Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
8286648 conjugacy classes of subgroups.
The subgroup lattice has 441 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#6342373 | C2 | 1 | 96 | yes | maximal, direct product factor |
| 2 | C23×#2848 | C2 | 1 | 7 | yes | maximal, complemented |
| 3 | C22×#14693 | C2 | 1 | 14 | yes | maximal, complemented |
| 4 | C22×#14680 | C2 | 1 | 7 | yes | maximal, complemented |
| 5 | C22×#14679 | C2 | 1 | 2 | yes | maximal |
| 6 | C28×C4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C29 | C22 | 1 | 1 | yes | characteristic |
| 8 | C27×C4 | — | 2 | 224 | no | — |
| 9 | C27×C4 | C22 | 1 | 48 | yes | — |
| 10 | C27×C4 | C22 | 1 | 7 | yes | — |
| 11 | C27×C4 | C22 | 1 | 7 | yes | — |
| 12 | C24×C22⋊Q8 | C22 | 1 | 7 | yes | complemented |
| 13 | C22×#2848 | — | 2 | 224 | no | — |
| 14 | C22×#2848 | C22 | 1 | 336 | yes | complemented |
| 15 | C23×#385 | C22 | 1 | 42 | yes | complemented |
| 16 | C23×#380 | C22 | 1 | 21 | yes | complemented |
| 17 | C23×#379 | C22 | 1 | 14 | yes | — |
| 18 | C23×#379 | C22 | 1 | 14 | yes | — |
| 19 | #6342373 | C22 | 1 | 1024 | yes | direct product factor |
| 20 | C2×#14693 | C22 | 1 | 672 | yes | complemented |
| 21 | C2×#14680 | C22 | 1 | 336 | yes | complemented |
| 22 | C2×#14679 | C22 | 1 | 96 | yes | — |
| 23 | C22×C22⋊#95 | C22 | 1 | 42 | yes | complemented |
| 24 | C28 | — | 2 | 112 | no | — |
| 25 | C28 | — | 2 | 112 | no | — |
| 26 | C28 | Q8 | 1 | 32 | yes | complemented |
| 27 | C28 | C23 | 1 | 24 | yes | — |
| 28 | C28 | C23 | 1 | 7 | yes | — |
| 29 | C25×Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 30 | C26×C4 | — | 2 | 14336 | no | — |
| 31 | C26×C4 | — | 2 | 112 | no | — |
| 32 | C26×C4 | — | 2 | 5376 | no | — |
| 33 | C26×C4 | — | 2 | 672 | no | — |
| 34 | C26×C4 | — | 2 | 672 | no | — |
| 35 | C26×C4 | D4 | 1 | 224 | yes | — |
| 36 | C26×C4 | C23 | 1 | 168 | yes | — |
| 37 | C26×C4 | C23 | 1 | 256 | yes | — |
| 38 | C26×C4 | C23 | 1 | 21 | yes | — |
| 39 | C26×C4 | C23 | 1 | 168 | yes | — |
| 40 | C26×C4 | C23 | 1 | 7 | yes | — |
| 41 | C23×C22⋊Q8 | — | 2 | 336 | no | — |
| 42 | C23×C22⋊Q8 | C23 | 1 | 168 | yes | complemented |
| 43 | C24×C4⋊C4 | C23 | 1 | 7 | yes | complemented |
| 44 | C24×C4⋊C4 | C23 | 1 | 14 | yes | complemented |
| 45 | C24×C22⋊C4 | C23 | 1 | 42 | yes | — |
| 46 | C24×C22⋊C4 | C23 | 1 | 14 | yes | — |
| 47 | C2×#2848 | — | 2 | 5376 | no | — |
| 48 | C2×#2848 | C23 | 1 | 1792 | yes | complemented |
| 49 | C22×#385 | — | 2 | 672 | no | — |
| 50 | C22×#385 | C23 | 1 | 1008 | yes | complemented |
| 51 | C22×#380 | — | 2 | 336 | no | — |
| 52 | C22×#380 | C23 | 1 | 504 | yes | complemented |
| 53 | C22×#379 | — | 2 | 224 | no | — |
| 54 | C22×#379 | — | 2 | 224 | no | — |
| 55 | C22×#379 | C23 | 1 | 336 | yes | — |
| 56 | C22×#379 | C23 | 1 | 336 | yes | — |
| 57 | C23×#95 | C23 | 1 | 42 | yes | complemented |
| 58 | #14693 | C23 | 1 | 3584 | yes | complemented |
| 59 | #14680 | C23 | 1 | 1792 | yes | complemented |
| 60 | #14679 | C23 | 1 | 512 | yes | — |
| 61 | C2×C22⋊#95 | C23 | 1 | 1008 | yes | complemented |
| 62 | C27 | — | 2 | 3584 | no | — |
| 63 | C27 | — | 2 | 10752 | no | — |
| 64 | C27 | — | 2 | 3584 | no | — |
| 65 | C27 | — | 2 | 1344 | no | — |
| 66 | C27 | — | 2 | 336 | no | — |
| 67 | C27 | — | 2 | 1344 | no | — |
| 68 | C27 | — | 2 | 336 | no | — |
| 69 | C27 | C2×D4 | 1 | 112 | yes | — |
| 70 | C27 | C2×Q8 | 1 | 112 | yes | — |
| 71 | C27 | C2×Q8 | 1 | 384 | yes | complemented |
| 72 | C27 | #41 | 1 | 112 | yes | — |
| 73 | C27 | C24 | 1 | 64 | yes | — |
| 74 | C27 | C24 | 1 | 84 | yes | — |
| 75 | C27 | C24 | 1 | 7 | yes | — |
| 76 | C24×Q8 | — | 2 | 56 | no | — |
| 77 | C24×Q8 | C24 | 1 | 12 | yes | complemented |
| 78 | C25×C4 | — | 2 | 131072 | no | — |
| 79 | C25×C4 | — | 2 | 10752 | no | — |
| 80 | C25×C4 | — | 2 | 14336 | no | — |
| 81 | C25×C4 | — | 2 | 172032 | no | — |
| 82 | C25×C4 | — | 2 | 14336 | no | — |
| 83 | C25×C4 | — | 2 | 1344 | no | — |
| 84 | C25×C4 | — | 2 | 336 | no | — |
| 85 | C25×C4 | — | 2 | 10752 | no | — |
| 86 | C25×C4 | — | 2 | 14336 | no | — |
| 87 | C25×C4 | — | 2 | 8064 | no | — |
| 88 | C25×C4 | — | 2 | 672 | no | — |
| 89 | C25×C4 | — | 2 | 8064 | no | — |
| 90 | C25×C4 | — | 2 | 224 | no | — |
| 91 | C25×C4 | C2×D4 | 1 | 2688 | yes | — |
| 92 | C25×C4 | C2×D4 | 1 | 336 | yes | — |
| 93 | C25×C4 | C2×D4 | 1 | 336 | yes | — |
| 94 | C25×C4 | C24 | 1 | 448 | yes | — |
| 95 | C25×C4 | C24 | 1 | 2 | yes | — |
| 96 | C25×C4 | C24 | 1 | 14 | yes | — |
| 97 | C25×C4 | C24 | 1 | 448 | yes | — |
| 98 | C25×C4 | C24 | 1 | 252 | yes | — |
| 99 | C25×C4 | C24 | 1 | 84 | yes | — |
| 100 | C25×C4 | C24 | 1 | 7 | yes | — |
| 101 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 102 | C22×C22⋊Q8 | — | 2 | 4032 | no | — |
| 103 | C22×C22⋊Q8 | — | 4 | 1792 | no | — |
| 104 | C22×C22⋊Q8 | C24 | 1 | 448 | yes | complemented |
| 105 | C23×C4⋊C4 | — | 2 | 168 | no | — |
| 106 | C23×C4⋊C4 | — | 2 | 336 | no | — |
| 107 | C23×C4⋊C4 | C24 | 1 | 84 | yes | complemented |
| 108 | C23×C4⋊C4 | C24 | 1 | 168 | yes | complemented |
| 109 | C23×C22⋊C4 | — | 2 | 336 | no | — |
| 110 | C23×C22⋊C4 | — | 2 | 336 | no | — |
| 111 | C23×C22⋊C4 | — | 2 | 672 | no | — |
| 112 | C23×C22⋊C4 | C24 | 1 | 504 | yes | — |
| 113 | C23×C22⋊C4 | C24 | 1 | 168 | yes | — |
| 114 | #2848 | — | 2 | 14336 | no | — |
| 115 | C2×#385 | — | 2 | 8064 | no | — |
| 116 | C2×#385 | C24 | 1 | 2688 | yes | complemented |
| 117 | C2×#380 | — | 2 | 4032 | no | — |
| 118 | C2×#380 | C24 | 1 | 1344 | yes | complemented |
| 119 | C2×#379 | — | 2 | 2688 | no | — |
| 120 | C2×#379 | — | 2 | 2688 | no | — |
| 121 | C2×#379 | C24 | 1 | 896 | yes | — |
| 122 | C2×#379 | C24 | 1 | 896 | yes | — |
| 123 | C22×#95 | — | 2 | 336 | no | — |
| 124 | C22×#95 | C24 | 1 | 504 | yes | complemented |
| 125 | C22⋊#95 | C24 | 1 | 2688 | yes | complemented |
| 126 | C26 | — | 2 | 16384 | no | — |
| 127 | C26 | — | 2 | 21504 | no | — |
| 128 | C26 | — | 2 | 3584 | no | — |
| 129 | C26 | — | 2 | 114688 | no | — |
| 130 | C26 | — | 2 | 114688 | no | — |
| 131 | C26 | — | 2 | 64512 | no | — |
| 132 | C26 | — | 2 | 10752 | no | — |
| 133 | C26 | — | 2 | 2688 | no | — |
| 134 | C26 | — | 2 | 5376 | no | — |
| 135 | C26 | — | 2 | 21504 | no | — |
| 136 | C26 | — | 2 | 2688 | no | — |
| 137 | C26 | — | 2 | 5376 | no | — |
| 138 | C26 | — | 2 | 1792 | no | — |
| 139 | C26 | — | 2 | 2016 | no | — |
| 140 | C26 | — | 2 | 112 | no | — |
| 141 | C26 | — | 2 | 1792 | no | — |
| 142 | C26 | — | 2 | 2016 | no | — |
| 143 | C26 | — | 2 | 112 | no | — |
| 144 | C26 | C22⋊Q8 | 1 | 1792 | yes | complemented |
| 145 | C26 | C22×D4 | 1 | 672 | yes | — |
| 146 | C26 | C22×D4 | 1 | 168 | yes | — |
| 147 | C26 | C22×Q8 | 1 | 672 | yes | — |
| 148 | C26 | C22×Q8 | 1 | 56 | yes | — |
| 149 | C26 | C22×Q8 | 1 | 512 | yes | complemented |
| 150 | C26 | C2×#41 | 1 | 672 | yes | — |
| 151 | C26 | C2×#41 | 1 | 168 | yes | — |
| 152 | C26 | C25 | 1 | 112 | yes | — |
| 153 | C26 | C25 | 1 | 42 | yes | — |
| 154 | C26 | C25 | 1 | 1 | yes | characteristic |
| 155 | C23×Q8 | — | 2 | 336 | no | — |
| 156 | C23×Q8 | — | 4 | 448 | no | — |
| 157 | C23×Q8 | C25 | 1 | 16 | yes | complemented |
| 158 | C24×C4 | — | 2 | 114688 | no | — |
| 159 | C24×C4 | — | 2 | 786432 | no | — |
| 160 | C24×C4 | — | 2 | 64512 | no | — |
| 161 | C24×C4 | — | 2 | 10752 | no | — |
| 162 | C24×C4 | — | 2 | 114688 | no | — |
| 163 | C24×C4 | — | 2 | 86016 | no | — |
| 164 | C24×C4 | — | 2 | 229376 | no | — |
| 165 | C24×C4 | — | 2 | 86016 | no | — |
| 166 | C24×C4 | — | 2 | 2688 | no | — |
| 167 | C24×C4 | — | 2 | 1792 | no | — |
| 168 | C24×C4 | — | 2 | 2016 | no | — |
| 169 | C24×C4 | — | 2 | 112 | no | — |
| 170 | C24×C4 | — | 2 | 5376 | no | — |
| 171 | C24×C4 | — | 2 | 64512 | no | — |
| 172 | C24×C4 | — | 2 | 5376 | no | — |
| 173 | C24×C4 | — | 2 | 10752 | no | — |
| 174 | C24×C4 | — | 2 | 4032 | no | — |
| 175 | C24×C4 | — | 2 | 10752 | no | — |
| 176 | C24×C4 | — | 2 | 1344 | no | — |
| 177 | C24×C4 | — | 2 | 56 | no | — |
| 178 | C24×C4 | — | 2 | 168 | no | — |
| 179 | C24×C4 | — | 2 | 224 | no | — |
| 180 | C24×C4 | #120 | 1 | 1792 | yes | — |
| 181 | C24×C4 | C22×D4 | 1 | 3584 | yes | — |
| 182 | C24×C4 | C22×D4 | 1 | 2016 | yes | — |
| 183 | C24×C4 | C22×D4 | 1 | 168 | yes | — |
| 184 | C24×C4 | C22×D4 | 1 | 2016 | yes | — |
| 185 | C24×C4 | C22×D4 | 1 | 56 | yes | — |
| 186 | C24×C4 | C25 | 1 | 12 | yes | — |
| 187 | C24×C4 | C25 | 1 | 84 | yes | — |
| 188 | C24×C4 | C25 | 1 | 336 | yes | — |
| 189 | C24×C4 | C25 | 1 | 42 | yes | — |
| 190 | C24×C4 | C25 | 1 | 112 | yes | — |
| 191 | C24×C4 | C25 | 1 | 6 | yes | — |
| 192 | C2×C22⋊Q8 | — | 2 | 5376 | no | — |
| 193 | C2×C22⋊Q8 | — | 4 | 10752 | no | — |
| 194 | C22×C4⋊C4 | — | 2 | 1008 | no | — |
| 195 | C22×C4⋊C4 | — | 2 | 2016 | no | — |
| 196 | C22×C4⋊C4 | — | 4 | 448 | no | — |
| 197 | C22×C4⋊C4 | — | 4 | 896 | no | — |
| 198 | C22×C4⋊C4 | C25 | 1 | 112 | yes | complemented |
| 199 | C22×C4⋊C4 | C25 | 1 | 224 | yes | complemented |
| 200 | C22×C22⋊C4 | — | 2 | 2016 | no | — |
| 201 | C22×C22⋊C4 | — | 2 | 2016 | no | — |
| 202 | C22×C22⋊C4 | — | 2 | 4032 | no | — |
| 203 | C22×C22⋊C4 | — | 4 | 896 | no | — |
| 204 | C22×C22⋊C4 | — | 4 | 2688 | no | — |
| 205 | C22×C22⋊C4 | C25 | 1 | 224 | yes | — |
| 206 | C22×C22⋊C4 | C25 | 1 | 672 | yes | — |
| 207 | #385 | — | 2 | 10752 | no | — |
| 208 | #380 | — | 2 | 5376 | no | — |
| 209 | #379 | — | 2 | 3584 | no | — |
| 210 | #379 | — | 2 | 3584 | no | — |
| 211 | C2×#95 | — | 2 | 2016 | no | — |
| 212 | C2×#95 | C25 | 1 | 672 | yes | complemented |
| 213 | C25 | — | 2 | 49152 | no | — |
| 214 | C25 | — | 2 | 14336 | no | — |
| 215 | C25 | — | 2 | 14336 | no | — |
| 216 | C25 | — | 2 | 10752 | no | — |
| 217 | C25 | — | 2 | 344064 | no | — |
| 218 | C25 | — | 2 | 524288 | no | — |
| 219 | C25 | — | 2 | 57344 | no | — |
| 220 | C25 | — | 2 | 344064 | no | — |
| 221 | C25 | — | 2 | 43008 | no | — |
| 222 | C25 | — | 2 | 57344 | no | — |
| 223 | C25 | — | 2 | 43008 | no | — |
| 224 | C25 | — | 2 | 32256 | no | — |
| 225 | C25 | — | 2 | 1344 | no | — |
| 226 | C25 | — | 2 | 336 | no | — |
| 227 | C25 | — | 2 | 1344 | no | — |
| 228 | C25 | — | 2 | 336 | no | — |
| 229 | C25 | — | 2 | 43008 | no | — |
| 230 | C25 | — | 2 | 8064 | no | — |
| 231 | C25 | — | 2 | 1344 | no | — |
| 232 | C25 | — | 2 | 16128 | no | — |
| 233 | C25 | — | 2 | 896 | no | — |
| 234 | C25 | — | 2 | 14336 | no | — |
| 235 | C25 | — | 2 | 8064 | no | — |
| 236 | C25 | — | 2 | 1344 | no | — |
| 237 | C25 | — | 2 | 16128 | no | — |
| 238 | C25 | — | 2 | 2688 | no | — |
| 239 | C25 | C2×#120 | 1 | 448 | yes | — |
| 240 | C25 | C2×C22⋊Q8 | 1 | 1344 | yes | — |
| 241 | C25 | C2×C22⋊Q8 | 1 | 5376 | yes | complemented |
| 242 | C25 | #525 | 1 | 1344 | yes | — |
| 243 | C25 | C23×D4 | 1 | 448 | yes | — |
| 244 | C25 | C23×D4 | 1 | 504 | yes | — |
| 245 | C25 | C23×D4 | 1 | 28 | yes | — |
| 246 | C25 | C23×Q8 | 1 | 448 | yes | — |
| 247 | C25 | C23×Q8 | 1 | 168 | yes | — |
| 248 | C25 | C23×Q8 | 1 | 4 | yes | — |
| 249 | C25 | C22×#41 | 1 | 448 | yes | — |
| 250 | C25 | C22×#41 | 1 | 504 | yes | — |
| 251 | C25 | C22×#41 | 1 | 28 | yes | — |
| 252 | C25 | C26 | 1 | 28 | yes | — |
| 253 | C25 | C26 | 1 | 3 | yes | — |
| 254 | C22×Q8 | — | 2 | 224 | no | — |
| 255 | C22×Q8 | — | 4 | 1344 | no | — |
| 256 | C22×Q8 | — | 8 | 512 | no | — |
| 257 | C23×C4 | — | 2 | 344064 | no | — |
| 258 | C23×C4 | — | 2 | 524288 | no | — |
| 259 | C23×C4 | — | 2 | 43008 | no | — |
| 260 | C23×C4 | — | 2 | 43008 | no | — |
| 261 | C23×C4 | — | 2 | 32256 | no | — |
| 262 | C23×C4 | — | 2 | 344064 | no | — |
| 263 | C23×C4 | — | 2 | 57344 | no | — |
| 264 | C23×C4 | — | 2 | 57344 | no | — |
| 265 | C23×C4 | — | 2 | 1344 | no | — |
| 266 | C23×C4 | — | 2 | 336 | no | — |
| 267 | C23×C4 | — | 2 | 8064 | no | — |
| 268 | C23×C4 | — | 2 | 1344 | no | — |
| 269 | C23×C4 | — | 2 | 2688 | no | — |
| 270 | C23×C4 | — | 2 | 896 | no | — |
| 271 | C23×C4 | — | 2 | 14336 | no | — |
| 272 | C23×C4 | — | 2 | 16128 | no | — |
| 273 | C23×C4 | — | 2 | 43008 | no | — |
| 274 | C23×C4 | — | 2 | 16128 | no | — |
| 275 | C23×C4 | — | 2 | 168 | no | — |
| 276 | C23×C4 | — | 2 | 504 | no | — |
| 277 | C23×C4 | — | 2 | 672 | no | — |
| 278 | C23×C4 | — | 4 | 224 | no | — |
| 279 | C23×C4 | — | 4 | 224 | no | — |
| 280 | C23×C4 | — | 4 | 1344 | no | — |
| 281 | C23×C4 | C2×#120 | 1 | 448 | yes | — |
| 282 | C23×C4 | C2×#120 | 1 | 5376 | yes | — |
| 283 | C23×C4 | C2×#120 | 1 | 448 | yes | — |
| 284 | C23×C4 | C23×D4 | 1 | 1344 | yes | — |
| 285 | C23×C4 | C23×D4 | 1 | 504 | yes | — |
| 286 | C23×C4 | C23×D4 | 1 | 1344 | yes | — |
| 287 | C23×C4 | C23×D4 | 1 | 168 | yes | — |
| 288 | C23×C4 | C26 | 1 | 8 | yes | — |
| 289 | C23×C4 | C26 | 1 | 56 | yes | — |
| 290 | C23×C4 | C26 | 1 | 28 | yes | — |
| 291 | C23×C4 | C26 | 1 | 4 | yes | — |
| 292 | C22⋊Q8 | — | 4 | 7168 | no | — |
| 293 | C2×C4⋊C4 | — | 2 | 672 | no | — |
| 294 | C2×C4⋊C4 | — | 2 | 1344 | no | — |
| 295 | C2×C4⋊C4 | — | 4 | 1344 | no | — |
| 296 | C2×C4⋊C4 | — | 4 | 2688 | no | — |
| 297 | C2×C22⋊C4 | — | 2 | 1344 | no | — |
| 298 | C2×C22⋊C4 | — | 2 | 1344 | no | — |
| 299 | C2×C22⋊C4 | — | 2 | 2688 | no | — |
| 300 | C2×C22⋊C4 | — | 4 | 2688 | no | — |
| 301 | C2×C22⋊C4 | — | 4 | 8064 | no | — |
| 302 | #95 | — | 2 | 1344 | no | — |
| 303 | C24 | — | 2 | 16384 | no | — |
| 304 | C24 | — | 2 | 3584 | no | — |
| 305 | C24 | — | 2 | 21504 | no | — |
| 306 | C24 | — | 2 | 786432 | no | — |
| 307 | C24 | — | 2 | 114688 | no | — |
| 308 | C24 | — | 2 | 10752 | no | — |
| 309 | C24 | — | 2 | 86016 | no | — |
| 310 | C24 | — | 2 | 114688 | no | — |
| 311 | C24 | — | 2 | 64512 | no | — |
| 312 | C24 | — | 2 | 86016 | no | — |
| 313 | C24 | — | 2 | 229376 | no | — |
| 314 | C24 | — | 2 | 1792 | no | — |
| 315 | C24 | — | 2 | 10752 | no | — |
| 316 | C24 | — | 2 | 64512 | no | — |
| 317 | C24 | — | 2 | 1792 | no | — |
| 318 | C24 | — | 2 | 10752 | no | — |
| 319 | C24 | — | 2 | 112 | no | — |
| 320 | C24 | — | 2 | 112 | no | — |
| 321 | C24 | — | 2 | 2688 | no | — |
| 322 | C24 | — | 2 | 2016 | no | — |
| 323 | C24 | — | 2 | 5376 | no | — |
| 324 | C24 | — | 2 | 1344 | no | — |
| 325 | C24 | — | 2 | 2688 | no | — |
| 326 | C24 | — | 2 | 2016 | no | — |
| 327 | C24 | — | 2 | 5376 | no | — |
| 328 | C24 | — | 2 | 4032 | no | — |
| 329 | C24 | #2848 | 1 | 3584 | yes | complemented |
| 330 | C24 | C22×#120 | 1 | 672 | yes | — |
| 331 | C24 | C22×#120 | 1 | 112 | yes | — |
| 332 | C24 | C22×C22⋊Q8 | 1 | 2016 | yes | — |
| 333 | C24 | C22×C22⋊Q8 | 1 | 112 | yes | — |
| 334 | C24 | C22×C22⋊Q8 | 1 | 1792 | yes | complemented |
| 335 | C24 | C2×#525 | 1 | 2016 | yes | — |
| 336 | C24 | C2×#525 | 1 | 336 | yes | — |
| 337 | C24 | C24×D4 | 1 | 168 | yes | — |
| 338 | C24 | C24×D4 | 1 | 42 | yes | — |
| 339 | C24 | C24×Q8 | 1 | 56 | yes | — |
| 340 | C24 | C24×Q8 | 1 | 6 | yes | — |
| 341 | C24 | C23×#41 | 1 | 168 | yes | — |
| 342 | C24 | C23×#41 | 1 | 42 | yes | — |
| 343 | C24 | C27 | 1 | 1 | yes | characteristic |
| 344 | C2×Q8 | — | 4 | 448 | no | — |
| 345 | C2×Q8 | — | 8 | 768 | no | — |
| 346 | C22×C4 | — | 2 | 114688 | no | — |
| 347 | C22×C4 | — | 2 | 10752 | no | — |
| 348 | C22×C4 | — | 2 | 64512 | no | — |
| 349 | C22×C4 | — | 2 | 114688 | no | — |
| 350 | C22×C4 | — | 2 | 1792 | no | — |
| 351 | C22×C4 | — | 2 | 112 | no | — |
| 352 | C22×C4 | — | 2 | 2688 | no | — |
| 353 | C22×C4 | — | 2 | 2016 | no | — |
| 354 | C22×C4 | — | 2 | 21504 | no | — |
| 355 | C22×C4 | — | 2 | 5376 | no | — |
| 356 | C22×C4 | — | 2 | 5376 | no | — |
| 357 | C22×C4 | — | 2 | 168 | no | — |
| 358 | C22×C4 | — | 2 | 56 | no | — |
| 359 | C22×C4 | — | 2 | 224 | no | — |
| 360 | C22×C4 | — | 4 | 336 | no | — |
| 361 | C22×C4 | — | 4 | 336 | no | — |
| 362 | C22×C4 | — | 4 | 2016 | no | — |
| 363 | C22×C4 | — | 8 | 128 | no | — |
| 364 | C22×C4 | — | 8 | 896 | no | — |
| 365 | C22×C4 | #2846 | 1 | 512 | yes | — |
| 366 | C22×C4 | C22×#120 | 1 | 672 | yes | — |
| 367 | C22×C4 | C22×#120 | 1 | 1792 | yes | — |
| 368 | C22×C4 | C22×#120 | 1 | 672 | yes | — |
| 369 | C22×C4 | C24×D4 | 1 | 168 | yes | — |
| 370 | C22×C4 | C24×D4 | 1 | 56 | yes | — |
| 371 | C4⋊C4 | — | 4 | 448 | no | — |
| 372 | C4⋊C4 | — | 4 | 896 | no | — |
| 373 | C22⋊C4 | — | 4 | 896 | no | — |
| 374 | C22⋊C4 | — | 4 | 2688 | no | — |
| 375 | C23 | — | 2 | 3584 | no | — |
| 376 | C23 | — | 2 | 131072 | no | — |
| 377 | C23 | — | 2 | 172032 | no | — |
| 378 | C23 | — | 2 | 10752 | no | — |
| 379 | C23 | — | 2 | 14336 | no | — |
| 380 | C23 | — | 2 | 14336 | no | — |
| 381 | C23 | — | 2 | 336 | no | — |
| 382 | C23 | — | 2 | 224 | no | — |
| 383 | C23 | — | 2 | 336 | no | — |
| 384 | C23 | — | 2 | 672 | no | — |
| 385 | C23 | — | 2 | 1344 | no | — |
| 386 | C23 | — | 2 | 8064 | no | — |
| 387 | C23 | — | 2 | 10752 | no | — |
| 388 | C23 | — | 2 | 1344 | no | — |
| 389 | C23 | — | 2 | 8064 | no | — |
| 390 | C23 | — | 2 | 14336 | no | — |
| 391 | C23 | C2×#2846 | 1 | 64 | yes | — |
| 392 | C23 | C2×#2848 | 1 | 448 | yes | — |
| 393 | C23 | C2×#2848 | 1 | 2688 | yes | complemented |
| 394 | C23 | #36614 | 1 | 448 | yes | — |
| 395 | C23 | C23×#120 | 1 | 112 | yes | — |
| 396 | C23 | C23×#120 | 1 | 84 | yes | — |
| 397 | C23 | C23×C22⋊Q8 | 1 | 336 | yes | — |
| 398 | C23 | C23×C22⋊Q8 | 1 | 84 | yes | — |
| 399 | C23 | C22×#525 | 1 | 336 | yes | — |
| 400 | C23 | C22×#525 | 1 | 252 | yes | — |
| 401 | C23 | C25×D4 | 1 | 7 | yes | — |
| 402 | C23 | C25×Q8 | 1 | 1 | yes | characteristic |
| 403 | C23 | C24×#41 | 1 | 7 | yes | — |
| 404 | Q8 | — | 8 | 128 | no | — |
| 405 | C2×C4 | — | 2 | 10752 | no | — |
| 406 | C2×C4 | — | 2 | 336 | no | — |
| 407 | C2×C4 | — | 2 | 1344 | no | — |
| 408 | C2×C4 | — | 2 | 3584 | no | — |
| 409 | C2×C4 | — | 4 | 56 | no | — |
| 410 | C2×C4 | — | 4 | 56 | no | — |
| 411 | C2×C4 | — | 4 | 336 | no | — |
| 412 | C2×C4 | — | 8 | 96 | no | — |
| 413 | C2×C4 | — | 8 | 672 | no | — |
| 414 | C2×C4 | C2×#2846 | 1 | 384 | yes | — |
| 415 | C2×C4 | C23×#120 | 1 | 112 | yes | — |
| 416 | C2×C4 | C23×#120 | 1 | 112 | yes | — |
| 417 | C22 | — | 2 | 14336 | no | — |
| 418 | C22 | — | 2 | 5376 | no | — |
| 419 | C22 | — | 2 | 112 | no | — |
| 420 | C22 | — | 2 | 672 | no | — |
| 421 | C22 | — | 2 | 112 | no | — |
| 422 | C22 | — | 2 | 672 | no | — |
| 423 | C22 | #6342373 | 1 | 256 | yes | direct product factor |
| 424 | C22 | C22×#2846 | 1 | 24 | yes | — |
| 425 | C22 | C22×#2848 | 1 | 168 | yes | — |
| 426 | C22 | C22×#2848 | 1 | 224 | yes | complemented |
| 427 | C22 | C2×#36614 | 1 | 168 | yes | — |
| 428 | C22 | C24×#120 | 1 | 7 | yes | — |
| 429 | C22 | C24×C22⋊Q8 | 1 | 7 | yes | — |
| 430 | C22 | C23×#525 | 1 | 21 | yes | — |
| 431 | C4 | — | 2 | 112 | no | — |
| 432 | C4 | — | 8 | 56 | no | — |
| 433 | C4 | — | 8 | 8 | no | — |
| 434 | C4 | C22×#2846 | 1 | 32 | yes | — |
| 435 | C2 | — | 2 | 224 | no | — |
| 436 | C2 | C23×#2846 | 1 | 1 | yes | characteristic |
| 437 | C2 | C22×#36614 | 1 | 7 | yes | — |
| 438 | C2 | C23×#2848 | 1 | 7 | yes | — |
| 439 | C2 | C2×#6342373 | 1 | 48 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C25 |
| commutator, Frattini, cosocle | C24 | C27 |
| prime radical | C29 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C26 ◁ G | |
| LECS | G ▷ C24 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#6342373 | C2 | direct (N × H) |
| 2. C23×#2848 | C2 | semidirect |
| 3. C22×#14693 | C2 | semidirect |
| 4. C22×#14680 | C2 | semidirect |
| 12. C24×C22⋊Q8 | C22 | semidirect |
| 14. C22×#2848 | C22 | semidirect |
| 15. C23×#385 | C22 | semidirect |
| 16. C23×#380 | C22 | semidirect |
| 19. #6342373 | C22 | direct (N × H) |
| 20. C2×#14693 | C22 | semidirect |
| 21. C2×#14680 | C22 | semidirect |
| 23. C22×C22⋊#95 | C22 | semidirect |
| 26. C28 | Q8 | semidirect |
| 29. C25×Q8 | C23 | semidirect |
| 42. C23×C22⋊Q8 | C23 | semidirect |
| 43. C24×C4⋊C4 | C23 | semidirect |
| 44. C24×C4⋊C4 | C23 | semidirect |
| 48. C2×#2848 | C23 | semidirect |
| 50. C22×#385 | C23 | semidirect |
| 52. C22×#380 | C23 | semidirect |
| 57. C23×#95 | C23 | semidirect |
| 58. #14693 | C23 | semidirect |
| 59. #14680 | C23 | semidirect |
| 61. C2×C22⋊#95 | C23 | semidirect |
| 71. C27 | C2×Q8 | semidirect |
| 77. C24×Q8 | C24 | semidirect |
| 104. C22×C22⋊Q8 | C24 | semidirect |
| 107. C23×C4⋊C4 | C24 | semidirect |
| 108. C23×C4⋊C4 | C24 | semidirect |
| 116. C2×#385 | C24 | semidirect |
| 118. C2×#380 | C24 | semidirect |
| 124. C22×#95 | C24 | semidirect |
| 125. C22⋊#95 | C24 | semidirect |
| 144. C26 | C22⋊Q8 | semidirect |
| 149. C26 | C22×Q8 | semidirect |
| 157. C23×Q8 | C25 | semidirect |
| 198. C22×C4⋊C4 | C25 | semidirect |
| 199. C22×C4⋊C4 | C25 | semidirect |
| 212. C2×#95 | C25 | semidirect |
| 241. C25 | C2×C22⋊Q8 | semidirect |
| 329. C24 | #2848 | semidirect |
| 334. C24 | C22×C22⋊Q8 | semidirect |
| 393. C23 | C2×#2848 | semidirect |
| 423. C22 | #6342373 | direct (N × H) |
| 426. C22 | C22×#2848 | semidirect |
| 439. C2 | C2×#6342373 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6342373 | 2 |
| C23×#2848 | 2 |
| C22×#14693 | 2 |
| C22×#14680 | 2 |
| C22×#14679 | 2 |
| C28×C4 | 2 |