Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1510 conjugacy classes of subgroups.
The subgroup lattice has 823 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7613824 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #507575 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #496127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #317087 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #145023 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #143211 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #141927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #140595 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #136885 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #136367 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #134641 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#3335 | — | 2 | 1 | no | — |
| 13 | #45356 | — | 2 | 1 | no | — |
| 14 | #33719 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×AGL(1,ℤ/16) | — | 2 | 1 | no | — |
| 16 | C2×#2180 | — | 2 | 1 | no | — |
| 17 | #31204 | — | 2 | 1 | no | — |
| 18 | #31203 | — | 2 | 1 | no | — |
| 19 | #28483 | C22 | 1 | 2 | yes | — |
| 20 | #28289 | — | 2 | 1 | no | — |
| 21 | #28224 | — | 2 | 1 | no | — |
| 22 | #26242 | — | 2 | 2 | no | — |
| 23 | #24776 | — | 2 | 2 | no | — |
| 24 | #24134 | — | 2 | 1 | no | — |
| 25 | #24128 | — | 2 | 1 | no | — |
| 26 | D4×#106 | C22 | 1 | 2 | yes | — |
| 27 | #21724 | C22 | 1 | 1 | yes | characteristic |
| 28 | #21707 | C22 | 1 | 1 | yes | characteristic |
| 29 | #21694 | C22 | 1 | 1 | yes | characteristic |
| 30 | #21683 | C22 | 1 | 1 | yes | characteristic |
| 31 | #19101 | C22 | 1 | 2 | yes | — |
| 32 | #13534 | — | 2 | 1 | no | — |
| 33 | #13371 | — | 2 | 1 | no | — |
| 34 | #13255 | C22 | 1 | 2 | yes | — |
| 35 | #13250 | — | 2 | 1 | no | — |
| 36 | #13249 | — | 2 | 1 | no | — |
| 37 | #13214 | C22 | 1 | 1 | yes | characteristic |
| 38 | #13210 | C22 | 1 | 1 | yes | characteristic |
| 39 | #13185 | C22 | 1 | 2 | yes | — |
| 40 | #12950 | — | 2 | 2 | no | — |
| 41 | #12903 | C22 | 1 | 1 | yes | characteristic |
| 42 | #12884 | C22 | 1 | 1 | yes | characteristic |
| 43 | #12541 | C22 | 1 | 1 | yes | characteristic |
| 44 | #11926 | C22 | 1 | 2 | yes | — |
| 45 | #11583 | C22 | 1 | 2 | yes | — |
| 46 | #11583 | C22 | 1 | 2 | yes | — |
| 47 | #10627 | — | 2 | 1 | no | — |
| 48 | #10012 | — | 2 | 1 | no | — |
| 49 | #9049 | — | 2 | 2 | no | — |
| 50 | #8780 | C22 | 1 | 1 | yes | characteristic |
| 51 | #8658 | C22 | 1 | 2 | yes | — |
| 52 | #7278 | C22 | 1 | 2 | yes | — |
| 53 | #7175 | C22 | 1 | 2 | yes | — |
| 54 | #7174 | C22 | 1 | 2 | yes | — |
| 55 | C2×#554 | — | 2 | 1 | no | — |
| 56 | C2×#547 | — | 2 | 1 | no | — |
| 57 | C2×#510 | — | 2 | 1 | no | — |
| 58 | C2×#509 | — | 2 | 1 | no | — |
| 59 | #3335 | — | 4 | 8 | no | — |
| 60 | C2×#498 | D4 | 1 | 1 | yes | characteristic |
| 61 | #3147 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×#495 | C23 | 1 | 1 | yes | characteristic |
| 63 | #3100 | — | 2 | 2 | no | — |
| 64 | C2×#481 | — | 2 | 2 | no | — |
| 65 | C2×#483 | — | 2 | 2 | no | — |
| 66 | C2×#475 | — | 2 | 1 | no | — |
| 67 | C2×#476 | — | 2 | 1 | no | — |
| 68 | C2×#465 | — | 2 | 2 | no | — |
| 69 | C2×#465 | — | 2 | 2 | no | — |
| 70 | C2×#444 | — | 2 | 1 | no | — |
| 71 | C2×#443 | — | 2 | 1 | no | — |
| 72 | C2×#442 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×#441 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×SD16 | — | 2 | 1 | no | — |
| 75 | #2932 | — | 2 | 1 | no | — |
| 76 | C2×C8×D4 | — | 2 | 1 | no | — |
| 77 | C2×C8×D4 | — | 2 | 1 | no | — |
| 78 | C2×C8×D4 | C23 | 1 | 2 | yes | — |
| 79 | C22×#106 | — | 2 | 2 | no | — |
| 80 | #2732 | — | 4 | 2 | no | — |
| 81 | #2694 | — | 4 | 2 | no | — |
| 82 | #2540 | — | 2 | 2 | no | — |
| 83 | #2536 | — | 2 | 1 | no | — |
| 84 | #2535 | — | 2 | 1 | no | — |
| 85 | #2456 | — | 4 | 2 | no | — |
| 86 | #2417 | — | 2 | 2 | no | — |
| 87 | #2416 | — | 2 | 2 | no | — |
| 88 | #2407 | — | 4 | 2 | no | — |
| 89 | #2397 | D4 | 1 | 1 | yes | characteristic |
| 90 | D4×C4⋊C4 | — | 2 | 2 | no | — |
| 91 | #2331 | — | 2 | 1 | no | — |
| 92 | #2326 | — | 2 | 1 | no | — |
| 93 | #2251 | — | 2 | 1 | no | — |
| 94 | #2250 | — | 2 | 1 | no | — |
| 95 | #2249 | — | 2 | 2 | no | — |
| 96 | AGL(1,ℤ/16) | — | 4 | 4 | no | — |
| 97 | #2180 | — | 4 | 4 | no | — |
| 98 | C2×#365 | — | 2 | 1 | no | — |
| 99 | C2×#365 | — | 2 | 1 | no | — |
| 100 | C2×#365 | — | 2 | 2 | no | — |
| 101 | #2150 | C23 | 1 | 2 | yes | — |
| 102 | C2×#362 | — | 2 | 1 | no | — |
| 103 | C2×#361 | — | 2 | 1 | no | — |
| 104 | C2×#360 | — | 2 | 2 | no | — |
| 105 | C2×#360 | — | 2 | 1 | no | — |
| 106 | C2×#360 | — | 2 | 1 | no | — |
| 107 | C2×#360 | — | 2 | 2 | no | — |
| 108 | C2×#347 | — | 2 | 1 | no | — |
| 109 | C2×#347 | — | 2 | 1 | no | — |
| 110 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 111 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 112 | #2066 | — | 2 | 2 | no | — |
| 113 | #2065 | — | 2 | 2 | no | — |
| 114 | #2036 | — | 2 | 2 | no | — |
| 115 | #2035 | — | 2 | 2 | no | — |
| 116 | #2034 | — | 2 | 2 | no | — |
| 117 | #2033 | — | 2 | 2 | no | — |
| 118 | #2001 | — | 2 | 2 | no | — |
| 119 | #1999 | — | 2 | 2 | no | — |
| 120 | #1993 | — | 2 | 1 | no | — |
| 121 | #1983 | — | 2 | 2 | no | — |
| 122 | #1975 | — | 2 | 1 | no | — |
| 123 | #1974 | — | 2 | 1 | no | — |
| 124 | #1972 | D4 | 1 | 1 | yes | characteristic |
| 125 | #1971 | D4 | 1 | 1 | yes | characteristic |
| 126 | #1968 | — | 2 | 1 | no | — |
| 127 | #1963 | — | 2 | 1 | no | — |
| 128 | #1959 | — | 2 | 1 | no | — |
| 129 | #1955 | — | 2 | 1 | no | — |
| 130 | #1955 | — | 2 | 1 | no | — |
| 131 | #1955 | D4 | 1 | 2 | yes | — |
| 132 | #1948 | — | 2 | 2 | no | — |
| 133 | #1944 | — | 2 | 1 | no | — |
| 134 | #1941 | D4 | 1 | 2 | yes | — |
| 135 | #1874 | — | 2 | 2 | no | — |
| 136 | #1872 | — | 2 | 2 | no | — |
| 137 | #1853 | — | 2 | 2 | no | — |
| 138 | #1853 | — | 2 | 2 | no | — |
| 139 | #1848 | C23 | 1 | 1 | yes | characteristic |
| 140 | #1846 | D4 | 1 | 1 | yes | characteristic |
| 141 | #1844 | C23 | 1 | 1 | yes | characteristic |
| 142 | #1843 | D4 | 1 | 1 | yes | characteristic |
| 143 | #1807 | — | 2 | 2 | no | — |
| 144 | #1805 | — | 2 | 1 | no | — |
| 145 | #1804 | — | 2 | 1 | no | — |
| 146 | #1776 | — | 2 | 1 | no | — |
| 147 | C4×#106 | C23 | 1 | 2 | yes | — |
| 148 | #1726 | C23 | 1 | 1 | yes | characteristic |
| 149 | #1669 | — | 2 | 2 | no | — |
| 150 | #1667 | — | 2 | 2 | no | — |
| 151 | #1665 | — | 4 | 2 | no | — |
| 152 | #1564 | C23 | 1 | 2 | yes | — |
| 153 | #1540 | — | 2 | 2 | no | — |
| 154 | #1486 | — | 2 | 2 | no | — |
| 155 | #1383 | — | 2 | 2 | no | — |
| 156 | #1376 | — | 2 | 1 | no | — |
| 157 | #1376 | — | 2 | 1 | no | — |
| 158 | #1360 | — | 4 | 2 | no | — |
| 159 | D4⋊C16 | — | 2 | 4 | no | — |
| 160 | D4⋊C16 | — | 4 | 2 | no | — |
| 161 | #1301 | — | 2 | 2 | no | — |
| 162 | #1281 | — | 2 | 1 | no | — |
| 163 | #1274 | — | 2 | 1 | no | — |
| 164 | C22×#41 | — | 4 | 1 | no | — |
| 165 | C2×#135 | — | 2 | 1 | no | — |
| 166 | C2×#135 | — | 2 | 1 | no | — |
| 167 | C22×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C22×SD16 | — | 2 | 1 | no | — |
| 169 | C22×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×#131 | — | 4 | 1 | no | — |
| 171 | C23×C8 | — | 2 | 2 | no | — |
| 172 | #554 | — | 4 | 4 | no | — |
| 173 | #554 | — | 8 | 2 | no | — |
| 174 | #547 | — | 4 | 4 | no | — |
| 175 | #547 | — | 8 | 2 | no | — |
| 176 | #532 | — | 2 | 1 | no | — |
| 177 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 178 | C2×#125 | — | 4 | 1 | no | — |
| 179 | C2×#124 | — | 2 | 1 | no | — |
| 180 | C2×#123 | — | 4 | 2 | no | — |
| 181 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 182 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 183 | C2×C22⋊Q8 | — | 4 | 2 | no | — |
| 184 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 185 | C2×#121 | — | 2 | 2 | no | — |
| 186 | C2×#121 | — | 2 | 2 | no | — |
| 187 | C2×#121 | — | 4 | 2 | no | — |
| 188 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 189 | C2×C4×D4 | — | 2 | 1 | no | — |
| 190 | C2×C4×D4 | — | 2 | 1 | no | — |
| 191 | C2×C4×D4 | — | 2 | 1 | no | — |
| 192 | C2×C4×D4 | — | 4 | 1 | no | — |
| 193 | C2×C4×D4 | — | 4 | 2 | no | — |
| 194 | C2×C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 195 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 196 | C22×C4⋊C4 | — | 2 | 2 | no | — |
| 197 | #510 | — | 4 | 2 | no | — |
| 198 | #510 | — | 4 | 2 | no | — |
| 199 | #509 | — | 4 | 2 | no | — |
| 200 | #509 | — | 4 | 2 | no | — |
| 201 | C2×Q32 | — | 2 | 2 | no | — |
| 202 | C2×SD32 | — | 2 | 2 | no | — |
| 203 | C2×SD32 | — | 2 | 2 | no | — |
| 204 | C2×D16 | — | 2 | 2 | no | — |
| 205 | C2×M32 | — | 2 | 1 | no | — |
| 206 | C2×M32 | — | 2 | 1 | no | — |
| 207 | C2×M32 | — | 2 | 2 | no | — |
| 208 | #498 | — | 2 | 4 | no | — |
| 209 | #495 | — | 2 | 1 | no | — |
| 210 | #495 | — | 2 | 1 | no | — |
| 211 | #495 | — | 2 | 1 | no | — |
| 212 | #495 | — | 2 | 1 | no | — |
| 213 | #495 | — | 2 | 1 | no | — |
| 214 | #495 | — | 2 | 1 | no | — |
| 215 | #494 | #41 | 1 | 1 | yes | characteristic, complemented |
| 216 | #493 | #41 | 1 | 1 | yes | characteristic, complemented |
| 217 | #492 | — | 2 | 1 | no | — |
| 218 | #483 | — | 4 | 8 | no | — |
| 219 | #481 | — | 4 | 8 | no | — |
| 220 | #480 | — | 4 | 2 | no | — |
| 221 | #476 | — | 4 | 4 | no | — |
| 222 | #475 | — | 4 | 4 | no | — |
| 223 | #474 | — | 4 | 2 | no | — |
| 224 | #465 | — | 4 | 4 | no | — |
| 225 | #465 | — | 4 | 4 | no | — |
| 226 | #465 | — | 8 | 2 | no | — |
| 227 | #465 | — | 8 | 2 | no | — |
| 228 | #459 | — | 4 | 2 | no | — |
| 229 | #447 | — | 4 | 2 | no | — |
| 230 | #444 | — | 4 | 2 | no | — |
| 231 | #444 | — | 4 | 2 | no | — |
| 232 | #443 | — | 8 | 2 | no | — |
| 233 | #442 | — | 4 | 2 | no | — |
| 234 | #441 | — | 4 | 2 | no | — |
| 235 | C4×SD16 | — | 4 | 4 | no | — |
| 236 | C4×D8 | — | 8 | 2 | no | — |
| 237 | #435 | — | 8 | 2 | no | — |
| 238 | C8×D4 | — | 2 | 2 | no | — |
| 239 | C8×D4 | — | 2 | 2 | no | — |
| 240 | C8×D4 | — | 2 | 2 | no | — |
| 241 | C8×D4 | — | 2 | 2 | no | — |
| 242 | C8×D4 | — | 4 | 4 | no | — |
| 243 | C8×D4 | — | 8 | 2 | no | — |
| 244 | #431 | — | 2 | 2 | no | — |
| 245 | C2×#108 | — | 2 | 1 | no | — |
| 246 | C2×#108 | — | 2 | 1 | no | — |
| 247 | C2×#107 | — | 2 | 1 | no | — |
| 248 | C2×#106 | — | 2 | 1 | no | — |
| 249 | C2×#106 | — | 2 | 2 | no | — |
| 250 | C2×#106 | — | 2 | 2 | no | — |
| 251 | C2×#106 | — | 2 | 1 | no | — |
| 252 | C2×#106 | — | 4 | 4 | no | — |
| 253 | C2×#106 | — | 4 | 4 | no | — |
| 254 | C2×#106 | C2×D4 | 1 | 2 | yes | — |
| 255 | C2×#106 | C2×D4 | 1 | 2 | yes | — |
| 256 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×#106 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | #423 | — | 2 | 1 | no | — |
| 259 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 260 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 261 | C2×C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 262 | C2×#104 | — | 4 | 1 | no | — |
| 263 | C2×#104 | — | 4 | 1 | no | — |
| 264 | C2×#103 | — | 2 | 2 | no | — |
| 265 | C2×#103 | — | 2 | 1 | no | — |
| 266 | C2×#103 | — | 2 | 2 | no | — |
| 267 | C2×#103 | — | 2 | 1 | no | — |
| 268 | C2×#102 | — | 2 | 2 | no | — |
| 269 | C2×#102 | — | 2 | 1 | no | — |
| 270 | C2×#102 | — | 2 | 2 | no | — |
| 271 | C2×#102 | — | 2 | 1 | no | — |
| 272 | #408 | — | 4 | 1 | no | — |
| 273 | C2×C22⋊C8 | — | 2 | 2 | no | — |
| 274 | C2×C22⋊C8 | — | 2 | 2 | no | — |
| 275 | C2×C22⋊C8 | — | 2 | 2 | no | — |
| 276 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 278 | C2×#97 | C2×D4 | 1 | 1 | yes | characteristic |
| 279 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 282 | #399 | — | 2 | 2 | no | — |
| 283 | #399 | — | 4 | 2 | no | — |
| 284 | #398 | — | 4 | 2 | no | — |
| 285 | #398 | — | 4 | 1 | no | — |
| 286 | #397 | — | 4 | 1 | no | — |
| 287 | #396 | — | 4 | 2 | no | — |
| 288 | #396 | — | 4 | 2 | no | — |
| 289 | #394 | — | 4 | 2 | no | — |
| 290 | #394 | — | 4 | 1 | no | — |
| 291 | #392 | — | 2 | 2 | no | — |
| 292 | #392 | — | 4 | 1 | no | — |
| 293 | #392 | — | 4 | 2 | no | — |
| 294 | #391 | — | 2 | 1 | no | — |
| 295 | #391 | — | 4 | 2 | no | — |
| 296 | #390 | — | 2 | 1 | no | — |
| 297 | #390 | — | 4 | 2 | no | — |
| 298 | #390 | — | 4 | 2 | no | — |
| 299 | #389 | — | 2 | 2 | no | — |
| 300 | #389 | — | 4 | 2 | no | — |
| 301 | #388 | — | 4 | 2 | no | — |
| 302 | #388 | — | 4 | 2 | no | — |
| 303 | #387 | — | 4 | 2 | no | — |
| 304 | #386 | — | 4 | 2 | no | — |
| 305 | #386 | — | 4 | 2 | no | — |
| 306 | #386 | — | 4 | 2 | no | — |
| 307 | #385 | — | 4 | 2 | no | — |
| 308 | #385 | — | 4 | 2 | no | — |
| 309 | #385 | — | 4 | 2 | no | — |
| 310 | #384 | — | 2 | 1 | no | — |
| 311 | #382 | — | 2 | 1 | no | — |
| 312 | #380 | — | 2 | 2 | no | — |
| 313 | #380 | — | 2 | 2 | no | — |
| 314 | #380 | — | 4 | 2 | no | — |
| 315 | C4×C4⋊C4 | — | 2 | 2 | no | — |
| 316 | #376 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | #365 | — | 4 | 2 | no | — |
| 318 | #365 | — | 4 | 2 | no | — |
| 319 | #365 | — | 8 | 2 | no | — |
| 320 | C4⋊C16 | — | 2 | 2 | no | — |
| 321 | C4⋊C16 | — | 2 | 2 | no | — |
| 322 | #362 | — | 4 | 2 | no | — |
| 323 | #361 | — | 4 | 2 | no | — |
| 324 | #360 | — | 4 | 2 | no | — |
| 325 | #360 | — | 4 | 2 | no | — |
| 326 | #360 | — | 4 | 4 | no | — |
| 327 | #360 | — | 8 | 2 | no | — |
| 328 | #347 | — | 2 | 4 | no | — |
| 329 | #347 | — | 4 | 2 | no | — |
| 330 | #346 | — | 2 | 1 | no | — |
| 331 | #346 | — | 2 | 1 | no | — |
| 332 | C4×C16 | — | 2 | 1 | no | — |
| 333 | C4×C16 | #41 | 1 | 2 | yes | complemented |
| 334 | #340 | — | 2 | 2 | no | — |
| 335 | #340 | — | 2 | 2 | no | — |
| 336 | #340 | — | 2 | 2 | no | — |
| 337 | #340 | — | 2 | 2 | no | — |
| 338 | #335 | — | 2 | 2 | no | — |
| 339 | #334 | — | 2 | 2 | no | — |
| 340 | #332 | — | 4 | 2 | no | — |
| 341 | #331 | — | 4 | 2 | no | — |
| 342 | D4⋊C8 | — | 8 | 2 | no | — |
| 343 | C2×#41 | — | 4 | 1 | no | — |
| 344 | C2×#41 | — | 8 | 4 | no | — |
| 345 | C2×#41 | — | 16 | 4 | no | — |
| 346 | C22×Q8 | — | 2 | 1 | no | — |
| 347 | C22×Q8 | — | 4 | 1 | no | — |
| 348 | C22×D4 | — | 2 | 1 | no | — |
| 349 | C22×D4 | — | 2 | 1 | no | — |
| 350 | C22×D4 | — | 2 | 1 | no | — |
| 351 | C22×D4 | — | 4 | 2 | no | — |
| 352 | C22×D4 | — | 4 | 2 | no | — |
| 353 | C22×D4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 354 | C23×C4 | — | 2 | 2 | no | — |
| 355 | C23×C4 | — | 4 | 1 | no | — |
| 356 | C23×C4 | — | 4 | 2 | no | — |
| 357 | C23×C4 | — | 4 | 2 | no | — |
| 358 | #135 | — | 4 | 1 | no | — |
| 359 | #135 | — | 4 | 1 | no | — |
| 360 | #135 | — | 4 | 1 | no | — |
| 361 | #135 | — | 4 | 1 | no | — |
| 362 | #135 | — | 4 | 2 | no | — |
| 363 | #135 | — | 4 | 2 | no | — |
| 364 | C2×Q16 | — | 2 | 1 | no | — |
| 365 | C2×Q16 | — | 2 | 1 | no | — |
| 366 | C2×Q16 | — | 2 | 1 | no | — |
| 367 | C2×Q16 | — | 2 | 1 | no | — |
| 368 | C2×Q16 | — | 4 | 1 | no | — |
| 369 | C2×Q16 | — | 4 | 1 | no | — |
| 370 | C2×SD16 | — | 4 | 1 | no | — |
| 371 | C2×SD16 | — | 4 | 1 | no | — |
| 372 | C2×SD16 | — | 4 | 1 | no | — |
| 373 | C2×SD16 | — | 4 | 1 | no | — |
| 374 | C2×SD16 | — | 4 | 2 | no | — |
| 375 | C2×SD16 | — | 4 | 2 | no | — |
| 376 | C2×D8 | — | 2 | 1 | no | — |
| 377 | C2×D8 | — | 2 | 1 | no | — |
| 378 | C2×D8 | — | 2 | 1 | no | — |
| 379 | C2×D8 | — | 2 | 1 | no | — |
| 380 | C2×D8 | — | 4 | 1 | no | — |
| 381 | C2×D8 | — | 4 | 1 | no | — |
| 382 | C2×D8 | — | 8 | 2 | no | — |
| 383 | #131 | — | 8 | 2 | no | — |
| 384 | #131 | — | 8 | 2 | no | — |
| 385 | C2×M16 | — | 4 | 1 | no | — |
| 386 | C2×M16 | — | 8 | 1 | no | — |
| 387 | C22×C8 | — | 2 | 2 | no | — |
| 388 | C22×C8 | — | 4 | 2 | no | — |
| 389 | C22×C8 | — | 4 | 2 | no | — |
| 390 | C22×C8 | — | 4 | 2 | no | — |
| 391 | C22×C8 | — | 4 | 2 | no | — |
| 392 | C22×C8 | — | 4 | 2 | no | — |
| 393 | C22×C8 | — | 4 | 2 | no | — |
| 394 | C22×C8 | — | 8 | 1 | no | — |
| 395 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 396 | C22×C8 | #120 | 1 | 1 | yes | characteristic |
| 397 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 398 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 399 | C4⋊Q8 | — | 2 | 4 | no | — |
| 400 | C4⋊Q8 | — | 2 | 1 | no | — |
| 401 | C4⋊Q8 | — | 4 | 2 | no | — |
| 402 | #127 | — | 2 | 1 | no | — |
| 403 | #125 | — | 8 | 4 | no | — |
| 404 | #124 | — | 4 | 1 | no | — |
| 405 | #124 | — | 4 | 1 | no | — |
| 406 | #124 | — | 4 | 1 | no | — |
| 407 | #124 | — | 4 | 2 | no | — |
| 408 | #123 | — | 8 | 8 | no | — |
| 409 | C22⋊Q8 | — | 4 | 4 | no | — |
| 410 | C22⋊Q8 | — | 8 | 8 | no | — |
| 411 | C22⋊Q8 | — | 8 | 2 | no | — |
| 412 | C22⋊Q8 | — | 8 | 4 | no | — |
| 413 | C22⋊Q8 | — | 8 | 2 | no | — |
| 414 | C22⋊Q8 | — | 8 | 2 | no | — |
| 415 | #121 | — | 4 | 4 | no | — |
| 416 | #121 | — | 4 | 2 | no | — |
| 417 | #121 | — | 8 | 2 | no | — |
| 418 | #121 | — | 8 | 2 | no | — |
| 419 | #121 | — | 8 | 2 | no | — |
| 420 | #121 | — | 16 | 4 | no | — |
| 421 | C4×Q8 | — | 4 | 2 | no | — |
| 422 | C4×Q8 | — | 4 | 2 | no | — |
| 423 | C4×D4 | — | 2 | 2 | no | — |
| 424 | C4×D4 | — | 2 | 2 | no | — |
| 425 | C4×D4 | — | 2 | 2 | no | — |
| 426 | C4×D4 | — | 2 | 2 | no | — |
| 427 | C4×D4 | — | 4 | 2 | no | — |
| 428 | C4×D4 | — | 4 | 2 | no | — |
| 429 | C4×D4 | — | 4 | 2 | no | — |
| 430 | C4×D4 | — | 4 | 2 | no | — |
| 431 | C4×D4 | — | 4 | 2 | no | — |
| 432 | C4×D4 | — | 8 | 1 | no | — |
| 433 | C4×D4 | — | 8 | 1 | no | — |
| 434 | C4×D4 | — | 8 | 4 | no | — |
| 435 | C4×D4 | — | 16 | 4 | no | — |
| 436 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 437 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 438 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 440 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 441 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 443 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 444 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 445 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 446 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 447 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 448 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 449 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 450 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 451 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 452 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 453 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 454 | C2×C4⋊C4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 455 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 456 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 457 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 458 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 459 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 460 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 461 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 462 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 463 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 464 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 465 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 466 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 467 | C2×C42 | — | 4 | 1 | no | — |
| 468 | C2×C42 | — | 4 | 2 | no | — |
| 469 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 470 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 471 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 472 | Q32 | — | 4 | 4 | no | — |
| 473 | SD32 | — | 4 | 4 | no | — |
| 474 | SD32 | — | 4 | 4 | no | — |
| 475 | D16 | — | 4 | 4 | no | — |
| 476 | M32 | — | 2 | 2 | no | — |
| 477 | M32 | — | 2 | 2 | no | — |
| 478 | M32 | — | 2 | 2 | no | — |
| 479 | M32 | — | 4 | 1 | no | — |
| 480 | M32 | — | 4 | 2 | no | — |
| 481 | M32 | — | 4 | 2 | no | — |
| 482 | C2×C16 | — | 2 | 2 | no | — |
| 483 | C2×C16 | — | 4 | 1 | no | — |
| 484 | C2×C16 | — | 4 | 2 | no | — |
| 485 | #108 | — | 4 | 1 | no | — |
| 486 | #108 | — | 4 | 1 | no | — |
| 487 | #108 | — | 4 | 2 | no | — |
| 488 | #107 | — | 8 | 2 | no | — |
| 489 | #107 | — | 8 | 1 | no | — |
| 490 | #106 | — | 2 | 4 | no | — |
| 491 | #106 | — | 2 | 2 | no | — |
| 492 | #106 | — | 2 | 2 | no | — |
| 493 | #106 | — | 2 | 2 | no | — |
| 494 | #106 | — | 4 | 4 | no | — |
| 495 | #106 | — | 4 | 4 | no | — |
| 496 | #106 | — | 4 | 2 | no | — |
| 497 | #106 | — | 4 | 1 | no | — |
| 498 | #106 | — | 4 | 1 | no | — |
| 499 | #106 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 500 | C4⋊C8 | — | 2 | 2 | no | — |
| 501 | C4⋊C8 | — | 2 | 2 | no | — |
| 502 | C4⋊C8 | — | 4 | 2 | no | — |
| 503 | C4⋊C8 | — | 4 | 2 | no | — |
| 504 | C4⋊C8 | — | 4 | 2 | no | — |
| 505 | C4⋊C8 | — | 8 | 1 | no | — |
| 506 | #104 | — | 8 | 2 | no | — |
| 507 | #104 | — | 8 | 2 | no | — |
| 508 | #103 | — | 4 | 4 | no | — |
| 509 | #103 | — | 4 | 2 | no | — |
| 510 | #103 | — | 8 | 1 | no | — |
| 511 | #103 | — | 8 | 2 | no | — |
| 512 | #102 | — | 4 | 4 | no | — |
| 513 | #102 | — | 4 | 2 | no | — |
| 514 | #102 | — | 8 | 2 | no | — |
| 515 | #102 | — | 8 | 1 | no | — |
| 516 | #102 | — | 8 | 2 | no | — |
| 517 | #102 | — | 8 | 2 | no | — |
| 518 | C22⋊C8 | — | 4 | 4 | no | — |
| 519 | C22⋊C8 | — | 4 | 2 | no | — |
| 520 | C22⋊C8 | — | 4 | 2 | no | — |
| 521 | C22⋊C8 | — | 4 | 2 | no | — |
| 522 | C22⋊C8 | — | 8 | 2 | no | — |
| 523 | C22⋊C8 | — | 8 | 2 | no | — |
| 524 | #97 | — | 2 | 2 | no | — |
| 525 | #97 | — | 2 | 2 | no | — |
| 526 | #97 | — | 4 | 1 | no | — |
| 527 | C4×C8 | — | 2 | 2 | no | — |
| 528 | C4×C8 | — | 2 | 2 | no | — |
| 529 | C4×C8 | — | 4 | 2 | no | — |
| 530 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 531 | C4×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 532 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 533 | C4×C8 | 2−1+4 | 1 | 1 | yes | characteristic |
| 534 | #95 | — | 2 | 2 | no | — |
| 535 | #95 | — | 4 | 2 | no | — |
| 536 | #95 | — | 4 | 2 | no | — |
| 537 | #95 | — | 4 | 2 | no | — |
| 538 | #95 | — | 4 | 1 | no | — |
| 539 | #95 | — | 4 | 1 | no | — |
| 540 | #95 | — | 4 | 2 | no | — |
| 541 | #95 | — | 4 | 2 | no | — |
| 542 | C24 | — | 2 | 2 | no | — |
| 543 | C24 | — | 4 | 1 | no | — |
| 544 | #41 | — | 8 | 1 | no | — |
| 545 | #41 | — | 8 | 1 | no | — |
| 546 | #41 | — | 8 | 1 | no | — |
| 547 | #41 | — | 8 | 1 | no | — |
| 548 | #41 | — | 16 | 16 | no | — |
| 549 | C2×Q8 | — | 4 | 4 | no | — |
| 550 | C2×Q8 | — | 4 | 1 | no | — |
| 551 | C2×Q8 | — | 4 | 1 | no | — |
| 552 | C2×Q8 | — | 4 | 1 | no | — |
| 553 | C2×Q8 | — | 4 | 1 | no | — |
| 554 | C2×Q8 | — | 4 | 1 | no | — |
| 555 | C2×Q8 | — | 4 | 1 | no | — |
| 556 | C2×Q8 | — | 4 | 1 | no | — |
| 557 | C2×Q8 | — | 16 | 2 | no | — |
| 558 | C2×D4 | — | 2 | 2 | no | — |
| 559 | C2×D4 | — | 2 | 2 | no | — |
| 560 | C2×D4 | — | 4 | 2 | no | — |
| 561 | C2×D4 | — | 4 | 4 | no | — |
| 562 | C2×D4 | — | 4 | 4 | no | — |
| 563 | C2×D4 | — | 4 | 4 | no | — |
| 564 | C2×D4 | — | 4 | 1 | no | — |
| 565 | C2×D4 | — | 4 | 1 | no | — |
| 566 | C2×D4 | — | 4 | 1 | no | — |
| 567 | C2×D4 | — | 4 | 1 | no | — |
| 568 | C2×D4 | — | 4 | 1 | no | — |
| 569 | C2×D4 | — | 4 | 1 | no | — |
| 570 | C2×D4 | — | 4 | 1 | no | — |
| 571 | C2×D4 | — | 4 | 2 | no | — |
| 572 | C2×D4 | — | 8 | 1 | no | — |
| 573 | C2×D4 | — | 8 | 4 | no | — |
| 574 | C2×D4 | — | 8 | 4 | no | — |
| 575 | C2×D4 | — | 8 | 1 | no | — |
| 576 | C2×D4 | — | 8 | 4 | no | — |
| 577 | C2×D4 | — | 16 | 2 | no | — |
| 578 | C2×D4 | — | 16 | 2 | no | — |
| 579 | C2×D4 | — | 16 | 2 | no | — |
| 580 | C22×C4 | — | 2 | 1 | no | — |
| 581 | C22×C4 | — | 2 | 1 | no | — |
| 582 | C22×C4 | — | 2 | 2 | no | — |
| 583 | C22×C4 | — | 4 | 2 | no | — |
| 584 | C22×C4 | — | 4 | 2 | no | — |
| 585 | C22×C4 | — | 4 | 2 | no | — |
| 586 | C22×C4 | — | 4 | 2 | no | — |
| 587 | C22×C4 | — | 4 | 2 | no | — |
| 588 | C22×C4 | — | 4 | 2 | no | — |
| 589 | C22×C4 | — | 4 | 2 | no | — |
| 590 | C22×C4 | — | 4 | 2 | no | — |
| 591 | C22×C4 | — | 4 | 1 | no | — |
| 592 | C22×C4 | — | 4 | 1 | no | — |
| 593 | C22×C4 | — | 4 | 1 | no | — |
| 594 | C22×C4 | — | 8 | 2 | no | — |
| 595 | C22×C4 | — | 8 | 4 | no | — |
| 596 | C22×C4 | — | 8 | 4 | no | — |
| 597 | C22×C4 | — | 8 | 4 | no | — |
| 598 | C22×C4 | — | 8 | 1 | no | — |
| 599 | C22×C4 | — | 16 | 2 | no | — |
| 600 | C22×C4 | — | 16 | 2 | no | — |
| 601 | C22×C4 | — | 16 | 2 | no | — |
| 602 | C22×C4 | — | 16 | 2 | no | — |
| 603 | C22×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 604 | C22×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 605 | Q16 | — | 4 | 1 | no | — |
| 606 | Q16 | — | 4 | 2 | no | — |
| 607 | Q16 | — | 4 | 1 | no | — |
| 608 | Q16 | — | 4 | 2 | no | — |
| 609 | Q16 | — | 8 | 1 | no | — |
| 610 | SD16 | — | 8 | 1 | no | — |
| 611 | SD16 | — | 8 | 1 | no | — |
| 612 | SD16 | — | 8 | 2 | no | — |
| 613 | SD16 | — | 8 | 2 | no | — |
| 614 | SD16 | — | 8 | 2 | no | — |
| 615 | D8 | — | 4 | 1 | no | — |
| 616 | D8 | — | 4 | 2 | no | — |
| 617 | D8 | — | 4 | 1 | no | — |
| 618 | D8 | — | 4 | 2 | no | — |
| 619 | D8 | — | 8 | 1 | no | — |
| 620 | D8 | — | 16 | 4 | no | — |
| 621 | M16 | — | 8 | 1 | no | — |
| 622 | M16 | — | 8 | 1 | no | — |
| 623 | M16 | — | 16 | 2 | no | — |
| 624 | C2×C8 | — | 2 | 1 | no | — |
| 625 | C2×C8 | — | 2 | 1 | no | — |
| 626 | C2×C8 | — | 2 | 1 | no | — |
| 627 | C2×C8 | — | 2 | 1 | no | — |
| 628 | C2×C8 | — | 2 | 1 | no | — |
| 629 | C2×C8 | — | 2 | 1 | no | — |
| 630 | C2×C8 | — | 2 | 1 | no | — |
| 631 | C2×C8 | — | 2 | 1 | no | — |
| 632 | C2×C8 | — | 4 | 2 | no | — |
| 633 | C2×C8 | — | 4 | 2 | no | — |
| 634 | C2×C8 | — | 4 | 2 | no | — |
| 635 | C2×C8 | — | 8 | 2 | no | — |
| 636 | C2×C8 | — | 8 | 2 | no | — |
| 637 | C2×C8 | — | 8 | 2 | no | — |
| 638 | C2×C8 | — | 8 | 2 | no | — |
| 639 | C2×C8 | — | 8 | 1 | no | — |
| 640 | C2×C8 | — | 8 | 2 | no | — |
| 641 | C2×C8 | — | 16 | 2 | no | — |
| 642 | C2×C8 | #525 | 1 | 1 | yes | characteristic |
| 643 | C2×C8 | #537 | 1 | 1 | yes | characteristic |
| 644 | C2×C8 | #548 | 1 | 1 | yes | characteristic |
| 645 | C2×C8 | #550 | 1 | 1 | yes | characteristic |
| 646 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 647 | C2×C8 | #576 | 1 | 2 | yes | — |
| 648 | C4⋊C4 | — | 2 | 2 | no | — |
| 649 | C4⋊C4 | — | 2 | 4 | no | — |
| 650 | C4⋊C4 | — | 2 | 2 | no | — |
| 651 | C4⋊C4 | — | 4 | 2 | no | — |
| 652 | C4⋊C4 | — | 4 | 4 | no | — |
| 653 | C4⋊C4 | — | 4 | 2 | no | — |
| 654 | C4⋊C4 | — | 4 | 1 | no | — |
| 655 | C4⋊C4 | — | 4 | 1 | no | — |
| 656 | C4⋊C4 | — | 4 | 2 | no | — |
| 657 | C4⋊C4 | — | 4 | 1 | no | — |
| 658 | C4⋊C4 | — | 4 | 1 | no | — |
| 659 | C4⋊C4 | — | 4 | 2 | no | — |
| 660 | C4⋊C4 | — | 4 | 2 | no | — |
| 661 | C4⋊C4 | — | 8 | 2 | no | — |
| 662 | C4⋊C4 | — | 8 | 1 | no | — |
| 663 | C4⋊C4 | — | 8 | 4 | no | — |
| 664 | C4⋊C4 | — | 8 | 4 | no | — |
| 665 | C4⋊C4 | — | 8 | 4 | no | — |
| 666 | C4⋊C4 | — | 16 | 2 | no | — |
| 667 | C4⋊C4 | — | 16 | 2 | no | — |
| 668 | C4⋊C4 | — | 16 | 2 | no | — |
| 669 | C22⋊C4 | — | 4 | 4 | no | — |
| 670 | C22⋊C4 | — | 4 | 2 | no | — |
| 671 | C22⋊C4 | — | 4 | 2 | no | — |
| 672 | C22⋊C4 | — | 8 | 2 | no | — |
| 673 | C22⋊C4 | — | 8 | 2 | no | — |
| 674 | C22⋊C4 | — | 8 | 4 | no | — |
| 675 | C22⋊C4 | — | 8 | 4 | no | — |
| 676 | C22⋊C4 | — | 8 | 4 | no | — |
| 677 | C22⋊C4 | — | 8 | 2 | no | — |
| 678 | C22⋊C4 | — | 8 | 2 | no | — |
| 679 | C22⋊C4 | — | 8 | 2 | no | — |
| 680 | C22⋊C4 | — | 16 | 2 | no | — |
| 681 | C22⋊C4 | — | 16 | 2 | no | — |
| 682 | C22⋊C4 | — | 16 | 2 | no | — |
| 683 | C22⋊C4 | — | 16 | 2 | no | — |
| 684 | C42 | — | 2 | 1 | no | — |
| 685 | C42 | — | 2 | 1 | no | — |
| 686 | C42 | — | 2 | 1 | no | — |
| 687 | C42 | — | 8 | 2 | no | — |
| 688 | C42 | — | 16 | 2 | no | — |
| 689 | C42 | #453 | 1 | 2 | yes | — |
| 690 | C42 | #546 | 1 | 1 | yes | characteristic |
| 691 | C42 | #547 | 1 | 1 | yes | characteristic |
| 692 | C42 | #577 | 1 | 2 | yes | — |
| 693 | C16 | — | 2 | 4 | no | — |
| 694 | C16 | — | 4 | 2 | no | — |
| 695 | C16 | — | 8 | 2 | no | — |
| 696 | C23 | — | 2 | 4 | no | — |
| 697 | C23 | — | 4 | 2 | no | — |
| 698 | C23 | — | 4 | 2 | no | — |
| 699 | C23 | — | 4 | 2 | no | — |
| 700 | C23 | — | 4 | 2 | no | — |
| 701 | C23 | — | 4 | 2 | no | — |
| 702 | C23 | — | 4 | 2 | no | — |
| 703 | C23 | — | 8 | 2 | no | — |
| 704 | C23 | — | 8 | 2 | no | — |
| 705 | C23 | — | 8 | 1 | no | — |
| 706 | C23 | — | 8 | 1 | no | — |
| 707 | C23 | — | 8 | 1 | no | — |
| 708 | C23 | — | 8 | 1 | no | — |
| 709 | C23 | #3003 | 1 | 1 | yes | characteristic |
| 710 | Q8 | — | 8 | 1 | no | — |
| 711 | Q8 | — | 8 | 1 | no | — |
| 712 | Q8 | — | 8 | 1 | no | — |
| 713 | Q8 | — | 8 | 1 | no | — |
| 714 | Q8 | — | 8 | 1 | no | — |
| 715 | Q8 | — | 8 | 1 | no | — |
| 716 | Q8 | — | 16 | 4 | no | — |
| 717 | D4 | — | 2 | 4 | no | — |
| 718 | D4 | — | 2 | 4 | no | — |
| 719 | D4 | — | 4 | 2 | no | — |
| 720 | D4 | — | 4 | 2 | no | — |
| 721 | D4 | — | 4 | 8 | no | — |
| 722 | D4 | — | 8 | 4 | no | — |
| 723 | D4 | — | 8 | 1 | no | — |
| 724 | D4 | — | 8 | 1 | no | — |
| 725 | D4 | — | 8 | 1 | no | — |
| 726 | D4 | — | 8 | 1 | no | — |
| 727 | D4 | — | 8 | 1 | no | — |
| 728 | D4 | — | 8 | 1 | no | — |
| 729 | D4 | — | 16 | 2 | no | — |
| 730 | D4 | — | 16 | 8 | no | — |
| 731 | D4 | — | 16 | 1 | no | — |
| 732 | D4 | — | 16 | 1 | no | — |
| 733 | D4 | — | 32 | 4 | no | — |
| 734 | C2×C4 | — | 2 | 2 | no | — |
| 735 | C2×C4 | — | 4 | 2 | no | — |
| 736 | C2×C4 | — | 4 | 2 | no | — |
| 737 | C2×C4 | — | 4 | 2 | no | — |
| 738 | C2×C4 | — | 4 | 2 | no | — |
| 739 | C2×C4 | — | 4 | 2 | no | — |
| 740 | C2×C4 | — | 4 | 4 | no | — |
| 741 | C2×C4 | — | 4 | 1 | no | — |
| 742 | C2×C4 | — | 4 | 2 | no | — |
| 743 | C2×C4 | — | 8 | 2 | no | — |
| 744 | C2×C4 | — | 8 | 2 | no | — |
| 745 | C2×C4 | — | 8 | 2 | no | — |
| 746 | C2×C4 | — | 8 | 2 | no | — |
| 747 | C2×C4 | — | 8 | 2 | no | — |
| 748 | C2×C4 | — | 8 | 2 | no | — |
| 749 | C2×C4 | — | 8 | 2 | no | — |
| 750 | C2×C4 | — | 8 | 2 | no | — |
| 751 | C2×C4 | — | 8 | 2 | no | — |
| 752 | C2×C4 | — | 8 | 2 | no | — |
| 753 | C2×C4 | — | 8 | 1 | no | — |
| 754 | C2×C4 | — | 8 | 1 | no | — |
| 755 | C2×C4 | — | 8 | 1 | no | — |
| 756 | C2×C4 | — | 8 | 1 | no | — |
| 757 | C2×C4 | — | 8 | 1 | no | — |
| 758 | C2×C4 | — | 8 | 2 | no | — |
| 759 | C2×C4 | — | 8 | 1 | no | — |
| 760 | C2×C4 | — | 16 | 4 | no | — |
| 761 | C2×C4 | — | 16 | 8 | no | — |
| 762 | C2×C4 | — | 16 | 1 | no | — |
| 763 | C2×C4 | — | 16 | 1 | no | — |
| 764 | C2×C4 | — | 32 | 4 | no | — |
| 765 | C2×C4 | #2407 | 1 | 1 | yes | characteristic |
| 766 | C2×C4 | #3003 | 1 | 1 | yes | characteristic |
| 767 | C2×C4 | #3008 | 1 | 1 | yes | characteristic |
| 768 | C2×C4 | #3010 | 1 | 1 | yes | characteristic |
| 769 | C2×C4 | C2×#453 | 1 | 1 | yes | characteristic |
| 770 | C2×C4 | #3018 | 1 | 1 | yes | characteristic |
| 771 | C2×C4 | #3306 | 1 | 2 | yes | — |
| 772 | C2×C4 | #3345 | 1 | 2 | yes | — |
| 773 | C8 | — | 2 | 1 | no | — |
| 774 | C8 | — | 2 | 1 | no | — |
| 775 | C8 | — | 4 | 1 | no | — |
| 776 | C8 | — | 4 | 1 | no | — |
| 777 | C8 | — | 8 | 2 | no | — |
| 778 | C8 | — | 16 | 2 | no | — |
| 779 | C8 | — | 16 | 1 | no | — |
| 780 | C8 | #3366 | 1 | 2 | yes | — |
| 781 | C8 | #3399 | 1 | 2 | yes | — |
| 782 | C22 | — | 2 | 2 | no | — |
| 783 | C22 | — | 4 | 4 | no | — |
| 784 | C22 | — | 4 | 4 | no | — |
| 785 | C22 | — | 4 | 4 | no | — |
| 786 | C22 | — | 8 | 2 | no | — |
| 787 | C22 | — | 8 | 2 | no | — |
| 788 | C22 | — | 8 | 2 | no | — |
| 789 | C22 | — | 8 | 2 | no | — |
| 790 | C22 | — | 16 | 1 | no | — |
| 791 | C22 | — | 16 | 2 | no | — |
| 792 | C22 | — | 16 | 1 | no | — |
| 793 | C22 | — | 16 | 1 | no | — |
| 794 | C22 | — | 16 | 1 | no | — |
| 795 | C22 | — | 16 | 2 | no | — |
| 796 | C22 | — | 16 | 2 | no | — |
| 797 | C22 | #18524 | 1 | 1 | yes | characteristic |
| 798 | C22 | #18598 | 1 | 1 | yes | characteristic |
| 799 | C22 | #24128 | 1 | 1 | yes | characteristic |
| 800 | C4 | — | 2 | 2 | no | — |
| 801 | C4 | — | 2 | 2 | no | — |
| 802 | C4 | — | 4 | 2 | no | — |
| 803 | C4 | — | 8 | 1 | no | — |
| 804 | C4 | — | 8 | 4 | no | — |
| 805 | C4 | — | 8 | 2 | no | — |
| 806 | C4 | — | 16 | 1 | no | — |
| 807 | C4 | — | 16 | 1 | no | — |
| 808 | C4 | — | 16 | 2 | no | — |
| 809 | C4 | — | 16 | 1 | no | — |
| 810 | C4 | — | 16 | 1 | no | — |
| 811 | C4 | #18610 | 1 | 1 | yes | characteristic |
| 812 | C4 | #18716 | 1 | 1 | yes | characteristic |
| 813 | C4 | #24176 | 1 | 1 | yes | characteristic |
| 814 | C4 | #24196 | 1 | 1 | yes | characteristic |
| 815 | C2 | — | 2 | 1 | no | — |
| 816 | C2 | — | 2 | 1 | no | — |
| 817 | C2 | — | 8 | 4 | no | — |
| 818 | C2 | — | 32 | 1 | no | — |
| 819 | C2 | — | 32 | 1 | no | — |
| 820 | C2 | #259187 | 1 | 1 | yes | characteristic |
| 821 | C2 | #500473 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #24128 |
| commutator, Frattini, cosocle | C2×C4×C8 | C24 |
| LCS | G ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #21683 ◁ 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. #7613824 | C2 | semidirect |
| 2. #507575 | C2 | semidirect |
| 3. #496127 | C2 | semidirect |
| 4. #317087 | C2 | semidirect |
| 5. #145023 | C2 | semidirect |
| 6. #143211 | C2 | semidirect |
| 7. #141927 | C2 | semidirect |
| 8. #140595 | C2 | semidirect |
| 9. #136885 | C2 | semidirect |
| 10. #136367 | C2 | semidirect |
| 11. #134641 | C2 | semidirect |
| 215. #494 | #41 | semidirect |
| 216. #493 | #41 | semidirect |
| 333. C4×C16 | #41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7613824 | 2 |
| #507575 | 2 |
| #496127 | 2 |
| #317087 | 2 |
| #145023 | 2 |
| #143211 | 2 |
| #141927 | 2 |
| #140595 | 2 |
| #136885 | 2 |
| #136367 | 2 |
| #134641 | 2 |