Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1531 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #62416 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #62360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #61383 | C2 | 1 | 2 | yes | maximal |
| 4 | #20010 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | SD16×Q16 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #19932 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #19928 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #19818 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #19812 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #19632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #19240 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #19126 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | C2×#1670 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #18925 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #18885 | C2 | 1 | 2 | yes | maximal |
| 16 | #18068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | C8×#137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 18 | #3503 | C22 | 1 | 2 | yes | — |
| 19 | #3502 | C22 | 1 | 2 | yes | — |
| 20 | #3395 | — | 2 | 1 | no | — |
| 21 | #3395 | C22 | 1 | 2 | yes | — |
| 22 | #3395 | C22 | 1 | 2 | yes | — |
| 23 | #3395 | C22 | 1 | 2 | yes | — |
| 24 | #3388 | — | 2 | 4 | no | — |
| 25 | #3387 | — | 2 | 4 | no | — |
| 26 | #3387 | C22 | 1 | 4 | yes | — |
| 27 | #3386 | C22 | 1 | 4 | yes | — |
| 28 | #3383 | C22 | 1 | 4 | yes | — |
| 29 | Q8×Q16 | — | 2 | 1 | no | — |
| 30 | Q8×Q16 | C22 | 1 | 2 | yes | — |
| 31 | Q8×SD16 | C22 | 1 | 4 | yes | — |
| 32 | #3363 | — | 2 | 2 | no | — |
| 33 | #3363 | C22 | 1 | 4 | yes | — |
| 34 | D4×Q16 | — | 2 | 2 | no | — |
| 35 | D4×Q16 | — | 2 | 2 | no | — |
| 36 | D4×Q16 | C22 | 1 | 2 | yes | — |
| 37 | D4×Q16 | C22 | 1 | 2 | yes | — |
| 38 | #3249 | — | 2 | 2 | no | — |
| 39 | #3249 | C22 | 1 | 2 | yes | — |
| 40 | #3230 | C22 | 1 | 2 | yes | — |
| 41 | #3209 | — | 2 | 2 | no | — |
| 42 | #3209 | C22 | 1 | 2 | yes | — |
| 43 | #3170 | — | 2 | 1 | no | — |
| 44 | #3170 | — | 2 | 2 | no | — |
| 45 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 46 | #3170 | C22 | 1 | 1 | yes | characteristic |
| 47 | #3165 | C22 | 1 | 2 | yes | — |
| 48 | #3163 | — | 2 | 2 | no | — |
| 49 | C2×#494 | — | 2 | 1 | no | — |
| 50 | C2×#494 | C22 | 1 | 1 | yes | characteristic |
| 51 | #3084 | — | 2 | 2 | no | — |
| 52 | #3082 | — | 2 | 2 | no | — |
| 53 | #3076 | C22 | 1 | 2 | yes | — |
| 54 | C2×#475 | C22 | 1 | 2 | yes | — |
| 55 | C8×#41 | C22 | 1 | 1 | yes | characteristic |
| 56 | #2962 | C22 | 1 | 2 | yes | — |
| 57 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 58 | #2947 | — | 2 | 2 | no | — |
| 59 | C4×#137 | C22 | 1 | 1 | yes | characteristic |
| 60 | #1723 | C22 | 1 | 4 | yes | — |
| 61 | #1713 | C22 | 1 | 2 | yes | — |
| 62 | #1707 | C22 | 1 | 2 | yes | — |
| 63 | #1694 | C22 | 1 | 4 | yes | — |
| 64 | #1692 | C22 | 1 | 4 | yes | — |
| 65 | #1684 | C22 | 1 | 2 | yes | — |
| 66 | #1683 | C22 | 1 | 2 | yes | — |
| 67 | #1676 | C22 | 1 | 1 | yes | characteristic |
| 68 | #1675 | C22 | 1 | 1 | yes | characteristic |
| 69 | #1674 | C22 | 1 | 4 | yes | — |
| 70 | #1672 | C22 | 1 | 4 | yes | — |
| 71 | #1670 | C22 | 1 | 2 | yes | — |
| 72 | #1670 | C22 | 1 | 1 | yes | characteristic |
| 73 | #1670 | C22 | 1 | 4 | yes | — |
| 74 | #1670 | C22 | 1 | 2 | yes | — |
| 75 | #1669 | C22 | 1 | 1 | yes | characteristic |
| 76 | #1649 | C22 | 1 | 4 | yes | — |
| 77 | #1648 | C22 | 1 | 4 | yes | — |
| 78 | #1648 | C22 | 1 | 4 | yes | — |
| 79 | #1648 | C22 | 1 | 4 | yes | — |
| 80 | #1645 | C22 | 1 | 4 | yes | — |
| 81 | #1645 | C22 | 1 | 4 | yes | — |
| 82 | #1637 | C22 | 1 | 4 | yes | — |
| 83 | #1636 | C22 | 1 | 4 | yes | — |
| 84 | #1591 | C22 | 1 | 2 | yes | — |
| 85 | #1584 | C22 | 1 | 4 | yes | — |
| 86 | #1579 | C22 | 1 | 2 | yes | — |
| 87 | SD16⋊C8 | C22 | 1 | 2 | yes | — |
| 88 | C8×Q16 | C22 | 1 | 2 | yes | — |
| 89 | C8×Q16 | C22 | 1 | 2 | yes | — |
| 90 | C8×SD16 | C22 | 1 | 2 | yes | — |
| 91 | #1565 | C22 | 1 | 1 | yes | characteristic |
| 92 | C2×#335 | C22 | 1 | 1 | yes | characteristic |
| 93 | #1542 | C22 | 1 | 2 | yes | — |
| 94 | C2×#332 | C22 | 1 | 2 | yes | — |
| 95 | #1481 | C22 | 1 | 2 | yes | — |
| 96 | #1479 | C22 | 1 | 1 | yes | characteristic |
| 97 | #1477 | C22 | 1 | 1 | yes | characteristic |
| 98 | C8×M16 | C22 | 1 | 1 | yes | characteristic |
| 99 | C2×#137 | D4 | 1 | 1 | yes | characteristic |
| 100 | C22×Q16 | — | 2 | 2 | no | — |
| 101 | C22×Q16 | — | 2 | 2 | no | — |
| 102 | C22×Q16 | — | 2 | 1 | no | — |
| 103 | C22×Q16 | — | 2 | 1 | no | — |
| 104 | Q82 | — | 2 | 2 | no | — |
| 105 | Q82 | — | 2 | 2 | no | — |
| 106 | Q82 | C23 | 1 | 4 | yes | — |
| 107 | #557 | — | 2 | 2 | no | — |
| 108 | #557 | — | 2 | 4 | no | — |
| 109 | #557 | — | 4 | 2 | no | — |
| 110 | #557 | C23 | 1 | 4 | yes | — |
| 111 | #557 | C23 | 1 | 4 | yes | — |
| 112 | #554 | — | 2 | 2 | no | — |
| 113 | #554 | — | 4 | 2 | no | — |
| 114 | D4×Q8 | — | 2 | 4 | no | — |
| 115 | D4×Q8 | C23 | 1 | 4 | yes | — |
| 116 | #544 | — | 2 | 2 | no | — |
| 117 | #544 | — | 2 | 2 | no | — |
| 118 | #544 | — | 4 | 2 | no | — |
| 119 | #544 | — | 4 | 2 | no | — |
| 120 | #533 | — | 2 | 2 | no | — |
| 121 | #533 | — | 2 | 4 | no | — |
| 122 | #533 | C23 | 1 | 2 | yes | — |
| 123 | #533 | C23 | 1 | 2 | yes | — |
| 124 | C2×C4⋊Q8 | — | 2 | 2 | no | — |
| 125 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 126 | #520 | — | 2 | 2 | no | — |
| 127 | #519 | — | 2 | 2 | no | — |
| 128 | C4×#41 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 130 | #501 | — | 2 | 4 | no | — |
| 131 | #501 | — | 2 | 4 | no | — |
| 132 | #501 | — | 2 | 4 | no | — |
| 133 | #500 | — | 2 | 2 | no | — |
| 134 | #500 | D4 | 1 | 1 | yes | characteristic |
| 135 | #500 | C23 | 1 | 1 | yes | characteristic |
| 136 | #500 | C23 | 1 | 4 | yes | — |
| 137 | #500 | C23 | 1 | 4 | yes | — |
| 138 | #499 | — | 2 | 4 | no | — |
| 139 | #498 | — | 2 | 4 | no | — |
| 140 | #498 | C23 | 1 | 4 | yes | — |
| 141 | #494 | — | 2 | 2 | no | — |
| 142 | #494 | — | 2 | 2 | no | — |
| 143 | #494 | — | 2 | 2 | no | — |
| 144 | #494 | — | 2 | 2 | no | — |
| 145 | #494 | — | 2 | 1 | no | — |
| 146 | #494 | — | 2 | 1 | no | — |
| 147 | #494 | D4 | 1 | 1 | yes | characteristic |
| 148 | #494 | C23 | 1 | 1 | yes | characteristic |
| 149 | #494 | C23 | 1 | 2 | yes | — |
| 150 | #494 | C23 | 1 | 2 | yes | — |
| 151 | #487 | — | 2 | 2 | no | — |
| 152 | #487 | — | 2 | 4 | no | — |
| 153 | #487 | D4 | 1 | 2 | yes | — |
| 154 | #487 | C23 | 1 | 2 | yes | — |
| 155 | #487 | C23 | 1 | 4 | yes | — |
| 156 | #484 | — | 4 | 2 | no | — |
| 157 | #479 | — | 2 | 2 | no | — |
| 158 | #479 | — | 2 | 4 | no | — |
| 159 | #479 | — | 2 | 4 | no | — |
| 160 | #479 | — | 2 | 4 | no | — |
| 161 | #478 | — | 2 | 2 | no | — |
| 162 | #478 | — | 2 | 4 | no | — |
| 163 | #477 | — | 2 | 2 | no | — |
| 164 | #477 | — | 2 | 4 | no | — |
| 165 | #477 | — | 2 | 4 | no | — |
| 166 | #477 | — | 2 | 4 | no | — |
| 167 | #477 | — | 4 | 2 | no | — |
| 168 | #477 | C23 | 1 | 2 | yes | — |
| 169 | #477 | C23 | 1 | 4 | yes | — |
| 170 | #476 | — | 2 | 4 | no | — |
| 171 | #476 | C23 | 1 | 2 | yes | — |
| 172 | #475 | — | 2 | 4 | no | — |
| 173 | #475 | — | 2 | 4 | no | — |
| 174 | #475 | — | 2 | 4 | no | — |
| 175 | #475 | C23 | 1 | 4 | yes | — |
| 176 | #475 | C23 | 1 | 4 | yes | — |
| 177 | #475 | C23 | 1 | 2 | yes | — |
| 178 | #474 | C23 | 1 | 2 | yes | — |
| 179 | #467 | — | 2 | 1 | no | — |
| 180 | #467 | — | 2 | 1 | no | — |
| 181 | #467 | — | 2 | 4 | no | — |
| 182 | #467 | — | 2 | 2 | no | — |
| 183 | #467 | — | 2 | 2 | no | — |
| 184 | #467 | D4 | 1 | 2 | yes | — |
| 185 | #467 | D4 | 1 | 2 | yes | — |
| 186 | #462 | — | 2 | 4 | no | — |
| 187 | #462 | — | 2 | 2 | no | — |
| 188 | #462 | — | 2 | 4 | no | — |
| 189 | #462 | — | 2 | 4 | no | — |
| 190 | #462 | — | 2 | 4 | no | — |
| 191 | #462 | C23 | 1 | 4 | yes | — |
| 192 | #462 | C23 | 1 | 4 | yes | — |
| 193 | #462 | C23 | 1 | 4 | yes | — |
| 194 | #451 | — | 2 | 4 | no | — |
| 195 | #451 | — | 2 | 4 | no | — |
| 196 | #451 | — | 2 | 4 | no | — |
| 197 | #446 | — | 2 | 4 | no | — |
| 198 | #446 | C23 | 1 | 4 | yes | — |
| 199 | C8×Q8 | — | 2 | 1 | no | — |
| 200 | C8×Q8 | — | 2 | 1 | no | — |
| 201 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 202 | C8×Q8 | C23 | 1 | 2 | yes | — |
| 203 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 204 | C8×Q8 | C23 | 1 | 4 | yes | — |
| 205 | C8×Q8 | C23 | 1 | 1 | yes | characteristic |
| 206 | #441 | — | 2 | 4 | no | — |
| 207 | #441 | D4 | 1 | 2 | yes | — |
| 208 | #440 | — | 2 | 4 | no | — |
| 209 | #440 | D4 | 1 | 2 | yes | — |
| 210 | C4×Q16 | — | 2 | 2 | no | — |
| 211 | C4×Q16 | — | 2 | 4 | no | — |
| 212 | C4×Q16 | — | 2 | 2 | no | — |
| 213 | C4×Q16 | — | 2 | 2 | no | — |
| 214 | C4×Q16 | — | 2 | 2 | no | — |
| 215 | C4×Q16 | — | 2 | 4 | no | — |
| 216 | C4×Q16 | — | 2 | 1 | no | — |
| 217 | C4×Q16 | — | 2 | 1 | no | — |
| 218 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 219 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 220 | C4×Q16 | C23 | 1 | 2 | yes | — |
| 221 | C4×SD16 | — | 2 | 4 | no | — |
| 222 | C4×SD16 | C23 | 1 | 2 | yes | — |
| 223 | C8×D4 | — | 2 | 1 | no | — |
| 224 | C8×D4 | — | 2 | 1 | no | — |
| 225 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 226 | C8×D4 | C23 | 1 | 1 | yes | characteristic |
| 227 | #431 | — | 2 | 1 | no | — |
| 228 | #431 | C23 | 1 | 1 | yes | characteristic |
| 229 | #431 | C23 | 1 | 1 | yes | characteristic |
| 230 | #428 | — | 2 | 2 | no | — |
| 231 | #428 | — | 2 | 2 | no | — |
| 232 | #428 | D4 | 1 | 1 | yes | characteristic |
| 233 | #427 | — | 2 | 2 | no | — |
| 234 | C2×#106 | — | 2 | 2 | no | — |
| 235 | #424 | — | 2 | 2 | no | — |
| 236 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 237 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 238 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 239 | #419 | D4 | 1 | 1 | yes | characteristic |
| 240 | #417 | D4 | 1 | 1 | yes | characteristic |
| 241 | #416 | — | 2 | 2 | no | — |
| 242 | C2×#103 | — | 2 | 2 | no | — |
| 243 | #405 | — | 2 | 2 | no | — |
| 244 | C4×M16 | C23 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×C8 | — | 2 | 1 | no | — |
| 246 | C2×C4×C8 | — | 2 | 1 | no | — |
| 247 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 248 | #335 | C23 | 1 | 1 | yes | characteristic |
| 249 | #335 | C23 | 1 | 2 | yes | — |
| 250 | #335 | C23 | 1 | 1 | yes | characteristic |
| 251 | #335 | C23 | 1 | 2 | yes | — |
| 252 | #334 | C23 | 1 | 2 | yes | — |
| 253 | #333 | C23 | 1 | 2 | yes | — |
| 254 | #333 | C23 | 1 | 2 | yes | — |
| 255 | #332 | C23 | 1 | 4 | yes | — |
| 256 | #332 | C23 | 1 | 4 | yes | — |
| 257 | #332 | C23 | 1 | 2 | yes | — |
| 258 | #332 | C23 | 1 | 2 | yes | — |
| 259 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 260 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 261 | Q8⋊C8 | C23 | 1 | 2 | yes | — |
| 262 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 263 | Q8⋊C8 | C23 | 1 | 4 | yes | — |
| 264 | D4⋊C8 | C23 | 1 | 2 | yes | — |
| 265 | #322 | C23 | 1 | 2 | yes | — |
| 266 | C82 | C23 | 1 | 2 | yes | — |
| 267 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C22×Q8 | — | 2 | 4 | no | — |
| 269 | C22×Q8 | — | 2 | 2 | no | — |
| 270 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | #137 | Q16 | 1 | 8 | yes | complemented |
| 272 | C2×Q16 | — | 2 | 4 | no | — |
| 273 | C2×Q16 | — | 2 | 4 | no | — |
| 274 | C2×Q16 | — | 2 | 4 | no | — |
| 275 | C2×Q16 | — | 2 | 2 | no | — |
| 276 | C2×Q16 | — | 2 | 2 | no | — |
| 277 | C2×Q16 | — | 2 | 1 | no | — |
| 278 | C2×Q16 | — | 2 | 2 | no | — |
| 279 | C2×Q16 | — | 2 | 2 | no | — |
| 280 | C2×Q16 | — | 2 | 1 | no | — |
| 281 | C2×Q16 | — | 8 | 2 | no | — |
| 282 | C2×Q16 | — | 8 | 4 | no | — |
| 283 | C2×Q16 | — | 8 | 2 | no | — |
| 284 | C2×Q16 | — | 8 | 4 | no | — |
| 285 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 286 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 287 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 288 | C2×SD16 | C2×D4 | 1 | 2 | yes | — |
| 289 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C22×C8 | — | 2 | 2 | no | — |
| 292 | C22×C8 | — | 2 | 1 | no | — |
| 293 | C22×C8 | — | 2 | 1 | no | — |
| 294 | C22×C8 | — | 2 | 1 | no | — |
| 295 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C4⋊Q8 | — | 2 | 4 | no | — |
| 298 | C4⋊Q8 | — | 2 | 4 | no | — |
| 299 | C4⋊Q8 | — | 2 | 4 | no | — |
| 300 | C4⋊Q8 | — | 2 | 4 | no | — |
| 301 | C4⋊Q8 | — | 2 | 4 | no | — |
| 302 | C4⋊Q8 | — | 2 | 2 | no | — |
| 303 | C4⋊Q8 | — | 2 | 2 | no | — |
| 304 | C4⋊Q8 | — | 2 | 2 | no | — |
| 305 | C4⋊Q8 | — | 4 | 2 | no | — |
| 306 | C4⋊Q8 | — | 4 | 2 | no | — |
| 307 | C4⋊Q8 | — | 4 | 4 | no | — |
| 308 | C4⋊Q8 | — | 4 | 2 | no | — |
| 309 | C4⋊Q8 | — | 4 | 4 | no | — |
| 310 | C4⋊Q8 | — | 4 | 4 | no | — |
| 311 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 312 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 313 | C4⋊Q8 | C24 | 1 | 4 | yes | — |
| 314 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 315 | C4⋊Q8 | C24 | 1 | 2 | yes | — |
| 316 | #125 | — | 2 | 4 | no | — |
| 317 | #125 | — | 2 | 4 | no | — |
| 318 | #125 | — | 2 | 2 | no | — |
| 319 | #125 | — | 2 | 2 | no | — |
| 320 | #125 | — | 4 | 2 | no | — |
| 321 | #125 | — | 4 | 4 | no | — |
| 322 | #125 | — | 4 | 4 | no | — |
| 323 | #125 | — | 4 | 4 | no | — |
| 324 | #125 | — | 4 | 2 | no | — |
| 325 | #125 | — | 4 | 4 | no | — |
| 326 | C22⋊Q8 | — | 2 | 2 | no | — |
| 327 | C22⋊Q8 | — | 2 | 2 | no | — |
| 328 | C22⋊Q8 | — | 2 | 2 | no | — |
| 329 | C22⋊Q8 | — | 2 | 4 | no | — |
| 330 | C22⋊Q8 | — | 4 | 4 | no | — |
| 331 | C22⋊Q8 | — | 4 | 4 | no | — |
| 332 | C22⋊Q8 | — | 4 | 4 | no | — |
| 333 | C22⋊Q8 | — | 4 | 4 | no | — |
| 334 | C22⋊Q8 | — | 4 | 2 | no | — |
| 335 | C22⋊Q8 | C2×D4 | 1 | 4 | yes | — |
| 336 | C4×Q8 | — | 2 | 1 | no | — |
| 337 | C4×Q8 | — | 2 | 2 | no | — |
| 338 | C4×Q8 | — | 2 | 1 | no | — |
| 339 | C4×Q8 | — | 2 | 4 | no | — |
| 340 | C4×Q8 | — | 2 | 4 | no | — |
| 341 | C4×Q8 | — | 2 | 4 | no | — |
| 342 | C4×Q8 | — | 2 | 4 | no | — |
| 343 | C4×Q8 | — | 2 | 4 | no | — |
| 344 | C4×Q8 | — | 2 | 4 | no | — |
| 345 | C4×Q8 | — | 2 | 2 | no | — |
| 346 | C4×Q8 | — | 2 | 2 | no | — |
| 347 | C4×Q8 | — | 4 | 4 | no | — |
| 348 | C4×Q8 | — | 4 | 2 | no | — |
| 349 | C4×Q8 | — | 4 | 2 | no | — |
| 350 | C4×Q8 | — | 4 | 2 | no | — |
| 351 | C4×Q8 | C2×D4 | 1 | 2 | yes | — |
| 352 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 353 | C4×Q8 | C24 | 1 | 2 | yes | — |
| 354 | C4×Q8 | C24 | 1 | 1 | yes | characteristic |
| 355 | C4×Q8 | C24 | 1 | 4 | yes | — |
| 356 | C4×D4 | — | 2 | 1 | no | — |
| 357 | C4×D4 | — | 2 | 1 | no | — |
| 358 | C4×D4 | — | 2 | 4 | no | — |
| 359 | C4×D4 | — | 4 | 4 | no | — |
| 360 | C4×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 361 | C4×D4 | C24 | 1 | 1 | yes | characteristic |
| 362 | #117 | — | 2 | 2 | no | — |
| 363 | #117 | — | 2 | 1 | no | — |
| 364 | #117 | — | 2 | 2 | no | — |
| 365 | #117 | — | 4 | 4 | no | — |
| 366 | #117 | — | 4 | 2 | no | — |
| 367 | #117 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 369 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 370 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 371 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 372 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 373 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C42 | — | 2 | 1 | no | — |
| 375 | C2×C42 | — | 2 | 1 | no | — |
| 376 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 377 | #107 | — | 2 | 4 | no | — |
| 378 | #107 | — | 2 | 4 | no | — |
| 379 | #107 | — | 2 | 1 | no | — |
| 380 | #107 | — | 2 | 1 | no | — |
| 381 | #107 | — | 2 | 2 | no | — |
| 382 | #107 | — | 2 | 2 | no | — |
| 383 | #107 | — | 2 | 4 | no | — |
| 384 | #107 | — | 4 | 4 | no | — |
| 385 | #107 | C2×D4 | 1 | 2 | yes | — |
| 386 | #107 | C2×D4 | 1 | 2 | yes | — |
| 387 | #107 | C2×D4 | 1 | 2 | yes | — |
| 388 | #106 | — | 2 | 4 | no | — |
| 389 | #106 | — | 2 | 4 | no | — |
| 390 | #106 | — | 2 | 4 | no | — |
| 391 | #106 | — | 2 | 4 | no | — |
| 392 | #106 | — | 2 | 2 | no | — |
| 393 | #106 | — | 2 | 2 | no | — |
| 394 | #106 | C2×D4 | 1 | 2 | yes | — |
| 395 | C4⋊C8 | — | 2 | 2 | no | — |
| 396 | C4⋊C8 | — | 2 | 2 | no | — |
| 397 | C4⋊C8 | — | 2 | 4 | no | — |
| 398 | C4⋊C8 | — | 2 | 4 | no | — |
| 399 | C4⋊C8 | — | 2 | 1 | no | — |
| 400 | C4⋊C8 | — | 2 | 1 | no | — |
| 401 | C4⋊C8 | — | 2 | 1 | no | — |
| 402 | C4⋊C8 | — | 2 | 2 | no | — |
| 403 | C4⋊C8 | — | 2 | 1 | no | — |
| 404 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 405 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 406 | C4⋊C8 | C24 | 1 | 2 | yes | — |
| 407 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 408 | C4⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 409 | #103 | — | 2 | 4 | no | — |
| 410 | #103 | — | 2 | 4 | no | — |
| 411 | #103 | — | 2 | 2 | no | — |
| 412 | #103 | — | 2 | 2 | no | — |
| 413 | #103 | — | 2 | 4 | no | — |
| 414 | #103 | — | 2 | 2 | no | — |
| 415 | #103 | — | 2 | 2 | no | — |
| 416 | #103 | — | 2 | 4 | no | — |
| 417 | #103 | — | 2 | 4 | no | — |
| 418 | #103 | — | 2 | 4 | no | — |
| 419 | #103 | — | 4 | 4 | no | — |
| 420 | #103 | C2×D4 | 1 | 2 | yes | — |
| 421 | #103 | C2×D4 | 1 | 2 | yes | — |
| 422 | #103 | C2×D4 | 1 | 2 | yes | — |
| 423 | #103 | C2×D4 | 1 | 4 | yes | — |
| 424 | #103 | C2×D4 | 1 | 4 | yes | — |
| 425 | #102 | — | 2 | 2 | no | — |
| 426 | #102 | — | 2 | 2 | no | — |
| 427 | #102 | C2×D4 | 1 | 2 | yes | — |
| 428 | C22⋊C8 | — | 2 | 1 | no | — |
| 429 | C22⋊C8 | — | 2 | 1 | no | — |
| 430 | C22⋊C8 | — | 2 | 1 | no | — |
| 431 | C22⋊C8 | — | 2 | 1 | no | — |
| 432 | #97 | — | 2 | 4 | no | — |
| 433 | #97 | C2×D4 | 1 | 2 | yes | — |
| 434 | C4×C8 | — | 2 | 1 | no | — |
| 435 | C4×C8 | — | 2 | 1 | no | — |
| 436 | C4×C8 | — | 2 | 2 | no | — |
| 437 | C4×C8 | — | 2 | 2 | no | — |
| 438 | C4×C8 | — | 2 | 4 | no | — |
| 439 | C4×C8 | — | 2 | 1 | no | — |
| 440 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 441 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 442 | C4×C8 | C24 | 1 | 2 | yes | — |
| 443 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 444 | C4×C8 | C24 | 1 | 2 | yes | — |
| 445 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 446 | #41 | — | 2 | 2 | no | — |
| 447 | #41 | C2×Q16 | 1 | 4 | yes | — |
| 448 | C2×Q8 | — | 2 | 1 | no | — |
| 449 | C2×Q8 | — | 2 | 2 | no | — |
| 450 | C2×Q8 | — | 2 | 2 | no | — |
| 451 | C2×Q8 | — | 2 | 2 | no | — |
| 452 | C2×Q8 | — | 2 | 4 | no | — |
| 453 | C2×Q8 | — | 2 | 2 | no | — |
| 454 | C2×Q8 | — | 4 | 4 | no | — |
| 455 | C2×Q8 | — | 4 | 4 | no | — |
| 456 | C2×Q8 | — | 4 | 2 | no | — |
| 457 | C2×Q8 | — | 8 | 2 | no | — |
| 458 | C2×Q8 | — | 8 | 2 | no | — |
| 459 | C2×Q8 | — | 8 | 4 | no | — |
| 460 | C2×Q8 | — | 8 | 4 | no | — |
| 461 | C2×Q8 | C2×Q16 | 1 | 4 | yes | complemented |
| 462 | C2×Q8 | C22×D4 | 1 | 4 | yes | — |
| 463 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 464 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×D4 | — | 2 | 1 | no | — |
| 466 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 467 | C22×C4 | — | 2 | 1 | no | — |
| 468 | C22×C4 | — | 2 | 1 | no | — |
| 469 | C22×C4 | — | 2 | 1 | no | — |
| 470 | C22×C4 | — | 2 | 1 | no | — |
| 471 | C22×C4 | — | 2 | 1 | no | — |
| 472 | C22×C4 | — | 4 | 4 | no | — |
| 473 | C22×C4 | — | 4 | 2 | no | — |
| 474 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 475 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 476 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 477 | Q16 | — | 2 | 4 | no | — |
| 478 | Q16 | — | 4 | 2 | no | — |
| 479 | Q16 | — | 4 | 4 | no | — |
| 480 | Q16 | — | 4 | 2 | no | — |
| 481 | Q16 | — | 4 | 4 | no | — |
| 482 | Q16 | — | 8 | 1 | no | — |
| 483 | Q16 | — | 8 | 2 | no | — |
| 484 | Q16 | — | 8 | 2 | no | — |
| 485 | Q16 | — | 8 | 4 | no | — |
| 486 | Q16 | — | 8 | 4 | no | — |
| 487 | Q16 | — | 8 | 4 | no | — |
| 488 | Q16 | C2×Q16 | 1 | 8 | yes | complemented |
| 489 | SD16 | C2×Q16 | 1 | 8 | yes | complemented |
| 490 | M16 | — | 2 | 2 | no | — |
| 491 | M16 | C2×Q16 | 1 | 4 | yes | complemented |
| 492 | C2×C8 | — | 2 | 2 | no | — |
| 493 | C2×C8 | — | 2 | 1 | no | — |
| 494 | C2×C8 | — | 2 | 1 | no | — |
| 495 | C2×C8 | — | 2 | 2 | no | — |
| 496 | C2×C8 | — | 2 | 2 | no | — |
| 497 | C2×C8 | — | 2 | 2 | no | — |
| 498 | C2×C8 | — | 2 | 2 | no | — |
| 499 | C2×C8 | — | 4 | 1 | no | — |
| 500 | C2×C8 | — | 4 | 2 | no | — |
| 501 | C2×C8 | — | 4 | 4 | no | — |
| 502 | C2×C8 | — | 4 | 2 | no | — |
| 503 | C2×C8 | — | 8 | 1 | no | — |
| 504 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 505 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 506 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 507 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 508 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 509 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 510 | C4⋊C4 | — | 2 | 2 | no | — |
| 511 | C4⋊C4 | — | 2 | 2 | no | — |
| 512 | C4⋊C4 | — | 2 | 2 | no | — |
| 513 | C4⋊C4 | — | 2 | 1 | no | — |
| 514 | C4⋊C4 | — | 2 | 2 | no | — |
| 515 | C4⋊C4 | — | 2 | 1 | no | — |
| 516 | C4⋊C4 | — | 2 | 4 | no | — |
| 517 | C4⋊C4 | — | 2 | 2 | no | — |
| 518 | C4⋊C4 | — | 2 | 1 | no | — |
| 519 | C4⋊C4 | — | 2 | 4 | no | — |
| 520 | C4⋊C4 | — | 2 | 2 | no | — |
| 521 | C4⋊C4 | — | 2 | 2 | no | — |
| 522 | C4⋊C4 | — | 2 | 2 | no | — |
| 523 | C4⋊C4 | — | 2 | 4 | no | — |
| 524 | C4⋊C4 | — | 2 | 4 | no | — |
| 525 | C4⋊C4 | — | 2 | 2 | no | — |
| 526 | C4⋊C4 | — | 4 | 4 | no | — |
| 527 | C4⋊C4 | — | 4 | 4 | no | — |
| 528 | C4⋊C4 | — | 4 | 4 | no | — |
| 529 | C4⋊C4 | — | 4 | 4 | no | — |
| 530 | C4⋊C4 | — | 4 | 4 | no | — |
| 531 | C4⋊C4 | — | 4 | 4 | no | — |
| 532 | C4⋊C4 | — | 4 | 4 | no | — |
| 533 | C4⋊C4 | — | 4 | 4 | no | — |
| 534 | C4⋊C4 | — | 4 | 4 | no | — |
| 535 | C4⋊C4 | — | 4 | 2 | no | — |
| 536 | C4⋊C4 | — | 4 | 2 | no | — |
| 537 | C4⋊C4 | — | 4 | 2 | no | — |
| 538 | C4⋊C4 | — | 4 | 2 | no | — |
| 539 | C4⋊C4 | C22×D4 | 1 | 2 | yes | — |
| 540 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 541 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 542 | C4⋊C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 543 | C22⋊C4 | — | 2 | 4 | no | — |
| 544 | C22⋊C4 | — | 2 | 1 | no | — |
| 545 | C22⋊C4 | — | 2 | 1 | no | — |
| 546 | C22⋊C4 | — | 2 | 1 | no | — |
| 547 | C22⋊C4 | — | 4 | 4 | no | — |
| 548 | C22⋊C4 | — | 4 | 2 | no | — |
| 549 | C42 | — | 2 | 1 | no | — |
| 550 | C42 | — | 2 | 1 | no | — |
| 551 | C42 | — | 2 | 2 | no | — |
| 552 | C42 | — | 2 | 1 | no | — |
| 553 | C42 | — | 2 | 2 | no | — |
| 554 | C42 | — | 2 | 4 | no | — |
| 555 | C42 | — | 4 | 4 | no | — |
| 556 | C42 | — | 4 | 4 | no | — |
| 557 | C42 | — | 4 | 4 | no | — |
| 558 | C42 | — | 4 | 2 | no | — |
| 559 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 560 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 561 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 562 | C42 | C25 | 1 | 1 | yes | characteristic |
| 563 | C23 | — | 2 | 1 | no | — |
| 564 | C23 | D42 | 1 | 1 | yes | characteristic |
| 565 | Q8 | — | 2 | 4 | no | — |
| 566 | Q8 | — | 2 | 2 | no | — |
| 567 | Q8 | — | 2 | 1 | no | — |
| 568 | Q8 | — | 2 | 4 | no | — |
| 569 | Q8 | — | 2 | 4 | no | — |
| 570 | Q8 | — | 4 | 4 | no | — |
| 571 | Q8 | — | 4 | 2 | no | — |
| 572 | Q8 | — | 4 | 4 | no | — |
| 573 | Q8 | — | 4 | 2 | no | — |
| 574 | Q8 | — | 8 | 2 | no | — |
| 575 | Q8 | — | 8 | 2 | no | — |
| 576 | Q8 | — | 16 | 2 | no | — |
| 577 | Q8 | — | 16 | 4 | no | — |
| 578 | Q8 | — | 16 | 4 | no | — |
| 579 | Q8 | C22×Q16 | 1 | 4 | yes | — |
| 580 | Q8 | C22×Q16 | 1 | 2 | yes | — |
| 581 | D4 | — | 2 | 4 | no | — |
| 582 | D4 | — | 2 | 1 | no | — |
| 583 | D4 | C22×Q16 | 1 | 2 | yes | — |
| 584 | C2×C4 | — | 2 | 1 | no | — |
| 585 | C2×C4 | — | 2 | 2 | no | — |
| 586 | C2×C4 | — | 2 | 4 | no | — |
| 587 | C2×C4 | — | 2 | 1 | no | — |
| 588 | C2×C4 | — | 2 | 4 | no | — |
| 589 | C2×C4 | — | 2 | 1 | no | — |
| 590 | C2×C4 | — | 2 | 1 | no | — |
| 591 | C2×C4 | — | 2 | 1 | no | — |
| 592 | C2×C4 | — | 2 | 2 | no | — |
| 593 | C2×C4 | — | 2 | 4 | no | — |
| 594 | C2×C4 | — | 2 | 4 | no | — |
| 595 | C2×C4 | — | 4 | 1 | no | — |
| 596 | C2×C4 | — | 4 | 2 | no | — |
| 597 | C2×C4 | — | 4 | 1 | no | — |
| 598 | C2×C4 | — | 4 | 1 | no | — |
| 599 | C2×C4 | — | 4 | 2 | no | — |
| 600 | C2×C4 | — | 4 | 2 | no | — |
| 601 | C2×C4 | — | 4 | 4 | no | — |
| 602 | C2×C4 | — | 8 | 1 | no | — |
| 603 | C2×C4 | — | 16 | 4 | no | — |
| 604 | C2×C4 | — | 16 | 2 | no | — |
| 605 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 606 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 608 | C2×C4 | C22×Q16 | 1 | 2 | yes | — |
| 609 | C2×C4 | #578 | 1 | 2 | yes | — |
| 610 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 611 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 612 | C2×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 613 | C8 | — | 2 | 1 | no | — |
| 614 | C8 | — | 2 | 1 | no | — |
| 615 | C8 | — | 2 | 1 | no | — |
| 616 | C8 | — | 2 | 2 | no | — |
| 617 | C8 | — | 4 | 2 | no | — |
| 618 | C8 | — | 4 | 1 | no | — |
| 619 | C8 | — | 4 | 2 | no | — |
| 620 | C8 | — | 4 | 1 | no | — |
| 621 | C8 | — | 4 | 2 | no | — |
| 622 | C8 | — | 4 | 2 | no | — |
| 623 | C8 | C22×Q16 | 1 | 4 | yes | — |
| 624 | C8 | #577 | 1 | 2 | yes | — |
| 625 | C22 | — | 2 | 1 | no | — |
| 626 | C22 | — | 2 | 1 | no | — |
| 627 | C22 | — | 2 | 2 | no | — |
| 628 | C22 | — | 4 | 1 | no | — |
| 629 | C22 | — | 4 | 1 | no | — |
| 630 | C22 | D4×Q16 | 1 | 2 | yes | — |
| 631 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 632 | C4 | — | 2 | 2 | no | — |
| 633 | C4 | — | 2 | 4 | no | — |
| 634 | C4 | — | 2 | 1 | no | — |
| 635 | C4 | — | 2 | 1 | no | — |
| 636 | C4 | — | 2 | 1 | no | — |
| 637 | C4 | — | 4 | 1 | no | — |
| 638 | C4 | — | 4 | 4 | no | — |
| 639 | C4 | — | 4 | 1 | no | — |
| 640 | C4 | — | 4 | 2 | no | — |
| 641 | C4 | — | 4 | 4 | no | — |
| 642 | C4 | — | 8 | 4 | no | — |
| 643 | C4 | — | 8 | 2 | no | — |
| 644 | C4 | — | 8 | 2 | no | — |
| 645 | C4 | D4×Q16 | 1 | 2 | yes | — |
| 646 | C4 | C23×Q16 | 1 | 1 | yes | characteristic |
| 647 | C4 | C2×#577 | 1 | 1 | yes | characteristic |
| 648 | C4 | C2×#578 | 1 | 1 | yes | characteristic |
| 649 | C4 | #3585 | 1 | 1 | yes | characteristic |
| 650 | C2 | — | 2 | 2 | no | — |
| 651 | C2 | — | 4 | 2 | no | — |
| 652 | C2 | C2×D4×Q16 | 1 | 1 | yes | characteristic |
| 653 | C2 | #61095 | 1 | 1 | yes | characteristic |
| 654 | C2 | #61108 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C42 | C25 |
| prime radical | C2×#41 | C2×D4 |
| 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 |
|---|---|---|
| 2. #62360 | C2 | semidirect |
| 4. #20010 | C2 | semidirect |
| 5. SD16×Q16 | C2 | semidirect |
| 6. #19932 | C2 | semidirect |
| 7. #19928 | C2 | semidirect |
| 8. #19818 | C2 | semidirect |
| 9. #19812 | C2 | semidirect |
| 10. #19632 | C2 | semidirect |
| 11. #19240 | C2 | semidirect |
| 13. C2×#1670 | C2 | semidirect |
| 14. #18925 | C2 | semidirect |
| 16. #18068 | C2 | semidirect |
| 271. #137 | Q16 | semidirect |
| 461. C2×Q8 | C2×Q16 | semidirect |
| 488. Q16 | C2×Q16 | semidirect |
| 489. SD16 | C2×Q16 | semidirect |
| 491. M16 | C2×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #62416 | 2 |
| #62360 | 2 |
| #61383 | 2 |
| #20010 | 2 |
| SD16×Q16 | 2 |
| #19932 | 2 |
| #19928 | 2 |
| #19818 | 2 |
| #19812 | 2 |
| #19632 | 2 |
| #19240 | 2 |
| #19126 | 2 |
| C2×#1670 | 2 |
| #18925 | 2 |
| #18885 | 2 |
| #18068 | 2 |
| C8×#137 | 2 |