Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1049 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 1049 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6365636 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #153539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #153469 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #153462 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #152616 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #152603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #139431 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #61891 | — | 2 | 1 | no | — |
| 9 | #61682 | — | 2 | 1 | no | — |
| 10 | #23361 | C22 | 1 | 1 | yes | characteristic |
| 11 | #20310 | — | 2 | 1 | no | — |
| 12 | #20294 | C4 | 1 | 2 | yes | complemented |
| 13 | #20260 | — | 2 | 2 | no | — |
| 14 | #20192 | — | 2 | 2 | no | — |
| 15 | #20138 | C4 | 1 | 2 | yes | complemented |
| 16 | #20067 | — | 2 | 1 | no | — |
| 17 | #19727 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19506 | — | 2 | 1 | no | — |
| 19 | #19437 | — | 2 | 1 | no | — |
| 20 | #18714 | C22 | 1 | 1 | yes | characteristic |
| 21 | #18610 | — | 2 | 1 | no | — |
| 22 | #18526 | C22 | 1 | 1 | yes | characteristic |
| 23 | #17951 | — | 2 | 1 | no | — |
| 24 | #13585 | C22 | 1 | 1 | yes | characteristic |
| 25 | #13584 | C22 | 1 | 1 | yes | characteristic |
| 26 | #12778 | — | 2 | 1 | no | — |
| 27 | #12760 | — | 2 | 1 | no | — |
| 28 | #11992 | C22 | 1 | 1 | yes | characteristic |
| 29 | #11837 | — | 2 | 1 | no | — |
| 30 | #7533 | — | 2 | 1 | no | — |
| 31 | #7529 | — | 2 | 1 | no | — |
| 32 | #7519 | — | 2 | 2 | no | — |
| 33 | #7516 | — | 2 | 2 | no | — |
| 34 | #7493 | — | 2 | 1 | no | — |
| 35 | #7490 | — | 2 | 1 | no | — |
| 36 | #7226 | — | 2 | 1 | no | — |
| 37 | #3549 | D4 | 1 | 1 | yes | characteristic |
| 38 | #3497 | — | 2 | 1 | no | — |
| 39 | C2×#559 | D4 | 1 | 1 | yes | characteristic |
| 40 | #3399 | — | 2 | 2 | no | — |
| 41 | #3399 | — | 2 | 2 | no | — |
| 42 | #3399 | — | 4 | 2 | no | — |
| 43 | #3373 | — | 2 | 2 | no | — |
| 44 | #3373 | — | 2 | 2 | no | — |
| 45 | #3373 | — | 4 | 2 | no | — |
| 46 | #3329 | — | 2 | 2 | no | — |
| 47 | #3321 | — | 4 | 2 | no | — |
| 48 | #3305 | — | 2 | 2 | no | — |
| 49 | D4×SD16 | — | 2 | 2 | no | — |
| 50 | #3274 | — | 2 | 2 | no | — |
| 51 | #3265 | — | 4 | 2 | no | — |
| 52 | #3214 | — | 2 | 1 | no | — |
| 53 | #3213 | — | 4 | 2 | no | — |
| 54 | #3207 | — | 2 | 1 | no | — |
| 55 | #3205 | — | 2 | 1 | no | — |
| 56 | #3205 | — | 2 | 1 | no | — |
| 57 | #3198 | — | 4 | 2 | no | — |
| 58 | #3184 | D4 | 1 | 1 | yes | characteristic |
| 59 | #3151 | C23 | 1 | 1 | yes | characteristic |
| 60 | #3112 | — | 2 | 1 | no | — |
| 61 | #3109 | — | 4 | 2 | no | — |
| 62 | #3103 | — | 2 | 1 | no | — |
| 63 | #3103 | — | 2 | 1 | no | — |
| 64 | #3010 | — | 4 | 2 | no | — |
| 65 | #2983 | — | 2 | 1 | no | — |
| 66 | #2981 | — | 2 | 1 | no | — |
| 67 | #2165 | — | 2 | 1 | no | — |
| 68 | #2128 | — | 4 | 1 | no | — |
| 69 | #2126 | — | 2 | 1 | no | — |
| 70 | C2×#353 | — | 2 | 1 | no | — |
| 71 | C2×#352 | — | 4 | 1 | no | — |
| 72 | #1910 | — | 4 | 1 | no | — |
| 73 | #1904 | — | 4 | 1 | no | — |
| 74 | #1903 | — | 4 | 1 | no | — |
| 75 | #1890 | — | 4 | 1 | no | — |
| 76 | #1887 | — | 2 | 1 | no | — |
| 77 | #1884 | — | 2 | 1 | no | — |
| 78 | #1841 | — | 2 | 1 | no | — |
| 79 | #1721 | — | 2 | 1 | no | — |
| 80 | #1721 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #1717 | — | 2 | 1 | no | — |
| 82 | #1715 | D4 | 1 | 1 | yes | characteristic |
| 83 | #1712 | D4 | 1 | 1 | yes | characteristic |
| 84 | #1708 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #1704 | — | 2 | 2 | no | — |
| 86 | #1701 | — | 2 | 2 | no | — |
| 87 | #1698 | — | 2 | 2 | no | — |
| 88 | #1688 | — | 2 | 2 | no | — |
| 89 | #1687 | — | 2 | 2 | no | — |
| 90 | #1686 | — | 2 | 2 | no | — |
| 91 | #1681 | — | 2 | 2 | no | — |
| 92 | #1667 | — | 2 | 2 | no | — |
| 93 | #1651 | — | 2 | 2 | no | — |
| 94 | #1642 | — | 2 | 2 | no | — |
| 95 | #1630 | — | 2 | 1 | no | — |
| 96 | #1630 | C2×C4 | 1 | 2 | yes | — |
| 97 | #1627 | — | 2 | 2 | no | — |
| 98 | #1624 | C2×C4 | 1 | 2 | yes | — |
| 99 | #1624 | D4 | 1 | 2 | yes | — |
| 100 | #1621 | — | 2 | 2 | no | — |
| 101 | #1620 | — | 2 | 1 | no | — |
| 102 | #1620 | D4 | 1 | 2 | yes | — |
| 103 | #1619 | — | 2 | 1 | no | — |
| 104 | #1619 | — | 2 | 1 | no | — |
| 105 | #1592 | — | 2 | 2 | no | — |
| 106 | #1590 | — | 2 | 2 | no | — |
| 107 | #1585 | — | 2 | 2 | no | — |
| 108 | #1582 | — | 2 | 2 | no | — |
| 109 | #1572 | — | 2 | 1 | no | — |
| 110 | #1555 | D4 | 1 | 1 | yes | characteristic |
| 111 | #1553 | — | 2 | 1 | no | — |
| 112 | #1543 | D4 | 1 | 1 | yes | characteristic |
| 113 | #1491 | — | 2 | 1 | no | — |
| 114 | #1484 | — | 2 | 1 | no | — |
| 115 | #1453 | D4 | 1 | 1 | yes | characteristic |
| 116 | #1409 | — | 2 | 1 | no | — |
| 117 | #1408 | — | 2 | 1 | no | — |
| 118 | #1408 | — | 2 | 1 | no | — |
| 119 | #1408 | — | 2 | 1 | no | — |
| 120 | #1359 | — | 2 | 1 | no | — |
| 121 | #1357 | — | 2 | 1 | no | — |
| 122 | #1341 | — | 4 | 1 | no | — |
| 123 | #1339 | — | 4 | 1 | no | — |
| 124 | C2×2−1+4 | — | 4 | 1 | no | — |
| 125 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 126 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 127 | C22×SD16 | — | 4 | 2 | no | — |
| 128 | #568 | — | 2 | 1 | no | — |
| 129 | H(3,𝔽4) | — | 4 | 1 | no | — |
| 130 | #559 | — | 2 | 1 | no | — |
| 131 | #559 | — | 4 | 2 | no | — |
| 132 | #559 | — | 4 | 1 | no | — |
| 133 | #559 | C22⋊C4 | 1 | 2 | yes | — |
| 134 | #555 | — | 4 | 1 | no | — |
| 135 | #555 | C22⋊C4 | 1 | 2 | yes | — |
| 136 | #550 | — | 2 | 2 | no | — |
| 137 | #550 | — | 4 | 1 | no | — |
| 138 | D4×Q8 | — | 2 | 2 | no | — |
| 139 | D4×Q8 | — | 4 | 1 | no | — |
| 140 | #548 | — | 4 | 2 | no | — |
| 141 | #548 | — | 8 | 1 | no | — |
| 142 | D42 | — | 2 | 1 | no | — |
| 143 | D42 | — | 4 | 1 | no | — |
| 144 | #537 | — | 4 | 1 | no | — |
| 145 | #537 | — | 8 | 1 | no | — |
| 146 | #535 | — | 4 | 2 | no | — |
| 147 | #535 | — | 4 | 1 | no | — |
| 148 | #532 | — | 2 | 1 | no | — |
| 149 | #532 | — | 2 | 1 | no | — |
| 150 | #532 | — | 4 | 2 | no | — |
| 151 | #532 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×#127 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×#124 | — | 4 | 1 | no | — |
| 154 | C2×#123 | — | 4 | 1 | no | — |
| 155 | #518 | — | 2 | 1 | no | — |
| 156 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 157 | C2×C4×D4 | — | 4 | 1 | no | — |
| 158 | #498 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 159 | #496 | — | 4 | 1 | no | — |
| 160 | #496 | — | 4 | 1 | no | — |
| 161 | #496 | — | 4 | 2 | no | — |
| 162 | #496 | — | 4 | 2 | no | — |
| 163 | #493 | — | 2 | 1 | no | — |
| 164 | #493 | — | 2 | 1 | no | — |
| 165 | #493 | — | 2 | 1 | no | — |
| 166 | #493 | — | 4 | 1 | no | — |
| 167 | #493 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 168 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | #493 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | #492 | — | 2 | 1 | no | — |
| 171 | #492 | C22×C4 | 1 | 1 | yes | characteristic |
| 172 | #492 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | #489 | — | 4 | 2 | no | — |
| 174 | #489 | — | 4 | 2 | no | — |
| 175 | #489 | — | 4 | 1 | no | — |
| 176 | #487 | — | 2 | 1 | no | — |
| 177 | #486 | — | 2 | 1 | no | — |
| 178 | #486 | — | 2 | 1 | no | — |
| 179 | #486 | — | 2 | 1 | no | — |
| 180 | #486 | — | 2 | 1 | no | — |
| 181 | #486 | — | 4 | 1 | no | — |
| 182 | #485 | — | 4 | 2 | no | — |
| 183 | #482 | — | 4 | 2 | no | — |
| 184 | #481 | — | 2 | 2 | no | — |
| 185 | #481 | — | 4 | 1 | no | — |
| 186 | #480 | — | 4 | 1 | no | — |
| 187 | #477 | — | 2 | 2 | no | — |
| 188 | #476 | — | 4 | 2 | no | — |
| 189 | #476 | — | 4 | 2 | no | — |
| 190 | #475 | — | 2 | 2 | no | — |
| 191 | #475 | — | 2 | 2 | no | — |
| 192 | #469 | — | 4 | 2 | no | — |
| 193 | #469 | — | 4 | 1 | no | — |
| 194 | #468 | — | 4 | 2 | no | — |
| 195 | #466 | — | 4 | 2 | no | — |
| 196 | #465 | — | 4 | 2 | no | — |
| 197 | #463 | — | 4 | 2 | no | — |
| 198 | #463 | — | 4 | 2 | no | — |
| 199 | #463 | — | 4 | 2 | no | — |
| 200 | #463 | — | 4 | 2 | no | — |
| 201 | #463 | — | 4 | 2 | no | — |
| 202 | #461 | — | 2 | 2 | no | — |
| 203 | #460 | — | 2 | 2 | no | — |
| 204 | #460 | — | 2 | 2 | no | — |
| 205 | #460 | — | 2 | 2 | no | — |
| 206 | #459 | — | 2 | 2 | no | — |
| 207 | #459 | — | 2 | 2 | no | — |
| 208 | #459 | — | 2 | 2 | no | — |
| 209 | #459 | — | 4 | 2 | no | — |
| 210 | #459 | — | 4 | 2 | no | — |
| 211 | #459 | — | 4 | 2 | no | — |
| 212 | #450 | — | 4 | 2 | no | — |
| 213 | #449 | — | 4 | 2 | no | — |
| 214 | #449 | — | 4 | 2 | no | — |
| 215 | #449 | — | 4 | 2 | no | — |
| 216 | #449 | — | 4 | 2 | no | — |
| 217 | #448 | — | 2 | 2 | no | — |
| 218 | #448 | — | 4 | 2 | no | — |
| 219 | #448 | — | 4 | 2 | no | — |
| 220 | #448 | — | 4 | 1 | no | — |
| 221 | #448 | — | 4 | 1 | no | — |
| 222 | #447 | — | 4 | 2 | no | — |
| 223 | #447 | — | 4 | 2 | no | — |
| 224 | #447 | — | 4 | 2 | no | — |
| 225 | #446 | — | 2 | 2 | no | — |
| 226 | #446 | — | 2 | 2 | no | — |
| 227 | #446 | — | 4 | 2 | no | — |
| 228 | #442 | — | 4 | 1 | no | — |
| 229 | #442 | — | 4 | 2 | no | — |
| 230 | #442 | — | 4 | 2 | no | — |
| 231 | #442 | — | 4 | 2 | no | — |
| 232 | #442 | — | 4 | 2 | no | — |
| 233 | #440 | — | 4 | 2 | no | — |
| 234 | C4×SD16 | — | 2 | 2 | no | — |
| 235 | C4×SD16 | — | 2 | 2 | no | — |
| 236 | C4×SD16 | — | 4 | 2 | no | — |
| 237 | #436 | — | 2 | 2 | no | — |
| 238 | #435 | — | 4 | 2 | no | — |
| 239 | C8×D4 | — | 2 | 2 | no | — |
| 240 | #432 | — | 2 | 1 | no | — |
| 241 | #432 | — | 4 | 2 | no | — |
| 242 | #431 | — | 2 | 1 | no | — |
| 243 | #431 | — | 2 | 1 | no | — |
| 244 | #421 | — | 4 | 1 | no | — |
| 245 | #419 | — | 4 | 2 | no | — |
| 246 | #418 | — | 4 | 1 | no | — |
| 247 | #418 | — | 8 | 1 | no | — |
| 248 | #416 | — | 4 | 2 | no | — |
| 249 | C2×#100 | — | 2 | 1 | no | — |
| 250 | #410 | — | 2 | 1 | no | — |
| 251 | #410 | — | 4 | 1 | no | — |
| 252 | C2×#99 | — | 4 | 1 | no | — |
| 253 | #408 | — | 4 | 2 | no | — |
| 254 | C4×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | #381 | — | 8 | 1 | no | — |
| 256 | #364 | — | 4 | 1 | no | — |
| 257 | #354 | — | 4 | 1 | no | — |
| 258 | #353 | — | 4 | 1 | no | — |
| 259 | #353 | — | 4 | 1 | no | — |
| 260 | #353 | — | 4 | 1 | no | — |
| 261 | #353 | — | 8 | 2 | no | — |
| 262 | #352 | — | 8 | 2 | no | — |
| 263 | #349 | — | 4 | 1 | no | — |
| 264 | #347 | — | 4 | 1 | no | — |
| 265 | #344 | — | 4 | 1 | no | — |
| 266 | #342 | — | 8 | 1 | no | — |
| 267 | #339 | — | 4 | 1 | no | — |
| 268 | #338 | — | 2 | 1 | no | — |
| 269 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 270 | H(3,ℤ/4) | — | 8 | 1 | no | — |
| 271 | #335 | — | 2 | 2 | no | — |
| 272 | #334 | — | 2 | 2 | no | — |
| 273 | #333 | C22⋊C4 | 1 | 2 | yes | — |
| 274 | #332 | — | 2 | 2 | no | — |
| 275 | #331 | — | 2 | 2 | no | — |
| 276 | #331 | — | 2 | 1 | no | — |
| 277 | #331 | — | 2 | 1 | no | — |
| 278 | #331 | C22⋊C4 | 1 | 2 | yes | — |
| 279 | Q8⋊C8 | — | 2 | 2 | no | — |
| 280 | Q8⋊C8 | — | 2 | 2 | no | — |
| 281 | D4⋊C8 | — | 2 | 2 | no | — |
| 282 | D4⋊C8 | — | 2 | 2 | no | — |
| 283 | #322 | — | 2 | 1 | no | — |
| 284 | #322 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 285 | C82 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 286 | 2−1+4 | — | 16 | 4 | no | — |
| 287 | C2×#41 | — | 2 | 1 | no | — |
| 288 | C2×#41 | — | 4 | 1 | no | — |
| 289 | C2×#41 | — | 4 | 1 | no | — |
| 290 | C2×#41 | — | 4 | 2 | no | — |
| 291 | C2×#41 | — | 8 | 2 | no | — |
| 292 | C2×#41 | — | 8 | 1 | no | — |
| 293 | C22×Q8 | — | 2 | 1 | no | — |
| 294 | C22×Q8 | — | 4 | 2 | no | — |
| 295 | C22×Q8 | — | 8 | 1 | no | — |
| 296 | C22×D4 | — | 2 | 1 | no | — |
| 297 | C22×D4 | — | 4 | 1 | no | — |
| 298 | C22×D4 | — | 4 | 2 | no | — |
| 299 | C22×D4 | — | 4 | 1 | no | — |
| 300 | C23×C4 | — | 4 | 1 | no | — |
| 301 | AGL(1,ℤ/8) | — | 16 | 1 | no | — |
| 302 | AGL(1,ℤ/8) | — | 16 | 1 | no | — |
| 303 | AGL(1,ℤ/8) | — | 16 | 4 | no | — |
| 304 | C2×SD16 | — | 2 | 2 | no | — |
| 305 | C2×SD16 | — | 2 | 2 | no | — |
| 306 | C2×SD16 | — | 4 | 1 | no | — |
| 307 | C2×SD16 | — | 4 | 1 | no | — |
| 308 | C2×SD16 | — | 4 | 2 | no | — |
| 309 | C2×SD16 | — | 4 | 2 | no | — |
| 310 | C2×SD16 | — | 4 | 2 | no | — |
| 311 | C2×SD16 | — | 4 | 2 | no | — |
| 312 | C2×SD16 | — | 16 | 4 | no | — |
| 313 | C2×D8 | — | 4 | 1 | no | — |
| 314 | C2×D8 | — | 4 | 1 | no | — |
| 315 | C2×D8 | — | 4 | 1 | no | — |
| 316 | C2×D8 | — | 4 | 2 | no | — |
| 317 | C2×D8 | — | 4 | 2 | no | — |
| 318 | C2×D8 | — | 4 | 2 | no | — |
| 319 | C2×D8 | — | 4 | 2 | no | — |
| 320 | C2×D8 | — | 4 | 2 | no | — |
| 321 | C2×D8 | — | 4 | 2 | no | — |
| 322 | #131 | — | 16 | 1 | no | — |
| 323 | C2×M16 | — | 2 | 1 | no | — |
| 324 | C2×M16 | — | 4 | 2 | no | — |
| 325 | C2×M16 | — | 4 | 1 | no | — |
| 326 | C2×M16 | — | 8 | 1 | no | — |
| 327 | C22×C8 | — | 4 | 2 | no | — |
| 328 | C4⋊Q8 | — | 2 | 1 | no | — |
| 329 | C4⋊Q8 | — | 2 | 1 | no | — |
| 330 | C4⋊Q8 | — | 4 | 2 | no | — |
| 331 | C4⋊Q8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 332 | #127 | — | 2 | 1 | no | — |
| 333 | #127 | — | 2 | 1 | no | — |
| 334 | #127 | — | 2 | 1 | no | — |
| 335 | #127 | — | 4 | 1 | no | — |
| 336 | #127 | — | 4 | 2 | no | — |
| 337 | #127 | — | 4 | 2 | no | — |
| 338 | #127 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 339 | #127 | #120 | 1 | 1 | yes | characteristic |
| 340 | #127 | #120 | 1 | 1 | yes | characteristic |
| 341 | #124 | — | 2 | 1 | no | — |
| 342 | #124 | — | 4 | 1 | no | — |
| 343 | #124 | — | 4 | 2 | no | — |
| 344 | #124 | — | 4 | 2 | no | — |
| 345 | #124 | — | 4 | 2 | no | — |
| 346 | #124 | — | 4 | 1 | no | — |
| 347 | #124 | — | 8 | 2 | no | — |
| 348 | #124 | — | 8 | 2 | no | — |
| 349 | #124 | — | 8 | 2 | no | — |
| 350 | #123 | — | 4 | 2 | no | — |
| 351 | #123 | — | 4 | 2 | no | — |
| 352 | #123 | — | 8 | 1 | no | — |
| 353 | #123 | — | 8 | 1 | no | — |
| 354 | C22⋊Q8 | — | 4 | 2 | no | — |
| 355 | C22⋊Q8 | — | 8 | 2 | no | — |
| 356 | C22⋊Q8 | — | 8 | 2 | no | — |
| 357 | C22⋊Q8 | — | 8 | 1 | no | — |
| 358 | #121 | — | 2 | 2 | no | — |
| 359 | #121 | — | 4 | 1 | no | — |
| 360 | #121 | — | 4 | 2 | no | — |
| 361 | #121 | — | 4 | 2 | no | — |
| 362 | #121 | — | 4 | 1 | no | — |
| 363 | #121 | — | 4 | 1 | no | — |
| 364 | #121 | — | 4 | 2 | no | — |
| 365 | #121 | — | 4 | 1 | no | — |
| 366 | #121 | — | 8 | 2 | no | — |
| 367 | #121 | — | 8 | 1 | no | — |
| 368 | #121 | — | 8 | 1 | no | — |
| 369 | #121 | — | 8 | 2 | no | — |
| 370 | #121 | — | 8 | 2 | no | — |
| 371 | #120 | — | 8 | 1 | no | — |
| 372 | #120 | — | 8 | 2 | no | — |
| 373 | #120 | — | 8 | 1 | no | — |
| 374 | C4×Q8 | — | 2 | 2 | no | — |
| 375 | C4×Q8 | — | 2 | 2 | no | — |
| 376 | C4×Q8 | — | 4 | 1 | no | — |
| 377 | C4×Q8 | — | 4 | 1 | no | — |
| 378 | C4×D4 | — | 2 | 2 | no | — |
| 379 | C4×D4 | — | 4 | 1 | no | — |
| 380 | C4×D4 | — | 4 | 1 | no | — |
| 381 | C4×D4 | — | 4 | 1 | no | — |
| 382 | C4×D4 | — | 4 | 2 | no | — |
| 383 | C4×D4 | — | 4 | 2 | no | — |
| 384 | C4×D4 | — | 4 | 2 | no | — |
| 385 | C4×D4 | — | 4 | 2 | no | — |
| 386 | C4×D4 | — | 4 | 1 | no | — |
| 387 | C4×D4 | — | 8 | 2 | no | — |
| 388 | C4×D4 | — | 8 | 2 | no | — |
| 389 | C4×D4 | — | 16 | 1 | no | — |
| 390 | #117 | — | 4 | 1 | no | — |
| 391 | #117 | — | 4 | 2 | no | — |
| 392 | #117 | — | 4 | 1 | no | — |
| 393 | #117 | — | 8 | 1 | no | — |
| 394 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 395 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 396 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 397 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 398 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 399 | C2×C22⋊C4 | — | 8 | 1 | no | — |
| 400 | C2×C42 | — | 4 | 1 | no | — |
| 401 | C2×C42 | #120 | 1 | 1 | yes | characteristic |
| 402 | M32 | — | 8 | 1 | no | — |
| 403 | #107 | — | 4 | 2 | no | — |
| 404 | #106 | — | 2 | 2 | no | — |
| 405 | #106 | — | 2 | 2 | no | — |
| 406 | #106 | — | 4 | 2 | no | — |
| 407 | #106 | — | 4 | 1 | no | — |
| 408 | C4⋊C8 | — | 2 | 2 | no | — |
| 409 | C4⋊C8 | — | 2 | 2 | no | — |
| 410 | C4⋊C8 | — | 2 | 2 | no | — |
| 411 | C4⋊C8 | — | 4 | 2 | no | — |
| 412 | C4⋊C8 | — | 4 | 2 | no | — |
| 413 | #104 | — | 16 | 1 | no | — |
| 414 | #103 | — | 2 | 2 | no | — |
| 415 | #103 | — | 2 | 2 | no | — |
| 416 | #103 | — | 4 | 2 | no | — |
| 417 | #103 | — | 4 | 2 | no | — |
| 418 | #103 | — | 4 | 2 | no | — |
| 419 | #103 | — | 4 | 2 | no | — |
| 420 | #102 | — | 2 | 2 | no | — |
| 421 | #102 | — | 2 | 2 | no | — |
| 422 | #102 | — | 4 | 2 | no | — |
| 423 | #102 | — | 4 | 2 | no | — |
| 424 | #102 | — | 4 | 2 | no | — |
| 425 | #102 | — | 4 | 2 | no | — |
| 426 | #102 | — | 4 | 2 | no | — |
| 427 | #102 | — | 4 | 2 | no | — |
| 428 | #102 | — | 4 | 2 | no | — |
| 429 | #102 | — | 4 | 2 | no | — |
| 430 | #102 | — | 8 | 1 | no | — |
| 431 | #102 | — | 16 | 1 | no | — |
| 432 | #102 | — | 16 | 2 | no | — |
| 433 | #100 | — | 8 | 1 | no | — |
| 434 | #99 | — | 8 | 1 | no | — |
| 435 | #99 | — | 8 | 1 | no | — |
| 436 | #99 | — | 8 | 1 | no | — |
| 437 | #99 | — | 8 | 1 | no | — |
| 438 | #99 | — | 8 | 1 | no | — |
| 439 | C22⋊C8 | — | 2 | 2 | no | — |
| 440 | C22⋊C8 | — | 4 | 2 | no | — |
| 441 | C22⋊C8 | — | 4 | 2 | no | — |
| 442 | C22⋊C8 | — | 4 | 1 | no | — |
| 443 | C22⋊C8 | — | 4 | 1 | no | — |
| 444 | #97 | — | 2 | 1 | no | — |
| 445 | #97 | — | 4 | 1 | no | — |
| 446 | #97 | — | 4 | 2 | no | — |
| 447 | #97 | — | 4 | 2 | no | — |
| 448 | C4×C8 | — | 2 | 1 | no | — |
| 449 | C4×C8 | — | 2 | 1 | no | — |
| 450 | C4×C8 | — | 4 | 1 | no | — |
| 451 | C4×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 452 | C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 453 | #95 | — | 16 | 2 | no | — |
| 454 | C24 | — | 4 | 1 | no | — |
| 455 | C24 | — | 8 | 1 | no | — |
| 456 | #41 | — | 8 | 1 | no | — |
| 457 | #41 | — | 8 | 1 | no | — |
| 458 | #41 | — | 8 | 4 | no | — |
| 459 | #41 | — | 16 | 2 | no | — |
| 460 | #41 | — | 16 | 2 | no | — |
| 461 | #41 | — | 16 | 2 | no | — |
| 462 | #41 | — | 16 | 8 | no | — |
| 463 | #41 | — | 16 | 4 | no | — |
| 464 | C2×Q8 | — | 2 | 2 | no | — |
| 465 | C2×Q8 | — | 2 | 1 | no | — |
| 466 | C2×Q8 | — | 4 | 1 | no | — |
| 467 | C2×Q8 | — | 4 | 1 | no | — |
| 468 | C2×Q8 | — | 4 | 1 | no | — |
| 469 | C2×Q8 | — | 8 | 2 | no | — |
| 470 | C2×Q8 | — | 8 | 2 | no | — |
| 471 | C2×Q8 | — | 8 | 4 | no | — |
| 472 | C2×Q8 | — | 16 | 2 | no | — |
| 473 | C2×Q8 | — | 16 | 4 | no | — |
| 474 | C2×D4 | — | 2 | 2 | no | — |
| 475 | C2×D4 | — | 2 | 1 | no | — |
| 476 | C2×D4 | — | 2 | 1 | no | — |
| 477 | C2×D4 | — | 2 | 1 | no | — |
| 478 | C2×D4 | — | 4 | 1 | no | — |
| 479 | C2×D4 | — | 4 | 1 | no | — |
| 480 | C2×D4 | — | 4 | 1 | no | — |
| 481 | C2×D4 | — | 4 | 1 | no | — |
| 482 | C2×D4 | — | 4 | 1 | no | — |
| 483 | C2×D4 | — | 4 | 1 | no | — |
| 484 | C2×D4 | — | 4 | 2 | no | — |
| 485 | C2×D4 | — | 4 | 1 | no | — |
| 486 | C2×D4 | — | 4 | 2 | no | — |
| 487 | C2×D4 | — | 4 | 1 | no | — |
| 488 | C2×D4 | — | 4 | 1 | no | — |
| 489 | C2×D4 | — | 4 | 1 | no | — |
| 490 | C2×D4 | — | 8 | 1 | no | — |
| 491 | C2×D4 | — | 8 | 1 | no | — |
| 492 | C2×D4 | — | 8 | 1 | no | — |
| 493 | C2×D4 | — | 8 | 2 | no | — |
| 494 | C2×D4 | — | 8 | 2 | no | — |
| 495 | C2×D4 | — | 8 | 2 | no | — |
| 496 | C2×D4 | — | 8 | 1 | no | — |
| 497 | C2×D4 | — | 16 | 2 | no | — |
| 498 | C2×D4 | — | 16 | 2 | no | — |
| 499 | C2×D4 | — | 16 | 2 | no | — |
| 500 | C2×D4 | — | 16 | 1 | no | — |
| 501 | C2×D4 | — | 16 | 1 | no | — |
| 502 | C22×C4 | — | 2 | 1 | no | — |
| 503 | C22×C4 | — | 4 | 2 | no | — |
| 504 | C22×C4 | — | 4 | 1 | no | — |
| 505 | C22×C4 | — | 4 | 1 | no | — |
| 506 | C22×C4 | — | 4 | 1 | no | — |
| 507 | C22×C4 | — | 4 | 2 | no | — |
| 508 | C22×C4 | — | 8 | 1 | no | — |
| 509 | C22×C4 | — | 8 | 2 | no | — |
| 510 | C22×C4 | — | 8 | 1 | no | — |
| 511 | C22×C4 | — | 8 | 2 | no | — |
| 512 | C22×C4 | — | 8 | 2 | no | — |
| 513 | C22×C4 | — | 16 | 1 | no | — |
| 514 | C22×C4 | — | 16 | 1 | no | — |
| 515 | C22×C4 | — | 16 | 1 | no | — |
| 516 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 517 | SD16 | — | 8 | 2 | no | — |
| 518 | SD16 | — | 8 | 2 | no | — |
| 519 | SD16 | — | 8 | 4 | no | — |
| 520 | SD16 | — | 16 | 2 | no | — |
| 521 | SD16 | — | 16 | 1 | no | — |
| 522 | SD16 | — | 16 | 1 | no | — |
| 523 | SD16 | — | 16 | 2 | no | — |
| 524 | SD16 | — | 16 | 2 | no | — |
| 525 | D8 | — | 16 | 2 | no | — |
| 526 | D8 | — | 16 | 2 | no | — |
| 527 | D8 | — | 16 | 1 | no | — |
| 528 | D8 | — | 16 | 1 | no | — |
| 529 | D8 | — | 16 | 2 | no | — |
| 530 | D8 | — | 16 | 1 | no | — |
| 531 | D8 | — | 16 | 2 | no | — |
| 532 | D8 | — | 16 | 2 | no | — |
| 533 | D8 | — | 16 | 2 | no | — |
| 534 | M16 | — | 8 | 1 | no | — |
| 535 | M16 | — | 8 | 1 | no | — |
| 536 | M16 | — | 8 | 1 | no | — |
| 537 | M16 | — | 16 | 2 | no | — |
| 538 | M16 | — | 16 | 1 | no | — |
| 539 | C2×C8 | — | 2 | 2 | no | — |
| 540 | C2×C8 | — | 2 | 2 | no | — |
| 541 | C2×C8 | — | 2 | 1 | no | — |
| 542 | C2×C8 | — | 2 | 1 | no | — |
| 543 | C2×C8 | — | 4 | 2 | no | — |
| 544 | C2×C8 | — | 4 | 2 | no | — |
| 545 | C2×C8 | — | 8 | 1 | no | — |
| 546 | C2×C8 | — | 8 | 2 | no | — |
| 547 | C2×C8 | — | 16 | 2 | no | — |
| 548 | C4⋊C4 | — | 2 | 2 | no | — |
| 549 | C4⋊C4 | — | 2 | 2 | no | — |
| 550 | C4⋊C4 | — | 4 | 1 | no | — |
| 551 | C4⋊C4 | — | 4 | 1 | no | — |
| 552 | C4⋊C4 | — | 4 | 1 | no | — |
| 553 | C4⋊C4 | — | 4 | 2 | no | — |
| 554 | C4⋊C4 | — | 4 | 1 | no | — |
| 555 | C4⋊C4 | — | 4 | 2 | no | — |
| 556 | C4⋊C4 | — | 4 | 1 | no | — |
| 557 | C4⋊C4 | — | 8 | 2 | no | — |
| 558 | C4⋊C4 | — | 8 | 1 | no | — |
| 559 | C4⋊C4 | — | 16 | 1 | no | — |
| 560 | C22⋊C4 | — | 4 | 2 | no | — |
| 561 | C22⋊C4 | — | 4 | 2 | no | — |
| 562 | C22⋊C4 | — | 4 | 2 | no | — |
| 563 | C22⋊C4 | — | 8 | 1 | no | — |
| 564 | C22⋊C4 | — | 8 | 1 | no | — |
| 565 | C22⋊C4 | — | 8 | 1 | no | — |
| 566 | C22⋊C4 | — | 8 | 2 | no | — |
| 567 | C22⋊C4 | — | 8 | 2 | no | — |
| 568 | C22⋊C4 | — | 8 | 1 | no | — |
| 569 | C22⋊C4 | — | 8 | 2 | no | — |
| 570 | C22⋊C4 | — | 8 | 2 | no | — |
| 571 | C22⋊C4 | — | 8 | 2 | no | — |
| 572 | C22⋊C4 | — | 8 | 1 | no | — |
| 573 | C22⋊C4 | — | 8 | 1 | no | — |
| 574 | C22⋊C4 | — | 16 | 1 | no | — |
| 575 | C22⋊C4 | — | 16 | 1 | no | — |
| 576 | C22⋊C4 | — | 16 | 1 | no | — |
| 577 | C22⋊C4 | — | 16 | 1 | no | — |
| 578 | C42 | — | 2 | 1 | no | — |
| 579 | C42 | — | 4 | 2 | no | — |
| 580 | C42 | — | 4 | 2 | no | — |
| 581 | C42 | — | 4 | 2 | no | — |
| 582 | C42 | — | 8 | 1 | no | — |
| 583 | C42 | — | 16 | 1 | no | — |
| 584 | C42 | #379 | 1 | 1 | yes | characteristic |
| 585 | C42 | #458 | 1 | 1 | yes | characteristic |
| 586 | C16 | — | 16 | 1 | no | — |
| 587 | C23 | — | 4 | 2 | no | — |
| 588 | C23 | — | 4 | 1 | no | — |
| 589 | C23 | — | 4 | 1 | no | — |
| 590 | C23 | — | 4 | 1 | no | — |
| 591 | C23 | — | 8 | 1 | no | — |
| 592 | C23 | — | 8 | 1 | no | — |
| 593 | C23 | — | 8 | 1 | no | — |
| 594 | C23 | — | 16 | 2 | no | — |
| 595 | C23 | — | 32 | 1 | no | — |
| 596 | C23 | — | 32 | 2 | no | — |
| 597 | C23 | #2196 | 1 | 1 | yes | characteristic |
| 598 | Q8 | — | 4 | 2 | no | — |
| 599 | Q8 | — | 4 | 2 | no | — |
| 600 | Q8 | — | 8 | 1 | no | — |
| 601 | Q8 | — | 8 | 2 | no | — |
| 602 | Q8 | — | 8 | 2 | no | — |
| 603 | Q8 | — | 16 | 1 | no | — |
| 604 | Q8 | — | 16 | 4 | no | — |
| 605 | D4 | — | 4 | 2 | no | — |
| 606 | D4 | — | 4 | 2 | no | — |
| 607 | D4 | — | 8 | 1 | no | — |
| 608 | D4 | — | 8 | 1 | no | — |
| 609 | D4 | — | 8 | 1 | no | — |
| 610 | D4 | — | 8 | 2 | no | — |
| 611 | D4 | — | 8 | 2 | no | — |
| 612 | D4 | — | 8 | 2 | no | — |
| 613 | D4 | — | 8 | 2 | no | — |
| 614 | D4 | — | 8 | 2 | no | — |
| 615 | D4 | — | 16 | 1 | no | — |
| 616 | D4 | — | 16 | 1 | no | — |
| 617 | D4 | — | 16 | 1 | no | — |
| 618 | D4 | — | 16 | 1 | no | — |
| 619 | D4 | — | 16 | 2 | no | — |
| 620 | D4 | — | 16 | 1 | no | — |
| 621 | D4 | — | 16 | 2 | no | — |
| 622 | D4 | — | 16 | 2 | no | — |
| 623 | D4 | — | 16 | 4 | no | — |
| 624 | D4 | — | 16 | 2 | no | — |
| 625 | D4 | — | 32 | 2 | no | — |
| 626 | D4 | — | 32 | 2 | no | — |
| 627 | C2×C4 | — | 2 | 1 | no | — |
| 628 | C2×C4 | — | 2 | 1 | no | — |
| 629 | C2×C4 | — | 4 | 1 | no | — |
| 630 | C2×C4 | — | 4 | 2 | no | — |
| 631 | C2×C4 | — | 4 | 2 | no | — |
| 632 | C2×C4 | — | 4 | 2 | no | — |
| 633 | C2×C4 | — | 4 | 1 | no | — |
| 634 | C2×C4 | — | 4 | 2 | no | — |
| 635 | C2×C4 | — | 8 | 1 | no | — |
| 636 | C2×C4 | — | 8 | 1 | no | — |
| 637 | C2×C4 | — | 8 | 2 | no | — |
| 638 | C2×C4 | — | 8 | 2 | no | — |
| 639 | C2×C4 | — | 8 | 2 | no | — |
| 640 | C2×C4 | — | 8 | 1 | no | — |
| 641 | C2×C4 | — | 16 | 2 | no | — |
| 642 | C2×C4 | — | 16 | 1 | no | — |
| 643 | C2×C4 | — | 16 | 4 | no | — |
| 644 | C2×C4 | — | 16 | 4 | no | — |
| 645 | C2×C4 | — | 16 | 2 | no | — |
| 646 | C2×C4 | — | 16 | 1 | no | — |
| 647 | C2×C4 | — | 32 | 1 | no | — |
| 648 | C2×C4 | — | 32 | 2 | no | — |
| 649 | C2×C4 | — | 32 | 1 | no | — |
| 650 | C2×C4 | — | 32 | 1 | no | — |
| 651 | C2×C4 | — | 32 | 2 | no | — |
| 652 | C2×C4 | #1790 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | #2196 | 1 | 1 | yes | characteristic |
| 654 | C8 | — | 4 | 1 | no | — |
| 655 | C8 | — | 4 | 2 | no | — |
| 656 | C8 | — | 4 | 1 | no | — |
| 657 | C8 | — | 4 | 2 | no | — |
| 658 | C8 | — | 8 | 2 | no | — |
| 659 | C8 | — | 8 | 2 | no | — |
| 660 | C8 | — | 16 | 1 | no | — |
| 661 | C22 | — | 2 | 1 | no | — |
| 662 | C22 | — | 4 | 1 | no | — |
| 663 | C22 | — | 8 | 2 | no | — |
| 664 | C22 | — | 8 | 2 | no | — |
| 665 | C22 | — | 8 | 1 | no | — |
| 666 | C22 | — | 8 | 1 | no | — |
| 667 | C22 | — | 8 | 1 | no | — |
| 668 | C22 | — | 8 | 2 | no | — |
| 669 | C22 | — | 16 | 1 | no | — |
| 670 | C22 | — | 16 | 1 | no | — |
| 671 | C22 | — | 16 | 1 | no | — |
| 672 | C22 | — | 16 | 1 | no | — |
| 673 | C22 | — | 16 | 1 | no | — |
| 674 | C22 | — | 16 | 2 | no | — |
| 675 | C22 | — | 16 | 1 | no | — |
| 676 | C22 | — | 32 | 1 | no | — |
| 677 | C22 | — | 64 | 2 | no | — |
| 678 | C22 | #12759 | 1 | 1 | yes | characteristic |
| 679 | C4 | — | 2 | 2 | no | — |
| 680 | C4 | — | 2 | 1 | no | — |
| 681 | C4 | — | 2 | 1 | no | — |
| 682 | C4 | — | 4 | 1 | no | — |
| 683 | C4 | — | 8 | 2 | no | — |
| 684 | C4 | — | 8 | 2 | no | — |
| 685 | C4 | — | 8 | 1 | no | — |
| 686 | C4 | — | 8 | 2 | no | — |
| 687 | C4 | — | 16 | 1 | no | — |
| 688 | C4 | — | 32 | 1 | no | — |
| 689 | C4 | — | 64 | 1 | no | — |
| 690 | C4 | — | 64 | 1 | no | — |
| 691 | C2 | — | 2 | 1 | no | — |
| 692 | C2 | — | 4 | 1 | no | — |
| 693 | C2 | — | 16 | 1 | no | — |
| 694 | C2 | — | 16 | 1 | no | — |
| 695 | C2 | — | 16 | 2 | no | — |
| 696 | C2 | — | 16 | 1 | no | — |
| 697 | C2 | — | 32 | 1 | no | — |
| 698 | C2 | #152191 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #152191 |
| commutator | #492 | C22×C4 |
| Frattini, cosocle | #3151 | C23 |
| prime radical | #6365636 | C2 |
| LCS | G ▷ #492 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ #3151 ◁ G | |
| LECS | G ▷ #3151 ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #153539 | C2 | semidirect |
| 3. #153469 | C2 | semidirect |
| 4. #153462 | C2 | semidirect |
| 5. #152616 | C2 | semidirect |
| 6. #152603 | C2 | semidirect |
| 7. #139431 | C2 | semidirect |
| 12. #20294 | C4 | semidirect |
| 15. #20138 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6365636 | 2 |
| #153539 | 2 |
| #153469 | 2 |
| #153462 | 2 |
| #152616 | 2 |
| #152603 | 2 |
| #139431 | 2 |