Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1658 conjugacy classes of subgroups.
The subgroup lattice has 625 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #61378 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #61326 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #61292 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #31183 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #28300 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #28243 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #28218 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #27810 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #26854 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #26081 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #25433 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #24318 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #24181 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #23048 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #21737 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #21694 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #21659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #3507 | C22 | 1 | 2 | yes | — |
| 19 | #3501 | C22 | 1 | 2 | yes | — |
| 20 | #3389 | — | 2 | 4 | no | — |
| 21 | #3384 | — | 2 | 4 | no | — |
| 22 | #3376 | — | 2 | 4 | no | — |
| 23 | #3373 | — | 2 | 2 | no | — |
| 24 | #3372 | — | 2 | 2 | no | — |
| 25 | #3361 | — | 2 | 2 | no | — |
| 26 | #3360 | — | 2 | 4 | no | — |
| 27 | #3359 | — | 2 | 2 | no | — |
| 28 | #3349 | — | 2 | 4 | no | — |
| 29 | #3344 | — | 2 | 4 | no | — |
| 30 | #3163 | C22 | 1 | 2 | yes | — |
| 31 | #3162 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3137 | C22 | 1 | 4 | yes | — |
| 34 | #3131 | C22 | 1 | 1 | yes | characteristic |
| 35 | #3097 | C22 | 1 | 4 | yes | — |
| 36 | #3084 | C22 | 1 | 4 | yes | — |
| 37 | #3081 | C22 | 1 | 4 | yes | — |
| 38 | #3078 | C22 | 1 | 2 | yes | — |
| 39 | #3078 | C22 | 1 | 2 | yes | — |
| 40 | #3077 | C22 | 1 | 2 | yes | — |
| 41 | C2×#472 | C22 | 1 | 2 | yes | — |
| 42 | #3059 | C22 | 1 | 2 | yes | — |
| 43 | #3042 | C22 | 1 | 4 | yes | — |
| 44 | #3036 | C22 | 1 | 2 | yes | — |
| 45 | #2961 | C22 | 1 | 1 | yes | characteristic |
| 46 | #2960 | C22 | 1 | 2 | yes | — |
| 47 | #2948 | C22 | 1 | 2 | yes | — |
| 48 | #2946 | C22 | 1 | 4 | yes | — |
| 49 | C2×#442 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#441 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×C4×SD16 | C22 | 1 | 2 | yes | — |
| 52 | #2932 | C22 | 1 | 1 | yes | characteristic |
| 53 | #2912 | C22 | 1 | 2 | yes | — |
| 54 | #2326 | C22 | 1 | 2 | yes | — |
| 55 | #2090 | C22 | 1 | 4 | yes | — |
| 56 | #2064 | C22 | 1 | 4 | yes | — |
| 57 | #2060 | C22 | 1 | 4 | yes | — |
| 58 | #2051 | C22 | 1 | 4 | yes | — |
| 59 | #2046 | C22 | 1 | 4 | yes | — |
| 60 | #2038 | C22 | 1 | 4 | yes | — |
| 61 | #2028 | C22 | 1 | 4 | yes | — |
| 62 | #2003 | C22 | 1 | 4 | yes | — |
| 63 | #1995 | C22 | 1 | 2 | yes | — |
| 64 | #1995 | C22 | 1 | 1 | yes | characteristic |
| 65 | #1979 | C22 | 1 | 2 | yes | — |
| 66 | #1972 | C22 | 1 | 1 | yes | characteristic |
| 67 | #1971 | C22 | 1 | 1 | yes | characteristic |
| 68 | #1968 | C22 | 1 | 2 | yes | — |
| 69 | #1963 | C22 | 1 | 1 | yes | characteristic |
| 70 | #1959 | C22 | 1 | 2 | yes | — |
| 71 | #1951 | C22 | 1 | 2 | yes | — |
| 72 | #1945 | C22 | 1 | 2 | yes | — |
| 73 | #1945 | C22 | 1 | 2 | yes | — |
| 74 | #1938 | C22 | 1 | 2 | yes | — |
| 75 | #1937 | C22 | 1 | 2 | yes | — |
| 76 | #1931 | C22 | 1 | 4 | yes | — |
| 77 | #1930 | C22 | 1 | 4 | yes | — |
| 78 | #1885 | C22 | 1 | 4 | yes | — |
| 79 | #1883 | C22 | 1 | 4 | yes | — |
| 80 | #1859 | C22 | 1 | 4 | yes | — |
| 81 | #1856 | C22 | 1 | 4 | yes | — |
| 82 | #1849 | C22 | 1 | 1 | yes | characteristic |
| 83 | #1844 | C22 | 1 | 1 | yes | characteristic |
| 84 | #1837 | C22 | 1 | 1 | yes | characteristic |
| 85 | #1815 | C22 | 1 | 2 | yes | — |
| 86 | #1801 | C22 | 1 | 2 | yes | — |
| 87 | #1800 | C22 | 1 | 2 | yes | — |
| 88 | #1773 | C22 | 1 | 2 | yes | — |
| 89 | #1773 | C22 | 1 | 2 | yes | — |
| 90 | #1765 | C22 | 1 | 2 | yes | — |
| 91 | #1764 | C22 | 1 | 2 | yes | — |
| 92 | #1726 | C22 | 1 | 1 | yes | characteristic |
| 93 | C2×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 94 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 95 | C22×SD16 | C23 | 1 | 2 | yes | — |
| 96 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#131 | C23 | 1 | 2 | yes | — |
| 98 | #559 | — | 2 | 2 | no | — |
| 99 | #557 | — | 2 | 2 | no | — |
| 100 | #556 | — | 2 | 2 | no | — |
| 101 | #556 | — | 2 | 4 | no | — |
| 102 | #554 | — | 2 | 2 | no | — |
| 103 | #554 | — | 2 | 2 | no | — |
| 104 | #554 | — | 2 | 2 | no | — |
| 105 | #554 | — | 2 | 4 | no | — |
| 106 | #554 | — | 2 | 4 | no | — |
| 107 | #552 | — | 2 | 4 | no | — |
| 108 | D4×Q8 | — | 2 | 2 | no | — |
| 109 | D4×Q8 | — | 2 | 2 | no | — |
| 110 | #544 | C23 | 1 | 4 | yes | — |
| 111 | #543 | — | 4 | 2 | no | — |
| 112 | #539 | — | 4 | 2 | no | — |
| 113 | #536 | C23 | 1 | 4 | yes | — |
| 114 | #533 | C23 | 1 | 2 | yes | — |
| 115 | #533 | C23 | 1 | 1 | yes | characteristic |
| 116 | #532 | C23 | 1 | 1 | yes | characteristic |
| 117 | #529 | — | 4 | 2 | no | — |
| 118 | C2×#124 | C23 | 1 | 2 | yes | — |
| 119 | C2×C22⋊Q8 | — | 4 | 2 | no | — |
| 120 | #520 | C23 | 1 | 4 | yes | — |
| 121 | #518 | C23 | 1 | 4 | yes | — |
| 122 | C2×C4×Q8 | C23 | 1 | 2 | yes | — |
| 123 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 124 | #501 | — | 2 | 4 | no | — |
| 125 | #501 | D4 | 1 | 4 | yes | — |
| 126 | #501 | D4 | 1 | 4 | yes | — |
| 127 | #499 | — | 2 | 2 | no | — |
| 128 | #498 | — | 2 | 2 | no | — |
| 129 | #495 | — | 2 | 4 | no | — |
| 130 | #491 | — | 2 | 4 | no | — |
| 131 | #489 | — | 2 | 4 | no | — |
| 132 | #488 | — | 2 | 4 | no | — |
| 133 | #488 | D4 | 1 | 4 | yes | — |
| 134 | #487 | — | 2 | 4 | no | — |
| 135 | #487 | D4 | 1 | 2 | yes | — |
| 136 | #486 | D4 | 1 | 2 | yes | — |
| 137 | #485 | — | 2 | 4 | no | — |
| 138 | #485 | — | 2 | 4 | no | — |
| 139 | #484 | — | 2 | 4 | no | — |
| 140 | #483 | — | 2 | 4 | no | — |
| 141 | #479 | — | 2 | 4 | no | — |
| 142 | #479 | — | 2 | 4 | no | — |
| 143 | #479 | — | 2 | 4 | no | — |
| 144 | #478 | — | 2 | 4 | no | — |
| 145 | #478 | — | 2 | 4 | no | — |
| 146 | #478 | — | 2 | 4 | no | — |
| 147 | #478 | — | 2 | 4 | no | — |
| 148 | #477 | — | 2 | 2 | no | — |
| 149 | #477 | — | 2 | 2 | no | — |
| 150 | #476 | — | 2 | 2 | no | — |
| 151 | #476 | — | 2 | 4 | no | — |
| 152 | #476 | — | 2 | 4 | no | — |
| 153 | #475 | — | 2 | 2 | no | — |
| 154 | #475 | — | 2 | 2 | no | — |
| 155 | #475 | — | 2 | 4 | no | — |
| 156 | #474 | — | 2 | 2 | no | — |
| 157 | #474 | — | 2 | 4 | no | — |
| 158 | #472 | — | 2 | 8 | no | — |
| 159 | #470 | — | 2 | 2 | no | — |
| 160 | #470 | — | 2 | 2 | no | — |
| 161 | #467 | — | 2 | 4 | no | — |
| 162 | #463 | — | 2 | 4 | no | — |
| 163 | #463 | — | 2 | 4 | no | — |
| 164 | #463 | — | 2 | 4 | no | — |
| 165 | #461 | — | 2 | 2 | no | — |
| 166 | #461 | — | 2 | 4 | no | — |
| 167 | #461 | — | 2 | 4 | no | — |
| 168 | #459 | — | 2 | 2 | no | — |
| 169 | #446 | — | 2 | 4 | no | — |
| 170 | #446 | — | 2 | 2 | no | — |
| 171 | #446 | — | 2 | 2 | no | — |
| 172 | C8×Q8 | — | 2 | 2 | no | — |
| 173 | C8×Q8 | — | 2 | 2 | no | — |
| 174 | #442 | — | 2 | 2 | no | — |
| 175 | #442 | — | 2 | 2 | no | — |
| 176 | #442 | — | 2 | 4 | no | — |
| 177 | #442 | — | 2 | 4 | no | — |
| 178 | #441 | — | 2 | 4 | no | — |
| 179 | #440 | — | 2 | 4 | no | — |
| 180 | C4×SD16 | — | 2 | 4 | no | — |
| 181 | C4×SD16 | — | 2 | 2 | no | — |
| 182 | C4×SD16 | — | 2 | 2 | no | — |
| 183 | C4×SD16 | — | 2 | 2 | no | — |
| 184 | C4×SD16 | — | 2 | 2 | no | — |
| 185 | C4×D8 | — | 2 | 4 | no | — |
| 186 | C4×D8 | — | 2 | 4 | no | — |
| 187 | #435 | — | 2 | 4 | no | — |
| 188 | C2×#108 | C23 | 1 | 2 | yes | — |
| 189 | C2×#108 | C23 | 1 | 2 | yes | — |
| 190 | #428 | — | 2 | 4 | no | — |
| 191 | #428 | C23 | 1 | 4 | yes | — |
| 192 | #428 | C23 | 1 | 4 | yes | — |
| 193 | #428 | C23 | 1 | 4 | yes | — |
| 194 | #427 | — | 2 | 2 | no | — |
| 195 | #427 | C23 | 1 | 2 | yes | — |
| 196 | #427 | C23 | 1 | 2 | yes | — |
| 197 | C2×#106 | — | 2 | 2 | no | — |
| 198 | C2×#106 | C23 | 1 | 2 | yes | — |
| 199 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 200 | C2×#106 | C23 | 1 | 1 | yes | characteristic |
| 201 | #424 | C23 | 1 | 2 | yes | — |
| 202 | #424 | C23 | 1 | 4 | yes | — |
| 203 | #423 | C23 | 1 | 1 | yes | characteristic |
| 204 | #423 | C23 | 1 | 1 | yes | characteristic |
| 205 | #423 | C23 | 1 | 2 | yes | — |
| 206 | C2×#104 | C23 | 1 | 2 | yes | — |
| 207 | C2×#104 | C23 | 1 | 2 | yes | — |
| 208 | #419 | C23 | 1 | 4 | yes | — |
| 209 | #419 | C23 | 1 | 4 | yes | — |
| 210 | #418 | C23 | 1 | 4 | yes | — |
| 211 | #417 | C23 | 1 | 4 | yes | — |
| 212 | #416 | C23 | 1 | 2 | yes | — |
| 213 | #416 | C23 | 1 | 2 | yes | — |
| 214 | C2×#103 | C23 | 1 | 2 | yes | — |
| 215 | C2×#103 | C23 | 1 | 2 | yes | — |
| 216 | C2×#102 | C23 | 1 | 2 | yes | — |
| 217 | C2×#102 | C23 | 1 | 2 | yes | — |
| 218 | C2×#101 | C23 | 1 | 4 | yes | — |
| 219 | C2×#100 | C23 | 1 | 4 | yes | — |
| 220 | #408 | C23 | 1 | 2 | yes | — |
| 221 | #405 | C23 | 1 | 4 | yes | — |
| 222 | #405 | C23 | 1 | 2 | yes | — |
| 223 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 224 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 225 | C2×#97 | C23 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 229 | #391 | C23 | 1 | 2 | yes | — |
| 230 | #390 | C23 | 1 | 2 | yes | — |
| 231 | #388 | — | 4 | 2 | no | — |
| 232 | #385 | — | 4 | 2 | no | — |
| 233 | #384 | C23 | 1 | 2 | yes | — |
| 234 | #376 | C23 | 1 | 1 | yes | characteristic |
| 235 | #343 | C23 | 1 | 4 | yes | — |
| 236 | #343 | C23 | 1 | 4 | yes | — |
| 237 | #341 | C23 | 1 | 2 | yes | — |
| 238 | #341 | C23 | 1 | 2 | yes | — |
| 239 | #339 | C23 | 1 | 2 | yes | — |
| 240 | #339 | C23 | 1 | 4 | yes | — |
| 241 | #339 | C23 | 1 | 2 | yes | — |
| 242 | #339 | C23 | 1 | 4 | yes | — |
| 243 | C2×#41 | C24 | 1 | 2 | yes | — |
| 244 | C22×Q8 | — | 4 | 2 | no | — |
| 245 | C22×Q8 | C24 | 1 | 2 | yes | — |
| 246 | C22×D4 | C24 | 1 | 2 | yes | — |
| 247 | C23×C4 | — | 2 | 2 | no | — |
| 248 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 249 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 250 | C2×Q16 | — | 2 | 2 | no | — |
| 251 | C2×Q16 | — | 2 | 2 | no | — |
| 252 | C2×Q16 | — | 2 | 2 | no | — |
| 253 | C2×SD16 | — | 2 | 4 | no | — |
| 254 | C2×SD16 | — | 2 | 4 | no | — |
| 255 | C2×SD16 | — | 2 | 2 | no | — |
| 256 | C2×SD16 | — | 2 | 2 | no | — |
| 257 | C2×SD16 | — | 4 | 2 | no | — |
| 258 | C2×D8 | — | 2 | 4 | no | — |
| 259 | C2×D8 | — | 2 | 2 | no | — |
| 260 | C2×D8 | — | 2 | 2 | no | — |
| 261 | C2×D8 | #41 | 1 | 4 | yes | — |
| 262 | #131 | — | 2 | 4 | no | — |
| 263 | #131 | — | 2 | 4 | no | — |
| 264 | C2×M16 | — | 2 | 2 | no | — |
| 265 | C2×M16 | C24 | 1 | 2 | yes | — |
| 266 | C2×M16 | C24 | 1 | 4 | yes | — |
| 267 | C2×M16 | C24 | 1 | 2 | yes | — |
| 268 | C22×C8 | — | 2 | 2 | no | — |
| 269 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 270 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 271 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 272 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 273 | C4⋊Q8 | — | 2 | 4 | no | — |
| 274 | C4⋊Q8 | — | 2 | 4 | no | — |
| 275 | C4⋊Q8 | — | 2 | 4 | no | — |
| 276 | C4⋊Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 277 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 278 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 279 | C4⋊Q8 | C2×D4 | 1 | 2 | yes | — |
| 280 | #127 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | #126 | — | 4 | 4 | no | — |
| 282 | #126 | — | 4 | 4 | no | — |
| 283 | #125 | — | 2 | 4 | no | — |
| 284 | #125 | — | 2 | 4 | no | — |
| 285 | #125 | — | 4 | 2 | no | — |
| 286 | #125 | — | 4 | 4 | no | — |
| 287 | #125 | C2×D4 | 1 | 4 | yes | — |
| 288 | #125 | C2×D4 | 1 | 2 | yes | — |
| 289 | #124 | — | 2 | 4 | no | — |
| 290 | #124 | — | 2 | 4 | no | — |
| 291 | #124 | — | 2 | 4 | no | — |
| 292 | #124 | — | 4 | 2 | no | — |
| 293 | #124 | C2×D4 | 1 | 2 | yes | — |
| 294 | #123 | — | 4 | 4 | no | — |
| 295 | #123 | — | 4 | 4 | no | — |
| 296 | C22⋊Q8 | — | 2 | 2 | no | — |
| 297 | C22⋊Q8 | — | 2 | 2 | no | — |
| 298 | C22⋊Q8 | — | 2 | 2 | no | — |
| 299 | C22⋊Q8 | — | 2 | 4 | no | — |
| 300 | C22⋊Q8 | — | 2 | 4 | no | — |
| 301 | C22⋊Q8 | — | 4 | 4 | no | — |
| 302 | C22⋊Q8 | — | 4 | 4 | no | — |
| 303 | C22⋊Q8 | — | 4 | 4 | no | — |
| 304 | C22⋊Q8 | — | 4 | 4 | no | — |
| 305 | C22⋊Q8 | — | 4 | 4 | no | — |
| 306 | C22⋊Q8 | — | 4 | 2 | no | — |
| 307 | C22⋊Q8 | — | 4 | 2 | no | — |
| 308 | C22⋊Q8 | — | 4 | 4 | no | — |
| 309 | C22⋊Q8 | — | 4 | 4 | no | — |
| 310 | #121 | — | 2 | 2 | no | — |
| 311 | C4×Q8 | — | 2 | 2 | no | — |
| 312 | C4×Q8 | — | 2 | 2 | no | — |
| 313 | C4×Q8 | — | 2 | 2 | no | — |
| 314 | C4×Q8 | — | 2 | 4 | no | — |
| 315 | C4×Q8 | — | 2 | 2 | no | — |
| 316 | C4×Q8 | — | 2 | 2 | no | — |
| 317 | C4×Q8 | — | 2 | 2 | no | — |
| 318 | C4×Q8 | — | 2 | 2 | no | — |
| 319 | C4×Q8 | — | 4 | 2 | no | — |
| 320 | C4×D4 | — | 2 | 4 | no | — |
| 321 | C4×D4 | — | 2 | 4 | no | — |
| 322 | C4×D4 | — | 2 | 4 | no | — |
| 323 | C4×D4 | — | 2 | 4 | no | — |
| 324 | C4×D4 | — | 2 | 4 | no | — |
| 325 | C4×D4 | — | 2 | 2 | no | — |
| 326 | C4×D4 | — | 2 | 2 | no | — |
| 327 | C4×D4 | — | 2 | 2 | no | — |
| 328 | C4×D4 | — | 2 | 2 | no | — |
| 329 | C4×D4 | — | 2 | 2 | no | — |
| 330 | C4×D4 | — | 4 | 4 | no | — |
| 331 | C4×D4 | — | 4 | 2 | no | — |
| 332 | #117 | — | 2 | 4 | no | — |
| 333 | #117 | — | 4 | 4 | no | — |
| 334 | #117 | C24 | 1 | 2 | yes | — |
| 335 | #117 | C24 | 1 | 4 | yes | — |
| 336 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 337 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 338 | C2×C4⋊C4 | — | 4 | 4 | no | — |
| 339 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 340 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 341 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 342 | C2×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 343 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 344 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 345 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 346 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 347 | C2×C42 | — | 2 | 2 | no | — |
| 348 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 349 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 350 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 351 | #108 | — | 2 | 4 | no | — |
| 352 | #108 | — | 4 | 2 | no | — |
| 353 | #107 | — | 2 | 4 | no | — |
| 354 | #107 | — | 2 | 4 | no | — |
| 355 | #107 | — | 2 | 4 | no | — |
| 356 | #107 | C2×D4 | 1 | 4 | yes | — |
| 357 | #107 | C2×D4 | 1 | 4 | yes | — |
| 358 | #106 | — | 2 | 2 | no | — |
| 359 | #106 | — | 2 | 2 | no | — |
| 360 | #106 | — | 2 | 2 | no | — |
| 361 | #106 | — | 2 | 2 | no | — |
| 362 | #106 | — | 2 | 4 | no | — |
| 363 | #106 | — | 2 | 4 | no | — |
| 364 | #106 | — | 2 | 4 | no | — |
| 365 | #106 | C2×D4 | 1 | 2 | yes | — |
| 366 | #106 | C2×D4 | 1 | 2 | yes | — |
| 367 | #106 | C2×D4 | 1 | 2 | yes | — |
| 368 | #106 | C2×D4 | 1 | 2 | yes | — |
| 369 | C4⋊C8 | — | 2 | 4 | no | — |
| 370 | C4⋊C8 | — | 2 | 4 | no | — |
| 371 | C4⋊C8 | — | 2 | 4 | no | — |
| 372 | C4⋊C8 | — | 2 | 2 | no | — |
| 373 | C4⋊C8 | — | 2 | 2 | no | — |
| 374 | C4⋊C8 | — | 2 | 2 | no | — |
| 375 | C4⋊C8 | — | 2 | 2 | no | — |
| 376 | #104 | — | 2 | 4 | no | — |
| 377 | #104 | — | 4 | 2 | no | — |
| 378 | #103 | — | 2 | 4 | no | — |
| 379 | #103 | — | 2 | 2 | no | — |
| 380 | #103 | — | 2 | 2 | no | — |
| 381 | #103 | — | 2 | 4 | no | — |
| 382 | #103 | — | 2 | 4 | no | — |
| 383 | #103 | — | 2 | 4 | no | — |
| 384 | #103 | — | 2 | 4 | no | — |
| 385 | #103 | — | 2 | 4 | no | — |
| 386 | #103 | C2×D4 | 1 | 4 | yes | — |
| 387 | #103 | C2×D4 | 1 | 4 | yes | — |
| 388 | #102 | — | 2 | 4 | no | — |
| 389 | #102 | — | 2 | 2 | no | — |
| 390 | #102 | — | 2 | 2 | no | — |
| 391 | #102 | — | 2 | 4 | no | — |
| 392 | #102 | — | 2 | 4 | no | — |
| 393 | #102 | — | 2 | 4 | no | — |
| 394 | #102 | C2×D4 | 1 | 4 | yes | — |
| 395 | #102 | C2×D4 | 1 | 4 | yes | — |
| 396 | #101 | — | 4 | 4 | no | — |
| 397 | #100 | — | 2 | 8 | no | — |
| 398 | C22⋊C8 | — | 2 | 4 | no | — |
| 399 | #97 | — | 2 | 4 | no | — |
| 400 | #97 | — | 2 | 2 | no | — |
| 401 | #97 | — | 2 | 2 | no | — |
| 402 | #97 | — | 2 | 2 | no | — |
| 403 | #97 | C2×D4 | 1 | 4 | yes | — |
| 404 | C4×C8 | — | 2 | 2 | no | — |
| 405 | C4×C8 | — | 2 | 4 | no | — |
| 406 | C4×C8 | — | 2 | 2 | no | — |
| 407 | C4×C8 | — | 4 | 1 | no | — |
| 408 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 409 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 410 | #95 | — | 2 | 2 | no | — |
| 411 | #95 | — | 4 | 2 | no | — |
| 412 | C24 | — | 2 | 2 | no | — |
| 413 | #41 | — | 2 | 2 | no | — |
| 414 | #41 | — | 2 | 2 | no | — |
| 415 | #41 | — | 2 | 2 | no | — |
| 416 | #41 | — | 2 | 2 | no | — |
| 417 | C2×Q8 | — | 2 | 2 | no | — |
| 418 | C2×Q8 | — | 2 | 2 | no | — |
| 419 | C2×Q8 | — | 2 | 2 | no | — |
| 420 | C2×Q8 | — | 2 | 2 | no | — |
| 421 | C2×Q8 | — | 2 | 2 | no | — |
| 422 | C2×Q8 | — | 2 | 2 | no | — |
| 423 | C2×Q8 | — | 2 | 2 | no | — |
| 424 | C2×Q8 | — | 2 | 2 | no | — |
| 425 | C2×Q8 | — | 2 | 2 | no | — |
| 426 | C2×Q8 | — | 4 | 4 | no | — |
| 427 | C2×Q8 | — | 16 | 4 | no | — |
| 428 | C2×Q8 | C22×D4 | 1 | 2 | yes | — |
| 429 | C2×D4 | — | 2 | 2 | no | — |
| 430 | C2×D4 | — | 2 | 2 | no | — |
| 431 | C2×D4 | — | 2 | 2 | no | — |
| 432 | C2×D4 | — | 2 | 2 | no | — |
| 433 | C2×D4 | — | 2 | 2 | no | — |
| 434 | C2×D4 | — | 2 | 2 | no | — |
| 435 | C2×D4 | — | 2 | 2 | no | — |
| 436 | C2×D4 | C22×D4 | 1 | 2 | yes | — |
| 437 | C2×D4 | C2×#41 | 1 | 4 | yes | — |
| 438 | C22×C4 | — | 2 | 1 | no | — |
| 439 | C22×C4 | — | 2 | 2 | no | — |
| 440 | C22×C4 | — | 2 | 1 | no | — |
| 441 | C22×C4 | — | 2 | 2 | no | — |
| 442 | C22×C4 | — | 2 | 2 | no | — |
| 443 | C22×C4 | — | 2 | 2 | no | — |
| 444 | C22×C4 | — | 4 | 4 | no | — |
| 445 | C22×C4 | — | 4 | 4 | no | — |
| 446 | C22×C4 | — | 4 | 4 | no | — |
| 447 | C22×C4 | — | 4 | 2 | no | — |
| 448 | C22×C4 | — | 4 | 2 | no | — |
| 449 | C22×C4 | — | 16 | 2 | no | — |
| 450 | C22×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 451 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 452 | Q16 | — | 4 | 4 | no | — |
| 453 | SD16 | — | 4 | 4 | no | — |
| 454 | SD16 | — | 4 | 4 | no | — |
| 455 | SD16 | — | 4 | 8 | no | — |
| 456 | D8 | — | 2 | 8 | no | — |
| 457 | D8 | — | 4 | 8 | no | — |
| 458 | M16 | — | 2 | 2 | no | — |
| 459 | M16 | — | 2 | 4 | no | — |
| 460 | M16 | — | 2 | 2 | no | — |
| 461 | M16 | — | 2 | 2 | no | — |
| 462 | M16 | — | 2 | 2 | no | — |
| 463 | M16 | — | 2 | 4 | no | — |
| 464 | M16 | — | 4 | 4 | no | — |
| 465 | C2×C8 | — | 2 | 1 | no | — |
| 466 | C2×C8 | — | 2 | 1 | no | — |
| 467 | C2×C8 | — | 2 | 1 | no | — |
| 468 | C2×C8 | — | 2 | 1 | no | — |
| 469 | C2×C8 | — | 2 | 1 | no | — |
| 470 | C2×C8 | — | 2 | 1 | no | — |
| 471 | C2×C8 | — | 2 | 2 | no | — |
| 472 | C2×C8 | — | 2 | 4 | no | — |
| 473 | C2×C8 | — | 2 | 2 | no | — |
| 474 | C2×C8 | — | 4 | 4 | no | — |
| 475 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 476 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 477 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 478 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 479 | C2×C8 | C2×#41 | 1 | 2 | yes | — |
| 480 | C2×C8 | 2−1+4 | 1 | 2 | yes | — |
| 481 | C4⋊C4 | — | 2 | 4 | no | — |
| 482 | C4⋊C4 | — | 2 | 2 | no | — |
| 483 | C4⋊C4 | — | 2 | 4 | no | — |
| 484 | C4⋊C4 | — | 2 | 2 | no | — |
| 485 | C4⋊C4 | — | 2 | 2 | no | — |
| 486 | C4⋊C4 | — | 2 | 4 | no | — |
| 487 | C4⋊C4 | — | 2 | 2 | no | — |
| 488 | C4⋊C4 | — | 2 | 2 | no | — |
| 489 | C4⋊C4 | — | 2 | 2 | no | — |
| 490 | C4⋊C4 | — | 2 | 2 | no | — |
| 491 | C4⋊C4 | — | 2 | 2 | no | — |
| 492 | C4⋊C4 | — | 4 | 4 | no | — |
| 493 | C4⋊C4 | — | 4 | 4 | no | — |
| 494 | C4⋊C4 | — | 4 | 4 | no | — |
| 495 | C4⋊C4 | — | 4 | 4 | no | — |
| 496 | C4⋊C4 | — | 4 | 4 | no | — |
| 497 | C4⋊C4 | — | 4 | 4 | no | — |
| 498 | C4⋊C4 | — | 4 | 2 | no | — |
| 499 | C4⋊C4 | — | 4 | 2 | no | — |
| 500 | C4⋊C4 | — | 16 | 2 | no | — |
| 501 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 502 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 503 | C4⋊C4 | C22×D4 | 1 | 4 | yes | — |
| 504 | C22⋊C4 | — | 2 | 2 | no | — |
| 505 | C22⋊C4 | — | 2 | 4 | no | — |
| 506 | C22⋊C4 | — | 2 | 4 | no | — |
| 507 | C22⋊C4 | — | 4 | 4 | no | — |
| 508 | C22⋊C4 | — | 4 | 4 | no | — |
| 509 | C22⋊C4 | — | 4 | 8 | no | — |
| 510 | C22⋊C4 | — | 4 | 4 | no | — |
| 511 | C22⋊C4 | — | 4 | 4 | no | — |
| 512 | C22⋊C4 | — | 4 | 4 | no | — |
| 513 | C22⋊C4 | — | 4 | 2 | no | — |
| 514 | C22⋊C4 | — | 4 | 2 | no | — |
| 515 | C22⋊C4 | — | 16 | 2 | no | — |
| 516 | C42 | — | 2 | 2 | no | — |
| 517 | C42 | — | 2 | 4 | no | — |
| 518 | C42 | — | 2 | 1 | no | — |
| 519 | C42 | — | 2 | 1 | no | — |
| 520 | C42 | — | 2 | 1 | no | — |
| 521 | C42 | — | 4 | 4 | no | — |
| 522 | C42 | — | 4 | 2 | no | — |
| 523 | C42 | — | 4 | 2 | no | — |
| 524 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 525 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 526 | C42 | C22×D4 | 1 | 2 | yes | — |
| 527 | C42 | 2−1+4 | 1 | 2 | yes | — |
| 528 | C23 | — | 2 | 2 | no | — |
| 529 | C23 | — | 2 | 4 | no | — |
| 530 | C23 | — | 4 | 2 | no | — |
| 531 | C23 | — | 4 | 2 | no | — |
| 532 | C23 | — | 8 | 2 | no | — |
| 533 | C23 | — | 8 | 2 | no | — |
| 534 | C23 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 535 | Q8 | — | 2 | 2 | no | — |
| 536 | Q8 | — | 2 | 2 | no | — |
| 537 | Q8 | — | 4 | 4 | no | — |
| 538 | Q8 | — | 4 | 2 | no | — |
| 539 | Q8 | — | 4 | 2 | no | — |
| 540 | Q8 | — | 4 | 2 | no | — |
| 541 | Q8 | — | 4 | 2 | no | — |
| 542 | Q8 | — | 8 | 2 | no | — |
| 543 | Q8 | — | 8 | 2 | no | — |
| 544 | Q8 | — | 16 | 4 | no | — |
| 545 | D4 | — | 2 | 4 | no | — |
| 546 | D4 | — | 2 | 2 | no | — |
| 547 | D4 | — | 2 | 4 | no | — |
| 548 | D4 | — | 2 | 2 | no | — |
| 549 | D4 | — | 4 | 2 | no | — |
| 550 | D4 | — | 4 | 2 | no | — |
| 551 | D4 | — | 4 | 2 | no | — |
| 552 | D4 | — | 4 | 2 | no | — |
| 553 | D4 | — | 8 | 2 | no | — |
| 554 | C2×C4 | — | 2 | 4 | no | — |
| 555 | C2×C4 | — | 2 | 4 | no | — |
| 556 | C2×C4 | — | 2 | 4 | no | — |
| 557 | C2×C4 | — | 2 | 2 | no | — |
| 558 | C2×C4 | — | 2 | 2 | no | — |
| 559 | C2×C4 | — | 4 | 2 | no | — |
| 560 | C2×C4 | — | 4 | 2 | no | — |
| 561 | C2×C4 | — | 4 | 2 | no | — |
| 562 | C2×C4 | — | 4 | 2 | no | — |
| 563 | C2×C4 | — | 4 | 2 | no | — |
| 564 | C2×C4 | — | 4 | 2 | no | — |
| 565 | C2×C4 | — | 4 | 2 | no | — |
| 566 | C2×C4 | — | 4 | 2 | no | — |
| 567 | C2×C4 | — | 4 | 2 | no | — |
| 568 | C2×C4 | — | 4 | 1 | no | — |
| 569 | C2×C4 | — | 4 | 2 | no | — |
| 570 | C2×C4 | — | 8 | 4 | no | — |
| 571 | C2×C4 | — | 8 | 2 | no | — |
| 572 | C2×C4 | — | 8 | 2 | no | — |
| 573 | C2×C4 | — | 16 | 2 | no | — |
| 574 | C2×C4 | — | 16 | 4 | no | — |
| 575 | C2×C4 | — | 16 | 4 | no | — |
| 576 | C2×C4 | — | 16 | 4 | no | — |
| 577 | C2×C4 | D42 | 1 | 2 | yes | — |
| 578 | C2×C4 | D42 | 1 | 2 | yes | — |
| 579 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 580 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 581 | C2×C4 | C22×#41 | 1 | 1 | yes | characteristic |
| 582 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 583 | C2×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 584 | C2×C4 | #585 | 1 | 1 | yes | characteristic |
| 585 | C8 | — | 2 | 2 | no | — |
| 586 | C8 | — | 2 | 2 | no | — |
| 587 | C8 | — | 2 | 2 | no | — |
| 588 | C8 | — | 4 | 2 | no | — |
| 589 | C8 | — | 4 | 4 | no | — |
| 590 | C8 | — | 4 | 2 | no | — |
| 591 | C8 | #548 | 1 | 4 | yes | — |
| 592 | C22 | — | 2 | 2 | no | — |
| 593 | C22 | — | 4 | 2 | no | — |
| 594 | C22 | — | 4 | 4 | no | — |
| 595 | C22 | — | 4 | 4 | no | — |
| 596 | C22 | — | 8 | 4 | no | — |
| 597 | C22 | — | 8 | 2 | no | — |
| 598 | C22 | — | 8 | 2 | no | — |
| 599 | C22 | — | 16 | 2 | no | — |
| 600 | C22 | C2×D42 | 1 | 1 | yes | characteristic |
| 601 | C22 | #3520 | 1 | 1 | yes | characteristic |
| 602 | C22 | #3547 | 1 | 1 | yes | characteristic |
| 603 | C4 | — | 2 | 2 | no | — |
| 604 | C4 | — | 2 | 2 | no | — |
| 605 | C4 | — | 4 | 2 | no | — |
| 606 | C4 | — | 4 | 2 | no | — |
| 607 | C4 | — | 4 | 4 | no | — |
| 608 | C4 | — | 4 | 4 | no | — |
| 609 | C4 | — | 4 | 4 | no | — |
| 610 | C4 | — | 8 | 1 | no | — |
| 611 | C4 | — | 8 | 2 | no | — |
| 612 | C4 | — | 8 | 2 | no | — |
| 613 | C4 | — | 8 | 2 | no | — |
| 614 | C4 | C2×#548 | 1 | 1 | yes | characteristic |
| 615 | C4 | D4×#41 | 1 | 1 | yes | characteristic |
| 616 | C4 | #3497 | 1 | 1 | yes | characteristic |
| 617 | C4 | #3499 | 1 | 1 | yes | characteristic |
| 618 | C2 | — | 2 | 1 | no | — |
| 619 | C2 | — | 2 | 1 | no | — |
| 620 | C2 | — | 8 | 2 | no | — |
| 621 | C2 | — | 8 | 4 | no | — |
| 622 | C2 | #59654 | 1 | 1 | yes | characteristic |
| 623 | C2 | #61107 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C2×D42 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #28243 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #61378 | C2 | semidirect |
| 2. #61326 | C2 | semidirect |
| 3. #61292 | C2 | semidirect |
| 4. #31183 | C2 | semidirect |
| 5. #28300 | C2 | semidirect |
| 7. #28218 | C2 | semidirect |
| 8. #27810 | C2 | semidirect |
| 9. #26854 | C2 | semidirect |
| 10. #26081 | C2 | semidirect |
| 11. #25433 | C2 | semidirect |
| 12. #24318 | C2 | semidirect |
| 13. #24181 | C2 | semidirect |
| 14. #23048 | C2 | semidirect |
| 15. #21737 | C2 | semidirect |
| 16. #21694 | C2 | semidirect |
| 17. #21659 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #61378 | 2 |
| #61326 | 2 |
| #61292 | 2 |
| #31183 | 2 |
| #28300 | 2 |
| #28243 | 2 |
| #28218 | 2 |
| #27810 | 2 |
| #26854 | 2 |
| #26081 | 2 |
| #25433 | 2 |
| #24318 | 2 |
| #24181 | 2 |
| #23048 | 2 |
| #21737 | 2 |
| #21694 | 2 |
| #21659 | 2 |