Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
488 conjugacy classes of subgroups.
The subgroup lattice has 464 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #19534 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #19533 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #18863 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #18863 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #10664 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10648 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #10646 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10529 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #10529 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10031 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #9528 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #9528 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #9286 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #9286 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #8460 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #3502 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3255 | C22 | 1 | 1 | yes | characteristic |
| 18 | #3255 | C22 | 1 | 1 | yes | characteristic |
| 19 | #3249 | C22 | 1 | 1 | yes | characteristic |
| 20 | #3231 | C22 | 1 | 1 | yes | characteristic |
| 21 | #3231 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3113 | C22 | 1 | 1 | yes | characteristic |
| 23 | #3113 | C22 | 1 | 1 | yes | characteristic |
| 24 | #2985 | C22 | 1 | 1 | yes | characteristic |
| 25 | #2985 | C22 | 1 | 1 | yes | characteristic |
| 26 | #1985 | C22 | 1 | 1 | yes | characteristic |
| 27 | #1838 | C22 | 1 | 1 | yes | characteristic |
| 28 | #1704 | — | 2 | 1 | no | — |
| 29 | #1700 | — | 2 | 1 | no | — |
| 30 | #1694 | — | 2 | 1 | no | — |
| 31 | #1692 | — | 2 | 1 | no | — |
| 32 | #1684 | — | 2 | 1 | no | — |
| 33 | #1680 | — | 2 | 1 | no | — |
| 34 | #1674 | — | 2 | 1 | no | — |
| 35 | #1672 | — | 2 | 1 | no | — |
| 36 | #1653 | — | 2 | 1 | no | — |
| 37 | #1653 | — | 2 | 1 | no | — |
| 38 | #1648 | — | 2 | 1 | no | — |
| 39 | #1648 | — | 2 | 1 | no | — |
| 40 | #1645 | — | 2 | 1 | no | — |
| 41 | #1645 | — | 2 | 1 | no | — |
| 42 | #1645 | — | 2 | 1 | no | — |
| 43 | #1645 | — | 2 | 1 | no | — |
| 44 | #1571 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1570 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1559 | C22 | 1 | 1 | yes | characteristic |
| 47 | #1559 | C22 | 1 | 1 | yes | characteristic |
| 48 | #1559 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1559 | C22 | 1 | 1 | yes | characteristic |
| 50 | #1552 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1552 | C22 | 1 | 1 | yes | characteristic |
| 52 | #1531 | C22 | 1 | 1 | yes | characteristic |
| 53 | #1531 | C22 | 1 | 1 | yes | characteristic |
| 54 | #1531 | C22 | 1 | 1 | yes | characteristic |
| 55 | #1531 | C22 | 1 | 1 | yes | characteristic |
| 56 | #1497 | C22 | 1 | 1 | yes | characteristic |
| 57 | #1497 | C22 | 1 | 1 | yes | characteristic |
| 58 | #1487 | C22 | 1 | 1 | yes | characteristic |
| 59 | #1487 | C22 | 1 | 1 | yes | characteristic |
| 60 | #1467 | C22 | 1 | 1 | yes | characteristic |
| 61 | #1307 | C22 | 1 | 1 | yes | characteristic |
| 62 | #1307 | C22 | 1 | 1 | yes | characteristic |
| 63 | #1290 | C22 | 1 | 1 | yes | characteristic |
| 64 | #1287 | C22 | 1 | 1 | yes | characteristic |
| 65 | #1287 | C22 | 1 | 1 | yes | characteristic |
| 66 | #1275 | C22 | 1 | 1 | yes | characteristic |
| 67 | Q82 | — | 2 | 1 | no | — |
| 68 | Q82 | — | 2 | 1 | no | — |
| 69 | #557 | — | 2 | 1 | no | — |
| 70 | #557 | — | 2 | 1 | no | — |
| 71 | #557 | — | 4 | 1 | no | — |
| 72 | #557 | — | 4 | 1 | no | — |
| 73 | #544 | — | 2 | 1 | no | — |
| 74 | #544 | — | 4 | 1 | no | — |
| 75 | #533 | — | 4 | 1 | no | — |
| 76 | #533 | C23 | 1 | 1 | yes | characteristic |
| 77 | #533 | C23 | 1 | 1 | yes | characteristic |
| 78 | #533 | C23 | 1 | 1 | yes | characteristic |
| 79 | #533 | C23 | 1 | 1 | yes | characteristic |
| 80 | #519 | — | 2 | 1 | no | — |
| 81 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 82 | #500 | D4 | 1 | 1 | yes | characteristic |
| 83 | #500 | D4 | 1 | 1 | yes | characteristic |
| 84 | #498 | D4 | 1 | 1 | yes | characteristic |
| 85 | #498 | D4 | 1 | 1 | yes | characteristic |
| 86 | #487 | D4 | 1 | 1 | yes | characteristic |
| 87 | #487 | D4 | 1 | 1 | yes | characteristic |
| 88 | #487 | D4 | 1 | 1 | yes | characteristic |
| 89 | #487 | D4 | 1 | 1 | yes | characteristic |
| 90 | #485 | — | 4 | 1 | no | — |
| 91 | #485 | — | 4 | 1 | no | — |
| 92 | #483 | — | 2 | 1 | no | — |
| 93 | #483 | — | 2 | 1 | no | — |
| 94 | #479 | — | 4 | 1 | no | — |
| 95 | #479 | — | 4 | 1 | no | — |
| 96 | #477 | — | 2 | 1 | no | — |
| 97 | #477 | — | 2 | 1 | no | — |
| 98 | #475 | — | 2 | 1 | no | — |
| 99 | #475 | — | 2 | 1 | no | — |
| 100 | #475 | — | 2 | 1 | no | — |
| 101 | #475 | — | 2 | 1 | no | — |
| 102 | #475 | — | 2 | 1 | no | — |
| 103 | #475 | — | 2 | 1 | no | — |
| 104 | #470 | — | 4 | 1 | no | — |
| 105 | #470 | — | 4 | 1 | no | — |
| 106 | #467 | — | 4 | 1 | no | — |
| 107 | #462 | — | 2 | 1 | no | — |
| 108 | #462 | — | 2 | 1 | no | — |
| 109 | #462 | — | 2 | 1 | no | — |
| 110 | #462 | — | 2 | 1 | no | — |
| 111 | #462 | — | 2 | 1 | no | — |
| 112 | #462 | — | 2 | 1 | no | — |
| 113 | #462 | — | 2 | 1 | no | — |
| 114 | #462 | — | 2 | 1 | no | — |
| 115 | #451 | — | 2 | 1 | no | — |
| 116 | #451 | — | 2 | 1 | no | — |
| 117 | #446 | — | 2 | 1 | no | — |
| 118 | #446 | — | 2 | 1 | no | — |
| 119 | #446 | — | 4 | 1 | no | — |
| 120 | #446 | — | 4 | 1 | no | — |
| 121 | C8×Q8 | — | 2 | 1 | no | — |
| 122 | C8×Q8 | — | 2 | 1 | no | — |
| 123 | #441 | — | 4 | 1 | no | — |
| 124 | #441 | — | 4 | 1 | no | — |
| 125 | #433 | — | 4 | 1 | no | — |
| 126 | #433 | — | 4 | 1 | no | — |
| 127 | #432 | C23 | 1 | 1 | yes | characteristic |
| 128 | #432 | C23 | 1 | 1 | yes | characteristic |
| 129 | #432 | C23 | 1 | 1 | yes | characteristic |
| 130 | #432 | C23 | 1 | 1 | yes | characteristic |
| 131 | #431 | C23 | 1 | 1 | yes | characteristic |
| 132 | #431 | C23 | 1 | 1 | yes | characteristic |
| 133 | #423 | C23 | 1 | 1 | yes | characteristic |
| 134 | #423 | C23 | 1 | 1 | yes | characteristic |
| 135 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 136 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 137 | #341 | — | 4 | 1 | no | — |
| 138 | #336 | — | 4 | 1 | no | — |
| 139 | #335 | — | 2 | 1 | no | — |
| 140 | #335 | — | 2 | 1 | no | — |
| 141 | #334 | — | 2 | 1 | no | — |
| 142 | #334 | — | 2 | 1 | no | — |
| 143 | #333 | — | 2 | 1 | no | — |
| 144 | #333 | — | 2 | 1 | no | — |
| 145 | #333 | — | 2 | 1 | no | — |
| 146 | #333 | — | 2 | 1 | no | — |
| 147 | #332 | — | 2 | 1 | no | — |
| 148 | #332 | — | 2 | 1 | no | — |
| 149 | #332 | — | 2 | 1 | no | — |
| 150 | #332 | — | 2 | 1 | no | — |
| 151 | #332 | — | 2 | 1 | no | — |
| 152 | #332 | — | 2 | 1 | no | — |
| 153 | #332 | — | 2 | 1 | no | — |
| 154 | #332 | — | 2 | 1 | no | — |
| 155 | #330 | — | 4 | 1 | no | — |
| 156 | #330 | — | 4 | 1 | no | — |
| 157 | #330 | — | 4 | 1 | no | — |
| 158 | #330 | — | 4 | 1 | no | — |
| 159 | Q8⋊C8 | — | 2 | 1 | no | — |
| 160 | Q8⋊C8 | — | 2 | 1 | no | — |
| 161 | Q8⋊C8 | — | 2 | 1 | no | — |
| 162 | Q8⋊C8 | — | 2 | 1 | no | — |
| 163 | Q8⋊C8 | — | 2 | 1 | no | — |
| 164 | Q8⋊C8 | — | 2 | 1 | no | — |
| 165 | Q8⋊C8 | — | 2 | 1 | no | — |
| 166 | Q8⋊C8 | — | 2 | 1 | no | — |
| 167 | #324 | — | 4 | 1 | no | — |
| 168 | C22×Q8 | #41 | 1 | 1 | yes | characteristic |
| 169 | C2×Q16 | — | 4 | 1 | no | — |
| 170 | C2×Q16 | — | 4 | 1 | no | — |
| 171 | C2×Q16 | — | 4 | 1 | no | — |
| 172 | C2×Q16 | — | 4 | 1 | no | — |
| 173 | C2×Q16 | — | 4 | 1 | no | — |
| 174 | C2×M16 | — | 2 | 1 | no | — |
| 175 | C2×M16 | — | 2 | 1 | no | — |
| 176 | C22×C8 | — | 2 | 1 | no | — |
| 177 | C22×C8 | — | 2 | 1 | no | — |
| 178 | C4⋊Q8 | — | 4 | 1 | no | — |
| 179 | C4⋊Q8 | — | 4 | 1 | no | — |
| 180 | C4⋊Q8 | — | 4 | 1 | no | — |
| 181 | C4⋊Q8 | — | 4 | 1 | no | — |
| 182 | C4⋊Q8 | — | 4 | 2 | no | — |
| 183 | C4⋊Q8 | — | 4 | 2 | no | — |
| 184 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | #125 | — | 2 | 1 | no | — |
| 193 | #125 | — | 2 | 1 | no | — |
| 194 | #125 | — | 2 | 1 | no | — |
| 195 | #125 | — | 2 | 1 | no | — |
| 196 | #125 | — | 4 | 1 | no | — |
| 197 | #125 | — | 4 | 1 | no | — |
| 198 | #125 | — | 4 | 2 | no | — |
| 199 | #125 | — | 4 | 2 | no | — |
| 200 | #125 | — | 4 | 2 | no | — |
| 201 | C22⋊Q8 | — | 2 | 1 | no | — |
| 202 | C22⋊Q8 | — | 2 | 1 | no | — |
| 203 | C22⋊Q8 | — | 2 | 1 | no | — |
| 204 | C22⋊Q8 | — | 2 | 1 | no | — |
| 205 | C22⋊Q8 | — | 2 | 1 | no | — |
| 206 | C22⋊Q8 | — | 2 | 1 | no | — |
| 207 | C22⋊Q8 | — | 2 | 1 | no | — |
| 208 | C22⋊Q8 | — | 2 | 1 | no | — |
| 209 | C22⋊Q8 | — | 4 | 2 | no | — |
| 210 | C4×Q8 | — | 2 | 1 | no | — |
| 211 | C4×Q8 | — | 2 | 1 | no | — |
| 212 | C4×Q8 | — | 2 | 1 | no | — |
| 213 | C4×Q8 | — | 2 | 1 | no | — |
| 214 | C4×Q8 | — | 2 | 1 | no | — |
| 215 | C4×Q8 | — | 2 | 1 | no | — |
| 216 | C4×Q8 | — | 2 | 1 | no | — |
| 217 | C4×Q8 | — | 2 | 1 | no | — |
| 218 | C4×Q8 | — | 2 | 1 | no | — |
| 219 | C4×Q8 | — | 2 | 1 | no | — |
| 220 | C4×Q8 | — | 2 | 1 | no | — |
| 221 | C4×Q8 | — | 2 | 1 | no | — |
| 222 | C4×Q8 | — | 4 | 1 | no | — |
| 223 | C4×Q8 | — | 4 | 1 | no | — |
| 224 | C4×Q8 | — | 4 | 1 | no | — |
| 225 | C4×Q8 | — | 4 | 1 | no | — |
| 226 | C4×Q8 | — | 4 | 1 | no | — |
| 227 | C4×Q8 | — | 4 | 1 | no | — |
| 228 | C4×Q8 | — | 4 | 2 | no | — |
| 229 | #117 | — | 2 | 1 | no | — |
| 230 | #117 | — | 2 | 1 | no | — |
| 231 | #117 | — | 2 | 1 | no | — |
| 232 | #117 | — | 2 | 1 | no | — |
| 233 | #117 | — | 4 | 2 | no | — |
| 234 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C2×C4⋊C4 | #41 | 1 | 1 | yes | characteristic |
| 236 | C2×C42 | — | 2 | 1 | no | — |
| 237 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 238 | #107 | — | 4 | 1 | no | — |
| 239 | #107 | — | 4 | 1 | no | — |
| 240 | #107 | — | 4 | 1 | no | — |
| 241 | #106 | — | 4 | 1 | no | — |
| 242 | #106 | — | 4 | 1 | no | — |
| 243 | #106 | — | 4 | 1 | no | — |
| 244 | #106 | — | 4 | 1 | no | — |
| 245 | #106 | — | 4 | 1 | no | — |
| 246 | #106 | — | 4 | 1 | no | — |
| 247 | C4⋊C8 | — | 2 | 1 | no | — |
| 248 | C4⋊C8 | — | 2 | 1 | no | — |
| 249 | C4⋊C8 | — | 2 | 1 | no | — |
| 250 | C4⋊C8 | — | 2 | 1 | no | — |
| 251 | C4⋊C8 | — | 2 | 1 | no | — |
| 252 | C4⋊C8 | — | 2 | 1 | no | — |
| 253 | C4⋊C8 | — | 2 | 1 | no | — |
| 254 | C4⋊C8 | — | 2 | 1 | no | — |
| 255 | C4⋊C8 | — | 2 | 1 | no | — |
| 256 | C4⋊C8 | — | 2 | 1 | no | — |
| 257 | C4⋊C8 | — | 2 | 1 | no | — |
| 258 | C4⋊C8 | — | 2 | 1 | no | — |
| 259 | C4⋊C8 | — | 4 | 1 | no | — |
| 260 | C4⋊C8 | — | 4 | 1 | no | — |
| 261 | C4⋊C8 | — | 4 | 1 | no | — |
| 262 | C4⋊C8 | — | 4 | 1 | no | — |
| 263 | #103 | — | 4 | 1 | no | — |
| 264 | #103 | — | 4 | 1 | no | — |
| 265 | #103 | — | 4 | 1 | no | — |
| 266 | #103 | — | 4 | 1 | no | — |
| 267 | #103 | — | 4 | 1 | no | — |
| 268 | #103 | — | 4 | 1 | no | — |
| 269 | #103 | — | 4 | 1 | no | — |
| 270 | #103 | — | 4 | 1 | no | — |
| 271 | #103 | — | 4 | 1 | no | — |
| 272 | #103 | — | 4 | 1 | no | — |
| 273 | #103 | — | 4 | 1 | no | — |
| 274 | #103 | — | 4 | 1 | no | — |
| 275 | #103 | — | 4 | 1 | no | — |
| 276 | #103 | — | 4 | 1 | no | — |
| 277 | C22⋊C8 | — | 2 | 1 | no | — |
| 278 | C22⋊C8 | — | 2 | 1 | no | — |
| 279 | C22⋊C8 | — | 2 | 1 | no | — |
| 280 | C22⋊C8 | — | 2 | 1 | no | — |
| 281 | C22⋊C8 | — | 2 | 1 | no | — |
| 282 | C22⋊C8 | — | 2 | 1 | no | — |
| 283 | #97 | — | 2 | 1 | no | — |
| 284 | #97 | — | 2 | 1 | no | — |
| 285 | #97 | — | 2 | 1 | no | — |
| 286 | #97 | — | 2 | 1 | no | — |
| 287 | #97 | — | 2 | 1 | no | — |
| 288 | #97 | — | 2 | 1 | no | — |
| 289 | #97 | — | 4 | 1 | no | — |
| 290 | #97 | — | 4 | 1 | no | — |
| 291 | C4×C8 | — | 4 | 1 | no | — |
| 292 | C4×C8 | — | 4 | 1 | no | — |
| 293 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×Q8 | — | 2 | 1 | no | — |
| 298 | C2×Q8 | — | 2 | 1 | no | — |
| 299 | C2×Q8 | — | 2 | 1 | no | — |
| 300 | C2×Q8 | — | 2 | 1 | no | — |
| 301 | C2×Q8 | — | 2 | 1 | no | — |
| 302 | C2×Q8 | — | 2 | 1 | no | — |
| 303 | C2×Q8 | — | 2 | 1 | no | — |
| 304 | C2×Q8 | — | 2 | 1 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 2 | 1 | no | — |
| 307 | C2×Q8 | — | 4 | 2 | no | — |
| 308 | C2×Q8 | — | 4 | 2 | no | — |
| 309 | C22×C4 | — | 2 | 1 | no | — |
| 310 | C22×C4 | — | 2 | 1 | no | — |
| 311 | C22×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 312 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 313 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 314 | Q16 | — | 8 | 2 | no | — |
| 315 | Q16 | — | 8 | 2 | no | — |
| 316 | Q16 | — | 16 | 1 | no | — |
| 317 | Q16 | — | 16 | 1 | no | — |
| 318 | Q16 | — | 16 | 1 | no | — |
| 319 | M16 | — | 8 | 1 | no | — |
| 320 | M16 | — | 8 | 1 | no | — |
| 321 | C2×C8 | — | 2 | 1 | no | — |
| 322 | C2×C8 | — | 2 | 1 | no | — |
| 323 | C2×C8 | — | 2 | 1 | no | — |
| 324 | C2×C8 | — | 2 | 1 | no | — |
| 325 | C2×C8 | — | 4 | 1 | no | — |
| 326 | C2×C8 | — | 4 | 1 | no | — |
| 327 | C2×C8 | — | 4 | 1 | no | — |
| 328 | C2×C8 | — | 4 | 1 | no | — |
| 329 | C2×C8 | — | 4 | 1 | no | — |
| 330 | C2×C8 | — | 4 | 1 | no | — |
| 331 | C2×C8 | — | 4 | 1 | no | — |
| 332 | C2×C8 | — | 4 | 1 | no | — |
| 333 | C2×C8 | — | 4 | 1 | no | — |
| 334 | C2×C8 | — | 4 | 1 | no | — |
| 335 | C2×C8 | — | 8 | 1 | no | — |
| 336 | C4⋊C4 | — | 2 | 1 | no | — |
| 337 | C4⋊C4 | — | 2 | 1 | no | — |
| 338 | C4⋊C4 | — | 2 | 1 | no | — |
| 339 | C4⋊C4 | — | 2 | 1 | no | — |
| 340 | C4⋊C4 | — | 2 | 1 | no | — |
| 341 | C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C4⋊C4 | — | 2 | 1 | no | — |
| 344 | C4⋊C4 | — | 2 | 1 | no | — |
| 345 | C4⋊C4 | — | 2 | 1 | no | — |
| 346 | C4⋊C4 | — | 2 | 1 | no | — |
| 347 | C4⋊C4 | — | 2 | 1 | no | — |
| 348 | C4⋊C4 | — | 2 | 1 | no | — |
| 349 | C4⋊C4 | — | 2 | 1 | no | — |
| 350 | C4⋊C4 | — | 2 | 1 | no | — |
| 351 | C4⋊C4 | — | 2 | 1 | no | — |
| 352 | C4⋊C4 | — | 2 | 1 | no | — |
| 353 | C4⋊C4 | — | 2 | 1 | no | — |
| 354 | C4⋊C4 | — | 4 | 2 | no | — |
| 355 | C4⋊C4 | — | 4 | 2 | no | — |
| 356 | C4⋊C4 | — | 4 | 2 | no | — |
| 357 | C4⋊C4 | — | 4 | 2 | no | — |
| 358 | C4⋊C4 | — | 4 | 2 | no | — |
| 359 | C4⋊C4 | — | 4 | 1 | no | — |
| 360 | C4⋊C4 | — | 4 | 1 | no | — |
| 361 | C4⋊C4 | — | 4 | 1 | no | — |
| 362 | C4⋊C4 | — | 4 | 1 | no | — |
| 363 | C4⋊C4 | — | 4 | 1 | no | — |
| 364 | C4⋊C4 | — | 4 | 1 | no | — |
| 365 | C4⋊C4 | — | 4 | 1 | no | — |
| 366 | C4⋊C4 | — | 4 | 1 | no | — |
| 367 | C4⋊C4 | — | 4 | 1 | no | — |
| 368 | C4⋊C4 | — | 4 | 1 | no | — |
| 369 | C22⋊C4 | — | 4 | 1 | no | — |
| 370 | C22⋊C4 | — | 4 | 1 | no | — |
| 371 | C22⋊C4 | — | 4 | 1 | no | — |
| 372 | C22⋊C4 | — | 4 | 1 | no | — |
| 373 | C42 | — | 4 | 2 | no | — |
| 374 | C42 | — | 4 | 2 | no | — |
| 375 | C42 | — | 4 | 1 | no | — |
| 376 | C42 | — | 4 | 1 | no | — |
| 377 | C42 | — | 4 | 1 | no | — |
| 378 | C42 | — | 4 | 1 | no | — |
| 379 | C42 | — | 4 | 1 | no | — |
| 380 | C42 | — | 4 | 1 | no | — |
| 381 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 382 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 383 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 384 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 385 | C23 | #538 | 1 | 1 | yes | characteristic |
| 386 | Q8 | — | 2 | 2 | no | — |
| 387 | Q8 | — | 2 | 2 | no | — |
| 388 | Q8 | — | 4 | 1 | no | — |
| 389 | Q8 | — | 4 | 1 | no | — |
| 390 | Q8 | — | 4 | 1 | no | — |
| 391 | Q8 | — | 4 | 1 | no | — |
| 392 | Q8 | — | 4 | 1 | no | — |
| 393 | Q8 | — | 4 | 1 | no | — |
| 394 | Q8 | — | 4 | 1 | no | — |
| 395 | Q8 | — | 4 | 1 | no | — |
| 396 | Q8 | — | 4 | 1 | no | — |
| 397 | Q8 | — | 4 | 1 | no | — |
| 398 | Q8 | — | 8 | 1 | no | — |
| 399 | Q8 | — | 8 | 1 | no | — |
| 400 | Q8 | — | 8 | 1 | no | — |
| 401 | Q8 | — | 8 | 1 | no | — |
| 402 | Q8 | — | 16 | 2 | no | — |
| 403 | C2×C4 | — | 2 | 1 | no | — |
| 404 | C2×C4 | — | 2 | 1 | no | — |
| 405 | C2×C4 | — | 2 | 2 | no | — |
| 406 | C2×C4 | — | 4 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 1 | no | — |
| 408 | C2×C4 | — | 4 | 1 | no | — |
| 409 | C2×C4 | — | 4 | 1 | no | — |
| 410 | C2×C4 | — | 4 | 1 | no | — |
| 411 | C2×C4 | — | 4 | 1 | no | — |
| 412 | C2×C4 | — | 4 | 1 | no | — |
| 413 | C2×C4 | — | 4 | 1 | no | — |
| 414 | C2×C4 | — | 4 | 1 | no | — |
| 415 | C2×C4 | — | 4 | 1 | no | — |
| 416 | C2×C4 | — | 4 | 1 | no | — |
| 417 | C2×C4 | — | 4 | 1 | no | — |
| 418 | C2×C4 | — | 4 | 1 | no | — |
| 419 | C2×C4 | — | 8 | 1 | no | — |
| 420 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 421 | C2×C4 | #534 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | #560 | 1 | 1 | yes | characteristic |
| 426 | C8 | — | 4 | 1 | no | — |
| 427 | C8 | — | 4 | 1 | no | — |
| 428 | C8 | — | 4 | 1 | no | — |
| 429 | C8 | — | 4 | 1 | no | — |
| 430 | C8 | — | 8 | 1 | no | — |
| 431 | C8 | — | 8 | 1 | no | — |
| 432 | C8 | — | 8 | 1 | no | — |
| 433 | C8 | — | 8 | 1 | no | — |
| 434 | C8 | — | 8 | 1 | no | — |
| 435 | C8 | — | 8 | 1 | no | — |
| 436 | C8 | — | 8 | 1 | no | — |
| 437 | C8 | — | 8 | 1 | no | — |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 2 | 1 | no | — |
| 440 | C22 | — | 2 | 1 | no | — |
| 441 | C22 | #2668 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 2 | 1 | no | — |
| 444 | C4 | — | 2 | 1 | no | — |
| 445 | C4 | — | 2 | 1 | no | — |
| 446 | C4 | — | 2 | 1 | no | — |
| 447 | C4 | — | 4 | 2 | no | — |
| 448 | C4 | — | 8 | 1 | no | — |
| 449 | C4 | — | 8 | 1 | no | — |
| 450 | C4 | — | 8 | 1 | no | — |
| 451 | C4 | — | 8 | 1 | no | — |
| 452 | C4 | — | 8 | 1 | no | — |
| 453 | C4 | — | 8 | 1 | no | — |
| 454 | C4 | — | 8 | 1 | no | — |
| 455 | C4 | — | 8 | 1 | no | — |
| 456 | C4 | — | 8 | 1 | no | — |
| 457 | C4 | #3289 | 1 | 1 | yes | characteristic |
| 458 | C4 | #3290 | 1 | 1 | yes | characteristic |
| 459 | C2 | — | 4 | 1 | no | — |
| 460 | C2 | #30430 | 1 | 1 | yes | characteristic |
| 461 | C2 | #30435 | 1 | 1 | yes | characteristic |
| 462 | C2 | #30443 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #2668 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| prime radical | C23 | #538 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19534 | 2 |
| #19533 | 2 |
| #18863 | 2 |
| #10664 | 2 |
| #10648 | 2 |
| #10646 | 2 |
| #10529 | 2 |
| #10031 | 2 |
| #9528 | 2 |
| #9286 | 2 |
| #8460 | 2 |