Finite Group DatabasebetaFinite Group DatabasebetaOrder 4096.
1613 conjugacy classes of subgroups.
The subgroup lattice has 641 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72227224 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72227222 | — | 2 | 2 | no | — |
| 3 | #72225434 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72225431 | — | 2 | 2 | no | — |
| 5 | #72225428 | — | 2 | 2 | no | — |
| 6 | #72225426 | — | 2 | 2 | no | — |
| 7 | #72225358 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #72225357 | — | 2 | 2 | no | — |
| 9 | #72225354 | — | 2 | 2 | no | — |
| 10 | #72216544 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #72216257 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #72216251 | C4 | 1 | 1 | yes | characteristic |
| 13 | #72216251 | C4 | 1 | 1 | yes | characteristic |
| 14 | #72216249 | C22 | 1 | 1 | yes | characteristic |
| 15 | #72216249 | C22 | 1 | 1 | yes | characteristic |
| 16 | #72216247 | C22 | 1 | 2 | yes | — |
| 17 | #72216244 | — | 2 | 2 | no | — |
| 18 | #72216241 | — | 2 | 2 | no | — |
| 19 | #72216239 | C4 | 1 | 1 | yes | characteristic |
| 20 | #72216236 | C4 | 1 | 1 | yes | characteristic |
| 21 | #72216215 | C22 | 1 | 2 | yes | — |
| 22 | #72216182 | C22 | 1 | 1 | yes | characteristic |
| 23 | #498550 | — | 2 | 2 | no | — |
| 24 | #496112 | — | 2 | 2 | no | — |
| 25 | #496112 | — | 2 | 2 | no | — |
| 26 | #491485 | — | 2 | 2 | no | — |
| 27 | #491465 | C2×C4 | 1 | 1 | yes | characteristic |
| 28 | #491465 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | #483943 | — | 4 | 4 | no | — |
| 30 | #483601 | — | 4 | 2 | no | — |
| 31 | #213237 | — | 2 | 1 | no | — |
| 32 | #213237 | D4 | 1 | 2 | yes | — |
| 33 | #151981 | — | 2 | 2 | no | — |
| 34 | C2×#7456 | — | 2 | 2 | no | — |
| 35 | #150071 | — | 4 | 4 | no | — |
| 36 | #141812 | — | 2 | 2 | no | — |
| 37 | #141812 | — | 2 | 2 | no | — |
| 38 | #141786 | — | 4 | 4 | no | — |
| 39 | #141684 | — | 2 | 2 | no | — |
| 40 | #141684 | — | 2 | 2 | no | — |
| 41 | #141671 | — | 2 | 1 | no | — |
| 42 | #141671 | D4 | 1 | 2 | yes | — |
| 43 | #140841 | — | 2 | 4 | no | — |
| 44 | #140752 | — | 4 | 2 | no | — |
| 45 | #136683 | — | 4 | 4 | no | — |
| 46 | #135796 | — | 2 | 2 | no | — |
| 47 | #135781 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | #135781 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #129090 | D4 | 1 | 2 | yes | — |
| 50 | #129088 | D4 | 1 | 2 | yes | — |
| 51 | #129051 | — | 2 | 2 | no | — |
| 52 | C8×#346 | — | 2 | 1 | no | — |
| 53 | C8×#346 | C23 | 1 | 1 | yes | characteristic |
| 54 | #124213 | — | 2 | 2 | no | — |
| 55 | #123406 | C8 | 1 | 1 | yes | characteristic, complemented |
| 56 | #123406 | C8 | 1 | 1 | yes | characteristic, complemented |
| 57 | #123405 | — | 2 | 2 | no | — |
| 58 | #123404 | C8 | 1 | 1 | yes | characteristic, complemented |
| 59 | #123403 | C8 | 1 | 1 | yes | characteristic, complemented |
| 60 | C2×#7052 | — | 2 | 1 | no | — |
| 61 | C2×#7052 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | C2×C162 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | #94018 | — | 2 | 2 | no | — |
| 64 | #93926 | — | 4 | 4 | no | — |
| 65 | #93264 | — | 2 | 2 | no | — |
| 66 | #33733 | — | 4 | 4 | no | — |
| 67 | #33713 | — | 2 | 2 | no | — |
| 68 | #33713 | — | 2 | 2 | no | — |
| 69 | C2×#2179 | — | 4 | 2 | no | — |
| 70 | C2×#2179 | — | 4 | 2 | no | — |
| 71 | C2×#2179 | — | 4 | 2 | no | — |
| 72 | C2×#2179 | — | 4 | 2 | no | — |
| 73 | #33443 | — | 4 | 4 | no | — |
| 74 | #21705 | — | 2 | 2 | no | — |
| 75 | #21705 | — | 4 | 1 | no | — |
| 76 | #19603 | — | 2 | 1 | no | — |
| 77 | #19603 | C22⋊C4 | 1 | 2 | yes | — |
| 78 | #17956 | — | 4 | 2 | no | — |
| 79 | #17956 | — | 4 | 2 | no | — |
| 80 | C2×#1422 | — | 4 | 2 | no | — |
| 81 | C2×#1398 | — | 4 | 2 | no | — |
| 82 | #13242 | — | 4 | 2 | no | — |
| 83 | #13242 | — | 4 | 2 | no | — |
| 84 | #13242 | — | 4 | 2 | no | — |
| 85 | #13242 | — | 4 | 2 | no | — |
| 86 | #13208 | — | 2 | 4 | no | — |
| 87 | #13208 | — | 4 | 2 | no | — |
| 88 | #13197 | — | 4 | 4 | no | — |
| 89 | #12982 | — | 8 | 2 | no | — |
| 90 | #12909 | — | 2 | 2 | no | — |
| 91 | #12909 | — | 2 | 2 | no | — |
| 92 | C4×#364 | — | 2 | 2 | no | — |
| 93 | C4×#346 | — | 2 | 2 | no | — |
| 94 | C4×#346 | C2×D4 | 1 | 2 | yes | — |
| 95 | #12521 | — | 2 | 2 | no | — |
| 96 | #12518 | — | 2 | 2 | no | — |
| 97 | #12518 | — | 2 | 2 | no | — |
| 98 | #12517 | — | 2 | 1 | no | — |
| 99 | #12517 | M16 | 1 | 2 | yes | — |
| 100 | #12516 | C2×C8 | 1 | 1 | yes | characteristic |
| 101 | #12516 | C2×C8 | 1 | 1 | yes | characteristic |
| 102 | #12515 | — | 2 | 2 | no | — |
| 103 | #12515 | C2×C8 | 1 | 1 | yes | characteristic |
| 104 | #12515 | C2×C8 | 1 | 1 | yes | characteristic |
| 105 | #12509 | — | 2 | 2 | no | — |
| 106 | #12509 | — | 2 | 2 | no | — |
| 107 | #12503 | — | 4 | 4 | no | — |
| 108 | #12086 | — | 8 | 8 | no | — |
| 109 | #12068 | — | 8 | 8 | no | — |
| 110 | #12045 | — | 8 | 8 | no | — |
| 111 | #12023 | — | 4 | 4 | no | — |
| 112 | C2×#1369 | — | 2 | 2 | no | — |
| 113 | #11999 | — | 2 | 2 | no | — |
| 114 | #11671 | — | 4 | 4 | no | — |
| 115 | #11671 | — | 4 | 4 | no | — |
| 116 | #11604 | — | 4 | 4 | no | — |
| 117 | #11602 | — | 4 | 4 | no | — |
| 118 | #11405 | — | 4 | 2 | no | — |
| 119 | C2×#1311 | — | 2 | 2 | no | — |
| 120 | C2×#1311 | #41 | 1 | 2 | yes | — |
| 121 | C2×C8×C16 | — | 2 | 1 | no | — |
| 122 | C2×C8×C16 | — | 2 | 1 | no | — |
| 123 | C2×C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C2×C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | #9856 | — | 2 | 2 | no | — |
| 126 | #9856 | — | 4 | 1 | no | — |
| 127 | #9844 | — | 4 | 2 | no | — |
| 128 | #9844 | — | 4 | 2 | no | — |
| 129 | #8823 | — | 2 | 1 | no | — |
| 130 | #8823 | C22⋊C4 | 1 | 2 | yes | — |
| 131 | #8266 | — | 2 | 2 | no | — |
| 132 | C4×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | #7468 | — | 4 | 2 | no | — |
| 134 | #7456 | — | 2 | 4 | no | — |
| 135 | #7456 | — | 4 | 2 | no | — |
| 136 | #7389 | — | 8 | 8 | no | — |
| 137 | #7161 | D8 | 1 | 4 | yes | — |
| 138 | #7157 | — | 2 | 2 | no | — |
| 139 | #7140 | — | 4 | 2 | no | — |
| 140 | #7106 | — | 8 | 2 | no | — |
| 141 | #7052 | — | 2 | 2 | no | — |
| 142 | #7052 | — | 4 | 2 | no | — |
| 143 | C162 | — | 2 | 1 | no | — |
| 144 | C162 | C2×C8 | 1 | 1 | yes | characteristic |
| 145 | C162 | C2×C8 | 1 | 1 | yes | characteristic |
| 146 | C2×#508 | — | 4 | 2 | no | — |
| 147 | C2×#508 | — | 4 | 2 | no | — |
| 148 | C2×#508 | — | 4 | 2 | no | — |
| 149 | C2×#508 | — | 4 | 2 | no | — |
| 150 | #3407 | — | 8 | 2 | no | — |
| 151 | #3169 | — | 4 | 2 | no | — |
| 152 | #3169 | — | 4 | 2 | no | — |
| 153 | #3147 | — | 2 | 2 | no | — |
| 154 | #3147 | — | 4 | 1 | no | — |
| 155 | C2×#443 | — | 4 | 4 | no | — |
| 156 | C2×#443 | — | 8 | 2 | no | — |
| 157 | #2931 | — | 4 | 2 | no | — |
| 158 | #2931 | — | 8 | 1 | no | — |
| 159 | C2×M64 | — | 8 | 2 | no | — |
| 160 | #2252 | — | 4 | 4 | no | — |
| 161 | #2249 | — | 4 | 2 | no | — |
| 162 | #2249 | — | 4 | 2 | no | — |
| 163 | #2249 | — | 4 | 2 | no | — |
| 164 | #2249 | — | 4 | 2 | no | — |
| 165 | #2248 | — | 2 | 4 | no | — |
| 166 | #2248 | — | 4 | 2 | no | — |
| 167 | #2247 | — | 2 | 2 | no | — |
| 168 | #2247 | — | 2 | 2 | no | — |
| 169 | #2246 | — | 2 | 2 | no | — |
| 170 | #2246 | — | 2 | 2 | no | — |
| 171 | #2246 | — | 4 | 4 | no | — |
| 172 | #2240 | — | 4 | 4 | no | — |
| 173 | #2240 | — | 4 | 4 | no | — |
| 174 | #2215 | — | 8 | 8 | no | — |
| 175 | #2179 | — | 8 | 4 | no | — |
| 176 | #2179 | — | 8 | 4 | no | — |
| 177 | #2179 | — | 8 | 4 | no | — |
| 178 | #2179 | — | 8 | 4 | no | — |
| 179 | #2179 | — | 16 | 2 | no | — |
| 180 | #2179 | — | 16 | 2 | no | — |
| 181 | #2179 | — | 16 | 4 | no | — |
| 182 | C4×D16 | — | 8 | 8 | no | — |
| 183 | #2171 | — | 8 | 8 | no | — |
| 184 | #2170 | — | 16 | 4 | no | — |
| 185 | C2×#368 | — | 4 | 2 | no | — |
| 186 | C2×#368 | — | 4 | 2 | no | — |
| 187 | C2×#368 | — | 4 | 2 | no | — |
| 188 | C2×#368 | — | 4 | 2 | no | — |
| 189 | C2×#364 | — | 2 | 4 | no | — |
| 190 | C2×#359 | — | 4 | 4 | no | — |
| 191 | C2×#359 | — | 4 | 4 | no | — |
| 192 | C2×#359 | — | 8 | 2 | no | — |
| 193 | C2×#359 | — | 8 | 2 | no | — |
| 194 | #2117 | — | 8 | 4 | no | — |
| 195 | #2115 | — | 8 | 2 | no | — |
| 196 | C4×M32 | — | 4 | 2 | no | — |
| 197 | C2×#346 | — | 4 | 4 | no | — |
| 198 | C2×#346 | C2×D8 | 1 | 2 | yes | — |
| 199 | C2×#346 | #135 | 1 | 2 | yes | — |
| 200 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 201 | C2×#346 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 202 | C2×C4×C16 | — | 2 | 2 | no | — |
| 203 | C2×C4×C16 | — | 2 | 2 | no | — |
| 204 | C2×C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 205 | C2×C4×C16 | #121 | 1 | 2 | yes | — |
| 206 | #1974 | — | 4 | 4 | no | — |
| 207 | #1974 | — | 8 | 2 | no | — |
| 208 | #1962 | — | 4 | 2 | no | — |
| 209 | #1962 | — | 8 | 1 | no | — |
| 210 | #1848 | — | 2 | 2 | no | — |
| 211 | #1848 | — | 4 | 1 | no | — |
| 212 | C42×C8 | — | 2 | 1 | no | — |
| 213 | C42×C8 | #120 | 1 | 1 | yes | characteristic |
| 214 | #1713 | — | 2 | 1 | no | — |
| 215 | #1713 | C22⋊C8 | 1 | 2 | yes | — |
| 216 | #1712 | — | 2 | 1 | no | — |
| 217 | #1712 | C22⋊C8 | 1 | 2 | yes | — |
| 218 | #1709 | — | 2 | 2 | no | — |
| 219 | #1709 | — | 4 | 1 | no | — |
| 220 | #1706 | — | 4 | 2 | no | — |
| 221 | #1706 | — | 4 | 2 | no | — |
| 222 | #1589 | — | 8 | 4 | no | — |
| 223 | #1589 | — | 8 | 4 | no | — |
| 224 | C8×D8 | — | 8 | 4 | no | — |
| 225 | C8×D8 | — | 8 | 4 | no | — |
| 226 | #1567 | — | 4 | 2 | no | — |
| 227 | #1567 | — | 4 | 2 | no | — |
| 228 | #1564 | — | 4 | 2 | no | — |
| 229 | #1492 | — | 8 | 2 | no | — |
| 230 | #1492 | — | 8 | 2 | no | — |
| 231 | #1450 | — | 4 | 2 | no | — |
| 232 | C2×C82 | — | 2 | 1 | no | — |
| 233 | C2×C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 234 | C2×C82 | #123 | 1 | 1 | yes | characteristic |
| 235 | #1422 | — | 4 | 4 | no | — |
| 236 | #1422 | — | 8 | 2 | no | — |
| 237 | #1398 | — | 8 | 4 | no | — |
| 238 | #1376 | — | 4 | 2 | no | — |
| 239 | #1372 | — | 8 | 8 | no | — |
| 240 | #1369 | — | 4 | 4 | no | — |
| 241 | #1368 | — | 4 | 4 | no | — |
| 242 | #1336 | — | 8 | 8 | no | — |
| 243 | #1335 | — | 16 | 4 | no | — |
| 244 | #1331 | — | 8 | 8 | no | — |
| 245 | #1331 | — | 8 | 8 | no | — |
| 246 | #1313 | — | 8 | 4 | no | — |
| 247 | #1311 | — | 2 | 8 | no | — |
| 248 | #1311 | — | 2 | 2 | no | — |
| 249 | #1311 | — | 2 | 2 | no | — |
| 250 | C8×C16 | — | 2 | 2 | no | — |
| 251 | C8×C16 | — | 2 | 1 | no | — |
| 252 | C8×C16 | — | 2 | 1 | no | — |
| 253 | C8×C16 | — | 4 | 1 | no | — |
| 254 | C8×C16 | — | 4 | 1 | no | — |
| 255 | C8×C16 | — | 4 | 1 | no | — |
| 256 | C8×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 257 | C8×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 258 | C8×C16 | #131 | 1 | 2 | yes | — |
| 259 | #1276 | — | 4 | 2 | no | — |
| 260 | C2×#135 | — | 4 | 4 | no | — |
| 261 | C2×#135 | — | 8 | 2 | no | — |
| 262 | C2×#131 | — | 8 | 2 | no | — |
| 263 | C2×#131 | — | 16 | 1 | no | — |
| 264 | #532 | — | 4 | 2 | no | — |
| 265 | #532 | — | 8 | 1 | no | — |
| 266 | #508 | — | 8 | 4 | no | — |
| 267 | #508 | — | 8 | 4 | no | — |
| 268 | #508 | — | 8 | 4 | no | — |
| 269 | #508 | — | 8 | 4 | no | — |
| 270 | #508 | — | 16 | 2 | no | — |
| 271 | #508 | — | 16 | 2 | no | — |
| 272 | #508 | — | 16 | 2 | no | — |
| 273 | #508 | — | 16 | 2 | no | — |
| 274 | C2×Q32 | — | 4 | 2 | no | — |
| 275 | C2×Q32 | — | 4 | 2 | no | — |
| 276 | C2×Q32 | — | 4 | 2 | no | — |
| 277 | C2×Q32 | — | 4 | 2 | no | — |
| 278 | C2×SD32 | — | 4 | 4 | no | — |
| 279 | C2×SD32 | — | 4 | 4 | no | — |
| 280 | C2×SD32 | — | 8 | 2 | no | — |
| 281 | C2×SD32 | — | 8 | 2 | no | — |
| 282 | C2×D16 | — | 4 | 2 | no | — |
| 283 | C2×D16 | — | 4 | 2 | no | — |
| 284 | C2×D16 | — | 4 | 2 | no | — |
| 285 | C2×D16 | — | 4 | 2 | no | — |
| 286 | C2×D16 | — | 8 | 8 | no | — |
| 287 | #504 | — | 16 | 8 | no | — |
| 288 | C2×M32 | — | 4 | 4 | no | — |
| 289 | C2×M32 | — | 32 | 2 | no | — |
| 290 | C22×C16 | — | 2 | 4 | no | — |
| 291 | C22×C16 | — | 4 | 2 | no | — |
| 292 | C22×C16 | C4×D8 | 1 | 2 | yes | — |
| 293 | C22×C16 | #442 | 1 | 2 | yes | — |
| 294 | C22×C16 | #459 | 1 | 2 | yes | — |
| 295 | C22×C16 | #463 | 1 | 2 | yes | — |
| 296 | #500 | — | 4 | 2 | no | — |
| 297 | #500 | — | 4 | 2 | no | — |
| 298 | #495 | — | 4 | 4 | no | — |
| 299 | #495 | — | 8 | 2 | no | — |
| 300 | #494 | — | 2 | 2 | no | — |
| 301 | #494 | — | 4 | 1 | no | — |
| 302 | #493 | — | 2 | 2 | no | — |
| 303 | #493 | — | 4 | 2 | no | — |
| 304 | #493 | — | 4 | 2 | no | — |
| 305 | #493 | — | 4 | 1 | no | — |
| 306 | #492 | — | 4 | 2 | no | — |
| 307 | #492 | — | 8 | 1 | no | — |
| 308 | #486 | — | 8 | 2 | no | — |
| 309 | #486 | — | 8 | 2 | no | — |
| 310 | #466 | — | 8 | 4 | no | — |
| 311 | #466 | — | 8 | 4 | no | — |
| 312 | #443 | — | 8 | 4 | no | — |
| 313 | #443 | — | 8 | 4 | no | — |
| 314 | #443 | — | 8 | 4 | no | — |
| 315 | #443 | — | 8 | 4 | no | — |
| 316 | #443 | — | 16 | 4 | no | — |
| 317 | #443 | — | 16 | 4 | no | — |
| 318 | C4×D8 | — | 8 | 4 | no | — |
| 319 | C4×D8 | — | 8 | 4 | no | — |
| 320 | #436 | — | 16 | 2 | no | — |
| 321 | #436 | — | 16 | 2 | no | — |
| 322 | C8×D4 | — | 16 | 2 | no | — |
| 323 | C8×D4 | — | 16 | 2 | no | — |
| 324 | #431 | — | 8 | 2 | no | — |
| 325 | C2×#108 | — | 4 | 4 | no | — |
| 326 | C2×#108 | — | 8 | 2 | no | — |
| 327 | #423 | — | 4 | 2 | no | — |
| 328 | #423 | — | 8 | 1 | no | — |
| 329 | C2×#104 | — | 8 | 4 | no | — |
| 330 | C2×#104 | — | 16 | 2 | no | — |
| 331 | #408 | — | 8 | 2 | no | — |
| 332 | #408 | — | 16 | 1 | no | — |
| 333 | C2×C4×C8 | — | 2 | 1 | no | — |
| 334 | C2×C4×C8 | — | 2 | 1 | no | — |
| 335 | C2×C4×C8 | — | 4 | 2 | no | — |
| 336 | C2×C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×C8 | #447 | 1 | 2 | yes | — |
| 338 | C2×C4×C8 | #449 | 1 | 2 | yes | — |
| 339 | C2×C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 340 | C43 | #453 | 1 | 1 | yes | characteristic |
| 341 | M64 | — | 8 | 4 | no | — |
| 342 | M64 | — | 16 | 2 | no | — |
| 343 | C2×C32 | — | 16 | 2 | no | — |
| 344 | #368 | — | 8 | 4 | no | — |
| 345 | #368 | — | 8 | 4 | no | — |
| 346 | #368 | — | 16 | 2 | no | — |
| 347 | #368 | — | 16 | 2 | no | — |
| 348 | #366 | — | 8 | 8 | no | — |
| 349 | #364 | — | 4 | 4 | no | — |
| 350 | #364 | — | 4 | 4 | no | — |
| 351 | #359 | — | 8 | 8 | no | — |
| 352 | #359 | — | 16 | 4 | no | — |
| 353 | #359 | — | 16 | 2 | no | — |
| 354 | #359 | — | 16 | 2 | no | — |
| 355 | #359 | — | 16 | 4 | no | — |
| 356 | #357 | — | 8 | 8 | no | — |
| 357 | #357 | — | 8 | 8 | no | — |
| 358 | #350 | — | 16 | 8 | no | — |
| 359 | #349 | — | 32 | 2 | no | — |
| 360 | #346 | — | 2 | 4 | no | — |
| 361 | #346 | — | 2 | 4 | no | — |
| 362 | #346 | — | 4 | 2 | no | — |
| 363 | #346 | — | 4 | 2 | no | — |
| 364 | #346 | — | 8 | 2 | no | — |
| 365 | #346 | — | 8 | 8 | no | — |
| 366 | C4×C16 | — | 2 | 2 | no | — |
| 367 | C4×C16 | — | 2 | 2 | no | — |
| 368 | C4×C16 | — | 2 | 4 | no | — |
| 369 | C4×C16 | — | 2 | 4 | no | — |
| 370 | C4×C16 | — | 2 | 2 | no | — |
| 371 | C4×C16 | — | 2 | 2 | no | — |
| 372 | C4×C16 | — | 4 | 2 | no | — |
| 373 | C4×C16 | — | 8 | 2 | no | — |
| 374 | C4×C16 | C8×D4 | 1 | 2 | yes | — |
| 375 | C4×C16 | #435 | 1 | 2 | yes | — |
| 376 | C4×C16 | #443 | 1 | 2 | yes | — |
| 377 | C4×C16 | #444 | 1 | 2 | yes | — |
| 378 | #335 | — | 8 | 2 | no | — |
| 379 | #335 | — | 8 | 4 | no | — |
| 380 | #335 | — | 8 | 4 | no | — |
| 381 | #334 | — | 8 | 2 | no | — |
| 382 | D4⋊C8 | — | 16 | 4 | no | — |
| 383 | D4⋊C8 | — | 16 | 4 | no | — |
| 384 | #322 | — | 8 | 2 | no | — |
| 385 | C82 | — | 2 | 4 | no | — |
| 386 | C82 | — | 2 | 1 | no | — |
| 387 | C82 | — | 2 | 2 | no | — |
| 388 | C82 | — | 8 | 2 | no | — |
| 389 | C82 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 390 | C82 | #408 | 1 | 1 | yes | characteristic |
| 391 | C2×#41 | — | 8 | 2 | no | — |
| 392 | C2×#41 | — | 16 | 1 | no | — |
| 393 | #135 | — | 8 | 4 | no | — |
| 394 | #135 | — | 8 | 4 | no | — |
| 395 | #135 | — | 8 | 4 | no | — |
| 396 | #135 | — | 8 | 4 | no | — |
| 397 | #135 | — | 16 | 2 | no | — |
| 398 | #135 | — | 16 | 2 | no | — |
| 399 | #135 | — | 16 | 2 | no | — |
| 400 | #135 | — | 16 | 2 | no | — |
| 401 | C2×Q16 | — | 4 | 4 | no | — |
| 402 | C2×Q16 | — | 8 | 2 | no | — |
| 403 | C2×SD16 | — | 8 | 4 | no | — |
| 404 | C2×SD16 | — | 16 | 2 | no | — |
| 405 | C2×D8 | — | 4 | 4 | no | — |
| 406 | C2×D8 | — | 8 | 4 | no | — |
| 407 | C2×D8 | — | 8 | 4 | no | — |
| 408 | C2×D8 | — | 8 | 2 | no | — |
| 409 | #131 | — | 16 | 4 | no | — |
| 410 | #131 | — | 16 | 4 | no | — |
| 411 | #131 | — | 32 | 4 | no | — |
| 412 | C2×M16 | — | 8 | 2 | no | — |
| 413 | C2×M16 | — | 16 | 2 | no | — |
| 414 | C2×M16 | — | 16 | 1 | no | — |
| 415 | C2×M16 | — | 32 | 1 | no | — |
| 416 | C22×C8 | — | 2 | 2 | no | — |
| 417 | C22×C8 | — | 4 | 1 | no | — |
| 418 | C22×C8 | — | 16 | 2 | no | — |
| 419 | C22×C8 | — | 32 | 1 | no | — |
| 420 | C22×C8 | #1619 | 1 | 1 | yes | characteristic |
| 421 | C22×C8 | #1620 | 1 | 1 | yes | characteristic |
| 422 | C22×C8 | #1879 | 1 | 2 | yes | — |
| 423 | C4⋊Q8 | — | 4 | 2 | no | — |
| 424 | C4⋊Q8 | — | 8 | 1 | no | — |
| 425 | #127 | — | 4 | 2 | no | — |
| 426 | #127 | — | 8 | 1 | no | — |
| 427 | #124 | — | 8 | 2 | no | — |
| 428 | #124 | — | 16 | 1 | no | — |
| 429 | #121 | — | 16 | 2 | no | — |
| 430 | #121 | — | 16 | 2 | no | — |
| 431 | C4×D4 | — | 16 | 2 | no | — |
| 432 | C4×D4 | — | 16 | 2 | no | — |
| 433 | C2×C42 | — | 4 | 1 | no | — |
| 434 | C2×C42 | #1621 | 1 | 2 | yes | — |
| 435 | C2×C42 | #1887 | 1 | 1 | yes | characteristic |
| 436 | Q32 | — | 8 | 4 | no | — |
| 437 | Q32 | — | 8 | 4 | no | — |
| 438 | Q32 | — | 16 | 2 | no | — |
| 439 | Q32 | — | 16 | 2 | no | — |
| 440 | SD32 | — | 8 | 8 | no | — |
| 441 | SD32 | — | 16 | 4 | no | — |
| 442 | SD32 | — | 16 | 4 | no | — |
| 443 | SD32 | — | 16 | 4 | no | — |
| 444 | D16 | — | 8 | 4 | no | — |
| 445 | D16 | — | 8 | 4 | no | — |
| 446 | D16 | — | 16 | 2 | no | — |
| 447 | D16 | — | 16 | 2 | no | — |
| 448 | D16 | — | 16 | 16 | no | — |
| 449 | M32 | — | 8 | 4 | no | — |
| 450 | M32 | — | 8 | 4 | no | — |
| 451 | M32 | — | 32 | 4 | no | — |
| 452 | C2×C16 | — | 2 | 4 | no | — |
| 453 | C2×C16 | — | 2 | 2 | no | — |
| 454 | C2×C16 | — | 2 | 2 | no | — |
| 455 | C2×C16 | — | 2 | 4 | no | — |
| 456 | C2×C16 | — | 2 | 2 | no | — |
| 457 | C2×C16 | — | 2 | 2 | no | — |
| 458 | C2×C16 | — | 2 | 2 | no | — |
| 459 | C2×C16 | — | 2 | 2 | no | — |
| 460 | C2×C16 | — | 2 | 2 | no | — |
| 461 | C2×C16 | — | 2 | 2 | no | — |
| 462 | C2×C16 | — | 4 | 8 | no | — |
| 463 | C2×C16 | — | 4 | 4 | no | — |
| 464 | C2×C16 | — | 8 | 4 | no | — |
| 465 | C2×C16 | — | 8 | 4 | no | — |
| 466 | C2×C16 | — | 32 | 4 | no | — |
| 467 | C2×C16 | C8×D8 | 1 | 2 | yes | — |
| 468 | C2×C16 | #1580 | 1 | 2 | yes | — |
| 469 | C2×C16 | #1581 | 1 | 2 | yes | — |
| 470 | C2×C16 | #1586 | 1 | 2 | yes | — |
| 471 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 472 | C2×C16 | AGL(1,ℤ/16) | 1 | 4 | yes | — |
| 473 | #108 | — | 8 | 4 | no | — |
| 474 | #108 | — | 8 | 4 | no | — |
| 475 | #108 | — | 16 | 2 | no | — |
| 476 | #108 | — | 16 | 2 | no | — |
| 477 | #107 | — | 8 | 4 | no | — |
| 478 | #107 | — | 8 | 4 | no | — |
| 479 | C4⋊C8 | — | 16 | 2 | no | — |
| 480 | C4⋊C8 | — | 16 | 2 | no | — |
| 481 | C4⋊C8 | — | 16 | 2 | no | — |
| 482 | #104 | — | 16 | 4 | no | — |
| 483 | #104 | — | 16 | 4 | no | — |
| 484 | #104 | — | 32 | 4 | no | — |
| 485 | #102 | — | 16 | 4 | no | — |
| 486 | #102 | — | 16 | 4 | no | — |
| 487 | C22⋊C8 | — | 16 | 2 | no | — |
| 488 | C22⋊C8 | — | 32 | 2 | no | — |
| 489 | C22⋊C8 | — | 32 | 2 | no | — |
| 490 | C4×C8 | — | 2 | 2 | no | — |
| 491 | C4×C8 | — | 2 | 2 | no | — |
| 492 | C4×C8 | — | 2 | 2 | no | — |
| 493 | C4×C8 | — | 2 | 2 | no | — |
| 494 | C4×C8 | — | 2 | 2 | no | — |
| 495 | C4×C8 | — | 2 | 2 | no | — |
| 496 | C4×C8 | — | 2 | 2 | no | — |
| 497 | C4×C8 | — | 2 | 1 | no | — |
| 498 | C4×C8 | — | 2 | 1 | no | — |
| 499 | C4×C8 | — | 4 | 1 | no | — |
| 500 | C4×C8 | — | 8 | 4 | no | — |
| 501 | C4×C8 | — | 16 | 2 | no | — |
| 502 | C4×C8 | #1869 | 1 | 1 | yes | characteristic |
| 503 | C4×C8 | #1876 | 1 | 2 | yes | — |
| 504 | C4×C8 | #1884 | 1 | 1 | yes | characteristic |
| 505 | C32 | — | 16 | 4 | no | — |
| 506 | #41 | — | 16 | 4 | no | — |
| 507 | #41 | — | 16 | 4 | no | — |
| 508 | #41 | — | 32 | 2 | no | — |
| 509 | #41 | — | 32 | 2 | no | — |
| 510 | C2×Q8 | — | 8 | 2 | no | — |
| 511 | C2×Q8 | — | 16 | 1 | no | — |
| 512 | C2×D4 | — | 8 | 2 | no | — |
| 513 | C2×D4 | — | 16 | 2 | no | — |
| 514 | C2×D4 | — | 16 | 2 | no | — |
| 515 | C2×D4 | — | 16 | 2 | no | — |
| 516 | C2×D4 | — | 16 | 1 | no | — |
| 517 | C2×D4 | — | 32 | 1 | no | — |
| 518 | C22×C4 | — | 2 | 1 | no | — |
| 519 | C22×C4 | — | 2 | 2 | no | — |
| 520 | C22×C4 | — | 16 | 2 | no | — |
| 521 | C22×C4 | — | 32 | 1 | no | — |
| 522 | C22×C4 | #9061 | 1 | 1 | yes | characteristic |
| 523 | Q16 | — | 8 | 4 | no | — |
| 524 | Q16 | — | 8 | 4 | no | — |
| 525 | Q16 | — | 16 | 2 | no | — |
| 526 | Q16 | — | 16 | 2 | no | — |
| 527 | SD16 | — | 16 | 4 | no | — |
| 528 | SD16 | — | 16 | 4 | no | — |
| 529 | SD16 | — | 32 | 2 | no | — |
| 530 | SD16 | — | 32 | 2 | no | — |
| 531 | D8 | — | 8 | 4 | no | — |
| 532 | D8 | — | 8 | 4 | no | — |
| 533 | D8 | — | 16 | 8 | no | — |
| 534 | D8 | — | 16 | 8 | no | — |
| 535 | D8 | — | 16 | 2 | no | — |
| 536 | D8 | — | 16 | 2 | no | — |
| 537 | M16 | — | 16 | 4 | no | — |
| 538 | M16 | — | 32 | 4 | no | — |
| 539 | M16 | — | 32 | 2 | no | — |
| 540 | M16 | — | 64 | 2 | no | — |
| 541 | C2×C8 | — | 2 | 2 | no | — |
| 542 | C2×C8 | — | 2 | 2 | no | — |
| 543 | C2×C8 | — | 2 | 2 | no | — |
| 544 | C2×C8 | — | 2 | 2 | no | — |
| 545 | C2×C8 | — | 2 | 1 | no | — |
| 546 | C2×C8 | — | 4 | 4 | no | — |
| 547 | C2×C8 | — | 4 | 2 | no | — |
| 548 | C2×C8 | — | 8 | 2 | no | — |
| 549 | C2×C8 | — | 16 | 2 | no | — |
| 550 | C2×C8 | — | 32 | 2 | no | — |
| 551 | C2×C8 | — | 32 | 2 | no | — |
| 552 | C2×C8 | — | 32 | 2 | no | — |
| 553 | C2×C8 | — | 32 | 1 | no | — |
| 554 | C2×C8 | — | 64 | 2 | no | — |
| 555 | C2×C8 | #8947 | 1 | 2 | yes | — |
| 556 | C2×C8 | #9053 | 1 | 2 | yes | — |
| 557 | C2×C8 | #12310 | 1 | 2 | yes | — |
| 558 | C2×C8 | #13033 | 1 | 2 | yes | — |
| 559 | C2×C8 | #13036 | 1 | 2 | yes | — |
| 560 | C2×C8 | #13037 | 1 | 2 | yes | — |
| 561 | C2×C8 | #13040 | 1 | 2 | yes | — |
| 562 | C4⋊C4 | — | 16 | 2 | no | — |
| 563 | C4⋊C4 | — | 16 | 2 | no | — |
| 564 | C22⋊C4 | — | 32 | 2 | no | — |
| 565 | C22⋊C4 | — | 32 | 2 | no | — |
| 566 | C42 | — | 2 | 1 | no | — |
| 567 | C42 | — | 2 | 2 | no | — |
| 568 | C42 | — | 2 | 2 | no | — |
| 569 | C42 | — | 8 | 2 | no | — |
| 570 | C42 | #8959 | 1 | 1 | yes | characteristic |
| 571 | C42 | #9069 | 1 | 1 | yes | characteristic |
| 572 | C16 | — | 2 | 8 | no | — |
| 573 | C16 | — | 2 | 2 | no | — |
| 574 | C16 | — | 2 | 2 | no | — |
| 575 | C16 | — | 4 | 4 | no | — |
| 576 | C16 | — | 4 | 2 | no | — |
| 577 | C16 | — | 4 | 2 | no | — |
| 578 | C16 | — | 8 | 4 | no | — |
| 579 | C16 | — | 16 | 4 | no | — |
| 580 | C16 | #12067 | 1 | 4 | yes | — |
| 581 | C16 | #12078 | 1 | 4 | yes | — |
| 582 | C23 | — | 16 | 2 | no | — |
| 583 | C23 | — | 32 | 1 | no | — |
| 584 | C23 | #137550 | 1 | 1 | yes | characteristic |
| 585 | Q8 | — | 16 | 4 | no | — |
| 586 | Q8 | — | 32 | 2 | no | — |
| 587 | D4 | — | 16 | 4 | no | — |
| 588 | D4 | — | 32 | 4 | no | — |
| 589 | D4 | — | 32 | 4 | no | — |
| 590 | D4 | — | 32 | 4 | no | — |
| 591 | D4 | — | 32 | 2 | no | — |
| 592 | D4 | — | 64 | 2 | no | — |
| 593 | C2×C4 | — | 2 | 1 | no | — |
| 594 | C2×C4 | — | 2 | 1 | no | — |
| 595 | C2×C4 | — | 4 | 2 | no | — |
| 596 | C2×C4 | — | 4 | 2 | no | — |
| 597 | C2×C4 | — | 8 | 2 | no | — |
| 598 | C2×C4 | — | 16 | 2 | no | — |
| 599 | C2×C4 | — | 32 | 2 | no | — |
| 600 | C2×C4 | — | 32 | 2 | no | — |
| 601 | C2×C4 | — | 32 | 1 | no | — |
| 602 | C2×C4 | — | 64 | 1 | no | — |
| 603 | C2×C4 | — | 64 | 1 | no | — |
| 604 | C2×C4 | #99599 | 1 | 1 | yes | characteristic |
| 605 | C2×C4 | #137546 | 1 | 2 | yes | — |
| 606 | C2×C4 | #137549 | 1 | 2 | yes | — |
| 607 | C2×C4 | #137551 | 1 | 1 | yes | characteristic |
| 608 | C8 | — | 2 | 4 | no | — |
| 609 | C8 | — | 2 | 2 | no | — |
| 610 | C8 | — | 4 | 2 | no | — |
| 611 | C8 | — | 4 | 1 | no | — |
| 612 | C8 | — | 8 | 2 | no | — |
| 613 | C8 | — | 32 | 2 | no | — |
| 614 | C8 | — | 64 | 2 | no | — |
| 615 | C8 | — | 64 | 1 | no | — |
| 616 | C8 | #136703 | 1 | 2 | yes | — |
| 617 | C8 | #136707 | 1 | 2 | yes | — |
| 618 | C8 | #137499 | 1 | 2 | yes | — |
| 619 | C8 | #137501 | 1 | 2 | yes | — |
| 620 | C22 | — | 4 | 1 | no | — |
| 621 | C22 | — | 32 | 2 | no | — |
| 622 | C22 | — | 64 | 2 | no | — |
| 623 | C22 | — | 64 | 2 | no | — |
| 624 | C22 | — | 64 | 1 | no | — |
| 625 | C22 | #72216426 | 1 | 1 | yes | characteristic |
| 626 | C22 | #72225245 | 1 | 2 | yes | — |
| 627 | C4 | — | 2 | 2 | no | — |
| 628 | C4 | — | 4 | 1 | no | — |
| 629 | C4 | — | 8 | 2 | no | — |
| 630 | C4 | — | 32 | 2 | no | — |
| 631 | C4 | — | 64 | 1 | no | — |
| 632 | C4 | #72214397 | 1 | 1 | yes | characteristic |
| 633 | C4 | #72225244 | 1 | 2 | yes | — |
| 634 | C4 | #72225246 | 1 | 1 | yes | characteristic |
| 635 | C2 | — | 2 | 1 | no | — |
| 636 | C2 | — | 2 | 2 | no | — |
| 637 | C2 | — | 64 | 2 | no | — |
| 638 | C2 | — | 128 | 1 | no | — |
| 639 | C2 | #72225250 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #72214397 |
| commutator | C8×C16 | C22×C8 |
| Frattini, cosocle | C8×#346 | C23 |
| socle | C2 | #72225250 |
| prime radical | #72216236 | C4 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ C42×C8 ◁ C8×#346 ◁ G | |
| LECS | G ▷ C8×#346 ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72227224 | C2 | semidirect |
| 3. #72225434 | C2 | semidirect |
| 7. #72225358 | C2 | semidirect |
| 10. #72216544 | C2 | semidirect |
| 55. #123406 | C8 | semidirect |
| 56. #123406 | C8 | semidirect |
| 58. #123404 | C8 | semidirect |
| 59. #123403 | C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72227224 | 2 |
| #72225434 | 2 |
| #72225358 | 2 |
| #72216544 | 2 |
| #72216257 | 2 |