Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1123 conjugacy classes of subgroups.
The subgroup lattice has 914 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #498334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #497555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #488990 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #229212 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #220900 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #141760 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #140297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #140221 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #138716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #138653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #137517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #136424 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #136401 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #128757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #128717 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#3334 | C22 | 1 | 1 | yes | characteristic |
| 17 | #33707 | C22 | 1 | 1 | yes | characteristic |
| 18 | #33580 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×AGL(1,ℤ/16) | — | 2 | 1 | no | — |
| 20 | D4×M32 | C22 | 1 | 1 | yes | characteristic |
| 21 | #23180 | C22 | 1 | 1 | yes | characteristic |
| 22 | #22670 | C22 | 1 | 1 | yes | characteristic |
| 23 | D4×#108 | C22 | 1 | 1 | yes | characteristic |
| 24 | #22431 | — | 2 | 1 | no | — |
| 25 | #19101 | C22 | 1 | 1 | yes | characteristic |
| 26 | #17994 | — | 2 | 1 | no | — |
| 27 | C2×#1594 | C22 | 1 | 1 | yes | characteristic |
| 28 | #13290 | C22 | 1 | 1 | yes | characteristic |
| 29 | #13279 | C22 | 1 | 1 | yes | characteristic |
| 30 | #13210 | C22 | 1 | 1 | yes | characteristic |
| 31 | #13183 | C22 | 1 | 1 | yes | characteristic |
| 32 | #13153 | — | 2 | 1 | no | — |
| 33 | #13067 | — | 2 | 1 | no | — |
| 34 | #13037 | — | 2 | 1 | no | — |
| 35 | #13004 | — | 2 | 1 | no | — |
| 36 | #12955 | — | 2 | 1 | no | — |
| 37 | #12886 | C22 | 1 | 1 | yes | characteristic |
| 38 | #12871 | — | 2 | 1 | no | — |
| 39 | #12818 | C22 | 1 | 1 | yes | characteristic |
| 40 | #12666 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4×#361 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#1387 | — | 2 | 1 | no | — |
| 43 | #12344 | C4 | 1 | 2 | yes | complemented |
| 44 | #12344 | C4 | 1 | 2 | yes | complemented |
| 45 | #12340 | C4 | 1 | 2 | yes | complemented |
| 46 | #12340 | C4 | 1 | 2 | yes | complemented |
| 47 | #11940 | C22 | 1 | 1 | yes | characteristic |
| 48 | #11925 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11593 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11583 | C22 | 1 | 1 | yes | characteristic |
| 51 | #11404 | C22 | 1 | 1 | yes | characteristic |
| 52 | #9862 | C22 | 1 | 1 | yes | characteristic |
| 53 | #9836 | C22 | 1 | 1 | yes | characteristic |
| 54 | #9740 | C22 | 1 | 1 | yes | characteristic |
| 55 | #9630 | C22 | 1 | 1 | yes | characteristic |
| 56 | #9590 | — | 2 | 1 | no | — |
| 57 | #9227 | — | 2 | 1 | no | — |
| 58 | #8991 | — | 2 | 1 | no | — |
| 59 | #8981 | — | 2 | 1 | no | — |
| 60 | #8930 | — | 2 | 1 | no | — |
| 61 | #8642 | C22 | 1 | 1 | yes | characteristic |
| 62 | #8446 | — | 2 | 1 | no | — |
| 63 | #8294 | C22 | 1 | 1 | yes | characteristic |
| 64 | #8202 | C22 | 1 | 1 | yes | characteristic |
| 65 | #7280 | C22 | 1 | 1 | yes | characteristic |
| 66 | #7278 | C22 | 1 | 1 | yes | characteristic |
| 67 | #7173 | C22 | 1 | 1 | yes | characteristic |
| 68 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 69 | #7158 | C22 | 1 | 1 | yes | characteristic |
| 70 | #7152 | C22 | 1 | 1 | yes | characteristic |
| 71 | C2×#547 | — | 2 | 1 | no | — |
| 72 | C2×#509 | — | 2 | 1 | no | — |
| 73 | C22×M32 | — | 2 | 1 | no | — |
| 74 | #3334 | — | 2 | 1 | no | — |
| 75 | #3334 | — | 2 | 1 | no | — |
| 76 | #3334 | — | 2 | 2 | no | — |
| 77 | #3334 | — | 4 | 1 | no | — |
| 78 | #3334 | C2×C4 | 1 | 2 | yes | — |
| 79 | #3334 | C2×C4 | 1 | 2 | yes | — |
| 80 | C2×#500 | C23 | 1 | 1 | yes | characteristic |
| 81 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 82 | #3100 | — | 2 | 1 | no | — |
| 83 | C2×#480 | — | 4 | 1 | no | — |
| 84 | C2×#474 | — | 2 | 1 | no | — |
| 85 | C2×#466 | — | 2 | 1 | no | — |
| 86 | C2×#444 | — | 2 | 1 | no | — |
| 87 | C2×#442 | — | 2 | 1 | no | — |
| 88 | C2×C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 89 | #2935 | — | 2 | 1 | no | — |
| 90 | D4×M16 | — | 2 | 1 | no | — |
| 91 | C2×#436 | — | 2 | 1 | no | — |
| 92 | C2×C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 93 | C22×#108 | — | 2 | 1 | no | — |
| 94 | C22×#107 | — | 2 | 1 | no | — |
| 95 | C2×#417 | — | 4 | 1 | no | — |
| 96 | D4×C4⋊C4 | — | 2 | 1 | no | — |
| 97 | #2243 | — | 4 | 1 | no | — |
| 98 | #2241 | C2×C4 | 1 | 2 | yes | complemented |
| 99 | #2240 | C2×C4 | 1 | 2 | yes | complemented |
| 100 | #2210 | — | 2 | 2 | no | — |
| 101 | #2208 | C2×C4 | 1 | 2 | yes | — |
| 102 | #2206 | C2×C4 | 1 | 2 | yes | — |
| 103 | AGL(1,ℤ/16) | — | 4 | 4 | no | — |
| 104 | #2169 | — | 2 | 1 | no | — |
| 105 | #2168 | — | 4 | 1 | no | — |
| 106 | D4×C16 | — | 2 | 1 | no | — |
| 107 | C2×#365 | — | 2 | 1 | no | — |
| 108 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 109 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×#361 | — | 2 | 1 | no | — |
| 111 | C2×#361 | D4 | 1 | 1 | yes | characteristic |
| 112 | C2×#361 | D4 | 1 | 1 | yes | characteristic |
| 113 | C2×#360 | — | 2 | 1 | no | — |
| 114 | C2×#360 | — | 2 | 1 | no | — |
| 115 | #2139 | — | 2 | 1 | no | — |
| 116 | #2139 | — | 4 | 1 | no | — |
| 117 | #2112 | — | 2 | 1 | no | — |
| 118 | C2×#347 | — | 2 | 1 | no | — |
| 119 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 120 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 121 | #1990 | — | 2 | 1 | no | — |
| 122 | #1981 | — | 2 | 1 | no | — |
| 123 | #1980 | — | 2 | 1 | no | — |
| 124 | #1975 | — | 2 | 1 | no | — |
| 125 | #1956 | — | 2 | 1 | no | — |
| 126 | #1950 | — | 2 | 1 | no | — |
| 127 | #1943 | — | 2 | 1 | no | — |
| 128 | #1894 | — | 4 | 1 | no | — |
| 129 | #1876 | — | 4 | 1 | no | — |
| 130 | #1872 | — | 4 | 1 | no | — |
| 131 | #1864 | — | 4 | 1 | no | — |
| 132 | #1855 | — | 4 | 1 | no | — |
| 133 | #1848 | C23 | 1 | 1 | yes | characteristic |
| 134 | #1844 | C23 | 1 | 1 | yes | characteristic |
| 135 | #1810 | — | 2 | 1 | no | — |
| 136 | #1802 | — | 2 | 1 | no | — |
| 137 | #1802 | — | 2 | 1 | no | — |
| 138 | #1788 | — | 4 | 1 | no | — |
| 139 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 140 | #1770 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×#102 | D4 | 1 | 1 | yes | characteristic |
| 142 | #1669 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 143 | #1669 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 144 | #1667 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 145 | #1667 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 146 | #1665 | — | 2 | 1 | no | — |
| 147 | #1665 | — | 2 | 1 | no | — |
| 148 | #1594 | — | 2 | 2 | no | — |
| 149 | #1594 | — | 4 | 1 | no | — |
| 150 | #1589 | — | 4 | 1 | no | — |
| 151 | #1581 | — | 4 | 1 | no | — |
| 152 | #1581 | — | 4 | 1 | no | — |
| 153 | C8×D8 | — | 4 | 1 | no | — |
| 154 | #1571 | — | 2 | 1 | no | — |
| 155 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 156 | C2×#334 | C23 | 1 | 1 | yes | characteristic |
| 157 | #1540 | — | 2 | 1 | no | — |
| 158 | C2×#332 | — | 2 | 1 | no | — |
| 159 | #1492 | — | 2 | 1 | no | — |
| 160 | #1492 | — | 2 | 1 | no | — |
| 161 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 162 | C2×D4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 163 | C8×M16 | — | 2 | 1 | no | — |
| 164 | C2×#322 | C23 | 1 | 1 | yes | characteristic |
| 165 | #1387 | — | 2 | 1 | no | — |
| 166 | #1387 | — | 2 | 1 | no | — |
| 167 | #1387 | — | 2 | 1 | no | — |
| 168 | #1387 | — | 2 | 1 | no | — |
| 169 | #1387 | — | 2 | 1 | no | — |
| 170 | #1387 | D4 | 1 | 1 | yes | characteristic |
| 171 | #1387 | D4 | 1 | 1 | yes | characteristic |
| 172 | #1383 | — | 2 | 1 | no | — |
| 173 | #1383 | — | 4 | 1 | no | — |
| 174 | #1375 | — | 2 | 1 | no | — |
| 175 | #1364 | C2×C4 | 1 | 2 | yes | complemented |
| 176 | #1364 | C2×C4 | 1 | 2 | yes | complemented |
| 177 | #1360 | — | 4 | 1 | no | — |
| 178 | #1331 | C2×C4 | 1 | 2 | yes | — |
| 179 | #1331 | C2×C4 | 1 | 2 | yes | — |
| 180 | D4⋊C16 | C2×C4 | 1 | 2 | yes | complemented |
| 181 | D4⋊C16 | C2×C4 | 1 | 2 | yes | complemented |
| 182 | #1313 | — | 4 | 1 | no | — |
| 183 | #1303 | — | 2 | 1 | no | — |
| 184 | #1296 | — | 2 | 1 | no | — |
| 185 | #1279 | D4 | 1 | 1 | yes | characteristic |
| 186 | #1278 | — | 2 | 1 | no | — |
| 187 | #1277 | D4 | 1 | 1 | yes | characteristic |
| 188 | C22×#41 | — | 4 | 1 | no | — |
| 189 | C2×#135 | — | 2 | 1 | no | — |
| 190 | C2×#135 | — | 2 | 1 | no | — |
| 191 | C22×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×#131 | — | 4 | 1 | no | — |
| 193 | C22×M16 | — | 4 | 1 | no | — |
| 194 | C22×M16 | — | 4 | 1 | no | — |
| 195 | C23×C8 | — | 2 | 1 | no | — |
| 196 | #547 | — | 2 | 2 | no | — |
| 197 | #547 | — | 2 | 2 | no | — |
| 198 | #547 | — | 4 | 2 | no | — |
| 199 | #547 | — | 4 | 1 | no | — |
| 200 | #547 | — | 4 | 1 | no | — |
| 201 | #547 | — | 8 | 1 | no | — |
| 202 | #532 | — | 2 | 1 | no | — |
| 203 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 204 | C2×#123 | — | 8 | 1 | no | — |
| 205 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 206 | C2×#121 | — | 4 | 1 | no | — |
| 207 | C2×C4×D4 | — | 2 | 1 | no | — |
| 208 | C2×C4×D4 | — | 4 | 1 | no | — |
| 209 | C2×C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 211 | C22×C4⋊C4 | — | 4 | 1 | no | — |
| 212 | #509 | — | 4 | 2 | no | — |
| 213 | #509 | — | 4 | 2 | no | — |
| 214 | C2×SD32 | — | 2 | 2 | no | — |
| 215 | C2×D16 | — | 2 | 2 | no | — |
| 216 | C2×M32 | — | 2 | 1 | no | — |
| 217 | C2×M32 | — | 2 | 1 | no | — |
| 218 | C2×M32 | — | 2 | 1 | no | — |
| 219 | C2×M32 | — | 4 | 1 | no | — |
| 220 | C2×M32 | — | 4 | 2 | no | — |
| 221 | C2×M32 | — | 8 | 1 | no | — |
| 222 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C22×C16 | — | 4 | 1 | no | — |
| 225 | #500 | — | 2 | 1 | no | — |
| 226 | #500 | — | 2 | 1 | no | — |
| 227 | #500 | — | 2 | 1 | no | — |
| 228 | #500 | C22×C4 | 1 | 2 | yes | — |
| 229 | #495 | — | 2 | 1 | no | — |
| 230 | #495 | — | 2 | 1 | no | — |
| 231 | #494 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 233 | #492 | — | 2 | 1 | no | — |
| 234 | #480 | — | 4 | 2 | no | — |
| 235 | #480 | — | 4 | 2 | no | — |
| 236 | #480 | — | 4 | 2 | no | — |
| 237 | #480 | — | 4 | 2 | no | — |
| 238 | #480 | — | 4 | 1 | no | — |
| 239 | #474 | — | 2 | 1 | no | — |
| 240 | #474 | — | 2 | 1 | no | — |
| 241 | #474 | — | 2 | 2 | no | — |
| 242 | #474 | — | 2 | 2 | no | — |
| 243 | #474 | — | 4 | 2 | no | — |
| 244 | #466 | — | 2 | 2 | no | — |
| 245 | #466 | — | 2 | 2 | no | — |
| 246 | #466 | — | 4 | 1 | no | — |
| 247 | #466 | — | 4 | 1 | no | — |
| 248 | #459 | — | 2 | 1 | no | — |
| 249 | #459 | — | 2 | 1 | no | — |
| 250 | #447 | — | 4 | 1 | no | — |
| 251 | #444 | — | 4 | 2 | no | — |
| 252 | #444 | — | 8 | 1 | no | — |
| 253 | #442 | — | 4 | 2 | no | — |
| 254 | #442 | — | 8 | 1 | no | — |
| 255 | C4×D8 | — | 2 | 1 | no | — |
| 256 | C4×D8 | — | 2 | 1 | no | — |
| 257 | C4×D8 | — | 4 | 1 | no | — |
| 258 | C4×D8 | — | 4 | 1 | no | — |
| 259 | C4×D8 | C22×C4 | 1 | 2 | yes | — |
| 260 | C4×D8 | #41 | 1 | 2 | yes | — |
| 261 | #436 | — | 4 | 2 | no | — |
| 262 | #436 | — | 4 | 1 | no | — |
| 263 | #436 | — | 4 | 1 | no | — |
| 264 | #436 | — | 8 | 1 | no | — |
| 265 | #435 | — | 8 | 1 | no | — |
| 266 | #435 | — | 8 | 1 | no | — |
| 267 | C8×D4 | — | 2 | 1 | no | — |
| 268 | C8×D4 | — | 2 | 1 | no | — |
| 269 | C8×D4 | — | 4 | 1 | no | — |
| 270 | C8×D4 | — | 4 | 1 | no | — |
| 271 | C8×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 272 | C8×D4 | C22×C4 | 1 | 1 | yes | characteristic |
| 273 | C8×D4 | #41 | 1 | 1 | yes | characteristic |
| 274 | C8×D4 | #41 | 1 | 1 | yes | characteristic |
| 275 | #431 | — | 2 | 1 | no | — |
| 276 | C2×#108 | — | 2 | 1 | no | — |
| 277 | C2×#108 | — | 2 | 1 | no | — |
| 278 | C2×#108 | — | 4 | 2 | no | — |
| 279 | C2×#108 | — | 4 | 1 | no | — |
| 280 | C2×#108 | — | 8 | 1 | no | — |
| 281 | C2×#108 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×#108 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C2×#107 | — | 2 | 1 | no | — |
| 284 | C2×#107 | — | 2 | 1 | no | — |
| 285 | C2×#107 | — | 2 | 2 | no | — |
| 286 | C2×#107 | — | 2 | 2 | no | — |
| 287 | C2×#107 | — | 4 | 1 | no | — |
| 288 | C2×#107 | — | 4 | 1 | no | — |
| 289 | C2×#107 | — | 4 | 1 | no | — |
| 290 | C2×#107 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×#106 | — | 2 | 1 | no | — |
| 292 | C2×#106 | — | 2 | 1 | no | — |
| 293 | #423 | — | 2 | 1 | no | — |
| 294 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 295 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×#104 | — | 4 | 1 | no | — |
| 298 | C2×#104 | — | 4 | 1 | no | — |
| 299 | #417 | — | 8 | 4 | no | — |
| 300 | C2×#103 | — | 4 | 1 | no | — |
| 301 | C2×#103 | — | 4 | 1 | no | — |
| 302 | C2×#103 | — | 4 | 1 | no | — |
| 303 | C2×#103 | — | 4 | 1 | no | — |
| 304 | C2×#102 | — | 2 | 1 | no | — |
| 305 | C2×#102 | — | 2 | 1 | no | — |
| 306 | C2×#102 | — | 4 | 1 | no | — |
| 307 | C2×#102 | — | 4 | 1 | no | — |
| 308 | C2×#102 | — | 4 | 1 | no | — |
| 309 | #408 | — | 4 | 1 | no | — |
| 310 | #407 | — | 4 | 1 | no | — |
| 311 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 312 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 313 | C4×M16 | — | 2 | 1 | no | — |
| 314 | C2×#97 | — | 2 | 1 | no | — |
| 315 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 318 | #389 | — | 4 | 1 | no | — |
| 319 | #385 | — | 8 | 1 | no | — |
| 320 | #384 | — | 2 | 1 | no | — |
| 321 | #380 | — | 4 | 1 | no | — |
| 322 | C4×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | #365 | — | 4 | 2 | no | — |
| 324 | C4⋊C16 | — | 2 | 1 | no | — |
| 325 | C4⋊C16 | — | 2 | 1 | no | — |
| 326 | C4⋊C16 | — | 2 | 1 | no | — |
| 327 | C4⋊C16 | C22×C4 | 1 | 2 | yes | — |
| 328 | #361 | — | 2 | 2 | no | — |
| 329 | #361 | — | 4 | 1 | no | — |
| 330 | #361 | — | 8 | 1 | no | — |
| 331 | #360 | — | 4 | 2 | no | — |
| 332 | #360 | — | 8 | 1 | no | — |
| 333 | #358 | — | 2 | 2 | no | — |
| 334 | #358 | — | 4 | 2 | no | — |
| 335 | #357 | — | 2 | 2 | no | — |
| 336 | #357 | — | 4 | 2 | no | — |
| 337 | C22⋊C16 | — | 4 | 1 | no | — |
| 338 | C22⋊C16 | — | 4 | 1 | no | — |
| 339 | #347 | — | 4 | 2 | no | — |
| 340 | #346 | — | 2 | 1 | no | — |
| 341 | #346 | — | 2 | 1 | no | — |
| 342 | C4×C16 | — | 2 | 1 | no | — |
| 343 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 344 | #341 | — | 2 | 1 | no | — |
| 345 | #341 | — | 4 | 1 | no | — |
| 346 | #340 | — | 2 | 1 | no | — |
| 347 | #340 | — | 4 | 1 | no | — |
| 348 | #340 | — | 4 | 1 | no | — |
| 349 | #340 | — | 8 | 1 | no | — |
| 350 | #336 | — | 2 | 1 | no | — |
| 351 | #335 | — | 4 | 1 | no | — |
| 352 | #335 | — | 4 | 1 | no | — |
| 353 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 354 | #335 | C22×C4 | 1 | 1 | yes | characteristic |
| 355 | #334 | — | 2 | 1 | no | — |
| 356 | #334 | — | 2 | 1 | no | — |
| 357 | #334 | — | 2 | 1 | no | — |
| 358 | #332 | — | 2 | 1 | no | — |
| 359 | #332 | — | 2 | 1 | no | — |
| 360 | #332 | — | 8 | 1 | no | — |
| 361 | #331 | — | 2 | 1 | no | — |
| 362 | #331 | — | 2 | 1 | no | — |
| 363 | D4⋊C8 | — | 2 | 1 | no | — |
| 364 | D4⋊C8 | — | 2 | 1 | no | — |
| 365 | D4⋊C8 | — | 4 | 2 | no | — |
| 366 | D4⋊C8 | — | 4 | 1 | no | — |
| 367 | D4⋊C8 | — | 4 | 1 | no | — |
| 368 | D4⋊C8 | — | 8 | 1 | no | — |
| 369 | #322 | — | 2 | 1 | no | — |
| 370 | #322 | — | 2 | 1 | no | — |
| 371 | #322 | — | 4 | 1 | no | — |
| 372 | C82 | — | 4 | 1 | no | — |
| 373 | C2×#41 | — | 4 | 2 | no | — |
| 374 | C2×#41 | — | 4 | 2 | no | — |
| 375 | C2×#41 | — | 4 | 1 | no | — |
| 376 | C2×#41 | — | 8 | 2 | no | — |
| 377 | C2×#41 | — | 8 | 2 | no | — |
| 378 | C2×#41 | — | 8 | 2 | no | — |
| 379 | C2×#41 | — | 16 | 1 | no | — |
| 380 | C2×#41 | — | 16 | 1 | no | — |
| 381 | C22×Q8 | — | 4 | 1 | no | — |
| 382 | C22×D4 | — | 2 | 1 | no | — |
| 383 | C22×D4 | — | 8 | 1 | no | — |
| 384 | C22×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 385 | C23×C4 | — | 2 | 1 | no | — |
| 386 | C23×C4 | — | 4 | 1 | no | — |
| 387 | C23×C4 | — | 8 | 1 | no | — |
| 388 | C23×C4 | — | 8 | 1 | no | — |
| 389 | #135 | — | 4 | 1 | no | — |
| 390 | #135 | — | 4 | 1 | no | — |
| 391 | #135 | — | 4 | 1 | no | — |
| 392 | #135 | — | 4 | 1 | no | — |
| 393 | #135 | — | 8 | 1 | no | — |
| 394 | #135 | — | 8 | 1 | no | — |
| 395 | C2×Q16 | — | 2 | 1 | no | — |
| 396 | C2×Q16 | — | 2 | 1 | no | — |
| 397 | C2×SD16 | — | 4 | 1 | no | — |
| 398 | C2×SD16 | — | 4 | 1 | no | — |
| 399 | C2×D8 | — | 2 | 1 | no | — |
| 400 | C2×D8 | — | 2 | 1 | no | — |
| 401 | C2×D8 | — | 2 | 1 | no | — |
| 402 | C2×D8 | — | 2 | 1 | no | — |
| 403 | C2×D8 | — | 2 | 1 | no | — |
| 404 | C2×D8 | — | 2 | 1 | no | — |
| 405 | C2×D8 | — | 2 | 1 | no | — |
| 406 | C2×D8 | — | 4 | 1 | no | — |
| 407 | C2×D8 | — | 4 | 1 | no | — |
| 408 | C2×D8 | C4×D4 | 1 | 2 | yes | — |
| 409 | #131 | — | 8 | 2 | no | — |
| 410 | #131 | — | 16 | 1 | no | — |
| 411 | C2×M16 | — | 2 | 1 | no | — |
| 412 | C2×M16 | — | 2 | 1 | no | — |
| 413 | C2×M16 | — | 4 | 1 | no | — |
| 414 | C2×M16 | — | 8 | 1 | no | — |
| 415 | C2×M16 | — | 8 | 1 | no | — |
| 416 | C2×M16 | — | 8 | 2 | no | — |
| 417 | C2×M16 | — | 8 | 2 | no | — |
| 418 | C2×M16 | — | 8 | 2 | no | — |
| 419 | C2×M16 | — | 16 | 1 | no | — |
| 420 | C2×M16 | — | 16 | 1 | no | — |
| 421 | C22×C8 | — | 2 | 1 | no | — |
| 422 | C22×C8 | — | 2 | 1 | no | — |
| 423 | C22×C8 | — | 2 | 1 | no | — |
| 424 | C22×C8 | — | 2 | 1 | no | — |
| 425 | C22×C8 | — | 2 | 1 | no | — |
| 426 | C22×C8 | — | 2 | 1 | no | — |
| 427 | C22×C8 | — | 2 | 1 | no | — |
| 428 | C22×C8 | — | 2 | 1 | no | — |
| 429 | C22×C8 | — | 4 | 1 | no | — |
| 430 | C22×C8 | — | 4 | 1 | no | — |
| 431 | C22×C8 | — | 4 | 1 | no | — |
| 432 | C22×C8 | — | 4 | 1 | no | — |
| 433 | C22×C8 | — | 4 | 1 | no | — |
| 434 | C22×C8 | — | 8 | 1 | no | — |
| 435 | C22×C8 | — | 8 | 1 | no | — |
| 436 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 438 | C4⋊Q8 | — | 2 | 2 | no | — |
| 439 | C4⋊Q8 | — | 2 | 1 | no | — |
| 440 | C4⋊Q8 | — | 4 | 1 | no | — |
| 441 | C4⋊Q8 | — | 4 | 1 | no | — |
| 442 | C4⋊Q8 | — | 4 | 1 | no | — |
| 443 | #127 | — | 2 | 1 | no | — |
| 444 | #124 | — | 4 | 1 | no | — |
| 445 | #123 | — | 8 | 2 | no | — |
| 446 | #123 | — | 8 | 2 | no | — |
| 447 | #123 | — | 8 | 2 | no | — |
| 448 | #123 | — | 8 | 2 | no | — |
| 449 | C22⋊Q8 | — | 4 | 2 | no | — |
| 450 | C22⋊Q8 | — | 4 | 2 | no | — |
| 451 | C22⋊Q8 | — | 8 | 2 | no | — |
| 452 | #121 | — | 4 | 2 | no | — |
| 453 | #121 | — | 4 | 2 | no | — |
| 454 | #121 | — | 4 | 1 | no | — |
| 455 | #121 | — | 4 | 1 | no | — |
| 456 | #121 | — | 8 | 1 | no | — |
| 457 | #121 | — | 8 | 1 | no | — |
| 458 | C4×D4 | — | 2 | 2 | no | — |
| 459 | C4×D4 | — | 2 | 1 | no | — |
| 460 | C4×D4 | — | 2 | 2 | no | — |
| 461 | C4×D4 | — | 2 | 1 | no | — |
| 462 | C4×D4 | — | 4 | 1 | no | — |
| 463 | C4×D4 | — | 4 | 1 | no | — |
| 464 | C4×D4 | — | 4 | 1 | no | — |
| 465 | C4×D4 | — | 4 | 1 | no | — |
| 466 | C4×D4 | — | 8 | 2 | no | — |
| 467 | C4×D4 | — | 16 | 1 | no | — |
| 468 | C4×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 469 | C4×D4 | C4×D4 | 1 | 1 | yes | characteristic |
| 470 | C4×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 471 | C4×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 472 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 473 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 474 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 475 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 476 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 477 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 478 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 479 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 480 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 481 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 482 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 483 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 484 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 485 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 486 | C2×C4⋊C4 | — | 16 | 1 | no | — |
| 487 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 488 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 489 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 490 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 491 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 492 | C2×C42 | — | 2 | 1 | no | — |
| 493 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 494 | SD32 | — | 4 | 4 | no | — |
| 495 | D16 | — | 4 | 4 | no | — |
| 496 | M32 | — | 2 | 1 | no | — |
| 497 | M32 | — | 2 | 1 | no | — |
| 498 | M32 | — | 2 | 1 | no | — |
| 499 | M32 | — | 2 | 1 | no | — |
| 500 | M32 | — | 4 | 1 | no | — |
| 501 | M32 | — | 4 | 1 | no | — |
| 502 | M32 | — | 4 | 1 | no | — |
| 503 | M32 | — | 4 | 1 | no | — |
| 504 | M32 | — | 4 | 1 | no | — |
| 505 | M32 | — | 4 | 1 | no | — |
| 506 | M32 | — | 8 | 2 | no | — |
| 507 | C2×C16 | — | 2 | 2 | no | — |
| 508 | C2×C16 | — | 2 | 2 | no | — |
| 509 | C2×C16 | — | 2 | 1 | no | — |
| 510 | C2×C16 | — | 2 | 1 | no | — |
| 511 | C2×C16 | — | 4 | 1 | no | — |
| 512 | C2×C16 | — | 8 | 2 | no | — |
| 513 | #108 | — | 2 | 1 | no | — |
| 514 | #108 | — | 2 | 1 | no | — |
| 515 | #108 | — | 2 | 1 | no | — |
| 516 | #108 | — | 4 | 1 | no | — |
| 517 | #108 | — | 4 | 1 | no | — |
| 518 | #108 | — | 8 | 1 | no | — |
| 519 | #108 | — | 8 | 2 | no | — |
| 520 | #108 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 521 | #107 | — | 2 | 1 | no | — |
| 522 | #107 | — | 2 | 2 | no | — |
| 523 | #107 | — | 2 | 2 | no | — |
| 524 | #107 | — | 4 | 2 | no | — |
| 525 | #107 | — | 4 | 2 | no | — |
| 526 | #107 | — | 4 | 1 | no | — |
| 527 | #107 | — | 4 | 1 | no | — |
| 528 | #107 | — | 4 | 1 | no | — |
| 529 | #107 | — | 4 | 1 | no | — |
| 530 | #107 | C4×D4 | 1 | 2 | yes | — |
| 531 | #106 | — | 4 | 1 | no | — |
| 532 | #106 | — | 4 | 1 | no | — |
| 533 | #106 | — | 8 | 1 | no | — |
| 534 | C4⋊C8 | — | 2 | 1 | no | — |
| 535 | C4⋊C8 | — | 2 | 1 | no | — |
| 536 | C4⋊C8 | — | 2 | 1 | no | — |
| 537 | C4⋊C8 | — | 2 | 1 | no | — |
| 538 | C4⋊C8 | — | 2 | 1 | no | — |
| 539 | C4⋊C8 | — | 4 | 1 | no | — |
| 540 | C4⋊C8 | — | 4 | 1 | no | — |
| 541 | C4⋊C8 | — | 4 | 1 | no | — |
| 542 | C4⋊C8 | — | 4 | 1 | no | — |
| 543 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 544 | C4⋊C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 545 | #104 | — | 8 | 2 | no | — |
| 546 | #104 | — | 16 | 1 | no | — |
| 547 | #103 | — | 8 | 2 | no | — |
| 548 | #103 | — | 8 | 2 | no | — |
| 549 | #103 | — | 16 | 1 | no | — |
| 550 | #103 | — | 16 | 1 | no | — |
| 551 | #102 | — | 2 | 2 | no | — |
| 552 | #102 | — | 2 | 2 | no | — |
| 553 | #102 | — | 4 | 2 | no | — |
| 554 | #102 | — | 4 | 2 | no | — |
| 555 | #102 | — | 4 | 2 | no | — |
| 556 | #102 | — | 4 | 1 | no | — |
| 557 | #102 | — | 4 | 1 | no | — |
| 558 | #102 | — | 4 | 1 | no | — |
| 559 | #102 | — | 4 | 1 | no | — |
| 560 | #102 | — | 8 | 2 | no | — |
| 561 | #102 | — | 8 | 2 | no | — |
| 562 | C22⋊C8 | — | 2 | 1 | no | — |
| 563 | C22⋊C8 | — | 2 | 1 | no | — |
| 564 | C22⋊C8 | — | 2 | 1 | no | — |
| 565 | C22⋊C8 | — | 2 | 1 | no | — |
| 566 | C22⋊C8 | — | 4 | 1 | no | — |
| 567 | C22⋊C8 | — | 8 | 1 | no | — |
| 568 | C22⋊C8 | — | 8 | 1 | no | — |
| 569 | C22⋊C8 | — | 8 | 1 | no | — |
| 570 | C22⋊C8 | — | 8 | 1 | no | — |
| 571 | C22⋊C8 | — | 8 | 2 | no | — |
| 572 | #97 | — | 4 | 1 | no | — |
| 573 | #97 | — | 4 | 1 | no | — |
| 574 | #97 | — | 4 | 1 | no | — |
| 575 | C4×C8 | — | 2 | 1 | no | — |
| 576 | C4×C8 | — | 2 | 1 | no | — |
| 577 | C4×C8 | — | 2 | 1 | no | — |
| 578 | C4×C8 | — | 2 | 1 | no | — |
| 579 | C4×C8 | — | 4 | 1 | no | — |
| 580 | C4×C8 | — | 4 | 1 | no | — |
| 581 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 582 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 583 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 584 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 585 | #95 | — | 2 | 1 | no | — |
| 586 | #95 | — | 8 | 1 | no | — |
| 587 | C24 | — | 2 | 1 | no | — |
| 588 | C24 | — | 4 | 1 | no | — |
| 589 | #41 | — | 8 | 4 | no | — |
| 590 | #41 | — | 8 | 4 | no | — |
| 591 | #41 | — | 8 | 1 | no | — |
| 592 | #41 | — | 8 | 1 | no | — |
| 593 | #41 | — | 8 | 1 | no | — |
| 594 | #41 | — | 8 | 1 | no | — |
| 595 | #41 | — | 16 | 2 | no | — |
| 596 | #41 | — | 16 | 2 | no | — |
| 597 | #41 | — | 16 | 4 | no | — |
| 598 | #41 | — | 16 | 4 | no | — |
| 599 | C2×Q8 | — | 4 | 1 | no | — |
| 600 | C2×Q8 | — | 4 | 2 | no | — |
| 601 | C2×Q8 | — | 8 | 1 | no | — |
| 602 | C2×Q8 | — | 8 | 1 | no | — |
| 603 | C2×Q8 | — | 8 | 1 | no | — |
| 604 | C2×Q8 | — | 8 | 1 | no | — |
| 605 | C2×Q8 | — | 8 | 1 | no | — |
| 606 | C2×D4 | — | 2 | 2 | no | — |
| 607 | C2×D4 | — | 2 | 2 | no | — |
| 608 | C2×D4 | — | 2 | 1 | no | — |
| 609 | C2×D4 | — | 4 | 1 | no | — |
| 610 | C2×D4 | — | 4 | 1 | no | — |
| 611 | C2×D4 | — | 4 | 1 | no | — |
| 612 | C2×D4 | — | 4 | 1 | no | — |
| 613 | C2×D4 | — | 4 | 1 | no | — |
| 614 | C2×D4 | — | 4 | 1 | no | — |
| 615 | C2×D4 | — | 4 | 1 | no | — |
| 616 | C2×D4 | — | 4 | 1 | no | — |
| 617 | C2×D4 | — | 4 | 1 | no | — |
| 618 | C2×D4 | — | 8 | 2 | no | — |
| 619 | C2×D4 | — | 8 | 2 | no | — |
| 620 | C2×D4 | — | 8 | 1 | no | — |
| 621 | C2×D4 | — | 16 | 2 | no | — |
| 622 | C2×D4 | — | 16 | 2 | no | — |
| 623 | C2×D4 | #442 | 1 | 1 | yes | characteristic |
| 624 | C2×D4 | #442 | 1 | 1 | yes | characteristic |
| 625 | C22×C4 | — | 2 | 1 | no | — |
| 626 | C22×C4 | — | 2 | 1 | no | — |
| 627 | C22×C4 | — | 2 | 1 | no | — |
| 628 | C22×C4 | — | 2 | 1 | no | — |
| 629 | C22×C4 | — | 2 | 1 | no | — |
| 630 | C22×C4 | — | 4 | 1 | no | — |
| 631 | C22×C4 | — | 4 | 1 | no | — |
| 632 | C22×C4 | — | 4 | 1 | no | — |
| 633 | C22×C4 | — | 4 | 1 | no | — |
| 634 | C22×C4 | — | 4 | 1 | no | — |
| 635 | C22×C4 | — | 4 | 2 | no | — |
| 636 | C22×C4 | — | 4 | 2 | no | — |
| 637 | C22×C4 | — | 4 | 1 | no | — |
| 638 | C22×C4 | — | 8 | 1 | no | — |
| 639 | C22×C4 | — | 8 | 1 | no | — |
| 640 | C22×C4 | — | 8 | 1 | no | — |
| 641 | C22×C4 | — | 8 | 1 | no | — |
| 642 | C22×C4 | — | 8 | 2 | no | — |
| 643 | C22×C4 | — | 8 | 2 | no | — |
| 644 | C22×C4 | — | 8 | 1 | no | — |
| 645 | C22×C4 | — | 8 | 1 | no | — |
| 646 | C22×C4 | — | 8 | 1 | no | — |
| 647 | C22×C4 | — | 16 | 2 | no | — |
| 648 | C22×C4 | — | 16 | 2 | no | — |
| 649 | C22×C4 | — | 16 | 2 | no | — |
| 650 | C22×C4 | — | 16 | 2 | no | — |
| 651 | C22×C4 | — | 32 | 1 | no | — |
| 652 | C22×C4 | D42 | 1 | 1 | yes | characteristic |
| 653 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 654 | C22×C4 | #577 | 1 | 1 | yes | characteristic |
| 655 | Q16 | — | 4 | 1 | no | — |
| 656 | Q16 | — | 4 | 1 | no | — |
| 657 | Q16 | — | 8 | 1 | no | — |
| 658 | SD16 | — | 8 | 1 | no | — |
| 659 | SD16 | — | 8 | 1 | no | — |
| 660 | SD16 | — | 16 | 1 | no | — |
| 661 | D8 | — | 2 | 2 | no | — |
| 662 | D8 | — | 2 | 2 | no | — |
| 663 | D8 | — | 4 | 1 | no | — |
| 664 | D8 | — | 4 | 1 | no | — |
| 665 | D8 | — | 4 | 1 | no | — |
| 666 | D8 | — | 4 | 1 | no | — |
| 667 | D8 | — | 8 | 1 | no | — |
| 668 | D8 | — | 8 | 2 | no | — |
| 669 | D8 | — | 16 | 1 | no | — |
| 670 | M16 | — | 2 | 2 | no | — |
| 671 | M16 | — | 4 | 1 | no | — |
| 672 | M16 | — | 4 | 1 | no | — |
| 673 | M16 | — | 4 | 1 | no | — |
| 674 | M16 | — | 8 | 1 | no | — |
| 675 | M16 | — | 8 | 1 | no | — |
| 676 | M16 | — | 16 | 2 | no | — |
| 677 | M16 | — | 16 | 2 | no | — |
| 678 | M16 | — | 16 | 4 | no | — |
| 679 | C2×C8 | — | 2 | 1 | no | — |
| 680 | C2×C8 | — | 2 | 1 | no | — |
| 681 | C2×C8 | — | 2 | 1 | no | — |
| 682 | C2×C8 | — | 2 | 1 | no | — |
| 683 | C2×C8 | — | 4 | 1 | no | — |
| 684 | C2×C8 | — | 4 | 1 | no | — |
| 685 | C2×C8 | — | 4 | 1 | no | — |
| 686 | C2×C8 | — | 4 | 1 | no | — |
| 687 | C2×C8 | — | 4 | 1 | no | — |
| 688 | C2×C8 | — | 4 | 1 | no | — |
| 689 | C2×C8 | — | 4 | 1 | no | — |
| 690 | C2×C8 | — | 4 | 1 | no | — |
| 691 | C2×C8 | — | 4 | 1 | no | — |
| 692 | C2×C8 | — | 4 | 1 | no | — |
| 693 | C2×C8 | — | 4 | 1 | no | — |
| 694 | C2×C8 | — | 4 | 1 | no | — |
| 695 | C2×C8 | — | 4 | 1 | no | — |
| 696 | C2×C8 | — | 4 | 1 | no | — |
| 697 | C2×C8 | — | 4 | 1 | no | — |
| 698 | C2×C8 | — | 4 | 1 | no | — |
| 699 | C2×C8 | — | 4 | 1 | no | — |
| 700 | C2×C8 | — | 4 | 1 | no | — |
| 701 | C2×C8 | — | 4 | 1 | no | — |
| 702 | C2×C8 | — | 4 | 1 | no | — |
| 703 | C2×C8 | — | 4 | 1 | no | — |
| 704 | C2×C8 | — | 8 | 1 | no | — |
| 705 | C2×C8 | — | 8 | 1 | no | — |
| 706 | C2×C8 | — | 8 | 1 | no | — |
| 707 | C2×C8 | — | 8 | 1 | no | — |
| 708 | C2×C8 | — | 8 | 1 | no | — |
| 709 | C2×C8 | — | 16 | 2 | no | — |
| 710 | C2×C8 | — | 16 | 2 | no | — |
| 711 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 712 | C2×C8 | #518 | 1 | 1 | yes | characteristic |
| 713 | C2×C8 | #546 | 1 | 1 | yes | characteristic |
| 714 | C2×C8 | #551 | 1 | 1 | yes | characteristic |
| 715 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 716 | C2×C8 | #575 | 1 | 1 | yes | characteristic |
| 717 | C2×C8 | #576 | 1 | 1 | yes | characteristic |
| 718 | C2×C8 | #578 | 1 | 1 | yes | characteristic |
| 719 | C4⋊C4 | — | 2 | 1 | no | — |
| 720 | C4⋊C4 | — | 2 | 2 | no | — |
| 721 | C4⋊C4 | — | 4 | 1 | no | — |
| 722 | C4⋊C4 | — | 4 | 1 | no | — |
| 723 | C4⋊C4 | — | 4 | 1 | no | — |
| 724 | C4⋊C4 | — | 4 | 2 | no | — |
| 725 | C4⋊C4 | — | 4 | 1 | no | — |
| 726 | C4⋊C4 | — | 4 | 2 | no | — |
| 727 | C4⋊C4 | — | 4 | 1 | no | — |
| 728 | C4⋊C4 | — | 8 | 2 | no | — |
| 729 | C4⋊C4 | — | 8 | 2 | no | — |
| 730 | C4⋊C4 | — | 8 | 1 | no | — |
| 731 | C4⋊C4 | — | 8 | 1 | no | — |
| 732 | C4⋊C4 | — | 8 | 1 | no | — |
| 733 | C4⋊C4 | — | 8 | 1 | no | — |
| 734 | C4⋊C4 | — | 8 | 1 | no | — |
| 735 | C4⋊C4 | — | 8 | 1 | no | — |
| 736 | C4⋊C4 | — | 16 | 1 | no | — |
| 737 | C4⋊C4 | — | 16 | 2 | no | — |
| 738 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 739 | C4⋊C4 | #442 | 1 | 1 | yes | characteristic |
| 740 | C22⋊C4 | — | 2 | 1 | no | — |
| 741 | C22⋊C4 | — | 2 | 1 | no | — |
| 742 | C22⋊C4 | — | 2 | 1 | no | — |
| 743 | C22⋊C4 | — | 2 | 1 | no | — |
| 744 | C22⋊C4 | — | 4 | 2 | no | — |
| 745 | C22⋊C4 | — | 4 | 2 | no | — |
| 746 | C22⋊C4 | — | 8 | 2 | no | — |
| 747 | C22⋊C4 | — | 8 | 2 | no | — |
| 748 | C22⋊C4 | — | 8 | 1 | no | — |
| 749 | C22⋊C4 | — | 8 | 1 | no | — |
| 750 | C22⋊C4 | — | 16 | 2 | no | — |
| 751 | C42 | — | 4 | 1 | no | — |
| 752 | C42 | — | 4 | 1 | no | — |
| 753 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 754 | C42 | #546 | 1 | 1 | yes | characteristic |
| 755 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 756 | C42 | #576 | 1 | 1 | yes | characteristic |
| 757 | C16 | — | 4 | 2 | no | — |
| 758 | C16 | — | 4 | 1 | no | — |
| 759 | C16 | — | 4 | 2 | no | — |
| 760 | C16 | — | 4 | 1 | no | — |
| 761 | C16 | — | 8 | 1 | no | — |
| 762 | C23 | — | 2 | 1 | no | — |
| 763 | C23 | — | 2 | 1 | no | — |
| 764 | C23 | — | 4 | 2 | no | — |
| 765 | C23 | — | 4 | 1 | no | — |
| 766 | C23 | — | 4 | 1 | no | — |
| 767 | C23 | — | 4 | 2 | no | — |
| 768 | C23 | — | 8 | 1 | no | — |
| 769 | C23 | — | 8 | 1 | no | — |
| 770 | C23 | — | 8 | 1 | no | — |
| 771 | C23 | — | 8 | 1 | no | — |
| 772 | C23 | — | 8 | 1 | no | — |
| 773 | C23 | — | 8 | 1 | no | — |
| 774 | C23 | — | 8 | 1 | no | — |
| 775 | C23 | — | 8 | 1 | no | — |
| 776 | C23 | #3265 | 1 | 1 | yes | characteristic |
| 777 | Q8 | — | 8 | 1 | no | — |
| 778 | Q8 | — | 8 | 1 | no | — |
| 779 | Q8 | — | 8 | 2 | no | — |
| 780 | Q8 | — | 8 | 2 | no | — |
| 781 | Q8 | — | 16 | 1 | no | — |
| 782 | Q8 | — | 16 | 1 | no | — |
| 783 | D4 | — | 2 | 1 | no | — |
| 784 | D4 | — | 2 | 1 | no | — |
| 785 | D4 | — | 2 | 1 | no | — |
| 786 | D4 | — | 4 | 2 | no | — |
| 787 | D4 | — | 4 | 2 | no | — |
| 788 | D4 | — | 4 | 2 | no | — |
| 789 | D4 | — | 8 | 1 | no | — |
| 790 | D4 | — | 8 | 1 | no | — |
| 791 | D4 | — | 8 | 1 | no | — |
| 792 | D4 | — | 8 | 1 | no | — |
| 793 | D4 | — | 8 | 1 | no | — |
| 794 | D4 | — | 8 | 1 | no | — |
| 795 | D4 | — | 16 | 1 | no | — |
| 796 | D4 | — | 16 | 4 | no | — |
| 797 | D4 | — | 16 | 4 | no | — |
| 798 | D4 | — | 16 | 1 | no | — |
| 799 | D4 | — | 16 | 1 | no | — |
| 800 | D4 | AGL(1,ℤ/16) | 1 | 2 | yes | complemented |
| 801 | C2×C4 | — | 2 | 1 | no | — |
| 802 | C2×C4 | — | 2 | 1 | no | — |
| 803 | C2×C4 | — | 2 | 1 | no | — |
| 804 | C2×C4 | — | 2 | 1 | no | — |
| 805 | C2×C4 | — | 4 | 1 | no | — |
| 806 | C2×C4 | — | 4 | 1 | no | — |
| 807 | C2×C4 | — | 4 | 1 | no | — |
| 808 | C2×C4 | — | 4 | 1 | no | — |
| 809 | C2×C4 | — | 4 | 1 | no | — |
| 810 | C2×C4 | — | 4 | 1 | no | — |
| 811 | C2×C4 | — | 4 | 1 | no | — |
| 812 | C2×C4 | — | 4 | 1 | no | — |
| 813 | C2×C4 | — | 4 | 1 | no | — |
| 814 | C2×C4 | — | 4 | 1 | no | — |
| 815 | C2×C4 | — | 4 | 1 | no | — |
| 816 | C2×C4 | — | 4 | 2 | no | — |
| 817 | C2×C4 | — | 8 | 2 | no | — |
| 818 | C2×C4 | — | 8 | 2 | no | — |
| 819 | C2×C4 | — | 8 | 1 | no | — |
| 820 | C2×C4 | — | 8 | 1 | no | — |
| 821 | C2×C4 | — | 8 | 2 | no | — |
| 822 | C2×C4 | — | 8 | 2 | no | — |
| 823 | C2×C4 | — | 8 | 1 | no | — |
| 824 | C2×C4 | — | 8 | 1 | no | — |
| 825 | C2×C4 | — | 8 | 1 | no | — |
| 826 | C2×C4 | — | 8 | 2 | no | — |
| 827 | C2×C4 | — | 8 | 1 | no | — |
| 828 | C2×C4 | — | 16 | 4 | no | — |
| 829 | C2×C4 | — | 16 | 4 | no | — |
| 830 | C2×C4 | — | 16 | 1 | no | — |
| 831 | C2×C4 | — | 16 | 1 | no | — |
| 832 | C2×C4 | — | 16 | 1 | no | — |
| 833 | C2×C4 | — | 16 | 1 | no | — |
| 834 | C2×C4 | — | 16 | 1 | no | — |
| 835 | C2×C4 | — | 16 | 1 | no | — |
| 836 | C2×C4 | — | 16 | 1 | no | — |
| 837 | C2×C4 | — | 32 | 4 | no | — |
| 838 | C2×C4 | #2358 | 1 | 1 | yes | characteristic |
| 839 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 840 | C2×C4 | #2946 | 1 | 1 | yes | characteristic |
| 841 | C2×C4 | #3264 | 1 | 1 | yes | characteristic |
| 842 | C2×C4 | #3264 | 1 | 1 | yes | characteristic |
| 843 | C2×C4 | #3269 | 1 | 1 | yes | characteristic |
| 844 | C2×C4 | #3290 | 1 | 1 | yes | characteristic |
| 845 | C2×C4 | #3290 | 1 | 1 | yes | characteristic |
| 846 | C2×C4 | #3306 | 1 | 1 | yes | characteristic |
| 847 | C2×C4 | #3318 | 1 | 1 | yes | characteristic |
| 848 | C8 | — | 2 | 1 | no | — |
| 849 | C8 | — | 2 | 1 | no | — |
| 850 | C8 | — | 4 | 2 | no | — |
| 851 | C8 | — | 4 | 1 | no | — |
| 852 | C8 | — | 4 | 1 | no | — |
| 853 | C8 | — | 8 | 1 | no | — |
| 854 | C8 | — | 8 | 1 | no | — |
| 855 | C8 | — | 8 | 1 | no | — |
| 856 | C8 | — | 8 | 1 | no | — |
| 857 | C8 | — | 8 | 1 | no | — |
| 858 | C8 | — | 8 | 1 | no | — |
| 859 | C8 | — | 16 | 1 | no | — |
| 860 | C8 | — | 16 | 1 | no | — |
| 861 | C8 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 862 | C8 | #2951 | 1 | 1 | yes | characteristic |
| 863 | C8 | #3322 | 1 | 1 | yes | characteristic |
| 864 | C8 | #3330 | 1 | 1 | yes | characteristic |
| 865 | C22 | — | 2 | 1 | no | — |
| 866 | C22 | — | 2 | 1 | no | — |
| 867 | C22 | — | 2 | 2 | no | — |
| 868 | C22 | — | 4 | 1 | no | — |
| 869 | C22 | — | 4 | 1 | no | — |
| 870 | C22 | — | 4 | 1 | no | — |
| 871 | C22 | — | 4 | 1 | no | — |
| 872 | C22 | — | 4 | 1 | no | — |
| 873 | C22 | — | 8 | 2 | no | — |
| 874 | C22 | — | 8 | 2 | no | — |
| 875 | C22 | — | 8 | 2 | no | — |
| 876 | C22 | — | 8 | 2 | no | — |
| 877 | C22 | — | 8 | 2 | no | — |
| 878 | C22 | — | 16 | 1 | no | — |
| 879 | C22 | — | 16 | 1 | no | — |
| 880 | C22 | — | 16 | 1 | no | — |
| 881 | C22 | — | 16 | 1 | no | — |
| 882 | C22 | — | 16 | 1 | no | — |
| 883 | C22 | — | 16 | 1 | no | — |
| 884 | C22 | — | 16 | 1 | no | — |
| 885 | C22 | #20030 | 1 | 1 | yes | characteristic |
| 886 | C22 | #20083 | 1 | 1 | yes | characteristic |
| 887 | C22 | #22858 | 1 | 1 | yes | characteristic |
| 888 | C4 | — | 2 | 1 | no | — |
| 889 | C4 | — | 2 | 1 | no | — |
| 890 | C4 | — | 2 | 1 | no | — |
| 891 | C4 | — | 4 | 1 | no | — |
| 892 | C4 | — | 4 | 1 | no | — |
| 893 | C4 | — | 8 | 2 | no | — |
| 894 | C4 | — | 16 | 1 | no | — |
| 895 | C4 | — | 16 | 1 | no | — |
| 896 | C4 | — | 16 | 2 | no | — |
| 897 | C4 | — | 32 | 1 | no | — |
| 898 | C4 | #20022 | 1 | 1 | yes | characteristic |
| 899 | C4 | #20058 | 1 | 1 | yes | characteristic |
| 900 | C4 | #22878 | 1 | 1 | yes | characteristic |
| 901 | C4 | #22895 | 1 | 1 | yes | characteristic |
| 902 | C4 | C2×AGL(1,ℤ/16) | 1 | 1 | yes | characteristic |
| 903 | C4 | #33471 | 1 | 1 | yes | characteristic |
| 904 | C2 | — | 2 | 1 | no | — |
| 905 | C2 | — | 2 | 1 | no | — |
| 906 | C2 | — | 4 | 2 | no | — |
| 907 | C2 | — | 8 | 1 | no | — |
| 908 | C2 | — | 16 | 2 | no | — |
| 909 | C2 | — | 32 | 1 | no | — |
| 910 | C2 | #227342 | 1 | 1 | yes | characteristic |
| 911 | C2 | #498116 | 1 | 1 | yes | characteristic |
| 912 | C2 | #498125 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #22858 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #488990 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #8202 ◁ G | |
| LECS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #498334 | C2 | semidirect |
| 2. #497555 | C2 | semidirect |
| 4. #229212 | C2 | semidirect |
| 5. #220900 | C2 | semidirect |
| 6. #141760 | C2 | semidirect |
| 7. #140297 | C2 | semidirect |
| 8. #140221 | C2 | semidirect |
| 9. #138716 | C2 | semidirect |
| 10. #138653 | C2 | semidirect |
| 11. #137517 | C2 | semidirect |
| 12. #136424 | C2 | semidirect |
| 13. #136401 | C2 | semidirect |
| 14. #128757 | C2 | semidirect |
| 15. #128717 | C2 | semidirect |
| 43. #12344 | C4 | semidirect |
| 44. #12344 | C4 | semidirect |
| 45. #12340 | C4 | semidirect |
| 46. #12340 | C4 | semidirect |
| 98. #2241 | C2×C4 | semidirect |
| 99. #2240 | C2×C4 | semidirect |
| 142. #1669 | C2×C4 | semidirect |
| 143. #1669 | C2×C4 | semidirect |
| 144. #1667 | C2×C4 | semidirect |
| 145. #1667 | C2×C4 | semidirect |
| 175. #1364 | C2×C4 | semidirect |
| 176. #1364 | C2×C4 | semidirect |
| 180. D4⋊C16 | C2×C4 | semidirect |
| 181. D4⋊C16 | C2×C4 | semidirect |
| 800. D4 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #498334 | 2 |
| #497555 | 2 |
| #488990 | 2 |
| #229212 | 2 |
| #220900 | 2 |
| #141760 | 2 |
| #140297 | 2 |
| #140221 | 2 |
| #138716 | 2 |
| #138653 | 2 |
| #137517 | 2 |
| #136424 | 2 |
| #136401 | 2 |
| #128757 | 2 |
| #128717 | 2 |