | 8 | 1 | no | — |
| 629 | C22⋊C4 | — | 8 | 1 | no | — |
| 630 | C22⋊C4 | — | 8 | 1 | no | — |
| 631 | C22⋊C4 | — | 8 | 1 | no | — |
| 632 | C22⋊C4 | — | 8 | 1 | no | — |
| 633 | C22⋊C4 | — | 8 | 1 | no | — |
| 634 | C22⋊C4 | — | 8 | 1 | no | — |
| 635 | C22⋊C4 | — | 8 | 1 | no | — |
| 636 | C22⋊C4 | — | 8 | 1 | no | — |
| 637 | C22⋊C4 | — | 8 | 1 | no | — |
| 638 | C22⋊C4 | — | 8 | 1 | no | — |
| 639 | C22⋊C4 | — | 8 | 1 | no | — |
| 640 | C22⋊C4 | — | 16 | 1 | no | — |
| 641 | C22⋊C4 | #357 | 1 | 1 | yes | characteristic |
| 642 | C22⋊C4 | #357 | 1 | 1 | yes | characteristic |
| 643 | C42 | — | 2 | 1 | no | — |
| 644 | C42 | — | 8 | 1 | no | — |
| 645 | C42 | — | 8 | 1 | no | — |
| 646 | C42 | — | 8 | 1 | no | — |
| 647 | C42 | — | 8 | 1 | no | — |
| 648 | C42 | — | 8 | 1 | no | — |
| 649 | C42 | — | 8 | 1 | no | — |
| 650 | C42 | — | 16 | 1 | no | — |
| 651 | C16 | — | 2 | 1 | no | — |
| 652 | C16 | — | 2 | 1 | no | — |
| 653 | C16 | — | 2 | 1 | no | — |
| 654 | C16 | — | 4 | 1 | no | — |
| 655 | C16 | — | 4 | 1 | no | — |
| 656 | C16 | #410 | 1 | 1 | yes | characteristic |
| 657 | C16 | #410 | 1 | 1 | yes | characteristic |
| 658 | C23 | — | 2 | 1 | no | — |
| 659 | C23 | — | 4 | 1 | no | — |
| 660 | C23 | — | 8 | 1 | no | — |
| 661 | C23 | — | 8 | 1 | no | — |
| 662 | C23 | — | 8 | 1 | no | — |
| 663 | C23 | — | 16 | 2 | no | — |
| 664 | C23 | — | 32 | 1 | no | — |
| 665 | C23 | — | 32 | 1 | no | — |
| 666 | C23 | C2×#357 | 1 | 1 | yes | characteristic |
| 667 | C23 | #2184 | 1 | 1 | yes | characteristic |
| 668 | C23 | #2187 | 1 | 1 | yes | characteristic |
| 669 | Q8 | — | 4 | 1 | no | — |
| 670 | Q8 | — | 32 | 1 | no | — |
| 671 | Q8 | — | 32 | 1 | no | — |
| 672 | D4 | — | 4 | 1 | no | — |
| 673 | D4 | — | 4 | 1 | no | — |
| 674 | D4 | — | 4 | 1 | no | — |
| 675 | D4 | — | 8 | 1 | no | — |
| 676 | D4 | — | 8 | 1 | no | — |
| 677 | D4 | — | 8 | 1 | no | — |
| 678 | D4 | — | 8 | 1 | no | — |
| 679 | D4 | — | 8 | 1 | no | — |
| 680 | D4 | — | 8 | 1 | no | — |
| 681 | D4 | — | 16 | 2 | no | — |
| 682 | D4 | — | 16 | 2 | no | — |
| 683 | D4 | — | 16 | 2 | no | — |
| 684 | D4 | — | 32 | 1 | no | — |
| 685 | D4 | — | 32 | 1 | no | — |
| 686 | D4 | — | 32 | 1 | no | — |
| 687 | D4 | — | 32 | 1 | no | — |
| 688 | D4 | — | 32 | 1 | no | — |
| 689 | D4 | — | 32 | 1 | no | — |
| 690 | C2×C4 | — | 2 | 1 | no | — |
| 691 | C2×C4 | — | 2 | 1 | no | — |
| 692 | C2×C4 | — | 2 | 1 | no | — |
| 693 | C2×C4 | — | 2 | 1 | no | — |
| 694 | C2×C4 | — | 2 | 1 | no | — |
| 695 | C2×C4 | — | 2 | 1 | no | — |
| 696 | C2×C4 | — | 2 | 1 | no | — |
| 697 | C2×C4 | — | 2 | 1 | no | — |
| 698 | C2×C4 | — | 2 | 1 | no | — |
| 699 | C2×C4 | — | 4 | 2 | no | — |
| 700 | C2×C4 | — | 4 | 1 | no | — |
| 701 | C2×C4 | — | 4 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 1 | no | — |
| 703 | C2×C4 | — | 8 | 1 | no | — |
| 704 | C2×C4 | — | 8 | 1 | no | — |
| 705 | C2×C4 | — | 8 | 1 | no | — |
| 706 | C2×C4 | — | 8 | 1 | no | — |
| 707 | C2×C4 | — | 8 | 1 | no | — |
| 708 | C2×C4 | — | 8 | 1 | no | — |
| 709 | C2×C4 | — | 16 | 2 | no | — |
| 710 | C2×C4 | — | 32 | 1 | no | — |
| 711 | C2×C4 | — | 32 | 1 | no | — |
| 712 | C2×C4 | — | 32 | 1 | no | — |
| 713 | C2×C4 | — | 32 | 1 | no | — |
| 714 | C2×C4 | — | 32 | 1 | no | — |
| 715 | C2×C4 | — | 32 | 1 | no | — |
| 716 | C2×C4 | — | 32 | 1 | no | — |
| 717 | C2×C4 | — | 32 | 1 | no | — |
| 718 | C2×C4 | — | 32 | 1 | no | — |
| 719 | C2×C4 | #1786 | 1 | 1 | yes | characteristic |
| 720 | C2×C4 | #2140 | 1 | 1 | yes | characteristic |
| 721 | C2×C4 | #2184 | 1 | 1 | yes | characteristic |
| 722 | C2×C4 | #2187 | 1 | 1 | yes | characteristic |
| 723 | C8 | — | 2 | 1 | no | — |
| 724 | C8 | — | 2 | 1 | no | — |
| 725 | C8 | — | 2 | 1 | no | — |
| 726 | C8 | — | 4 | 1 | no | — |
| 727 | C8 | — | 4 | 1 | no | — |
| 728 | C8 | — | 32 | 1 | no | — |
| 729 | C8 | #1782 | 1 | 1 | yes | characteristic |
| 730 | C8 | #1796 | 1 | 1 | yes | characteristic |
| 731 | C22 | — | 2 | 1 | no | — |
| 732 | C22 | — | 2 | 1 | no | — |
| 733 | C22 | — | 2 | 1 | no | — |
| 734 | C22 | — | 4 | 1 | no | — |
| 735 | C22 | — | 4 | 1 | no | — |
| 736 | C22 | — | 4 | 1 | no | — |
| 737 | C22 | — | 4 | 1 | no | — |
| 738 | C22 | — | 4 | 1 | no | — |
| 739 | C22 | — | 4 | 1 | no | — |
| 740 | C22 | — | 16 | 1 | no | — |
| 741 | C22 | — | 16 | 1 | no | — |
| 742 | C22 | — | 16 | 1 | no | — |
| 743 | C22 | — | 16 | 1 | no | — |
| 744 | C22 | — | 16 | 1 | no | — |
| 745 | C22 | — | 16 | 1 | no | — |
| 746 | C22 | — | 16 | 1 | no | — |
| 747 | C22 | — | 64 | 2 | no | — |
| 748 | C22 | #12731 | 1 | 1 | yes | characteristic |
| 749 | C4 | — | 2 | 1 | no | — |
| 750 | C4 | — | 2 | 1 | no | — |
| 751 | C4 | — | 2 | 1 | no | — |
| 752 | C4 | — | 4 | 1 | no | — |
| 753 | C4 | — | 4 | 1 | no | — |
| 754 | C4 | — | 4 | 1 | no | — |
| 755 | C4 | — | 16 | 1 | no | — |
| 756 | C4 | — | 16 | 1 | no | — |
| 757 | C4 | — | 16 | 1 | no | — |
| 758 | C4 | — | 16 | 1 | no | — |
| 759 | C4 | — | 16 | 1 | no | — |
| 760 | C4 | — | 16 | 1 | no | — |
| 761 | C4 | — | 64 | 1 | no | — |
| 762 | C4 | #8376 | 1 | 1 | yes | characteristic |
| 763 | C4 | #12742 | 1 | 1 | yes | characteristic |
| 764 | C2 | — | 2 | 1 | no | — |
| 765 | C2 | — | 4 | 1 | no | — |
| 766 | C2 | — | 4 | 1 | no | — |
| 767 | C2 | — | 4 | 1 | no | — |
| 768 | C2 | — | 8 | 1 | no | — |
| 769 | C2 | — | 32 | 1 | no | — |
| 770 | C2 | — | 32 | 1 | no | — |
| 771 | C2 | #130798 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #130798 |
| commutator | C22×C16 | C22×C4 |
| Frattini, cosocle | C2×#504 | C23 |
| prime radical | #7623826 | C2 |
| LCS | G ▷ C22×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #33433 ◁ G | |
| LECS | G ▷ C2×#504 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #152372 | C2 | semidirect |
| 3. #152371 | C2 | semidirect |
| 4. #150881 | C2 | semidirect |
| 5. #150879 | C2 | semidirect |
| 6. #149670 | C2 | semidirect |
| 7. #134774 | C2 | semidirect |
| 17. #33730 | C4 | semidirect |
| 22. C2×#2218 | C4 | semidirect |
| 23. #33456 | C4 | semidirect |
| 26. #33409 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7623826 | 2 |
| #152372 | 2 |
| #152371 | 2 |
| #150881 | 2 |
| #150879 | 2 |
| #149670 | 2 |
| #134774 | 2 |