Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1003 conjugacy classes of subgroups.
The subgroup lattice has 860 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #498621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #498578 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #491517 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #231640 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #231527 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #141312 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #141298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #141294 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #141235 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #137579 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #137549 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #137546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #137516 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #129184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #129175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #33717 | C22 | 1 | 1 | yes | characteristic |
| 17 | #33717 | C22 | 1 | 1 | yes | characteristic |
| 18 | #33707 | C22 | 1 | 1 | yes | characteristic |
| 19 | #33707 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×AGL(1,ℤ/16) | — | 2 | 1 | no | — |
| 21 | #23223 | — | 2 | 1 | no | — |
| 22 | #23188 | C22 | 1 | 1 | yes | characteristic |
| 23 | #23180 | C22 | 1 | 1 | yes | characteristic |
| 24 | #23180 | C22 | 1 | 1 | yes | characteristic |
| 25 | #23162 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19603 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#1706 | C22 | 1 | 1 | yes | characteristic |
| 28 | #18066 | — | 2 | 1 | no | — |
| 29 | #13279 | C22 | 1 | 1 | yes | characteristic |
| 30 | #13257 | C22 | 1 | 1 | yes | characteristic |
| 31 | #13255 | C22 | 1 | 1 | yes | characteristic |
| 32 | #13255 | C22 | 1 | 1 | yes | characteristic |
| 33 | #13249 | — | 2 | 1 | no | — |
| 34 | #13153 | — | 2 | 1 | no | — |
| 35 | #13143 | — | 2 | 1 | no | — |
| 36 | #13040 | — | 2 | 1 | no | — |
| 37 | #13037 | — | 2 | 1 | no | — |
| 38 | #12955 | — | 2 | 1 | no | — |
| 39 | C4×#365 | C22 | 1 | 1 | yes | characteristic |
| 40 | #12666 | C22 | 1 | 1 | yes | characteristic |
| 41 | #12666 | C22 | 1 | 1 | yes | characteristic |
| 42 | #12650 | — | 2 | 1 | no | — |
| 43 | #12527 | C4 | 1 | 2 | yes | complemented |
| 44 | #12527 | C4 | 1 | 2 | yes | complemented |
| 45 | #12526 | C4 | 1 | 2 | yes | complemented |
| 46 | #12525 | C4 | 1 | 2 | yes | complemented |
| 47 | #12000 | C22 | 1 | 1 | yes | characteristic |
| 48 | #11996 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11940 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11931 | C22 | 1 | 1 | yes | characteristic |
| 51 | #11925 | C22 | 1 | 1 | yes | characteristic |
| 52 | #11925 | C22 | 1 | 1 | yes | characteristic |
| 53 | #11402 | C22 | 1 | 1 | yes | characteristic |
| 54 | #9753 | C22 | 1 | 1 | yes | characteristic |
| 55 | #9753 | C22 | 1 | 1 | yes | characteristic |
| 56 | #9747 | — | 2 | 1 | no | — |
| 57 | #9743 | C22 | 1 | 1 | yes | characteristic |
| 58 | #9739 | C22 | 1 | 1 | yes | characteristic |
| 59 | #9719 | — | 2 | 1 | no | — |
| 60 | #9064 | — | 2 | 1 | no | — |
| 61 | #9063 | — | 2 | 1 | no | — |
| 62 | #9053 | — | 2 | 1 | no | — |
| 63 | #9053 | — | 2 | 1 | no | — |
| 64 | C8×#108 | C22 | 1 | 1 | yes | characteristic |
| 65 | #8283 | C22 | 1 | 1 | yes | characteristic |
| 66 | #8282 | C22 | 1 | 1 | yes | characteristic |
| 67 | #7174 | C22 | 1 | 1 | yes | characteristic |
| 68 | #7173 | C22 | 1 | 1 | yes | characteristic |
| 69 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 70 | #7168 | C22 | 1 | 1 | yes | characteristic |
| 71 | C2×#509 | — | 2 | 1 | no | — |
| 72 | C2×#509 | — | 2 | 1 | no | — |
| 73 | C2×#509 | — | 4 | 1 | no | — |
| 74 | #3169 | — | 2 | 1 | no | — |
| 75 | #3169 | — | 2 | 1 | no | — |
| 76 | C2×#500 | C23 | 1 | 1 | yes | characteristic |
| 77 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 78 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#493 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×#492 | — | 2 | 1 | no | — |
| 81 | C2×#486 | — | 2 | 1 | no | — |
| 82 | C2×#444 | — | 2 | 1 | no | — |
| 83 | C2×#444 | — | 2 | 1 | no | — |
| 84 | C2×#442 | — | 2 | 1 | no | — |
| 85 | #2935 | — | 2 | 1 | no | — |
| 86 | #2935 | — | 2 | 1 | no | — |
| 87 | #2369 | — | 2 | 1 | no | — |
| 88 | #2366 | — | 2 | 1 | no | — |
| 89 | #2250 | — | 2 | 2 | no | — |
| 90 | #2250 | — | 4 | 1 | no | — |
| 91 | #2248 | C2×C4 | 1 | 2 | yes | — |
| 92 | #2248 | C2×C4 | 1 | 2 | yes | — |
| 93 | #2246 | C2×C4 | 1 | 2 | yes | — |
| 94 | #2246 | C2×C4 | 1 | 2 | yes | — |
| 95 | #2243 | — | 2 | 2 | no | — |
| 96 | #2243 | — | 4 | 1 | no | — |
| 97 | #2241 | C2×C4 | 1 | 2 | yes | complemented |
| 98 | #2241 | C2×C4 | 1 | 2 | yes | complemented |
| 99 | #2240 | C2×C4 | 1 | 2 | yes | complemented |
| 100 | #2240 | C2×C4 | 1 | 2 | yes | complemented |
| 101 | AGL(1,ℤ/16) | — | 4 | 4 | no | — |
| 102 | C2×#365 | D4 | 1 | 1 | yes | characteristic |
| 103 | C2×#365 | D4 | 1 | 1 | yes | characteristic |
| 104 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 105 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×#361 | — | 2 | 1 | no | — |
| 107 | C2×#361 | — | 2 | 1 | no | — |
| 108 | C2×#360 | — | 2 | 1 | no | — |
| 109 | C2×#360 | — | 2 | 1 | no | — |
| 110 | C2×#360 | — | 2 | 1 | no | — |
| 111 | C2×#360 | — | 2 | 1 | no | — |
| 112 | #2139 | — | 2 | 1 | no | — |
| 113 | #2139 | — | 2 | 1 | no | — |
| 114 | #2139 | — | 4 | 1 | no | — |
| 115 | C2×#347 | — | 2 | 1 | no | — |
| 116 | C2×#347 | — | 2 | 1 | no | — |
| 117 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 118 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 119 | #1987 | — | 2 | 1 | no | — |
| 120 | #1987 | — | 2 | 1 | no | — |
| 121 | #1982 | — | 2 | 1 | no | — |
| 122 | #1982 | — | 2 | 1 | no | — |
| 123 | #1980 | — | 2 | 1 | no | — |
| 124 | #1980 | — | 2 | 1 | no | — |
| 125 | #1975 | — | 2 | 1 | no | — |
| 126 | #1975 | — | 2 | 1 | no | — |
| 127 | #1972 | — | 2 | 1 | no | — |
| 128 | #1943 | — | 2 | 1 | no | — |
| 129 | #1936 | — | 4 | 1 | no | — |
| 130 | #1925 | — | 4 | 1 | no | — |
| 131 | #1918 | — | 4 | 1 | no | — |
| 132 | #1879 | — | 4 | 1 | no | — |
| 133 | #1876 | — | 4 | 1 | no | — |
| 134 | #1876 | — | 4 | 1 | no | — |
| 135 | #1862 | — | 4 | 1 | no | — |
| 136 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 137 | #1776 | — | 2 | 1 | no | — |
| 138 | C4×#107 | D4 | 1 | 1 | yes | characteristic |
| 139 | C4×#106 | C23 | 1 | 1 | yes | characteristic |
| 140 | #1770 | — | 2 | 1 | no | — |
| 141 | #1770 | C23 | 1 | 1 | yes | characteristic |
| 142 | #1770 | C23 | 1 | 1 | yes | characteristic |
| 143 | #1762 | — | 4 | 1 | no | — |
| 144 | #1713 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 145 | #1712 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 146 | #1709 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 147 | #1709 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 148 | #1706 | — | 2 | 1 | no | — |
| 149 | #1706 | — | 2 | 1 | no | — |
| 150 | #1706 | — | 2 | 1 | no | — |
| 151 | #1706 | — | 2 | 1 | no | — |
| 152 | #1706 | C2×C4 | 1 | 2 | yes | — |
| 153 | #1706 | C2×C4 | 1 | 2 | yes | — |
| 154 | #1589 | — | 4 | 1 | no | — |
| 155 | #1581 | — | 4 | 1 | no | — |
| 156 | #1581 | — | 4 | 1 | no | — |
| 157 | C8×D8 | — | 4 | 1 | no | — |
| 158 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 159 | C2×#335 | D4 | 1 | 1 | yes | characteristic |
| 160 | C2×#334 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×#333 | — | 2 | 1 | no | — |
| 162 | C2×#331 | — | 2 | 1 | no | — |
| 163 | #1502 | — | 2 | 1 | no | — |
| 164 | #1502 | — | 2 | 1 | no | — |
| 165 | #1480 | — | 2 | 1 | no | — |
| 166 | #1480 | — | 2 | 1 | no | — |
| 167 | C8×M16 | — | 2 | 1 | no | — |
| 168 | C2×C82 | C23 | 1 | 1 | yes | characteristic |
| 169 | #1387 | — | 2 | 1 | no | — |
| 170 | #1387 | — | 2 | 1 | no | — |
| 171 | #1383 | D4 | 1 | 1 | yes | characteristic |
| 172 | #1383 | D4 | 1 | 1 | yes | characteristic |
| 173 | #1375 | — | 2 | 1 | no | — |
| 174 | #1375 | — | 2 | 1 | no | — |
| 175 | #1368 | — | 2 | 2 | no | — |
| 176 | #1367 | — | 2 | 1 | no | — |
| 177 | #1367 | — | 2 | 1 | no | — |
| 178 | #1364 | — | 4 | 1 | no | — |
| 179 | #1361 | — | 4 | 1 | no | — |
| 180 | #1360 | — | 4 | 1 | no | — |
| 181 | #1360 | — | 4 | 1 | no | — |
| 182 | #1312 | C2×C4 | 1 | 2 | yes | complemented |
| 183 | #1312 | C2×C4 | 1 | 2 | yes | complemented |
| 184 | #1279 | — | 2 | 1 | no | — |
| 185 | #1279 | D4 | 1 | 1 | yes | characteristic |
| 186 | #1279 | D4 | 1 | 1 | yes | characteristic |
| 187 | #1278 | — | 2 | 1 | no | — |
| 188 | C2×#135 | — | 2 | 1 | no | — |
| 189 | C2×#135 | — | 2 | 1 | no | — |
| 190 | C2×#135 | — | 2 | 1 | no | — |
| 191 | C2×#135 | — | 2 | 1 | no | — |
| 192 | C22×SD16 | — | 8 | 1 | no | — |
| 193 | C22×D8 | — | 2 | 1 | no | — |
| 194 | C22×D8 | — | 2 | 1 | no | — |
| 195 | C2×#131 | — | 4 | 1 | no | — |
| 196 | C2×#131 | — | 4 | 1 | no | — |
| 197 | #532 | — | 2 | 1 | no | — |
| 198 | #532 | — | 2 | 1 | no | — |
| 199 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 200 | C2×#127 | — | 2 | 1 | no | — |
| 201 | C2×C4×D4 | — | 4 | 1 | no | — |
| 202 | C2×C4×D4 | — | 4 | 1 | no | — |
| 203 | #509 | — | 4 | 2 | no | — |
| 204 | #509 | — | 4 | 2 | no | — |
| 205 | #509 | — | 8 | 1 | no | — |
| 206 | #509 | — | 8 | 1 | no | — |
| 207 | #509 | — | 8 | 2 | no | — |
| 208 | #509 | — | 8 | 2 | no | — |
| 209 | C2×SD32 | — | 2 | 2 | no | — |
| 210 | C2×SD32 | — | 2 | 2 | no | — |
| 211 | C2×SD32 | — | 4 | 2 | no | — |
| 212 | C2×D16 | — | 2 | 2 | no | — |
| 213 | C2×D16 | — | 2 | 2 | no | — |
| 214 | C2×D16 | — | 4 | 2 | no | — |
| 215 | C2×M32 | — | 2 | 1 | no | — |
| 216 | C2×M32 | — | 2 | 1 | no | — |
| 217 | C2×M32 | — | 2 | 1 | no | — |
| 218 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | #500 | — | 2 | 1 | no | — |
| 221 | #500 | — | 2 | 1 | no | — |
| 222 | #500 | — | 2 | 1 | no | — |
| 223 | #500 | — | 2 | 1 | no | — |
| 224 | #500 | — | 2 | 1 | no | — |
| 225 | #500 | C22×C4 | 1 | 2 | yes | — |
| 226 | #495 | — | 2 | 1 | no | — |
| 227 | #495 | — | 2 | 1 | no | — |
| 228 | #495 | — | 2 | 1 | no | — |
| 229 | #495 | — | 2 | 1 | no | — |
| 230 | #494 | C22×C4 | 1 | 1 | yes | characteristic |
| 231 | #494 | C22×C4 | 1 | 1 | yes | characteristic |
| 232 | #493 | — | 2 | 1 | no | — |
| 233 | #493 | — | 2 | 1 | no | — |
| 234 | #493 | — | 2 | 1 | no | — |
| 235 | #493 | — | 2 | 1 | no | — |
| 236 | #493 | — | 2 | 1 | no | — |
| 237 | #493 | C22×C4 | 1 | 2 | yes | — |
| 238 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 239 | #493 | C22×C4 | 1 | 1 | yes | characteristic |
| 240 | #492 | — | 2 | 2 | no | — |
| 241 | #492 | — | 2 | 2 | no | — |
| 242 | #492 | — | 2 | 1 | no | — |
| 243 | #492 | — | 2 | 1 | no | — |
| 244 | #492 | — | 8 | 1 | no | — |
| 245 | #486 | — | 2 | 2 | no | — |
| 246 | #486 | — | 2 | 2 | no | — |
| 247 | #486 | — | 2 | 1 | no | — |
| 248 | #486 | — | 2 | 1 | no | — |
| 249 | #486 | — | 2 | 1 | no | — |
| 250 | #486 | — | 2 | 1 | no | — |
| 251 | #486 | — | 4 | 1 | no | — |
| 252 | #486 | — | 4 | 1 | no | — |
| 253 | #466 | — | 4 | 1 | no | — |
| 254 | #466 | — | 4 | 1 | no | — |
| 255 | #466 | — | 8 | 1 | no | — |
| 256 | #444 | — | 4 | 2 | no | — |
| 257 | #444 | — | 4 | 2 | no | — |
| 258 | #444 | — | 8 | 1 | no | — |
| 259 | #444 | — | 8 | 1 | no | — |
| 260 | #442 | — | 4 | 2 | no | — |
| 261 | #442 | — | 8 | 1 | no | — |
| 262 | C4×D8 | — | 4 | 1 | no | — |
| 263 | C4×D8 | — | 4 | 1 | no | — |
| 264 | C4×D8 | — | 8 | 1 | no | — |
| 265 | #436 | — | 4 | 1 | no | — |
| 266 | #436 | — | 4 | 1 | no | — |
| 267 | #435 | — | 8 | 1 | no | — |
| 268 | #435 | — | 8 | 1 | no | — |
| 269 | C8×D4 | — | 4 | 1 | no | — |
| 270 | C8×D4 | — | 4 | 1 | no | — |
| 271 | #431 | — | 2 | 1 | no | — |
| 272 | C2×#108 | C2×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×#108 | C2×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×#107 | — | 2 | 1 | no | — |
| 275 | C2×#107 | — | 2 | 1 | no | — |
| 276 | C2×#107 | — | 2 | 1 | no | — |
| 277 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 280 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C4⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×#104 | — | 4 | 1 | no | — |
| 283 | C2×#104 | — | 4 | 1 | no | — |
| 284 | C2×#104 | — | 4 | 1 | no | — |
| 285 | C2×#104 | — | 4 | 1 | no | — |
| 286 | C2×#102 | — | 4 | 1 | no | — |
| 287 | C2×#102 | — | 4 | 1 | no | — |
| 288 | C2×#102 | — | 4 | 1 | no | — |
| 289 | C2×#102 | — | 4 | 1 | no | — |
| 290 | C2×#102 | — | 4 | 1 | no | — |
| 291 | C2×#102 | — | 4 | 1 | no | — |
| 292 | #408 | — | 4 | 1 | no | — |
| 293 | #408 | — | 4 | 1 | no | — |
| 294 | C4×M16 | — | 2 | 1 | no | — |
| 295 | C2×#97 | — | 2 | 1 | no | — |
| 296 | C2×#97 | — | 2 | 1 | no | — |
| 297 | C2×#97 | — | 4 | 1 | no | — |
| 298 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 301 | #391 | — | 8 | 1 | no | — |
| 302 | #390 | — | 4 | 1 | no | — |
| 303 | #390 | — | 4 | 1 | no | — |
| 304 | #389 | — | 4 | 1 | no | — |
| 305 | #389 | — | 4 | 1 | no | — |
| 306 | #386 | — | 8 | 1 | no | — |
| 307 | C4×C4⋊C4 | — | 2 | 1 | no | — |
| 308 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4×C4⋊C4 | — | 4 | 1 | no | — |
| 310 | C4×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 311 | C4×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 312 | #365 | — | 2 | 2 | no | — |
| 313 | #365 | — | 4 | 1 | no | — |
| 314 | C4⋊C16 | — | 2 | 1 | no | — |
| 315 | C4⋊C16 | — | 2 | 1 | no | — |
| 316 | C4⋊C16 | — | 2 | 1 | no | — |
| 317 | C4⋊C16 | — | 2 | 1 | no | — |
| 318 | #361 | — | 4 | 2 | no | — |
| 319 | #361 | — | 8 | 1 | no | — |
| 320 | #360 | — | 4 | 2 | no | — |
| 321 | #360 | — | 4 | 2 | no | — |
| 322 | #360 | — | 8 | 1 | no | — |
| 323 | #360 | — | 8 | 1 | no | — |
| 324 | #358 | — | 2 | 2 | no | — |
| 325 | #358 | — | 2 | 2 | no | — |
| 326 | #358 | — | 4 | 2 | no | — |
| 327 | #357 | — | 2 | 2 | no | — |
| 328 | #357 | — | 2 | 2 | no | — |
| 329 | #357 | — | 4 | 2 | no | — |
| 330 | #347 | — | 4 | 2 | no | — |
| 331 | #347 | — | 8 | 1 | no | — |
| 332 | #346 | — | 2 | 1 | no | — |
| 333 | #346 | #41 | 1 | 2 | yes | — |
| 334 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 335 | C4×C16 | C22×C4 | 1 | 2 | yes | — |
| 336 | #341 | — | 2 | 1 | no | — |
| 337 | #340 | — | 2 | 1 | no | — |
| 338 | #340 | — | 2 | 1 | no | — |
| 339 | #340 | — | 4 | 1 | no | — |
| 340 | #340 | — | 4 | 1 | no | — |
| 341 | #340 | — | 4 | 1 | no | — |
| 342 | #340 | — | 4 | 1 | no | — |
| 343 | #336 | — | 2 | 1 | no | — |
| 344 | #336 | — | 2 | 1 | no | — |
| 345 | #336 | — | 4 | 1 | no | — |
| 346 | #335 | — | 2 | 1 | no | — |
| 347 | #335 | — | 2 | 1 | no | — |
| 348 | #335 | — | 2 | 1 | no | — |
| 349 | #334 | — | 2 | 1 | no | — |
| 350 | #334 | — | 2 | 1 | no | — |
| 351 | #334 | — | 2 | 1 | no | — |
| 352 | #333 | — | 8 | 1 | no | — |
| 353 | #331 | — | 8 | 1 | no | — |
| 354 | #327 | — | 8 | 1 | no | — |
| 355 | #327 | — | 8 | 1 | no | — |
| 356 | D4⋊C8 | — | 4 | 1 | no | — |
| 357 | D4⋊C8 | — | 4 | 1 | no | — |
| 358 | D4⋊C8 | — | 4 | 1 | no | — |
| 359 | D4⋊C8 | — | 4 | 1 | no | — |
| 360 | #322 | — | 4 | 1 | no | — |
| 361 | C82 | — | 4 | 1 | no | — |
| 362 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 363 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 364 | C82 | #41 | 1 | 1 | yes | characteristic |
| 365 | C82 | #41 | 1 | 1 | yes | characteristic |
| 366 | C2×#41 | — | 4 | 1 | no | — |
| 367 | C2×#41 | — | 4 | 1 | no | — |
| 368 | C22×Q8 | — | 4 | 1 | no | — |
| 369 | C22×D4 | — | 4 | 1 | no | — |
| 370 | C22×D4 | — | 4 | 1 | no | — |
| 371 | C22×D4 | — | 4 | 1 | no | — |
| 372 | C23×C4 | — | 8 | 1 | no | — |
| 373 | #135 | — | 4 | 1 | no | — |
| 374 | #135 | — | 4 | 1 | no | — |
| 375 | #135 | — | 4 | 1 | no | — |
| 376 | #135 | — | 4 | 1 | no | — |
| 377 | #135 | — | 4 | 1 | no | — |
| 378 | #135 | — | 4 | 1 | no | — |
| 379 | #135 | — | 4 | 1 | no | — |
| 380 | #135 | — | 4 | 1 | no | — |
| 381 | #135 | — | 8 | 1 | no | — |
| 382 | #135 | — | 8 | 1 | no | — |
| 383 | #135 | — | 8 | 1 | no | — |
| 384 | #135 | — | 8 | 1 | no | — |
| 385 | C2×Q16 | — | 2 | 1 | no | — |
| 386 | C2×Q16 | — | 2 | 1 | no | — |
| 387 | C2×Q16 | — | 2 | 1 | no | — |
| 388 | C2×Q16 | — | 2 | 1 | no | — |
| 389 | C2×SD16 | — | 4 | 1 | no | — |
| 390 | C2×SD16 | — | 4 | 1 | no | — |
| 391 | C2×SD16 | — | 4 | 1 | no | — |
| 392 | C2×SD16 | — | 4 | 1 | no | — |
| 393 | C2×SD16 | — | 8 | 2 | no | — |
| 394 | C2×SD16 | — | 8 | 2 | no | — |
| 395 | C2×SD16 | — | 16 | 2 | no | — |
| 396 | C2×SD16 | — | 16 | 2 | no | — |
| 397 | C2×D8 | — | 2 | 2 | no | — |
| 398 | C2×D8 | — | 2 | 1 | no | — |
| 399 | C2×D8 | — | 2 | 1 | no | — |
| 400 | C2×D8 | — | 2 | 2 | no | — |
| 401 | C2×D8 | — | 2 | 1 | no | — |
| 402 | C2×D8 | — | 2 | 1 | no | — |
| 403 | C2×D8 | — | 4 | 1 | no | — |
| 404 | C2×D8 | — | 4 | 1 | no | — |
| 405 | C2×D8 | — | 4 | 1 | no | — |
| 406 | C2×D8 | — | 4 | 1 | no | — |
| 407 | C2×D8 | — | 4 | 1 | no | — |
| 408 | C2×D8 | — | 4 | 1 | no | — |
| 409 | C2×D8 | — | 4 | 1 | no | — |
| 410 | C2×D8 | — | 4 | 1 | no | — |
| 411 | C2×D8 | — | 8 | 1 | no | — |
| 412 | C2×D8 | — | 8 | 1 | no | — |
| 413 | C2×D8 | — | 8 | 1 | no | — |
| 414 | #131 | — | 8 | 2 | no | — |
| 415 | #131 | — | 8 | 2 | no | — |
| 416 | #131 | — | 16 | 1 | no | — |
| 417 | #131 | — | 16 | 1 | no | — |
| 418 | C2×M16 | — | 2 | 1 | no | — |
| 419 | C2×M16 | — | 2 | 1 | no | — |
| 420 | C2×M16 | — | 8 | 1 | no | — |
| 421 | C2×M16 | — | 8 | 1 | no | — |
| 422 | C22×C8 | — | 2 | 1 | no | — |
| 423 | C22×C8 | — | 2 | 1 | no | — |
| 424 | C22×C8 | — | 2 | 1 | no | — |
| 425 | C22×C8 | — | 4 | 1 | no | — |
| 426 | C22×C8 | — | 8 | 1 | no | — |
| 427 | C22×C8 | — | 8 | 1 | no | — |
| 428 | C22×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 429 | C22×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 430 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 431 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 432 | C4⋊Q8 | — | 2 | 2 | no | — |
| 433 | C4⋊Q8 | — | 2 | 1 | no | — |
| 434 | C4⋊Q8 | — | 2 | 1 | no | — |
| 435 | C4⋊Q8 | — | 4 | 1 | no | — |
| 436 | C4⋊Q8 | — | 4 | 1 | no | — |
| 437 | C4⋊Q8 | — | 4 | 1 | no | — |
| 438 | #127 | — | 2 | 2 | no | — |
| 439 | #127 | — | 2 | 1 | no | — |
| 440 | #127 | — | 2 | 1 | no | — |
| 441 | #127 | — | 4 | 1 | no | — |
| 442 | #127 | — | 4 | 1 | no | — |
| 443 | #127 | — | 4 | 1 | no | — |
| 444 | #124 | — | 4 | 1 | no | — |
| 445 | #124 | — | 4 | 1 | no | — |
| 446 | #121 | — | 4 | 1 | no | — |
| 447 | #121 | — | 4 | 1 | no | — |
| 448 | #121 | — | 4 | 1 | no | — |
| 449 | #121 | — | 4 | 1 | no | — |
| 450 | C4×D4 | — | 4 | 1 | no | — |
| 451 | C4×D4 | — | 4 | 1 | no | — |
| 452 | C4×D4 | — | 4 | 1 | no | — |
| 453 | C4×D4 | — | 4 | 1 | no | — |
| 454 | C4×D4 | — | 8 | 2 | no | — |
| 455 | C4×D4 | — | 8 | 2 | no | — |
| 456 | C4×D4 | — | 16 | 1 | no | — |
| 457 | C4×D4 | — | 16 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 459 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 460 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 461 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 462 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 463 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 464 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 465 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 466 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 467 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 468 | C2×C42 | — | 2 | 1 | no | — |
| 469 | C2×C42 | — | 2 | 1 | no | — |
| 470 | C2×C42 | — | 4 | 1 | no | — |
| 471 | C2×C42 | — | 8 | 1 | no | — |
| 472 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 473 | SD32 | — | 4 | 4 | no | — |
| 474 | SD32 | — | 8 | 2 | no | — |
| 475 | SD32 | — | 8 | 4 | no | — |
| 476 | D16 | — | 4 | 4 | no | — |
| 477 | D16 | — | 8 | 2 | no | — |
| 478 | D16 | — | 8 | 4 | no | — |
| 479 | M32 | — | 2 | 1 | no | — |
| 480 | M32 | — | 2 | 1 | no | — |
| 481 | M32 | — | 2 | 1 | no | — |
| 482 | M32 | — | 2 | 1 | no | — |
| 483 | M32 | — | 4 | 1 | no | — |
| 484 | M32 | — | 4 | 1 | no | — |
| 485 | M32 | — | 4 | 1 | no | — |
| 486 | M32 | — | 4 | 1 | no | — |
| 487 | M32 | — | 4 | 1 | no | — |
| 488 | M32 | — | 4 | 1 | no | — |
| 489 | C2×C16 | — | 2 | 2 | no | — |
| 490 | C2×C16 | — | 4 | 1 | no | — |
| 491 | C2×C16 | — | 4 | 1 | no | — |
| 492 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 493 | C2×C16 | C4×D4 | 1 | 2 | yes | — |
| 494 | #108 | — | 2 | 1 | no | — |
| 495 | #108 | — | 2 | 1 | no | — |
| 496 | #108 | — | 2 | 1 | no | — |
| 497 | #108 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 498 | #107 | — | 2 | 2 | no | — |
| 499 | #107 | — | 2 | 2 | no | — |
| 500 | #107 | — | 4 | 1 | no | — |
| 501 | #107 | — | 4 | 1 | no | — |
| 502 | #107 | — | 4 | 1 | no | — |
| 503 | #107 | — | 4 | 1 | no | — |
| 504 | #107 | — | 8 | 1 | no | — |
| 505 | #107 | — | 8 | 1 | no | — |
| 506 | #106 | — | 2 | 1 | no | — |
| 507 | #106 | — | 2 | 1 | no | — |
| 508 | #106 | — | 2 | 1 | no | — |
| 509 | #106 | — | 2 | 1 | no | — |
| 510 | C4⋊C8 | — | 2 | 1 | no | — |
| 511 | C4⋊C8 | — | 2 | 1 | no | — |
| 512 | C4⋊C8 | — | 2 | 1 | no | — |
| 513 | C4⋊C8 | — | 2 | 1 | no | — |
| 514 | C4⋊C8 | — | 4 | 1 | no | — |
| 515 | C4⋊C8 | — | 4 | 1 | no | — |
| 516 | C4⋊C8 | — | 4 | 1 | no | — |
| 517 | #104 | — | 8 | 2 | no | — |
| 518 | #104 | — | 8 | 2 | no | — |
| 519 | #104 | — | 16 | 1 | no | — |
| 520 | #104 | — | 16 | 1 | no | — |
| 521 | #102 | — | 4 | 2 | no | — |
| 522 | #102 | — | 4 | 2 | no | — |
| 523 | #102 | — | 4 | 2 | no | — |
| 524 | #102 | — | 4 | 2 | no | — |
| 525 | #102 | — | 4 | 1 | no | — |
| 526 | #102 | — | 4 | 1 | no | — |
| 527 | #102 | — | 4 | 1 | no | — |
| 528 | #102 | — | 4 | 1 | no | — |
| 529 | #102 | — | 8 | 1 | no | — |
| 530 | #102 | — | 8 | 1 | no | — |
| 531 | #102 | — | 8 | 2 | no | — |
| 532 | #102 | — | 8 | 2 | no | — |
| 533 | #102 | — | 16 | 1 | no | — |
| 534 | #102 | — | 16 | 1 | no | — |
| 535 | C22⋊C8 | — | 4 | 1 | no | — |
| 536 | C22⋊C8 | — | 8 | 1 | no | — |
| 537 | C22⋊C8 | — | 8 | 1 | no | — |
| 538 | C22⋊C8 | — | 8 | 1 | no | — |
| 539 | C22⋊C8 | — | 8 | 1 | no | — |
| 540 | #97 | — | 4 | 1 | no | — |
| 541 | #97 | — | 4 | 1 | no | — |
| 542 | #97 | — | 4 | 1 | no | — |
| 543 | #97 | — | 4 | 1 | no | — |
| 544 | #97 | — | 4 | 1 | no | — |
| 545 | #97 | — | 16 | 1 | no | — |
| 546 | C4×C8 | — | 2 | 1 | no | — |
| 547 | C4×C8 | — | 4 | 1 | no | — |
| 548 | C4×C8 | — | 4 | 1 | no | — |
| 549 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 550 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 551 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 552 | C4×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 553 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 554 | C4×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 555 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 556 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 557 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 558 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 559 | #95 | — | 2 | 1 | no | — |
| 560 | #95 | — | 2 | 1 | no | — |
| 561 | #95 | — | 4 | 1 | no | — |
| 562 | #95 | — | 8 | 1 | no | — |
| 563 | #95 | — | 8 | 1 | no | — |
| 564 | C24 | — | 8 | 1 | no | — |
| 565 | #41 | — | 8 | 1 | no | — |
| 566 | #41 | — | 8 | 1 | no | — |
| 567 | #41 | — | 8 | 1 | no | — |
| 568 | #41 | — | 8 | 1 | no | — |
| 569 | #41 | — | 8 | 1 | no | — |
| 570 | #41 | — | 8 | 1 | no | — |
| 571 | #41 | — | 8 | 1 | no | — |
| 572 | #41 | — | 8 | 1 | no | — |
| 573 | C2×Q8 | — | 4 | 1 | no | — |
| 574 | C2×Q8 | — | 4 | 1 | no | — |
| 575 | C2×Q8 | — | 4 | 2 | no | — |
| 576 | C2×Q8 | — | 8 | 1 | no | — |
| 577 | C2×Q8 | — | 16 | 1 | no | — |
| 578 | C2×Q8 | — | 16 | 1 | no | — |
| 579 | C2×D4 | — | 4 | 1 | no | — |
| 580 | C2×D4 | — | 4 | 1 | no | — |
| 581 | C2×D4 | — | 4 | 2 | no | — |
| 582 | C2×D4 | — | 4 | 2 | no | — |
| 583 | C2×D4 | — | 4 | 1 | no | — |
| 584 | C2×D4 | — | 4 | 1 | no | — |
| 585 | C2×D4 | — | 4 | 1 | no | — |
| 586 | C2×D4 | — | 4 | 1 | no | — |
| 587 | C2×D4 | — | 4 | 2 | no | — |
| 588 | C2×D4 | — | 8 | 1 | no | — |
| 589 | C2×D4 | — | 8 | 1 | no | — |
| 590 | C2×D4 | — | 8 | 1 | no | — |
| 591 | C2×D4 | — | 8 | 1 | no | — |
| 592 | C2×D4 | — | 8 | 1 | no | — |
| 593 | C2×D4 | — | 8 | 1 | no | — |
| 594 | C2×D4 | — | 8 | 1 | no | — |
| 595 | C2×D4 | — | 8 | 1 | no | — |
| 596 | C2×D4 | — | 8 | 1 | no | — |
| 597 | C2×D4 | — | 8 | 1 | no | — |
| 598 | C2×D4 | — | 8 | 1 | no | — |
| 599 | C2×D4 | — | 8 | 1 | no | — |
| 600 | C2×D4 | — | 8 | 1 | no | — |
| 601 | C2×D4 | — | 16 | 1 | no | — |
| 602 | C2×D4 | — | 16 | 1 | no | — |
| 603 | C22×C4 | — | 4 | 1 | no | — |
| 604 | C22×C4 | — | 4 | 1 | no | — |
| 605 | C22×C4 | — | 4 | 1 | no | — |
| 606 | C22×C4 | — | 4 | 1 | no | — |
| 607 | C22×C4 | — | 8 | 1 | no | — |
| 608 | C22×C4 | — | 8 | 1 | no | — |
| 609 | C22×C4 | — | 8 | 1 | no | — |
| 610 | C22×C4 | — | 16 | 2 | no | — |
| 611 | C22×C4 | — | 16 | 2 | no | — |
| 612 | C22×C4 | — | 32 | 1 | no | — |
| 613 | C22×C4 | D42 | 1 | 1 | yes | characteristic |
| 614 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 615 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 616 | Q16 | — | 4 | 1 | no | — |
| 617 | Q16 | — | 4 | 1 | no | — |
| 618 | Q16 | — | 4 | 1 | no | — |
| 619 | Q16 | — | 4 | 1 | no | — |
| 620 | Q16 | — | 8 | 1 | no | — |
| 621 | Q16 | — | 8 | 1 | no | — |
| 622 | SD16 | — | 8 | 1 | no | — |
| 623 | SD16 | — | 8 | 1 | no | — |
| 624 | SD16 | — | 8 | 1 | no | — |
| 625 | SD16 | — | 8 | 1 | no | — |
| 626 | SD16 | — | 16 | 1 | no | — |
| 627 | SD16 | — | 16 | 1 | no | — |
| 628 | SD16 | — | 16 | 4 | no | — |
| 629 | SD16 | — | 16 | 4 | no | — |
| 630 | D8 | — | 4 | 1 | no | — |
| 631 | D8 | — | 4 | 2 | no | — |
| 632 | D8 | — | 4 | 1 | no | — |
| 633 | D8 | — | 4 | 1 | no | — |
| 634 | D8 | — | 4 | 2 | no | — |
| 635 | D8 | — | 4 | 1 | no | — |
| 636 | D8 | — | 8 | 1 | no | — |
| 637 | D8 | — | 8 | 2 | no | — |
| 638 | D8 | — | 8 | 1 | no | — |
| 639 | D8 | — | 8 | 2 | no | — |
| 640 | D8 | — | 8 | 1 | no | — |
| 641 | D8 | — | 8 | 1 | no | — |
| 642 | D8 | — | 16 | 1 | no | — |
| 643 | D8 | — | 16 | 1 | no | — |
| 644 | D8 | — | 16 | 2 | no | — |
| 645 | M16 | — | 2 | 2 | no | — |
| 646 | M16 | — | 4 | 1 | no | — |
| 647 | M16 | — | 4 | 1 | no | — |
| 648 | M16 | — | 4 | 1 | no | — |
| 649 | M16 | — | 16 | 2 | no | — |
| 650 | M16 | — | 16 | 2 | no | — |
| 651 | C2×C8 | — | 2 | 1 | no | — |
| 652 | C2×C8 | — | 2 | 1 | no | — |
| 653 | C2×C8 | — | 2 | 1 | no | — |
| 654 | C2×C8 | — | 2 | 1 | no | — |
| 655 | C2×C8 | — | 4 | 1 | no | — |
| 656 | C2×C8 | — | 4 | 1 | no | — |
| 657 | C2×C8 | — | 4 | 2 | no | — |
| 658 | C2×C8 | — | 4 | 1 | no | — |
| 659 | C2×C8 | — | 4 | 1 | no | — |
| 660 | C2×C8 | — | 4 | 1 | no | — |
| 661 | C2×C8 | — | 4 | 1 | no | — |
| 662 | C2×C8 | — | 4 | 1 | no | — |
| 663 | C2×C8 | — | 4 | 1 | no | — |
| 664 | C2×C8 | — | 4 | 1 | no | — |
| 665 | C2×C8 | — | 4 | 1 | no | — |
| 666 | C2×C8 | — | 8 | 1 | no | — |
| 667 | C2×C8 | — | 8 | 1 | no | — |
| 668 | C2×C8 | — | 8 | 1 | no | — |
| 669 | C2×C8 | — | 8 | 1 | no | — |
| 670 | C2×C8 | — | 16 | 2 | no | — |
| 671 | C2×C8 | — | 16 | 2 | no | — |
| 672 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 673 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 674 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 675 | C2×C8 | #442 | 1 | 1 | yes | characteristic |
| 676 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 677 | C2×C8 | #518 | 1 | 1 | yes | characteristic |
| 678 | C2×C8 | #550 | 1 | 1 | yes | characteristic |
| 679 | C2×C8 | #559 | 1 | 1 | yes | characteristic |
| 680 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 681 | C2×C8 | #575 | 1 | 1 | yes | characteristic |
| 682 | C2×C8 | #576 | 1 | 1 | yes | characteristic |
| 683 | C2×C8 | #577 | 1 | 1 | yes | characteristic |
| 684 | C4⋊C4 | — | 4 | 1 | no | — |
| 685 | C4⋊C4 | — | 4 | 1 | no | — |
| 686 | C4⋊C4 | — | 4 | 1 | no | — |
| 687 | C4⋊C4 | — | 4 | 1 | no | — |
| 688 | C4⋊C4 | — | 4 | 2 | no | — |
| 689 | C4⋊C4 | — | 4 | 2 | no | — |
| 690 | C4⋊C4 | — | 4 | 1 | no | — |
| 691 | C4⋊C4 | — | 4 | 1 | no | — |
| 692 | C4⋊C4 | — | 4 | 1 | no | — |
| 693 | C4⋊C4 | — | 4 | 1 | no | — |
| 694 | C4⋊C4 | — | 4 | 1 | no | — |
| 695 | C4⋊C4 | — | 4 | 1 | no | — |
| 696 | C4⋊C4 | — | 4 | 1 | no | — |
| 697 | C4⋊C4 | — | 4 | 1 | no | — |
| 698 | C4⋊C4 | — | 8 | 1 | no | — |
| 699 | C4⋊C4 | — | 8 | 1 | no | — |
| 700 | C4⋊C4 | — | 32 | 1 | no | — |
| 701 | C22⋊C4 | — | 8 | 1 | no | — |
| 702 | C22⋊C4 | — | 8 | 1 | no | — |
| 703 | C22⋊C4 | — | 8 | 1 | no | — |
| 704 | C22⋊C4 | — | 8 | 1 | no | — |
| 705 | C22⋊C4 | — | 16 | 2 | no | — |
| 706 | C22⋊C4 | — | 16 | 2 | no | — |
| 707 | C22⋊C4 | — | 32 | 1 | no | — |
| 708 | C42 | — | 4 | 1 | no | — |
| 709 | C42 | — | 4 | 1 | no | — |
| 710 | C42 | — | 4 | 1 | no | — |
| 711 | C42 | — | 4 | 1 | no | — |
| 712 | C42 | — | 8 | 1 | no | — |
| 713 | C42 | — | 8 | 1 | no | — |
| 714 | C42 | — | 32 | 1 | no | — |
| 715 | C42 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 716 | C42 | #550 | 1 | 1 | yes | characteristic |
| 717 | C42 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 718 | C42 | #576 | 1 | 1 | yes | characteristic |
| 719 | C16 | — | 2 | 2 | no | — |
| 720 | C16 | — | 2 | 2 | no | — |
| 721 | C16 | — | 4 | 2 | no | — |
| 722 | C16 | — | 8 | 1 | no | — |
| 723 | C16 | — | 8 | 1 | no | — |
| 724 | C23 | — | 8 | 1 | no | — |
| 725 | C23 | — | 8 | 1 | no | — |
| 726 | C23 | — | 8 | 2 | no | — |
| 727 | C23 | — | 16 | 1 | no | — |
| 728 | C23 | — | 16 | 1 | no | — |
| 729 | C23 | — | 16 | 1 | no | — |
| 730 | C23 | — | 16 | 1 | no | — |
| 731 | C23 | — | 16 | 1 | no | — |
| 732 | C23 | — | 16 | 1 | no | — |
| 733 | C23 | #3274 | 1 | 1 | yes | characteristic |
| 734 | Q8 | — | 8 | 1 | no | — |
| 735 | Q8 | — | 8 | 1 | no | — |
| 736 | Q8 | — | 8 | 1 | no | — |
| 737 | Q8 | — | 8 | 1 | no | — |
| 738 | Q8 | — | 16 | 2 | no | — |
| 739 | Q8 | — | 32 | 1 | no | — |
| 740 | D4 | — | 8 | 2 | no | — |
| 741 | D4 | — | 8 | 1 | no | — |
| 742 | D4 | — | 8 | 1 | no | — |
| 743 | D4 | — | 8 | 2 | no | — |
| 744 | D4 | — | 8 | 1 | no | — |
| 745 | D4 | — | 8 | 1 | no | — |
| 746 | D4 | — | 8 | 1 | no | — |
| 747 | D4 | — | 8 | 1 | no | — |
| 748 | D4 | — | 8 | 2 | no | — |
| 749 | D4 | — | 8 | 1 | no | — |
| 750 | D4 | — | 8 | 1 | no | — |
| 751 | D4 | — | 8 | 2 | no | — |
| 752 | D4 | — | 16 | 1 | no | — |
| 753 | D4 | — | 16 | 1 | no | — |
| 754 | D4 | — | 16 | 2 | no | — |
| 755 | D4 | — | 16 | 1 | no | — |
| 756 | D4 | — | 16 | 1 | no | — |
| 757 | D4 | — | 16 | 1 | no | — |
| 758 | D4 | — | 16 | 1 | no | — |
| 759 | D4 | — | 16 | 1 | no | — |
| 760 | D4 | — | 16 | 1 | no | — |
| 761 | D4 | — | 16 | 1 | no | — |
| 762 | D4 | — | 16 | 1 | no | — |
| 763 | D4 | — | 32 | 1 | no | — |
| 764 | C2×C4 | — | 2 | 1 | no | — |
| 765 | C2×C4 | — | 2 | 1 | no | — |
| 766 | C2×C4 | — | 4 | 1 | no | — |
| 767 | C2×C4 | — | 8 | 1 | no | — |
| 768 | C2×C4 | — | 8 | 1 | no | — |
| 769 | C2×C4 | — | 8 | 1 | no | — |
| 770 | C2×C4 | — | 8 | 1 | no | — |
| 771 | C2×C4 | — | 8 | 1 | no | — |
| 772 | C2×C4 | — | 8 | 1 | no | — |
| 773 | C2×C4 | — | 8 | 1 | no | — |
| 774 | C2×C4 | — | 8 | 1 | no | — |
| 775 | C2×C4 | — | 8 | 1 | no | — |
| 776 | C2×C4 | — | 8 | 1 | no | — |
| 777 | C2×C4 | — | 8 | 1 | no | — |
| 778 | C2×C4 | — | 8 | 2 | no | — |
| 779 | C2×C4 | — | 8 | 1 | no | — |
| 780 | C2×C4 | — | 8 | 1 | no | — |
| 781 | C2×C4 | — | 8 | 1 | no | — |
| 782 | C2×C4 | — | 16 | 1 | no | — |
| 783 | C2×C4 | — | 16 | 1 | no | — |
| 784 | C2×C4 | — | 16 | 1 | no | — |
| 785 | C2×C4 | — | 16 | 1 | no | — |
| 786 | C2×C4 | — | 16 | 1 | no | — |
| 787 | C2×C4 | — | 16 | 1 | no | — |
| 788 | C2×C4 | — | 32 | 4 | no | — |
| 789 | C2×C4 | #2366 | 1 | 1 | yes | characteristic |
| 790 | C2×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 791 | C2×C4 | #2948 | 1 | 1 | yes | characteristic |
| 792 | C2×C4 | #3264 | 1 | 1 | yes | characteristic |
| 793 | C2×C4 | #3271 | 1 | 1 | yes | characteristic |
| 794 | C2×C4 | #3274 | 1 | 1 | yes | characteristic |
| 795 | C2×C4 | #3288 | 1 | 1 | yes | characteristic |
| 796 | C2×C4 | #3288 | 1 | 1 | yes | characteristic |
| 797 | C2×C4 | #3399 | 1 | 1 | yes | characteristic |
| 798 | C2×C4 | #3399 | 1 | 1 | yes | characteristic |
| 799 | C8 | — | 2 | 2 | no | — |
| 800 | C8 | — | 2 | 1 | no | — |
| 801 | C8 | — | 2 | 1 | no | — |
| 802 | C8 | — | 2 | 1 | no | — |
| 803 | C8 | — | 2 | 1 | no | — |
| 804 | C8 | — | 2 | 1 | no | — |
| 805 | C8 | — | 2 | 1 | no | — |
| 806 | C8 | — | 4 | 1 | no | — |
| 807 | C8 | — | 4 | 2 | no | — |
| 808 | C8 | — | 8 | 1 | no | — |
| 809 | C8 | — | 8 | 1 | no | — |
| 810 | C8 | — | 8 | 1 | no | — |
| 811 | C8 | — | 16 | 1 | no | — |
| 812 | C8 | — | 16 | 1 | no | — |
| 813 | C8 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 814 | C8 | #2946 | 1 | 1 | yes | characteristic |
| 815 | C8 | #3397 | 1 | 1 | yes | characteristic |
| 816 | C8 | #3403 | 1 | 1 | yes | characteristic |
| 817 | C22 | — | 2 | 1 | no | — |
| 818 | C22 | — | 2 | 1 | no | — |
| 819 | C22 | — | 16 | 2 | no | — |
| 820 | C22 | — | 16 | 1 | no | — |
| 821 | C22 | — | 16 | 1 | no | — |
| 822 | C22 | — | 16 | 2 | no | — |
| 823 | C22 | — | 16 | 1 | no | — |
| 824 | C22 | — | 16 | 1 | no | — |
| 825 | C22 | — | 16 | 1 | no | — |
| 826 | C22 | — | 16 | 1 | no | — |
| 827 | C22 | — | 16 | 2 | no | — |
| 828 | C22 | — | 32 | 1 | no | — |
| 829 | C22 | — | 32 | 1 | no | — |
| 830 | C22 | — | 32 | 1 | no | — |
| 831 | C22 | — | 32 | 1 | no | — |
| 832 | C22 | #20170 | 1 | 1 | yes | characteristic |
| 833 | C22 | #20282 | 1 | 1 | yes | characteristic |
| 834 | C22 | #23188 | 1 | 1 | yes | characteristic |
| 835 | C4 | — | 2 | 1 | no | — |
| 836 | C4 | — | 2 | 1 | no | — |
| 837 | C4 | — | 2 | 1 | no | — |
| 838 | C4 | — | 16 | 1 | no | — |
| 839 | C4 | — | 16 | 1 | no | — |
| 840 | C4 | — | 16 | 1 | no | — |
| 841 | C4 | — | 16 | 1 | no | — |
| 842 | C4 | — | 16 | 2 | no | — |
| 843 | C4 | — | 16 | 1 | no | — |
| 844 | C4 | — | 16 | 1 | no | — |
| 845 | C4 | #20160 | 1 | 1 | yes | characteristic |
| 846 | C4 | #20272 | 1 | 1 | yes | characteristic |
| 847 | C4 | #23195 | 1 | 1 | yes | characteristic |
| 848 | C4 | #23202 | 1 | 1 | yes | characteristic |
| 849 | C4 | #33468 | 1 | 1 | yes | characteristic |
| 850 | C4 | #33469 | 1 | 1 | yes | characteristic |
| 851 | C2 | — | 2 | 1 | no | — |
| 852 | C2 | — | 2 | 1 | no | — |
| 853 | C2 | — | 32 | 1 | no | — |
| 854 | C2 | — | 32 | 1 | no | — |
| 855 | C2 | — | 32 | 2 | no | — |
| 856 | C2 | #231650 | 1 | 1 | yes | characteristic |
| 857 | C2 | #498580 | 1 | 1 | yes | characteristic |
| 858 | C2 | #498582 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #23188 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #491517 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #8282 ◁ 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. #498621 | C2 | semidirect |
| 2. #498578 | C2 | semidirect |
| 4. #231640 | C2 | semidirect |
| 5. #231527 | C2 | semidirect |
| 6. #141312 | C2 | semidirect |
| 7. #141298 | C2 | semidirect |
| 8. #141294 | C2 | semidirect |
| 9. #141235 | C2 | semidirect |
| 10. #137579 | C2 | semidirect |
| 11. #137549 | C2 | semidirect |
| 12. #137546 | C2 | semidirect |
| 13. #137516 | C2 | semidirect |
| 14. #129184 | C2 | semidirect |
| 15. #129175 | C2 | semidirect |
| 43. #12527 | C4 | semidirect |
| 44. #12527 | C4 | semidirect |
| 45. #12526 | C4 | semidirect |
| 46. #12525 | C4 | semidirect |
| 97. #2241 | C2×C4 | semidirect |
| 98. #2241 | C2×C4 | semidirect |
| 99. #2240 | C2×C4 | semidirect |
| 100. #2240 | C2×C4 | semidirect |
| 144. #1713 | C2×C4 | semidirect |
| 145. #1712 | C2×C4 | semidirect |
| 146. #1709 | C2×C4 | semidirect |
| 147. #1709 | C2×C4 | semidirect |
| 182. #1312 | C2×C4 | semidirect |
| 183. #1312 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #498621 | 2 |
| #498578 | 2 |
| #491517 | 2 |
| #231640 | 2 |
| #231527 | 2 |
| #141312 | 2 |
| #141298 | 2 |
| #141294 | 2 |
| #141235 | 2 |
| #137579 | 2 |
| #137549 | 2 |
| #137546 | 2 |
| #137516 | 2 |
| #129184 | 2 |
| #129175 | 2 |