Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1499 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61821 | C2 | 1 | 2 | yes | maximal |
| 2 | #61372 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×Q8×Q16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | Q162 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20008 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #19817 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #19664 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #19405 | C2 | 1 | 2 | yes | maximal |
| 9 | #19209 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #19118 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #18915 | C2 | 1 | 2 | yes | maximal |
| 12 | #18769 | C2 | 1 | 2 | yes | maximal |
| 13 | #17903 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #17856 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #3502 | C22 | 1 | 2 | yes | — |
| 16 | C2×Q82 | C22 | 1 | 2 | yes | — |
| 17 | #3390 | — | 2 | 2 | no | — |
| 18 | #3387 | C22 | 1 | 4 | yes | — |
| 19 | #3383 | — | 2 | 2 | no | — |
| 20 | #3383 | C22 | 1 | 2 | yes | — |
| 21 | Q8×Q16 | — | 2 | 4 | no | — |
| 22 | Q8×Q16 | — | 2 | 2 | no | — |
| 23 | Q8×Q16 | — | 2 | 2 | no | — |
| 24 | Q8×Q16 | C22 | 1 | 4 | yes | — |
| 25 | Q8×Q16 | C22 | 1 | 2 | yes | — |
| 26 | Q8×Q16 | C22 | 1 | 8 | yes | — |
| 27 | Q8×Q16 | C22 | 1 | 4 | yes | — |
| 28 | #3363 | — | 2 | 4 | no | — |
| 29 | #3363 | C22 | 1 | 8 | yes | — |
| 30 | #3230 | — | 2 | 4 | no | — |
| 31 | #3230 | C22 | 1 | 2 | yes | — |
| 32 | #3230 | C22 | 1 | 2 | yes | — |
| 33 | #3209 | C22 | 1 | 2 | yes | — |
| 34 | #3164 | — | 2 | 1 | no | — |
| 35 | #3160 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#500 | — | 2 | 1 | no | — |
| 37 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 38 | #3104 | — | 2 | 4 | no | — |
| 39 | #3104 | C22 | 1 | 2 | yes | — |
| 40 | #3104 | C22 | 1 | 1 | yes | characteristic |
| 41 | #3082 | — | 2 | 2 | no | — |
| 42 | #3078 | C22 | 1 | 2 | yes | — |
| 43 | C2×#477 | — | 2 | 2 | no | — |
| 44 | C2×#477 | C22 | 1 | 2 | yes | — |
| 45 | #2982 | C22 | 1 | 2 | yes | — |
| 46 | #2960 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 48 | #2950 | — | 2 | 1 | no | — |
| 49 | C2×C4×Q16 | — | 2 | 1 | no | — |
| 50 | C2×C4×Q16 | C22 | 1 | 1 | yes | characteristic |
| 51 | #1723 | C22 | 1 | 4 | yes | — |
| 52 | #1713 | C22 | 1 | 2 | yes | — |
| 53 | #1710 | C22 | 1 | 2 | yes | — |
| 54 | #1696 | C22 | 1 | 4 | yes | — |
| 55 | #1684 | C22 | 1 | 8 | yes | — |
| 56 | #1676 | C22 | 1 | 4 | yes | — |
| 57 | #1676 | C22 | 1 | 2 | yes | — |
| 58 | #1676 | C22 | 1 | 8 | yes | — |
| 59 | #1674 | C22 | 1 | 2 | yes | — |
| 60 | #1672 | C22 | 1 | 4 | yes | — |
| 61 | #1645 | C22 | 1 | 8 | yes | — |
| 62 | #1636 | C22 | 1 | 8 | yes | — |
| 63 | #1633 | C22 | 1 | 8 | yes | — |
| 64 | #1633 | C22 | 1 | 8 | yes | — |
| 65 | #1584 | C22 | 1 | 4 | yes | — |
| 66 | #1579 | C22 | 1 | 4 | yes | — |
| 67 | C8×Q16 | C22 | 1 | 4 | yes | — |
| 68 | C8×Q16 | C22 | 1 | 4 | yes | — |
| 69 | #1571 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1564 | C22 | 1 | 1 | yes | characteristic |
| 71 | #1548 | C22 | 1 | 2 | yes | — |
| 72 | #1542 | C22 | 1 | 2 | yes | — |
| 73 | #1487 | C22 | 1 | 1 | yes | characteristic |
| 74 | #1481 | C22 | 1 | 1 | yes | characteristic |
| 75 | #1479 | C22 | 1 | 2 | yes | — |
| 76 | #1450 | C22 | 1 | 1 | yes | characteristic |
| 77 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 78 | Q82 | — | 2 | 2 | no | — |
| 79 | Q82 | — | 2 | 4 | no | — |
| 80 | Q82 | — | 2 | 4 | no | — |
| 81 | Q82 | — | 4 | 2 | no | — |
| 82 | Q82 | C23 | 1 | 8 | yes | — |
| 83 | Q82 | C23 | 1 | 4 | yes | — |
| 84 | #557 | — | 2 | 2 | no | — |
| 85 | #557 | — | 2 | 4 | no | — |
| 86 | #557 | — | 4 | 2 | no | — |
| 87 | #557 | C23 | 1 | 4 | yes | — |
| 88 | #544 | — | 2 | 2 | no | — |
| 89 | #544 | — | 4 | 2 | no | — |
| 90 | #533 | — | 2 | 4 | no | — |
| 91 | #533 | C23 | 1 | 2 | yes | — |
| 92 | #533 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 94 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 95 | C2×C4⋊Q8 | — | 4 | 2 | no | — |
| 96 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 97 | #519 | — | 2 | 2 | no | — |
| 98 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 99 | C2×C4×Q8 | — | 2 | 2 | no | — |
| 100 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 101 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 102 | #501 | — | 2 | 4 | no | — |
| 103 | #500 | — | 2 | 2 | no | — |
| 104 | #500 | — | 2 | 4 | no | — |
| 105 | #500 | — | 2 | 4 | no | — |
| 106 | #500 | — | 2 | 8 | no | — |
| 107 | #500 | — | 2 | 2 | no | — |
| 108 | #500 | — | 2 | 1 | no | — |
| 109 | #500 | — | 2 | 1 | no | — |
| 110 | #500 | C23 | 1 | 2 | yes | — |
| 111 | #500 | C23 | 1 | 2 | yes | — |
| 112 | #500 | C23 | 1 | 1 | yes | characteristic |
| 113 | #500 | C23 | 1 | 4 | yes | — |
| 114 | #500 | C23 | 1 | 1 | yes | characteristic |
| 115 | #499 | — | 2 | 2 | no | — |
| 116 | #499 | — | 2 | 1 | no | — |
| 117 | #499 | — | 2 | 1 | no | — |
| 118 | #498 | C23 | 1 | 2 | yes | — |
| 119 | #494 | C23 | 1 | 4 | yes | — |
| 120 | #487 | — | 2 | 2 | no | — |
| 121 | #487 | — | 2 | 8 | no | — |
| 122 | #487 | C23 | 1 | 4 | yes | — |
| 123 | #487 | C23 | 1 | 4 | yes | — |
| 124 | #484 | — | 2 | 4 | no | — |
| 125 | #484 | — | 2 | 2 | no | — |
| 126 | #484 | — | 2 | 4 | no | — |
| 127 | #484 | D4 | 1 | 2 | yes | — |
| 128 | #479 | — | 2 | 4 | no | — |
| 129 | #479 | — | 2 | 4 | no | — |
| 130 | #479 | — | 2 | 4 | no | — |
| 131 | #477 | — | 2 | 4 | no | — |
| 132 | #477 | — | 2 | 8 | no | — |
| 133 | #477 | — | 2 | 4 | no | — |
| 134 | #477 | — | 2 | 8 | no | — |
| 135 | #477 | — | 2 | 8 | no | — |
| 136 | #477 | — | 2 | 4 | no | — |
| 137 | #477 | — | 2 | 8 | no | — |
| 138 | #477 | — | 2 | 8 | no | — |
| 139 | #477 | D4 | 1 | 2 | yes | — |
| 140 | #477 | C23 | 1 | 8 | yes | — |
| 141 | #477 | C23 | 1 | 4 | yes | — |
| 142 | #477 | C23 | 1 | 4 | yes | — |
| 143 | #477 | C23 | 1 | 8 | yes | — |
| 144 | #475 | — | 2 | 4 | no | — |
| 145 | #475 | C23 | 1 | 4 | yes | — |
| 146 | #462 | — | 2 | 8 | no | — |
| 147 | #462 | — | 4 | 2 | no | — |
| 148 | #462 | D4 | 1 | 2 | yes | — |
| 149 | #462 | C23 | 1 | 4 | yes | — |
| 150 | #451 | — | 2 | 2 | no | — |
| 151 | #451 | — | 4 | 2 | no | — |
| 152 | #451 | D4 | 1 | 2 | yes | — |
| 153 | #446 | — | 2 | 1 | no | — |
| 154 | #446 | C23 | 1 | 2 | yes | — |
| 155 | C8×Q8 | — | 2 | 4 | no | — |
| 156 | C8×Q8 | — | 2 | 1 | no | — |
| 157 | C8×Q8 | — | 2 | 1 | no | — |
| 158 | C8×Q8 | — | 2 | 1 | no | — |
| 159 | C8×Q8 | C23 | 1 | 8 | yes | — |
| 160 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 161 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 162 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 163 | #441 | — | 2 | 4 | no | — |
| 164 | C4×Q16 | — | 2 | 8 | no | — |
| 165 | C4×Q16 | — | 2 | 4 | no | — |
| 166 | C4×Q16 | — | 2 | 4 | no | — |
| 167 | C4×Q16 | — | 2 | 2 | no | — |
| 168 | C4×Q16 | — | 2 | 2 | no | — |
| 169 | C4×Q16 | — | 2 | 4 | no | — |
| 170 | C4×Q16 | — | 2 | 8 | no | — |
| 171 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 172 | C4×Q16 | D4 | 1 | 2 | yes | — |
| 173 | C4×Q16 | C23 | 1 | 4 | yes | — |
| 174 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 175 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 176 | #431 | — | 2 | 4 | no | — |
| 177 | #431 | C23 | 1 | 2 | yes | — |
| 178 | #431 | C23 | 1 | 1 | yes | characteristic |
| 179 | #431 | C23 | 1 | 1 | yes | characteristic |
| 180 | #428 | — | 2 | 2 | no | — |
| 181 | #427 | — | 2 | 1 | no | — |
| 182 | #427 | — | 2 | 1 | no | — |
| 183 | C2×#107 | — | 2 | 1 | no | — |
| 184 | C2×#107 | — | 2 | 1 | no | — |
| 185 | C2×#107 | — | 2 | 2 | no | — |
| 186 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 187 | #424 | — | 2 | 1 | no | — |
| 188 | #423 | C23 | 1 | 1 | yes | characteristic |
| 189 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 190 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 191 | #419 | — | 2 | 2 | no | — |
| 192 | C2×#103 | — | 2 | 2 | no | — |
| 193 | C2×#103 | D4 | 1 | 2 | yes | — |
| 194 | #405 | — | 2 | 1 | no | — |
| 195 | C2×C4×C8 | — | 2 | 1 | no | — |
| 196 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 197 | #335 | C23 | 1 | 2 | yes | — |
| 198 | #335 | C23 | 1 | 4 | yes | — |
| 199 | #334 | C23 | 1 | 2 | yes | — |
| 200 | #333 | C23 | 1 | 4 | yes | — |
| 201 | #333 | C23 | 1 | 8 | yes | — |
| 202 | #332 | C23 | 1 | 4 | yes | — |
| 203 | Q8⋊C8 | C23 | 1 | 8 | yes | — |
| 204 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 205 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 206 | #322 | C23 | 1 | 2 | yes | — |
| 207 | C82 | C23 | 1 | 2 | yes | — |
| 208 | C22×Q8 | — | 2 | 2 | no | — |
| 209 | C22×Q8 | — | 4 | 2 | no | — |
| 210 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C22×Q8 | C2×D4 | 1 | 2 | yes | — |
| 212 | C2×Q16 | — | 2 | 4 | no | — |
| 213 | C2×Q16 | — | 4 | 4 | no | — |
| 214 | C2×Q16 | Q16 | 1 | 8 | yes | complemented |
| 215 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 216 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 217 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 218 | C2×M16 | — | 2 | 1 | no | — |
| 219 | C22×C8 | — | 2 | 1 | no | — |
| 220 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4⋊Q8 | — | 2 | 8 | no | — |
| 223 | C4⋊Q8 | — | 2 | 8 | no | — |
| 224 | C4⋊Q8 | — | 2 | 4 | no | — |
| 225 | C4⋊Q8 | — | 2 | 4 | no | — |
| 226 | C4⋊Q8 | — | 2 | 4 | no | — |
| 227 | C4⋊Q8 | — | 2 | 2 | no | — |
| 228 | C4⋊Q8 | — | 2 | 2 | no | — |
| 229 | C4⋊Q8 | — | 2 | 2 | no | — |
| 230 | C4⋊Q8 | — | 4 | 4 | no | — |
| 231 | C4⋊Q8 | — | 4 | 4 | no | — |
| 232 | C4⋊Q8 | — | 4 | 8 | no | — |
| 233 | C4⋊Q8 | — | 4 | 4 | no | — |
| 234 | C4⋊Q8 | — | 4 | 8 | no | — |
| 235 | C4⋊Q8 | — | 4 | 2 | no | — |
| 236 | C4⋊Q8 | — | 4 | 4 | no | — |
| 237 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 240 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 241 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 242 | #125 | — | 2 | 4 | no | — |
| 243 | #125 | — | 2 | 2 | no | — |
| 244 | #125 | — | 2 | 1 | no | — |
| 245 | #125 | — | 4 | 4 | no | — |
| 246 | #125 | — | 4 | 4 | no | — |
| 247 | #125 | — | 4 | 2 | no | — |
| 248 | #125 | — | 4 | 4 | no | — |
| 249 | C22⋊Q8 | — | 2 | 1 | no | — |
| 250 | C22⋊Q8 | — | 2 | 2 | no | — |
| 251 | C22⋊Q8 | — | 2 | 2 | no | — |
| 252 | C22⋊Q8 | — | 4 | 4 | no | — |
| 253 | C22⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 254 | C4×Q8 | — | 2 | 2 | no | — |
| 255 | C4×Q8 | — | 2 | 1 | no | — |
| 256 | C4×Q8 | — | 2 | 1 | no | — |
| 257 | C4×Q8 | — | 2 | 2 | no | — |
| 258 | C4×Q8 | — | 2 | 1 | no | — |
| 259 | C4×Q8 | — | 2 | 8 | no | — |
| 260 | C4×Q8 | — | 2 | 8 | no | — |
| 261 | C4×Q8 | — | 2 | 4 | no | — |
| 262 | C4×Q8 | — | 2 | 4 | no | — |
| 263 | C4×Q8 | — | 2 | 4 | no | — |
| 264 | C4×Q8 | — | 2 | 4 | no | — |
| 265 | C4×Q8 | — | 2 | 2 | no | — |
| 266 | C4×Q8 | — | 2 | 2 | no | — |
| 267 | C4×Q8 | — | 4 | 4 | no | — |
| 268 | C4×Q8 | — | 4 | 4 | no | — |
| 269 | C4×Q8 | — | 4 | 4 | no | — |
| 270 | C4×Q8 | — | 4 | 2 | no | — |
| 271 | C4×Q8 | — | 4 | 2 | no | — |
| 272 | C4×Q8 | C2×D4 | 1 | 4 | yes | — |
| 273 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 274 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 275 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 276 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 277 | #117 | — | 2 | 1 | no | — |
| 278 | #117 | — | 2 | 2 | no | — |
| 279 | #117 | — | 4 | 4 | no | — |
| 280 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 281 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 282 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 283 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 284 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 285 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 286 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 288 | C2×C42 | — | 2 | 1 | no | — |
| 289 | C2×C42 | — | 2 | 2 | no | — |
| 290 | C2×C42 | — | 4 | 2 | no | — |
| 291 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 292 | #107 | — | 2 | 2 | no | — |
| 293 | #107 | — | 2 | 2 | no | — |
| 294 | #107 | — | 2 | 2 | no | — |
| 295 | #107 | — | 2 | 2 | no | — |
| 296 | #107 | — | 2 | 1 | no | — |
| 297 | #107 | — | 2 | 1 | no | — |
| 298 | #107 | — | 2 | 1 | no | — |
| 299 | #107 | — | 2 | 1 | no | — |
| 300 | #107 | — | 2 | 8 | no | — |
| 301 | #107 | — | 2 | 8 | no | — |
| 302 | #107 | — | 2 | 4 | no | — |
| 303 | #107 | — | 2 | 8 | no | — |
| 304 | #107 | — | 2 | 4 | no | — |
| 305 | #107 | C2×D4 | 1 | 2 | yes | — |
| 306 | #107 | C2×D4 | 1 | 2 | yes | — |
| 307 | #107 | C2×D4 | 1 | 4 | yes | — |
| 308 | #106 | — | 2 | 2 | no | — |
| 309 | #106 | — | 2 | 2 | no | — |
| 310 | #106 | — | 2 | 4 | no | — |
| 311 | C4⋊C8 | — | 2 | 2 | no | — |
| 312 | C4⋊C8 | — | 2 | 2 | no | — |
| 313 | C4⋊C8 | — | 2 | 2 | no | — |
| 314 | C4⋊C8 | — | 2 | 2 | no | — |
| 315 | C4⋊C8 | — | 2 | 8 | no | — |
| 316 | C4⋊C8 | — | 2 | 1 | no | — |
| 317 | C4⋊C8 | — | 2 | 1 | no | — |
| 318 | C4⋊C8 | — | 2 | 1 | no | — |
| 319 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 320 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 321 | C4⋊C8 | C24 | 1 | 4 | yes | — |
| 322 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 323 | #103 | — | 2 | 8 | no | — |
| 324 | #103 | — | 2 | 4 | no | — |
| 325 | #103 | — | 2 | 4 | no | — |
| 326 | #103 | — | 2 | 4 | no | — |
| 327 | #103 | — | 2 | 8 | no | — |
| 328 | #103 | — | 2 | 8 | no | — |
| 329 | #103 | — | 2 | 4 | no | — |
| 330 | #103 | — | 4 | 4 | no | — |
| 331 | #103 | C2×D4 | 1 | 4 | yes | — |
| 332 | #103 | C2×D4 | 1 | 4 | yes | — |
| 333 | #103 | C2×D4 | 1 | 4 | yes | — |
| 334 | #103 | C2×D4 | 1 | 4 | yes | — |
| 335 | C22⋊C8 | — | 2 | 2 | no | — |
| 336 | C22⋊C8 | — | 2 | 1 | no | — |
| 337 | C22⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 338 | #97 | — | 2 | 2 | no | — |
| 339 | C4×C8 | — | 2 | 2 | no | — |
| 340 | C4×C8 | — | 2 | 2 | no | — |
| 341 | C4×C8 | — | 2 | 2 | no | — |
| 342 | C4×C8 | — | 2 | 8 | no | — |
| 343 | C4×C8 | — | 2 | 2 | no | — |
| 344 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 345 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 346 | C4×C8 | C24 | 1 | 2 | yes | — |
| 347 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 348 | C4×C8 | C24 | 1 | 2 | yes | — |
| 349 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 350 | C2×Q8 | — | 2 | 4 | no | — |
| 351 | C2×Q8 | — | 2 | 1 | no | — |
| 352 | C2×Q8 | — | 2 | 2 | no | — |
| 353 | C2×Q8 | — | 2 | 1 | no | — |
| 354 | C2×Q8 | — | 2 | 4 | no | — |
| 355 | C2×Q8 | — | 2 | 2 | no | — |
| 356 | C2×Q8 | — | 2 | 4 | no | — |
| 357 | C2×Q8 | — | 2 | 2 | no | — |
| 358 | C2×Q8 | — | 4 | 4 | no | — |
| 359 | C2×Q8 | — | 4 | 8 | no | — |
| 360 | C2×Q8 | — | 4 | 2 | no | — |
| 361 | C2×Q8 | — | 16 | 2 | no | — |
| 362 | C2×Q8 | — | 16 | 4 | no | — |
| 363 | C2×Q8 | C2×Q16 | 1 | 8 | yes | — |
| 364 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 365 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 366 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 367 | C22×C4 | — | 2 | 1 | no | — |
| 368 | C22×C4 | — | 2 | 2 | no | — |
| 369 | C22×C4 | — | 2 | 1 | no | — |
| 370 | C22×C4 | — | 2 | 2 | no | — |
| 371 | C22×C4 | — | 4 | 2 | no | — |
| 372 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 373 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 374 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 375 | Q16 | — | 2 | 8 | no | — |
| 376 | Q16 | — | 4 | 8 | no | — |
| 377 | Q16 | — | 16 | 4 | no | — |
| 378 | Q16 | C2×Q16 | 1 | 8 | yes | — |
| 379 | Q16 | C2×Q16 | 1 | 8 | yes | — |
| 380 | M16 | — | 4 | 2 | no | — |
| 381 | C2×C8 | — | 2 | 2 | no | — |
| 382 | C2×C8 | — | 2 | 4 | no | — |
| 383 | C2×C8 | — | 2 | 2 | no | — |
| 384 | C2×C8 | — | 2 | 2 | no | — |
| 385 | C2×C8 | — | 2 | 2 | no | — |
| 386 | C2×C8 | — | 4 | 2 | no | — |
| 387 | C2×C8 | C2×Q16 | 1 | 4 | yes | — |
| 388 | C2×C8 | C22×D4 | 1 | 4 | yes | — |
| 389 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 391 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 393 | C4⋊C4 | — | 2 | 4 | no | — |
| 394 | C4⋊C4 | — | 2 | 2 | no | — |
| 395 | C4⋊C4 | — | 2 | 2 | no | — |
| 396 | C4⋊C4 | — | 2 | 1 | no | — |
| 397 | C4⋊C4 | — | 2 | 1 | no | — |
| 398 | C4⋊C4 | — | 2 | 1 | no | — |
| 399 | C4⋊C4 | — | 2 | 2 | no | — |
| 400 | C4⋊C4 | — | 2 | 1 | no | — |
| 401 | C4⋊C4 | — | 2 | 4 | no | — |
| 402 | C4⋊C4 | — | 2 | 2 | no | — |
| 403 | C4⋊C4 | — | 2 | 2 | no | — |
| 404 | C4⋊C4 | — | 2 | 4 | no | — |
| 405 | C4⋊C4 | — | 2 | 2 | no | — |
| 406 | C4⋊C4 | — | 2 | 2 | no | — |
| 407 | C4⋊C4 | — | 2 | 4 | no | — |
| 408 | C4⋊C4 | — | 2 | 2 | no | — |
| 409 | C4⋊C4 | — | 2 | 2 | no | — |
| 410 | C4⋊C4 | — | 4 | 8 | no | — |
| 411 | C4⋊C4 | — | 4 | 8 | no | — |
| 412 | C4⋊C4 | — | 4 | 4 | no | — |
| 413 | C4⋊C4 | — | 4 | 4 | no | — |
| 414 | C4⋊C4 | — | 4 | 4 | no | — |
| 415 | C4⋊C4 | — | 4 | 4 | no | — |
| 416 | C4⋊C4 | — | 4 | 4 | no | — |
| 417 | C4⋊C4 | — | 4 | 2 | no | — |
| 418 | C4⋊C4 | — | 4 | 2 | no | — |
| 419 | C4⋊C4 | — | 4 | 2 | no | — |
| 420 | C4⋊C4 | — | 4 | 2 | no | — |
| 421 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 422 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 423 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 424 | C22⋊C4 | — | 2 | 2 | no | — |
| 425 | C22⋊C4 | — | 4 | 2 | no | — |
| 426 | C42 | — | 2 | 4 | no | — |
| 427 | C42 | — | 2 | 2 | no | — |
| 428 | C42 | — | 2 | 4 | no | — |
| 429 | C42 | — | 2 | 2 | no | — |
| 430 | C42 | — | 2 | 2 | no | — |
| 431 | C42 | — | 4 | 8 | no | — |
| 432 | C42 | — | 4 | 4 | no | — |
| 433 | C42 | — | 4 | 4 | no | — |
| 434 | C42 | — | 4 | 2 | 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 | D42 | 1 | 1 | yes | characteristic |
| 440 | Q8 | — | 2 | 4 | no | — |
| 441 | Q8 | — | 2 | 8 | no | — |
| 442 | Q8 | — | 2 | 4 | no | — |
| 443 | Q8 | — | 2 | 2 | no | — |
| 444 | Q8 | — | 2 | 4 | no | — |
| 445 | Q8 | — | 4 | 4 | no | — |
| 446 | Q8 | — | 8 | 1 | no | — |
| 447 | Q8 | — | 8 | 2 | no | — |
| 448 | Q8 | — | 8 | 4 | no | — |
| 449 | Q8 | — | 16 | 2 | no | — |
| 450 | Q8 | — | 16 | 4 | no | — |
| 451 | Q8 | — | 16 | 8 | no | — |
| 452 | Q8 | C22×Q16 | 1 | 8 | yes | — |
| 453 | Q8 | #578 | 1 | 4 | yes | — |
| 454 | C2×C4 | — | 2 | 4 | no | — |
| 455 | C2×C4 | — | 2 | 4 | no | — |
| 456 | C2×C4 | — | 2 | 2 | no | — |
| 457 | C2×C4 | — | 2 | 8 | no | — |
| 458 | C2×C4 | — | 2 | 2 | no | — |
| 459 | C2×C4 | — | 2 | 4 | no | — |
| 460 | C2×C4 | — | 2 | 2 | no | — |
| 461 | C2×C4 | — | 2 | 2 | no | — |
| 462 | C2×C4 | — | 2 | 2 | no | — |
| 463 | C2×C4 | — | 4 | 1 | no | — |
| 464 | C2×C4 | — | 4 | 2 | no | — |
| 465 | C2×C4 | — | 4 | 2 | no | — |
| 466 | C2×C4 | — | 4 | 2 | no | — |
| 467 | C2×C4 | — | 4 | 4 | no | — |
| 468 | C2×C4 | — | 8 | 2 | no | — |
| 469 | C2×C4 | — | 8 | 4 | no | — |
| 470 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 471 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 473 | C2×C4 | C22×Q16 | 1 | 2 | yes | — |
| 474 | C2×C4 | #578 | 1 | 2 | yes | — |
| 475 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 476 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 477 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 478 | C8 | — | 2 | 1 | no | — |
| 479 | C8 | — | 2 | 1 | no | — |
| 480 | C8 | — | 2 | 4 | no | — |
| 481 | C8 | — | 4 | 2 | no | — |
| 482 | C8 | — | 4 | 2 | no | — |
| 483 | C8 | — | 4 | 2 | no | — |
| 484 | C8 | — | 4 | 4 | no | — |
| 485 | C8 | C22×Q16 | 1 | 2 | yes | — |
| 486 | C8 | C22×Q16 | 1 | 2 | yes | — |
| 487 | C22 | — | 2 | 1 | no | — |
| 488 | C22 | — | 2 | 1 | no | — |
| 489 | C22 | D4×Q16 | 1 | 2 | yes | — |
| 490 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 491 | C4 | — | 2 | 8 | no | — |
| 492 | C4 | — | 2 | 4 | no | — |
| 493 | C4 | — | 2 | 1 | no | — |
| 494 | C4 | — | 2 | 1 | no | — |
| 495 | C4 | — | 2 | 1 | no | — |
| 496 | C4 | — | 4 | 2 | no | — |
| 497 | C4 | — | 4 | 2 | no | — |
| 498 | C4 | — | 4 | 4 | no | — |
| 499 | C4 | — | 4 | 2 | no | — |
| 500 | C4 | — | 8 | 2 | no | — |
| 501 | C4 | — | 8 | 4 | no | — |
| 502 | C4 | — | 8 | 2 | no | — |
| 503 | C4 | D4×Q16 | 1 | 2 | yes | — |
| 504 | C4 | C23×Q16 | 1 | 1 | yes | characteristic |
| 505 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 506 | C4 | C2×#578 | 1 | 2 | yes | — |
| 507 | C2 | — | 2 | 2 | no | — |
| 508 | C2 | C2×D4×Q16 | 1 | 1 | yes | characteristic |
| 509 | C2 | #61053 | 1 | 1 | yes | characteristic |
| 510 | C2 | #61106 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | C23 | D42 |
| 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 |
|---|---|---|
| 4. Q162 | C2 | semidirect |
| 5. #20008 | C2 | semidirect |
| 6. #19817 | C2 | semidirect |
| 214. C2×Q16 | Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61821 | 2 |
| #61372 | 2 |
| C2×Q8×Q16 | 2 |
| Q162 | 2 |
| #20008 | 2 |
| #19817 | 2 |
| #19664 | 2 |
| #19405 | 2 |
| #19209 | 2 |
| #19118 | 2 |
| #18915 | 2 |
| #18769 | 2 |
| #17903 | 2 |
| #17856 | 2 |