Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
18038 conjugacy classes of subgroups.
The subgroup lattice has 516 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6034457 | C2 | 1 | 7 | yes | maximal, complemented |
| 2 | #5720743 | C2 | 1 | 21 | yes | maximal, complemented |
| 3 | #4140675 | C2 | 1 | 21 | yes | maximal, complemented |
| 4 | #2032030 | C2 | 1 | 7 | yes | maximal, complemented |
| 5 | #2032030 | C2 | 1 | 7 | yes | maximal, complemented |
| 6 | C2×#2801 | C22 | 1 | 7 | yes | complemented |
| 7 | C2×#2679 | C22 | 1 | 21 | yes | — |
| 8 | C2×#2846 | C22 | 1 | 7 | yes | complemented |
| 9 | C2×#2846 | C22 | 1 | 7 | yes | complemented |
| 10 | #17204 | C22 | 1 | 7 | yes | complemented |
| 11 | #17159 | C22 | 1 | 21 | yes | complemented |
| 12 | #17123 | C22 | 1 | 21 | yes | complemented |
| 13 | #16865 | C22 | 1 | 21 | yes | complemented |
| 14 | #16865 | C22 | 1 | 21 | yes | complemented |
| 15 | #16587 | C22 | 1 | 21 | yes | complemented |
| 16 | #16548 | C22 | 1 | 21 | yes | complemented |
| 17 | #16347 | C22 | 1 | 21 | yes | complemented |
| 18 | #16255 | C22 | 1 | 21 | yes | complemented |
| 19 | #16255 | C22 | 1 | 21 | yes | complemented |
| 20 | #16255 | C22 | 1 | 21 | yes | complemented |
| 21 | #16255 | C22 | 1 | 21 | yes | complemented |
| 22 | #15947 | C22 | 1 | 7 | yes | — |
| 23 | #15947 | C22 | 1 | 21 | yes | — |
| 24 | #15777 | C22 | 1 | 21 | yes | complemented |
| 25 | #15615 | C22 | 1 | 21 | yes | complemented |
| 26 | #15348 | C22 | 1 | 21 | yes | complemented |
| 27 | #15283 | C22 | 1 | 21 | yes | complemented |
| 28 | #15283 | C22 | 1 | 21 | yes | complemented |
| 29 | #15281 | C22 | 1 | 21 | yes | complemented |
| 30 | #15281 | C22 | 1 | 21 | yes | complemented |
| 31 | #15268 | C22 | 1 | 21 | yes | complemented |
| 32 | #15268 | C22 | 1 | 21 | yes | complemented |
| 33 | #15268 | C22 | 1 | 21 | yes | complemented |
| 34 | #15268 | C22 | 1 | 21 | yes | complemented |
| 35 | #15141 | C22 | 1 | 7 | yes | complemented |
| 36 | #14986 | C22 | 1 | 21 | yes | complemented |
| 37 | #14949 | C22 | 1 | 21 | yes | complemented |
| 38 | #14563 | C22 | 1 | 21 | yes | complemented |
| 39 | #14358 | C22 | 1 | 21 | yes | complemented |
| 40 | #14358 | C22 | 1 | 21 | yes | complemented |
| 41 | C27 | C23 | 1 | 1 | yes | characteristic, complemented |
| 42 | C27 | C23 | 1 | 1 | yes | characteristic, complemented |
| 43 | C22×#120 | C23 | 1 | 21 | yes | — |
| 44 | C22×#120 | C23 | 1 | 21 | yes | — |
| 45 | C22×#120 | C23 | 1 | 21 | yes | — |
| 46 | C22×#120 | C23 | 1 | 21 | yes | — |
| 47 | C22×#120 | C23 | 1 | 7 | yes | — |
| 48 | C22×#120 | C23 | 1 | 7 | yes | — |
| 49 | #2846 | — | 4 | 28 | no | — |
| 50 | #2846 | — | 4 | 28 | no | — |
| 51 | #2801 | — | 4 | 28 | no | — |
| 52 | #2679 | — | 4 | 84 | no | — |
| 53 | C2×#401 | C23 | 1 | 7 | yes | complemented |
| 54 | C2×#399 | C23 | 1 | 7 | yes | complemented |
| 55 | C2×#399 | C23 | 1 | 7 | yes | complemented |
| 56 | C2×#397 | C23 | 1 | 21 | yes | complemented |
| 57 | C2×#397 | C23 | 1 | 21 | yes | complemented |
| 58 | C2×#396 | C23 | 1 | 7 | yes | complemented |
| 59 | C2×#396 | C23 | 1 | 7 | yes | complemented |
| 60 | C2×#396 | C23 | 1 | 7 | yes | complemented |
| 61 | C2×#396 | C23 | 1 | 7 | yes | complemented |
| 62 | C2×#394 | C23 | 1 | 21 | yes | — |
| 63 | C2×#394 | C23 | 1 | 21 | yes | — |
| 64 | C2×#394 | C23 | 1 | 21 | yes | — |
| 65 | C2×#394 | C23 | 1 | 21 | yes | — |
| 66 | C2×#394 | C23 | 1 | 21 | yes | — |
| 67 | C2×#394 | C23 | 1 | 21 | yes | — |
| 68 | C2×#390 | C23 | 1 | 21 | yes | — |
| 69 | C2×#390 | C23 | 1 | 21 | yes | — |
| 70 | C2×#390 | C23 | 1 | 21 | yes | — |
| 71 | C2×#389 | C23 | 1 | 21 | yes | complemented |
| 72 | C2×#388 | C23 | 1 | 21 | yes | complemented |
| 73 | C2×#388 | C23 | 1 | 21 | yes | complemented |
| 74 | C2×#388 | C23 | 1 | 21 | yes | complemented |
| 75 | C2×#388 | C23 | 1 | 21 | yes | complemented |
| 76 | C2×#379 | C23 | 1 | 21 | yes | complemented |
| 77 | C2×#379 | C23 | 1 | 21 | yes | complemented |
| 78 | C2×#379 | C23 | 1 | 21 | yes | complemented |
| 79 | C2×#379 | C23 | 1 | 21 | yes | complemented |
| 80 | C2×#379 | C23 | 1 | 7 | yes | complemented |
| 81 | C2×#379 | C23 | 1 | 7 | yes | complemented |
| 82 | #1443 | C23 | 1 | 7 | yes | complemented |
| 83 | #1442 | C23 | 1 | 21 | yes | complemented |
| 84 | #1442 | C23 | 1 | 21 | yes | complemented |
| 85 | #1441 | C23 | 1 | 21 | yes | complemented |
| 86 | #1441 | C23 | 1 | 21 | yes | complemented |
| 87 | #1440 | C23 | 1 | 21 | yes | complemented |
| 88 | #1440 | C23 | 1 | 21 | yes | complemented |
| 89 | #1440 | C23 | 1 | 21 | yes | complemented |
| 90 | #1440 | C23 | 1 | 21 | yes | complemented |
| 91 | #1439 | C23 | 1 | 21 | yes | complemented |
| 92 | #1439 | C23 | 1 | 21 | yes | complemented |
| 93 | #1439 | C23 | 1 | 21 | yes | complemented |
| 94 | #1439 | C23 | 1 | 21 | yes | complemented |
| 95 | #1439 | C23 | 1 | 21 | yes | complemented |
| 96 | #1439 | C23 | 1 | 21 | yes | complemented |
| 97 | #1439 | C23 | 1 | 21 | yes | complemented |
| 98 | #1439 | C23 | 1 | 21 | yes | complemented |
| 99 | #1439 | C23 | 1 | 21 | yes | complemented |
| 100 | #1439 | C23 | 1 | 21 | yes | complemented |
| 101 | #1439 | C23 | 1 | 21 | yes | complemented |
| 102 | #1439 | C23 | 1 | 21 | yes | complemented |
| 103 | #1438 | C23 | 1 | 21 | yes | — |
| 104 | #1438 | C23 | 1 | 21 | yes | — |
| 105 | #1438 | C23 | 1 | 21 | yes | — |
| 106 | #1438 | C23 | 1 | 21 | yes | — |
| 107 | #1438 | C23 | 1 | 21 | yes | — |
| 108 | #1438 | C23 | 1 | 21 | yes | — |
| 109 | #1438 | C23 | 1 | 21 | yes | — |
| 110 | #1438 | C23 | 1 | 21 | yes | — |
| 111 | #1438 | C23 | 1 | 21 | yes | — |
| 112 | #1438 | C23 | 1 | 21 | yes | — |
| 113 | #1438 | C23 | 1 | 21 | yes | — |
| 114 | #1438 | C23 | 1 | 21 | yes | — |
| 115 | #1437 | C23 | 1 | 21 | yes | complemented |
| 116 | #1437 | C23 | 1 | 21 | yes | complemented |
| 117 | #1437 | C23 | 1 | 21 | yes | complemented |
| 118 | #1437 | C23 | 1 | 21 | yes | complemented |
| 119 | #1436 | C23 | 1 | 21 | yes | complemented |
| 120 | #1436 | C23 | 1 | 21 | yes | complemented |
| 121 | C4×#95 | C23 | 1 | 7 | yes | complemented |
| 122 | C26 | — | 4 | 14 | no | — |
| 123 | C26 | — | 4 | 14 | no | — |
| 124 | C26 | — | 8 | 7 | no | — |
| 125 | C26 | — | 8 | 7 | no | — |
| 126 | C26 | — | 8 | 1 | no | — |
| 127 | C26 | — | 8 | 1 | no | — |
| 128 | C26 | C24 | 1 | 7 | yes | — |
| 129 | C26 | C24 | 1 | 7 | yes | — |
| 130 | C23×D4 | C24 | 1 | 21 | yes | — |
| 131 | C23×D4 | C24 | 1 | 21 | yes | — |
| 132 | C23×D4 | C24 | 1 | 7 | yes | — |
| 133 | C2×#120 | — | 2 | 84 | no | — |
| 134 | C2×#120 | — | 2 | 84 | no | — |
| 135 | C2×#120 | — | 4 | 42 | no | — |
| 136 | C2×#120 | — | 4 | 42 | no | — |
| 137 | C2×#120 | — | 4 | 42 | no | — |
| 138 | C2×#120 | — | 4 | 42 | no | — |
| 139 | C2×#120 | — | 4 | 42 | no | — |
| 140 | C2×#120 | — | 4 | 42 | no | — |
| 141 | C2×#120 | — | 4 | 14 | no | — |
| 142 | C2×#120 | — | 4 | 14 | no | — |
| 143 | C2×#120 | — | 8 | 21 | no | — |
| 144 | C2×#120 | — | 8 | 21 | no | — |
| 145 | C2×#120 | — | 8 | 7 | no | — |
| 146 | C2×#120 | — | 8 | 21 | no | — |
| 147 | C2×#120 | — | 8 | 21 | no | — |
| 148 | C2×#120 | — | 8 | 7 | no | — |
| 149 | C2×#120 | — | 8 | 7 | no | — |
| 150 | C2×#120 | — | 8 | 7 | no | — |
| 151 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 152 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 153 | C22×C4⋊C4 | C24 | 1 | 21 | yes | — |
| 154 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 155 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 156 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 157 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 158 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 159 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 160 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 161 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 162 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 163 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 164 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 165 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 166 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 167 | C22×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 168 | C22×C42 | C24 | 1 | 21 | yes | — |
| 169 | #401 | — | 4 | 14 | no | — |
| 170 | #399 | — | 4 | 14 | no | — |
| 171 | #399 | — | 8 | 7 | no | — |
| 172 | #397 | — | 8 | 21 | no | — |
| 173 | #397 | — | 8 | 21 | no | — |
| 174 | #396 | — | 4 | 14 | no | — |
| 175 | #396 | — | 8 | 7 | no | — |
| 176 | #396 | — | 8 | 7 | no | — |
| 177 | #396 | — | 8 | 7 | no | — |
| 178 | #394 | — | 2 | 84 | no | — |
| 179 | #394 | — | 4 | 42 | no | — |
| 180 | #394 | — | 4 | 42 | no | — |
| 181 | #394 | — | 4 | 42 | no | — |
| 182 | #394 | — | 4 | 42 | no | — |
| 183 | #394 | — | 4 | 42 | no | — |
| 184 | #390 | — | 4 | 42 | no | — |
| 185 | #390 | — | 4 | 42 | no | — |
| 186 | #390 | — | 4 | 42 | no | — |
| 187 | #389 | — | 4 | 42 | no | — |
| 188 | #388 | — | 4 | 42 | no | — |
| 189 | #388 | — | 4 | 42 | no | — |
| 190 | #388 | — | 8 | 21 | no | — |
| 191 | #388 | — | 8 | 21 | no | — |
| 192 | #379 | — | 4 | 14 | no | — |
| 193 | #379 | — | 4 | 42 | no | — |
| 194 | #379 | — | 4 | 42 | no | — |
| 195 | #379 | — | 4 | 14 | no | — |
| 196 | #379 | — | 4 | 42 | no | — |
| 197 | #379 | — | 4 | 42 | no | — |
| 198 | C2×#95 | C24 | 1 | 21 | yes | — |
| 199 | C2×#95 | C24 | 1 | 21 | yes | — |
| 200 | C2×#95 | C24 | 1 | 7 | yes | — |
| 201 | C2×#95 | C24 | 1 | 7 | yes | — |
| 202 | C2×#95 | C24 | 1 | 7 | yes | — |
| 203 | C2×#95 | C24 | 1 | 21 | yes | — |
| 204 | C2×#95 | C24 | 1 | 21 | yes | — |
| 205 | C2×#95 | C24 | 1 | 21 | yes | — |
| 206 | C2×#95 | C24 | 1 | 21 | yes | — |
| 207 | C2×#95 | C24 | 1 | 21 | yes | — |
| 208 | C2×#95 | C24 | 1 | 21 | yes | — |
| 209 | C2×#95 | C24 | 1 | 21 | yes | — |
| 210 | C25 | — | 2 | 42 | no | — |
| 211 | C25 | — | 2 | 42 | no | — |
| 212 | C25 | — | 4 | 21 | no | — |
| 213 | C25 | — | 4 | 21 | no | — |
| 214 | C25 | — | 4 | 7 | no | — |
| 215 | C25 | — | 4 | 7 | no | — |
| 216 | C25 | — | 4 | 21 | no | — |
| 217 | C25 | — | 4 | 21 | no | — |
| 218 | C25 | — | 4 | 21 | no | — |
| 219 | C25 | — | 4 | 21 | no | — |
| 220 | C25 | — | 4 | 7 | no | — |
| 221 | C25 | — | 4 | 7 | no | — |
| 222 | C25 | — | 4 | 7 | no | — |
| 223 | C25 | — | 4 | 7 | no | — |
| 224 | C25 | — | 8 | 168 | no | — |
| 225 | C25 | — | 8 | 168 | no | — |
| 226 | C25 | — | 8 | 56 | no | — |
| 227 | C25 | — | 8 | 56 | no | — |
| 228 | C25 | — | 8 | 56 | no | — |
| 229 | C25 | — | 8 | 56 | no | — |
| 230 | C25 | C25 | 1 | 7 | yes | — |
| 231 | C25 | C25 | 1 | 7 | yes | — |
| 232 | C22×D4 | — | 2 | 42 | no | — |
| 233 | C22×D4 | — | 2 | 42 | no | — |
| 234 | C22×D4 | — | 2 | 42 | no | — |
| 235 | C22×D4 | — | 2 | 42 | no | — |
| 236 | C22×D4 | — | 4 | 21 | no | — |
| 237 | C22×D4 | — | 4 | 21 | no | — |
| 238 | C22×D4 | — | 4 | 21 | no | — |
| 239 | C22×D4 | — | 4 | 21 | no | — |
| 240 | C22×D4 | — | 4 | 21 | no | — |
| 241 | C22×D4 | — | 4 | 21 | no | — |
| 242 | C22×D4 | — | 4 | 21 | no | — |
| 243 | C22×D4 | — | 4 | 21 | no | — |
| 244 | C22×D4 | — | 4 | 21 | no | — |
| 245 | C22×D4 | — | 4 | 21 | no | — |
| 246 | C22×D4 | — | 4 | 21 | no | — |
| 247 | C22×D4 | — | 4 | 21 | no | — |
| 248 | C22×D4 | H(5,𝔽2) | 1 | 28 | yes | — |
| 249 | C23×C4 | C25 | 1 | 21 | yes | — |
| 250 | C23×C4 | C25 | 1 | 21 | yes | — |
| 251 | C23×C4 | C25 | 1 | 7 | yes | — |
| 252 | #120 | — | 8 | 168 | no | — |
| 253 | #120 | — | 8 | 168 | no | — |
| 254 | #120 | — | 8 | 168 | no | — |
| 255 | #120 | — | 8 | 168 | no | — |
| 256 | #120 | — | 8 | 56 | no | — |
| 257 | #120 | — | 8 | 56 | no | — |
| 258 | C2×C4⋊C4 | — | 2 | 42 | no | — |
| 259 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 260 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 261 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 262 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 263 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 264 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 265 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 266 | C2×C4⋊C4 | — | 4 | 21 | no | — |
| 267 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 268 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 269 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 270 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 271 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 272 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 273 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 274 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 275 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 276 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 277 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 278 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 279 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 280 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 281 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 282 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 283 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 284 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 285 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 286 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 287 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 288 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 289 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 290 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 291 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 292 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 293 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 294 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 295 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 296 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 297 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 298 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 299 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 300 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 301 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 302 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 303 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 304 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 305 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 306 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 307 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 308 | C2×C22⋊C4 | — | 4 | 21 | no | — |
| 309 | C2×C42 | — | 4 | 21 | no | — |
| 310 | C2×C42 | — | 4 | 21 | no | — |
| 311 | C2×C42 | — | 4 | 21 | no | — |
| 312 | #95 | — | 2 | 42 | no | — |
| 313 | #95 | — | 4 | 21 | no | — |
| 314 | #95 | — | 4 | 21 | no | — |
| 315 | #95 | — | 4 | 21 | no | — |
| 316 | #95 | — | 4 | 21 | no | — |
| 317 | #95 | — | 4 | 21 | no | — |
| 318 | #95 | — | 4 | 21 | no | — |
| 319 | #95 | — | 4 | 7 | no | — |
| 320 | #95 | — | 4 | 7 | no | — |
| 321 | #95 | — | 4 | 7 | no | — |
| 322 | #95 | — | 4 | 21 | no | — |
| 323 | #95 | — | 4 | 21 | no | — |
| 324 | C24 | — | 2 | 21 | no | — |
| 325 | C24 | — | 2 | 21 | no | — |
| 326 | C24 | — | 2 | 21 | no | — |
| 327 | C24 | — | 2 | 21 | no | — |
| 328 | C24 | — | 2 | 7 | no | — |
| 329 | C24 | — | 2 | 7 | no | — |
| 330 | C24 | — | 2 | 7 | no | — |
| 331 | C24 | — | 2 | 7 | no | — |
| 332 | C24 | — | 2 | 21 | no | — |
| 333 | C24 | — | 2 | 21 | no | — |
| 334 | C24 | — | 2 | 21 | no | — |
| 335 | C24 | — | 2 | 21 | no | — |
| 336 | C24 | — | 4 | 84 | no | — |
| 337 | C24 | — | 4 | 84 | no | — |
| 338 | C24 | — | 4 | 84 | no | — |
| 339 | C24 | — | 4 | 84 | no | — |
| 340 | C24 | — | 4 | 28 | no | — |
| 341 | C24 | — | 4 | 28 | no | — |
| 342 | C24 | — | 8 | 42 | no | — |
| 343 | C24 | — | 8 | 42 | no | — |
| 344 | C24 | — | 8 | 42 | no | — |
| 345 | C24 | — | 8 | 42 | no | — |
| 346 | C24 | — | 8 | 42 | no | — |
| 347 | C24 | — | 8 | 42 | no | — |
| 348 | C24 | — | 8 | 42 | no | — |
| 349 | C24 | — | 8 | 42 | no | — |
| 350 | C24 | — | 8 | 42 | no | — |
| 351 | C24 | — | 8 | 42 | no | — |
| 352 | C24 | — | 8 | 42 | no | — |
| 353 | C24 | — | 8 | 42 | no | — |
| 354 | C24 | — | 8 | 42 | no | — |
| 355 | C24 | — | 8 | 42 | no | — |
| 356 | C24 | — | 8 | 14 | no | — |
| 357 | C24 | — | 8 | 14 | no | — |
| 358 | C24 | — | 8 | 42 | no | — |
| 359 | C24 | — | 8 | 42 | no | — |
| 360 | C24 | — | 8 | 42 | no | — |
| 361 | C24 | — | 8 | 42 | no | — |
| 362 | C24 | — | 8 | 448 | no | — |
| 363 | C24 | — | 8 | 448 | no | — |
| 364 | C24 | — | 8 | 448 | no | — |
| 365 | C24 | — | 8 | 448 | no | — |
| 366 | C24 | — | 8 | 64 | no | — |
| 367 | C24 | — | 8 | 64 | no | — |
| 368 | C24 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 369 | C24 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 370 | C24 | C26 | 1 | 1 | yes | characteristic |
| 371 | C2×D4 | — | 4 | 84 | no | — |
| 372 | C2×D4 | — | 4 | 84 | no | — |
| 373 | C2×D4 | — | 4 | 84 | no | — |
| 374 | C2×D4 | — | 8 | 42 | no | — |
| 375 | C2×D4 | — | 8 | 42 | no | — |
| 376 | C2×D4 | — | 8 | 42 | no | — |
| 377 | C2×D4 | — | 8 | 42 | no | — |
| 378 | C2×D4 | — | 8 | 42 | no | — |
| 379 | C2×D4 | — | 8 | 42 | no | — |
| 380 | C2×D4 | — | 8 | 42 | no | — |
| 381 | C2×D4 | — | 8 | 42 | no | — |
| 382 | C2×D4 | — | 16 | 21 | no | — |
| 383 | C2×D4 | — | 16 | 7 | no | — |
| 384 | C2×D4 | — | 16 | 21 | no | — |
| 385 | C2×D4 | — | 16 | 21 | no | — |
| 386 | C2×D4 | — | 16 | 21 | no | — |
| 387 | C2×D4 | — | 16 | 21 | no | — |
| 388 | C22×C4 | — | 2 | 21 | no | — |
| 389 | C22×C4 | — | 2 | 21 | no | — |
| 390 | C22×C4 | — | 2 | 21 | no | — |
| 391 | C22×C4 | — | 2 | 21 | no | — |
| 392 | C22×C4 | — | 2 | 21 | no | — |
| 393 | C22×C4 | — | 2 | 21 | no | — |
| 394 | C22×C4 | — | 2 | 21 | no | — |
| 395 | C22×C4 | — | 2 | 21 | no | — |
| 396 | C22×C4 | — | 2 | 21 | no | — |
| 397 | C22×C4 | — | 2 | 21 | no | — |
| 398 | C22×C4 | — | 2 | 21 | no | — |
| 399 | C22×C4 | — | 2 | 21 | no | — |
| 400 | C22×C4 | — | 2 | 21 | no | — |
| 401 | C22×C4 | — | 2 | 21 | no | — |
| 402 | C22×C4 | — | 2 | 21 | no | — |
| 403 | C22×C4 | — | 2 | 21 | no | — |
| 404 | C22×C4 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 405 | C4⋊C4 | — | 8 | 42 | no | — |
| 406 | C4⋊C4 | — | 16 | 21 | no | — |
| 407 | C4⋊C4 | — | 16 | 21 | no | — |
| 408 | C22⋊C4 | — | 4 | 84 | no | — |
| 409 | C22⋊C4 | — | 4 | 84 | no | — |
| 410 | C22⋊C4 | — | 8 | 42 | no | — |
| 411 | C22⋊C4 | — | 8 | 42 | no | — |
| 412 | C22⋊C4 | — | 8 | 42 | no | — |
| 413 | C22⋊C4 | — | 8 | 42 | no | — |
| 414 | C22⋊C4 | — | 8 | 42 | no | — |
| 415 | C22⋊C4 | — | 8 | 42 | no | — |
| 416 | C22⋊C4 | — | 8 | 42 | no | — |
| 417 | C22⋊C4 | — | 8 | 42 | no | — |
| 418 | C22⋊C4 | — | 8 | 42 | no | — |
| 419 | C22⋊C4 | — | 8 | 42 | no | — |
| 420 | C22⋊C4 | — | 8 | 42 | no | — |
| 421 | C22⋊C4 | — | 8 | 42 | no | — |
| 422 | C42 | — | 16 | 21 | no | — |
| 423 | C23 | — | 2 | 14 | no | — |
| 424 | C23 | — | 2 | 14 | no | — |
| 425 | C23 | — | 2 | 42 | no | — |
| 426 | C23 | — | 2 | 42 | no | — |
| 427 | C23 | — | 2 | 42 | no | — |
| 428 | C23 | — | 2 | 42 | no | — |
| 429 | C23 | — | 4 | 21 | no | — |
| 430 | C23 | — | 4 | 21 | no | — |
| 431 | C23 | — | 4 | 21 | no | — |
| 432 | C23 | — | 4 | 21 | no | — |
| 433 | C23 | — | 4 | 21 | no | — |
| 434 | C23 | — | 4 | 21 | no | — |
| 435 | C23 | — | 4 | 21 | no | — |
| 436 | C23 | — | 4 | 21 | no | — |
| 437 | C23 | — | 4 | 21 | no | — |
| 438 | C23 | — | 4 | 21 | no | — |
| 439 | C23 | — | 4 | 21 | no | — |
| 440 | C23 | — | 4 | 21 | no | — |
| 441 | C23 | — | 4 | 21 | no | — |
| 442 | C23 | — | 4 | 21 | no | — |
| 443 | C23 | — | 4 | 21 | no | — |
| 444 | C23 | — | 4 | 21 | no | — |
| 445 | C23 | — | 4 | 7 | no | — |
| 446 | C23 | — | 4 | 7 | no | — |
| 447 | C23 | — | 4 | 21 | no | — |
| 448 | C23 | — | 4 | 21 | no | — |
| 449 | C23 | — | 8 | 56 | no | — |
| 450 | C23 | — | 8 | 56 | no | — |
| 451 | C23 | — | 8 | 168 | no | — |
| 452 | C23 | — | 8 | 168 | no | — |
| 453 | C23 | — | 8 | 168 | no | — |
| 454 | C23 | — | 8 | 168 | no | — |
| 455 | C23 | — | 8 | 168 | no | — |
| 456 | C23 | — | 8 | 168 | no | — |
| 457 | C23 | — | 8 | 168 | no | — |
| 458 | C23 | — | 8 | 168 | no | — |
| 459 | C23 | — | 8 | 512 | no | — |
| 460 | C23 | — | 8 | 512 | no | — |
| 461 | C23 | — | 8 | 56 | no | — |
| 462 | C23 | — | 8 | 56 | no | — |
| 463 | C23 | — | 8 | 56 | no | — |
| 464 | C23 | — | 8 | 56 | no | — |
| 465 | C23 | C22×H(5,𝔽2) | 1 | 7 | yes | — |
| 466 | C23 | H(7,𝔽2) | 1 | 1 | yes | characteristic |
| 467 | C23 | H(7,𝔽2) | 1 | 7 | yes | — |
| 468 | D4 | — | 16 | 28 | no | — |
| 469 | D4 | — | 16 | 84 | no | — |
| 470 | D4 | — | 16 | 84 | no | — |
| 471 | C2×C4 | — | 2 | 42 | no | — |
| 472 | C2×C4 | — | 4 | 21 | no | — |
| 473 | C2×C4 | — | 4 | 7 | no | — |
| 474 | C2×C4 | — | 4 | 21 | no | — |
| 475 | C2×C4 | — | 4 | 21 | no | — |
| 476 | C2×C4 | — | 4 | 21 | no | — |
| 477 | C2×C4 | — | 4 | 21 | no | — |
| 478 | C2×C4 | — | 4 | 21 | no | — |
| 479 | C2×C4 | — | 4 | 21 | no | — |
| 480 | C2×C4 | — | 4 | 21 | no | — |
| 481 | C2×C4 | — | 4 | 21 | no | — |
| 482 | C2×C4 | — | 4 | 21 | no | — |
| 483 | C2×C4 | — | 4 | 21 | no | — |
| 484 | C2×C4 | — | 4 | 21 | no | — |
| 485 | C2×C4 | — | 4 | 21 | no | — |
| 486 | C2×C4 | — | 4 | 21 | no | — |
| 487 | C2×C4 | — | 4 | 21 | no | — |
| 488 | C22 | — | 4 | 42 | no | — |
| 489 | C22 | — | 4 | 42 | no | — |
| 490 | C22 | — | 4 | 14 | no | — |
| 491 | C22 | — | 4 | 14 | no | — |
| 492 | C22 | — | 4 | 42 | no | — |
| 493 | C22 | — | 4 | 42 | no | — |
| 494 | C22 | — | 8 | 224 | no | — |
| 495 | C22 | — | 8 | 224 | no | — |
| 496 | C22 | — | 8 | 7 | no | — |
| 497 | C22 | — | 8 | 21 | no | — |
| 498 | C22 | — | 8 | 21 | no | — |
| 499 | C22 | — | 8 | 7 | no | — |
| 500 | C22 | — | 8 | 21 | no | — |
| 501 | C22 | — | 8 | 21 | no | — |
| 502 | C22 | — | 8 | 7 | no | — |
| 503 | C22 | — | 8 | 7 | no | — |
| 504 | C22 | #62892 | 1 | 21 | yes | — |
| 505 | C22 | #62972 | 1 | 7 | yes | — |
| 506 | C22 | #63045 | 1 | 7 | yes | — |
| 507 | C4 | — | 4 | 14 | no | — |
| 508 | C4 | — | 8 | 21 | no | — |
| 509 | C4 | — | 8 | 21 | no | — |
| 510 | C2 | — | 8 | 14 | no | — |
| 511 | C2 | — | 8 | 14 | no | — |
| 512 | C2 | #10320507 | 1 | 7 | yes | — |
| 513 | C2 | #10504541 | 1 | 7 | yes | — |
| 514 | C2 | H(3,𝔽8) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C24 | C26 |
| 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. #6034457 | C2 | semidirect |
| 2. #5720743 | C2 | semidirect |
| 3. #4140675 | C2 | semidirect |
| 4. #2032030 | C2 | semidirect |
| 5. #2032030 | C2 | semidirect |
| 6. C2×#2801 | C22 | semidirect |
| 8. C2×#2846 | C22 | semidirect |
| 9. C2×#2846 | C22 | semidirect |
| 10. #17204 | C22 | semidirect |
| 11. #17159 | C22 | semidirect |
| 12. #17123 | C22 | semidirect |
| 13. #16865 | C22 | semidirect |
| 14. #16865 | C22 | semidirect |
| 15. #16587 | C22 | semidirect |
| 16. #16548 | C22 | semidirect |
| 17. #16347 | C22 | semidirect |
| 18. #16255 | C22 | semidirect |
| 19. #16255 | C22 | semidirect |
| 20. #16255 | C22 | semidirect |
| 21. #16255 | C22 | semidirect |
| 24. #15777 | C22 | semidirect |
| 25. #15615 | C22 | semidirect |
| 26. #15348 | C22 | semidirect |
| 27. #15283 | C22 | semidirect |
| 28. #15283 | C22 | semidirect |
| 29. #15281 | C22 | semidirect |
| 30. #15281 | C22 | semidirect |
| 31. #15268 | C22 | semidirect |
| 32. #15268 | C22 | semidirect |
| 33. #15268 | C22 | semidirect |
| 34. #15268 | C22 | semidirect |
| 35. #15141 | C22 | semidirect |
| 36. #14986 | C22 | semidirect |
| 37. #14949 | C22 | semidirect |
| 38. #14563 | C22 | semidirect |
| 39. #14358 | C22 | semidirect |
| 40. #14358 | C22 | semidirect |
| 41. C27 | C23 | semidirect |
| 42. C27 | C23 | semidirect |
| 53. C2×#401 | C23 | semidirect |
| 54. C2×#399 | C23 | semidirect |
| 55. C2×#399 | C23 | semidirect |
| 56. C2×#397 | C23 | semidirect |
| 57. C2×#397 | C23 | semidirect |
| 58. C2×#396 | C23 | semidirect |
| 59. C2×#396 | C23 | semidirect |
| 60. C2×#396 | C23 | semidirect |
| 61. C2×#396 | C23 | semidirect |
| 71. C2×#389 | C23 | semidirect |
| 72. C2×#388 | C23 | semidirect |
| 73. C2×#388 | C23 | semidirect |
| 74. C2×#388 | C23 | semidirect |
| 75. C2×#388 | C23 | semidirect |
| 76. C2×#379 | C23 | semidirect |
| 77. C2×#379 | C23 | semidirect |
| 78. C2×#379 | C23 | semidirect |
| 79. C2×#379 | C23 | semidirect |
| 80. C2×#379 | C23 | semidirect |
| 81. C2×#379 | C23 | semidirect |
| 82. #1443 | C23 | semidirect |
| 83. #1442 | C23 | semidirect |
| 84. #1442 | C23 | semidirect |
| 85. #1441 | C23 | semidirect |
| 86. #1441 | C23 | semidirect |
| 87. #1440 | C23 | semidirect |
| 88. #1440 | C23 | semidirect |
| 89. #1440 | C23 | semidirect |
| 90. #1440 | C23 | semidirect |
| 91. #1439 | C23 | semidirect |
| 92. #1439 | C23 | semidirect |
| 93. #1439 | C23 | semidirect |
| 94. #1439 | C23 | semidirect |
| 95. #1439 | C23 | semidirect |
| 96. #1439 | C23 | semidirect |
| 97. #1439 | C23 | semidirect |
| 98. #1439 | C23 | semidirect |
| 99. #1439 | C23 | semidirect |
| 100. #1439 | C23 | semidirect |
| 101. #1439 | C23 | semidirect |
| 102. #1439 | C23 | semidirect |
| 115. #1437 | C23 | semidirect |
| 116. #1437 | C23 | semidirect |
| 117. #1437 | C23 | semidirect |
| 118. #1437 | C23 | semidirect |
| 119. #1436 | C23 | semidirect |
| 120. #1436 | C23 | semidirect |
| 121. C4×#95 | C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6034457 | 2 |
| #5720743 | 2 |
| #4140675 | 2 |
| #2032030 | 2 |