Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2065 conjugacy classes of subgroups.
The subgroup lattice has 812 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227040 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72226999 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72226992 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×D8×D16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72225461 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72225459 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72216288 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×D4×D16 | — | 2 | 1 | no | — |
| 9 | C2×D82 | — | 2 | 1 | no | — |
| 10 | D8×D16 | — | 2 | 2 | no | — |
| 11 | D8×D16 | — | 2 | 2 | no | — |
| 12 | D8×D16 | — | 2 | 2 | no | — |
| 13 | D8×D16 | C4 | 1 | 4 | yes | — |
| 14 | C2×#12515 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#12430 | — | 2 | 1 | no | — |
| 16 | C2×#12424 | — | 2 | 1 | no | — |
| 17 | C2×#12316 | — | 2 | 2 | no | — |
| 18 | C2×C8×D16 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C16×D8 | C22 | 1 | 1 | yes | characteristic |
| 20 | #152899 | — | 2 | 2 | no | — |
| 21 | #152276 | — | 2 | 1 | no | — |
| 22 | #151026 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C8×M64 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #135781 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #135043 | — | 2 | 1 | no | — |
| 26 | #122930 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #94358 | — | 2 | 1 | no | — |
| 28 | #93869 | — | 2 | 2 | no | — |
| 29 | #93749 | — | 2 | 2 | no | — |
| 30 | #93745 | — | 2 | 2 | no | — |
| 31 | #93069 | — | 2 | 1 | no | — |
| 32 | C23×D16 | — | 4 | 1 | no | — |
| 33 | C2×D4×D8 | — | 2 | 2 | no | — |
| 34 | C2×D4×D8 | — | 4 | 1 | no | — |
| 35 | D4×D16 | — | 2 | 4 | no | — |
| 36 | D4×D16 | — | 2 | 4 | no | — |
| 37 | D4×D16 | — | 4 | 2 | no | — |
| 38 | D4×D16 | — | 4 | 2 | no | — |
| 39 | C2×#2246 | — | 2 | 1 | no | — |
| 40 | C2×#2246 | D4 | 1 | 2 | yes | — |
| 41 | C2×#2215 | — | 4 | 1 | no | — |
| 42 | C2×#2206 | — | 2 | 2 | no | — |
| 43 | C2×#2184 | — | 4 | 2 | no | — |
| 44 | C2×C4×D16 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×D4×C16 | — | 2 | 1 | no | — |
| 46 | D82 | — | 2 | 4 | no | — |
| 47 | D82 | — | 2 | 4 | no | — |
| 48 | D82 | — | 4 | 2 | no | — |
| 49 | D82 | — | 4 | 2 | no | — |
| 50 | C2×#1712 | — | 2 | 1 | no | — |
| 51 | C2×#1667 | — | 2 | 2 | no | — |
| 52 | C2×#1667 | — | 4 | 1 | no | — |
| 53 | C2×#1619 | — | 4 | 2 | no | — |
| 54 | C2×C8×D8 | — | 2 | 1 | no | — |
| 55 | C2×C8×D8 | D4 | 1 | 1 | yes | characteristic |
| 56 | #13627 | — | 2 | 1 | no | — |
| 57 | C2×#1419 | — | 4 | 4 | no | — |
| 58 | C2×#1419 | — | 4 | 1 | no | — |
| 59 | C4×M64 | — | 2 | 1 | no | — |
| 60 | #12909 | — | 2 | 1 | no | — |
| 61 | #12909 | — | 2 | 1 | no | — |
| 62 | #12515 | — | 2 | 1 | no | — |
| 63 | #12515 | — | 2 | 1 | no | — |
| 64 | #12515 | C2×C4 | 1 | 2 | yes | — |
| 65 | #12515 | D4 | 1 | 2 | yes | — |
| 66 | #12430 | — | 2 | 4 | no | — |
| 67 | #12430 | — | 2 | 4 | no | — |
| 68 | #12424 | — | 2 | 4 | no | — |
| 69 | #12424 | — | 2 | 4 | no | — |
| 70 | #12316 | — | 2 | 8 | no | — |
| 71 | #12316 | — | 2 | 8 | no | — |
| 72 | C8×D16 | — | 2 | 1 | no | — |
| 73 | C8×D16 | — | 2 | 1 | no | — |
| 74 | C8×D16 | C2×C4 | 1 | 2 | yes | — |
| 75 | C8×D16 | D4 | 1 | 2 | yes | — |
| 76 | C16×D8 | — | 2 | 1 | no | — |
| 77 | C16×D8 | — | 2 | 1 | no | — |
| 78 | C16×D8 | C2×C4 | 1 | 2 | yes | — |
| 79 | C16×D8 | D4 | 1 | 2 | yes | — |
| 80 | #12012 | — | 2 | 1 | no | — |
| 81 | C2×#1371 | D4 | 1 | 1 | yes | characteristic |
| 82 | C2×#1370 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×#1361 | — | 2 | 2 | no | — |
| 84 | #11657 | — | 4 | 1 | no | — |
| 85 | C2×#1331 | — | 2 | 1 | no | — |
| 86 | C2×D4⋊C16 | — | 2 | 1 | no | — |
| 87 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 88 | #8823 | — | 2 | 1 | no | — |
| 89 | #7478 | — | 4 | 1 | no | — |
| 90 | #7458 | — | 2 | 1 | no | — |
| 91 | #7458 | — | 2 | 1 | no | — |
| 92 | #7329 | — | 2 | 1 | no | — |
| 93 | C8×C32 | — | 2 | 1 | no | — |
| 94 | #7288 | — | 4 | 1 | no | — |
| 95 | #7101 | — | 2 | 1 | no | — |
| 96 | #7100 | — | 2 | 1 | no | — |
| 97 | C23×D8 | — | 4 | 2 | no | — |
| 98 | C23×D8 | — | 8 | 1 | no | — |
| 99 | C2×D42 | — | 4 | 2 | no | — |
| 100 | C22×D16 | — | 4 | 2 | no | — |
| 101 | C22×D16 | — | 4 | 4 | no | — |
| 102 | C22×D16 | — | 4 | 4 | no | — |
| 103 | C22×D16 | — | 4 | 1 | no | — |
| 104 | C22×D16 | — | 4 | 1 | no | — |
| 105 | C22×D16 | — | 4 | 2 | no | — |
| 106 | C22×D16 | — | 8 | 2 | no | — |
| 107 | C22×D16 | — | 8 | 2 | no | — |
| 108 | C22×D16 | — | 8 | 2 | no | — |
| 109 | C22×D16 | — | 8 | 2 | no | — |
| 110 | C22×D16 | D8 | 1 | 1 | yes | characteristic |
| 111 | C23×C16 | — | 4 | 1 | no | — |
| 112 | D4×D8 | — | 2 | 8 | no | — |
| 113 | D4×D8 | — | 4 | 4 | no | — |
| 114 | D4×D8 | — | 4 | 4 | no | — |
| 115 | D4×D8 | — | 4 | 4 | no | — |
| 116 | D4×D8 | — | 4 | 4 | no | — |
| 117 | D4×D8 | — | 8 | 2 | no | — |
| 118 | D4×D8 | — | 8 | 2 | no | — |
| 119 | D4×D8 | — | 8 | 2 | no | — |
| 120 | C2×#493 | — | 2 | 2 | no | — |
| 121 | C2×#493 | — | 4 | 1 | no | — |
| 122 | C2×#493 | — | 4 | 1 | no | — |
| 123 | C2×#466 | — | 4 | 2 | no | — |
| 124 | C2×#466 | — | 8 | 1 | no | — |
| 125 | C2×#459 | — | 4 | 2 | no | — |
| 126 | C2×#459 | — | 4 | 2 | no | — |
| 127 | C2×#447 | — | 8 | 2 | no | — |
| 128 | C2×#447 | — | 8 | 2 | no | — |
| 129 | C2×C4×D8 | — | 2 | 1 | no | — |
| 130 | C2×C4×D8 | D8 | 1 | 1 | yes | characteristic |
| 131 | C2×C8×D4 | — | 2 | 1 | no | — |
| 132 | C2×C8×D4 | — | 4 | 1 | no | — |
| 133 | C2×M64 | — | 2 | 2 | no | — |
| 134 | C2×M64 | — | 4 | 1 | no | — |
| 135 | #2246 | — | 2 | 2 | no | — |
| 136 | #2246 | — | 2 | 2 | no | — |
| 137 | #2246 | — | 2 | 2 | no | — |
| 138 | #2246 | — | 4 | 2 | no | — |
| 139 | #2246 | — | 4 | 1 | no | — |
| 140 | #2246 | — | 4 | 1 | no | — |
| 141 | #2246 | C22⋊C4 | 1 | 4 | yes | — |
| 142 | #2215 | — | 4 | 4 | no | — |
| 143 | #2215 | — | 4 | 4 | no | — |
| 144 | #2206 | — | 2 | 8 | no | — |
| 145 | #2206 | — | 4 | 4 | no | — |
| 146 | #2184 | — | 4 | 8 | no | — |
| 147 | #2184 | — | 4 | 8 | no | — |
| 148 | C4×D16 | — | 2 | 1 | no | — |
| 149 | C4×D16 | — | 2 | 1 | no | — |
| 150 | C4×D16 | C22⋊C4 | 1 | 2 | yes | — |
| 151 | C4×D16 | SD16 | 1 | 2 | yes | — |
| 152 | D4×C16 | — | 2 | 2 | no | — |
| 153 | D4×C16 | — | 2 | 2 | no | — |
| 154 | D4×C16 | — | 4 | 1 | no | — |
| 155 | D4×C16 | — | 4 | 1 | no | — |
| 156 | #2162 | — | 4 | 1 | no | — |
| 157 | C2×#368 | — | 4 | 2 | no | — |
| 158 | C2×#368 | — | 4 | 1 | no | — |
| 159 | C2×#368 | — | 4 | 1 | no | — |
| 160 | C2×#366 | D8 | 1 | 1 | yes | characteristic |
| 161 | C2×C4⋊C16 | — | 2 | 1 | no | — |
| 162 | C2×#357 | — | 2 | 1 | no | — |
| 163 | C2×#357 | — | 4 | 2 | no | — |
| 164 | C2×C22⋊C16 | — | 4 | 1 | no | — |
| 165 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | #1848 | — | 4 | 1 | no | — |
| 168 | #1712 | — | 2 | 2 | no | — |
| 169 | #1712 | — | 2 | 2 | no | — |
| 170 | #1712 | — | 4 | 1 | no | — |
| 171 | #1712 | — | 4 | 1 | no | — |
| 172 | #1667 | — | 2 | 8 | no | — |
| 173 | #1667 | — | 4 | 4 | no | — |
| 174 | #1667 | — | 4 | 4 | no | — |
| 175 | #1667 | — | 4 | 4 | no | — |
| 176 | #1619 | — | 4 | 8 | no | — |
| 177 | #1619 | — | 4 | 8 | no | — |
| 178 | C8×D8 | — | 2 | 2 | no | — |
| 179 | C8×D8 | — | 2 | 1 | no | — |
| 180 | C8×D8 | — | 2 | 2 | no | — |
| 181 | C8×D8 | — | 2 | 1 | no | — |
| 182 | C8×D8 | — | 4 | 1 | no | — |
| 183 | C8×D8 | — | 4 | 1 | no | — |
| 184 | C8×D8 | C22⋊C4 | 1 | 2 | yes | — |
| 185 | C8×D8 | SD16 | 1 | 2 | yes | — |
| 186 | #1567 | — | 4 | 1 | no | — |
| 187 | #1567 | — | 4 | 1 | no | — |
| 188 | C2×#335 | — | 2 | 1 | no | — |
| 189 | C2×#335 | D8 | 1 | 1 | yes | characteristic |
| 190 | C2×#331 | — | 4 | 2 | no | — |
| 191 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 192 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 193 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C4⋊C32 | — | 4 | 1 | no | — |
| 195 | C4⋊C32 | — | 4 | 1 | no | — |
| 196 | #1419 | — | 8 | 8 | no | — |
| 197 | #1419 | — | 8 | 2 | no | — |
| 198 | #1397 | — | 4 | 1 | no | — |
| 199 | C4×C32 | — | 4 | 1 | no | — |
| 200 | #1371 | — | 2 | 1 | no | — |
| 201 | #1371 | C22⋊C4 | 1 | 2 | yes | — |
| 202 | #1370 | — | 2 | 1 | no | — |
| 203 | #1370 | — | 4 | 1 | no | — |
| 204 | #1370 | C22⋊C4 | 1 | 2 | yes | — |
| 205 | #1367 | — | 4 | 1 | no | — |
| 206 | #1361 | — | 2 | 8 | no | — |
| 207 | #1331 | — | 2 | 2 | no | — |
| 208 | #1331 | — | 2 | 2 | no | — |
| 209 | #1331 | — | 8 | 2 | no | — |
| 210 | D4⋊C16 | — | 2 | 2 | no | — |
| 211 | D4⋊C16 | — | 2 | 2 | no | — |
| 212 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 213 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C23×D4 | — | 8 | 2 | no | — |
| 217 | C23×D4 | — | 8 | 2 | no | — |
| 218 | C22×D8 | — | 2 | 1 | no | — |
| 219 | C22×D8 | — | 4 | 8 | no | — |
| 220 | C22×D8 | — | 4 | 2 | no | — |
| 221 | C22×D8 | — | 4 | 2 | no | — |
| 222 | C22×D8 | — | 8 | 4 | no | — |
| 223 | C22×D8 | — | 8 | 2 | no | — |
| 224 | C22×D8 | — | 8 | 4 | no | — |
| 225 | C22×D8 | — | 8 | 4 | no | — |
| 226 | C22×D8 | — | 8 | 4 | no | — |
| 227 | C22×D8 | — | 8 | 2 | no | — |
| 228 | C22×D8 | — | 8 | 4 | no | — |
| 229 | C22×D8 | — | 8 | 1 | no | — |
| 230 | C22×D8 | — | 8 | 1 | no | — |
| 231 | C22×D8 | — | 16 | 1 | no | — |
| 232 | C22×D8 | — | 16 | 2 | no | — |
| 233 | C22×D8 | — | 16 | 2 | no | — |
| 234 | C22×D8 | — | 16 | 8 | no | — |
| 235 | C22×D8 | SD32 | 1 | 1 | yes | characteristic |
| 236 | C23×C8 | — | 4 | 1 | no | — |
| 237 | C23×C8 | — | 8 | 1 | no | — |
| 238 | D42 | — | 4 | 8 | no | — |
| 239 | D42 | — | 8 | 4 | no | — |
| 240 | D42 | — | 8 | 4 | no | — |
| 241 | D42 | — | 16 | 2 | no | — |
| 242 | C2×#127 | — | 4 | 2 | no | — |
| 243 | C2×#121 | — | 8 | 2 | no | — |
| 244 | C2×#121 | — | 8 | 2 | no | — |
| 245 | C2×#120 | — | 16 | 2 | no | — |
| 246 | C2×C4×D4 | — | 2 | 1 | no | — |
| 247 | C2×C4×D4 | — | 4 | 1 | no | — |
| 248 | C2×D16 | — | 2 | 1 | no | — |
| 249 | C2×D16 | — | 2 | 1 | no | — |
| 250 | C2×D16 | — | 2 | 1 | no | — |
| 251 | C2×D16 | — | 4 | 4 | no | — |
| 252 | C2×D16 | — | 4 | 8 | no | — |
| 253 | C2×D16 | — | 4 | 2 | no | — |
| 254 | C2×D16 | — | 4 | 2 | no | — |
| 255 | C2×D16 | — | 4 | 2 | no | — |
| 256 | C2×D16 | — | 4 | 2 | no | — |
| 257 | C2×D16 | — | 8 | 4 | no | — |
| 258 | C2×D16 | — | 8 | 4 | no | — |
| 259 | C2×D16 | — | 8 | 2 | no | — |
| 260 | C2×D16 | — | 8 | 8 | no | — |
| 261 | C2×D16 | — | 8 | 8 | no | — |
| 262 | C2×D16 | — | 8 | 8 | no | — |
| 263 | C2×D16 | — | 8 | 4 | no | — |
| 264 | C2×D16 | — | 8 | 4 | no | — |
| 265 | C2×D16 | — | 8 | 8 | no | — |
| 266 | C2×D16 | — | 8 | 1 | no | — |
| 267 | C2×D16 | — | 8 | 1 | no | — |
| 268 | C2×D16 | — | 8 | 1 | no | — |
| 269 | C2×D16 | — | 8 | 1 | no | — |
| 270 | C2×D16 | — | 16 | 1 | no | — |
| 271 | C2×D16 | — | 16 | 1 | no | — |
| 272 | C2×D16 | #102 | 1 | 2 | yes | — |
| 273 | C2×D16 | D16 | 1 | 2 | yes | — |
| 274 | C2×D16 | SD32 | 1 | 2 | yes | — |
| 275 | C22×C16 | — | 2 | 1 | no | — |
| 276 | C22×C16 | — | 4 | 1 | no | — |
| 277 | C22×C16 | — | 4 | 2 | no | — |
| 278 | C22×C16 | — | 4 | 2 | no | — |
| 279 | C22×C16 | — | 8 | 1 | no | — |
| 280 | C22×C16 | — | 8 | 1 | no | — |
| 281 | C22×C16 | — | 8 | 1 | no | — |
| 282 | C22×C16 | — | 8 | 1 | no | — |
| 283 | C22×C16 | C2×D8 | 1 | 1 | yes | characteristic |
| 284 | C22×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 285 | #493 | — | 2 | 4 | no | — |
| 286 | #493 | — | 4 | 2 | no | — |
| 287 | #493 | — | 4 | 2 | no | — |
| 288 | #493 | — | 4 | 2 | no | — |
| 289 | #493 | — | 4 | 2 | no | — |
| 290 | #493 | — | 4 | 2 | no | — |
| 291 | #493 | — | 4 | 2 | no | — |
| 292 | #493 | — | 4 | 2 | no | — |
| 293 | #493 | — | 8 | 1 | no | — |
| 294 | #493 | — | 8 | 1 | no | — |
| 295 | #493 | — | 16 | 1 | no | — |
| 296 | #466 | — | 4 | 8 | no | — |
| 297 | #466 | — | 8 | 4 | no | — |
| 298 | #466 | — | 8 | 4 | no | — |
| 299 | #466 | — | 8 | 4 | no | — |
| 300 | #459 | — | 4 | 8 | no | — |
| 301 | #459 | — | 4 | 8 | no | — |
| 302 | #459 | — | 8 | 4 | no | — |
| 303 | #459 | — | 8 | 4 | no | — |
| 304 | #447 | — | 8 | 8 | no | — |
| 305 | #447 | — | 8 | 8 | no | — |
| 306 | #447 | — | 8 | 8 | no | — |
| 307 | #447 | — | 8 | 8 | no | — |
| 308 | C4×D8 | — | 2 | 2 | no | — |
| 309 | C4×D8 | — | 2 | 1 | no | — |
| 310 | C4×D8 | — | 2 | 2 | no | — |
| 311 | C4×D8 | — | 2 | 1 | no | — |
| 312 | C4×D8 | — | 4 | 1 | no | — |
| 313 | C4×D8 | — | 4 | 1 | no | — |
| 314 | C4×D8 | #102 | 1 | 2 | yes | — |
| 315 | C4×D8 | D16 | 1 | 2 | yes | — |
| 316 | C8×D4 | — | 2 | 2 | no | — |
| 317 | C8×D4 | — | 2 | 2 | no | — |
| 318 | C8×D4 | — | 4 | 2 | no | — |
| 319 | C8×D4 | — | 4 | 2 | no | — |
| 320 | C8×D4 | — | 4 | 1 | no | — |
| 321 | C8×D4 | — | 4 | 1 | no | — |
| 322 | C8×D4 | — | 8 | 1 | no | — |
| 323 | C8×D4 | — | 8 | 1 | no | — |
| 324 | C2×#108 | — | 8 | 1 | no | — |
| 325 | C2×#108 | — | 8 | 1 | no | — |
| 326 | C2×#107 | — | 2 | 1 | no | — |
| 327 | C2×#107 | SD32 | 1 | 1 | yes | characteristic |
| 328 | #423 | — | 8 | 1 | no | — |
| 329 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 330 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 331 | C2×#102 | — | 2 | 1 | no | — |
| 332 | C2×#102 | — | 4 | 1 | no | — |
| 333 | C2×#102 | — | 8 | 2 | no | — |
| 334 | C2×#102 | — | 8 | 2 | no | — |
| 335 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 336 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 337 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 338 | C2×C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 339 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 340 | M64 | — | 2 | 4 | no | — |
| 341 | M64 | — | 4 | 2 | no | — |
| 342 | M64 | — | 8 | 1 | no | — |
| 343 | M64 | — | 8 | 1 | no | — |
| 344 | C2×C32 | — | 4 | 2 | no | — |
| 345 | C2×C32 | — | 8 | 1 | no | — |
| 346 | #368 | — | 8 | 4 | no | — |
| 347 | #368 | — | 8 | 1 | no | — |
| 348 | #368 | — | 8 | 1 | no | — |
| 349 | #368 | — | 16 | 1 | no | — |
| 350 | #366 | — | 2 | 1 | no | — |
| 351 | #366 | #102 | 1 | 2 | yes | — |
| 352 | C4⋊C16 | — | 2 | 2 | no | — |
| 353 | C4⋊C16 | — | 4 | 1 | no | — |
| 354 | C4⋊C16 | — | 8 | 1 | no | — |
| 355 | #357 | — | 2 | 2 | no | — |
| 356 | #357 | — | 2 | 2 | no | — |
| 357 | #357 | — | 4 | 8 | no | — |
| 358 | C22⋊C16 | — | 4 | 2 | no | — |
| 359 | C22⋊C16 | — | 4 | 2 | no | — |
| 360 | C22⋊C16 | — | 8 | 1 | no | — |
| 361 | C4×C16 | — | 2 | 1 | no | — |
| 362 | C4×C16 | — | 8 | 1 | no | — |
| 363 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 364 | C4×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 365 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 366 | C4×C16 | #120 | 1 | 1 | yes | characteristic |
| 367 | C4×C16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 368 | C4×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 369 | #335 | — | 2 | 2 | no | — |
| 370 | #335 | — | 2 | 1 | no | — |
| 371 | #335 | — | 4 | 1 | no | — |
| 372 | #335 | — | 8 | 1 | no | — |
| 373 | #335 | — | 8 | 1 | no | — |
| 374 | #335 | — | 16 | 1 | no | — |
| 375 | #335 | #102 | 1 | 2 | yes | — |
| 376 | #331 | — | 4 | 8 | no | — |
| 377 | D4⋊C8 | — | 2 | 2 | no | — |
| 378 | D4⋊C8 | — | 2 | 2 | no | — |
| 379 | D4⋊C8 | — | 4 | 2 | no | — |
| 380 | D4⋊C8 | — | 4 | 2 | no | — |
| 381 | C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 382 | C82 | #120 | 1 | 1 | yes | characteristic |
| 383 | C82 | C2×SD16 | 1 | 1 | yes | characteristic |
| 384 | C82 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 385 | C25 | — | 16 | 2 | no | — |
| 386 | C22×D4 | — | 2 | 1 | no | — |
| 387 | C22×D4 | — | 4 | 1 | no | — |
| 388 | C22×D4 | — | 8 | 8 | no | — |
| 389 | C22×D4 | — | 8 | 8 | no | — |
| 390 | C22×D4 | — | 8 | 2 | no | — |
| 391 | C22×D4 | — | 8 | 2 | no | — |
| 392 | C22×D4 | — | 8 | 2 | no | — |
| 393 | C22×D4 | — | 16 | 4 | no | — |
| 394 | C22×D4 | — | 16 | 2 | no | — |
| 395 | C22×D4 | — | 16 | 4 | no | — |
| 396 | C22×D4 | — | 16 | 4 | no | — |
| 397 | C22×D4 | — | 16 | 4 | no | — |
| 398 | C22×D4 | — | 16 | 2 | no | — |
| 399 | C22×D4 | — | 16 | 8 | no | — |
| 400 | C22×D4 | — | 32 | 2 | no | — |
| 401 | C22×D4 | — | 32 | 2 | no | — |
| 402 | C22×D4 | — | 32 | 4 | no | — |
| 403 | C23×C4 | — | 4 | 1 | no | — |
| 404 | C23×C4 | — | 8 | 1 | no | — |
| 405 | C2×D8 | — | 2 | 4 | no | — |
| 406 | C2×D8 | — | 2 | 2 | no | — |
| 407 | C2×D8 | — | 2 | 1 | no | — |
| 408 | C2×D8 | — | 2 | 2 | no | — |
| 409 | C2×D8 | — | 2 | 2 | no | — |
| 410 | C2×D8 | — | 4 | 4 | no | — |
| 411 | C2×D8 | — | 4 | 1 | no | — |
| 412 | C2×D8 | — | 4 | 1 | no | — |
| 413 | C2×D8 | — | 4 | 1 | no | — |
| 414 | C2×D8 | — | 4 | 4 | no | — |
| 415 | C2×D8 | — | 8 | 8 | no | — |
| 416 | C2×D8 | — | 8 | 16 | no | — |
| 417 | C2×D8 | — | 8 | 8 | no | — |
| 418 | C2×D8 | — | 8 | 2 | no | — |
| 419 | C2×D8 | — | 8 | 2 | no | — |
| 420 | C2×D8 | — | 8 | 2 | no | — |
| 421 | C2×D8 | — | 8 | 2 | no | — |
| 422 | C2×D8 | — | 8 | 2 | no | — |
| 423 | C2×D8 | — | 8 | 2 | no | — |
| 424 | C2×D8 | — | 8 | 2 | no | — |
| 425 | C2×D8 | — | 8 | 2 | no | — |
| 426 | C2×D8 | — | 8 | 2 | no | — |
| 427 | C2×D8 | — | 8 | 2 | no | — |
| 428 | C2×D8 | — | 16 | 4 | no | — |
| 429 | C2×D8 | — | 16 | 2 | no | — |
| 430 | C2×D8 | — | 16 | 2 | no | — |
| 431 | C2×D8 | — | 16 | 2 | no | — |
| 432 | C2×D8 | — | 16 | 2 | no | — |
| 433 | C2×D8 | — | 16 | 8 | no | — |
| 434 | C2×D8 | — | 16 | 8 | no | — |
| 435 | C2×D8 | — | 16 | 8 | no | — |
| 436 | C2×D8 | — | 16 | 4 | no | — |
| 437 | C2×D8 | — | 16 | 4 | no | — |
| 438 | C2×D8 | — | 16 | 16 | no | — |
| 439 | C2×D8 | — | 16 | 8 | no | — |
| 440 | C2×D8 | — | 16 | 8 | no | — |
| 441 | C2×D8 | — | 16 | 8 | no | — |
| 442 | C2×D8 | — | 32 | 2 | no | — |
| 443 | C2×D8 | — | 32 | 4 | no | — |
| 444 | C2×D8 | #357 | 1 | 2 | yes | — |
| 445 | C2×M16 | — | 16 | 1 | no | — |
| 446 | C22×C8 | — | 2 | 1 | no | — |
| 447 | C22×C8 | — | 4 | 1 | no | — |
| 448 | C22×C8 | — | 4 | 2 | no | — |
| 449 | C22×C8 | — | 4 | 2 | no | — |
| 450 | C22×C8 | — | 8 | 1 | no | — |
| 451 | C22×C8 | — | 8 | 1 | no | — |
| 452 | C22×C8 | — | 8 | 1 | no | — |
| 453 | C22×C8 | — | 8 | 1 | no | — |
| 454 | C22×C8 | — | 8 | 1 | no | — |
| 455 | C22×C8 | — | 8 | 2 | no | — |
| 456 | C22×C8 | — | 8 | 2 | no | — |
| 457 | C22×C8 | — | 16 | 4 | no | — |
| 458 | C22×C8 | #447 | 1 | 1 | yes | characteristic |
| 459 | C22×C8 | #453 | 1 | 1 | yes | characteristic |
| 460 | C22×C8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 461 | C22×C8 | #509 | 1 | 1 | yes | characteristic |
| 462 | #127 | — | 4 | 4 | no | — |
| 463 | #127 | — | 8 | 2 | no | — |
| 464 | #127 | — | 8 | 2 | no | — |
| 465 | #127 | — | 8 | 2 | no | — |
| 466 | #121 | — | 8 | 8 | no | — |
| 467 | #121 | — | 8 | 8 | no | — |
| 468 | #121 | — | 16 | 4 | no | — |
| 469 | #121 | — | 16 | 4 | no | — |
| 470 | #120 | — | 16 | 8 | no | — |
| 471 | #120 | — | 16 | 8 | no | — |
| 472 | C4×D4 | — | 2 | 2 | no | — |
| 473 | C4×D4 | — | 2 | 2 | no | — |
| 474 | C4×D4 | — | 4 | 1 | no | — |
| 475 | C4×D4 | — | 4 | 2 | no | — |
| 476 | C4×D4 | — | 4 | 1 | no | — |
| 477 | C4×D4 | — | 4 | 2 | no | — |
| 478 | C4×D4 | — | 8 | 1 | no | — |
| 479 | C4×D4 | — | 8 | 1 | no | — |
| 480 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 481 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 482 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 483 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 484 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 485 | C2×C42 | #447 | 1 | 1 | yes | characteristic |
| 486 | D16 | — | 2 | 2 | no | — |
| 487 | D16 | — | 2 | 2 | no | — |
| 488 | D16 | — | 2 | 2 | no | — |
| 489 | D16 | — | 8 | 8 | no | — |
| 490 | D16 | — | 8 | 16 | no | — |
| 491 | D16 | — | 8 | 2 | no | — |
| 492 | D16 | — | 8 | 2 | no | — |
| 493 | D16 | — | 8 | 2 | no | — |
| 494 | D16 | — | 8 | 2 | no | — |
| 495 | D16 | — | 16 | 2 | no | — |
| 496 | D16 | — | 16 | 2 | no | — |
| 497 | D16 | — | 16 | 4 | no | — |
| 498 | D16 | #357 | 1 | 4 | yes | — |
| 499 | C2×C16 | — | 2 | 2 | no | — |
| 500 | C2×C16 | — | 2 | 2 | no | — |
| 501 | C2×C16 | — | 2 | 1 | no | — |
| 502 | C2×C16 | — | 2 | 1 | no | — |
| 503 | C2×C16 | — | 2 | 1 | no | — |
| 504 | C2×C16 | — | 2 | 1 | no | — |
| 505 | C2×C16 | — | 4 | 2 | no | — |
| 506 | C2×C16 | — | 8 | 1 | no | — |
| 507 | C2×C16 | — | 8 | 1 | no | — |
| 508 | C2×C16 | — | 8 | 2 | no | — |
| 509 | C2×C16 | — | 8 | 2 | no | — |
| 510 | C2×C16 | — | 8 | 2 | no | — |
| 511 | C2×C16 | — | 8 | 2 | no | — |
| 512 | C2×C16 | — | 16 | 1 | no | — |
| 513 | C2×C16 | C2×#102 | 1 | 1 | yes | characteristic |
| 514 | C2×C16 | #418 | 1 | 1 | yes | characteristic |
| 515 | C2×C16 | #447 | 1 | 1 | yes | characteristic |
| 516 | C2×C16 | #450 | 1 | 1 | yes | characteristic |
| 517 | C2×C16 | C2×D16 | 1 | 1 | yes | characteristic |
| 518 | C2×C16 | C2×SD32 | 1 | 1 | yes | characteristic |
| 519 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 520 | C2×C16 | #509 | 1 | 1 | yes | characteristic |
| 521 | #108 | — | 16 | 2 | no | — |
| 522 | #108 | — | 16 | 1 | no | — |
| 523 | #108 | — | 16 | 1 | no | — |
| 524 | #107 | — | 2 | 1 | no | — |
| 525 | #107 | — | 2 | 2 | no | — |
| 526 | #107 | — | 4 | 1 | no | — |
| 527 | #107 | #357 | 1 | 2 | yes | — |
| 528 | C4⋊C8 | — | 2 | 2 | no | — |
| 529 | C4⋊C8 | — | 4 | 1 | no | — |
| 530 | C4⋊C8 | — | 4 | 2 | no | — |
| 531 | C4⋊C8 | — | 8 | 1 | no | — |
| 532 | C4⋊C8 | — | 16 | 1 | no | — |
| 533 | C4⋊C8 | — | 16 | 1 | no | — |
| 534 | #102 | — | 2 | 2 | no | — |
| 535 | #102 | — | 2 | 2 | no | — |
| 536 | #102 | — | 4 | 2 | no | — |
| 537 | #102 | — | 4 | 2 | no | — |
| 538 | #102 | — | 8 | 8 | no | — |
| 539 | #102 | — | 8 | 8 | no | — |
| 540 | C22⋊C8 | — | 4 | 2 | no | — |
| 541 | C22⋊C8 | — | 4 | 2 | no | — |
| 542 | C22⋊C8 | — | 8 | 2 | no | — |
| 543 | C22⋊C8 | — | 8 | 2 | no | — |
| 544 | C4×C8 | — | 2 | 1 | no | — |
| 545 | C4×C8 | #379 | 1 | 1 | yes | characteristic |
| 546 | C4×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 547 | C4×C8 | #418 | 1 | 1 | yes | characteristic |
| 548 | C4×C8 | #447 | 1 | 1 | yes | characteristic |
| 549 | C4×C8 | #450 | 1 | 1 | yes | characteristic |
| 550 | C4×C8 | #450 | 1 | 1 | yes | characteristic |
| 551 | C4×C8 | #450 | 1 | 1 | yes | characteristic |
| 552 | C4×C8 | #455 | 1 | 1 | yes | characteristic |
| 553 | C4×C8 | C2×D16 | 1 | 1 | yes | characteristic |
| 554 | C4×C8 | #509 | 1 | 1 | yes | characteristic |
| 555 | C32 | — | 4 | 4 | no | — |
| 556 | C32 | — | 16 | 1 | no | — |
| 557 | C24 | — | 4 | 1 | no | — |
| 558 | C24 | — | 8 | 1 | no | — |
| 559 | C24 | — | 16 | 8 | no | — |
| 560 | C24 | — | 16 | 2 | no | — |
| 561 | C24 | — | 32 | 8 | no | — |
| 562 | C24 | — | 32 | 4 | no | — |
| 563 | C24 | — | 32 | 4 | no | — |
| 564 | C24 | — | 64 | 4 | no | — |
| 565 | C2×D4 | — | 2 | 4 | no | — |
| 566 | C2×D4 | — | 2 | 2 | no | — |
| 567 | C2×D4 | — | 4 | 2 | no | — |
| 568 | C2×D4 | — | 4 | 2 | no | — |
| 569 | C2×D4 | — | 4 | 2 | no | — |
| 570 | C2×D4 | — | 4 | 1 | no | — |
| 571 | C2×D4 | — | 4 | 2 | no | — |
| 572 | C2×D4 | — | 8 | 1 | no | — |
| 573 | C2×D4 | — | 8 | 1 | no | — |
| 574 | C2×D4 | — | 8 | 1 | no | — |
| 575 | C2×D4 | — | 8 | 4 | no | — |
| 576 | C2×D4 | — | 8 | 4 | no | — |
| 577 | C2×D4 | — | 8 | 4 | no | — |
| 578 | C2×D4 | — | 16 | 4 | no | — |
| 579 | C2×D4 | — | 16 | 4 | no | — |
| 580 | C2×D4 | — | 16 | 8 | no | — |
| 581 | C2×D4 | — | 16 | 16 | no | — |
| 582 | C2×D4 | — | 16 | 8 | no | — |
| 583 | C2×D4 | — | 16 | 16 | no | — |
| 584 | C2×D4 | — | 16 | 2 | no | — |
| 585 | C2×D4 | — | 16 | 2 | no | — |
| 586 | C2×D4 | — | 16 | 2 | no | — |
| 587 | C2×D4 | — | 16 | 2 | no | — |
| 588 | C2×D4 | — | 16 | 2 | no | — |
| 589 | C2×D4 | — | 16 | 2 | no | — |
| 590 | C2×D4 | — | 16 | 2 | no | — |
| 591 | C2×D4 | — | 32 | 4 | no | — |
| 592 | C2×D4 | — | 32 | 8 | no | — |
| 593 | C2×D4 | — | 32 | 8 | no | — |
| 594 | C2×D4 | — | 32 | 8 | no | — |
| 595 | C2×D4 | — | 32 | 4 | no | — |
| 596 | C2×D4 | — | 32 | 4 | no | — |
| 597 | C2×D4 | — | 32 | 8 | no | — |
| 598 | C2×D4 | — | 32 | 16 | no | — |
| 599 | C2×D4 | — | 32 | 8 | no | — |
| 600 | C22×C4 | — | 4 | 1 | no | — |
| 601 | C22×C4 | — | 4 | 2 | no | — |
| 602 | C22×C4 | — | 4 | 2 | no | — |
| 603 | C22×C4 | — | 8 | 1 | no | — |
| 604 | C22×C4 | — | 8 | 1 | no | — |
| 605 | C22×C4 | — | 8 | 1 | no | — |
| 606 | C22×C4 | — | 8 | 1 | no | — |
| 607 | C22×C4 | — | 8 | 1 | no | — |
| 608 | C22×C4 | — | 8 | 2 | no | — |
| 609 | C22×C4 | — | 8 | 2 | no | — |
| 610 | C22×C4 | — | 16 | 2 | no | — |
| 611 | C22×C4 | — | 16 | 2 | no | — |
| 612 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 613 | C22×C4 | #2187 | 1 | 1 | yes | characteristic |
| 614 | C22×C4 | #2194 | 1 | 1 | yes | characteristic |
| 615 | D8 | — | 2 | 4 | no | — |
| 616 | D8 | — | 2 | 2 | no | — |
| 617 | D8 | — | 2 | 4 | no | — |
| 618 | D8 | — | 4 | 2 | no | — |
| 619 | D8 | — | 4 | 2 | no | — |
| 620 | D8 | — | 4 | 2 | no | — |
| 621 | D8 | — | 8 | 4 | no | — |
| 622 | D8 | — | 8 | 4 | no | — |
| 623 | D8 | — | 16 | 4 | no | — |
| 624 | D8 | — | 16 | 4 | no | — |
| 625 | D8 | — | 16 | 16 | no | — |
| 626 | D8 | — | 16 | 16 | no | — |
| 627 | D8 | — | 16 | 4 | no | — |
| 628 | D8 | — | 16 | 2 | no | — |
| 629 | D8 | — | 16 | 2 | no | — |
| 630 | D8 | — | 32 | 2 | no | — |
| 631 | D8 | — | 32 | 2 | no | — |
| 632 | D8 | — | 32 | 2 | no | — |
| 633 | D8 | — | 32 | 4 | no | — |
| 634 | D8 | — | 32 | 4 | no | — |
| 635 | D8 | #1419 | 1 | 4 | yes | complemented |
| 636 | M16 | — | 32 | 1 | no | — |
| 637 | M16 | — | 32 | 1 | no | — |
| 638 | C2×C8 | — | 2 | 1 | no | — |
| 639 | C2×C8 | — | 2 | 1 | no | — |
| 640 | C2×C8 | — | 2 | 1 | no | — |
| 641 | C2×C8 | — | 2 | 2 | no | — |
| 642 | C2×C8 | — | 2 | 1 | no | — |
| 643 | C2×C8 | — | 4 | 1 | no | — |
| 644 | C2×C8 | — | 4 | 2 | no | — |
| 645 | C2×C8 | — | 4 | 2 | no | — |
| 646 | C2×C8 | — | 8 | 1 | no | — |
| 647 | C2×C8 | — | 8 | 1 | no | — |
| 648 | C2×C8 | — | 8 | 2 | no | — |
| 649 | C2×C8 | — | 8 | 2 | no | — |
| 650 | C2×C8 | — | 8 | 2 | no | — |
| 651 | C2×C8 | — | 8 | 2 | no | — |
| 652 | C2×C8 | — | 8 | 2 | no | — |
| 653 | C2×C8 | — | 16 | 4 | no | — |
| 654 | C2×C8 | — | 16 | 2 | no | — |
| 655 | C2×C8 | — | 16 | 4 | no | — |
| 656 | C2×C8 | — | 32 | 1 | no | — |
| 657 | C2×C8 | #1629 | 1 | 1 | yes | characteristic |
| 658 | C2×C8 | #1639 | 1 | 1 | yes | characteristic |
| 659 | C2×C8 | #1786 | 1 | 1 | yes | characteristic |
| 660 | C2×C8 | #1792 | 1 | 1 | yes | characteristic |
| 661 | C2×C8 | C2×#357 | 1 | 1 | yes | characteristic |
| 662 | C2×C8 | #2140 | 1 | 1 | yes | characteristic |
| 663 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 664 | C2×C8 | #2184 | 1 | 1 | yes | characteristic |
| 665 | C2×C8 | #2187 | 1 | 1 | yes | characteristic |
| 666 | C2×C8 | #2187 | 1 | 1 | yes | characteristic |
| 667 | C2×C8 | #2192 | 1 | 1 | yes | characteristic |
| 668 | C2×C8 | #2194 | 1 | 1 | yes | characteristic |
| 669 | C4⋊C4 | — | 2 | 2 | no | — |
| 670 | C4⋊C4 | — | 4 | 1 | no | — |
| 671 | C4⋊C4 | — | 4 | 2 | no | — |
| 672 | C4⋊C4 | — | 8 | 1 | no | — |
| 673 | C22⋊C4 | — | 4 | 2 | no | — |
| 674 | C22⋊C4 | — | 4 | 2 | no | — |
| 675 | C22⋊C4 | — | 8 | 2 | no | — |
| 676 | C22⋊C4 | — | 8 | 2 | no | — |
| 677 | C22⋊C4 | — | 16 | 8 | no | — |
| 678 | C42 | #1639 | 1 | 1 | yes | characteristic |
| 679 | C42 | #1786 | 1 | 1 | yes | characteristic |
| 680 | C42 | #2184 | 1 | 1 | yes | characteristic |
| 681 | C42 | #2192 | 1 | 1 | yes | characteristic |
| 682 | C16 | — | 2 | 2 | no | — |
| 683 | C16 | — | 2 | 2 | no | — |
| 684 | C16 | — | 2 | 1 | no | — |
| 685 | C16 | — | 2 | 1 | no | — |
| 686 | C16 | — | 8 | 2 | no | — |
| 687 | C16 | — | 32 | 1 | no | — |
| 688 | C16 | C2×#357 | 1 | 1 | yes | characteristic |
| 689 | C16 | #2140 | 1 | 1 | yes | characteristic |
| 690 | C16 | #2184 | 1 | 1 | yes | characteristic |
| 691 | C16 | #2187 | 1 | 1 | yes | characteristic |
| 692 | C23 | — | 4 | 4 | no | — |
| 693 | C23 | — | 4 | 2 | no | — |
| 694 | C23 | — | 8 | 2 | no | — |
| 695 | C23 | — | 8 | 1 | no | — |
| 696 | C23 | — | 8 | 1 | no | — |
| 697 | C23 | — | 8 | 2 | no | — |
| 698 | C23 | — | 8 | 2 | no | — |
| 699 | C23 | — | 8 | 2 | no | — |
| 700 | C23 | — | 16 | 2 | no | — |
| 701 | C23 | — | 16 | 2 | no | — |
| 702 | C23 | — | 16 | 4 | no | — |
| 703 | C23 | — | 32 | 4 | no | — |
| 704 | C23 | — | 32 | 4 | no | — |
| 705 | C23 | — | 32 | 16 | no | — |
| 706 | C23 | — | 32 | 16 | no | — |
| 707 | C23 | — | 32 | 2 | no | — |
| 708 | C23 | — | 32 | 2 | no | — |
| 709 | C23 | — | 64 | 8 | no | — |
| 710 | C23 | — | 64 | 16 | no | — |
| 711 | C23 | — | 64 | 16 | no | — |
| 712 | C23 | #12320 | 1 | 1 | yes | characteristic |
| 713 | D4 | — | 2 | 4 | no | — |
| 714 | D4 | — | 4 | 4 | no | — |
| 715 | D4 | — | 4 | 4 | no | — |
| 716 | D4 | — | 4 | 2 | no | — |
| 717 | D4 | — | 8 | 2 | no | — |
| 718 | D4 | — | 8 | 2 | no | — |
| 719 | D4 | — | 8 | 2 | no | — |
| 720 | D4 | — | 16 | 4 | no | — |
| 721 | D4 | — | 16 | 4 | no | — |
| 722 | D4 | — | 16 | 4 | no | — |
| 723 | D4 | — | 16 | 4 | no | — |
| 724 | D4 | — | 32 | 4 | no | — |
| 725 | D4 | — | 32 | 4 | no | — |
| 726 | D4 | — | 32 | 16 | no | — |
| 727 | D4 | — | 32 | 16 | no | — |
| 728 | D4 | — | 32 | 2 | no | — |
| 729 | D4 | — | 32 | 2 | no | — |
| 730 | D4 | — | 64 | 2 | no | — |
| 731 | C2×C4 | — | 2 | 1 | no | — |
| 732 | C2×C4 | — | 2 | 1 | no | — |
| 733 | C2×C4 | — | 4 | 1 | no | — |
| 734 | C2×C4 | — | 4 | 2 | no | — |
| 735 | C2×C4 | — | 8 | 1 | no | — |
| 736 | C2×C4 | — | 8 | 1 | no | — |
| 737 | C2×C4 | — | 8 | 2 | no | — |
| 738 | C2×C4 | — | 8 | 2 | no | — |
| 739 | C2×C4 | — | 8 | 2 | no | — |
| 740 | C2×C4 | — | 8 | 2 | no | — |
| 741 | C2×C4 | — | 8 | 2 | no | — |
| 742 | C2×C4 | — | 16 | 4 | no | — |
| 743 | C2×C4 | — | 16 | 2 | no | — |
| 744 | C2×C4 | — | 16 | 2 | no | — |
| 745 | C2×C4 | — | 16 | 2 | no | — |
| 746 | C2×C4 | #8443 | 1 | 1 | yes | characteristic |
| 747 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 748 | C2×C4 | #12312 | 1 | 1 | yes | characteristic |
| 749 | C2×C4 | #12316 | 1 | 1 | yes | characteristic |
| 750 | C2×C4 | #12316 | 1 | 1 | yes | characteristic |
| 751 | C2×C4 | #12320 | 1 | 1 | yes | characteristic |
| 752 | C2×C4 | #12368 | 1 | 1 | yes | characteristic |
| 753 | C2×C4 | #12372 | 1 | 1 | yes | characteristic |
| 754 | C2×C4 | #12731 | 1 | 1 | yes | characteristic |
| 755 | C2×C4 | #12748 | 1 | 1 | yes | characteristic |
| 756 | C8 | — | 2 | 2 | no | — |
| 757 | C8 | — | 2 | 1 | no | — |
| 758 | C8 | — | 2 | 1 | no | — |
| 759 | C8 | — | 2 | 1 | no | — |
| 760 | C8 | — | 2 | 1 | no | — |
| 761 | C8 | — | 2 | 1 | no | — |
| 762 | C8 | — | 4 | 1 | no | — |
| 763 | C8 | — | 8 | 2 | no | — |
| 764 | C8 | — | 16 | 2 | no | — |
| 765 | C8 | — | 64 | 1 | no | — |
| 766 | C8 | #12368 | 1 | 1 | yes | characteristic |
| 767 | C8 | #12372 | 1 | 1 | yes | characteristic |
| 768 | C8 | #12731 | 1 | 1 | yes | characteristic |
| 769 | C8 | #12748 | 1 | 1 | yes | characteristic |
| 770 | C8 | C2×#1419 | 1 | 2 | yes | — |
| 771 | C22 | — | 2 | 1 | no | — |
| 772 | C22 | — | 2 | 1 | no | — |
| 773 | C22 | — | 4 | 4 | no | — |
| 774 | C22 | — | 8 | 4 | no | — |
| 775 | C22 | — | 8 | 4 | no | — |
| 776 | C22 | — | 8 | 2 | no | — |
| 777 | C22 | — | 8 | 2 | no | — |
| 778 | C22 | — | 8 | 4 | no | — |
| 779 | C22 | — | 16 | 4 | no | — |
| 780 | C22 | — | 16 | 4 | no | — |
| 781 | C22 | — | 16 | 2 | no | — |
| 782 | C22 | — | 16 | 2 | no | — |
| 783 | C22 | — | 32 | 4 | no | — |
| 784 | C22 | — | 32 | 4 | no | — |
| 785 | C22 | — | 32 | 4 | no | — |
| 786 | C22 | — | 64 | 4 | no | — |
| 787 | C22 | — | 64 | 4 | no | — |
| 788 | C22 | — | 64 | 32 | no | — |
| 789 | C22 | #123285 | 1 | 1 | yes | characteristic |
| 790 | C22 | #123295 | 1 | 1 | yes | characteristic |
| 791 | C22 | #131848 | 1 | 1 | yes | characteristic |
| 792 | C4 | — | 2 | 1 | no | — |
| 793 | C4 | — | 2 | 1 | no | — |
| 794 | C4 | — | 2 | 1 | no | — |
| 795 | C4 | — | 8 | 2 | no | — |
| 796 | C4 | — | 16 | 2 | no | — |
| 797 | C4 | #123275 | 1 | 1 | yes | characteristic |
| 798 | C4 | #123295 | 1 | 1 | yes | characteristic |
| 799 | C4 | #131832 | 1 | 1 | yes | characteristic |
| 800 | C4 | #131848 | 1 | 1 | yes | characteristic |
| 801 | C4 | #152162 | 1 | 1 | yes | characteristic |
| 802 | C4 | #152176 | 1 | 1 | yes | characteristic |
| 803 | C2 | — | 2 | 1 | no | — |
| 804 | C2 | — | 2 | 1 | no | — |
| 805 | C2 | — | 8 | 4 | no | — |
| 806 | C2 | — | 16 | 4 | no | — |
| 807 | C2 | — | 64 | 4 | no | — |
| 808 | C2 | #72225182 | 1 | 1 | yes | characteristic |
| 809 | C2 | #72226864 | 1 | 1 | yes | characteristic |
| 810 | C2 | #72227106 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #131848 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| prime radical | C2×D8×D16 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C2×C82 ◁ C2×C16×D8 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227040 | C2 | semidirect |
| 2. #72226999 | C2 | semidirect |
| 3. #72226992 | C2 | semidirect |
| 5. #72225461 | C2 | semidirect |
| 6. #72225459 | C2 | semidirect |
| 7. #72216288 | C2 | semidirect |
| 22. #151026 | C22 | semidirect |
| 23. C8×M64 | C22 | semidirect |
| 24. #135781 | C22 | semidirect |
| 26. #122930 | C22 | semidirect |
| 635. D8 | #1419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227040 | 2 |
| #72226999 | 2 |
| #72226992 | 2 |
| C2×D8×D16 | 2 |
| #72225461 | 2 |
| #72225459 | 2 |
| #72216288 | 2 |