Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
10238 conjugacy classes of subgroups.
The subgroup lattice has 387 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6122150 | C2 | 1 | 7 | yes | maximal, complemented |
| 2 | #5884084 | C2 | 1 | 21 | yes | maximal, complemented |
| 3 | #4264062 | C2 | 1 | 21 | yes | maximal, complemented |
| 4 | #2075818 | C2 | 1 | 7 | yes | maximal, complemented |
| 5 | #2039982 | C2 | 1 | 7 | yes | maximal |
| 6 | #17223 | C22 | 1 | 7 | yes | complemented |
| 7 | #17201 | C22 | 1 | 21 | yes | complemented |
| 8 | #17194 | C22 | 1 | 21 | yes | complemented |
| 9 | #16929 | C22 | 1 | 21 | yes | complemented |
| 10 | #16929 | C22 | 1 | 21 | yes | complemented |
| 11 | #16917 | C22 | 1 | 21 | yes | complemented |
| 12 | #16788 | C22 | 1 | 21 | yes | complemented |
| 13 | #16772 | C22 | 1 | 21 | yes | complemented |
| 14 | #16635 | C22 | 1 | 21 | yes | complemented |
| 15 | #16391 | C22 | 1 | 21 | yes | — |
| 16 | #16375 | C22 | 1 | 21 | yes | complemented |
| 17 | #16297 | C22 | 1 | 21 | yes | — |
| 18 | #16246 | C22 | 1 | 21 | yes | complemented |
| 19 | #16106 | C22 | 1 | 21 | yes | complemented |
| 20 | #16106 | C22 | 1 | 21 | yes | complemented |
| 21 | #16011 | C22 | 1 | 21 | yes | complemented |
| 22 | #15986 | C22 | 1 | 21 | yes | — |
| 23 | #15910 | C22 | 1 | 21 | yes | complemented |
| 24 | #15467 | C22 | 1 | 7 | yes | — |
| 25 | #15467 | C22 | 1 | 21 | yes | — |
| 26 | #15362 | C22 | 1 | 21 | yes | complemented |
| 27 | #15353 | C22 | 1 | 21 | yes | complemented |
| 28 | #15297 | C22 | 1 | 21 | yes | — |
| 29 | #15284 | C22 | 1 | 21 | yes | — |
| 30 | #15282 | C22 | 1 | 21 | yes | — |
| 31 | #15115 | C22 | 1 | 21 | yes | complemented |
| 32 | #14910 | C22 | 1 | 7 | yes | complemented |
| 33 | #14902 | C22 | 1 | 21 | yes | complemented |
| 34 | #14711 | C22 | 1 | 7 | yes | complemented |
| 35 | #14679 | C22 | 1 | 7 | yes | — |
| 36 | #14569 | C22 | 1 | 21 | yes | complemented |
| 37 | #14562 | C22 | 1 | 7 | yes | complemented |
| 38 | #14537 | C22 | 1 | 21 | yes | complemented |
| 39 | #14366 | C22 | 1 | 21 | yes | — |
| 40 | #14365 | C22 | 1 | 21 | yes | — |
| 41 | C27 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×#126 | C23 | 1 | 7 | yes | — |
| 43 | C2×#399 | C23 | 1 | 7 | yes | — |
| 44 | C2×#397 | C23 | 1 | 21 | yes | — |
| 45 | C2×#396 | C23 | 1 | 7 | yes | — |
| 46 | C2×#395 | C23 | 1 | 7 | yes | complemented |
| 47 | C2×#393 | C23 | 1 | 21 | yes | — |
| 48 | C2×#393 | C23 | 1 | 21 | yes | — |
| 49 | C2×#393 | C23 | 1 | 7 | yes | — |
| 50 | C2×#391 | C23 | 1 | 21 | yes | complemented |
| 51 | C2×#389 | C23 | 1 | 21 | yes | complemented |
| 52 | C2×#388 | C23 | 1 | 21 | yes | — |
| 53 | C2×#388 | C23 | 1 | 21 | yes | — |
| 54 | C2×#388 | C23 | 1 | 21 | yes | — |
| 55 | C2×#383 | C23 | 1 | 7 | yes | complemented |
| 56 | C2×#379 | C23 | 1 | 21 | yes | — |
| 57 | C2×#379 | C23 | 1 | 21 | yes | — |
| 58 | C2×#379 | C23 | 1 | 21 | yes | — |
| 59 | C2×#379 | C23 | 1 | 21 | yes | — |
| 60 | C2×#379 | C23 | 1 | 7 | yes | — |
| 61 | C2×#379 | C23 | 1 | 7 | yes | — |
| 62 | C2×#376 | C23 | 1 | 7 | yes | complemented |
| 63 | C2×C43 | C23 | 1 | 1 | yes | characteristic, complemented |
| 64 | #1446 | C23 | 1 | 7 | yes | complemented |
| 65 | #1446 | C23 | 1 | 21 | yes | complemented |
| 66 | #1445 | C23 | 1 | 21 | yes | complemented |
| 67 | #1445 | C23 | 1 | 21 | yes | complemented |
| 68 | #1445 | C23 | 1 | 21 | yes | complemented |
| 69 | #1444 | C23 | 1 | 7 | yes | complemented |
| 70 | #1444 | C23 | 1 | 7 | yes | complemented |
| 71 | #1443 | C23 | 1 | 21 | yes | complemented |
| 72 | #1443 | C23 | 1 | 21 | yes | complemented |
| 73 | #1443 | C23 | 1 | 21 | yes | complemented |
| 74 | #1443 | C23 | 1 | 7 | yes | complemented |
| 75 | #1442 | C23 | 1 | 21 | yes | complemented |
| 76 | #1442 | C23 | 1 | 21 | yes | complemented |
| 77 | #1442 | C23 | 1 | 21 | yes | complemented |
| 78 | #1442 | C23 | 1 | 21 | yes | complemented |
| 79 | #1442 | C23 | 1 | 21 | yes | complemented |
| 80 | #1441 | C23 | 1 | 21 | yes | complemented |
| 81 | #1440 | C23 | 1 | 21 | yes | — |
| 82 | #1440 | C23 | 1 | 21 | yes | — |
| 83 | #1440 | C23 | 1 | 21 | yes | — |
| 84 | #1440 | C23 | 1 | 21 | yes | — |
| 85 | #1440 | C23 | 1 | 21 | yes | — |
| 86 | #1440 | C23 | 1 | 21 | yes | — |
| 87 | #1440 | C23 | 1 | 21 | yes | — |
| 88 | #1440 | C23 | 1 | 21 | yes | — |
| 89 | #1440 | C23 | 1 | 21 | yes | — |
| 90 | #1440 | C23 | 1 | 21 | yes | — |
| 91 | #1439 | C23 | 1 | 21 | yes | — |
| 92 | #1439 | C23 | 1 | 21 | yes | — |
| 93 | #1439 | C23 | 1 | 21 | yes | — |
| 94 | #1439 | C23 | 1 | 21 | yes | — |
| 95 | #1439 | C23 | 1 | 21 | yes | — |
| 96 | #1439 | C23 | 1 | 21 | yes | — |
| 97 | #1439 | C23 | 1 | 21 | yes | — |
| 98 | #1439 | C23 | 1 | 21 | yes | — |
| 99 | #1439 | C23 | 1 | 21 | yes | — |
| 100 | #1439 | C23 | 1 | 21 | yes | — |
| 101 | #1439 | C23 | 1 | 21 | yes | — |
| 102 | #1439 | C23 | 1 | 21 | yes | — |
| 103 | #1439 | C23 | 1 | 21 | yes | — |
| 104 | #1439 | C23 | 1 | 21 | yes | — |
| 105 | #1437 | C23 | 1 | 21 | yes | — |
| 106 | #1437 | C23 | 1 | 21 | yes | — |
| 107 | #1437 | C23 | 1 | 21 | yes | — |
| 108 | #1437 | C23 | 1 | 21 | yes | — |
| 109 | #1437 | C23 | 1 | 21 | yes | — |
| 110 | #1437 | C23 | 1 | 21 | yes | — |
| 111 | #1436 | C23 | 1 | 21 | yes | complemented |
| 112 | #1436 | C23 | 1 | 21 | yes | complemented |
| 113 | #1436 | C23 | 1 | 21 | yes | complemented |
| 114 | #1436 | C23 | 1 | 21 | yes | complemented |
| 115 | #1436 | C23 | 1 | 21 | yes | complemented |
| 116 | #1436 | C23 | 1 | 21 | yes | complemented |
| 117 | #1434 | C23 | 1 | 21 | yes | complemented |
| 118 | C26 | — | 4 | 14 | no | — |
| 119 | C26 | — | 8 | 7 | no | — |
| 120 | C26 | — | 8 | 1 | no | — |
| 121 | C26 | C24 | 1 | 7 | yes | — |
| 122 | C23×Q8 | C24 | 1 | 7 | yes | — |
| 123 | C2×#126 | — | 4 | 14 | no | — |
| 124 | C2×#126 | — | 8 | 7 | no | — |
| 125 | C2×#126 | — | 8 | 7 | no | — |
| 126 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 127 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 128 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 129 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 130 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 131 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 132 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 133 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 134 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 135 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 136 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 137 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 138 | C22×C22⋊C4 | C24 | 1 | 7 | yes | — |
| 139 | C22×C42 | C24 | 1 | 7 | yes | — |
| 140 | C22×C42 | C24 | 1 | 21 | yes | — |
| 141 | #399 | — | 8 | 7 | no | — |
| 142 | #397 | — | 4 | 42 | no | — |
| 143 | #396 | — | 4 | 14 | no | — |
| 144 | #395 | — | 8 | 7 | no | — |
| 145 | #393 | — | 4 | 42 | no | — |
| 146 | #393 | — | 8 | 21 | no | — |
| 147 | #393 | — | 8 | 7 | no | — |
| 148 | #391 | — | 8 | 21 | no | — |
| 149 | #389 | — | 8 | 21 | no | — |
| 150 | #388 | — | 8 | 21 | no | — |
| 151 | #388 | — | 8 | 21 | no | — |
| 152 | #388 | — | 8 | 21 | no | — |
| 153 | #383 | — | 8 | 7 | no | — |
| 154 | #379 | — | 4 | 42 | no | — |
| 155 | #379 | — | 4 | 42 | no | — |
| 156 | #379 | — | 8 | 7 | no | — |
| 157 | #379 | — | 8 | 21 | no | — |
| 158 | #379 | — | 8 | 7 | no | — |
| 159 | #379 | — | 8 | 21 | no | — |
| 160 | #376 | — | 8 | 7 | no | — |
| 161 | C2×#95 | C24 | 1 | 21 | yes | — |
| 162 | C2×#95 | C24 | 1 | 21 | yes | — |
| 163 | C2×#95 | C24 | 1 | 21 | yes | — |
| 164 | C2×#95 | C24 | 1 | 21 | yes | — |
| 165 | C2×#95 | C24 | 1 | 21 | yes | — |
| 166 | C2×#95 | C24 | 1 | 21 | yes | — |
| 167 | C2×#95 | C24 | 1 | 21 | yes | — |
| 168 | C2×#95 | C24 | 1 | 7 | yes | — |
| 169 | C2×#95 | C24 | 1 | 21 | yes | — |
| 170 | C2×#95 | C24 | 1 | 21 | yes | — |
| 171 | C2×#95 | C24 | 1 | 21 | yes | — |
| 172 | C2×#95 | C24 | 1 | 7 | yes | — |
| 173 | C2×#95 | C24 | 1 | 21 | yes | — |
| 174 | C2×#95 | C24 | 1 | 21 | yes | — |
| 175 | C2×#95 | C24 | 1 | 21 | yes | — |
| 176 | C2×#95 | C24 | 1 | 21 | yes | — |
| 177 | C2×#95 | C24 | 1 | 21 | yes | — |
| 178 | C2×#95 | C24 | 1 | 21 | yes | — |
| 179 | C43 | — | 8 | 1 | no | — |
| 180 | C25 | — | 2 | 42 | no | — |
| 181 | C25 | — | 4 | 21 | no | — |
| 182 | C25 | — | 4 | 7 | no | — |
| 183 | C25 | — | 4 | 21 | no | — |
| 184 | C25 | — | 4 | 21 | no | — |
| 185 | C25 | — | 4 | 7 | no | — |
| 186 | C25 | — | 4 | 7 | no | — |
| 187 | C25 | — | 8 | 168 | no | — |
| 188 | C25 | — | 8 | 56 | no | — |
| 189 | C25 | — | 8 | 56 | no | — |
| 190 | C25 | C25 | 1 | 7 | yes | — |
| 191 | C22×Q8 | — | 4 | 21 | no | — |
| 192 | C22×Q8 | — | 4 | 21 | no | — |
| 193 | C22×Q8 | — | 4 | 7 | no | — |
| 194 | C23×C4 | C25 | 1 | 7 | yes | — |
| 195 | C23×C4 | C25 | 1 | 21 | yes | — |
| 196 | C23×C4 | C25 | 1 | 7 | yes | — |
| 197 | C23×C4 | C25 | 1 | 21 | yes | — |
| 198 | #126 | — | 8 | 56 | no | — |
| 199 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 200 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 201 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 202 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 203 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 204 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 205 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 206 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 207 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 208 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 209 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 210 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 211 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 212 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 213 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 214 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 215 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 216 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 217 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 218 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 219 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 220 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 221 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 222 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 223 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 224 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 225 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 226 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 227 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 228 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 229 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 230 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 231 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 232 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 233 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 234 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 235 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 236 | C2×C42 | — | 4 | 7 | no | — |
| 237 | C2×C42 | — | 4 | 7 | no | — |
| 238 | C2×C42 | — | 4 | 7 | no | — |
| 239 | C2×C42 | — | 4 | 21 | no | — |
| 240 | C2×C42 | — | 4 | 21 | no | — |
| 241 | C2×C42 | — | 4 | 21 | no | — |
| 242 | #95 | — | 4 | 21 | no | — |
| 243 | #95 | — | 4 | 7 | no | — |
| 244 | #95 | — | 4 | 21 | no | — |
| 245 | #95 | — | 4 | 21 | no | — |
| 246 | #95 | — | 4 | 21 | no | — |
| 247 | #95 | — | 4 | 21 | no | — |
| 248 | #95 | — | 4 | 21 | no | — |
| 249 | #95 | — | 4 | 21 | no | — |
| 250 | #95 | — | 4 | 21 | no | — |
| 251 | #95 | — | 4 | 21 | no | — |
| 252 | #95 | — | 4 | 21 | no | — |
| 253 | #95 | — | 4 | 21 | no | — |
| 254 | #95 | — | 4 | 21 | no | — |
| 255 | #95 | — | 4 | 21 | no | — |
| 256 | #95 | — | 4 | 7 | no | — |
| 257 | #95 | — | 4 | 21 | no | — |
| 258 | #95 | — | 4 | 21 | no | — |
| 259 | #95 | — | 4 | 21 | no | — |
| 260 | C24 | — | 2 | 21 | no | — |
| 261 | C24 | — | 2 | 21 | no | — |
| 262 | C24 | — | 2 | 7 | no | — |
| 263 | C24 | — | 2 | 7 | no | — |
| 264 | C24 | — | 2 | 21 | no | — |
| 265 | C24 | — | 2 | 21 | no | — |
| 266 | C24 | — | 4 | 84 | no | — |
| 267 | C24 | — | 4 | 84 | no | — |
| 268 | C24 | — | 4 | 28 | no | — |
| 269 | C24 | — | 8 | 42 | no | — |
| 270 | C24 | — | 8 | 42 | no | — |
| 271 | C24 | — | 8 | 42 | no | — |
| 272 | C24 | — | 8 | 42 | no | — |
| 273 | C24 | — | 8 | 42 | no | — |
| 274 | C24 | — | 8 | 42 | no | — |
| 275 | C24 | — | 8 | 42 | no | — |
| 276 | C24 | — | 8 | 14 | no | — |
| 277 | C24 | — | 8 | 42 | no | — |
| 278 | C24 | — | 8 | 42 | no | — |
| 279 | C24 | — | 8 | 448 | no | — |
| 280 | C24 | — | 8 | 448 | no | — |
| 281 | C24 | — | 8 | 64 | no | — |
| 282 | C24 | #585 | 1 | 14 | yes | — |
| 283 | C24 | C26 | 1 | 1 | yes | characteristic |
| 284 | C2×Q8 | — | 8 | 42 | no | — |
| 285 | C2×Q8 | — | 16 | 21 | no | — |
| 286 | C2×Q8 | — | 16 | 7 | no | — |
| 287 | C22×C4 | — | 2 | 21 | no | — |
| 288 | C22×C4 | — | 2 | 21 | no | — |
| 289 | C22×C4 | — | 2 | 21 | no | — |
| 290 | C22×C4 | — | 2 | 21 | no | — |
| 291 | C22×C4 | — | 2 | 21 | no | — |
| 292 | C22×C4 | — | 2 | 21 | no | — |
| 293 | C22×C4 | — | 2 | 21 | no | — |
| 294 | C22×C4 | — | 2 | 21 | no | — |
| 295 | C22×C4 | — | 2 | 21 | no | — |
| 296 | C22×C4 | — | 2 | 21 | no | — |
| 297 | C22×C4 | — | 2 | 21 | no | — |
| 298 | C22×C4 | — | 2 | 7 | no | — |
| 299 | C22×C4 | — | 2 | 21 | no | — |
| 300 | C22×C4 | — | 2 | 21 | no | — |
| 301 | C22×C4 | — | 2 | 21 | no | — |
| 302 | C22×C4 | — | 2 | 21 | no | — |
| 303 | C22×C4 | — | 2 | 21 | no | — |
| 304 | C22×C4 | — | 2 | 21 | no | — |
| 305 | C22×C4 | — | 2 | 21 | no | — |
| 306 | C22×C4 | — | 2 | 7 | no | — |
| 307 | C4⋊C4 | — | 8 | 42 | no | — |
| 308 | C4⋊C4 | — | 8 | 42 | no | — |
| 309 | C4⋊C4 | — | 16 | 21 | no | — |
| 310 | C22⋊C4 | — | 8 | 42 | no | — |
| 311 | C22⋊C4 | — | 8 | 42 | no | — |
| 312 | C22⋊C4 | — | 8 | 42 | no | — |
| 313 | C22⋊C4 | — | 8 | 42 | no | — |
| 314 | C22⋊C4 | — | 16 | 21 | no | — |
| 315 | C22⋊C4 | — | 16 | 21 | no | — |
| 316 | C22⋊C4 | — | 16 | 21 | no | — |
| 317 | C22⋊C4 | — | 16 | 21 | no | — |
| 318 | C22⋊C4 | — | 16 | 21 | no | — |
| 319 | C22⋊C4 | — | 16 | 7 | no | — |
| 320 | C42 | — | 4 | 28 | no | — |
| 321 | C42 | — | 8 | 42 | no | — |
| 322 | C23 | — | 2 | 14 | no | — |
| 323 | C23 | — | 2 | 42 | no | — |
| 324 | C23 | — | 2 | 42 | no | — |
| 325 | C23 | — | 4 | 21 | no | — |
| 326 | C23 | — | 4 | 21 | no | — |
| 327 | C23 | — | 4 | 21 | no | — |
| 328 | C23 | — | 4 | 21 | no | — |
| 329 | C23 | — | 4 | 21 | no | — |
| 330 | C23 | — | 4 | 21 | no | — |
| 331 | C23 | — | 4 | 21 | no | — |
| 332 | C23 | — | 4 | 21 | no | — |
| 333 | C23 | — | 4 | 21 | no | — |
| 334 | C23 | — | 4 | 7 | no | — |
| 335 | C23 | — | 8 | 56 | no | — |
| 336 | C23 | — | 8 | 168 | no | — |
| 337 | C23 | — | 8 | 168 | no | — |
| 338 | C23 | — | 8 | 168 | no | — |
| 339 | C23 | — | 8 | 168 | no | — |
| 340 | C23 | — | 8 | 512 | no | — |
| 341 | C23 | — | 8 | 56 | no | — |
| 342 | C23 | — | 8 | 56 | no | — |
| 343 | C23 | C2×#585 | 1 | 7 | yes | — |
| 344 | C23 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 345 | C23 | H(7,𝔽2) | 1 | 7 | yes | — |
| 346 | Q8 | — | 16 | 28 | no | — |
| 347 | C2×C4 | — | 4 | 21 | no | — |
| 348 | C2×C4 | — | 4 | 21 | no | — |
| 349 | C2×C4 | — | 4 | 21 | no | — |
| 350 | C2×C4 | — | 4 | 21 | no | — |
| 351 | C2×C4 | — | 4 | 21 | no | — |
| 352 | C2×C4 | — | 4 | 21 | no | — |
| 353 | C2×C4 | — | 4 | 21 | no | — |
| 354 | C2×C4 | — | 4 | 21 | no | — |
| 355 | C2×C4 | — | 4 | 21 | no | — |
| 356 | C2×C4 | — | 4 | 21 | no | — |
| 357 | C2×C4 | — | 4 | 21 | no | — |
| 358 | C2×C4 | — | 4 | 21 | no | — |
| 359 | C2×C4 | — | 4 | 21 | no | — |
| 360 | C2×C4 | — | 4 | 21 | no | — |
| 361 | C2×C4 | — | 4 | 21 | no | — |
| 362 | C2×C4 | — | 4 | 21 | no | — |
| 363 | C2×C4 | — | 4 | 21 | no | — |
| 364 | C2×C4 | — | 4 | 7 | no | — |
| 365 | C2×C4 | — | 4 | 21 | no | — |
| 366 | C2×C4 | — | 4 | 7 | no | — |
| 367 | C22 | — | 4 | 42 | no | — |
| 368 | C22 | — | 4 | 42 | no | — |
| 369 | C22 | — | 4 | 14 | no | — |
| 370 | C22 | — | 8 | 224 | no | — |
| 371 | C22 | — | 8 | 7 | no | — |
| 372 | C22 | — | 8 | 21 | no | — |
| 373 | C22 | — | 8 | 21 | no | — |
| 374 | C22 | — | 8 | 7 | no | — |
| 375 | C22 | #62933 | 1 | 21 | yes | — |
| 376 | C22 | #62973 | 1 | 7 | yes | — |
| 377 | C22 | #63046 | 1 | 7 | yes | — |
| 378 | C4 | — | 8 | 7 | no | — |
| 379 | C4 | — | 8 | 21 | no | — |
| 380 | C4 | — | 8 | 21 | no | — |
| 381 | C4 | — | 8 | 7 | no | — |
| 382 | C2 | — | 8 | 14 | no | — |
| 383 | C2 | #10407820 | 1 | 7 | yes | — |
| 384 | C2 | #10464595 | 1 | 7 | yes | — |
| 385 | C2 | #10573989 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C26 |
| prime radical | C27 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #6122150 | C2 | semidirect |
| 2. #5884084 | C2 | semidirect |
| 3. #4264062 | C2 | semidirect |
| 4. #2075818 | C2 | semidirect |
| 6. #17223 | C22 | semidirect |
| 7. #17201 | C22 | semidirect |
| 8. #17194 | C22 | semidirect |
| 9. #16929 | C22 | semidirect |
| 10. #16929 | C22 | semidirect |
| 11. #16917 | C22 | semidirect |
| 12. #16788 | C22 | semidirect |
| 13. #16772 | C22 | semidirect |
| 14. #16635 | C22 | semidirect |
| 16. #16375 | C22 | semidirect |
| 18. #16246 | C22 | semidirect |
| 19. #16106 | C22 | semidirect |
| 20. #16106 | C22 | semidirect |
| 21. #16011 | C22 | semidirect |
| 23. #15910 | C22 | semidirect |
| 26. #15362 | C22 | semidirect |
| 27. #15353 | C22 | semidirect |
| 31. #15115 | C22 | semidirect |
| 32. #14910 | C22 | semidirect |
| 33. #14902 | C22 | semidirect |
| 34. #14711 | C22 | semidirect |
| 36. #14569 | C22 | semidirect |
| 37. #14562 | C22 | semidirect |
| 38. #14537 | C22 | semidirect |
| 46. C2×#395 | C23 | semidirect |
| 50. C2×#391 | C23 | semidirect |
| 51. C2×#389 | C23 | semidirect |
| 55. C2×#383 | C23 | semidirect |
| 62. C2×#376 | C23 | semidirect |
| 63. C2×C43 | C23 | semidirect |
| 64. #1446 | C23 | semidirect |
| 65. #1446 | C23 | semidirect |
| 66. #1445 | C23 | semidirect |
| 67. #1445 | C23 | semidirect |
| 68. #1445 | C23 | semidirect |
| 69. #1444 | C23 | semidirect |
| 70. #1444 | C23 | semidirect |
| 71. #1443 | C23 | semidirect |
| 72. #1443 | C23 | semidirect |
| 73. #1443 | C23 | semidirect |
| 74. #1443 | C23 | semidirect |
| 75. #1442 | C23 | semidirect |
| 76. #1442 | C23 | semidirect |
| 77. #1442 | C23 | semidirect |
| 78. #1442 | C23 | semidirect |
| 79. #1442 | C23 | semidirect |
| 80. #1441 | C23 | semidirect |
| 111. #1436 | C23 | semidirect |
| 112. #1436 | C23 | semidirect |
| 113. #1436 | C23 | semidirect |
| 114. #1436 | C23 | semidirect |
| 115. #1436 | C23 | semidirect |
| 116. #1436 | C23 | semidirect |
| 117. #1434 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6122150 | 2 |
| #5884084 | 2 |
| #4264062 | 2 |
| #2075818 | 2 |
| #2039982 | 2 |