Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
3045 conjugacy classes of subgroups.
The subgroup lattice has 889 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72225247 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #72225230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72225226 | — | 2 | 1 | no | — |
| 4 | #72225223 | — | 2 | 1 | no | — |
| 5 | #72225223 | C22 | 1 | 2 | yes | — |
| 6 | #72225220 | — | 2 | 1 | no | — |
| 7 | #72225206 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72225186 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #72225183 | — | 2 | 8 | no | — |
| 10 | #72225179 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #72225174 | — | 2 | 1 | no | — |
| 12 | #72225174 | C22 | 1 | 2 | yes | — |
| 13 | #72225172 | C22 | 1 | 4 | yes | — |
| 14 | #72225160 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #72225158 | C22 | 1 | 4 | yes | — |
| 16 | #72225138 | C22 | 1 | 1 | yes | characteristic |
| 17 | #72225132 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #72225131 | C22 | 1 | 4 | yes | — |
| 19 | #72225126 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#7333 | C22 | 1 | 2 | yes | — |
| 21 | C4×#7333 | C22 | 1 | 2 | yes | — |
| 22 | #72216341 | C2 | 1 | 1 | yes | maximal, characteristic |
| 23 | #72216324 | C4 | 1 | 4 | yes | — |
| 24 | C2×AGL(1,ℤ/32) | — | 2 | 8 | no | — |
| 25 | #72216315 | C22 | 1 | 4 | yes | — |
| 26 | #72216298 | C4 | 1 | 1 | yes | characteristic |
| 27 | #72216290 | C4 | 1 | 1 | yes | characteristic |
| 28 | #72216288 | C4 | 1 | 1 | yes | characteristic |
| 29 | #72216275 | C4 | 1 | 1 | yes | characteristic |
| 30 | #72216249 | C22 | 1 | 1 | yes | characteristic |
| 31 | C8×#1398 | C22 | 1 | 1 | yes | characteristic |
| 32 | #72216176 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 33 | #72216174 | — | 2 | 1 | no | — |
| 34 | #72216174 | C22 | 1 | 2 | yes | — |
| 35 | #72216172 | — | 2 | 1 | no | — |
| 36 | #72216172 | C22 | 1 | 2 | yes | — |
| 37 | #72216171 | — | 2 | 1 | no | — |
| 38 | #72216170 | — | 2 | 1 | no | — |
| 39 | #72216168 | C22 | 1 | 1 | yes | characteristic |
| 40 | #72216165 | C22 | 1 | 1 | yes | characteristic |
| 41 | #72216161 | C22 | 1 | 1 | yes | characteristic |
| 42 | #513051 | C2×C4 | 1 | 4 | yes | — |
| 43 | C2×#13658 | — | 2 | 8 | no | — |
| 44 | #496112 | — | 2 | 1 | no | — |
| 45 | #496112 | C23 | 1 | 2 | yes | — |
| 46 | #496104 | — | 2 | 1 | no | — |
| 47 | #496104 | C23 | 1 | 2 | yes | — |
| 48 | #496092 | — | 2 | 2 | no | — |
| 49 | #491465 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×#12515 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#12068 | — | 2 | 4 | no | — |
| 52 | C2×#12068 | — | 4 | 2 | no | — |
| 53 | C2×#12067 | — | 2 | 4 | no | — |
| 54 | C2×#12067 | — | 4 | 2 | no | — |
| 55 | #483583 | — | 4 | 2 | no | — |
| 56 | #213237 | — | 2 | 1 | no | — |
| 57 | C4×#1712 | — | 2 | 1 | no | — |
| 58 | #212800 | — | 2 | 2 | no | — |
| 59 | #212800 | — | 4 | 2 | no | — |
| 60 | #152984 | — | 2 | 8 | no | — |
| 61 | #152899 | C2×C4 | 1 | 4 | yes | — |
| 62 | #152896 | C2×C4 | 1 | 4 | yes | — |
| 63 | #152407 | C2×C4 | 1 | 4 | yes | — |
| 64 | C4×#1398 | C23 | 1 | 2 | yes | — |
| 65 | C4×#1398 | C23 | 1 | 2 | yes | — |
| 66 | #151728 | C8 | 1 | 4 | yes | complemented |
| 67 | #151726 | C8 | 1 | 2 | yes | complemented |
| 68 | #151724 | C8 | 1 | 2 | yes | complemented |
| 69 | AGL(1,ℤ/32) | — | 4 | 32 | no | — |
| 70 | C2×#7457 | — | 2 | 8 | no | — |
| 71 | C2×#7390 | — | 2 | 8 | no | — |
| 72 | C2×#7389 | — | 2 | 8 | no | — |
| 73 | C2×#7333 | — | 2 | 4 | no | — |
| 74 | C2×#7333 | D4 | 1 | 8 | yes | — |
| 75 | #149502 | — | 2 | 1 | no | — |
| 76 | #149499 | — | 2 | 1 | no | — |
| 77 | #149495 | C2×C4 | 1 | 2 | yes | — |
| 78 | C8×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C8×M64 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | #141684 | — | 2 | 1 | no | — |
| 81 | #141684 | C2×C4 | 1 | 2 | yes | — |
| 82 | #141681 | — | 2 | 1 | no | — |
| 83 | #141681 | C2×C4 | 1 | 2 | yes | — |
| 84 | #141671 | — | 2 | 1 | no | — |
| 85 | #141665 | — | 2 | 1 | no | — |
| 86 | #140753 | — | 2 | 4 | no | — |
| 87 | #140753 | — | 4 | 2 | no | — |
| 88 | #140751 | — | 2 | 4 | no | — |
| 89 | #140751 | — | 4 | 2 | no | — |
| 90 | #140743 | — | 4 | 2 | no | — |
| 91 | #140533 | — | 2 | 2 | no | — |
| 92 | #140533 | — | 2 | 2 | no | — |
| 93 | #140526 | — | 2 | 2 | no | — |
| 94 | #140526 | — | 2 | 2 | no | — |
| 95 | #140516 | — | 2 | 2 | no | — |
| 96 | #135781 | C2×C4 | 1 | 1 | yes | characteristic |
| 97 | #135778 | C2×C4 | 1 | 1 | yes | characteristic |
| 98 | #135718 | — | 2 | 1 | no | — |
| 99 | #135718 | C23 | 1 | 2 | yes | — |
| 100 | #135715 | — | 2 | 1 | no | — |
| 101 | #135715 | C23 | 1 | 2 | yes | — |
| 102 | #135713 | — | 2 | 1 | no | — |
| 103 | C4×#1313 | D4 | 1 | 1 | yes | characteristic |
| 104 | C4×#1313 | D4 | 1 | 1 | yes | characteristic |
| 105 | C4×#1313 | C23 | 1 | 1 | yes | characteristic |
| 106 | C4×#1313 | C23 | 1 | 1 | yes | characteristic |
| 107 | #126522 | D4 | 1 | 1 | yes | characteristic |
| 108 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 109 | #102117 | — | 2 | 2 | no | — |
| 110 | #102117 | — | 4 | 2 | no | — |
| 111 | #99295 | — | 2 | 1 | no | — |
| 112 | #94857 | D4 | 1 | 1 | yes | characteristic |
| 113 | C2×#2263 | — | 2 | 8 | no | — |
| 114 | #33713 | — | 2 | 1 | no | — |
| 115 | #33713 | C22×C4 | 1 | 2 | yes | — |
| 116 | C2×#2246 | — | 2 | 1 | no | — |
| 117 | C2×#2246 | C22×C4 | 1 | 2 | yes | — |
| 118 | C2×#2179 | — | 2 | 4 | no | — |
| 119 | C2×#2179 | — | 4 | 2 | no | — |
| 120 | C2×#2177 | — | 2 | 4 | no | — |
| 121 | C2×#2177 | — | 4 | 2 | no | — |
| 122 | C2×#2171 | — | 4 | 2 | no | — |
| 123 | C2×#2171 | — | 4 | 2 | no | — |
| 124 | #33434 | — | 4 | 2 | no | — |
| 125 | #21705 | — | 2 | 2 | no | — |
| 126 | C4×#493 | — | 2 | 2 | no | — |
| 127 | C4×#493 | — | 4 | 2 | no | — |
| 128 | C8×#127 | — | 4 | 2 | no | — |
| 129 | #19603 | — | 2 | 1 | no | — |
| 130 | C2×#1712 | — | 2 | 1 | no | — |
| 131 | #17956 | — | 4 | 2 | no | — |
| 132 | C2×#1580 | — | 4 | 2 | no | — |
| 133 | C2×#1580 | — | 4 | 2 | no | — |
| 134 | C2×#1580 | — | 8 | 4 | no | — |
| 135 | #13729 | — | 2 | 8 | no | — |
| 136 | #13727 | C2×C8 | 1 | 8 | yes | complemented |
| 137 | #13725 | C2×C8 | 1 | 8 | yes | complemented |
| 138 | #13658 | — | 4 | 16 | no | — |
| 139 | #13658 | — | 4 | 16 | no | — |
| 140 | C2×#1426 | — | 2 | 8 | no | — |
| 141 | C2×#1419 | — | 2 | 8 | no | — |
| 142 | C2×#1418 | — | 2 | 8 | no | — |
| 143 | C2×#1398 | — | 2 | 2 | no | — |
| 144 | C2×#1398 | C2×D4 | 1 | 4 | yes | — |
| 145 | C2×#1398 | C2×D4 | 1 | 4 | yes | — |
| 146 | C2×#1398 | #41 | 1 | 4 | yes | — |
| 147 | C4×M64 | — | 2 | 2 | no | — |
| 148 | C4×M64 | C22×C4 | 1 | 2 | yes | — |
| 149 | C4×M64 | C22×C4 | 1 | 2 | yes | — |
| 150 | #13242 | — | 2 | 4 | no | — |
| 151 | #13242 | — | 4 | 2 | no | — |
| 152 | #13239 | — | 2 | 4 | no | — |
| 153 | #13239 | — | 4 | 2 | no | — |
| 154 | #13208 | — | 2 | 2 | no | — |
| 155 | #13208 | — | 2 | 2 | no | — |
| 156 | #13202 | — | 2 | 2 | no | — |
| 157 | #13202 | — | 2 | 2 | no | — |
| 158 | #13196 | — | 4 | 2 | no | — |
| 159 | #13196 | — | 4 | 2 | no | — |
| 160 | #13191 | — | 4 | 2 | no | — |
| 161 | #12909 | — | 2 | 1 | no | — |
| 162 | #12909 | C22×C4 | 1 | 2 | yes | — |
| 163 | #12906 | — | 2 | 1 | no | — |
| 164 | #12906 | C22×C4 | 1 | 2 | yes | — |
| 165 | #12900 | — | 2 | 2 | no | — |
| 166 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C4×#346 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C4×#346 | C24 | 1 | 1 | yes | characteristic |
| 170 | #12518 | — | 2 | 1 | no | — |
| 171 | #12518 | C2×C8 | 1 | 2 | yes | complemented |
| 172 | #12517 | — | 2 | 1 | no | — |
| 173 | #12516 | C2×C8 | 1 | 1 | yes | characteristic, complemented |
| 174 | #12515 | — | 2 | 1 | no | — |
| 175 | #12515 | — | 2 | 1 | no | — |
| 176 | #12515 | C2×C8 | 1 | 2 | yes | — |
| 177 | #12515 | C2×C8 | 1 | 2 | yes | — |
| 178 | #12515 | C2×C8 | 1 | 1 | yes | characteristic, complemented |
| 179 | #12068 | — | 4 | 16 | no | — |
| 180 | #12068 | — | 8 | 8 | no | — |
| 181 | #12067 | — | 4 | 16 | no | — |
| 182 | #12067 | — | 8 | 8 | no | — |
| 183 | #12064 | — | 8 | 4 | no | — |
| 184 | #12062 | — | 8 | 4 | no | — |
| 185 | C2×#1369 | — | 2 | 4 | no | — |
| 186 | C2×#1369 | — | 4 | 2 | no | — |
| 187 | C2×#1368 | — | 2 | 4 | no | — |
| 188 | C2×#1368 | — | 4 | 2 | no | — |
| 189 | #11996 | — | 4 | 2 | no | — |
| 190 | C2×#1336 | — | 4 | 4 | no | — |
| 191 | C2×#1336 | — | 4 | 4 | no | — |
| 192 | C2×#1333 | — | 4 | 4 | no | — |
| 193 | C2×#1333 | — | 4 | 4 | no | — |
| 194 | #11584 | — | 4 | 4 | no | — |
| 195 | C2×#1313 | — | 2 | 2 | no | — |
| 196 | C2×#1313 | — | 2 | 2 | no | — |
| 197 | C2×#1313 | — | 2 | 2 | no | — |
| 198 | C2×#1313 | C2×D4 | 1 | 4 | yes | — |
| 199 | C2×#1312 | — | 2 | 2 | no | — |
| 200 | C2×#1311 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | C2×#1311 | #41 | 1 | 1 | yes | characteristic |
| 202 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 203 | C2×C8×C16 | #41 | 1 | 1 | yes | characteristic |
| 204 | #9856 | — | 2 | 2 | no | — |
| 205 | #9844 | — | 4 | 2 | no | — |
| 206 | #9824 | — | 2 | 2 | no | — |
| 207 | #9824 | — | 4 | 2 | no | — |
| 208 | #9659 | — | 4 | 2 | no | — |
| 209 | #9659 | — | 4 | 2 | no | — |
| 210 | #9659 | — | 8 | 4 | no | — |
| 211 | #9638 | — | 4 | 2 | no | — |
| 212 | #9638 | — | 4 | 4 | no | — |
| 213 | #8823 | — | 2 | 1 | no | — |
| 214 | #8818 | — | 2 | 1 | no | — |
| 215 | #8805 | — | 2 | 2 | no | — |
| 216 | #8805 | — | 4 | 2 | no | — |
| 217 | C4×#322 | — | 2 | 2 | no | — |
| 218 | C4×#322 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C4×#322 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C4×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | #7457 | — | 4 | 16 | no | — |
| 222 | #7390 | — | 4 | 16 | no | — |
| 223 | #7389 | — | 4 | 16 | no | — |
| 224 | #7333 | — | 2 | 16 | no | — |
| 225 | #7333 | — | 4 | 8 | no | — |
| 226 | #7332 | — | 4 | 2 | no | — |
| 227 | #7331 | — | 4 | 2 | no | — |
| 228 | #7330 | — | 2 | 4 | no | — |
| 229 | #7329 | — | 2 | 1 | no | — |
| 230 | #7329 | C2×C8 | 1 | 2 | yes | complemented |
| 231 | C8×C32 | — | 2 | 1 | no | — |
| 232 | C8×C32 | C2×C8 | 1 | 2 | yes | complemented |
| 233 | C2×#508 | — | 2 | 4 | no | — |
| 234 | C2×#508 | — | 4 | 2 | no | — |
| 235 | C22×D16 | — | 2 | 4 | no | — |
| 236 | C22×D16 | — | 4 | 2 | no | — |
| 237 | C2×#504 | — | 8 | 2 | no | — |
| 238 | #3169 | — | 4 | 2 | no | — |
| 239 | #3147 | — | 2 | 2 | no | — |
| 240 | C2×#493 | — | 2 | 2 | no | — |
| 241 | C2×#493 | — | 4 | 2 | no | — |
| 242 | C2×#443 | — | 4 | 2 | no | — |
| 243 | C2×#443 | — | 4 | 2 | no | — |
| 244 | C2×C4×D8 | — | 4 | 2 | no | — |
| 245 | C2×C4×D8 | — | 4 | 2 | no | — |
| 246 | C2×C4×D8 | — | 8 | 4 | no | — |
| 247 | #2931 | — | 4 | 2 | no | — |
| 248 | C2×C8×D4 | — | 8 | 2 | no | — |
| 249 | C2×C8×D4 | — | 8 | 4 | no | — |
| 250 | C4×#127 | — | 4 | 2 | no | — |
| 251 | #2263 | — | 4 | 16 | no | — |
| 252 | #2263 | — | 4 | 16 | no | — |
| 253 | C2×SD64 | — | 2 | 16 | no | — |
| 254 | C2×D32 | — | 2 | 16 | no | — |
| 255 | C2×M64 | — | 2 | 4 | no | — |
| 256 | C2×M64 | C4×D4 | 1 | 4 | yes | — |
| 257 | C2×M64 | C4×D4 | 1 | 4 | yes | — |
| 258 | #2249 | — | 2 | 4 | no | — |
| 259 | #2249 | — | 4 | 2 | no | — |
| 260 | #2248 | — | 2 | 2 | no | — |
| 261 | #2248 | — | 2 | 2 | no | — |
| 262 | #2247 | — | 2 | 1 | no | — |
| 263 | #2247 | C22×C8 | 1 | 2 | yes | — |
| 264 | #2246 | — | 2 | 2 | no | — |
| 265 | #2246 | — | 2 | 4 | no | — |
| 266 | #2246 | — | 2 | 2 | no | — |
| 267 | #2246 | — | 2 | 2 | no | — |
| 268 | #2246 | — | 2 | 1 | no | — |
| 269 | #2246 | — | 4 | 2 | no | — |
| 270 | #2246 | C22×C8 | 1 | 2 | yes | — |
| 271 | #2246 | C22×C8 | 1 | 4 | yes | — |
| 272 | #2179 | — | 4 | 8 | no | — |
| 273 | #2179 | — | 4 | 8 | no | — |
| 274 | #2179 | — | 8 | 4 | no | — |
| 275 | #2179 | — | 8 | 4 | no | — |
| 276 | #2177 | — | 4 | 8 | no | — |
| 277 | #2177 | — | 4 | 8 | no | — |
| 278 | #2177 | — | 8 | 4 | no | — |
| 279 | #2177 | — | 8 | 4 | no | — |
| 280 | #2171 | — | 8 | 8 | no | — |
| 281 | #2171 | — | 8 | 8 | no | — |
| 282 | #2169 | — | 8 | 4 | no | — |
| 283 | D4×C16 | — | 8 | 4 | no | — |
| 284 | C2×#368 | — | 2 | 4 | no | — |
| 285 | C2×#368 | — | 4 | 2 | no | — |
| 286 | C2×#367 | — | 2 | 4 | no | — |
| 287 | C2×#367 | — | 4 | 2 | no | — |
| 288 | C2×#364 | — | 4 | 2 | no | — |
| 289 | C2×#364 | — | 4 | 2 | no | — |
| 290 | #2150 | — | 4 | 2 | no | — |
| 291 | C2×#359 | — | 4 | 4 | no | — |
| 292 | C2×#359 | — | 4 | 4 | no | — |
| 293 | C2×#357 | — | 4 | 4 | no | — |
| 294 | C2×#357 | — | 4 | 4 | no | — |
| 295 | C2×#350 | — | 8 | 2 | no | — |
| 296 | C2×#350 | — | 8 | 2 | no | — |
| 297 | #2113 | — | 8 | 2 | no | — |
| 298 | C2×#346 | — | 2 | 1 | no | — |
| 299 | C2×#346 | — | 2 | 1 | no | — |
| 300 | C2×#346 | — | 2 | 1 | no | — |
| 301 | C2×#346 | #127 | 1 | 2 | yes | — |
| 302 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 303 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 304 | C2×#346 | C22×D4 | 1 | 2 | yes | — |
| 305 | C2×#346 | C2×#41 | 1 | 2 | yes | — |
| 306 | C2×C4×C16 | — | 2 | 1 | no | — |
| 307 | C2×C4×C16 | — | 2 | 1 | no | — |
| 308 | C2×C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 309 | C2×C4×C16 | C4×D4 | 1 | 1 | yes | characteristic |
| 310 | C2×C4×C16 | C23×C4 | 1 | 1 | yes | characteristic |
| 311 | C2×C4×C16 | C2×#41 | 1 | 1 | yes | characteristic |
| 312 | #1974 | — | 4 | 2 | no | — |
| 313 | #1974 | — | 4 | 2 | no | — |
| 314 | #1970 | — | 4 | 2 | no | — |
| 315 | #1970 | — | 4 | 2 | no | — |
| 316 | #1970 | — | 8 | 4 | no | — |
| 317 | #1962 | — | 4 | 2 | no | — |
| 318 | #1957 | — | 4 | 2 | no | — |
| 319 | #1957 | — | 4 | 4 | no | — |
| 320 | #1954 | — | 8 | 2 | no | — |
| 321 | #1954 | — | 8 | 4 | no | — |
| 322 | #1848 | — | 2 | 2 | no | — |
| 323 | #1845 | — | 2 | 2 | no | — |
| 324 | #1845 | — | 4 | 2 | no | — |
| 325 | #1842 | — | 4 | 2 | no | — |
| 326 | C42×C8 | — | 2 | 1 | no | — |
| 327 | C42×C8 | — | 2 | 1 | no | — |
| 328 | C42×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 329 | C42×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | #1713 | — | 2 | 1 | no | — |
| 331 | #1712 | — | 2 | 2 | no | — |
| 332 | #1712 | — | 2 | 2 | no | — |
| 333 | #1712 | — | 2 | 1 | no | — |
| 334 | #1712 | — | 4 | 2 | no | — |
| 335 | #1709 | — | 2 | 2 | no | — |
| 336 | #1706 | — | 4 | 2 | no | — |
| 337 | #1589 | — | 8 | 4 | no | — |
| 338 | #1580 | — | 8 | 8 | no | — |
| 339 | #1580 | — | 8 | 8 | no | — |
| 340 | #1580 | — | 16 | 16 | no | — |
| 341 | C8×D8 | — | 8 | 4 | no | — |
| 342 | #1567 | — | 4 | 2 | no | — |
| 343 | C2×#334 | — | 4 | 2 | no | — |
| 344 | C2×#334 | — | 4 | 2 | no | — |
| 345 | C2×#334 | — | 8 | 4 | no | — |
| 346 | #1492 | — | 4 | 4 | no | — |
| 347 | C2×D4⋊C8 | — | 8 | 2 | no | — |
| 348 | C2×D4⋊C8 | — | 8 | 2 | no | — |
| 349 | C2×D4⋊C8 | — | 8 | 8 | no | — |
| 350 | C2×#322 | — | 2 | 1 | no | — |
| 351 | C2×#322 | — | 2 | 1 | no | — |
| 352 | C2×#322 | — | 2 | 1 | no | — |
| 353 | C2×#322 | — | 4 | 4 | no | — |
| 354 | C2×#322 | #127 | 1 | 2 | yes | — |
| 355 | C2×C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 356 | C2×C82 | C4×D4 | 1 | 1 | yes | characteristic |
| 357 | C2×C82 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 358 | #1426 | — | 4 | 16 | no | — |
| 359 | #1419 | — | 4 | 16 | no | — |
| 360 | #1418 | — | 4 | 16 | no | — |
| 361 | #1398 | — | 2 | 8 | no | — |
| 362 | #1398 | — | 2 | 8 | no | — |
| 363 | #1398 | — | 4 | 4 | no | — |
| 364 | #1398 | AGL(1,ℤ/8) | 1 | 16 | yes | — |
| 365 | #1397 | — | 2 | 2 | no | — |
| 366 | #1397 | — | 4 | 2 | no | — |
| 367 | #1397 | #131 | 1 | 4 | yes | — |
| 368 | C4×C32 | — | 2 | 2 | no | — |
| 369 | C4×C32 | — | 4 | 2 | no | — |
| 370 | C4×C32 | C22×C8 | 1 | 4 | yes | — |
| 371 | #1369 | — | 4 | 8 | no | — |
| 372 | #1369 | — | 8 | 4 | no | — |
| 373 | #1368 | — | 4 | 8 | no | — |
| 374 | #1368 | — | 8 | 4 | no | — |
| 375 | #1367 | — | 8 | 4 | no | — |
| 376 | #1336 | — | 8 | 8 | no | — |
| 377 | #1336 | — | 8 | 8 | no | — |
| 378 | #1333 | — | 8 | 8 | no | — |
| 379 | #1333 | — | 8 | 8 | no | — |
| 380 | D4⋊C16 | — | 8 | 8 | no | — |
| 381 | #1313 | — | 2 | 8 | no | — |
| 382 | #1313 | — | 4 | 4 | no | — |
| 383 | #1313 | — | 4 | 4 | no | — |
| 384 | #1313 | — | 4 | 4 | no | — |
| 385 | #1312 | — | 4 | 4 | no | — |
| 386 | #1311 | — | 2 | 2 | no | — |
| 387 | #1311 | — | 2 | 2 | no | — |
| 388 | C8×C16 | — | 2 | 2 | no | — |
| 389 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 390 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 391 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 392 | C8×C16 | #131 | 1 | 1 | yes | characteristic |
| 393 | C2×#135 | — | 4 | 2 | no | — |
| 394 | C2×#135 | — | 4 | 2 | no | — |
| 395 | C22×D8 | — | 4 | 2 | no | — |
| 396 | C22×D8 | — | 4 | 2 | no | — |
| 397 | C22×D8 | — | 8 | 4 | no | — |
| 398 | C2×#131 | — | 8 | 2 | no | — |
| 399 | C23×C8 | — | 16 | 2 | no | — |
| 400 | #532 | — | 4 | 2 | no | — |
| 401 | C2×#127 | — | 4 | 2 | no | — |
| 402 | C2×C4×D4 | — | 8 | 4 | no | — |
| 403 | C2×C4×D4 | — | 8 | 2 | no | — |
| 404 | #508 | — | 4 | 8 | no | — |
| 405 | #508 | — | 4 | 8 | no | — |
| 406 | #508 | — | 8 | 4 | no | — |
| 407 | #508 | — | 8 | 4 | no | — |
| 408 | C2×Q32 | — | 2 | 4 | no | — |
| 409 | C2×Q32 | — | 4 | 2 | no | — |
| 410 | C2×SD32 | — | 4 | 4 | no | — |
| 411 | C2×SD32 | — | 4 | 4 | no | — |
| 412 | C2×D16 | — | 2 | 8 | no | — |
| 413 | C2×D16 | — | 2 | 4 | no | — |
| 414 | C2×D16 | — | 4 | 4 | no | — |
| 415 | C2×D16 | — | 4 | 4 | no | — |
| 416 | C2×D16 | — | 4 | 2 | no | — |
| 417 | C2×D16 | — | 4 | 4 | no | — |
| 418 | C2×D16 | — | 4 | 8 | no | — |
| 419 | C2×D16 | — | 4 | 8 | no | — |
| 420 | C2×D16 | — | 8 | 4 | no | — |
| 421 | C2×D16 | — | 8 | 4 | no | — |
| 422 | #504 | — | 16 | 4 | no | — |
| 423 | #504 | — | 16 | 4 | no | — |
| 424 | C2×M32 | — | 8 | 2 | no | — |
| 425 | C2×M32 | — | 16 | 2 | no | — |
| 426 | C22×C16 | — | 2 | 2 | no | — |
| 427 | C22×C16 | — | 4 | 1 | no | — |
| 428 | C22×C16 | — | 16 | 2 | no | — |
| 429 | C22×C16 | #442 | 1 | 2 | yes | — |
| 430 | C22×C16 | #442 | 1 | 2 | yes | — |
| 431 | C22×C16 | C2×C4×D4 | 1 | 2 | yes | — |
| 432 | C22×C16 | #532 | 1 | 2 | yes | — |
| 433 | #500 | — | 4 | 2 | no | — |
| 434 | #495 | — | 4 | 2 | no | — |
| 435 | #495 | — | 4 | 2 | no | — |
| 436 | #494 | — | 2 | 2 | no | — |
| 437 | #493 | — | 2 | 4 | no | — |
| 438 | #493 | — | 2 | 2 | no | — |
| 439 | #493 | — | 4 | 4 | no | — |
| 440 | #493 | — | 4 | 4 | no | — |
| 441 | #493 | — | 4 | 2 | no | — |
| 442 | #493 | — | 4 | 2 | no | — |
| 443 | #493 | — | 4 | 2 | no | — |
| 444 | #493 | — | 4 | 2 | no | — |
| 445 | #493 | — | 8 | 4 | no | — |
| 446 | #492 | — | 4 | 2 | no | — |
| 447 | #486 | — | 4 | 4 | no | — |
| 448 | #466 | — | 8 | 4 | no | — |
| 449 | #443 | — | 8 | 4 | no | — |
| 450 | #443 | — | 8 | 4 | no | — |
| 451 | #443 | — | 8 | 4 | no | — |
| 452 | #443 | — | 8 | 4 | no | — |
| 453 | C4×D8 | — | 8 | 4 | no | — |
| 454 | C4×D8 | — | 8 | 4 | no | — |
| 455 | C4×D8 | — | 8 | 4 | no | — |
| 456 | C4×D8 | — | 8 | 4 | no | — |
| 457 | C4×D8 | — | 8 | 4 | no | — |
| 458 | C4×D8 | — | 16 | 8 | no | — |
| 459 | C4×D8 | — | 16 | 8 | no | — |
| 460 | #436 | — | 8 | 4 | no | — |
| 461 | C8×D4 | — | 8 | 4 | no | — |
| 462 | C8×D4 | — | 16 | 4 | no | — |
| 463 | C8×D4 | — | 16 | 4 | no | — |
| 464 | C8×D4 | — | 16 | 16 | no | — |
| 465 | C2×#108 | — | 4 | 2 | no | — |
| 466 | C2×#108 | — | 4 | 2 | no | — |
| 467 | C2×#107 | — | 4 | 2 | no | — |
| 468 | C2×#107 | — | 4 | 2 | no | — |
| 469 | C2×#107 | — | 8 | 4 | no | — |
| 470 | #423 | — | 4 | 2 | no | — |
| 471 | C2×C4⋊C8 | — | 8 | 4 | no | — |
| 472 | C2×C4⋊C8 | — | 8 | 2 | no | — |
| 473 | C2×#104 | — | 8 | 2 | no | — |
| 474 | C2×#104 | — | 8 | 2 | no | — |
| 475 | C2×#102 | — | 8 | 8 | no | — |
| 476 | C2×#102 | — | 8 | 2 | no | — |
| 477 | C2×#102 | — | 8 | 2 | no | — |
| 478 | #408 | — | 8 | 2 | no | — |
| 479 | C2×C22⋊C8 | — | 16 | 2 | no | — |
| 480 | C2×C22⋊C8 | — | 16 | 4 | no | — |
| 481 | C2×C4×C8 | — | 2 | 4 | no | — |
| 482 | C2×C4×C8 | — | 2 | 2 | no | — |
| 483 | C2×C4×C8 | — | 4 | 2 | no | — |
| 484 | C2×C4×C8 | — | 4 | 2 | no | — |
| 485 | C2×C4×C8 | — | 4 | 1 | no | — |
| 486 | C2×C4×C8 | #442 | 1 | 2 | yes | — |
| 487 | C2×C4×C8 | #442 | 1 | 2 | yes | — |
| 488 | C2×C4×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 489 | C2×C4×C8 | C2×#127 | 1 | 1 | yes | characteristic |
| 490 | C2×C4×C8 | #532 | 1 | 1 | yes | characteristic |
| 491 | C2×C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 492 | C2×C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 493 | C2×C4×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 494 | #390 | — | 8 | 4 | no | — |
| 495 | #390 | — | 8 | 2 | no | — |
| 496 | #384 | — | 4 | 2 | no | — |
| 497 | C43 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 498 | SD64 | — | 4 | 32 | no | — |
| 499 | D32 | — | 4 | 32 | no | — |
| 500 | M64 | — | 2 | 4 | no | — |
| 501 | M64 | — | 4 | 4 | no | — |
| 502 | M64 | — | 4 | 4 | no | — |
| 503 | M64 | #442 | 1 | 8 | yes | — |
| 504 | M64 | #442 | 1 | 8 | yes | — |
| 505 | M64 | #444 | 1 | 8 | yes | — |
| 506 | C2×C32 | — | 2 | 4 | no | — |
| 507 | C2×C32 | — | 4 | 4 | no | — |
| 508 | C2×C32 | C8×D4 | 1 | 8 | yes | — |
| 509 | #368 | — | 4 | 8 | no | — |
| 510 | #368 | — | 8 | 4 | no | — |
| 511 | #367 | — | 4 | 8 | no | — |
| 512 | #367 | — | 8 | 4 | no | — |
| 513 | #364 | — | 8 | 4 | no | — |
| 514 | #364 | — | 8 | 4 | no | — |
| 515 | C4⋊C16 | — | 8 | 4 | no | — |
| 516 | #359 | — | 8 | 8 | no | — |
| 517 | #359 | — | 8 | 8 | no | — |
| 518 | #357 | — | 8 | 8 | no | — |
| 519 | #357 | — | 8 | 8 | no | — |
| 520 | #350 | — | 16 | 4 | no | — |
| 521 | #350 | — | 16 | 4 | no | — |
| 522 | C22⋊C16 | — | 16 | 4 | no | — |
| 523 | #346 | — | 2 | 4 | no | — |
| 524 | #346 | — | 2 | 4 | no | — |
| 525 | #346 | — | 2 | 4 | no | — |
| 526 | #346 | — | 2 | 4 | no | — |
| 527 | #346 | — | 4 | 2 | no | — |
| 528 | #346 | — | 4 | 2 | no | — |
| 529 | #346 | — | 4 | 2 | no | — |
| 530 | #346 | C2×AGL(1,ℤ/8) | 1 | 8 | yes | — |
| 531 | C4×C16 | — | 2 | 1 | no | — |
| 532 | C4×C16 | — | 2 | 1 | no | — |
| 533 | C4×C16 | — | 2 | 1 | no | — |
| 534 | C4×C16 | — | 2 | 1 | no | — |
| 535 | C4×C16 | — | 4 | 2 | no | — |
| 536 | C4×C16 | — | 4 | 2 | no | — |
| 537 | C4×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 538 | C4×C16 | C8×D4 | 1 | 1 | yes | characteristic |
| 539 | C4×C16 | #444 | 1 | 2 | yes | — |
| 540 | C4×C16 | C23×C8 | 1 | 1 | yes | characteristic |
| 541 | C4×C16 | C2×#131 | 1 | 1 | yes | characteristic |
| 542 | C4×C16 | C2×#131 | 1 | 2 | yes | — |
| 543 | #335 | — | 8 | 4 | no | — |
| 544 | #334 | — | 8 | 4 | no | — |
| 545 | #334 | — | 8 | 4 | no | — |
| 546 | #334 | — | 16 | 8 | no | — |
| 547 | D4⋊C8 | — | 8 | 8 | no | — |
| 548 | D4⋊C8 | — | 16 | 4 | no | — |
| 549 | D4⋊C8 | — | 16 | 4 | no | — |
| 550 | D4⋊C8 | — | 16 | 16 | no | — |
| 551 | #322 | — | 2 | 4 | no | — |
| 552 | #322 | — | 4 | 2 | no | — |
| 553 | #322 | — | 4 | 2 | no | — |
| 554 | #322 | — | 4 | 2 | no | — |
| 555 | #322 | — | 8 | 8 | no | — |
| 556 | C82 | — | 2 | 1 | no | — |
| 557 | C82 | — | 2 | 4 | no | — |
| 558 | C82 | — | 2 | 1 | no | — |
| 559 | C82 | C8×D4 | 1 | 1 | yes | characteristic |
| 560 | C82 | C8×D4 | 1 | 1 | yes | characteristic |
| 561 | C82 | #444 | 1 | 2 | yes | — |
| 562 | C2×#41 | — | 8 | 2 | no | — |
| 563 | C22×D4 | — | 8 | 2 | no | — |
| 564 | C22×D4 | — | 8 | 4 | no | — |
| 565 | C23×C4 | — | 16 | 2 | no | — |
| 566 | #135 | — | 8 | 4 | no | — |
| 567 | #135 | — | 8 | 4 | no | — |
| 568 | #135 | — | 8 | 4 | no | — |
| 569 | #135 | — | 8 | 4 | no | — |
| 570 | C2×Q16 | — | 4 | 2 | no | — |
| 571 | C2×Q16 | — | 4 | 2 | no | — |
| 572 | C2×SD16 | — | 8 | 2 | no | — |
| 573 | C2×SD16 | — | 8 | 2 | no | — |
| 574 | C2×D8 | — | 4 | 4 | no | — |
| 575 | C2×D8 | — | 4 | 2 | no | — |
| 576 | C2×D8 | — | 4 | 4 | no | — |
| 577 | C2×D8 | — | 4 | 2 | no | — |
| 578 | C2×D8 | — | 8 | 8 | no | — |
| 579 | C2×D8 | — | 8 | 8 | no | — |
| 580 | C2×D8 | — | 8 | 4 | no | — |
| 581 | C2×D8 | — | 8 | 2 | no | — |
| 582 | C2×D8 | — | 8 | 4 | no | — |
| 583 | C2×D8 | — | 8 | 4 | no | — |
| 584 | C2×D8 | — | 8 | 4 | no | — |
| 585 | C2×D8 | — | 8 | 4 | no | — |
| 586 | C2×D8 | — | 8 | 2 | no | — |
| 587 | C2×D8 | — | 16 | 8 | no | — |
| 588 | C2×D8 | — | 16 | 8 | no | — |
| 589 | #131 | — | 16 | 2 | no | — |
| 590 | #131 | — | 16 | 2 | no | — |
| 591 | #131 | — | 16 | 2 | no | — |
| 592 | #131 | — | 16 | 2 | no | — |
| 593 | C2×M16 | — | 8 | 2 | no | — |
| 594 | C2×M16 | — | 16 | 2 | no | — |
| 595 | C22×C8 | — | 2 | 2 | no | — |
| 596 | C22×C8 | — | 4 | 2 | no | — |
| 597 | C22×C8 | — | 8 | 1 | no | — |
| 598 | C22×C8 | — | 16 | 2 | no | — |
| 599 | C22×C8 | — | 16 | 2 | no | — |
| 600 | C22×C8 | — | 32 | 4 | no | — |
| 601 | C22×C8 | — | 32 | 8 | no | — |
| 602 | C22×C8 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 603 | C22×C8 | C4×#127 | 1 | 1 | yes | characteristic |
| 604 | C22×C8 | C2×#442 | 1 | 1 | yes | characteristic |
| 605 | C22×C8 | #3151 | 1 | 1 | yes | characteristic |
| 606 | C22×C8 | #3184 | 1 | 1 | yes | characteristic |
| 607 | C4⋊Q8 | — | 4 | 2 | no | — |
| 608 | #127 | — | 4 | 4 | no | — |
| 609 | #127 | — | 4 | 2 | no | — |
| 610 | #127 | — | 8 | 2 | no | — |
| 611 | #127 | — | 8 | 4 | no | — |
| 612 | #124 | — | 8 | 2 | no | — |
| 613 | #121 | — | 8 | 4 | no | — |
| 614 | C4×D4 | — | 8 | 4 | no | — |
| 615 | C4×D4 | — | 16 | 2 | no | — |
| 616 | C4×D4 | — | 16 | 2 | no | — |
| 617 | C4×D4 | — | 16 | 8 | no | — |
| 618 | C4×D4 | — | 16 | 8 | no | — |
| 619 | C4×D4 | — | 16 | 2 | no | — |
| 620 | C4×D4 | — | 16 | 2 | no | — |
| 621 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 622 | C2×C4⋊C4 | — | 8 | 4 | no | — |
| 623 | C2×C22⋊C4 | — | 16 | 2 | no | — |
| 624 | C2×C22⋊C4 | — | 16 | 4 | no | — |
| 625 | C2×C42 | — | 2 | 2 | no | — |
| 626 | C2×C42 | C2×#442 | 1 | 1 | yes | characteristic |
| 627 | C2×C42 | #3151 | 1 | 1 | yes | characteristic |
| 628 | C2×C42 | #3184 | 1 | 1 | yes | characteristic |
| 629 | Q32 | — | 4 | 8 | no | — |
| 630 | Q32 | — | 8 | 4 | no | — |
| 631 | SD32 | — | 8 | 8 | no | — |
| 632 | SD32 | — | 8 | 8 | no | — |
| 633 | D16 | — | 4 | 8 | no | — |
| 634 | D16 | — | 4 | 16 | no | — |
| 635 | D16 | — | 8 | 8 | no | — |
| 636 | D16 | — | 8 | 8 | no | — |
| 637 | D16 | — | 8 | 4 | no | — |
| 638 | D16 | — | 8 | 8 | no | — |
| 639 | M32 | — | 16 | 2 | no | — |
| 640 | M32 | — | 16 | 2 | no | — |
| 641 | M32 | — | 32 | 4 | no | — |
| 642 | C2×C16 | — | 2 | 2 | no | — |
| 643 | C2×C16 | — | 2 | 2 | no | — |
| 644 | C2×C16 | — | 2 | 2 | no | — |
| 645 | C2×C16 | — | 2 | 2 | no | — |
| 646 | C2×C16 | — | 2 | 2 | no | — |
| 647 | C2×C16 | — | 4 | 2 | no | — |
| 648 | C2×C16 | — | 4 | 2 | no | — |
| 649 | C2×C16 | — | 4 | 2 | no | — |
| 650 | C2×C16 | — | 8 | 1 | no | — |
| 651 | C2×C16 | — | 8 | 1 | no | — |
| 652 | C2×C16 | — | 8 | 1 | no | — |
| 653 | C2×C16 | — | 16 | 2 | no | — |
| 654 | C2×C16 | — | 32 | 4 | no | — |
| 655 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 656 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 657 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 658 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 659 | C2×C16 | C2×C8×D4 | 1 | 2 | yes | — |
| 660 | C2×C16 | #2931 | 1 | 2 | yes | — |
| 661 | C2×C16 | C2×#442 | 1 | 4 | yes | — |
| 662 | C2×C16 | C2×#444 | 1 | 4 | yes | — |
| 663 | C2×C16 | #3184 | 1 | 4 | yes | — |
| 664 | #108 | — | 8 | 4 | no | — |
| 665 | #108 | — | 8 | 4 | no | — |
| 666 | #107 | — | 8 | 4 | no | — |
| 667 | #107 | — | 8 | 4 | no | — |
| 668 | #107 | — | 8 | 4 | no | — |
| 669 | #107 | — | 16 | 8 | no | — |
| 670 | C4⋊C8 | — | 8 | 4 | no | — |
| 671 | C4⋊C8 | — | 16 | 2 | no | — |
| 672 | C4⋊C8 | — | 16 | 8 | no | — |
| 673 | C4⋊C8 | — | 16 | 2 | no | — |
| 674 | #104 | — | 16 | 4 | no | — |
| 675 | #104 | — | 16 | 4 | no | — |
| 676 | #102 | — | 8 | 8 | no | — |
| 677 | #102 | — | 16 | 4 | no | — |
| 678 | #102 | — | 16 | 16 | no | — |
| 679 | #102 | — | 16 | 4 | no | — |
| 680 | C22⋊C8 | — | 16 | 4 | no | — |
| 681 | C22⋊C8 | — | 32 | 4 | no | — |
| 682 | C22⋊C8 | — | 32 | 8 | no | — |
| 683 | C4×C8 | — | 2 | 2 | no | — |
| 684 | C4×C8 | — | 2 | 2 | no | — |
| 685 | C4×C8 | — | 2 | 2 | no | — |
| 686 | C4×C8 | — | 2 | 2 | no | — |
| 687 | C4×C8 | — | 2 | 2 | no | — |
| 688 | C4×C8 | — | 2 | 2 | no | — |
| 689 | C4×C8 | — | 4 | 2 | no | — |
| 690 | C4×C8 | — | 4 | 8 | no | — |
| 691 | C4×C8 | — | 4 | 2 | no | — |
| 692 | C4×C8 | — | 8 | 1 | no | — |
| 693 | C4×C8 | — | 8 | 1 | no | — |
| 694 | C4×C8 | — | 8 | 4 | no | — |
| 695 | C4×C8 | — | 8 | 4 | no | — |
| 696 | C4×C8 | #1580 | 1 | 2 | yes | — |
| 697 | C4×C8 | #1580 | 1 | 2 | yes | — |
| 698 | C4×C8 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 699 | C4×C8 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 700 | C4×C8 | #2931 | 1 | 1 | yes | characteristic |
| 701 | C4×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 702 | C4×C8 | C2×#444 | 1 | 1 | yes | characteristic |
| 703 | C4×C8 | #3151 | 1 | 4 | yes | — |
| 704 | C32 | — | 2 | 8 | no | — |
| 705 | C32 | — | 8 | 4 | no | — |
| 706 | C32 | #1580 | 1 | 16 | yes | complemented |
| 707 | C24 | — | 16 | 2 | no | — |
| 708 | #41 | — | 16 | 2 | no | — |
| 709 | #41 | — | 16 | 2 | no | — |
| 710 | #41 | — | 16 | 2 | no | — |
| 711 | #41 | — | 16 | 2 | no | — |
| 712 | C2×Q8 | — | 8 | 2 | no | — |
| 713 | C2×D4 | — | 8 | 4 | no | — |
| 714 | C2×D4 | — | 8 | 8 | no | — |
| 715 | C2×D4 | — | 8 | 2 | no | — |
| 716 | C2×D4 | — | 8 | 4 | no | — |
| 717 | C2×D4 | — | 16 | 8 | no | — |
| 718 | C2×D4 | — | 16 | 8 | no | — |
| 719 | C2×D4 | — | 16 | 2 | no | — |
| 720 | C2×D4 | — | 16 | 2 | no | — |
| 721 | C2×D4 | — | 16 | 4 | no | — |
| 722 | C2×D4 | — | 16 | 2 | no | — |
| 723 | C2×D4 | — | 16 | 2 | no | — |
| 724 | C2×D4 | — | 16 | 2 | no | — |
| 725 | C2×D4 | — | 16 | 2 | no | — |
| 726 | C22×C4 | — | 2 | 1 | no | — |
| 727 | C22×C4 | — | 2 | 1 | no | — |
| 728 | C22×C4 | — | 16 | 2 | no | — |
| 729 | C22×C4 | — | 16 | 2 | no | — |
| 730 | C22×C4 | — | 32 | 2 | no | — |
| 731 | C22×C4 | — | 32 | 2 | no | — |
| 732 | C22×C4 | — | 32 | 4 | no | — |
| 733 | C22×C4 | — | 32 | 4 | no | — |
| 734 | C22×C4 | #21690 | 1 | 1 | yes | characteristic |
| 735 | C22×C4 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 736 | Q16 | — | 8 | 4 | no | — |
| 737 | Q16 | — | 8 | 4 | no | — |
| 738 | SD16 | — | 16 | 4 | no | — |
| 739 | SD16 | — | 16 | 4 | no | — |
| 740 | D8 | — | 8 | 8 | no | — |
| 741 | D8 | — | 8 | 4 | no | — |
| 742 | D8 | — | 8 | 8 | no | — |
| 743 | D8 | — | 8 | 4 | no | — |
| 744 | D8 | — | 16 | 16 | no | — |
| 745 | D8 | — | 16 | 4 | no | — |
| 746 | D8 | — | 16 | 8 | no | — |
| 747 | D8 | — | 16 | 16 | no | — |
| 748 | D8 | — | 16 | 4 | no | — |
| 749 | M16 | — | 16 | 2 | no | — |
| 750 | M16 | — | 16 | 2 | no | — |
| 751 | M16 | — | 32 | 2 | no | — |
| 752 | M16 | — | 32 | 2 | no | — |
| 753 | C2×C8 | — | 2 | 1 | no | — |
| 754 | C2×C8 | — | 2 | 1 | no | — |
| 755 | C2×C8 | — | 2 | 8 | no | — |
| 756 | C2×C8 | — | 2 | 1 | no | — |
| 757 | C2×C8 | — | 2 | 1 | no | — |
| 758 | C2×C8 | — | 2 | 1 | no | — |
| 759 | C2×C8 | — | 4 | 4 | no | — |
| 760 | C2×C8 | — | 4 | 2 | no | — |
| 761 | C2×C8 | — | 8 | 2 | no | — |
| 762 | C2×C8 | — | 8 | 4 | no | — |
| 763 | C2×C8 | — | 16 | 2 | no | — |
| 764 | C2×C8 | — | 16 | 1 | no | — |
| 765 | C2×C8 | — | 16 | 2 | no | — |
| 766 | C2×C8 | — | 32 | 2 | no | — |
| 767 | C2×C8 | — | 32 | 2 | no | — |
| 768 | C2×C8 | — | 32 | 2 | no | — |
| 769 | C2×C8 | — | 32 | 4 | no | — |
| 770 | C2×C8 | — | 64 | 8 | no | — |
| 771 | C2×C8 | #12067 | 1 | 4 | yes | — |
| 772 | C2×C8 | #12067 | 1 | 4 | yes | — |
| 773 | C2×C8 | C2×#1580 | 1 | 1 | yes | characteristic |
| 774 | C2×C8 | #17962 | 1 | 1 | yes | characteristic |
| 775 | C2×C8 | #19745 | 1 | 2 | yes | — |
| 776 | C2×C8 | C8×#127 | 1 | 1 | yes | characteristic |
| 777 | C2×C8 | #21690 | 1 | 2 | yes | — |
| 778 | C2×C8 | #21706 | 1 | 1 | yes | characteristic |
| 779 | C2×C8 | #21706 | 1 | 2 | yes | — |
| 780 | C2×C8 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 781 | C2×C8 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 782 | C4⋊C4 | — | 8 | 4 | no | — |
| 783 | C4⋊C4 | — | 16 | 8 | no | — |
| 784 | C4⋊C4 | — | 16 | 2 | no | — |
| 785 | C4⋊C4 | — | 16 | 2 | no | — |
| 786 | C22⋊C4 | — | 16 | 4 | no | — |
| 787 | C22⋊C4 | — | 32 | 2 | no | — |
| 788 | C22⋊C4 | — | 32 | 2 | no | — |
| 789 | C22⋊C4 | — | 32 | 8 | no | — |
| 790 | C42 | — | 2 | 1 | no | — |
| 791 | C42 | — | 2 | 1 | no | — |
| 792 | C42 | — | 2 | 1 | no | — |
| 793 | C42 | — | 4 | 4 | no | — |
| 794 | C42 | C2×#1580 | 1 | 1 | yes | characteristic |
| 795 | C42 | #17962 | 1 | 1 | yes | characteristic |
| 796 | C42 | #19745 | 1 | 2 | yes | — |
| 797 | C42 | C2×AGL(1,ℤ/16) | 1 | 2 | yes | — |
| 798 | C16 | — | 2 | 4 | no | — |
| 799 | C16 | — | 4 | 2 | no | — |
| 800 | C16 | — | 8 | 2 | no | — |
| 801 | C16 | — | 16 | 1 | no | — |
| 802 | C16 | — | 32 | 2 | no | — |
| 803 | C16 | #12067 | 1 | 4 | yes | — |
| 804 | C16 | #12067 | 1 | 4 | yes | — |
| 805 | C16 | C2×#1580 | 1 | 4 | yes | — |
| 806 | C16 | #17962 | 1 | 4 | yes | — |
| 807 | C23 | — | 16 | 2 | no | — |
| 808 | C23 | — | 16 | 4 | no | — |
| 809 | C23 | — | 32 | 4 | no | — |
| 810 | C23 | — | 32 | 4 | no | — |
| 811 | C23 | — | 32 | 2 | no | — |
| 812 | C23 | — | 32 | 2 | no | — |
| 813 | C23 | #496124 | 1 | 1 | yes | characteristic |
| 814 | Q8 | — | 16 | 2 | no | — |
| 815 | Q8 | — | 16 | 2 | no | — |
| 816 | D4 | — | 16 | 4 | no | — |
| 817 | D4 | — | 16 | 2 | no | — |
| 818 | D4 | — | 16 | 4 | no | — |
| 819 | D4 | — | 16 | 2 | no | — |
| 820 | D4 | — | 16 | 16 | no | — |
| 821 | D4 | — | 16 | 8 | no | — |
| 822 | D4 | — | 32 | 8 | no | — |
| 823 | D4 | — | 32 | 2 | no | — |
| 824 | D4 | — | 32 | 2 | no | — |
| 825 | D4 | — | 32 | 2 | no | — |
| 826 | D4 | — | 32 | 2 | no | — |
| 827 | C2×C4 | — | 2 | 4 | no | — |
| 828 | C2×C4 | — | 2 | 2 | no | — |
| 829 | C2×C4 | — | 4 | 2 | no | — |
| 830 | C2×C4 | — | 4 | 2 | no | — |
| 831 | C2×C4 | — | 4 | 1 | no | — |
| 832 | C2×C4 | — | 16 | 2 | no | — |
| 833 | C2×C4 | — | 32 | 2 | no | — |
| 834 | C2×C4 | — | 32 | 2 | no | — |
| 835 | C2×C4 | — | 32 | 4 | no | — |
| 836 | C2×C4 | — | 32 | 2 | no | — |
| 837 | C2×C4 | — | 64 | 2 | no | — |
| 838 | C2×C4 | — | 64 | 2 | no | — |
| 839 | C2×C4 | — | 64 | 4 | no | — |
| 840 | C2×C4 | #212800 | 1 | 1 | yes | characteristic |
| 841 | C2×C4 | #212918 | 1 | 1 | yes | characteristic |
| 842 | C2×C4 | #213274 | 1 | 1 | yes | characteristic |
| 843 | C2×C4 | C2×#12067 | 1 | 2 | yes | — |
| 844 | C2×C4 | #483961 | 1 | 2 | yes | — |
| 845 | C2×C4 | #496124 | 1 | 1 | yes | characteristic |
| 846 | C2×C4 | #496124 | 1 | 1 | yes | characteristic |
| 847 | C2×C4 | #496124 | 1 | 1 | yes | characteristic |
| 848 | C8 | — | 2 | 2 | no | — |
| 849 | C8 | — | 2 | 4 | no | — |
| 850 | C8 | — | 4 | 1 | no | — |
| 851 | C8 | — | 8 | 2 | no | — |
| 852 | C8 | — | 16 | 2 | no | — |
| 853 | C8 | — | 32 | 1 | no | — |
| 854 | C8 | — | 32 | 2 | no | — |
| 855 | C8 | — | 64 | 2 | no | — |
| 856 | C8 | AGL(1,ℤ/32) | 1 | 8 | yes | complemented |
| 857 | C8 | #212800 | 1 | 2 | yes | — |
| 858 | C8 | #213274 | 1 | 2 | yes | — |
| 859 | C8 | C2×#12067 | 1 | 2 | yes | — |
| 860 | C8 | #483961 | 1 | 2 | yes | — |
| 861 | C22 | — | 2 | 2 | no | — |
| 862 | C22 | — | 32 | 2 | no | — |
| 863 | C22 | — | 32 | 4 | no | — |
| 864 | C22 | — | 32 | 8 | no | — |
| 865 | C22 | — | 32 | 4 | no | — |
| 866 | C22 | — | 64 | 2 | no | — |
| 867 | C22 | — | 64 | 2 | no | — |
| 868 | C22 | — | 64 | 4 | no | — |
| 869 | C22 | #72213975 | 1 | 1 | yes | characteristic |
| 870 | C22 | #72213983 | 1 | 1 | yes | characteristic |
| 871 | C22 | #72216174 | 1 | 1 | yes | characteristic |
| 872 | C4 | — | 2 | 2 | no | — |
| 873 | C4 | — | 4 | 2 | no | — |
| 874 | C4 | — | 8 | 1 | no | — |
| 875 | C4 | — | 32 | 2 | no | — |
| 876 | C4 | — | 64 | 2 | no | — |
| 877 | C4 | #72213975 | 1 | 1 | yes | characteristic |
| 878 | C4 | #72213983 | 1 | 1 | yes | characteristic |
| 879 | C4 | #72216170 | 1 | 1 | yes | characteristic |
| 880 | C4 | #72216174 | 1 | 1 | yes | characteristic |
| 881 | C4 | C2×AGL(1,ℤ/32) | 1 | 4 | yes | — |
| 882 | C2 | — | 2 | 1 | no | — |
| 883 | C2 | — | 2 | 1 | no | — |
| 884 | C2 | — | 64 | 2 | no | — |
| 885 | C2 | — | 64 | 4 | no | — |
| 886 | C2 | #72216176 | 1 | 1 | yes | characteristic |
| 887 | C2 | #72225247 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #72216174 |
| commutator | C4×C16 | C23×C8 |
| Frattini, cosocle | C4×#346 | C24 |
| prime radical | #72216275 | C4 |
| LCS | G ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C4×C82 ◁ #72216161 ◁ G | |
| LECS | G ▷ C4×#346 ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72225247 | C2 | semidirect |
| 2. #72225230 | C2 | semidirect |
| 7. #72225206 | C2 | semidirect |
| 8. #72225186 | C2 | semidirect |
| 10. #72225179 | C2 | semidirect |
| 14. #72225160 | C2 | semidirect |
| 17. #72225132 | C2 | semidirect |
| 32. #72216176 | C2 | semidirect |
| 66. #151728 | C8 | semidirect |
| 67. #151726 | C8 | semidirect |
| 68. #151724 | C8 | semidirect |
| 136. #13727 | C2×C8 | semidirect |
| 137. #13725 | C2×C8 | semidirect |
| 171. #12518 | C2×C8 | semidirect |
| 173. #12516 | C2×C8 | semidirect |
| 178. #12515 | C2×C8 | semidirect |
| 230. #7329 | C2×C8 | semidirect |
| 232. C8×C32 | C2×C8 | semidirect |
| 706. C32 | #1580 | semidirect |
| 856. C8 | AGL(1,ℤ/32) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72225247 | 2 |
| #72225230 | 2 |
| #72225206 | 2 |
| #72225186 | 2 |
| #72225179 | 2 |
| #72225160 | 2 |
| #72225132 | 2 |
| #72216341 | 2 |
| #72216176 | 2 |