Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
133197 conjugacy classes of subgroups.
The subgroup lattice has 332 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C24×#126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C25×C42 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×#2852 | C2 | 1 | 112 | yes | maximal, direct product factor |
| 4 | C23×#388 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C23×#387 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C23×#386 | C2 | 1 | 3 | yes | maximal |
| 7 | C23×#385 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C23×#383 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C25×D4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C26×C4 | C22 | 1 | 3 | yes | — |
| 11 | C23×#126 | — | 2 | 32 | no | — |
| 12 | C23×#126 | C22 | 1 | 56 | yes | complemented |
| 13 | C24×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 14 | C24×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 15 | C24×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 16 | C24×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 17 | C24×C22⋊C4 | C22 | 1 | 3 | yes | — |
| 18 | C24×C42 | — | 2 | 32 | no | — |
| 19 | C24×C42 | C22 | 1 | 3 | yes | — |
| 20 | C24×C42 | C22 | 1 | 1 | yes | characteristic |
| 21 | C24×C42 | C22 | 1 | 56 | yes | complemented |
| 22 | C2×#2852 | C22 | 1 | 1792 | yes | direct product factor |
| 23 | C22×#388 | C22 | 1 | 168 | yes | complemented |
| 24 | C22×#387 | C22 | 1 | 168 | yes | complemented |
| 25 | C22×#386 | C22 | 1 | 168 | yes | — |
| 26 | C22×#385 | C22 | 1 | 168 | yes | complemented |
| 27 | C22×#383 | C22 | 1 | 56 | yes | complemented |
| 28 | C23×#95 | C22 | 1 | 3 | yes | — |
| 29 | C23×#95 | C22 | 1 | 3 | yes | — |
| 30 | C23×#95 | C22 | 1 | 3 | yes | — |
| 31 | C23×#95 | C22 | 1 | 3 | yes | — |
| 32 | C27 | C23 | 1 | 1 | yes | characteristic |
| 33 | C27 | C23 | 1 | 1 | yes | characteristic |
| 34 | C24×D4 | — | 2 | 48 | no | — |
| 35 | C24×D4 | C23 | 1 | 28 | yes | — |
| 36 | C25×C4 | — | 2 | 48 | no | — |
| 37 | C25×C4 | — | 2 | 48 | no | — |
| 38 | C25×C4 | — | 2 | 48 | no | — |
| 39 | C25×C4 | C23 | 1 | 84 | yes | — |
| 40 | C25×C4 | C23 | 1 | 1 | yes | characteristic |
| 41 | C25×C4 | C23 | 1 | 3 | yes | — |
| 42 | C25×C4 | C23 | 1 | 3 | yes | — |
| 43 | C25×C4 | C23 | 1 | 3 | yes | — |
| 44 | C25×C4 | C23 | 1 | 3 | yes | — |
| 45 | C22×#126 | — | 2 | 896 | no | — |
| 46 | C22×#126 | C23 | 1 | 448 | yes | complemented |
| 47 | C23×C4⋊C4 | — | 2 | 48 | no | — |
| 48 | C23×C4⋊C4 | — | 2 | 48 | no | — |
| 49 | C23×C4⋊C4 | C23 | 1 | 84 | yes | — |
| 50 | C23×C4⋊C4 | C23 | 1 | 84 | yes | — |
| 51 | C23×C22⋊C4 | — | 2 | 48 | no | — |
| 52 | C23×C22⋊C4 | — | 2 | 48 | no | — |
| 53 | C23×C22⋊C4 | — | 2 | 48 | no | — |
| 54 | C23×C22⋊C4 | C23 | 1 | 84 | yes | — |
| 55 | C23×C22⋊C4 | C23 | 1 | 84 | yes | — |
| 56 | C23×C22⋊C4 | C23 | 1 | 84 | yes | — |
| 57 | C23×C42 | — | 2 | 896 | no | — |
| 58 | C23×C42 | — | 2 | 48 | no | — |
| 59 | C23×C42 | D4 | 1 | 32 | yes | complemented |
| 60 | C23×C42 | C23 | 1 | 84 | yes | — |
| 61 | C23×C42 | C23 | 1 | 28 | yes | — |
| 62 | C23×C42 | C23 | 1 | 448 | yes | complemented |
| 63 | #2852 | C23 | 1 | 4096 | yes | direct product factor |
| 64 | C2×#388 | C23 | 1 | 1344 | yes | complemented |
| 65 | C2×#387 | C23 | 1 | 1344 | yes | complemented |
| 66 | C2×#386 | C23 | 1 | 1344 | yes | — |
| 67 | C2×#385 | C23 | 1 | 1344 | yes | complemented |
| 68 | C2×#383 | C23 | 1 | 448 | yes | complemented |
| 69 | C22×#95 | C23 | 1 | 84 | yes | — |
| 70 | C22×#95 | C23 | 1 | 84 | yes | — |
| 71 | C22×#95 | C23 | 1 | 84 | yes | — |
| 72 | C22×#95 | C23 | 1 | 84 | yes | — |
| 73 | C26 | — | 2 | 8 | no | — |
| 74 | C26 | — | 2 | 24 | no | — |
| 75 | C26 | — | 2 | 8 | no | — |
| 76 | C26 | — | 2 | 24 | no | — |
| 77 | C26 | — | 2 | 24 | no | — |
| 78 | C26 | #41 | 1 | 48 | yes | — |
| 79 | C26 | C24 | 1 | 14 | yes | — |
| 80 | C26 | C24 | 1 | 14 | yes | — |
| 81 | C26 | C24 | 1 | 1 | yes | characteristic |
| 82 | C23×D4 | — | 2 | 672 | no | — |
| 83 | C23×D4 | — | 4 | 256 | no | — |
| 84 | C23×D4 | C24 | 1 | 112 | yes | — |
| 85 | C24×C4 | — | 2 | 1536 | no | — |
| 86 | C24×C4 | — | 2 | 24 | no | — |
| 87 | C24×C4 | — | 2 | 672 | no | — |
| 88 | C24×C4 | — | 2 | 24 | no | — |
| 89 | C24×C4 | — | 2 | 24 | no | — |
| 90 | C24×C4 | — | 2 | 24 | no | — |
| 91 | C24×C4 | — | 2 | 672 | no | — |
| 92 | C24×C4 | — | 2 | 672 | no | — |
| 93 | C24×C4 | — | 2 | 24 | no | — |
| 94 | C24×C4 | — | 2 | 24 | no | — |
| 95 | C24×C4 | — | 2 | 24 | no | — |
| 96 | C24×C4 | — | 2 | 24 | no | — |
| 97 | C24×C4 | — | 2 | 24 | no | — |
| 98 | C24×C4 | — | 2 | 24 | no | — |
| 99 | C24×C4 | — | 2 | 24 | no | — |
| 100 | C24×C4 | C2×D4 | 1 | 48 | yes | — |
| 101 | C24×C4 | #41 | 1 | 48 | yes | — |
| 102 | C24×C4 | C24 | 1 | 336 | yes | — |
| 103 | C24×C4 | C24 | 1 | 14 | yes | — |
| 104 | C24×C4 | C24 | 1 | 42 | yes | — |
| 105 | C24×C4 | C24 | 1 | 42 | yes | — |
| 106 | C24×C4 | C24 | 1 | 42 | yes | — |
| 107 | C24×C4 | C24 | 1 | 42 | yes | — |
| 108 | C2×#126 | — | 2 | 3584 | no | — |
| 109 | C2×#126 | C24 | 1 | 512 | yes | complemented |
| 110 | C22×C4⋊C4 | — | 2 | 672 | no | — |
| 111 | C22×C4⋊C4 | — | 2 | 672 | no | — |
| 112 | C22×C4⋊C4 | C24 | 1 | 336 | yes | — |
| 113 | C22×C4⋊C4 | C24 | 1 | 336 | yes | — |
| 114 | C22×C22⋊C4 | — | 2 | 672 | no | — |
| 115 | C22×C22⋊C4 | — | 2 | 672 | no | — |
| 116 | C22×C22⋊C4 | — | 2 | 672 | no | — |
| 117 | C22×C22⋊C4 | C24 | 1 | 336 | yes | — |
| 118 | C22×C22⋊C4 | C24 | 1 | 336 | yes | — |
| 119 | C22×C22⋊C4 | C24 | 1 | 336 | yes | — |
| 120 | C22×C42 | — | 2 | 672 | no | — |
| 121 | C22×C42 | — | 2 | 3584 | no | — |
| 122 | C22×C42 | C2×D4 | 1 | 448 | yes | complemented |
| 123 | C22×C42 | C24 | 1 | 336 | yes | — |
| 124 | C22×C42 | C24 | 1 | 112 | yes | — |
| 125 | C22×C42 | C24 | 1 | 512 | yes | complemented |
| 126 | #388 | C24 | 1 | 1536 | yes | complemented |
| 127 | #387 | C24 | 1 | 1536 | yes | complemented |
| 128 | #386 | C24 | 1 | 1536 | yes | — |
| 129 | #385 | C24 | 1 | 1536 | yes | complemented |
| 130 | #383 | C24 | 1 | 512 | yes | complemented |
| 131 | C2×#95 | C24 | 1 | 336 | yes | — |
| 132 | C2×#95 | C24 | 1 | 336 | yes | — |
| 133 | C2×#95 | C24 | 1 | 336 | yes | — |
| 134 | C2×#95 | C24 | 1 | 336 | yes | — |
| 135 | C25 | — | 2 | 384 | no | — |
| 136 | C25 | — | 2 | 384 | no | — |
| 137 | C25 | — | 2 | 56 | no | — |
| 138 | C25 | — | 2 | 168 | no | — |
| 139 | C25 | — | 2 | 56 | no | — |
| 140 | C25 | — | 2 | 168 | no | — |
| 141 | C25 | — | 2 | 168 | no | — |
| 142 | C25 | — | 4 | 192 | no | — |
| 143 | C25 | — | 4 | 64 | no | — |
| 144 | C25 | — | 4 | 192 | no | — |
| 145 | C25 | #126 | 1 | 256 | yes | complemented |
| 146 | C25 | C22×D4 | 1 | 8 | yes | — |
| 147 | C25 | C2×#41 | 1 | 336 | yes | — |
| 148 | C25 | C2×#41 | 1 | 24 | yes | — |
| 149 | C25 | C2×#41 | 1 | 24 | yes | — |
| 150 | C25 | C25 | 1 | 28 | yes | — |
| 151 | C25 | C25 | 1 | 28 | yes | — |
| 152 | C25 | C25 | 1 | 7 | yes | — |
| 153 | C22×D4 | — | 2 | 1344 | no | — |
| 154 | C22×D4 | — | 4 | 1792 | no | — |
| 155 | C22×D4 | C25 | 1 | 64 | yes | — |
| 156 | C23×C4 | — | 2 | 10752 | no | — |
| 157 | C23×C4 | — | 2 | 384 | no | — |
| 158 | C23×C4 | — | 2 | 384 | no | — |
| 159 | C23×C4 | — | 2 | 168 | no | — |
| 160 | C23×C4 | — | 2 | 1344 | no | — |
| 161 | C23×C4 | — | 2 | 168 | no | — |
| 162 | C23×C4 | — | 2 | 168 | no | — |
| 163 | C23×C4 | — | 2 | 168 | no | — |
| 164 | C23×C4 | — | 2 | 1344 | no | — |
| 165 | C23×C4 | — | 2 | 1344 | no | — |
| 166 | C23×C4 | — | 2 | 168 | no | — |
| 167 | C23×C4 | — | 2 | 168 | no | — |
| 168 | C23×C4 | — | 2 | 168 | no | — |
| 169 | C23×C4 | — | 2 | 168 | no | — |
| 170 | C23×C4 | — | 2 | 168 | no | — |
| 171 | C23×C4 | — | 2 | 168 | no | — |
| 172 | C23×C4 | — | 2 | 168 | no | — |
| 173 | C23×C4 | — | 4 | 192 | no | — |
| 174 | C23×C4 | — | 4 | 64 | no | — |
| 175 | C23×C4 | — | 4 | 192 | no | — |
| 176 | C23×C4 | C22×D4 | 1 | 336 | yes | — |
| 177 | C23×C4 | C2×#41 | 1 | 336 | yes | — |
| 178 | C23×C4 | C25 | 1 | 84 | yes | — |
| 179 | C23×C4 | C25 | 1 | 84 | yes | — |
| 180 | C23×C4 | C25 | 1 | 192 | yes | — |
| 181 | C23×C4 | C25 | 1 | 28 | yes | — |
| 182 | C23×C4 | C25 | 1 | 84 | yes | — |
| 183 | C23×C4 | C25 | 1 | 84 | yes | — |
| 184 | #126 | — | 2 | 2048 | no | — |
| 185 | C2×C4⋊C4 | — | 2 | 1344 | no | — |
| 186 | C2×C4⋊C4 | — | 2 | 1344 | no | — |
| 187 | C2×C4⋊C4 | C25 | 1 | 192 | yes | — |
| 188 | C2×C4⋊C4 | C25 | 1 | 192 | yes | — |
| 189 | C2×C22⋊C4 | — | 2 | 1344 | no | — |
| 190 | C2×C22⋊C4 | — | 2 | 1344 | no | — |
| 191 | C2×C22⋊C4 | — | 2 | 1344 | no | — |
| 192 | C2×C22⋊C4 | C25 | 1 | 192 | yes | — |
| 193 | C2×C22⋊C4 | C25 | 1 | 192 | yes | — |
| 194 | C2×C22⋊C4 | C25 | 1 | 192 | yes | — |
| 195 | C2×C42 | — | 2 | 1344 | no | — |
| 196 | C2×C42 | — | 2 | 2048 | no | — |
| 197 | C2×C42 | C22×D4 | 1 | 896 | yes | complemented |
| 198 | C2×C42 | C25 | 1 | 192 | yes | — |
| 199 | C2×C42 | C25 | 1 | 64 | yes | — |
| 200 | #95 | C25 | 1 | 192 | yes | — |
| 201 | #95 | C25 | 1 | 192 | yes | — |
| 202 | #95 | C25 | 1 | 192 | yes | — |
| 203 | #95 | C25 | 1 | 192 | yes | — |
| 204 | C24 | — | 2 | 56 | no | — |
| 205 | C24 | — | 2 | 168 | no | — |
| 206 | C24 | — | 2 | 2048 | no | — |
| 207 | C24 | — | 2 | 1344 | no | — |
| 208 | C24 | — | 2 | 1344 | no | — |
| 209 | C24 | — | 2 | 56 | no | — |
| 210 | C24 | — | 2 | 168 | no | — |
| 211 | C24 | — | 2 | 168 | no | — |
| 212 | C24 | — | 4 | 672 | no | — |
| 213 | C24 | — | 4 | 224 | no | — |
| 214 | C24 | — | 4 | 672 | no | — |
| 215 | C24 | — | 8 | 512 | no | — |
| 216 | C24 | #525 | 1 | 192 | yes | — |
| 217 | C24 | C2×#126 | 1 | 64 | yes | — |
| 218 | C24 | C2×#126 | 1 | 896 | yes | complemented |
| 219 | C24 | #529 | 1 | 192 | yes | — |
| 220 | C24 | C23×D4 | 1 | 28 | yes | — |
| 221 | C24 | C22×#41 | 1 | 336 | yes | — |
| 222 | C24 | C22×#41 | 1 | 84 | yes | — |
| 223 | C24 | C22×#41 | 1 | 84 | yes | — |
| 224 | C24 | C26 | 1 | 8 | yes | — |
| 225 | C24 | C26 | 1 | 8 | yes | — |
| 226 | C24 | C26 | 1 | 7 | yes | — |
| 227 | C2×D4 | — | 2 | 384 | no | — |
| 228 | C2×D4 | — | 4 | 1792 | no | — |
| 229 | C22×C4 | — | 2 | 10752 | no | — |
| 230 | C22×C4 | — | 2 | 168 | no | — |
| 231 | C22×C4 | — | 2 | 384 | no | — |
| 232 | C22×C4 | — | 2 | 168 | no | — |
| 233 | C22×C4 | — | 2 | 168 | no | — |
| 234 | C22×C4 | — | 2 | 168 | no | — |
| 235 | C22×C4 | — | 2 | 1344 | no | — |
| 236 | C22×C4 | — | 2 | 1344 | no | — |
| 237 | C22×C4 | — | 2 | 384 | no | — |
| 238 | C22×C4 | — | 2 | 384 | no | — |
| 239 | C22×C4 | — | 2 | 168 | no | — |
| 240 | C22×C4 | — | 2 | 168 | no | — |
| 241 | C22×C4 | — | 2 | 168 | no | — |
| 242 | C22×C4 | — | 2 | 168 | no | — |
| 243 | C22×C4 | — | 2 | 168 | no | — |
| 244 | C22×C4 | — | 2 | 168 | no | — |
| 245 | C22×C4 | — | 2 | 168 | no | — |
| 246 | C22×C4 | — | 4 | 672 | no | — |
| 247 | C22×C4 | — | 4 | 224 | no | — |
| 248 | C22×C4 | — | 4 | 672 | no | — |
| 249 | C22×C4 | C23×D4 | 1 | 336 | yes | — |
| 250 | C22×C4 | C22×#41 | 1 | 336 | yes | — |
| 251 | C22×C4 | C26 | 1 | 8 | yes | — |
| 252 | C22×C4 | C26 | 1 | 24 | yes | — |
| 253 | C22×C4 | C26 | 1 | 24 | yes | — |
| 254 | C22×C4 | C26 | 1 | 24 | yes | — |
| 255 | C22×C4 | C26 | 1 | 24 | yes | — |
| 256 | C4⋊C4 | — | 2 | 384 | no | — |
| 257 | C4⋊C4 | — | 2 | 384 | no | — |
| 258 | C22⋊C4 | — | 2 | 384 | no | — |
| 259 | C22⋊C4 | — | 2 | 384 | no | — |
| 260 | C22⋊C4 | — | 2 | 384 | no | — |
| 261 | C42 | — | 2 | 384 | no | — |
| 262 | C42 | C23×D4 | 1 | 256 | yes | complemented |
| 263 | C23 | — | 2 | 3584 | no | — |
| 264 | C23 | — | 2 | 8 | no | — |
| 265 | C23 | — | 2 | 24 | no | — |
| 266 | C23 | — | 2 | 672 | no | — |
| 267 | C23 | — | 2 | 672 | no | — |
| 268 | C23 | — | 2 | 8 | no | — |
| 269 | C23 | — | 2 | 24 | no | — |
| 270 | C23 | — | 2 | 24 | no | — |
| 271 | C23 | — | 4 | 336 | no | — |
| 272 | C23 | — | 4 | 112 | no | — |
| 273 | C23 | — | 4 | 336 | no | — |
| 274 | C23 | — | 8 | 896 | no | — |
| 275 | C23 | #2852 | 1 | 512 | yes | direct product factor |
| 276 | C23 | C2×#525 | 1 | 336 | yes | — |
| 277 | C23 | C22×#126 | 1 | 112 | yes | — |
| 278 | C23 | C22×#126 | 1 | 448 | yes | complemented |
| 279 | C23 | C2×#529 | 1 | 336 | yes | — |
| 280 | C23 | C24×D4 | 1 | 14 | yes | — |
| 281 | C23 | C23×#41 | 1 | 48 | yes | — |
| 282 | C23 | C23×#41 | 1 | 42 | yes | — |
| 283 | C23 | C23×#41 | 1 | 42 | yes | — |
| 284 | C23 | C27 | 1 | 1 | yes | characteristic |
| 285 | D4 | — | 4 | 256 | no | — |
| 286 | C2×C4 | — | 2 | 1536 | no | — |
| 287 | C2×C4 | — | 2 | 24 | no | — |
| 288 | C2×C4 | — | 2 | 24 | no | — |
| 289 | C2×C4 | — | 2 | 24 | no | — |
| 290 | C2×C4 | — | 2 | 24 | no | — |
| 291 | C2×C4 | — | 2 | 672 | no | — |
| 292 | C2×C4 | — | 2 | 672 | no | — |
| 293 | C2×C4 | — | 2 | 24 | no | — |
| 294 | C2×C4 | — | 2 | 24 | no | — |
| 295 | C2×C4 | — | 2 | 24 | no | — |
| 296 | C2×C4 | — | 2 | 24 | no | — |
| 297 | C2×C4 | — | 2 | 24 | no | — |
| 298 | C2×C4 | — | 2 | 24 | no | — |
| 299 | C2×C4 | — | 2 | 24 | no | — |
| 300 | C2×C4 | — | 4 | 336 | no | — |
| 301 | C2×C4 | — | 4 | 112 | no | — |
| 302 | C2×C4 | — | 4 | 336 | no | — |
| 303 | C2×C4 | C24×D4 | 1 | 48 | yes | — |
| 304 | C2×C4 | C23×#41 | 1 | 48 | yes | — |
| 305 | C22 | — | 2 | 48 | no | — |
| 306 | C22 | — | 2 | 48 | no | — |
| 307 | C22 | — | 2 | 896 | no | — |
| 308 | C22 | — | 4 | 24 | no | — |
| 309 | C22 | — | 4 | 8 | no | — |
| 310 | C22 | — | 4 | 24 | no | — |
| 311 | C22 | — | 8 | 224 | no | — |
| 312 | C22 | C2×#2852 | 1 | 448 | yes | direct product factor |
| 313 | C22 | C22×#525 | 1 | 84 | yes | — |
| 314 | C22 | C23×#126 | 1 | 28 | yes | — |
| 315 | C22 | C23×#126 | 1 | 32 | yes | complemented |
| 316 | C22 | C22×#529 | 1 | 84 | yes | — |
| 317 | C22 | C25×D4 | 1 | 1 | yes | characteristic |
| 318 | C22 | C24×#41 | 1 | 3 | yes | — |
| 319 | C22 | C24×#41 | 1 | 3 | yes | — |
| 320 | C4 | — | 2 | 48 | no | — |
| 321 | C4 | — | 2 | 48 | no | — |
| 322 | C4 | — | 4 | 24 | no | — |
| 323 | C4 | — | 4 | 8 | no | — |
| 324 | C4 | — | 4 | 24 | no | — |
| 325 | C2 | — | 2 | 32 | no | — |
| 326 | C2 | — | 8 | 8 | no | — |
| 327 | C2 | C22×#2852 | 1 | 56 | yes | direct product factor |
| 328 | C2 | C23×#525 | 1 | 3 | yes | — |
| 329 | C2 | C24×#126 | 1 | 1 | yes | characteristic |
| 330 | C2 | C23×#529 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C24 |
| commutator, Frattini, cosocle | C23 | C27 |
| prime radical | C25×D4 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C26 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×#126 | C2 | semidirect |
| 2. C25×C42 | C2 | semidirect |
| 3. C22×#2852 | C2 | direct (N × H) |
| 4. C23×#388 | C2 | semidirect |
| 5. C23×#387 | C2 | semidirect |
| 7. C23×#385 | C2 | semidirect |
| 8. C23×#383 | C2 | semidirect |
| 12. C23×#126 | C22 | semidirect |
| 21. C24×C42 | C22 | semidirect |
| 22. C2×#2852 | C22 | direct (N × H) |
| 23. C22×#388 | C22 | semidirect |
| 24. C22×#387 | C22 | semidirect |
| 26. C22×#385 | C22 | semidirect |
| 27. C22×#383 | C22 | semidirect |
| 46. C22×#126 | C23 | semidirect |
| 59. C23×C42 | D4 | semidirect |
| 62. C23×C42 | C23 | semidirect |
| 63. #2852 | C23 | direct (N × H) |
| 64. C2×#388 | C23 | semidirect |
| 65. C2×#387 | C23 | semidirect |
| 67. C2×#385 | C23 | semidirect |
| 68. C2×#383 | C23 | semidirect |
| 109. C2×#126 | C24 | semidirect |
| 122. C22×C42 | C2×D4 | semidirect |
| 125. C22×C42 | C24 | semidirect |
| 126. #388 | C24 | semidirect |
| 127. #387 | C24 | semidirect |
| 129. #385 | C24 | semidirect |
| 130. #383 | C24 | semidirect |
| 145. C25 | #126 | semidirect |
| 197. C2×C42 | C22×D4 | semidirect |
| 218. C24 | C2×#126 | semidirect |
| 262. C42 | C23×D4 | semidirect |
| 275. C23 | #2852 | direct (N × H) |
| 278. C23 | C22×#126 | semidirect |
| 312. C22 | C2×#2852 | direct (N × H) |
| 315. C22 | C23×#126 | semidirect |
| 327. C2 | C22×#2852 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#126 | 2 |
| C25×C42 | 2 |
| C22×#2852 | 2 |
| C23×#388 | 2 |
| C23×#387 | 2 |
| C23×#386 | 2 |
| C23×#385 | 2 |
| C23×#383 | 2 |