Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1630 conjugacy classes of subgroups.
The subgroup lattice has 526 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62531 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #61410 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20004 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #19965 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #19961 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C2×#1706 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #19276 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #19202 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #18654 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #18624 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #17958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C8×#135 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #3509 | C22 | 1 | 2 | yes | — |
| 14 | #3508 | C22 | 1 | 2 | yes | — |
| 15 | #3400 | — | 2 | 2 | no | — |
| 16 | #3400 | C22 | 1 | 4 | yes | complemented |
| 17 | #3397 | — | 2 | 2 | no | — |
| 18 | #3397 | C22 | 1 | 4 | yes | complemented |
| 19 | #3394 | — | 2 | 2 | no | — |
| 20 | #3394 | C22 | 1 | 4 | yes | complemented |
| 21 | #3392 | — | 2 | 2 | no | — |
| 22 | #3392 | C22 | 1 | 4 | yes | complemented |
| 23 | #3365 | C22 | 1 | 8 | yes | complemented |
| 24 | #3304 | C22 | 1 | 8 | yes | complemented |
| 25 | #3296 | — | 2 | 8 | no | — |
| 26 | #3229 | C22 | 1 | 2 | yes | — |
| 27 | #3228 | — | 2 | 2 | no | — |
| 28 | #3210 | — | 2 | 2 | no | — |
| 29 | #3208 | C22 | 1 | 2 | yes | — |
| 30 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3167 | — | 2 | 2 | no | — |
| 32 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3154 | — | 2 | 2 | no | — |
| 34 | C2×#493 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#492 | C22 | 1 | 2 | yes | — |
| 36 | #3131 | — | 2 | 2 | no | — |
| 37 | C2×#486 | C22 | 1 | 2 | yes | — |
| 38 | #3043 | — | 2 | 2 | no | — |
| 39 | #3042 | — | 2 | 2 | no | — |
| 40 | #3039 | C22 | 1 | 2 | yes | — |
| 41 | #3038 | C22 | 1 | 2 | yes | — |
| 42 | C8×#41 | C22 | 1 | 2 | yes | — |
| 43 | #2960 | C22 | 1 | 2 | yes | — |
| 44 | #2949 | — | 2 | 2 | no | — |
| 45 | C4×#135 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1706 | C22 | 1 | 4 | yes | — |
| 47 | #1706 | C22 | 1 | 4 | yes | — |
| 48 | #1686 | C22 | 1 | 8 | yes | complemented |
| 49 | #1682 | C22 | 1 | 8 | yes | complemented |
| 50 | #1681 | C22 | 1 | 8 | yes | complemented |
| 51 | #1666 | C22 | 1 | 8 | yes | complemented |
| 52 | #1650 | C22 | 1 | 8 | yes | complemented |
| 53 | #1648 | C22 | 1 | 8 | yes | complemented |
| 54 | #1621 | C22 | 1 | 8 | yes | — |
| 55 | #1620 | C22 | 1 | 8 | yes | — |
| 56 | #1591 | C22 | 1 | 4 | yes | complemented |
| 57 | C8×Q16 | C22 | 1 | 4 | yes | complemented |
| 58 | C8×Q16 | C22 | 1 | 2 | yes | complemented |
| 59 | C8×SD16 | C22 | 1 | 4 | yes | complemented |
| 60 | C8×D8 | C22 | 1 | 2 | yes | complemented |
| 61 | #1567 | C22 | 1 | 1 | yes | characteristic |
| 62 | #1564 | C22 | 1 | 1 | yes | characteristic |
| 63 | #1546 | C22 | 1 | 2 | yes | — |
| 64 | #1545 | C22 | 1 | 2 | yes | — |
| 65 | #1493 | C22 | 1 | 2 | yes | — |
| 66 | #1476 | C22 | 1 | 2 | yes | — |
| 67 | C2×C82 | C22 | 1 | 1 | yes | characteristic |
| 68 | C2×#137 | — | 2 | 2 | no | — |
| 69 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 70 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 71 | C22×SD16 | — | 2 | 2 | no | — |
| 72 | C22×SD16 | — | 2 | 2 | no | — |
| 73 | C22×D8 | — | 4 | 1 | no | — |
| 74 | #559 | — | 2 | 2 | no | — |
| 75 | #559 | C23 | 1 | 4 | yes | — |
| 76 | #557 | — | 2 | 2 | no | — |
| 77 | #557 | C23 | 1 | 4 | yes | — |
| 78 | #556 | — | 2 | 2 | no | — |
| 79 | #556 | C23 | 1 | 4 | yes | — |
| 80 | #552 | — | 2 | 4 | no | — |
| 81 | #552 | — | 4 | 2 | no | — |
| 82 | #550 | — | 2 | 2 | no | — |
| 83 | #550 | C23 | 1 | 4 | yes | — |
| 84 | #546 | — | 2 | 4 | no | — |
| 85 | #546 | — | 4 | 2 | no | — |
| 86 | #541 | — | 4 | 2 | no | — |
| 87 | #540 | — | 4 | 2 | no | — |
| 88 | #536 | — | 2 | 2 | no | — |
| 89 | #535 | — | 2 | 2 | no | — |
| 90 | #533 | — | 2 | 2 | no | — |
| 91 | #533 | — | 2 | 2 | no | — |
| 92 | #533 | C23 | 1 | 2 | yes | — |
| 93 | #532 | — | 2 | 2 | no | — |
| 94 | #532 | — | 2 | 2 | no | — |
| 95 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 96 | C2×#127 | C23 | 1 | 2 | yes | — |
| 97 | #519 | — | 2 | 2 | no | — |
| 98 | #518 | — | 2 | 2 | no | — |
| 99 | C4×#41 | C23 | 1 | 2 | yes | — |
| 100 | #500 | — | 4 | 1 | no | — |
| 101 | #500 | D4 | 1 | 1 | yes | characteristic |
| 102 | #500 | C23 | 1 | 4 | yes | — |
| 103 | #498 | — | 2 | 2 | no | — |
| 104 | #497 | — | 2 | 4 | no | — |
| 105 | #496 | — | 2 | 4 | no | — |
| 106 | #495 | — | 2 | 4 | no | — |
| 107 | #494 | D4 | 1 | 1 | yes | characteristic |
| 108 | #493 | — | 4 | 1 | no | — |
| 109 | #493 | C23 | 1 | 4 | yes | — |
| 110 | #492 | — | 2 | 4 | no | — |
| 111 | #492 | — | 2 | 2 | no | — |
| 112 | #492 | — | 2 | 2 | no | — |
| 113 | #492 | — | 2 | 2 | no | — |
| 114 | #492 | C23 | 1 | 4 | yes | — |
| 115 | #492 | C23 | 1 | 4 | yes | — |
| 116 | #488 | — | 2 | 8 | no | — |
| 117 | #487 | — | 2 | 2 | no | — |
| 118 | #487 | D4 | 1 | 2 | yes | — |
| 119 | #486 | — | 2 | 2 | no | — |
| 120 | #486 | — | 2 | 2 | no | — |
| 121 | #486 | — | 2 | 2 | no | — |
| 122 | #486 | C23 | 1 | 8 | yes | — |
| 123 | #483 | — | 2 | 4 | no | — |
| 124 | #482 | — | 2 | 8 | no | — |
| 125 | #478 | — | 2 | 8 | no | — |
| 126 | #475 | C23 | 1 | 8 | yes | — |
| 127 | #467 | D4 | 1 | 4 | yes | — |
| 128 | #465 | — | 2 | 8 | no | — |
| 129 | #464 | — | 2 | 8 | no | — |
| 130 | #464 | — | 2 | 4 | no | — |
| 131 | #464 | — | 2 | 4 | no | — |
| 132 | #463 | — | 2 | 4 | no | — |
| 133 | #463 | — | 2 | 4 | no | — |
| 134 | #462 | — | 2 | 2 | no | — |
| 135 | #462 | C23 | 1 | 4 | yes | — |
| 136 | #461 | — | 2 | 2 | no | — |
| 137 | #461 | — | 2 | 4 | no | — |
| 138 | #461 | — | 2 | 4 | no | — |
| 139 | #461 | C23 | 1 | 4 | yes | — |
| 140 | #460 | — | 2 | 2 | no | — |
| 141 | #460 | — | 2 | 4 | no | — |
| 142 | #460 | — | 2 | 4 | no | — |
| 143 | #460 | C23 | 1 | 8 | yes | — |
| 144 | #460 | C23 | 1 | 4 | yes | — |
| 145 | #459 | — | 2 | 2 | no | — |
| 146 | #459 | C23 | 1 | 4 | yes | — |
| 147 | #452 | — | 2 | 8 | no | — |
| 148 | #450 | — | 2 | 4 | no | — |
| 149 | #446 | — | 2 | 2 | no | — |
| 150 | #446 | C23 | 1 | 4 | yes | — |
| 151 | C8×Q8 | — | 2 | 2 | no | — |
| 152 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 153 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 154 | #440 | — | 2 | 4 | no | — |
| 155 | #440 | — | 2 | 4 | no | — |
| 156 | C4×Q16 | D4 | 1 | 1 | yes | characteristic |
| 157 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 158 | C4×Q16 | C23 | 1 | 1 | yes | characteristic |
| 159 | C4×SD16 | — | 2 | 4 | no | — |
| 160 | C4×SD16 | — | 2 | 4 | no | — |
| 161 | C4×SD16 | — | 2 | 8 | no | — |
| 162 | C4×SD16 | D4 | 1 | 2 | yes | — |
| 163 | C4×SD16 | C23 | 1 | 2 | yes | — |
| 164 | C4×D8 | D4 | 1 | 1 | yes | characteristic |
| 165 | C4×D8 | C23 | 1 | 1 | yes | characteristic |
| 166 | C8×D4 | — | 2 | 4 | no | — |
| 167 | C8×D4 | C23 | 1 | 4 | yes | — |
| 168 | #431 | — | 2 | 2 | no | — |
| 169 | #431 | C23 | 1 | 2 | yes | — |
| 170 | #427 | D4 | 1 | 1 | yes | characteristic |
| 171 | C2×#107 | — | 4 | 1 | no | — |
| 172 | #424 | — | 2 | 2 | no | — |
| 173 | #423 | C23 | 1 | 2 | yes | — |
| 174 | #419 | — | 2 | 2 | no | — |
| 175 | #418 | — | 2 | 2 | no | — |
| 176 | #416 | — | 2 | 8 | no | — |
| 177 | #416 | D4 | 1 | 2 | yes | — |
| 178 | C2×#102 | — | 2 | 4 | no | — |
| 179 | #405 | — | 2 | 2 | no | — |
| 180 | C2×C4×C8 | — | 2 | 2 | no | — |
| 181 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 184 | #335 | C23 | 1 | 2 | yes | — |
| 185 | #335 | C23 | 1 | 4 | yes | — |
| 186 | #334 | C23 | 1 | 2 | yes | — |
| 187 | #332 | C23 | 1 | 8 | yes | — |
| 188 | #331 | C23 | 1 | 8 | yes | — |
| 189 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 190 | Q8⋊C8 | C23 | 1 | 8 | yes | — |
| 191 | D4⋊C8 | C23 | 1 | 4 | yes | — |
| 192 | C82 | C23 | 1 | 2 | yes | — |
| 193 | C82 | C23 | 1 | 2 | yes | — |
| 194 | C2×#41 | — | 2 | 4 | no | — |
| 195 | C2×#41 | — | 4 | 2 | no | — |
| 196 | C2×#41 | C2×D4 | 1 | 2 | yes | — |
| 197 | C22×Q8 | — | 2 | 2 | no | — |
| 198 | C22×D4 | — | 2 | 2 | no | — |
| 199 | C22×D4 | — | 2 | 2 | no | — |
| 200 | C22×D4 | — | 2 | 2 | no | — |
| 201 | #137 | — | 8 | 4 | no | — |
| 202 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 203 | #135 | — | 2 | 4 | no | — |
| 204 | C2×Q16 | — | 2 | 4 | no | — |
| 205 | C2×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 207 | C2×SD16 | — | 2 | 4 | no | — |
| 208 | C2×SD16 | — | 2 | 8 | no | — |
| 209 | C2×SD16 | — | 2 | 4 | no | — |
| 210 | C2×SD16 | — | 2 | 4 | no | — |
| 211 | C2×SD16 | — | 2 | 4 | no | — |
| 212 | C2×SD16 | — | 2 | 4 | no | — |
| 213 | C2×SD16 | — | 2 | 4 | no | — |
| 214 | C2×SD16 | — | 4 | 8 | no | — |
| 215 | C2×SD16 | — | 8 | 4 | no | — |
| 216 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 217 | C2×D8 | — | 2 | 4 | no | — |
| 218 | C2×D8 | — | 4 | 4 | no | — |
| 219 | C2×D8 | — | 8 | 4 | no | — |
| 220 | C2×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×M16 | — | 2 | 2 | no | — |
| 222 | C22×C8 | — | 2 | 1 | no | — |
| 223 | C22×C8 | — | 2 | 4 | no | — |
| 224 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 225 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 226 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 227 | C4⋊Q8 | — | 2 | 4 | no | — |
| 228 | C4⋊Q8 | — | 2 | 2 | no | — |
| 229 | C4⋊Q8 | — | 2 | 2 | no | — |
| 230 | C4⋊Q8 | — | 2 | 2 | no | — |
| 231 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 232 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 233 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 234 | #127 | — | 2 | 4 | no | — |
| 235 | #127 | — | 2 | 2 | no | — |
| 236 | #127 | — | 2 | 2 | no | — |
| 237 | #127 | — | 2 | 2 | no | — |
| 238 | #127 | C24 | 1 | 4 | yes | — |
| 239 | #126 | — | 4 | 4 | no | — |
| 240 | #126 | — | 4 | 4 | no | — |
| 241 | #125 | — | 2 | 4 | no | — |
| 242 | #125 | — | 2 | 2 | no | — |
| 243 | #125 | — | 4 | 2 | no | — |
| 244 | #125 | — | 4 | 4 | no | — |
| 245 | #125 | — | 4 | 4 | no | — |
| 246 | #124 | — | 2 | 4 | no | — |
| 247 | #124 | — | 2 | 4 | no | — |
| 248 | #124 | — | 2 | 4 | no | — |
| 249 | #124 | — | 4 | 2 | no | — |
| 250 | #123 | — | 4 | 4 | no | — |
| 251 | #123 | — | 4 | 4 | no | — |
| 252 | #123 | — | 4 | 4 | no | — |
| 253 | C22⋊Q8 | — | 2 | 2 | no | — |
| 254 | C22⋊Q8 | — | 2 | 4 | no | — |
| 255 | C22⋊Q8 | — | 4 | 2 | no | — |
| 256 | C22⋊Q8 | — | 4 | 2 | no | — |
| 257 | C22⋊Q8 | — | 4 | 2 | no | — |
| 258 | C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 259 | #121 | — | 2 | 4 | no | — |
| 260 | #121 | — | 4 | 4 | no | — |
| 261 | #121 | — | 4 | 4 | no | — |
| 262 | #121 | — | 4 | 2 | no | — |
| 263 | #121 | — | 4 | 2 | no | — |
| 264 | #121 | — | 4 | 2 | no | — |
| 265 | #120 | — | 4 | 4 | no | — |
| 266 | C4×Q8 | — | 2 | 2 | no | — |
| 267 | C4×Q8 | — | 2 | 4 | no | — |
| 268 | C4×Q8 | — | 2 | 4 | no | — |
| 269 | C4×Q8 | — | 2 | 4 | no | — |
| 270 | C4×Q8 | — | 4 | 2 | no | — |
| 271 | C4×Q8 | — | 4 | 2 | no | — |
| 272 | C4×Q8 | — | 4 | 2 | no | — |
| 273 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 274 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 275 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 276 | C4×D4 | — | 2 | 2 | no | — |
| 277 | C4×D4 | — | 2 | 2 | no | — |
| 278 | C4×D4 | — | 2 | 4 | no | — |
| 279 | C4×D4 | — | 2 | 4 | no | — |
| 280 | C4×D4 | — | 2 | 4 | no | — |
| 281 | C4×D4 | — | 4 | 2 | no | — |
| 282 | C4×D4 | — | 4 | 2 | no | — |
| 283 | C4×D4 | — | 4 | 2 | no | — |
| 284 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 285 | C4×D4 | C24 | 1 | 2 | yes | — |
| 286 | #117 | — | 2 | 2 | no | — |
| 287 | #117 | — | 2 | 2 | no | — |
| 288 | #117 | — | 2 | 4 | no | — |
| 289 | #117 | — | 4 | 4 | no | — |
| 290 | #117 | — | 4 | 2 | no | — |
| 291 | #117 | C2×D4 | 1 | 2 | yes | — |
| 292 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 293 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 294 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 295 | C2×C42 | — | 2 | 2 | no | — |
| 296 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 297 | #107 | — | 4 | 4 | no | — |
| 298 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 299 | #107 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | #107 | C2×D4 | 1 | 4 | yes | — |
| 301 | #106 | — | 2 | 8 | no | — |
| 302 | #106 | C2×D4 | 1 | 2 | yes | — |
| 303 | C4⋊C8 | — | 2 | 4 | no | — |
| 304 | C4⋊C8 | — | 2 | 4 | no | — |
| 305 | C4⋊C8 | — | 2 | 4 | no | — |
| 306 | C4⋊C8 | — | 2 | 2 | no | — |
| 307 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 308 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 309 | #103 | — | 2 | 8 | no | — |
| 310 | #103 | — | 2 | 4 | no | — |
| 311 | #103 | — | 2 | 4 | no | — |
| 312 | #103 | C2×D4 | 1 | 8 | yes | — |
| 313 | #103 | C2×D4 | 1 | 2 | yes | — |
| 314 | #103 | C2×D4 | 1 | 2 | yes | — |
| 315 | #102 | — | 2 | 8 | no | — |
| 316 | #102 | — | 2 | 8 | no | — |
| 317 | #102 | — | 2 | 8 | no | — |
| 318 | #102 | — | 2 | 4 | no | — |
| 319 | #102 | — | 2 | 4 | no | — |
| 320 | #102 | C2×D4 | 1 | 2 | yes | — |
| 321 | #102 | C2×D4 | 1 | 2 | yes | — |
| 322 | C22⋊C8 | — | 2 | 2 | no | — |
| 323 | C22⋊C8 | — | 2 | 4 | no | — |
| 324 | #97 | — | 2 | 4 | no | — |
| 325 | C4×C8 | — | 2 | 4 | no | — |
| 326 | C4×C8 | — | 2 | 4 | no | — |
| 327 | C4×C8 | — | 2 | 2 | no | — |
| 328 | C4×C8 | — | 2 | 1 | no | — |
| 329 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 330 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 333 | C4×C8 | C24 | 1 | 2 | yes | — |
| 334 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 335 | C4×C8 | C24 | 1 | 2 | yes | — |
| 336 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 337 | C24 | — | 4 | 2 | no | — |
| 338 | #41 | — | 2 | 4 | no | — |
| 339 | #41 | — | 2 | 4 | no | — |
| 340 | #41 | — | 8 | 8 | no | — |
| 341 | #41 | — | 16 | 4 | no | — |
| 342 | C2×Q8 | — | 2 | 2 | no | — |
| 343 | C2×Q8 | — | 2 | 4 | no | — |
| 344 | C2×Q8 | — | 4 | 2 | no | — |
| 345 | C2×Q8 | — | 4 | 4 | no | — |
| 346 | C2×Q8 | — | 4 | 4 | no | — |
| 347 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 348 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 349 | C2×D4 | — | 2 | 2 | no | — |
| 350 | C2×D4 | — | 2 | 4 | no | — |
| 351 | C2×D4 | — | 2 | 4 | no | — |
| 352 | C2×D4 | — | 2 | 4 | no | — |
| 353 | C2×D4 | — | 4 | 4 | no | — |
| 354 | C2×D4 | — | 4 | 4 | no | — |
| 355 | C2×D4 | — | 4 | 2 | no | — |
| 356 | C2×D4 | — | 4 | 2 | no | — |
| 357 | C2×D4 | — | 4 | 2 | no | — |
| 358 | C2×D4 | — | 4 | 4 | no | — |
| 359 | C2×D4 | — | 4 | 4 | no | — |
| 360 | C2×D4 | — | 8 | 4 | no | — |
| 361 | C2×D4 | — | 8 | 4 | no | — |
| 362 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 363 | C22×C4 | — | 2 | 2 | no | — |
| 364 | C22×C4 | — | 2 | 2 | no | — |
| 365 | C22×C4 | — | 2 | 2 | no | — |
| 366 | C22×C4 | — | 4 | 4 | no | — |
| 367 | C22×C4 | — | 4 | 4 | no | — |
| 368 | C22×C4 | — | 4 | 2 | no | — |
| 369 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 370 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 371 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 372 | Q16 | — | 2 | 2 | no | — |
| 373 | Q16 | — | 4 | 4 | no | — |
| 374 | Q16 | — | 8 | 4 | no | — |
| 375 | SD16 | — | 2 | 4 | no | — |
| 376 | SD16 | — | 4 | 8 | no | — |
| 377 | SD16 | — | 4 | 8 | no | — |
| 378 | SD16 | — | 8 | 4 | no | — |
| 379 | SD16 | — | 8 | 4 | no | — |
| 380 | SD16 | — | 8 | 4 | no | — |
| 381 | SD16 | — | 8 | 8 | no | — |
| 382 | SD16 | — | 8 | 4 | no | — |
| 383 | D8 | — | 2 | 2 | no | — |
| 384 | D8 | — | 8 | 8 | no | — |
| 385 | D8 | — | 8 | 4 | no | — |
| 386 | M16 | — | 4 | 4 | no | — |
| 387 | C2×C8 | — | 2 | 4 | no | — |
| 388 | C2×C8 | — | 2 | 2 | no | — |
| 389 | C2×C8 | — | 2 | 2 | no | — |
| 390 | C2×C8 | — | 2 | 4 | no | — |
| 391 | C2×C8 | — | 2 | 4 | no | — |
| 392 | C2×C8 | — | 4 | 2 | no | — |
| 393 | C2×C8 | — | 8 | 4 | no | — |
| 394 | C2×C8 | #135 | 1 | 4 | yes | — |
| 395 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 396 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 397 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 398 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 400 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 401 | C4⋊C4 | — | 2 | 2 | no | — |
| 402 | C4⋊C4 | — | 2 | 2 | no | — |
| 403 | C4⋊C4 | — | 2 | 2 | no | — |
| 404 | C4⋊C4 | — | 2 | 2 | no | — |
| 405 | C4⋊C4 | — | 2 | 4 | no | — |
| 406 | C4⋊C4 | — | 2 | 2 | no | — |
| 407 | C4⋊C4 | — | 2 | 4 | no | — |
| 408 | C4⋊C4 | — | 2 | 4 | no | — |
| 409 | C4⋊C4 | — | 2 | 4 | no | — |
| 410 | C4⋊C4 | — | 4 | 4 | no | — |
| 411 | C4⋊C4 | — | 4 | 4 | no | — |
| 412 | C4⋊C4 | — | 4 | 4 | no | — |
| 413 | C4⋊C4 | — | 4 | 4 | no | — |
| 414 | C4⋊C4 | — | 4 | 2 | no | — |
| 415 | C4⋊C4 | — | 4 | 2 | no | — |
| 416 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 417 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 418 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 419 | C22⋊C4 | — | 2 | 2 | no | — |
| 420 | C22⋊C4 | — | 2 | 4 | no | — |
| 421 | C22⋊C4 | — | 2 | 2 | no | — |
| 422 | C22⋊C4 | — | 2 | 2 | no | — |
| 423 | C22⋊C4 | — | 4 | 4 | no | — |
| 424 | C22⋊C4 | — | 4 | 4 | no | — |
| 425 | C22⋊C4 | — | 4 | 4 | no | — |
| 426 | C22⋊C4 | — | 4 | 4 | no | — |
| 427 | C22⋊C4 | — | 4 | 4 | no | — |
| 428 | C22⋊C4 | — | 4 | 4 | no | — |
| 429 | C42 | — | 2 | 2 | no | — |
| 430 | C42 | — | 2 | 2 | no | — |
| 431 | C42 | — | 2 | 2 | no | — |
| 432 | C42 | — | 2 | 4 | no | — |
| 433 | C42 | — | 4 | 4 | no | — |
| 434 | C42 | — | 4 | 4 | no | — |
| 435 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 436 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 437 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 438 | C42 | C25 | 1 | 1 | yes | characteristic |
| 439 | C23 | — | 2 | 2 | no | — |
| 440 | C23 | — | 4 | 4 | no | — |
| 441 | C23 | — | 8 | 4 | no | — |
| 442 | C23 | — | 16 | 2 | no | — |
| 443 | C23 | — | 16 | 2 | no | — |
| 444 | C23 | D42 | 1 | 1 | yes | characteristic |
| 445 | Q8 | — | 2 | 8 | no | — |
| 446 | Q8 | — | 2 | 2 | no | — |
| 447 | Q8 | — | 2 | 2 | no | — |
| 448 | Q8 | — | 4 | 4 | no | — |
| 449 | Q8 | — | 4 | 4 | no | — |
| 450 | Q8 | — | 4 | 4 | no | — |
| 451 | Q8 | — | 8 | 4 | no | — |
| 452 | D4 | — | 2 | 2 | no | — |
| 453 | D4 | — | 2 | 2 | no | — |
| 454 | D4 | — | 4 | 4 | no | — |
| 455 | D4 | — | 4 | 8 | no | — |
| 456 | D4 | — | 4 | 4 | no | — |
| 457 | D4 | — | 4 | 4 | no | — |
| 458 | D4 | — | 8 | 4 | no | — |
| 459 | D4 | — | 8 | 4 | no | — |
| 460 | D4 | — | 8 | 4 | no | — |
| 461 | D4 | — | 16 | 2 | no | — |
| 462 | D4 | — | 16 | 4 | no | — |
| 463 | D4 | — | 16 | 4 | no | — |
| 464 | C2×C4 | — | 2 | 2 | no | — |
| 465 | C2×C4 | — | 2 | 2 | no | — |
| 466 | C2×C4 | — | 2 | 2 | no | — |
| 467 | C2×C4 | — | 2 | 2 | no | — |
| 468 | C2×C4 | — | 2 | 2 | no | — |
| 469 | C2×C4 | — | 2 | 4 | no | — |
| 470 | C2×C4 | — | 2 | 4 | no | — |
| 471 | C2×C4 | — | 4 | 4 | no | — |
| 472 | C2×C4 | — | 4 | 4 | no | — |
| 473 | C2×C4 | — | 4 | 4 | no | — |
| 474 | C2×C4 | — | 4 | 4 | no | — |
| 475 | C2×C4 | — | 8 | 4 | no | — |
| 476 | C2×C4 | — | 16 | 4 | no | — |
| 477 | C2×C4 | — | 16 | 4 | no | — |
| 478 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 479 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 480 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 481 | C2×C4 | C2×#135 | 1 | 2 | yes | — |
| 482 | C2×C4 | #576 | 1 | 2 | yes | — |
| 483 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 484 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 485 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 486 | C8 | — | 2 | 4 | no | — |
| 487 | C8 | — | 2 | 2 | no | — |
| 488 | C8 | — | 2 | 2 | no | — |
| 489 | C8 | — | 2 | 1 | no | — |
| 490 | C8 | — | 2 | 1 | no | — |
| 491 | C8 | — | 4 | 4 | no | — |
| 492 | C8 | — | 4 | 4 | no | — |
| 493 | C8 | C2×#135 | 1 | 2 | yes | — |
| 494 | C8 | C2×#135 | 1 | 2 | yes | — |
| 495 | C22 | — | 2 | 1 | no | — |
| 496 | C22 | — | 2 | 1 | no | — |
| 497 | C22 | — | 4 | 2 | no | — |
| 498 | C22 | — | 4 | 2 | no | — |
| 499 | C22 | — | 4 | 2 | no | — |
| 500 | C22 | — | 8 | 4 | no | — |
| 501 | C22 | — | 8 | 4 | no | — |
| 502 | C22 | — | 8 | 4 | no | — |
| 503 | C22 | — | 32 | 4 | no | — |
| 504 | C22 | #3287 | 1 | 2 | yes | — |
| 505 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 506 | C4 | — | 2 | 1 | no | — |
| 507 | C4 | — | 2 | 1 | no | — |
| 508 | C4 | — | 4 | 2 | no | — |
| 509 | C4 | — | 4 | 2 | no | — |
| 510 | C4 | — | 4 | 4 | no | — |
| 511 | C4 | — | 4 | 2 | no | — |
| 512 | C4 | — | 4 | 4 | no | — |
| 513 | C4 | — | 8 | 4 | no | — |
| 514 | C4 | #3287 | 1 | 2 | yes | — |
| 515 | C4 | #3291 | 1 | 2 | yes | — |
| 516 | C4 | C22×#135 | 1 | 1 | yes | characteristic |
| 517 | C4 | C2×#576 | 1 | 1 | yes | characteristic |
| 518 | C4 | #3584 | 1 | 2 | yes | — |
| 519 | C2 | — | 2 | 2 | no | — |
| 520 | C2 | — | 8 | 2 | no | — |
| 521 | C2 | — | 16 | 4 | no | — |
| 522 | C2 | C2×#3287 | 1 | 1 | yes | characteristic |
| 523 | C2 | #61088 | 1 | 1 | yes | characteristic |
| 524 | C2 | C2×#3291 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #62531 | C2 | semidirect |
| 2. #61410 | C2 | semidirect |
| 3. #20004 | C2 | semidirect |
| 4. #19965 | C2 | semidirect |
| 5. #19961 | C2 | semidirect |
| 6. C2×#1706 | C2 | semidirect |
| 7. #19276 | C2 | semidirect |
| 8. #19202 | C2 | semidirect |
| 9. #18654 | C2 | semidirect |
| 10. #18624 | C2 | semidirect |
| 11. #17958 | C2 | semidirect |
| 12. C8×#135 | C2 | semidirect |
| 16. #3400 | C22 | semidirect |
| 18. #3397 | C22 | semidirect |
| 20. #3394 | C22 | semidirect |
| 22. #3392 | C22 | semidirect |
| 23. #3365 | C22 | semidirect |
| 24. #3304 | C22 | semidirect |
| 48. #1686 | C22 | semidirect |
| 49. #1682 | C22 | semidirect |
| 50. #1681 | C22 | semidirect |
| 51. #1666 | C22 | semidirect |
| 52. #1650 | C22 | semidirect |
| 53. #1648 | C22 | semidirect |
| 56. #1591 | C22 | semidirect |
| 57. C8×Q16 | C22 | semidirect |
| 58. C8×Q16 | C22 | semidirect |
| 59. C8×SD16 | C22 | semidirect |
| 60. C8×D8 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62531 | 2 |
| #61410 | 2 |
| #20004 | 2 |
| #19965 | 2 |
| #19961 | 2 |
| C2×#1706 | 2 |
| #19276 | 2 |
| #19202 | 2 |
| #18654 | 2 |
| #18624 | 2 |
| #17958 | 2 |
| C8×#135 | 2 |