Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
2132 conjugacy classes of subgroups.
The subgroup lattice has 1033 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72287252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72287163 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72287120 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #72287038 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #72286674 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #72286589 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72227152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#12068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72223645 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #72217184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×AGL(1,ℤ/32) | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C22×#2179 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#2171 | — | 2 | 1 | no | — |
| 14 | #512830 | C4 | 1 | 1 | yes | characteristic |
| 15 | C2×#13658 | C22 | 1 | 2 | yes | — |
| 16 | #495862 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#12068 | — | 2 | 1 | no | — |
| 18 | C2×#12068 | — | 2 | 1 | no | — |
| 19 | C2×#12068 | — | 2 | 8 | no | — |
| 20 | C2×#12068 | C22 | 1 | 2 | yes | — |
| 21 | C2×#12068 | C22 | 1 | 2 | yes | — |
| 22 | C2×#12067 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C22×#1369 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×#1336 | — | 2 | 1 | no | — |
| 25 | C22×#1313 | C22 | 1 | 1 | yes | characteristic |
| 26 | #210728 | — | 2 | 1 | no | — |
| 27 | #152548 | C4 | 1 | 2 | yes | — |
| 28 | #152512 | C4 | 1 | 1 | yes | characteristic |
| 29 | #152453 | C4 | 1 | 2 | yes | — |
| 30 | #152426 | C4 | 1 | 1 | yes | characteristic |
| 31 | #152161 | C4 | 1 | 1 | yes | characteristic |
| 32 | #151972 | C22 | 1 | 2 | yes | — |
| 33 | #151891 | C22 | 1 | 1 | yes | characteristic |
| 34 | #151891 | C22 | 1 | 1 | yes | characteristic |
| 35 | AGL(1,ℤ/32) | — | 2 | 8 | no | — |
| 36 | C2×#7457 | C22 | 1 | 2 | yes | complemented |
| 37 | C2×#7390 | C22 | 1 | 2 | yes | complemented |
| 38 | C2×#7389 | C22 | 1 | 2 | yes | — |
| 39 | C2×#7389 | C22 | 1 | 2 | yes | — |
| 40 | C2×#7333 | C22 | 1 | 2 | yes | complemented |
| 41 | #140751 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #140354 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #140188 | — | 2 | 1 | no | — |
| 44 | #137612 | — | 2 | 1 | no | — |
| 45 | #134657 | C22 | 1 | 1 | yes | characteristic |
| 46 | #129165 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #128688 | — | 2 | 1 | no | — |
| 48 | #94059 | C22 | 1 | 2 | yes | complemented |
| 49 | #94030 | C22 | 1 | 2 | yes | complemented |
| 50 | #93997 | C22 | 1 | 2 | yes | complemented |
| 51 | C22×#508 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C22×#504 | — | 4 | 1 | no | — |
| 53 | C22×#443 | — | 2 | 1 | no | — |
| 54 | C2×#2263 | C2×C4 | 1 | 2 | yes | — |
| 55 | C2×#2215 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×#2179 | — | 2 | 4 | no | — |
| 57 | C2×#2179 | — | 2 | 4 | no | — |
| 58 | C2×#2179 | — | 2 | 1 | no | — |
| 59 | C2×#2179 | — | 2 | 1 | no | — |
| 60 | C2×#2179 | C2×C4 | 1 | 2 | yes | — |
| 61 | C2×#2179 | C23 | 1 | 2 | yes | — |
| 62 | C2×#2177 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×#2171 | — | 2 | 8 | no | — |
| 64 | C2×#2171 | — | 2 | 2 | no | — |
| 65 | C2×#2171 | — | 2 | 2 | no | — |
| 66 | C2×#2171 | — | 4 | 1 | no | — |
| 67 | C2×#2171 | — | 4 | 1 | no | — |
| 68 | C2×#2171 | — | 4 | 4 | no | — |
| 69 | C22×#368 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C22×#364 | — | 2 | 1 | no | — |
| 71 | C22×#359 | — | 2 | 1 | no | — |
| 72 | C22×#350 | — | 4 | 1 | no | — |
| 73 | C22×#346 | D4 | 1 | 1 | yes | characteristic |
| 74 | C22×#346 | C23 | 1 | 1 | yes | characteristic |
| 75 | C4×#466 | — | 2 | 1 | no | — |
| 76 | C8×#121 | — | 4 | 1 | no | — |
| 77 | C2×#1580 | — | 2 | 1 | no | — |
| 78 | C22×#322 | D4 | 1 | 1 | yes | characteristic |
| 79 | #13663 | C8 | 1 | 4 | yes | complemented |
| 80 | #13662 | C8 | 1 | 2 | yes | complemented |
| 81 | #13661 | C8 | 1 | 2 | yes | complemented |
| 82 | #13658 | — | 2 | 4 | no | — |
| 83 | #13658 | — | 2 | 4 | no | — |
| 84 | C2×#1426 | C2×C4 | 1 | 2 | yes | — |
| 85 | C2×#1419 | C2×C4 | 1 | 2 | yes | — |
| 86 | C2×#1418 | C2×C4 | 1 | 2 | yes | — |
| 87 | C2×#1418 | C2×C4 | 1 | 2 | yes | — |
| 88 | #13616 | C2×C4 | 1 | 2 | yes | — |
| 89 | #13553 | — | 2 | 1 | no | — |
| 90 | #13553 | C2×C4 | 1 | 1 | yes | characteristic |
| 91 | #13553 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | C2×#1398 | C23 | 1 | 2 | yes | — |
| 93 | C2×#1398 | C23 | 1 | 2 | yes | — |
| 94 | #13239 | C2×C4 | 1 | 1 | yes | characteristic |
| 95 | #13168 | C2×C4 | 1 | 1 | yes | characteristic |
| 96 | #13149 | — | 2 | 1 | no | — |
| 97 | #13059 | — | 2 | 1 | no | — |
| 98 | #12835 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | #12674 | C23 | 1 | 1 | yes | characteristic |
| 100 | #12637 | — | 2 | 1 | no | — |
| 101 | #12068 | — | 2 | 8 | no | — |
| 102 | #12068 | — | 2 | 8 | no | — |
| 103 | #12068 | — | 2 | 4 | no | — |
| 104 | #12068 | — | 2 | 4 | no | — |
| 105 | #12068 | — | 2 | 4 | no | — |
| 106 | #12068 | D4 | 1 | 8 | yes | complemented |
| 107 | #12067 | — | 2 | 4 | no | — |
| 108 | C2×#1369 | — | 2 | 4 | no | — |
| 109 | C2×#1369 | — | 2 | 1 | no | — |
| 110 | C2×#1369 | C23 | 1 | 2 | yes | — |
| 111 | C2×#1368 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×#1368 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×#1336 | — | 2 | 8 | no | — |
| 114 | C2×#1336 | — | 2 | 2 | no | — |
| 115 | C2×#1336 | — | 2 | 2 | no | — |
| 116 | C2×#1333 | — | 2 | 1 | no | — |
| 117 | C2×#1333 | — | 2 | 1 | no | — |
| 118 | C2×#1313 | — | 2 | 4 | no | — |
| 119 | C2×#1313 | D4 | 1 | 1 | yes | characteristic |
| 120 | C2×#1313 | D4 | 1 | 1 | yes | characteristic |
| 121 | C2×#1313 | C23 | 1 | 1 | yes | characteristic |
| 122 | C2×#1313 | C23 | 1 | 1 | yes | characteristic |
| 123 | #9659 | — | 2 | 1 | no | — |
| 124 | #9595 | — | 2 | 1 | no | — |
| 125 | #9556 | — | 4 | 1 | no | — |
| 126 | #9072 | — | 4 | 1 | no | — |
| 127 | #8595 | — | 2 | 1 | no | — |
| 128 | #8284 | — | 2 | 1 | no | — |
| 129 | #8200 | — | 4 | 1 | no | — |
| 130 | #7478 | C2×C4 | 1 | 2 | yes | — |
| 131 | #7474 | C2×C4 | 1 | 2 | yes | — |
| 132 | #7466 | — | 2 | 1 | no | — |
| 133 | #7466 | C2×C4 | 1 | 2 | yes | — |
| 134 | #7457 | — | 2 | 4 | no | — |
| 135 | #7390 | — | 2 | 4 | no | — |
| 136 | #7389 | — | 2 | 4 | no | — |
| 137 | #7389 | — | 2 | 4 | no | — |
| 138 | #7333 | — | 2 | 4 | no | — |
| 139 | #7178 | — | 2 | 1 | no | — |
| 140 | #7178 | — | 2 | 1 | no | — |
| 141 | #7156 | — | 2 | 1 | no | — |
| 142 | C22×#135 | — | 2 | 1 | no | — |
| 143 | C22×#131 | — | 4 | 1 | no | — |
| 144 | C2×#508 | — | 2 | 4 | no | — |
| 145 | C2×#508 | — | 2 | 4 | no | — |
| 146 | C2×#508 | — | 2 | 1 | no | — |
| 147 | C2×#508 | — | 2 | 1 | no | — |
| 148 | C2×#508 | C2×C8 | 1 | 2 | yes | complemented |
| 149 | C2×#508 | C22×C4 | 1 | 2 | yes | — |
| 150 | C22×Q32 | C2×C8 | 1 | 1 | yes | characteristic, complemented |
| 151 | C22×SD32 | — | 2 | 1 | no | — |
| 152 | C22×D16 | C2×C8 | 1 | 1 | yes | characteristic, complemented |
| 153 | C22×D16 | C22×C4 | 1 | 1 | yes | characteristic |
| 154 | C2×#504 | — | 4 | 8 | no | — |
| 155 | C2×#504 | — | 4 | 2 | no | — |
| 156 | C2×#504 | — | 4 | 2 | no | — |
| 157 | C2×#504 | — | 8 | 1 | no | — |
| 158 | C2×#504 | — | 8 | 1 | no | — |
| 159 | C2×#504 | — | 8 | 4 | no | — |
| 160 | C22×M32 | — | 4 | 1 | no | — |
| 161 | C22×M32 | — | 8 | 1 | no | — |
| 162 | C23×C16 | — | 2 | 1 | no | — |
| 163 | C23×C16 | — | 8 | 1 | no | — |
| 164 | C23×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 165 | C23×C16 | #41 | 1 | 1 | yes | characteristic |
| 166 | C2×#466 | — | 2 | 1 | no | — |
| 167 | C2×#443 | — | 2 | 4 | no | — |
| 168 | C2×#443 | — | 2 | 4 | no | — |
| 169 | C2×#443 | — | 2 | 2 | no | — |
| 170 | C2×#443 | — | 2 | 2 | no | — |
| 171 | C2×#443 | — | 4 | 2 | no | — |
| 172 | C2×#443 | — | 4 | 2 | no | — |
| 173 | C2×#443 | — | 4 | 1 | no | — |
| 174 | C2×#443 | — | 4 | 1 | no | — |
| 175 | C2×C4×D8 | — | 2 | 1 | no | — |
| 176 | C2×C8×D4 | — | 4 | 1 | no | — |
| 177 | C2×C8×D4 | — | 8 | 1 | no | — |
| 178 | C22×#108 | — | 2 | 1 | no | — |
| 179 | C22×#104 | — | 4 | 1 | no | — |
| 180 | C22×C4×C8 | — | 2 | 1 | no | — |
| 181 | C22×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C4×#121 | — | 4 | 1 | no | — |
| 183 | #2263 | — | 2 | 4 | no | — |
| 184 | #2263 | — | 2 | 4 | no | — |
| 185 | C2×SD64 | C2×C8 | 1 | 4 | yes | complemented |
| 186 | C2×D32 | C2×C8 | 1 | 4 | yes | complemented |
| 187 | C2×M64 | — | 2 | 2 | no | — |
| 188 | C2×M64 | C22×C4 | 1 | 2 | yes | — |
| 189 | C2×M64 | C22×C4 | 1 | 2 | yes | — |
| 190 | #2215 | — | 2 | 1 | no | — |
| 191 | #2215 | — | 2 | 1 | no | — |
| 192 | #2215 | C2×C8 | 1 | 2 | yes | — |
| 193 | #2215 | C2×C8 | 1 | 2 | yes | — |
| 194 | #2179 | — | 2 | 4 | no | — |
| 195 | #2179 | — | 2 | 8 | no | — |
| 196 | #2179 | — | 2 | 4 | no | — |
| 197 | #2179 | — | 2 | 4 | no | — |
| 198 | #2179 | — | 2 | 4 | no | — |
| 199 | #2179 | — | 2 | 2 | no | — |
| 200 | #2179 | — | 2 | 2 | no | — |
| 201 | #2179 | C2×D4 | 1 | 4 | yes | — |
| 202 | #2179 | #41 | 1 | 4 | yes | — |
| 203 | #2177 | — | 2 | 2 | no | — |
| 204 | #2177 | — | 2 | 2 | no | — |
| 205 | #2171 | — | 2 | 8 | no | — |
| 206 | #2171 | — | 2 | 8 | no | — |
| 207 | #2171 | — | 4 | 8 | no | — |
| 208 | #2171 | — | 4 | 8 | no | — |
| 209 | #2171 | — | 4 | 4 | no | — |
| 210 | #2171 | — | 4 | 4 | no | — |
| 211 | C2×#368 | — | 2 | 1 | no | — |
| 212 | C2×#368 | — | 2 | 4 | no | — |
| 213 | C2×#368 | C22×C4 | 1 | 2 | yes | — |
| 214 | C2×#367 | C22×C4 | 1 | 1 | yes | characteristic |
| 215 | C2×#367 | C22×C4 | 1 | 1 | yes | characteristic |
| 216 | C2×#366 | C22×C4 | 1 | 1 | yes | characteristic |
| 217 | C2×#364 | — | 2 | 4 | no | — |
| 218 | C2×#364 | — | 2 | 2 | no | — |
| 219 | C2×#364 | — | 4 | 2 | no | — |
| 220 | C2×#364 | — | 4 | 1 | no | — |
| 221 | C2×#359 | — | 2 | 8 | no | — |
| 222 | C2×#359 | — | 2 | 2 | no | — |
| 223 | C2×#359 | — | 2 | 2 | no | — |
| 224 | C2×#357 | — | 2 | 1 | no | — |
| 225 | C2×#357 | — | 2 | 1 | no | — |
| 226 | C2×#357 | — | 2 | 1 | no | — |
| 227 | C2×#350 | — | 4 | 8 | no | — |
| 228 | C2×#350 | — | 4 | 2 | no | — |
| 229 | C2×#350 | — | 4 | 2 | no | — |
| 230 | C2×#346 | — | 2 | 1 | no | — |
| 231 | C2×#346 | — | 2 | 2 | no | — |
| 232 | C2×#346 | — | 2 | 2 | no | — |
| 233 | C2×#346 | — | 2 | 2 | no | — |
| 234 | C2×#346 | — | 2 | 2 | no | — |
| 235 | C2×#346 | C22×C4 | 1 | 1 | yes | characteristic |
| 236 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C2×#346 | #41 | 1 | 1 | yes | characteristic |
| 240 | C2×#346 | C24 | 1 | 1 | yes | characteristic |
| 241 | #1970 | — | 2 | 1 | no | — |
| 242 | #1954 | — | 4 | 1 | no | — |
| 243 | #1942 | — | 2 | 1 | no | — |
| 244 | #1939 | — | 4 | 1 | no | — |
| 245 | #1934 | — | 4 | 1 | no | — |
| 246 | #1923 | — | 8 | 1 | no | — |
| 247 | #1893 | — | 4 | 1 | no | — |
| 248 | #1869 | — | 8 | 1 | no | — |
| 249 | #1808 | — | 2 | 1 | no | — |
| 250 | #1797 | — | 4 | 1 | no | — |
| 251 | C4×#107 | — | 2 | 1 | no | — |
| 252 | C8×C4⋊C4 | — | 4 | 1 | no | — |
| 253 | C4×#102 | — | 4 | 1 | no | — |
| 254 | C8×C22⋊C4 | — | 8 | 1 | no | — |
| 255 | #1580 | — | 4 | 2 | no | — |
| 256 | #1580 | — | 4 | 2 | no | — |
| 257 | C2×#334 | — | 2 | 1 | no | — |
| 258 | C2×#334 | — | 2 | 1 | no | — |
| 259 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 260 | C2×D4⋊C8 | — | 4 | 1 | no | — |
| 261 | C2×#322 | — | 2 | 2 | no | — |
| 262 | C2×#322 | — | 2 | 1 | no | — |
| 263 | C2×#322 | — | 4 | 1 | no | — |
| 264 | C2×#322 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×#322 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | #1426 | — | 2 | 4 | no | — |
| 267 | #1419 | — | 2 | 4 | no | — |
| 268 | #1418 | — | 2 | 4 | no | — |
| 269 | #1418 | — | 2 | 4 | no | — |
| 270 | #1416 | C2×C8 | 1 | 4 | yes | complemented |
| 271 | #1415 | C2×C8 | 1 | 4 | yes | complemented |
| 272 | C22⋊C32 | — | 2 | 1 | no | — |
| 273 | C22⋊C32 | — | 2 | 1 | no | — |
| 274 | C22⋊C32 | — | 4 | 1 | no | — |
| 275 | C22⋊C32 | — | 4 | 1 | no | — |
| 276 | C22⋊C32 | C2×C8 | 1 | 2 | yes | complemented |
| 277 | C22⋊C32 | C2×C8 | 1 | 2 | yes | complemented |
| 278 | #1398 | — | 2 | 2 | no | — |
| 279 | #1398 | — | 2 | 2 | no | — |
| 280 | #1398 | — | 2 | 2 | no | — |
| 281 | #1398 | — | 2 | 2 | no | — |
| 282 | #1380 | — | 2 | 1 | no | — |
| 283 | #1380 | — | 2 | 1 | no | — |
| 284 | #1380 | — | 2 | 1 | no | — |
| 285 | #1369 | — | 2 | 4 | no | — |
| 286 | #1369 | — | 2 | 2 | no | — |
| 287 | #1369 | C2×D4 | 1 | 4 | yes | — |
| 288 | #1368 | — | 2 | 2 | no | — |
| 289 | #1368 | — | 2 | 2 | no | — |
| 290 | #1336 | — | 2 | 8 | no | — |
| 291 | #1336 | — | 2 | 8 | no | — |
| 292 | #1333 | — | 4 | 2 | no | — |
| 293 | #1333 | — | 4 | 2 | no | — |
| 294 | #1313 | — | 2 | 2 | no | — |
| 295 | #1313 | — | 2 | 2 | no | — |
| 296 | #1313 | — | 2 | 2 | no | — |
| 297 | #1313 | C2×D4 | 1 | 4 | yes | — |
| 298 | #1279 | — | 4 | 1 | no | — |
| 299 | #1279 | — | 4 | 1 | no | — |
| 300 | #1277 | — | 4 | 1 | no | — |
| 301 | C22×#41 | — | 4 | 1 | no | — |
| 302 | C2×#135 | — | 2 | 4 | no | — |
| 303 | C2×#135 | — | 2 | 4 | no | — |
| 304 | C2×#135 | — | 2 | 2 | no | — |
| 305 | C2×#135 | — | 2 | 2 | no | — |
| 306 | C2×#135 | — | 4 | 2 | no | — |
| 307 | C2×#135 | — | 4 | 2 | no | — |
| 308 | C2×#135 | — | 4 | 1 | no | — |
| 309 | C2×#135 | — | 4 | 1 | no | — |
| 310 | C22×Q16 | — | 2 | 1 | no | — |
| 311 | C22×SD16 | — | 4 | 1 | no | — |
| 312 | C22×D8 | — | 2 | 1 | no | — |
| 313 | C22×D8 | — | 2 | 1 | no | — |
| 314 | C2×#131 | — | 4 | 4 | no | — |
| 315 | C2×#131 | — | 4 | 4 | no | — |
| 316 | C2×#131 | — | 4 | 2 | no | — |
| 317 | C2×#131 | — | 4 | 2 | no | — |
| 318 | C2×#131 | — | 8 | 1 | no | — |
| 319 | C2×#131 | — | 8 | 2 | no | — |
| 320 | C2×#131 | — | 8 | 1 | no | — |
| 321 | C2×#131 | — | 8 | 2 | no | — |
| 322 | C22×M16 | — | 4 | 1 | no | — |
| 323 | C22×M16 | — | 8 | 1 | no | — |
| 324 | C23×C8 | — | 4 | 1 | no | — |
| 325 | C23×C8 | — | 8 | 1 | no | — |
| 326 | C23×C8 | — | 8 | 1 | no | — |
| 327 | C23×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 328 | C23×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 329 | C2×#121 | — | 4 | 1 | no | — |
| 330 | C2×C4×D4 | — | 4 | 1 | no | — |
| 331 | C2×C4×D4 | — | 8 | 1 | no | — |
| 332 | C22×C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 333 | #508 | — | 2 | 4 | no | — |
| 334 | #508 | — | 2 | 8 | no | — |
| 335 | #508 | — | 2 | 4 | no | — |
| 336 | #508 | — | 2 | 4 | no | — |
| 337 | #508 | — | 2 | 4 | no | — |
| 338 | #508 | — | 2 | 2 | no | — |
| 339 | #508 | — | 2 | 2 | no | — |
| 340 | #508 | C4×D4 | 1 | 4 | yes | — |
| 341 | #508 | #131 | 1 | 4 | yes | — |
| 342 | C2×Q32 | — | 2 | 4 | no | — |
| 343 | C2×Q32 | — | 2 | 1 | no | — |
| 344 | C2×Q32 | C22×C8 | 1 | 2 | yes | — |
| 345 | C2×SD32 | — | 2 | 8 | no | — |
| 346 | C2×SD32 | — | 2 | 2 | no | — |
| 347 | C2×SD32 | — | 2 | 2 | no | — |
| 348 | C2×D16 | — | 2 | 4 | no | — |
| 349 | C2×D16 | — | 2 | 2 | no | — |
| 350 | C2×D16 | — | 2 | 2 | no | — |
| 351 | C2×D16 | — | 2 | 1 | no | — |
| 352 | C2×D16 | — | 2 | 1 | no | — |
| 353 | C2×D16 | C22×C8 | 1 | 2 | yes | — |
| 354 | C2×D16 | C22×C8 | 1 | 2 | yes | — |
| 355 | #504 | — | 4 | 8 | no | — |
| 356 | #504 | — | 4 | 8 | no | — |
| 357 | #504 | — | 8 | 8 | no | — |
| 358 | #504 | — | 8 | 8 | no | — |
| 359 | #504 | — | 8 | 4 | no | — |
| 360 | #504 | — | 8 | 4 | no | — |
| 361 | C2×M32 | — | 4 | 4 | no | — |
| 362 | C2×M32 | — | 4 | 2 | no | — |
| 363 | C2×M32 | — | 8 | 8 | no | — |
| 364 | C2×M32 | — | 8 | 2 | no | — |
| 365 | C2×M32 | — | 8 | 2 | no | — |
| 366 | C2×M32 | — | 8 | 1 | no | — |
| 367 | C2×M32 | — | 8 | 2 | no | — |
| 368 | C22×C16 | — | 2 | 2 | no | — |
| 369 | C22×C16 | — | 2 | 2 | no | — |
| 370 | C22×C16 | — | 2 | 4 | no | — |
| 371 | C22×C16 | — | 2 | 1 | no | — |
| 372 | C22×C16 | — | 2 | 1 | no | — |
| 373 | C22×C16 | — | 2 | 1 | no | — |
| 374 | C22×C16 | — | 2 | 1 | no | — |
| 375 | C22×C16 | — | 2 | 2 | no | — |
| 376 | C22×C16 | — | 4 | 1 | no | — |
| 377 | C22×C16 | — | 4 | 1 | no | — |
| 378 | C22×C16 | — | 4 | 1 | no | — |
| 379 | C22×C16 | — | 4 | 2 | no | — |
| 380 | C22×C16 | — | 8 | 8 | no | — |
| 381 | C22×C16 | — | 8 | 2 | no | — |
| 382 | C22×C16 | — | 8 | 2 | no | — |
| 383 | C22×C16 | — | 8 | 1 | no | — |
| 384 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 385 | C22×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 386 | C22×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 387 | C22×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 388 | C22×C16 | #131 | 1 | 1 | yes | characteristic |
| 389 | C22×C16 | #131 | 1 | 1 | yes | characteristic |
| 390 | C22×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 391 | C22×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 392 | #466 | — | 2 | 2 | no | — |
| 393 | #466 | — | 2 | 2 | no | — |
| 394 | #466 | — | 4 | 1 | no | — |
| 395 | #466 | — | 4 | 1 | no | — |
| 396 | #443 | — | 2 | 8 | no | — |
| 397 | #443 | — | 2 | 4 | no | — |
| 398 | #443 | — | 2 | 4 | no | — |
| 399 | #443 | — | 4 | 4 | no | — |
| 400 | #443 | — | 4 | 4 | no | — |
| 401 | #443 | — | 4 | 4 | no | — |
| 402 | #443 | — | 4 | 4 | no | — |
| 403 | #443 | — | 4 | 4 | no | — |
| 404 | #443 | — | 4 | 2 | no | — |
| 405 | #443 | — | 4 | 2 | no | — |
| 406 | C4×D8 | — | 4 | 1 | no | — |
| 407 | C4×D8 | — | 4 | 1 | no | — |
| 408 | C4×D8 | — | 4 | 1 | no | — |
| 409 | C4×D8 | — | 4 | 1 | no | — |
| 410 | C8×D4 | — | 8 | 2 | no | — |
| 411 | C8×D4 | — | 8 | 2 | no | — |
| 412 | C8×D4 | — | 16 | 4 | no | — |
| 413 | C2×#108 | — | 2 | 4 | no | — |
| 414 | C2×#108 | — | 2 | 2 | no | — |
| 415 | C2×#108 | — | 4 | 2 | no | — |
| 416 | C2×#108 | — | 4 | 1 | no | — |
| 417 | C2×#107 | — | 2 | 1 | no | — |
| 418 | C2×#107 | — | 2 | 1 | no | — |
| 419 | C2×#107 | — | 2 | 1 | no | — |
| 420 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 421 | C2×C4⋊C8 | — | 4 | 1 | no | — |
| 422 | C2×C4⋊C8 | — | 8 | 1 | no | — |
| 423 | C2×#104 | — | 4 | 4 | no | — |
| 424 | C2×#104 | — | 4 | 4 | no | — |
| 425 | C2×#104 | — | 4 | 2 | no | — |
| 426 | C2×#104 | — | 4 | 2 | no | — |
| 427 | C2×#102 | — | 4 | 1 | no | — |
| 428 | C2×#102 | — | 4 | 1 | no | — |
| 429 | C2×#102 | — | 4 | 1 | no | — |
| 430 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 431 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 432 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 433 | C2×C22⋊C8 | — | 8 | 1 | no | — |
| 434 | C2×C4×C8 | — | 2 | 1 | no | — |
| 435 | C2×C4×C8 | — | 2 | 1 | no | — |
| 436 | C2×C4×C8 | — | 2 | 1 | no | — |
| 437 | C2×C4×C8 | — | 2 | 1 | no | — |
| 438 | C2×C4×C8 | — | 2 | 1 | no | — |
| 439 | C2×C4×C8 | — | 2 | 1 | no | — |
| 440 | C2×C4×C8 | — | 4 | 2 | no | — |
| 441 | C2×C4×C8 | — | 4 | 1 | no | — |
| 442 | C2×C4×C8 | — | 8 | 1 | no | — |
| 443 | C2×C4×C8 | — | 8 | 1 | no | — |
| 444 | C2×C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 445 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 446 | C2×C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 447 | C2×C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 448 | #390 | — | 4 | 1 | no | — |
| 449 | #389 | — | 4 | 1 | no | — |
| 450 | #388 | — | 8 | 1 | no | — |
| 451 | #386 | — | 8 | 1 | no | — |
| 452 | #380 | — | 4 | 1 | no | — |
| 453 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 454 | C4×C22⋊C4 | — | 8 | 1 | no | — |
| 455 | SD64 | — | 2 | 8 | no | — |
| 456 | D32 | — | 2 | 8 | no | — |
| 457 | M64 | — | 2 | 2 | no | — |
| 458 | M64 | — | 2 | 2 | no | — |
| 459 | M64 | — | 2 | 2 | no | — |
| 460 | M64 | — | 2 | 2 | no | — |
| 461 | M64 | — | 4 | 2 | no | — |
| 462 | M64 | — | 4 | 2 | no | — |
| 463 | C2×C32 | — | 2 | 2 | no | — |
| 464 | C2×C32 | — | 4 | 2 | no | — |
| 465 | C2×C32 | C22×C8 | 1 | 4 | yes | — |
| 466 | #368 | — | 2 | 4 | no | — |
| 467 | #368 | — | 2 | 2 | no | — |
| 468 | #368 | C4×D4 | 1 | 4 | yes | — |
| 469 | #367 | — | 2 | 2 | no | — |
| 470 | #367 | — | 2 | 2 | no | — |
| 471 | #366 | — | 2 | 1 | no | — |
| 472 | #366 | C22×C8 | 1 | 2 | yes | — |
| 473 | #364 | — | 2 | 4 | no | — |
| 474 | #364 | — | 4 | 4 | no | — |
| 475 | #364 | — | 4 | 2 | no | — |
| 476 | #359 | — | 2 | 8 | no | — |
| 477 | #359 | — | 2 | 4 | no | — |
| 478 | #359 | — | 2 | 4 | no | — |
| 479 | #357 | — | 2 | 2 | no | — |
| 480 | #357 | — | 2 | 2 | no | — |
| 481 | #357 | — | 4 | 2 | no | — |
| 482 | #357 | — | 4 | 2 | no | — |
| 483 | #350 | — | 4 | 8 | no | — |
| 484 | #350 | — | 4 | 8 | no | — |
| 485 | #346 | — | 2 | 4 | no | — |
| 486 | #346 | — | 2 | 2 | no | — |
| 487 | #346 | — | 2 | 2 | no | — |
| 488 | #346 | — | 2 | 1 | no | — |
| 489 | #346 | — | 2 | 1 | no | — |
| 490 | #346 | — | 2 | 1 | no | — |
| 491 | #346 | — | 2 | 1 | no | — |
| 492 | #346 | #120 | 1 | 2 | yes | — |
| 493 | #346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 494 | #346 | C22×D4 | 1 | 2 | yes | — |
| 495 | #346 | C2×#41 | 1 | 2 | yes | — |
| 496 | #340 | — | 4 | 1 | no | — |
| 497 | #340 | — | 4 | 1 | no | — |
| 498 | #340 | — | 4 | 1 | no | — |
| 499 | #336 | — | 8 | 1 | no | — |
| 500 | #336 | — | 8 | 1 | no | — |
| 501 | #336 | — | 8 | 1 | no | — |
| 502 | #334 | — | 4 | 1 | no | — |
| 503 | #334 | — | 4 | 1 | no | — |
| 504 | #334 | — | 4 | 1 | no | — |
| 505 | #334 | — | 4 | 1 | no | — |
| 506 | D4⋊C8 | — | 8 | 2 | no | — |
| 507 | D4⋊C8 | — | 8 | 2 | no | — |
| 508 | #322 | — | 2 | 1 | no | — |
| 509 | #322 | — | 2 | 1 | no | — |
| 510 | #322 | — | 2 | 1 | no | — |
| 511 | #322 | — | 4 | 2 | no | — |
| 512 | #322 | #120 | 1 | 2 | yes | — |
| 513 | C2×#41 | — | 4 | 4 | no | — |
| 514 | C2×#41 | — | 4 | 4 | no | — |
| 515 | C2×#41 | — | 4 | 2 | no | — |
| 516 | C2×#41 | — | 4 | 2 | no | — |
| 517 | C2×#41 | — | 8 | 2 | no | — |
| 518 | C2×#41 | — | 8 | 2 | no | — |
| 519 | C2×#41 | — | 8 | 1 | no | — |
| 520 | C2×#41 | — | 8 | 1 | no | — |
| 521 | C22×Q8 | — | 4 | 1 | no | — |
| 522 | C22×D4 | — | 4 | 1 | no | — |
| 523 | C22×D4 | — | 4 | 1 | no | — |
| 524 | C22×D4 | — | 8 | 1 | no | — |
| 525 | C22×D4 | — | 8 | 1 | no | — |
| 526 | C23×C4 | — | 2 | 1 | no | — |
| 527 | C23×C4 | — | 8 | 1 | no | — |
| 528 | C23×C4 | — | 8 | 1 | no | — |
| 529 | C23×C4 | #442 | 1 | 1 | yes | characteristic |
| 530 | #135 | — | 2 | 8 | no | — |
| 531 | #135 | — | 2 | 4 | no | — |
| 532 | #135 | — | 2 | 4 | no | — |
| 533 | #135 | — | 4 | 4 | no | — |
| 534 | #135 | — | 4 | 4 | no | — |
| 535 | #135 | — | 4 | 4 | no | — |
| 536 | #135 | — | 4 | 4 | no | — |
| 537 | #135 | — | 4 | 4 | no | — |
| 538 | #135 | — | 4 | 2 | no | — |
| 539 | #135 | — | 4 | 2 | no | — |
| 540 | C2×Q16 | — | 2 | 4 | no | — |
| 541 | C2×Q16 | — | 2 | 2 | no | — |
| 542 | C2×Q16 | — | 4 | 2 | no | — |
| 543 | C2×Q16 | — | 4 | 1 | no | — |
| 544 | C2×SD16 | — | 4 | 4 | no | — |
| 545 | C2×SD16 | — | 4 | 4 | no | — |
| 546 | C2×SD16 | — | 4 | 2 | no | — |
| 547 | C2×SD16 | — | 4 | 2 | no | — |
| 548 | C2×D8 | — | 2 | 4 | no | — |
| 549 | C2×D8 | — | 2 | 2 | no | — |
| 550 | C2×D8 | — | 2 | 2 | no | — |
| 551 | C2×D8 | — | 4 | 2 | no | — |
| 552 | C2×D8 | — | 4 | 1 | no | — |
| 553 | C2×D8 | — | 4 | 1 | no | — |
| 554 | C2×D8 | — | 4 | 1 | no | — |
| 555 | C2×D8 | — | 4 | 1 | no | — |
| 556 | C2×D8 | — | 4 | 1 | no | — |
| 557 | C2×D8 | — | 4 | 1 | no | — |
| 558 | #131 | — | 4 | 8 | no | — |
| 559 | #131 | — | 4 | 4 | no | — |
| 560 | #131 | — | 4 | 4 | no | — |
| 561 | #131 | — | 8 | 4 | no | — |
| 562 | #131 | — | 8 | 4 | no | — |
| 563 | #131 | — | 8 | 4 | no | — |
| 564 | #131 | — | 8 | 2 | no | — |
| 565 | #131 | — | 8 | 4 | no | — |
| 566 | #131 | — | 8 | 2 | no | — |
| 567 | #131 | — | 8 | 4 | no | — |
| 568 | C2×M16 | — | 4 | 4 | no | — |
| 569 | C2×M16 | — | 4 | 2 | no | — |
| 570 | C2×M16 | — | 8 | 4 | no | — |
| 571 | C2×M16 | — | 8 | 4 | no | — |
| 572 | C2×M16 | — | 8 | 2 | no | — |
| 573 | C2×M16 | — | 8 | 2 | no | — |
| 574 | C2×M16 | — | 8 | 2 | no | — |
| 575 | C2×M16 | — | 8 | 1 | no | — |
| 576 | C22×C8 | — | 2 | 1 | no | — |
| 577 | C22×C8 | — | 2 | 1 | no | — |
| 578 | C22×C8 | — | 2 | 1 | no | — |
| 579 | C22×C8 | — | 2 | 1 | no | — |
| 580 | C22×C8 | — | 2 | 1 | no | — |
| 581 | C22×C8 | — | 2 | 2 | no | — |
| 582 | C22×C8 | — | 2 | 1 | no | — |
| 583 | C22×C8 | — | 2 | 1 | no | — |
| 584 | C22×C8 | — | 2 | 1 | no | — |
| 585 | C22×C8 | — | 4 | 1 | no | — |
| 586 | C22×C8 | — | 4 | 1 | no | — |
| 587 | C22×C8 | — | 8 | 4 | no | — |
| 588 | C22×C8 | — | 8 | 2 | no | — |
| 589 | C22×C8 | — | 8 | 4 | no | — |
| 590 | C22×C8 | — | 8 | 2 | no | — |
| 591 | C22×C8 | — | 8 | 2 | no | — |
| 592 | C22×C8 | — | 8 | 1 | no | — |
| 593 | C22×C8 | — | 8 | 2 | no | — |
| 594 | C22×C8 | — | 8 | 1 | no | — |
| 595 | C22×C8 | — | 8 | 1 | no | — |
| 596 | C22×C8 | — | 16 | 2 | no | — |
| 597 | C22×C8 | — | 16 | 1 | no | — |
| 598 | C22×C8 | — | 16 | 2 | no | — |
| 599 | C22×C8 | — | 16 | 2 | no | — |
| 600 | C22×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 601 | C22×C8 | C8×D4 | 1 | 1 | yes | characteristic |
| 602 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 603 | C22×C8 | #442 | 1 | 1 | yes | characteristic |
| 604 | C22×C8 | #444 | 1 | 1 | yes | characteristic |
| 605 | C22×C8 | #444 | 1 | 1 | yes | characteristic |
| 606 | C22×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 607 | C22×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 608 | #121 | — | 4 | 2 | no | — |
| 609 | #121 | — | 4 | 2 | no | — |
| 610 | #121 | — | 8 | 1 | no | — |
| 611 | #121 | — | 8 | 1 | no | — |
| 612 | C4×D4 | — | 8 | 1 | no | — |
| 613 | C4×D4 | — | 8 | 1 | no | — |
| 614 | C4×D4 | — | 8 | 1 | no | — |
| 615 | C4×D4 | — | 8 | 1 | no | — |
| 616 | C4×D4 | — | 16 | 2 | no | — |
| 617 | C4×D4 | — | 16 | 2 | no | — |
| 618 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 619 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 620 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 621 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 622 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 623 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 624 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 625 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 626 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 627 | C2×C42 | — | 2 | 1 | no | — |
| 628 | C2×C42 | — | 2 | 1 | no | — |
| 629 | C2×C42 | — | 2 | 1 | no | — |
| 630 | C2×C42 | — | 4 | 1 | no | — |
| 631 | C2×C42 | — | 8 | 1 | no | — |
| 632 | C2×C42 | #442 | 1 | 1 | yes | characteristic |
| 633 | C2×C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 634 | Q32 | — | 2 | 4 | no | — |
| 635 | Q32 | — | 2 | 2 | no | — |
| 636 | Q32 | C8×D4 | 1 | 4 | yes | complemented |
| 637 | SD32 | — | 2 | 8 | no | — |
| 638 | SD32 | — | 2 | 4 | no | — |
| 639 | SD32 | — | 2 | 4 | no | — |
| 640 | D16 | — | 2 | 4 | no | — |
| 641 | D16 | — | 2 | 2 | no | — |
| 642 | D16 | — | 2 | 4 | no | — |
| 643 | D16 | — | 4 | 2 | no | — |
| 644 | D16 | C8×D4 | 1 | 4 | yes | complemented |
| 645 | M32 | — | 4 | 4 | no | — |
| 646 | M32 | — | 8 | 8 | no | — |
| 647 | M32 | — | 8 | 8 | no | — |
| 648 | M32 | — | 8 | 4 | no | — |
| 649 | M32 | — | 8 | 2 | no | — |
| 650 | C2×C16 | — | 2 | 1 | no | — |
| 651 | C2×C16 | — | 2 | 1 | no | — |
| 652 | C2×C16 | — | 2 | 1 | no | — |
| 653 | C2×C16 | — | 2 | 1 | no | — |
| 654 | C2×C16 | — | 2 | 2 | no | — |
| 655 | C2×C16 | — | 2 | 2 | no | — |
| 656 | C2×C16 | — | 2 | 2 | no | — |
| 657 | C2×C16 | — | 2 | 2 | no | — |
| 658 | C2×C16 | — | 2 | 1 | no | — |
| 659 | C2×C16 | — | 2 | 1 | no | — |
| 660 | C2×C16 | — | 2 | 2 | no | — |
| 661 | C2×C16 | — | 2 | 2 | no | — |
| 662 | C2×C16 | — | 2 | 1 | no | — |
| 663 | C2×C16 | — | 4 | 2 | no | — |
| 664 | C2×C16 | — | 4 | 2 | no | — |
| 665 | C2×C16 | — | 4 | 4 | no | — |
| 666 | C2×C16 | — | 4 | 1 | no | — |
| 667 | C2×C16 | — | 4 | 1 | no | — |
| 668 | C2×C16 | — | 4 | 4 | no | — |
| 669 | C2×C16 | — | 4 | 1 | no | — |
| 670 | C2×C16 | — | 4 | 1 | no | — |
| 671 | C2×C16 | — | 8 | 8 | no | — |
| 672 | C2×C16 | — | 8 | 8 | no | — |
| 673 | C2×C16 | — | 8 | 4 | no | — |
| 674 | C2×C16 | — | 8 | 2 | no | — |
| 675 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 676 | C2×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 677 | C2×C16 | C2×C4×D4 | 1 | 2 | yes | — |
| 678 | C2×C16 | #525 | 1 | 2 | yes | — |
| 679 | C2×C16 | C23×C8 | 1 | 1 | yes | characteristic |
| 680 | C2×C16 | C2×#131 | 1 | 2 | yes | — |
| 681 | C2×C16 | C2×#131 | 1 | 1 | yes | characteristic |
| 682 | #108 | — | 2 | 4 | no | — |
| 683 | #108 | — | 4 | 4 | no | — |
| 684 | #108 | — | 4 | 2 | no | — |
| 685 | #107 | — | 2 | 2 | no | — |
| 686 | #107 | — | 4 | 1 | no | — |
| 687 | #107 | — | 4 | 1 | no | — |
| 688 | #107 | — | 4 | 1 | no | — |
| 689 | #107 | — | 4 | 1 | no | — |
| 690 | #107 | — | 4 | 1 | no | — |
| 691 | C4⋊C8 | — | 8 | 1 | no | — |
| 692 | C4⋊C8 | — | 8 | 1 | no | — |
| 693 | C4⋊C8 | — | 8 | 1 | no | — |
| 694 | C4⋊C8 | — | 8 | 1 | no | — |
| 695 | C4⋊C8 | — | 16 | 2 | no | — |
| 696 | #104 | — | 4 | 8 | no | — |
| 697 | #104 | — | 4 | 4 | no | — |
| 698 | #104 | — | 4 | 4 | no | — |
| 699 | #102 | — | 4 | 2 | no | — |
| 700 | #102 | — | 4 | 2 | no | — |
| 701 | #102 | — | 8 | 1 | no | — |
| 702 | #102 | — | 8 | 2 | no | — |
| 703 | #102 | — | 8 | 1 | no | — |
| 704 | C22⋊C8 | — | 16 | 2 | no | — |
| 705 | C22⋊C8 | — | 16 | 2 | no | — |
| 706 | C22⋊C8 | — | 16 | 2 | no | — |
| 707 | C22⋊C8 | — | 16 | 2 | no | — |
| 708 | C4×C8 | — | 2 | 1 | no | — |
| 709 | C4×C8 | — | 2 | 1 | no | — |
| 710 | C4×C8 | — | 2 | 1 | no | — |
| 711 | C4×C8 | — | 2 | 1 | no | — |
| 712 | C4×C8 | — | 2 | 1 | no | — |
| 713 | C4×C8 | — | 2 | 1 | no | — |
| 714 | C4×C8 | — | 2 | 2 | no | — |
| 715 | C4×C8 | — | 4 | 1 | no | — |
| 716 | C4×C8 | — | 4 | 1 | no | — |
| 717 | C4×C8 | — | 4 | 1 | no | — |
| 718 | C4×C8 | — | 8 | 2 | no | — |
| 719 | C4×C8 | — | 16 | 2 | no | — |
| 720 | C4×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 721 | C4×C8 | #525 | 1 | 1 | yes | characteristic |
| 722 | C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 723 | C4×C8 | #575 | 1 | 1 | yes | characteristic |
| 724 | #95 | — | 8 | 1 | no | — |
| 725 | #95 | — | 8 | 1 | no | — |
| 726 | #95 | — | 8 | 1 | no | — |
| 727 | C32 | — | 2 | 4 | no | — |
| 728 | C32 | — | 4 | 2 | no | — |
| 729 | C32 | — | 8 | 2 | no | — |
| 730 | C24 | — | 8 | 1 | no | — |
| 731 | C24 | — | 8 | 1 | no | — |
| 732 | C24 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 733 | #41 | — | 4 | 8 | no | — |
| 734 | #41 | — | 4 | 4 | no | — |
| 735 | #41 | — | 4 | 4 | no | — |
| 736 | #41 | — | 8 | 4 | no | — |
| 737 | #41 | — | 8 | 4 | no | — |
| 738 | #41 | — | 8 | 4 | no | — |
| 739 | #41 | — | 8 | 4 | no | — |
| 740 | #41 | — | 8 | 4 | no | — |
| 741 | #41 | — | 8 | 2 | no | — |
| 742 | #41 | — | 8 | 2 | no | — |
| 743 | C2×Q8 | — | 4 | 4 | no | — |
| 744 | C2×Q8 | — | 4 | 2 | no | — |
| 745 | C2×Q8 | — | 8 | 2 | no | — |
| 746 | C2×Q8 | — | 8 | 1 | no | — |
| 747 | C2×D4 | — | 4 | 4 | no | — |
| 748 | C2×D4 | — | 4 | 2 | no | — |
| 749 | C2×D4 | — | 4 | 2 | no | — |
| 750 | C2×D4 | — | 8 | 2 | no | — |
| 751 | C2×D4 | — | 8 | 4 | no | — |
| 752 | C2×D4 | — | 8 | 4 | no | — |
| 753 | C2×D4 | — | 8 | 2 | no | — |
| 754 | C2×D4 | — | 8 | 2 | no | — |
| 755 | C2×D4 | — | 8 | 2 | no | — |
| 756 | C2×D4 | — | 8 | 2 | no | — |
| 757 | C2×D4 | — | 8 | 1 | no | — |
| 758 | C2×D4 | — | 8 | 1 | no | — |
| 759 | C2×D4 | — | 8 | 1 | no | — |
| 760 | C2×D4 | — | 8 | 1 | no | — |
| 761 | C2×D4 | — | 8 | 1 | no | — |
| 762 | C2×D4 | — | 8 | 1 | no | — |
| 763 | C2×D4 | — | 16 | 2 | no | — |
| 764 | C2×D4 | — | 16 | 2 | no | — |
| 765 | C22×C4 | — | 2 | 1 | no | — |
| 766 | C22×C4 | — | 2 | 1 | no | — |
| 767 | C22×C4 | — | 2 | 1 | no | — |
| 768 | C22×C4 | — | 2 | 1 | no | — |
| 769 | C22×C4 | — | 2 | 1 | no | — |
| 770 | C22×C4 | — | 2 | 1 | no | — |
| 771 | C22×C4 | — | 4 | 1 | no | — |
| 772 | C22×C4 | — | 4 | 1 | no | — |
| 773 | C22×C4 | — | 4 | 2 | no | — |
| 774 | C22×C4 | — | 8 | 4 | no | — |
| 775 | C22×C4 | — | 8 | 4 | no | — |
| 776 | C22×C4 | — | 8 | 1 | no | — |
| 777 | C22×C4 | — | 8 | 1 | no | — |
| 778 | C22×C4 | — | 8 | 2 | no | — |
| 779 | C22×C4 | — | 8 | 2 | no | — |
| 780 | C22×C4 | — | 8 | 1 | no | — |
| 781 | C22×C4 | — | 8 | 1 | no | — |
| 782 | C22×C4 | — | 8 | 1 | no | — |
| 783 | C22×C4 | — | 16 | 1 | no | — |
| 784 | C22×C4 | — | 16 | 1 | no | — |
| 785 | C22×C4 | — | 16 | 1 | no | — |
| 786 | C22×C4 | — | 16 | 1 | no | — |
| 787 | C22×C4 | — | 16 | 1 | no | — |
| 788 | C22×C4 | — | 16 | 1 | no | — |
| 789 | C22×C4 | #1580 | 1 | 1 | yes | characteristic |
| 790 | C22×C4 | #1580 | 1 | 1 | yes | characteristic |
| 791 | C22×C4 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 792 | C22×C4 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 793 | C22×C4 | AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 794 | C22×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 795 | Q16 | — | 2 | 4 | no | — |
| 796 | Q16 | — | 4 | 4 | no | — |
| 797 | Q16 | — | 4 | 2 | no | — |
| 798 | SD16 | — | 4 | 8 | no | — |
| 799 | SD16 | — | 4 | 4 | no | — |
| 800 | SD16 | — | 4 | 4 | no | — |
| 801 | D8 | — | 2 | 4 | no | — |
| 802 | D8 | — | 4 | 4 | no | — |
| 803 | D8 | — | 4 | 2 | no | — |
| 804 | D8 | — | 4 | 2 | no | — |
| 805 | D8 | — | 4 | 2 | no | — |
| 806 | D8 | — | 8 | 1 | no | — |
| 807 | D8 | — | 8 | 1 | no | — |
| 808 | M16 | — | 4 | 4 | no | — |
| 809 | M16 | — | 8 | 4 | no | — |
| 810 | M16 | — | 8 | 4 | no | — |
| 811 | M16 | — | 8 | 8 | no | — |
| 812 | M16 | — | 8 | 4 | no | — |
| 813 | M16 | — | 8 | 2 | no | — |
| 814 | C2×C8 | — | 2 | 2 | no | — |
| 815 | C2×C8 | — | 2 | 2 | no | — |
| 816 | C2×C8 | — | 2 | 2 | no | — |
| 817 | C2×C8 | — | 2 | 2 | no | — |
| 818 | C2×C8 | — | 2 | 1 | no | — |
| 819 | C2×C8 | — | 2 | 1 | no | — |
| 820 | C2×C8 | — | 2 | 1 | no | — |
| 821 | C2×C8 | — | 2 | 1 | no | — |
| 822 | C2×C8 | — | 2 | 1 | no | — |
| 823 | C2×C8 | — | 2 | 1 | no | — |
| 824 | C2×C8 | — | 2 | 1 | no | — |
| 825 | C2×C8 | — | 2 | 1 | no | — |
| 826 | C2×C8 | — | 2 | 1 | no | — |
| 827 | C2×C8 | — | 2 | 1 | no | — |
| 828 | C2×C8 | — | 2 | 1 | no | — |
| 829 | C2×C8 | — | 2 | 1 | no | — |
| 830 | C2×C8 | — | 2 | 1 | no | — |
| 831 | C2×C8 | — | 2 | 1 | no | — |
| 832 | C2×C8 | — | 4 | 2 | no | — |
| 833 | C2×C8 | — | 8 | 4 | no | — |
| 834 | C2×C8 | — | 8 | 4 | no | — |
| 835 | C2×C8 | — | 8 | 8 | no | — |
| 836 | C2×C8 | — | 8 | 4 | no | — |
| 837 | C2×C8 | — | 8 | 1 | no | — |
| 838 | C2×C8 | — | 8 | 1 | no | — |
| 839 | C2×C8 | — | 8 | 2 | no | — |
| 840 | C2×C8 | — | 8 | 1 | no | — |
| 841 | C2×C8 | — | 8 | 1 | no | — |
| 842 | C2×C8 | — | 8 | 1 | no | — |
| 843 | C2×C8 | — | 16 | 4 | no | — |
| 844 | C2×C8 | — | 16 | 1 | no | — |
| 845 | C2×C8 | — | 16 | 1 | no | — |
| 846 | C2×C8 | — | 16 | 1 | no | — |
| 847 | C2×C8 | — | 16 | 1 | no | — |
| 848 | C2×C8 | — | 16 | 1 | no | — |
| 849 | C2×C8 | — | 16 | 1 | no | — |
| 850 | C2×C8 | — | 32 | 4 | no | — |
| 851 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 852 | C2×C8 | #1580 | 1 | 1 | yes | characteristic |
| 853 | C2×C8 | AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 854 | C2×C8 | C4×#120 | 1 | 1 | yes | characteristic |
| 855 | C2×C8 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 856 | C2×C8 | #2929 | 1 | 1 | yes | characteristic |
| 857 | C2×C8 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 858 | C2×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 859 | C2×C8 | #2955 | 1 | 1 | yes | characteristic |
| 860 | C2×C8 | #3003 | 1 | 1 | yes | characteristic |
| 861 | C2×C8 | #3114 | 1 | 1 | yes | characteristic |
| 862 | C4⋊C4 | — | 4 | 2 | no | — |
| 863 | C4⋊C4 | — | 8 | 1 | no | — |
| 864 | C4⋊C4 | — | 8 | 1 | no | — |
| 865 | C4⋊C4 | — | 8 | 1 | no | — |
| 866 | C4⋊C4 | — | 8 | 1 | no | — |
| 867 | C4⋊C4 | — | 8 | 1 | no | — |
| 868 | C4⋊C4 | — | 16 | 2 | no | — |
| 869 | C22⋊C4 | — | 8 | 2 | no | — |
| 870 | C22⋊C4 | — | 8 | 2 | no | — |
| 871 | C22⋊C4 | — | 16 | 1 | no | — |
| 872 | C22⋊C4 | — | 16 | 1 | no | — |
| 873 | C22⋊C4 | — | 16 | 2 | no | — |
| 874 | C22⋊C4 | — | 16 | 2 | no | — |
| 875 | C22⋊C4 | — | 16 | 2 | no | — |
| 876 | C42 | — | 2 | 1 | no | — |
| 877 | C42 | — | 2 | 1 | no | — |
| 878 | C42 | — | 2 | 1 | no | — |
| 879 | C42 | — | 4 | 1 | no | — |
| 880 | C42 | — | 4 | 1 | no | — |
| 881 | C42 | — | 16 | 1 | no | — |
| 882 | C42 | — | 16 | 1 | no | — |
| 883 | C42 | #3006 | 1 | 1 | yes | characteristic |
| 884 | C42 | #3109 | 1 | 1 | yes | characteristic |
| 885 | C16 | — | 2 | 1 | no | — |
| 886 | C16 | — | 2 | 1 | no | — |
| 887 | C16 | — | 2 | 2 | no | — |
| 888 | C16 | — | 4 | 2 | no | — |
| 889 | C16 | — | 4 | 2 | no | — |
| 890 | C16 | — | 4 | 1 | no | — |
| 891 | C16 | — | 8 | 4 | no | — |
| 892 | C16 | C2×C8×D4 | 1 | 2 | yes | — |
| 893 | C16 | #2929 | 1 | 2 | yes | — |
| 894 | C23 | — | 2 | 1 | no | — |
| 895 | C23 | — | 2 | 2 | no | — |
| 896 | C23 | — | 2 | 1 | no | — |
| 897 | C23 | — | 4 | 1 | no | — |
| 898 | C23 | — | 8 | 4 | no | — |
| 899 | C23 | — | 8 | 2 | no | — |
| 900 | C23 | — | 8 | 2 | no | — |
| 901 | C23 | — | 16 | 2 | no | — |
| 902 | C23 | — | 16 | 1 | no | — |
| 903 | C23 | — | 16 | 1 | no | — |
| 904 | C23 | — | 16 | 1 | no | — |
| 905 | C23 | — | 16 | 1 | no | — |
| 906 | C23 | — | 16 | 2 | no | — |
| 907 | C23 | — | 16 | 1 | no | — |
| 908 | C23 | — | 16 | 1 | no | — |
| 909 | C23 | #12067 | 1 | 1 | yes | characteristic |
| 910 | C23 | #12067 | 1 | 1 | yes | characteristic |
| 911 | C23 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 912 | Q8 | — | 4 | 4 | no | — |
| 913 | Q8 | — | 8 | 4 | no | — |
| 914 | Q8 | — | 8 | 2 | no | — |
| 915 | D4 | — | 4 | 4 | no | — |
| 916 | D4 | — | 8 | 4 | no | — |
| 917 | D4 | — | 8 | 8 | no | — |
| 918 | D4 | — | 8 | 4 | no | — |
| 919 | D4 | — | 8 | 4 | no | — |
| 920 | D4 | — | 8 | 2 | no | — |
| 921 | D4 | — | 8 | 2 | no | — |
| 922 | D4 | — | 8 | 2 | no | — |
| 923 | D4 | — | 16 | 4 | no | — |
| 924 | D4 | — | 16 | 4 | no | — |
| 925 | D4 | — | 16 | 1 | no | — |
| 926 | D4 | — | 16 | 1 | no | — |
| 927 | C2×C4 | — | 2 | 1 | no | — |
| 928 | C2×C4 | — | 2 | 1 | no | — |
| 929 | C2×C4 | — | 2 | 1 | no | — |
| 930 | C2×C4 | — | 2 | 1 | no | — |
| 931 | C2×C4 | — | 2 | 1 | no | — |
| 932 | C2×C4 | — | 2 | 1 | no | — |
| 933 | C2×C4 | — | 2 | 1 | no | — |
| 934 | C2×C4 | — | 2 | 1 | no | — |
| 935 | C2×C4 | — | 2 | 1 | no | — |
| 936 | C2×C4 | — | 2 | 1 | no | — |
| 937 | C2×C4 | — | 2 | 1 | no | — |
| 938 | C2×C4 | — | 2 | 1 | no | — |
| 939 | C2×C4 | — | 4 | 1 | no | — |
| 940 | C2×C4 | — | 4 | 1 | no | — |
| 941 | C2×C4 | — | 4 | 1 | no | — |
| 942 | C2×C4 | — | 4 | 1 | no | — |
| 943 | C2×C4 | — | 4 | 1 | no | — |
| 944 | C2×C4 | — | 8 | 8 | no | — |
| 945 | C2×C4 | — | 8 | 2 | no | — |
| 946 | C2×C4 | — | 8 | 2 | no | — |
| 947 | C2×C4 | — | 8 | 4 | no | — |
| 948 | C2×C4 | — | 8 | 2 | no | — |
| 949 | C2×C4 | — | 8 | 4 | no | — |
| 950 | C2×C4 | — | 8 | 4 | no | — |
| 951 | C2×C4 | — | 8 | 2 | no | — |
| 952 | C2×C4 | — | 16 | 1 | no | — |
| 953 | C2×C4 | — | 16 | 1 | no | — |
| 954 | C2×C4 | — | 16 | 1 | no | — |
| 955 | C2×C4 | — | 16 | 1 | no | — |
| 956 | C2×C4 | — | 16 | 1 | no | — |
| 957 | C2×C4 | — | 16 | 1 | no | — |
| 958 | C2×C4 | — | 16 | 1 | no | — |
| 959 | C2×C4 | — | 16 | 1 | no | — |
| 960 | C2×C4 | — | 32 | 1 | no | — |
| 961 | C2×C4 | — | 32 | 1 | no | — |
| 962 | C2×C4 | — | 32 | 1 | no | — |
| 963 | C2×C4 | — | 32 | 1 | no | — |
| 964 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 965 | C2×C4 | #12067 | 1 | 1 | yes | characteristic |
| 966 | C2×C4 | C2×#1580 | 1 | 1 | yes | characteristic |
| 967 | C2×C4 | #17907 | 1 | 1 | yes | characteristic |
| 968 | C2×C4 | #21452 | 1 | 1 | yes | characteristic |
| 969 | C2×C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 970 | C2×C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 971 | C2×C4 | #33468 | 1 | 1 | yes | characteristic |
| 972 | C8 | — | 2 | 1 | no | — |
| 973 | C8 | — | 2 | 1 | no | — |
| 974 | C8 | — | 2 | 1 | no | — |
| 975 | C8 | — | 2 | 1 | no | — |
| 976 | C8 | — | 2 | 2 | no | — |
| 977 | C8 | — | 8 | 2 | no | — |
| 978 | C8 | — | 8 | 4 | no | — |
| 979 | C8 | — | 16 | 1 | no | — |
| 980 | C8 | — | 32 | 1 | no | — |
| 981 | C8 | — | 32 | 1 | no | — |
| 982 | C8 | C8×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 983 | C8 | #17914 | 1 | 1 | yes | characteristic |
| 984 | C8 | C8×#120 | 1 | 1 | yes | characteristic |
| 985 | C8 | #21467 | 1 | 1 | yes | characteristic |
| 986 | C22 | — | 2 | 1 | no | — |
| 987 | C22 | — | 2 | 1 | no | — |
| 988 | C22 | — | 2 | 1 | no | — |
| 989 | C22 | — | 2 | 1 | no | — |
| 990 | C22 | — | 2 | 1 | no | — |
| 991 | C22 | — | 2 | 1 | no | — |
| 992 | C22 | — | 2 | 1 | no | — |
| 993 | C22 | — | 4 | 2 | no | — |
| 994 | C22 | — | 4 | 2 | no | — |
| 995 | C22 | — | 8 | 4 | no | — |
| 996 | C22 | — | 16 | 8 | no | — |
| 997 | C22 | — | 16 | 2 | no | — |
| 998 | C22 | — | 16 | 2 | no | — |
| 999 | C22 | — | 16 | 2 | no | — |
| 1000 | C22 | — | 16 | 2 | no | — |
| 1001 | C22 | — | 16 | 2 | no | — |
| 1002 | C22 | — | 32 | 1 | no | — |
| 1003 | C22 | — | 32 | 1 | no | — |
| 1004 | C22 | — | 32 | 1 | no | — |
| 1005 | C22 | — | 32 | 1 | no | — |
| 1006 | C22 | AGL(1,ℤ/32) | 1 | 2 | yes | complemented |
| 1007 | C22 | C2×#12067 | 1 | 1 | yes | characteristic |
| 1008 | C22 | #483875 | 1 | 1 | yes | characteristic |
| 1009 | C22 | #495721 | 1 | 1 | yes | characteristic |
| 1010 | C4 | — | 2 | 1 | no | — |
| 1011 | C4 | — | 2 | 1 | no | — |
| 1012 | C4 | — | 4 | 1 | no | — |
| 1013 | C4 | — | 4 | 1 | no | — |
| 1014 | C4 | — | 8 | 1 | no | — |
| 1015 | C4 | — | 8 | 4 | no | — |
| 1016 | C4 | — | 16 | 2 | no | — |
| 1017 | C4 | — | 32 | 1 | no | — |
| 1018 | C4 | — | 32 | 1 | no | — |
| 1019 | C4 | #208650 | 1 | 1 | yes | characteristic |
| 1020 | C4 | #483590 | 1 | 1 | yes | characteristic |
| 1021 | C4 | #483878 | 1 | 1 | yes | characteristic |
| 1022 | C4 | #495725 | 1 | 1 | yes | characteristic |
| 1023 | C2 | — | 2 | 1 | no | — |
| 1024 | C2 | — | 2 | 1 | no | — |
| 1025 | C2 | — | 2 | 2 | no | — |
| 1026 | C2 | — | 4 | 1 | no | — |
| 1027 | C2 | — | 16 | 4 | no | — |
| 1028 | C2 | — | 32 | 2 | no | — |
| 1029 | C2 | C2×AGL(1,ℤ/32) | 1 | 1 | yes | characteristic |
| 1030 | C2 | #72223646 | 1 | 1 | yes | characteristic |
| 1031 | C2 | #72225051 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×#12067 |
| commutator | C2×C16 | C23×C8 |
| Frattini, cosocle | C2×#346 | C24 |
| prime radical | #512830 | C4 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C22×C4×C8 ◁ C22×#1313 ◁ G | |
| LECS | G ▷ C2×#346 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72287252 | C2 | semidirect |
| 2. #72287163 | C2 | semidirect |
| 3. #72287120 | C2 | semidirect |
| 4. #72287038 | C2 | semidirect |
| 6. #72286589 | C2 | semidirect |
| 7. #72227152 | C2 | semidirect |
| 8. C22×#12068 | C2 | semidirect |
| 9. #72223645 | C2 | semidirect |
| 10. #72217184 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/32) | C2 | semidirect |
| 22. C2×#12067 | C22 | semidirect |
| 36. C2×#7457 | C22 | semidirect |
| 37. C2×#7390 | C22 | semidirect |
| 40. C2×#7333 | C22 | semidirect |
| 41. #140751 | C22 | semidirect |
| 42. #140354 | C22 | semidirect |
| 46. #129165 | C22 | semidirect |
| 48. #94059 | C22 | semidirect |
| 49. #94030 | C22 | semidirect |
| 50. #93997 | C22 | semidirect |
| 79. #13663 | C8 | semidirect |
| 80. #13662 | C8 | semidirect |
| 81. #13661 | C8 | semidirect |
| 106. #12068 | D4 | semidirect |
| 148. C2×#508 | C2×C8 | semidirect |
| 150. C22×Q32 | C2×C8 | semidirect |
| 152. C22×D16 | C2×C8 | semidirect |
| 185. C2×SD64 | C2×C8 | semidirect |
| 186. C2×D32 | C2×C8 | semidirect |
| 270. #1416 | C2×C8 | semidirect |
| 271. #1415 | C2×C8 | semidirect |
| 276. C22⋊C32 | C2×C8 | semidirect |
| 277. C22⋊C32 | C2×C8 | semidirect |
| 636. Q32 | C8×D4 | semidirect |
| 644. D16 | C8×D4 | semidirect |
| 1006. C22 | AGL(1,ℤ/32) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72287252 | 2 |
| #72287163 | 2 |
| #72287120 | 2 |
| #72287038 | 2 |
| #72286674 | 2 |
| #72286589 | 2 |
| #72227152 | 2 |
| C22×#12068 | 2 |
| #72223645 | 2 |
| #72217184 | 2 |
| C2×AGL(1,ℤ/32) | 2 |