Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
933 conjugacy classes of subgroups.
The subgroup lattice has 563 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #7624863 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #512993 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #505706 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #151510 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #151509 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #151495 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #150878 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #149671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #62332 | — | 2 | 1 | no | — |
| 10 | #33902 | — | 2 | 2 | no | — |
| 11 | #33899 | — | 2 | 2 | no | — |
| 12 | #33898 | — | 2 | 2 | no | — |
| 13 | #33850 | — | 2 | 2 | no | — |
| 14 | #33821 | C22 | 1 | 1 | yes | characteristic |
| 15 | #33819 | C22 | 1 | 1 | yes | characteristic |
| 16 | #33770 | — | 2 | 1 | no | — |
| 17 | #33770 | C22 | 1 | 2 | yes | — |
| 18 | #33736 | — | 2 | 1 | no | — |
| 19 | #33611 | — | 2 | 1 | no | — |
| 20 | #33611 | C22 | 1 | 2 | yes | — |
| 21 | #33434 | C22 | 1 | 1 | yes | characteristic |
| 22 | #33414 | C22 | 1 | 1 | yes | characteristic |
| 23 | #27693 | — | 2 | 1 | no | — |
| 24 | #13718 | — | 2 | 2 | no | — |
| 25 | #13718 | C22 | 1 | 4 | yes | — |
| 26 | #13717 | — | 2 | 2 | no | — |
| 27 | #13717 | C22 | 1 | 4 | yes | — |
| 28 | C2×#1426 | — | 2 | 2 | no | — |
| 29 | #13625 | — | 2 | 2 | no | — |
| 30 | #13556 | C22 | 1 | 2 | yes | — |
| 31 | #13519 | C22 | 1 | 2 | yes | — |
| 32 | #13499 | C22 | 1 | 2 | yes | — |
| 33 | #13169 | — | 2 | 1 | no | — |
| 34 | #12877 | — | 2 | 1 | no | — |
| 35 | #12841 | — | 2 | 1 | no | — |
| 36 | #12839 | C22 | 1 | 1 | yes | characteristic |
| 37 | #7423 | C22 | 1 | 4 | yes | — |
| 38 | #7422 | C22 | 1 | 4 | yes | — |
| 39 | #7364 | C22 | 1 | 2 | yes | — |
| 40 | #7337 | C22 | 1 | 2 | yes | — |
| 41 | #3548 | — | 4 | 1 | no | — |
| 42 | C2×#508 | — | 2 | 1 | no | — |
| 43 | C2×#508 | D4 | 1 | 2 | yes | — |
| 44 | C2×#504 | D4 | 1 | 1 | yes | characteristic |
| 45 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 46 | #3338 | — | 2 | 2 | no | — |
| 47 | #3334 | — | 2 | 2 | no | — |
| 48 | #3333 | — | 4 | 2 | no | — |
| 49 | #3330 | — | 4 | 2 | no | — |
| 50 | #3287 | — | 2 | 2 | no | — |
| 51 | #3283 | — | 2 | 2 | no | — |
| 52 | #3254 | — | 4 | 1 | no | — |
| 53 | #3203 | — | 4 | 1 | no | — |
| 54 | #3203 | — | 4 | 1 | no | — |
| 55 | #3170 | — | 2 | 1 | no | — |
| 56 | #3169 | — | 2 | 1 | no | — |
| 57 | #3061 | — | 2 | 2 | no | — |
| 58 | #3061 | — | 2 | 2 | no | — |
| 59 | #2931 | D4 | 1 | 1 | yes | characteristic |
| 60 | #2916 | — | 2 | 1 | no | — |
| 61 | C2×M64 | — | 2 | 2 | no | — |
| 62 | #2254 | — | 2 | 1 | no | — |
| 63 | #2248 | — | 2 | 1 | no | — |
| 64 | #2241 | — | 2 | 1 | no | — |
| 65 | #2240 | — | 2 | 1 | no | — |
| 66 | #2235 | — | 2 | 2 | no | — |
| 67 | #2235 | — | 2 | 2 | no | — |
| 68 | #2233 | — | 2 | 2 | no | — |
| 69 | #2233 | — | 2 | 2 | no | — |
| 70 | #2226 | — | 2 | 2 | no | — |
| 71 | #2225 | — | 2 | 2 | no | — |
| 72 | #2219 | — | 2 | 1 | no | — |
| 73 | #2219 | — | 2 | 1 | no | — |
| 74 | #2219 | D4 | 1 | 2 | yes | — |
| 75 | #2219 | C23 | 1 | 2 | yes | — |
| 76 | #2218 | — | 2 | 1 | no | — |
| 77 | #2218 | — | 2 | 1 | no | — |
| 78 | #2218 | D4 | 1 | 2 | yes | — |
| 79 | #2218 | C23 | 1 | 2 | yes | — |
| 80 | #2217 | — | 2 | 2 | no | — |
| 81 | #2217 | — | 2 | 2 | no | — |
| 82 | #2217 | — | 2 | 2 | no | — |
| 83 | #2217 | — | 2 | 2 | no | — |
| 84 | #2209 | — | 2 | 2 | no | — |
| 85 | #2206 | — | 2 | 2 | no | — |
| 86 | #2189 | — | 2 | 2 | no | — |
| 87 | #2189 | — | 2 | 2 | no | — |
| 88 | #2186 | — | 2 | 2 | no | — |
| 89 | #2186 | — | 2 | 2 | no | — |
| 90 | C4×SD32 | — | 2 | 2 | no | — |
| 91 | C4×SD32 | — | 2 | 2 | no | — |
| 92 | #2169 | — | 2 | 2 | no | — |
| 93 | D4×C16 | — | 2 | 2 | no | — |
| 94 | #2161 | — | 2 | 2 | no | — |
| 95 | #2161 | C23 | 1 | 2 | yes | — |
| 96 | C2×#368 | — | 2 | 2 | no | — |
| 97 | C2×#368 | — | 2 | 1 | no | — |
| 98 | #2158 | — | 2 | 1 | no | — |
| 99 | C2×#367 | — | 2 | 1 | no | — |
| 100 | C2×#367 | D4 | 1 | 2 | yes | — |
| 101 | #2150 | C23 | 1 | 1 | yes | characteristic |
| 102 | #2139 | — | 2 | 2 | no | — |
| 103 | #2139 | — | 2 | 2 | no | — |
| 104 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 105 | #2113 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C16 | D4 | 1 | 1 | yes | characteristic |
| 107 | #2102 | — | 4 | 1 | no | — |
| 108 | #2098 | — | 4 | 1 | no | — |
| 109 | #1945 | — | 2 | 2 | no | — |
| 110 | #1884 | — | 4 | 1 | no | — |
| 111 | #1868 | — | 4 | 1 | no | — |
| 112 | #1814 | — | 2 | 2 | no | — |
| 113 | #1812 | — | 2 | 1 | no | — |
| 114 | #1426 | — | 2 | 4 | no | — |
| 115 | #1426 | — | 2 | 4 | no | — |
| 116 | #1420 | — | 2 | 4 | no | — |
| 117 | #1419 | — | 2 | 4 | no | — |
| 118 | #1400 | — | 2 | 2 | no | — |
| 119 | #1400 | C23 | 1 | 4 | yes | — |
| 120 | #1389 | — | 2 | 2 | no | — |
| 121 | #1384 | C23 | 1 | 2 | yes | — |
| 122 | #1382 | — | 2 | 2 | no | — |
| 123 | C2×#135 | — | 2 | 2 | no | — |
| 124 | C2×#135 | — | 2 | 2 | no | — |
| 125 | #568 | — | 4 | 1 | no | — |
| 126 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | #562 | — | 8 | 1 | no | — |
| 129 | #562 | — | 8 | 1 | no | — |
| 130 | #554 | — | 4 | 2 | no | — |
| 131 | #554 | — | 8 | 1 | no | — |
| 132 | #550 | — | 4 | 2 | no | — |
| 133 | #550 | — | 8 | 1 | no | — |
| 134 | #547 | — | 4 | 2 | no | — |
| 135 | #547 | — | 4 | 2 | no | — |
| 136 | #540 | — | 8 | 2 | no | — |
| 137 | #537 | — | 4 | 2 | no | — |
| 138 | #537 | — | 4 | 2 | no | — |
| 139 | #537 | — | 8 | 2 | no | — |
| 140 | #533 | — | 4 | 1 | no | — |
| 141 | #532 | — | 4 | 1 | no | — |
| 142 | #532 | D8 | 1 | 1 | yes | characteristic |
| 143 | #508 | — | 4 | 2 | no | — |
| 144 | #508 | — | 4 | 2 | no | — |
| 145 | #508 | — | 8 | 1 | no | — |
| 146 | #508 | — | 8 | 1 | no | — |
| 147 | C2×Q32 | — | 2 | 1 | no | — |
| 148 | C2×Q32 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×SD32 | — | 2 | 2 | no | — |
| 150 | C2×SD32 | — | 2 | 2 | no | — |
| 151 | C2×D16 | — | 2 | 1 | no | — |
| 152 | C2×D16 | C2×D4 | 1 | 2 | yes | — |
| 153 | #504 | — | 4 | 1 | no | — |
| 154 | #504 | — | 4 | 1 | no | — |
| 155 | #504 | — | 4 | 1 | no | — |
| 156 | #504 | — | 4 | 1 | no | — |
| 157 | C2×M32 | — | 2 | 1 | no | — |
| 158 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 160 | C2×M32 | C24 | 1 | 1 | yes | characteristic |
| 161 | C22×C16 | — | 2 | 1 | no | — |
| 162 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C22×C16 | C2×D4 | 1 | 2 | yes | — |
| 164 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | #500 | — | 2 | 1 | no | — |
| 166 | #500 | — | 2 | 1 | no | — |
| 167 | #494 | — | 2 | 1 | no | — |
| 168 | #493 | — | 2 | 1 | no | — |
| 169 | #487 | — | 4 | 1 | no | — |
| 170 | #486 | — | 4 | 1 | no | — |
| 171 | #484 | — | 4 | 2 | no | — |
| 172 | #484 | — | 4 | 2 | no | — |
| 173 | #480 | — | 4 | 2 | no | — |
| 174 | #480 | — | 4 | 2 | no | — |
| 175 | #477 | — | 4 | 2 | no | — |
| 176 | #474 | — | 4 | 2 | no | — |
| 177 | #468 | — | 4 | 2 | no | — |
| 178 | #468 | — | 4 | 2 | no | — |
| 179 | #468 | — | 4 | 2 | no | — |
| 180 | #468 | — | 4 | 2 | no | — |
| 181 | #467 | — | 2 | 2 | no | — |
| 182 | #467 | — | 2 | 2 | no | — |
| 183 | #467 | — | 2 | 2 | no | — |
| 184 | #467 | — | 4 | 1 | no | — |
| 185 | #466 | — | 2 | 2 | no | — |
| 186 | #466 | — | 2 | 2 | no | — |
| 187 | #466 | — | 2 | 2 | no | — |
| 188 | #466 | — | 4 | 1 | no | — |
| 189 | #461 | — | 4 | 2 | no | — |
| 190 | #460 | — | 4 | 2 | no | — |
| 191 | #452 | — | 4 | 2 | no | — |
| 192 | #452 | — | 4 | 2 | no | — |
| 193 | #449 | — | 4 | 2 | no | — |
| 194 | #449 | — | 4 | 2 | no | — |
| 195 | C4×Q16 | — | 2 | 2 | no | — |
| 196 | C4×Q16 | — | 4 | 1 | no | — |
| 197 | C4×D8 | — | 2 | 2 | no | — |
| 198 | C4×D8 | — | 4 | 1 | no | — |
| 199 | #436 | — | 2 | 2 | no | — |
| 200 | C8×D4 | — | 2 | 2 | no | — |
| 201 | #430 | — | 4 | 2 | no | — |
| 202 | #430 | — | 4 | 1 | no | — |
| 203 | C2×#108 | — | 2 | 2 | no | — |
| 204 | C2×#108 | — | 4 | 2 | no | — |
| 205 | #427 | — | 2 | 2 | no | — |
| 206 | C2×#107 | — | 2 | 2 | no | — |
| 207 | C2×#107 | — | 2 | 2 | no | — |
| 208 | #424 | — | 4 | 2 | no | — |
| 209 | #423 | D8 | 1 | 1 | yes | characteristic |
| 210 | #421 | — | 4 | 2 | no | — |
| 211 | #417 | — | 4 | 2 | no | — |
| 212 | #417 | — | 4 | 2 | no | — |
| 213 | #410 | — | 4 | 1 | no | — |
| 214 | #408 | D8 | 1 | 1 | yes | characteristic |
| 215 | #408 | D8 | 1 | 1 | yes | characteristic |
| 216 | C2×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | M64 | — | 2 | 4 | no | — |
| 218 | M64 | — | 4 | 2 | no | — |
| 219 | C2×C32 | — | 4 | 2 | no | — |
| 220 | #368 | — | 2 | 4 | no | — |
| 221 | #368 | — | 4 | 1 | no | — |
| 222 | #368 | — | 4 | 1 | no | — |
| 223 | #367 | — | 2 | 1 | no | — |
| 224 | #367 | — | 2 | 1 | no | — |
| 225 | #367 | — | 2 | 2 | no | — |
| 226 | #367 | — | 2 | 2 | no | — |
| 227 | #367 | — | 4 | 1 | no | — |
| 228 | #367 | C2×D4 | 1 | 2 | yes | — |
| 229 | #367 | C2×D4 | 1 | 2 | yes | — |
| 230 | #366 | — | 4 | 1 | no | — |
| 231 | C4⋊C16 | — | 2 | 2 | no | — |
| 232 | #358 | — | 2 | 2 | no | — |
| 233 | #358 | — | 2 | 2 | no | — |
| 234 | #358 | — | 2 | 2 | no | — |
| 235 | #358 | — | 2 | 2 | no | — |
| 236 | #357 | — | 2 | 2 | no | — |
| 237 | #357 | — | 2 | 2 | no | — |
| 238 | #357 | — | 2 | 2 | no | — |
| 239 | #357 | — | 2 | 2 | no | — |
| 240 | C22⋊C16 | — | 2 | 2 | no | — |
| 241 | C22⋊C16 | — | 2 | 2 | no | — |
| 242 | C4×C16 | — | 2 | 1 | no | — |
| 243 | C4×C16 | — | 2 | 1 | no | — |
| 244 | #344 | — | 4 | 2 | no | — |
| 245 | #339 | — | 4 | 2 | no | — |
| 246 | H(3,ℤ/4) | — | 4 | 1 | no | — |
| 247 | C2×#41 | — | 4 | 2 | no | — |
| 248 | C2×#41 | — | 4 | 2 | no | — |
| 249 | C2×#41 | — | 8 | 1 | no | — |
| 250 | C2×#41 | — | 8 | 2 | no | — |
| 251 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 252 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 253 | #135 | — | 8 | 2 | no | — |
| 254 | #135 | — | 8 | 2 | no | — |
| 255 | #135 | — | 8 | 2 | no | — |
| 256 | #135 | — | 8 | 2 | no | — |
| 257 | C2×Q16 | — | 2 | 2 | no | — |
| 258 | C2×Q16 | — | 4 | 1 | no | — |
| 259 | C2×SD16 | — | 4 | 2 | no | — |
| 260 | C2×SD16 | — | 4 | 2 | no | — |
| 261 | C2×D8 | — | 2 | 2 | no | — |
| 262 | C2×D8 | — | 4 | 1 | no | — |
| 263 | #131 | — | 4 | 1 | no | — |
| 264 | #131 | — | 4 | 1 | no | — |
| 265 | #131 | — | 4 | 1 | no | — |
| 266 | #131 | — | 4 | 1 | no | — |
| 267 | #131 | — | 16 | 2 | no | — |
| 268 | C2×M16 | — | 2 | 1 | no | — |
| 269 | C2×M16 | — | 4 | 2 | no | — |
| 270 | C2×M16 | — | 8 | 2 | no | — |
| 271 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 272 | C2×M16 | C2×D8 | 1 | 1 | yes | characteristic |
| 273 | C2×M16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 274 | C22×C8 | — | 2 | 1 | no | — |
| 275 | C22×C8 | #120 | 1 | 2 | yes | — |
| 276 | C22×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 277 | C22×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 278 | C4⋊Q8 | — | 4 | 1 | no | — |
| 279 | C4⋊Q8 | — | 4 | 1 | no | — |
| 280 | C4⋊Q8 | — | 4 | 1 | no | — |
| 281 | C4⋊Q8 | SD32 | 1 | 1 | yes | characteristic |
| 282 | #127 | — | 4 | 1 | no | — |
| 283 | #127 | — | 8 | 2 | no | — |
| 284 | #127 | SD32 | 1 | 1 | yes | characteristic |
| 285 | #125 | — | 8 | 2 | no | — |
| 286 | #125 | — | 8 | 1 | no | — |
| 287 | #124 | — | 8 | 1 | no | — |
| 288 | #124 | SD32 | 1 | 1 | yes | characteristic |
| 289 | #124 | SD32 | 1 | 1 | yes | characteristic |
| 290 | #123 | — | 8 | 2 | no | — |
| 291 | #123 | — | 8 | 2 | no | — |
| 292 | #123 | — | 8 | 2 | no | — |
| 293 | #123 | — | 8 | 2 | no | — |
| 294 | C22⋊Q8 | — | 4 | 2 | no | — |
| 295 | C22⋊Q8 | — | 4 | 2 | no | — |
| 296 | C22⋊Q8 | — | 4 | 2 | no | — |
| 297 | C22⋊Q8 | — | 8 | 2 | no | — |
| 298 | C22⋊Q8 | — | 8 | 2 | no | — |
| 299 | C22⋊Q8 | — | 8 | 2 | no | — |
| 300 | C22⋊Q8 | — | 8 | 1 | no | — |
| 301 | C22⋊Q8 | — | 8 | 2 | no | — |
| 302 | C22⋊Q8 | — | 8 | 2 | no | — |
| 303 | #121 | — | 2 | 2 | no | — |
| 304 | #121 | — | 4 | 2 | no | — |
| 305 | #121 | — | 4 | 2 | no | — |
| 306 | #121 | — | 4 | 2 | no | — |
| 307 | #121 | — | 8 | 2 | no | — |
| 308 | #121 | — | 8 | 2 | no | — |
| 309 | #121 | — | 8 | 1 | no | — |
| 310 | #121 | — | 8 | 2 | no | — |
| 311 | #121 | — | 8 | 2 | no | — |
| 312 | #121 | — | 8 | 2 | no | — |
| 313 | #121 | — | 8 | 2 | no | — |
| 314 | #121 | — | 8 | 2 | no | — |
| 315 | #121 | — | 8 | 2 | no | — |
| 316 | #121 | — | 8 | 2 | no | — |
| 317 | C4×Q8 | — | 4 | 2 | no | — |
| 318 | C4×Q8 | — | 8 | 1 | no | — |
| 319 | C4×D4 | — | 2 | 2 | no | — |
| 320 | C4×D4 | — | 4 | 2 | no | — |
| 321 | C4×D4 | — | 8 | 2 | no | — |
| 322 | C4×D4 | — | 8 | 2 | no | — |
| 323 | C4×D4 | — | 8 | 1 | no | — |
| 324 | #117 | — | 4 | 2 | no | — |
| 325 | #117 | — | 8 | 1 | no | — |
| 326 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 327 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 328 | C2×C4⋊C4 | — | 8 | 2 | no | — |
| 329 | C2×C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 330 | Q32 | — | 4 | 2 | no | — |
| 331 | Q32 | — | 8 | 1 | no | — |
| 332 | SD32 | — | 4 | 2 | no | — |
| 333 | SD32 | — | 4 | 2 | no | — |
| 334 | SD32 | — | 8 | 2 | no | — |
| 335 | D16 | — | 4 | 2 | no | — |
| 336 | D16 | — | 8 | 1 | no | — |
| 337 | M32 | — | 4 | 2 | no | — |
| 338 | M32 | — | 4 | 1 | no | — |
| 339 | M32 | — | 4 | 1 | no | — |
| 340 | M32 | — | 8 | 1 | no | — |
| 341 | C2×C16 | — | 2 | 1 | no | — |
| 342 | C2×C16 | — | 2 | 1 | no | — |
| 343 | C2×C16 | — | 2 | 2 | no | — |
| 344 | C2×C16 | — | 2 | 2 | no | — |
| 345 | C2×C16 | — | 2 | 1 | no | — |
| 346 | C2×C16 | — | 2 | 1 | no | — |
| 347 | C2×C16 | — | 4 | 1 | no | — |
| 348 | C2×C16 | — | 4 | 1 | no | — |
| 349 | C2×C16 | — | 4 | 1 | no | — |
| 350 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 351 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 352 | C2×C16 | C22×D4 | 1 | 2 | yes | — |
| 353 | #108 | — | 4 | 2 | no | — |
| 354 | #108 | — | 4 | 2 | no | — |
| 355 | #108 | — | 8 | 2 | no | — |
| 356 | #107 | — | 2 | 2 | no | — |
| 357 | #107 | — | 2 | 2 | no | — |
| 358 | #107 | — | 4 | 2 | no | — |
| 359 | #107 | — | 4 | 1 | no | — |
| 360 | #107 | — | 4 | 1 | no | — |
| 361 | #107 | — | 4 | 2 | no | — |
| 362 | #107 | — | 4 | 2 | no | — |
| 363 | #106 | — | 4 | 2 | no | — |
| 364 | C4⋊C8 | — | 2 | 2 | no | — |
| 365 | C4⋊C8 | — | 16 | 2 | no | — |
| 366 | #104 | — | 16 | 2 | no | — |
| 367 | #103 | — | 4 | 2 | no | — |
| 368 | #103 | — | 4 | 2 | no | — |
| 369 | #103 | — | 4 | 2 | no | — |
| 370 | #103 | — | 4 | 2 | no | — |
| 371 | #102 | — | 4 | 2 | no | — |
| 372 | #102 | — | 4 | 2 | no | — |
| 373 | #102 | — | 4 | 2 | no | — |
| 374 | #102 | — | 4 | 2 | no | — |
| 375 | #99 | — | 8 | 2 | no | — |
| 376 | C22⋊C8 | — | 2 | 2 | no | — |
| 377 | C22⋊C8 | — | 2 | 2 | no | — |
| 378 | C4×C8 | — | 2 | 1 | no | — |
| 379 | C4×C8 | — | 2 | 1 | no | — |
| 380 | C32 | — | 4 | 4 | no | — |
| 381 | #41 | — | 4 | 1 | no | — |
| 382 | #41 | — | 4 | 1 | no | — |
| 383 | #41 | — | 4 | 1 | no | — |
| 384 | #41 | — | 4 | 1 | no | — |
| 385 | #41 | — | 16 | 2 | no | — |
| 386 | #41 | — | 16 | 2 | no | — |
| 387 | #41 | — | 16 | 2 | no | — |
| 388 | #41 | — | 16 | 2 | no | — |
| 389 | #41 | — | 32 | 2 | no | — |
| 390 | #41 | — | 32 | 4 | no | — |
| 391 | C2×Q8 | — | 4 | 2 | no | — |
| 392 | C2×Q8 | — | 8 | 1 | no | — |
| 393 | C2×Q8 | — | 8 | 1 | no | — |
| 394 | C2×Q8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 395 | C2×Q8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 396 | C2×D4 | — | 2 | 2 | no | — |
| 397 | C2×D4 | — | 2 | 1 | no | — |
| 398 | C2×D4 | — | 4 | 2 | no | — |
| 399 | C2×D4 | — | 8 | 1 | no | — |
| 400 | C2×D4 | — | 8 | 1 | no | — |
| 401 | C2×D4 | — | 8 | 2 | no | — |
| 402 | C2×D4 | — | 8 | 2 | no | — |
| 403 | C2×D4 | — | 8 | 2 | no | — |
| 404 | C2×D4 | — | 8 | 2 | no | — |
| 405 | C2×D4 | — | 8 | 2 | no | — |
| 406 | C2×D4 | C2×SD32 | 1 | 1 | yes | characteristic |
| 407 | C2×D4 | C2×SD32 | 1 | 1 | yes | characteristic |
| 408 | C2×D4 | #509 | 1 | 2 | yes | — |
| 409 | C22×C4 | — | 2 | 1 | no | — |
| 410 | C22×C4 | — | 2 | 1 | no | — |
| 411 | C22×C4 | — | 8 | 2 | no | — |
| 412 | C22×C4 | — | 8 | 2 | no | — |
| 413 | C22×C4 | — | 8 | 2 | no | — |
| 414 | C22×C4 | — | 8 | 2 | no | — |
| 415 | C22×C4 | — | 8 | 2 | no | — |
| 416 | C22×C4 | #447 | 1 | 2 | yes | — |
| 417 | C22×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 418 | Q16 | — | 4 | 2 | no | — |
| 419 | Q16 | — | 4 | 2 | no | — |
| 420 | Q16 | — | 16 | 1 | no | — |
| 421 | SD16 | — | 16 | 2 | no | — |
| 422 | SD16 | — | 16 | 2 | no | — |
| 423 | D8 | — | 4 | 2 | no | — |
| 424 | D8 | — | 4 | 2 | no | — |
| 425 | D8 | — | 16 | 1 | no | — |
| 426 | M16 | — | 4 | 1 | no | — |
| 427 | M16 | — | 4 | 2 | no | — |
| 428 | M16 | — | 4 | 1 | no | — |
| 429 | M16 | — | 8 | 1 | no | — |
| 430 | M16 | — | 8 | 2 | no | — |
| 431 | M16 | — | 8 | 2 | no | — |
| 432 | M16 | — | 16 | 2 | no | — |
| 433 | C2×C8 | — | 2 | 1 | no | — |
| 434 | C2×C8 | — | 2 | 2 | no | — |
| 435 | C2×C8 | — | 2 | 1 | no | — |
| 436 | C2×C8 | — | 2 | 2 | no | — |
| 437 | C2×C8 | — | 2 | 1 | no | — |
| 438 | C2×C8 | — | 2 | 1 | no | — |
| 439 | C2×C8 | — | 4 | 1 | no | — |
| 440 | C2×C8 | — | 4 | 1 | no | — |
| 441 | C2×C8 | — | 4 | 1 | no | — |
| 442 | C2×C8 | — | 8 | 2 | no | — |
| 443 | C2×C8 | — | 16 | 2 | no | — |
| 444 | C2×C8 | #447 | 1 | 2 | yes | — |
| 445 | C2×C8 | C2×#120 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 447 | C4⋊C4 | — | 2 | 2 | no | — |
| 448 | C4⋊C4 | — | 4 | 2 | no | — |
| 449 | C4⋊C4 | — | 4 | 2 | no | — |
| 450 | C4⋊C4 | — | 8 | 2 | no | — |
| 451 | C4⋊C4 | — | 8 | 1 | no | — |
| 452 | C4⋊C4 | — | 8 | 2 | no | — |
| 453 | C4⋊C4 | — | 8 | 1 | no | — |
| 454 | C4⋊C4 | — | 8 | 1 | no | — |
| 455 | C4⋊C4 | — | 8 | 1 | no | — |
| 456 | C4⋊C4 | — | 8 | 2 | no | — |
| 457 | C4⋊C4 | — | 8 | 2 | no | — |
| 458 | C4⋊C4 | — | 8 | 2 | no | — |
| 459 | C4⋊C4 | — | 8 | 2 | no | — |
| 460 | C4⋊C4 | — | 8 | 2 | no | — |
| 461 | C22⋊C4 | — | 2 | 2 | no | — |
| 462 | C22⋊C4 | — | 2 | 2 | no | — |
| 463 | C22⋊C4 | — | 8 | 2 | no | — |
| 464 | C22⋊C4 | — | 8 | 2 | no | — |
| 465 | C22⋊C4 | — | 8 | 2 | no | — |
| 466 | C22⋊C4 | — | 8 | 2 | no | — |
| 467 | C22⋊C4 | — | 8 | 2 | no | — |
| 468 | C22⋊C4 | — | 8 | 2 | no | — |
| 469 | C22⋊C4 | — | 8 | 2 | no | — |
| 470 | C22⋊C4 | — | 8 | 2 | no | — |
| 471 | C42 | — | 2 | 1 | no | — |
| 472 | C42 | — | 8 | 2 | no | — |
| 473 | C42 | — | 8 | 2 | no | — |
| 474 | C42 | C2×SD32 | 1 | 1 | yes | characteristic |
| 475 | C42 | C2×SD32 | 1 | 1 | yes | characteristic |
| 476 | C16 | — | 2 | 2 | no | — |
| 477 | C16 | — | 2 | 1 | no | — |
| 478 | C16 | — | 4 | 1 | no | — |
| 479 | C16 | — | 4 | 1 | no | — |
| 480 | C16 | #458 | 1 | 1 | yes | characteristic |
| 481 | C16 | #458 | 1 | 1 | yes | characteristic |
| 482 | C23 | — | 2 | 1 | no | — |
| 483 | C23 | — | 8 | 2 | no | — |
| 484 | C23 | #2187 | 1 | 2 | yes | — |
| 485 | C23 | C2×#509 | 1 | 1 | yes | characteristic |
| 486 | Q8 | — | 4 | 1 | no | — |
| 487 | Q8 | — | 4 | 1 | no | — |
| 488 | Q8 | — | 8 | 2 | no | — |
| 489 | Q8 | — | 8 | 2 | no | — |
| 490 | Q8 | — | 16 | 2 | no | — |
| 491 | Q8 | — | 32 | 1 | no | — |
| 492 | D4 | — | 4 | 1 | no | — |
| 493 | D4 | — | 4 | 2 | no | — |
| 494 | D4 | — | 4 | 1 | no | — |
| 495 | D4 | — | 4 | 4 | no | — |
| 496 | D4 | — | 8 | 1 | no | — |
| 497 | D4 | — | 8 | 2 | no | — |
| 498 | D4 | — | 8 | 2 | no | — |
| 499 | D4 | — | 16 | 2 | no | — |
| 500 | D4 | — | 32 | 1 | no | — |
| 501 | D4 | — | 32 | 2 | no | — |
| 502 | D4 | — | 32 | 2 | no | — |
| 503 | D4 | — | 32 | 2 | no | — |
| 504 | D4 | — | 32 | 2 | no | — |
| 505 | D4 | — | 32 | 2 | no | — |
| 506 | C2×C4 | — | 2 | 1 | no | — |
| 507 | C2×C4 | — | 2 | 1 | no | — |
| 508 | C2×C4 | — | 2 | 2 | no | — |
| 509 | C2×C4 | — | 2 | 1 | no | — |
| 510 | C2×C4 | — | 2 | 2 | no | — |
| 511 | C2×C4 | — | 2 | 1 | no | — |
| 512 | C2×C4 | — | 2 | 1 | no | — |
| 513 | C2×C4 | — | 4 | 2 | no | — |
| 514 | C2×C4 | — | 4 | 1 | no | — |
| 515 | C2×C4 | — | 4 | 1 | no | — |
| 516 | C2×C4 | — | 8 | 2 | no | — |
| 517 | C2×C4 | — | 8 | 2 | no | — |
| 518 | C2×C4 | — | 8 | 2 | no | — |
| 519 | C2×C4 | — | 16 | 4 | no | — |
| 520 | C2×C4 | — | 16 | 2 | no | — |
| 521 | C2×C4 | — | 32 | 2 | no | — |
| 522 | C2×C4 | — | 32 | 2 | no | — |
| 523 | C2×C4 | — | 32 | 2 | no | — |
| 524 | C2×C4 | — | 32 | 2 | no | — |
| 525 | C2×C4 | #2187 | 1 | 2 | yes | — |
| 526 | C2×C4 | C2×#447 | 1 | 1 | yes | characteristic |
| 527 | C2×C4 | C22×SD32 | 1 | 1 | yes | characteristic |
| 528 | C8 | — | 2 | 1 | no | — |
| 529 | C8 | — | 2 | 2 | no | — |
| 530 | C8 | — | 4 | 1 | no | — |
| 531 | C8 | — | 4 | 1 | no | — |
| 532 | C8 | — | 16 | 2 | no | — |
| 533 | C8 | #3022 | 1 | 1 | yes | characteristic |
| 534 | C8 | C2×#458 | 1 | 1 | yes | characteristic |
| 535 | C22 | — | 2 | 1 | no | — |
| 536 | C22 | — | 2 | 2 | no | — |
| 537 | C22 | — | 4 | 1 | no | — |
| 538 | C22 | — | 4 | 2 | no | — |
| 539 | C22 | — | 4 | 2 | no | — |
| 540 | C22 | — | 4 | 1 | no | — |
| 541 | C22 | — | 16 | 2 | no | — |
| 542 | C22 | — | 16 | 2 | no | — |
| 543 | C22 | — | 16 | 2 | no | — |
| 544 | C22 | C2×#2187 | 1 | 1 | yes | characteristic |
| 545 | C4 | — | 2 | 2 | no | — |
| 546 | C4 | — | 2 | 2 | no | — |
| 547 | C4 | — | 2 | 1 | no | — |
| 548 | C4 | — | 4 | 1 | no | — |
| 549 | C4 | — | 4 | 1 | no | — |
| 550 | C4 | — | 16 | 2 | no | — |
| 551 | C4 | — | 16 | 2 | no | — |
| 552 | C4 | — | 16 | 2 | no | — |
| 553 | C4 | — | 32 | 2 | no | — |
| 554 | C4 | #18202 | 1 | 1 | yes | characteristic |
| 555 | C4 | #33531 | 1 | 1 | yes | characteristic |
| 556 | C2 | — | 2 | 1 | no | — |
| 557 | C2 | — | 4 | 1 | no | — |
| 558 | C2 | — | 4 | 2 | no | — |
| 559 | C2 | — | 8 | 1 | no | — |
| 560 | C2 | — | 32 | 2 | no | — |
| 561 | C2 | #486654 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #486654 |
| commutator, Frattini, cosocle | C2×M32 | C24 |
| prime radical | #7624863 | C2 |
| LCS | G ▷ C2×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #33434 ◁ G | |
| LECS | G ▷ C2×M32 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #512993 | C2 | semidirect |
| 3. #505706 | C2 | semidirect |
| 4. #151510 | C2 | semidirect |
| 5. #151509 | C2 | semidirect |
| 6. #151495 | C2 | semidirect |
| 7. #150878 | C2 | semidirect |
| 8. #149671 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7624863 | 2 |
| #512993 | 2 |
| #505706 | 2 |
| #151510 | 2 |
| #151509 | 2 |
| #151495 | 2 |
| #150878 | 2 |
| #149671 | 2 |