Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1477 conjugacy classes of subgroups.
The subgroup lattice has 786 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6358256 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #483608 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #481421 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #225782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #141841 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #141326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #138561 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #137059 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #135068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #131816 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #128751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | D8×#41 | C22 | 1 | 2 | yes | — |
| 13 | #61038 | — | 2 | 1 | no | — |
| 14 | #33484 | C22 | 1 | 2 | yes | complemented |
| 15 | #19889 | C4 | 1 | 2 | yes | — |
| 16 | #19888 | — | 2 | 1 | no | — |
| 17 | #19887 | C4 | 1 | 2 | yes | — |
| 18 | #19886 | — | 2 | 2 | no | — |
| 19 | #19885 | C4 | 1 | 2 | yes | — |
| 20 | #19884 | — | 2 | 1 | no | — |
| 21 | #19883 | C4 | 1 | 2 | yes | — |
| 22 | #19603 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19133 | — | 2 | 1 | no | — |
| 24 | #19125 | C22 | 1 | 2 | yes | — |
| 25 | #18516 | — | 2 | 2 | no | — |
| 26 | #18055 | — | 2 | 1 | no | — |
| 27 | C2×#1589 | C22 | 1 | 1 | yes | characteristic |
| 28 | C8×#135 | C22 | 1 | 1 | yes | characteristic |
| 29 | #17834 | C22 | 1 | 2 | yes | complemented |
| 30 | C4×#361 | C22 | 1 | 1 | yes | characteristic |
| 31 | #12062 | — | 2 | 1 | no | — |
| 32 | #12061 | — | 2 | 1 | no | — |
| 33 | #12057 | — | 2 | 2 | no | — |
| 34 | #12013 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #11751 | C22 | 1 | 2 | yes | complemented |
| 36 | #11680 | C22 | 1 | 2 | yes | complemented |
| 37 | #11680 | C22 | 1 | 2 | yes | complemented |
| 38 | #11678 | — | 2 | 2 | no | — |
| 39 | #11667 | — | 2 | 2 | no | — |
| 40 | #11663 | C22 | 1 | 2 | yes | — |
| 41 | #11654 | — | 2 | 2 | no | — |
| 42 | #11652 | C22 | 1 | 2 | yes | complemented |
| 43 | #11615 | C22 | 1 | 2 | yes | complemented |
| 44 | #11599 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#1333 | — | 2 | 2 | no | — |
| 46 | #11402 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #9634 | — | 2 | 1 | no | — |
| 48 | #8900 | — | 2 | 2 | no | — |
| 49 | #8824 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #8670 | C22 | 1 | 2 | yes | complemented |
| 51 | C8×#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #7292 | C22 | 1 | 2 | yes | complemented |
| 53 | #7176 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #7159 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C2×#575 | — | 4 | 1 | no | — |
| 56 | D4×#41 | — | 2 | 2 | no | — |
| 57 | #3391 | C2×C4 | 1 | 2 | yes | — |
| 58 | Q8×D8 | C2×C4 | 1 | 2 | yes | — |
| 59 | #3358 | — | 2 | 2 | no | — |
| 60 | #3334 | — | 2 | 2 | no | — |
| 61 | #3334 | C2×C4 | 1 | 2 | yes | — |
| 62 | #3294 | — | 2 | 2 | no | — |
| 63 | #3294 | — | 4 | 2 | no | — |
| 64 | D4×D8 | — | 2 | 2 | no | — |
| 65 | D4×D8 | C2×C4 | 1 | 2 | yes | — |
| 66 | #3278 | — | 2 | 2 | no | — |
| 67 | #3277 | — | 4 | 1 | no | — |
| 68 | #3276 | — | 2 | 2 | no | — |
| 69 | #3275 | — | 4 | 2 | no | — |
| 70 | #3274 | — | 2 | 2 | no | — |
| 71 | #3273 | — | 4 | 1 | no | — |
| 72 | #3272 | — | 2 | 2 | no | — |
| 73 | #3169 | — | 2 | 1 | no | — |
| 74 | #3169 | — | 2 | 2 | no | — |
| 75 | #3169 | C23 | 1 | 2 | yes | — |
| 76 | #3147 | — | 2 | 1 | no | — |
| 77 | #3100 | — | 2 | 2 | no | — |
| 78 | #3100 | — | 4 | 2 | no | — |
| 79 | #3054 | — | 4 | 1 | no | — |
| 80 | #3035 | — | 2 | 2 | no | — |
| 81 | #3002 | — | 4 | 2 | no | — |
| 82 | #2990 | — | 2 | 2 | no | — |
| 83 | C8×#41 | C23 | 1 | 2 | yes | — |
| 84 | C4×#135 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×C4×D8 | — | 2 | 2 | no | — |
| 86 | C2×C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#436 | — | 2 | 1 | no | — |
| 88 | #2183 | — | 2 | 2 | no | — |
| 89 | #2168 | — | 4 | 2 | no | — |
| 90 | D4×C16 | — | 2 | 2 | no | — |
| 91 | #2163 | — | 2 | 2 | no | — |
| 92 | #2163 | C23 | 1 | 2 | yes | — |
| 93 | C2×#361 | — | 2 | 1 | no | — |
| 94 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 95 | C4×M32 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×#346 | — | 2 | 2 | no | — |
| 97 | #1837 | — | 2 | 1 | no | — |
| 98 | C4×#108 | C23 | 1 | 1 | yes | characteristic |
| 99 | #1713 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | #1712 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | #1709 | — | 2 | 1 | no | — |
| 102 | #1706 | — | 2 | 1 | no | — |
| 103 | #1706 | C2×C4 | 1 | 2 | yes | — |
| 104 | #1689 | — | 2 | 2 | no | — |
| 105 | #1687 | — | 2 | 2 | no | — |
| 106 | #1685 | — | 2 | 2 | no | — |
| 107 | #1685 | — | 2 | 2 | no | — |
| 108 | #1682 | — | 2 | 2 | no | — |
| 109 | #1681 | — | 2 | 2 | no | — |
| 110 | #1674 | C2×C4 | 1 | 2 | yes | — |
| 111 | #1673 | C2×C4 | 1 | 2 | yes | — |
| 112 | #1668 | C2×C4 | 1 | 2 | yes | — |
| 113 | #1667 | C2×C4 | 1 | 2 | yes | — |
| 114 | #1649 | — | 2 | 2 | no | — |
| 115 | #1647 | — | 2 | 2 | no | — |
| 116 | #1641 | — | 2 | 2 | no | — |
| 117 | #1639 | — | 2 | 2 | no | — |
| 118 | #1627 | — | 2 | 2 | no | — |
| 119 | #1625 | — | 2 | 2 | no | — |
| 120 | #1621 | — | 2 | 2 | no | — |
| 121 | #1619 | — | 2 | 2 | no | — |
| 122 | #1591 | — | 4 | 1 | no | — |
| 123 | #1589 | — | 2 | 1 | no | — |
| 124 | #1589 | — | 2 | 1 | no | — |
| 125 | #1589 | C2×C4 | 1 | 2 | yes | — |
| 126 | #1589 | C2×C4 | 1 | 2 | yes | — |
| 127 | #1585 | — | 4 | 2 | no | — |
| 128 | C8×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 129 | C8×Q16 | D4 | 1 | 1 | yes | characteristic |
| 130 | C8×SD16 | C2×C4 | 1 | 2 | yes | — |
| 131 | C8×SD16 | D4 | 1 | 2 | yes | — |
| 132 | C8×D8 | — | 4 | 1 | no | — |
| 133 | C8×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 134 | C8×D8 | D4 | 1 | 1 | yes | characteristic |
| 135 | #1574 | — | 2 | 2 | no | — |
| 136 | #1573 | — | 4 | 2 | no | — |
| 137 | #1568 | — | 2 | 2 | no | — |
| 138 | #1567 | — | 2 | 1 | no | — |
| 139 | #1566 | C23 | 1 | 2 | yes | — |
| 140 | #1564 | D4 | 1 | 1 | yes | characteristic |
| 141 | #1564 | C23 | 1 | 1 | yes | characteristic |
| 142 | C2×#335 | C23 | 1 | 1 | yes | characteristic |
| 143 | C2×#334 | — | 2 | 2 | no | — |
| 144 | #1540 | — | 2 | 2 | no | — |
| 145 | #1489 | — | 2 | 2 | no | — |
| 146 | #1476 | D4 | 1 | 2 | yes | — |
| 147 | C2×D4⋊C8 | — | 2 | 1 | no | — |
| 148 | C8×M16 | — | 2 | 1 | no | — |
| 149 | C2×C82 | C23 | 1 | 1 | yes | characteristic |
| 150 | #1387 | — | 2 | 1 | no | — |
| 151 | #1370 | — | 2 | 1 | no | — |
| 152 | #1367 | — | 2 | 1 | no | — |
| 153 | #1349 | — | 4 | 2 | no | — |
| 154 | Q8⋊C16 | — | 2 | 2 | no | — |
| 155 | #1333 | — | 2 | 2 | no | — |
| 156 | #1333 | — | 2 | 2 | no | — |
| 157 | #1333 | — | 2 | 2 | no | — |
| 158 | #1333 | — | 2 | 2 | no | — |
| 159 | #1333 | — | 2 | 2 | no | — |
| 160 | #1333 | — | 2 | 2 | no | — |
| 161 | #1333 | — | 4 | 2 | no | — |
| 162 | #1333 | D4 | 1 | 2 | yes | — |
| 163 | #1333 | D4 | 1 | 2 | yes | — |
| 164 | D4⋊C16 | — | 2 | 2 | no | — |
| 165 | #1312 | — | 2 | 1 | no | — |
| 166 | #1312 | — | 2 | 1 | no | — |
| 167 | #1299 | — | 2 | 2 | no | — |
| 168 | #1278 | — | 2 | 1 | no | — |
| 169 | C22×#41 | — | 4 | 2 | no | — |
| 170 | #575 | — | 8 | 8 | no | — |
| 171 | C2×#137 | — | 4 | 2 | no | — |
| 172 | C2×#137 | — | 4 | 2 | no | — |
| 173 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 174 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 175 | C2×#135 | — | 4 | 2 | no | — |
| 176 | C2×#135 | — | 4 | 1 | no | — |
| 177 | C2×#135 | — | 4 | 1 | no | — |
| 178 | C2×#135 | SD16 | 1 | 1 | yes | characteristic |
| 179 | C22×D8 | — | 2 | 2 | no | — |
| 180 | C22×D8 | #41 | 1 | 1 | yes | characteristic |
| 181 | C22×M16 | — | 4 | 1 | no | — |
| 182 | #550 | — | 2 | 2 | no | — |
| 183 | D4×Q8 | — | 2 | 2 | no | — |
| 184 | #548 | — | 4 | 2 | no | — |
| 185 | #547 | — | 2 | 2 | no | — |
| 186 | #547 | — | 4 | 2 | no | — |
| 187 | #546 | — | 4 | 2 | no | — |
| 188 | #546 | — | 8 | 2 | no | — |
| 189 | D42 | — | 2 | 2 | no | — |
| 190 | D42 | — | 4 | 2 | no | — |
| 191 | #532 | — | 2 | 2 | no | — |
| 192 | #532 | — | 4 | 2 | no | — |
| 193 | #525 | — | 4 | 2 | no | — |
| 194 | #525 | — | 8 | 2 | no | — |
| 195 | C4×#41 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×C4×D4 | — | 2 | 1 | no | — |
| 197 | C2×C4×D4 | — | 4 | 2 | no | — |
| 198 | C2×M32 | — | 2 | 1 | no | — |
| 199 | C2×M32 | — | 2 | 1 | no | — |
| 200 | C22×C16 | — | 4 | 2 | no | — |
| 201 | #500 | — | 2 | 2 | no | — |
| 202 | #500 | — | 2 | 1 | no | — |
| 203 | #500 | C22×C4 | 1 | 2 | yes | — |
| 204 | #495 | — | 4 | 1 | no | — |
| 205 | #495 | — | 4 | 1 | no | — |
| 206 | #494 | — | 2 | 1 | no | — |
| 207 | #493 | — | 2 | 2 | no | — |
| 208 | #493 | — | 2 | 1 | no | — |
| 209 | #493 | — | 2 | 1 | no | — |
| 210 | #493 | C22×C4 | 1 | 2 | yes | — |
| 211 | #492 | — | 2 | 2 | no | — |
| 212 | #486 | — | 2 | 2 | no | — |
| 213 | #486 | — | 2 | 2 | no | — |
| 214 | #486 | — | 4 | 2 | no | — |
| 215 | #480 | — | 4 | 2 | no | — |
| 216 | #480 | — | 4 | 2 | no | — |
| 217 | #480 | — | 4 | 2 | no | — |
| 218 | #474 | — | 2 | 2 | no | — |
| 219 | #474 | — | 2 | 2 | no | — |
| 220 | #474 | — | 4 | 2 | no | — |
| 221 | #474 | — | 4 | 2 | no | — |
| 222 | #470 | — | 4 | 2 | no | — |
| 223 | #469 | — | 4 | 2 | no | — |
| 224 | #468 | — | 4 | 2 | no | — |
| 225 | #468 | — | 4 | 2 | no | — |
| 226 | #466 | — | 2 | 2 | no | — |
| 227 | #466 | — | 2 | 2 | no | — |
| 228 | #466 | — | 2 | 2 | no | — |
| 229 | #466 | — | 2 | 2 | no | — |
| 230 | #466 | — | 4 | 2 | no | — |
| 231 | #466 | — | 8 | 1 | no | — |
| 232 | #464 | — | 4 | 2 | no | — |
| 233 | #463 | — | 4 | 2 | no | — |
| 234 | #462 | — | 2 | 2 | no | — |
| 235 | #461 | — | 2 | 2 | no | — |
| 236 | #460 | — | 2 | 2 | no | — |
| 237 | #459 | — | 2 | 2 | no | — |
| 238 | #459 | — | 2 | 2 | no | — |
| 239 | #459 | — | 2 | 2 | no | — |
| 240 | #459 | — | 4 | 2 | no | — |
| 241 | #459 | — | 4 | 2 | no | — |
| 242 | #452 | — | 4 | 2 | no | — |
| 243 | #452 | — | 4 | 2 | no | — |
| 244 | #451 | — | 4 | 2 | no | — |
| 245 | #450 | — | 4 | 2 | no | — |
| 246 | #449 | — | 4 | 2 | no | — |
| 247 | #449 | — | 4 | 2 | no | — |
| 248 | #448 | — | 4 | 2 | no | — |
| 249 | #447 | — | 4 | 2 | no | — |
| 250 | #447 | — | 4 | 2 | no | — |
| 251 | #447 | — | 4 | 2 | no | — |
| 252 | #447 | — | 4 | 2 | no | — |
| 253 | #446 | — | 4 | 2 | no | — |
| 254 | C8×Q8 | C22×C4 | 1 | 2 | yes | — |
| 255 | C8×Q8 | C2×D4 | 1 | 2 | yes | — |
| 256 | C4×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 257 | C4×Q16 | D8 | 1 | 1 | yes | characteristic |
| 258 | C4×SD16 | C22⋊C4 | 1 | 2 | yes | — |
| 259 | C4×SD16 | D8 | 1 | 2 | yes | — |
| 260 | C4×D8 | — | 2 | 2 | no | — |
| 261 | C4×D8 | — | 2 | 2 | no | — |
| 262 | C4×D8 | — | 2 | 1 | no | — |
| 263 | C4×D8 | — | 2 | 2 | no | — |
| 264 | C4×D8 | — | 2 | 1 | no | — |
| 265 | C4×D8 | — | 2 | 2 | no | — |
| 266 | C4×D8 | — | 4 | 2 | no | — |
| 267 | C4×D8 | — | 4 | 2 | no | — |
| 268 | C4×D8 | — | 4 | 2 | no | — |
| 269 | C4×D8 | — | 8 | 1 | no | — |
| 270 | C4×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 271 | C4×D8 | D8 | 1 | 1 | yes | characteristic |
| 272 | C4×D8 | C22×C4 | 1 | 2 | yes | — |
| 273 | C4×D8 | C2×D4 | 1 | 2 | yes | — |
| 274 | #436 | — | 2 | 2 | no | — |
| 275 | #436 | — | 2 | 2 | no | — |
| 276 | #436 | — | 4 | 1 | no | — |
| 277 | #436 | — | 4 | 1 | no | — |
| 278 | #435 | — | 8 | 2 | no | — |
| 279 | C8×D4 | — | 2 | 2 | no | — |
| 280 | C8×D4 | — | 2 | 2 | no | — |
| 281 | C8×D4 | — | 4 | 2 | no | — |
| 282 | C8×D4 | C22×C4 | 1 | 2 | yes | — |
| 283 | C8×D4 | C2×D4 | 1 | 2 | yes | — |
| 284 | #432 | — | 4 | 2 | no | — |
| 285 | #431 | — | 2 | 2 | no | — |
| 286 | #431 | — | 2 | 1 | no | — |
| 287 | #431 | C2×D4 | 1 | 2 | yes | — |
| 288 | C2×#108 | — | 2 | 1 | no | — |
| 289 | #427 | SD16 | 1 | 1 | yes | characteristic |
| 290 | C2×#107 | — | 2 | 2 | no | — |
| 291 | C2×#107 | #41 | 1 | 1 | yes | characteristic |
| 292 | #423 | — | 2 | 2 | no | — |
| 293 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 294 | C2×C4⋊C8 | — | 4 | 2 | no | — |
| 295 | #416 | — | 4 | 2 | no | — |
| 296 | #416 | SD16 | 1 | 2 | yes | — |
| 297 | C2×#102 | — | 2 | 1 | no | — |
| 298 | C2×#102 | — | 4 | 2 | no | — |
| 299 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 300 | C4×M16 | — | 2 | 1 | no | — |
| 301 | C2×C4×C8 | — | 2 | 2 | no | — |
| 302 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 305 | C4⋊C16 | — | 2 | 2 | no | — |
| 306 | C4⋊C16 | — | 4 | 2 | no | — |
| 307 | #361 | — | 4 | 2 | no | — |
| 308 | C22⋊C16 | — | 2 | 2 | no | — |
| 309 | C22⋊C16 | — | 4 | 2 | no | — |
| 310 | #346 | — | 2 | 2 | no | — |
| 311 | #346 | — | 2 | 1 | no | — |
| 312 | #346 | — | 4 | 2 | no | — |
| 313 | #346 | C2×D4 | 1 | 2 | yes | — |
| 314 | C4×C16 | — | 2 | 1 | no | — |
| 315 | C4×C16 | — | 2 | 1 | no | — |
| 316 | #341 | — | 2 | 1 | no | — |
| 317 | #341 | — | 8 | 1 | no | — |
| 318 | #335 | — | 2 | 1 | no | — |
| 319 | #335 | — | 2 | 1 | no | — |
| 320 | #335 | — | 4 | 2 | no | — |
| 321 | #335 | — | 4 | 1 | no | — |
| 322 | #335 | — | 4 | 1 | no | — |
| 323 | #335 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 324 | #335 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 325 | #335 | C22×C4 | 1 | 2 | yes | — |
| 326 | #334 | — | 2 | 2 | no | — |
| 327 | #334 | — | 2 | 2 | no | — |
| 328 | #334 | — | 4 | 2 | no | — |
| 329 | #334 | C22⋊C4 | 1 | 2 | yes | — |
| 330 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | #334 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | #332 | — | 2 | 2 | no | — |
| 333 | #332 | — | 2 | 2 | no | — |
| 334 | #331 | — | 2 | 2 | no | — |
| 335 | #331 | — | 2 | 2 | no | — |
| 336 | Q8⋊C8 | — | 4 | 2 | no | — |
| 337 | Q8⋊C8 | C22⋊C4 | 1 | 2 | yes | — |
| 338 | Q8⋊C8 | C22⋊C4 | 1 | 2 | yes | — |
| 339 | D4⋊C8 | — | 2 | 2 | no | — |
| 340 | D4⋊C8 | — | 2 | 2 | no | — |
| 341 | D4⋊C8 | — | 4 | 2 | no | — |
| 342 | D4⋊C8 | C22⋊C4 | 1 | 2 | yes | — |
| 343 | D4⋊C8 | C22⋊C4 | 1 | 2 | yes | — |
| 344 | #322 | — | 4 | 1 | no | — |
| 345 | C82 | — | 4 | 1 | no | — |
| 346 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 347 | C82 | C22×C4 | 1 | 1 | yes | characteristic |
| 348 | C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 349 | C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×#41 | — | 4 | 2 | no | — |
| 351 | C2×#41 | — | 4 | 2 | no | — |
| 352 | C2×#41 | — | 4 | 2 | no | — |
| 353 | C2×#41 | — | 8 | 2 | no | — |
| 354 | C2×#41 | — | 8 | 2 | no | — |
| 355 | C2×#41 | — | 8 | 8 | no | — |
| 356 | C2×#41 | — | 16 | 4 | no | — |
| 357 | C2×#41 | C2×SD16 | 1 | 2 | yes | — |
| 358 | C22×Q8 | — | 4 | 2 | no | — |
| 359 | C22×D4 | — | 2 | 1 | no | — |
| 360 | C22×D4 | — | 4 | 2 | no | — |
| 361 | C22×D4 | — | 4 | 2 | no | — |
| 362 | C22×D4 | — | 8 | 2 | no | — |
| 363 | C23×C4 | — | 4 | 1 | no | — |
| 364 | C23×C4 | — | 8 | 2 | no | — |
| 365 | #137 | — | 8 | 8 | no | — |
| 366 | #137 | — | 8 | 8 | no | — |
| 367 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 368 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 369 | #135 | — | 2 | 4 | no | — |
| 370 | #135 | — | 8 | 4 | no | — |
| 371 | #135 | — | 8 | 8 | no | — |
| 372 | #135 | — | 16 | 2 | no | — |
| 373 | C2×Q16 | — | 4 | 2 | no | — |
| 374 | C2×Q16 | — | 4 | 1 | no | — |
| 375 | C2×Q16 | — | 4 | 1 | no | — |
| 376 | C2×Q16 | #102 | 1 | 1 | yes | characteristic |
| 377 | C2×SD16 | — | 4 | 2 | no | — |
| 378 | C2×SD16 | — | 4 | 2 | no | — |
| 379 | C2×SD16 | — | 4 | 2 | no | — |
| 380 | C2×SD16 | — | 4 | 2 | no | — |
| 381 | C2×SD16 | #102 | 1 | 2 | yes | — |
| 382 | C2×D8 | — | 2 | 2 | no | — |
| 383 | C2×D8 | — | 2 | 2 | no | — |
| 384 | C2×D8 | — | 2 | 1 | no | — |
| 385 | C2×D8 | — | 4 | 1 | no | — |
| 386 | C2×D8 | — | 4 | 1 | no | — |
| 387 | C2×D8 | — | 4 | 2 | no | — |
| 388 | C2×D8 | — | 4 | 2 | no | — |
| 389 | C2×D8 | — | 4 | 4 | no | — |
| 390 | C2×D8 | — | 4 | 2 | no | — |
| 391 | C2×D8 | — | 4 | 1 | no | — |
| 392 | C2×D8 | — | 4 | 1 | no | — |
| 393 | C2×D8 | — | 8 | 1 | no | — |
| 394 | C2×D8 | — | 8 | 2 | no | — |
| 395 | C2×D8 | #102 | 1 | 1 | yes | characteristic |
| 396 | C2×D8 | C4×D4 | 1 | 2 | yes | — |
| 397 | C2×M16 | — | 4 | 2 | no | — |
| 398 | C2×M16 | — | 4 | 2 | no | — |
| 399 | C2×M16 | — | 4 | 1 | no | — |
| 400 | C2×M16 | — | 4 | 2 | no | — |
| 401 | C2×M16 | — | 8 | 4 | no | — |
| 402 | C22×C8 | — | 2 | 1 | no | — |
| 403 | C22×C8 | — | 2 | 2 | no | — |
| 404 | C22×C8 | — | 2 | 2 | no | — |
| 405 | C22×C8 | — | 4 | 1 | no | — |
| 406 | C22×C8 | — | 8 | 2 | no | — |
| 407 | C22×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 408 | C22×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 409 | C22×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 410 | C22×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 411 | C4⋊Q8 | — | 2 | 2 | no | — |
| 412 | C4⋊Q8 | — | 4 | 2 | no | — |
| 413 | #127 | — | 2 | 2 | no | — |
| 414 | #127 | — | 4 | 2 | no | — |
| 415 | #124 | — | 4 | 2 | no | — |
| 416 | #124 | — | 8 | 2 | no | — |
| 417 | #123 | — | 8 | 2 | no | — |
| 418 | #123 | — | 8 | 2 | no | — |
| 419 | #123 | — | 8 | 2 | no | — |
| 420 | C22⋊Q8 | — | 4 | 2 | no | — |
| 421 | C22⋊Q8 | — | 4 | 2 | no | — |
| 422 | C22⋊Q8 | — | 8 | 2 | no | — |
| 423 | C22⋊Q8 | — | 8 | 2 | no | — |
| 424 | #121 | — | 4 | 2 | no | — |
| 425 | #121 | — | 4 | 2 | no | — |
| 426 | #121 | — | 4 | 2 | no | — |
| 427 | #121 | — | 4 | 2 | no | — |
| 428 | #121 | — | 4 | 2 | no | — |
| 429 | #121 | — | 4 | 2 | no | — |
| 430 | #121 | — | 8 | 2 | no | — |
| 431 | #121 | — | 8 | 2 | no | — |
| 432 | #121 | — | 8 | 2 | no | — |
| 433 | #120 | — | 8 | 2 | no | — |
| 434 | #120 | — | 8 | 2 | no | — |
| 435 | #120 | — | 8 | 2 | no | — |
| 436 | C4×Q8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 437 | C4×Q8 | C2×D8 | 1 | 2 | yes | — |
| 438 | C4×D4 | — | 2 | 2 | no | — |
| 439 | C4×D4 | — | 2 | 2 | no | — |
| 440 | C4×D4 | — | 2 | 2 | no | — |
| 441 | C4×D4 | — | 2 | 2 | no | — |
| 442 | C4×D4 | — | 4 | 2 | no | — |
| 443 | C4×D4 | — | 4 | 2 | no | — |
| 444 | C4×D4 | — | 4 | 2 | no | — |
| 445 | C4×D4 | — | 4 | 1 | no | — |
| 446 | C4×D4 | — | 4 | 1 | no | — |
| 447 | C4×D4 | — | 4 | 2 | no | — |
| 448 | C4×D4 | — | 8 | 2 | no | — |
| 449 | C4×D4 | — | 8 | 2 | no | — |
| 450 | C4×D4 | — | 8 | 2 | no | — |
| 451 | C4×D4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 452 | C4×D4 | C2×D8 | 1 | 2 | yes | — |
| 453 | #117 | — | 2 | 2 | no | — |
| 454 | #117 | C2×SD16 | 1 | 2 | yes | — |
| 455 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 456 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 457 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 458 | C2×C22⋊C4 | — | 8 | 2 | no | — |
| 459 | C2×C42 | — | 2 | 2 | no | — |
| 460 | C2×C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 461 | M32 | — | 4 | 1 | no | — |
| 462 | M32 | — | 4 | 1 | no | — |
| 463 | M32 | — | 8 | 1 | no | — |
| 464 | C2×C16 | — | 2 | 2 | no | — |
| 465 | C2×C16 | — | 4 | 2 | no | — |
| 466 | C2×C16 | — | 4 | 1 | no | — |
| 467 | C2×C16 | — | 8 | 4 | no | — |
| 468 | #108 | — | 2 | 2 | no | — |
| 469 | #108 | — | 4 | 1 | no | — |
| 470 | #107 | — | 2 | 1 | no | — |
| 471 | #107 | — | 2 | 2 | no | — |
| 472 | #107 | — | 2 | 2 | no | — |
| 473 | #107 | — | 4 | 2 | no | — |
| 474 | #107 | — | 4 | 2 | no | — |
| 475 | #107 | — | 8 | 1 | no | — |
| 476 | #107 | #102 | 1 | 1 | yes | characteristic |
| 477 | #107 | #102 | 1 | 1 | yes | characteristic |
| 478 | #107 | C4×D4 | 1 | 2 | yes | — |
| 479 | #106 | #102 | 1 | 2 | yes | — |
| 480 | C4⋊C8 | — | 2 | 2 | no | — |
| 481 | C4⋊C8 | — | 2 | 2 | no | — |
| 482 | C4⋊C8 | — | 2 | 2 | no | — |
| 483 | C4⋊C8 | — | 2 | 1 | no | — |
| 484 | C4⋊C8 | — | 2 | 1 | no | — |
| 485 | C4⋊C8 | — | 4 | 2 | no | — |
| 486 | C4⋊C8 | — | 4 | 1 | no | — |
| 487 | C4⋊C8 | — | 4 | 2 | no | — |
| 488 | C4⋊C8 | — | 8 | 2 | no | — |
| 489 | C4⋊C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 490 | C4⋊C8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 491 | #103 | — | 4 | 2 | no | — |
| 492 | #103 | — | 4 | 2 | no | — |
| 493 | #103 | #102 | 1 | 2 | yes | — |
| 494 | #103 | #102 | 1 | 2 | yes | — |
| 495 | #102 | — | 2 | 2 | no | — |
| 496 | #102 | — | 2 | 2 | no | — |
| 497 | #102 | — | 4 | 2 | no | — |
| 498 | #102 | — | 4 | 2 | no | — |
| 499 | #102 | — | 4 | 2 | no | — |
| 500 | #102 | — | 4 | 2 | no | — |
| 501 | #102 | — | 4 | 2 | no | — |
| 502 | #102 | — | 4 | 2 | no | — |
| 503 | #102 | — | 4 | 2 | no | — |
| 504 | #102 | — | 4 | 2 | no | — |
| 505 | #102 | — | 8 | 2 | no | — |
| 506 | #102 | #102 | 1 | 2 | yes | — |
| 507 | #102 | #102 | 1 | 2 | yes | — |
| 508 | C22⋊C8 | — | 2 | 2 | no | — |
| 509 | C22⋊C8 | — | 2 | 2 | no | — |
| 510 | C22⋊C8 | — | 2 | 2 | no | — |
| 511 | C22⋊C8 | — | 4 | 1 | no | — |
| 512 | C22⋊C8 | — | 4 | 2 | no | — |
| 513 | C22⋊C8 | — | 4 | 2 | no | — |
| 514 | C22⋊C8 | — | 8 | 2 | no | — |
| 515 | #97 | — | 4 | 1 | no | — |
| 516 | #97 | — | 8 | 2 | no | — |
| 517 | C4×C8 | — | 2 | 2 | no | — |
| 518 | C4×C8 | — | 2 | 2 | no | — |
| 519 | C4×C8 | — | 2 | 2 | no | — |
| 520 | C4×C8 | — | 2 | 1 | no | — |
| 521 | C4×C8 | — | 4 | 1 | no | — |
| 522 | C4×C8 | — | 4 | 1 | no | — |
| 523 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 524 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 525 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 526 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 527 | C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 528 | C4×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 529 | C4×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 530 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 531 | C4×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 532 | C4×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 533 | C24 | — | 4 | 1 | no | — |
| 534 | C24 | — | 8 | 2 | no | — |
| 535 | #41 | — | 2 | 4 | no | — |
| 536 | #41 | — | 4 | 2 | no | — |
| 537 | #41 | — | 8 | 4 | no | — |
| 538 | #41 | — | 8 | 4 | no | — |
| 539 | #41 | — | 8 | 4 | no | — |
| 540 | #41 | — | 8 | 4 | no | — |
| 541 | #41 | — | 16 | 8 | no | — |
| 542 | #41 | — | 16 | 2 | no | — |
| 543 | #41 | — | 16 | 8 | no | — |
| 544 | #41 | — | 16 | 2 | no | — |
| 545 | C2×Q8 | — | 4 | 2 | no | — |
| 546 | C2×Q8 | — | 8 | 2 | no | — |
| 547 | C2×Q8 | — | 8 | 4 | no | — |
| 548 | C2×Q8 | — | 16 | 2 | no | — |
| 549 | C2×Q8 | C2×#102 | 1 | 2 | yes | — |
| 550 | C2×D4 | — | 2 | 2 | no | — |
| 551 | C2×D4 | — | 2 | 2 | no | — |
| 552 | C2×D4 | — | 4 | 2 | no | — |
| 553 | C2×D4 | — | 4 | 2 | no | — |
| 554 | C2×D4 | — | 4 | 2 | no | — |
| 555 | C2×D4 | — | 4 | 1 | no | — |
| 556 | C2×D4 | — | 8 | 1 | no | — |
| 557 | C2×D4 | — | 8 | 1 | no | — |
| 558 | C2×D4 | — | 8 | 2 | no | — |
| 559 | C2×D4 | — | 8 | 2 | no | — |
| 560 | C2×D4 | — | 8 | 2 | no | — |
| 561 | C2×D4 | — | 8 | 4 | no | — |
| 562 | C2×D4 | — | 8 | 2 | no | — |
| 563 | C2×D4 | — | 8 | 4 | no | — |
| 564 | C2×D4 | — | 8 | 2 | no | — |
| 565 | C2×D4 | — | 8 | 2 | no | — |
| 566 | C2×D4 | — | 16 | 2 | no | — |
| 567 | C2×D4 | — | 16 | 2 | no | — |
| 568 | C2×D4 | — | 16 | 8 | no | — |
| 569 | C2×D4 | C2×#102 | 1 | 2 | yes | — |
| 570 | C22×C4 | — | 2 | 2 | no | — |
| 571 | C22×C4 | — | 2 | 2 | no | — |
| 572 | C22×C4 | — | 2 | 2 | no | — |
| 573 | C22×C4 | — | 4 | 1 | no | — |
| 574 | C22×C4 | — | 4 | 2 | no | — |
| 575 | C22×C4 | — | 4 | 2 | no | — |
| 576 | C22×C4 | — | 8 | 2 | no | — |
| 577 | C22×C4 | — | 8 | 2 | no | — |
| 578 | C22×C4 | — | 8 | 2 | no | — |
| 579 | C22×C4 | — | 8 | 2 | no | — |
| 580 | C22×C4 | — | 8 | 2 | no | — |
| 581 | C22×C4 | — | 8 | 2 | no | — |
| 582 | C22×C4 | — | 16 | 8 | no | — |
| 583 | C22×C4 | #546 | 1 | 1 | yes | characteristic |
| 584 | C22×C4 | C22×SD16 | 1 | 1 | yes | characteristic |
| 585 | C22×C4 | #576 | 1 | 1 | yes | characteristic |
| 586 | Q16 | — | 2 | 2 | no | — |
| 587 | Q16 | — | 8 | 2 | no | — |
| 588 | Q16 | — | 8 | 4 | no | — |
| 589 | Q16 | — | 16 | 1 | no | — |
| 590 | SD16 | — | 2 | 4 | no | — |
| 591 | SD16 | — | 8 | 4 | no | — |
| 592 | SD16 | — | 8 | 4 | no | — |
| 593 | SD16 | — | 8 | 4 | no | — |
| 594 | SD16 | — | 16 | 2 | no | — |
| 595 | D8 | — | 2 | 2 | no | — |
| 596 | D8 | — | 2 | 2 | no | — |
| 597 | D8 | — | 4 | 2 | no | — |
| 598 | D8 | — | 4 | 2 | no | — |
| 599 | D8 | — | 8 | 1 | no | — |
| 600 | D8 | — | 8 | 2 | no | — |
| 601 | D8 | — | 8 | 2 | no | — |
| 602 | D8 | — | 8 | 4 | no | — |
| 603 | D8 | — | 8 | 4 | no | — |
| 604 | D8 | — | 16 | 1 | no | — |
| 605 | D8 | — | 16 | 2 | no | — |
| 606 | D8 | — | 16 | 2 | no | — |
| 607 | D8 | #361 | 1 | 4 | yes | complemented |
| 608 | M16 | — | 4 | 2 | no | — |
| 609 | M16 | — | 8 | 4 | no | — |
| 610 | M16 | — | 8 | 1 | no | — |
| 611 | M16 | — | 8 | 4 | no | — |
| 612 | M16 | — | 16 | 2 | no | — |
| 613 | C2×C8 | — | 2 | 2 | no | — |
| 614 | C2×C8 | — | 2 | 1 | no | — |
| 615 | C2×C8 | — | 2 | 1 | no | — |
| 616 | C2×C8 | — | 2 | 2 | no | — |
| 617 | C2×C8 | — | 2 | 2 | no | — |
| 618 | C2×C8 | — | 2 | 1 | no | — |
| 619 | C2×C8 | — | 2 | 1 | no | — |
| 620 | C2×C8 | — | 4 | 1 | no | — |
| 621 | C2×C8 | — | 4 | 1 | no | — |
| 622 | C2×C8 | — | 4 | 2 | no | — |
| 623 | C2×C8 | — | 4 | 2 | no | — |
| 624 | C2×C8 | — | 4 | 2 | no | — |
| 625 | C2×C8 | — | 4 | 1 | no | — |
| 626 | C2×C8 | — | 4 | 1 | no | — |
| 627 | C2×C8 | — | 8 | 2 | no | — |
| 628 | C2×C8 | — | 8 | 1 | no | — |
| 629 | C2×C8 | — | 8 | 2 | no | — |
| 630 | C2×C8 | — | 8 | 1 | no | — |
| 631 | C2×C8 | — | 8 | 2 | no | — |
| 632 | C2×C8 | — | 32 | 2 | no | — |
| 633 | C2×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 634 | C2×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 635 | C2×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 636 | C2×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 637 | C2×C8 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 638 | C2×C8 | #518 | 1 | 1 | yes | characteristic |
| 639 | C2×C8 | D42 | 1 | 1 | yes | characteristic |
| 640 | C2×C8 | #546 | 1 | 1 | yes | characteristic |
| 641 | C4⋊C4 | — | 2 | 2 | no | — |
| 642 | C4⋊C4 | — | 2 | 2 | no | — |
| 643 | C4⋊C4 | — | 2 | 2 | no | — |
| 644 | C4⋊C4 | — | 4 | 1 | no | — |
| 645 | C4⋊C4 | — | 4 | 2 | no | — |
| 646 | C4⋊C4 | — | 4 | 2 | no | — |
| 647 | C4⋊C4 | — | 8 | 2 | no | — |
| 648 | C4⋊C4 | — | 8 | 2 | no | — |
| 649 | C4⋊C4 | C2×#102 | 1 | 2 | yes | — |
| 650 | C4⋊C4 | C2×#102 | 1 | 2 | yes | — |
| 651 | C22⋊C4 | — | 2 | 2 | no | — |
| 652 | C22⋊C4 | — | 2 | 2 | no | — |
| 653 | C22⋊C4 | — | 2 | 2 | no | — |
| 654 | C22⋊C4 | — | 4 | 2 | no | — |
| 655 | C22⋊C4 | — | 4 | 2 | no | — |
| 656 | C22⋊C4 | — | 8 | 2 | no | — |
| 657 | C22⋊C4 | — | 8 | 2 | no | — |
| 658 | C22⋊C4 | — | 8 | 2 | no | — |
| 659 | C22⋊C4 | — | 8 | 2 | no | — |
| 660 | C22⋊C4 | — | 8 | 2 | no | — |
| 661 | C22⋊C4 | — | 8 | 2 | no | — |
| 662 | C42 | — | 2 | 2 | no | — |
| 663 | C42 | — | 2 | 2 | no | — |
| 664 | C42 | — | 2 | 2 | no | — |
| 665 | C42 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 666 | C42 | D42 | 1 | 1 | yes | characteristic |
| 667 | C42 | C22×D8 | 1 | 1 | yes | characteristic |
| 668 | C42 | #577 | 1 | 1 | yes | characteristic |
| 669 | C16 | — | 4 | 2 | no | — |
| 670 | C16 | — | 8 | 2 | no | — |
| 671 | C16 | — | 8 | 1 | no | — |
| 672 | C23 | — | 2 | 2 | no | — |
| 673 | C23 | — | 4 | 2 | no | — |
| 674 | C23 | — | 8 | 2 | no | — |
| 675 | C23 | — | 8 | 2 | no | — |
| 676 | C23 | — | 16 | 1 | no | — |
| 677 | C23 | — | 16 | 1 | no | — |
| 678 | C23 | — | 16 | 4 | no | — |
| 679 | C23 | — | 16 | 4 | no | — |
| 680 | C23 | — | 32 | 2 | no | — |
| 681 | C23 | #3295 | 1 | 1 | yes | characteristic |
| 682 | Q8 | — | 2 | 2 | no | — |
| 683 | Q8 | — | 2 | 2 | no | — |
| 684 | Q8 | — | 8 | 2 | no | — |
| 685 | Q8 | — | 8 | 2 | no | — |
| 686 | Q8 | — | 16 | 4 | no | — |
| 687 | D4 | — | 2 | 2 | no | — |
| 688 | D4 | — | 4 | 4 | no | — |
| 689 | D4 | — | 4 | 2 | no | — |
| 690 | D4 | — | 4 | 2 | no | — |
| 691 | D4 | — | 8 | 2 | no | — |
| 692 | D4 | — | 8 | 2 | no | — |
| 693 | D4 | — | 8 | 2 | no | — |
| 694 | D4 | — | 8 | 2 | no | — |
| 695 | D4 | — | 16 | 1 | no | — |
| 696 | D4 | — | 16 | 2 | no | — |
| 697 | D4 | — | 16 | 4 | no | — |
| 698 | D4 | — | 16 | 4 | no | — |
| 699 | D4 | — | 16 | 4 | no | — |
| 700 | D4 | — | 16 | 4 | no | — |
| 701 | D4 | — | 16 | 4 | no | — |
| 702 | D4 | — | 32 | 2 | no | — |
| 703 | D4 | C2×#361 | 1 | 4 | yes | — |
| 704 | C2×C4 | — | 2 | 1 | no | — |
| 705 | C2×C4 | — | 2 | 1 | no | — |
| 706 | C2×C4 | — | 2 | 1 | no | — |
| 707 | C2×C4 | — | 2 | 1 | no | — |
| 708 | C2×C4 | — | 2 | 2 | no | — |
| 709 | C2×C4 | — | 2 | 2 | no | — |
| 710 | C2×C4 | — | 2 | 2 | no | — |
| 711 | C2×C4 | — | 4 | 1 | no | — |
| 712 | C2×C4 | — | 4 | 4 | no | — |
| 713 | C2×C4 | — | 4 | 2 | no | — |
| 714 | C2×C4 | — | 4 | 2 | no | — |
| 715 | C2×C4 | — | 4 | 2 | no | — |
| 716 | C2×C4 | — | 8 | 2 | no | — |
| 717 | C2×C4 | — | 8 | 4 | no | — |
| 718 | C2×C4 | — | 8 | 2 | no | — |
| 719 | C2×C4 | — | 8 | 2 | no | — |
| 720 | C2×C4 | — | 8 | 2 | no | — |
| 721 | C2×C4 | — | 8 | 2 | no | — |
| 722 | C2×C4 | — | 16 | 4 | no | — |
| 723 | C2×C4 | — | 16 | 4 | no | — |
| 724 | C2×C4 | — | 16 | 4 | no | — |
| 725 | C2×C4 | — | 16 | 4 | no | — |
| 726 | C2×C4 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 727 | C2×C4 | C22×#102 | 1 | 1 | yes | characteristic |
| 728 | C2×C4 | #2897 | 1 | 1 | yes | characteristic |
| 729 | C2×C4 | D4×D8 | 1 | 1 | yes | characteristic |
| 730 | C2×C4 | D4×SD16 | 1 | 1 | yes | characteristic |
| 731 | C2×C4 | #3294 | 1 | 1 | yes | characteristic |
| 732 | C8 | — | 2 | 1 | no | — |
| 733 | C8 | — | 2 | 1 | no | — |
| 734 | C8 | — | 2 | 1 | no | — |
| 735 | C8 | — | 2 | 1 | no | — |
| 736 | C8 | — | 2 | 1 | no | — |
| 737 | C8 | — | 2 | 1 | no | — |
| 738 | C8 | — | 4 | 1 | no | — |
| 739 | C8 | — | 4 | 1 | no | — |
| 740 | C8 | — | 4 | 2 | no | — |
| 741 | C8 | — | 4 | 2 | no | — |
| 742 | C8 | — | 8 | 1 | no | — |
| 743 | C8 | — | 8 | 1 | no | — |
| 744 | C8 | — | 8 | 2 | no | — |
| 745 | C8 | — | 8 | 2 | no | — |
| 746 | C8 | — | 16 | 2 | no | — |
| 747 | C8 | C2×#361 | 1 | 2 | yes | — |
| 748 | C8 | #2955 | 1 | 1 | yes | characteristic |
| 749 | C8 | #2956 | 1 | 1 | yes | characteristic |
| 750 | C22 | — | 2 | 1 | no | — |
| 751 | C22 | — | 2 | 1 | no | — |
| 752 | C22 | — | 2 | 1 | no | — |
| 753 | C22 | — | 2 | 4 | no | — |
| 754 | C22 | — | 4 | 2 | no | — |
| 755 | C22 | — | 4 | 2 | no | — |
| 756 | C22 | — | 8 | 2 | no | — |
| 757 | C22 | — | 8 | 2 | no | — |
| 758 | C22 | — | 8 | 2 | no | — |
| 759 | C22 | — | 16 | 2 | no | — |
| 760 | C22 | — | 16 | 2 | no | — |
| 761 | C22 | — | 16 | 2 | no | — |
| 762 | C22 | — | 32 | 2 | no | — |
| 763 | C22 | — | 32 | 8 | no | — |
| 764 | C22 | D4×#102 | 1 | 1 | yes | characteristic |
| 765 | C4 | — | 2 | 1 | no | — |
| 766 | C4 | — | 2 | 1 | no | — |
| 767 | C4 | — | 2 | 1 | no | — |
| 768 | C4 | — | 2 | 1 | no | — |
| 769 | C4 | — | 4 | 2 | no | — |
| 770 | C4 | — | 4 | 2 | no | — |
| 771 | C4 | — | 4 | 2 | no | — |
| 772 | C4 | — | 8 | 2 | no | — |
| 773 | C4 | — | 16 | 2 | no | — |
| 774 | C4 | #22453 | 1 | 1 | yes | characteristic |
| 775 | C4 | #22461 | 1 | 1 | yes | characteristic |
| 776 | C4 | C22×#361 | 1 | 1 | yes | characteristic |
| 777 | C4 | #33392 | 1 | 1 | yes | characteristic |
| 778 | C2 | — | 4 | 1 | no | — |
| 779 | C2 | — | 4 | 4 | no | — |
| 780 | C2 | — | 16 | 2 | no | — |
| 781 | C2 | — | 32 | 2 | no | — |
| 782 | C2 | #221034 | 1 | 1 | yes | characteristic |
| 783 | C2 | D4×#361 | 1 | 1 | yes | characteristic |
| 784 | C2 | #497409 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×#102 |
| commutator | C4×C8 | C23×C4 |
| Frattini, cosocle | C2×C4×C8 | C24 |
| prime radical | #6358256 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ C8×#135 ◁ 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 |
|---|---|---|
| 2. #483608 | C2 | semidirect |
| 3. #481421 | C2 | semidirect |
| 4. #225782 | C2 | semidirect |
| 5. #141841 | C2 | semidirect |
| 6. #141326 | C2 | semidirect |
| 7. #138561 | C2 | semidirect |
| 8. #137059 | C2 | semidirect |
| 9. #135068 | C2 | semidirect |
| 10. #131816 | C2 | semidirect |
| 11. #128751 | C2 | semidirect |
| 14. #33484 | C22 | semidirect |
| 29. #17834 | C22 | semidirect |
| 34. #12013 | C22 | semidirect |
| 35. #11751 | C22 | semidirect |
| 36. #11680 | C22 | semidirect |
| 37. #11680 | C22 | semidirect |
| 42. #11652 | C22 | semidirect |
| 43. #11615 | C22 | semidirect |
| 46. #11402 | C22 | semidirect |
| 49. #8824 | C22 | semidirect |
| 50. #8670 | C22 | semidirect |
| 51. C8×#108 | C22 | semidirect |
| 52. #7292 | C22 | semidirect |
| 53. #7176 | C22 | semidirect |
| 54. #7159 | C22 | semidirect |
| 607. D8 | #361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6358256 | 2 |
| #483608 | 2 |
| #481421 | 2 |
| #225782 | 2 |
| #141841 | 2 |
| #141326 | 2 |
| #138561 | 2 |
| #137059 | 2 |
| #135068 | 2 |
| #131816 | 2 |
| #128751 | 2 |