Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1949656 conjugacy classes of subgroups.
The subgroup lattice has 740 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#37450 | C2 | 1 | 224 | yes | maximal, direct product factor |
| 2 | C23×#2815 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C23×#2504 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C23×#2280 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C23×#2619 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C23×#2617 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | C25×#121 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C23×#2433 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C23×#2403 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C26×D4 | C22 | 1 | 4 | yes | — |
| 11 | C26×D4 | C22 | 1 | 2 | yes | complemented |
| 12 | C27×C4 | C22 | 1 | 1 | yes | characteristic |
| 13 | C24×#127 | C22 | 1 | 4 | yes | complemented |
| 14 | C24×#121 | — | 2 | 128 | no | — |
| 15 | C24×#121 | C22 | 1 | 4 | yes | — |
| 16 | C24×#121 | C22 | 1 | 4 | yes | — |
| 17 | C24×#121 | C22 | 1 | 4 | yes | complemented |
| 18 | C24×#121 | C22 | 1 | 4 | yes | complemented |
| 19 | C24×#121 | C22 | 1 | 224 | yes | complemented |
| 20 | C24×#120 | C22 | 1 | 16 | yes | complemented |
| 21 | C24×#117 | C22 | 1 | 2 | yes | complemented |
| 22 | C25×C4⋊C4 | C22 | 1 | 2 | yes | complemented |
| 23 | C25×C22⋊C4 | C22 | 1 | 4 | yes | complemented |
| 24 | C2×#37450 | C22 | 1 | 7168 | yes | direct product factor |
| 25 | C22×#2815 | C22 | 1 | 448 | yes | complemented |
| 26 | C22×#2504 | C22 | 1 | 448 | yes | complemented |
| 27 | C22×#2433 | C22 | 1 | 448 | yes | complemented |
| 28 | C22×#2403 | C22 | 1 | 448 | yes | complemented |
| 29 | C22×#2619 | C22 | 1 | 448 | yes | complemented |
| 30 | C22×#2617 | C22 | 1 | 896 | yes | complemented |
| 31 | C23×#397 | C22 | 1 | 16 | yes | complemented |
| 32 | C23×#394 | C22 | 1 | 16 | yes | complemented |
| 33 | C23×#392 | C22 | 1 | 16 | yes | complemented |
| 34 | C23×#392 | C22 | 1 | 16 | yes | complemented |
| 35 | C23×#390 | C22 | 1 | 8 | yes | complemented |
| 36 | C23×#386 | C22 | 1 | 16 | yes | complemented |
| 37 | C23×#382 | C22 | 1 | 4 | yes | complemented |
| 38 | C22×#2280 | C22 | 1 | 112 | yes | complemented |
| 39 | C23×#381 | C22 | 1 | 2 | yes | complemented |
| 40 | C23×#380 | C22 | 1 | 4 | yes | complemented |
| 41 | C23×#379 | C22 | 1 | 2 | yes | — |
| 42 | C23×C4×C22⋊C4 | C22 | 1 | 4 | yes | complemented |
| 43 | C28 | C23 | 1 | 1 | yes | characteristic |
| 44 | C28 | C23 | 1 | 4 | yes | — |
| 45 | C25×D4 | — | 2 | 128 | no | — |
| 46 | C25×D4 | — | 2 | 64 | no | — |
| 47 | C25×D4 | — | 4 | 64 | no | — |
| 48 | C25×D4 | — | 4 | 128 | no | — |
| 49 | C25×D4 | C23 | 1 | 8 | yes | — |
| 50 | C25×D4 | C23 | 1 | 4 | yes | — |
| 51 | C25×D4 | C23 | 1 | 4 | yes | — |
| 52 | C25×D4 | C23 | 1 | 224 | yes | — |
| 53 | C25×D4 | C23 | 1 | 8 | yes | — |
| 54 | C25×D4 | C23 | 1 | 16 | yes | — |
| 55 | C25×D4 | C23 | 1 | 112 | yes | complemented |
| 56 | C26×C4 | — | 4 | 32 | no | — |
| 57 | C26×C4 | D4 | 1 | 64 | yes | complemented |
| 58 | C26×C4 | C23 | 1 | 2 | yes | — |
| 59 | C26×C4 | C23 | 1 | 1 | yes | characteristic |
| 60 | C26×C4 | C23 | 1 | 4 | yes | — |
| 61 | C26×C4 | C23 | 1 | 2 | yes | — |
| 62 | C26×C4 | C23 | 1 | 1 | yes | characteristic |
| 63 | C26×C4 | C23 | 1 | 56 | yes | — |
| 64 | C23×#127 | — | 4 | 64 | no | — |
| 65 | C23×#127 | C23 | 1 | 224 | yes | complemented |
| 66 | C23×#121 | — | 2 | 128 | no | — |
| 67 | C23×#121 | — | 2 | 128 | no | — |
| 68 | C23×#121 | — | 2 | 128 | no | — |
| 69 | C23×#121 | — | 2 | 128 | no | — |
| 70 | C23×#121 | — | 2 | 7168 | no | — |
| 71 | C23×#121 | C23 | 1 | 224 | yes | — |
| 72 | C23×#121 | C23 | 1 | 224 | yes | — |
| 73 | C23×#121 | C23 | 1 | 224 | yes | complemented |
| 74 | C23×#121 | C23 | 1 | 224 | yes | complemented |
| 75 | C23×#121 | C23 | 1 | 3584 | yes | complemented |
| 76 | C23×#120 | — | 4 | 256 | no | — |
| 77 | C23×#120 | C23 | 1 | 896 | yes | complemented |
| 78 | C23×#117 | — | 4 | 32 | no | — |
| 79 | C23×#117 | C23 | 1 | 112 | yes | complemented |
| 80 | C24×C4⋊C4 | — | 2 | 64 | no | — |
| 81 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 82 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 83 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 84 | C24×C4⋊C4 | C23 | 1 | 112 | yes | complemented |
| 85 | C24×C22⋊C4 | — | 2 | 128 | no | — |
| 86 | C24×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 87 | C24×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 88 | C24×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 89 | C24×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 90 | C24×C22⋊C4 | C23 | 1 | 32 | yes | — |
| 91 | C24×C22⋊C4 | C23 | 1 | 224 | yes | complemented |
| 92 | C24×C42 | C23 | 1 | 4 | yes | — |
| 93 | #37450 | C23 | 1 | 32768 | yes | direct product factor |
| 94 | C2×#2815 | C23 | 1 | 7168 | yes | complemented |
| 95 | C2×#2504 | C23 | 1 | 7168 | yes | complemented |
| 96 | C2×#2433 | C23 | 1 | 7168 | yes | complemented |
| 97 | C2×#2403 | C23 | 1 | 7168 | yes | complemented |
| 98 | C2×#2619 | C23 | 1 | 7168 | yes | complemented |
| 99 | C2×#2617 | C23 | 1 | 14336 | yes | complemented |
| 100 | C22×#397 | C23 | 1 | 896 | yes | complemented |
| 101 | C22×#394 | C23 | 1 | 896 | yes | complemented |
| 102 | C22×#392 | C23 | 1 | 896 | yes | complemented |
| 103 | C22×#392 | C23 | 1 | 896 | yes | complemented |
| 104 | C22×#390 | C23 | 1 | 448 | yes | complemented |
| 105 | C22×#386 | C23 | 1 | 896 | yes | complemented |
| 106 | C22×#382 | C23 | 1 | 224 | yes | complemented |
| 107 | C2×#2280 | C23 | 1 | 1792 | yes | complemented |
| 108 | C22×#381 | C23 | 1 | 112 | yes | complemented |
| 109 | C22×#380 | C23 | 1 | 224 | yes | complemented |
| 110 | C22×#379 | C23 | 1 | 112 | yes | — |
| 111 | C22×C4×C22⋊C4 | C23 | 1 | 224 | yes | complemented |
| 112 | C23×#95 | C23 | 1 | 8 | yes | — |
| 113 | C23×#95 | C23 | 1 | 16 | yes | — |
| 114 | C27 | — | 2 | 64 | no | — |
| 115 | C27 | — | 2 | 64 | no | — |
| 116 | C27 | — | 2 | 128 | no | — |
| 117 | C27 | — | 4 | 16 | no | — |
| 118 | C27 | — | 4 | 64 | no | — |
| 119 | C27 | — | 4 | 64 | no | — |
| 120 | C27 | C2×D4 | 1 | 32 | yes | — |
| 121 | C27 | C24 | 1 | 8 | yes | — |
| 122 | C27 | C24 | 1 | 1 | yes | characteristic |
| 123 | C27 | C24 | 1 | 28 | yes | — |
| 124 | C27 | C24 | 1 | 2 | yes | — |
| 125 | C27 | C24 | 1 | 112 | yes | — |
| 126 | C24×D4 | — | 2 | 128 | no | — |
| 127 | C24×D4 | — | 2 | 3584 | no | — |
| 128 | C24×D4 | — | 2 | 128 | no | — |
| 129 | C24×D4 | — | 2 | 256 | no | — |
| 130 | C24×D4 | — | 2 | 64 | no | — |
| 131 | C24×D4 | — | 2 | 64 | no | — |
| 132 | C24×D4 | — | 2 | 1792 | no | — |
| 133 | C24×D4 | — | 2 | 128 | no | — |
| 134 | C24×D4 | — | 4 | 1792 | no | — |
| 135 | C24×D4 | — | 4 | 64 | no | — |
| 136 | C24×D4 | — | 4 | 128 | no | — |
| 137 | C24×D4 | — | 4 | 2048 | no | — |
| 138 | C24×D4 | — | 4 | 256 | no | — |
| 139 | C24×D4 | — | 4 | 128 | no | — |
| 140 | C24×D4 | — | 4 | 3584 | no | — |
| 141 | C24×D4 | — | 4 | 4096 | no | — |
| 142 | C24×D4 | C24 | 1 | 224 | yes | — |
| 143 | C24×D4 | C24 | 1 | 112 | yes | — |
| 144 | C24×D4 | C24 | 1 | 1792 | yes | — |
| 145 | C24×D4 | C24 | 1 | 224 | yes | — |
| 146 | C24×D4 | C24 | 1 | 112 | yes | — |
| 147 | C24×D4 | C24 | 1 | 448 | yes | — |
| 148 | C24×D4 | C24 | 1 | 896 | yes | complemented |
| 149 | C25×C4 | — | 2 | 64 | no | — |
| 150 | C25×C4 | — | 2 | 32 | no | — |
| 151 | C25×C4 | — | 2 | 64 | no | — |
| 152 | C25×C4 | — | 4 | 1024 | no | — |
| 153 | C25×C4 | — | 4 | 896 | no | — |
| 154 | C25×C4 | — | 4 | 16 | no | — |
| 155 | C25×C4 | — | 4 | 32 | no | — |
| 156 | C25×C4 | — | 4 | 64 | no | — |
| 157 | C25×C4 | C2×D4 | 1 | 64 | yes | — |
| 158 | C25×C4 | C2×D4 | 1 | 32 | yes | — |
| 159 | C25×C4 | C2×D4 | 1 | 64 | yes | — |
| 160 | C25×C4 | C2×D4 | 1 | 32 | yes | — |
| 161 | C25×C4 | C2×D4 | 1 | 1792 | yes | complemented |
| 162 | C25×C4 | C24 | 1 | 8 | yes | — |
| 163 | C25×C4 | C24 | 1 | 8 | yes | — |
| 164 | C25×C4 | C24 | 1 | 56 | yes | — |
| 165 | C25×C4 | C24 | 1 | 28 | yes | — |
| 166 | C25×C4 | C24 | 1 | 2 | yes | — |
| 167 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 168 | C25×C4 | C24 | 1 | 112 | yes | — |
| 169 | C25×C4 | C24 | 1 | 56 | yes | — |
| 170 | C25×C4 | C24 | 1 | 28 | yes | — |
| 171 | C25×C4 | C24 | 1 | 448 | yes | — |
| 172 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 173 | C22×#127 | — | 4 | 1792 | no | — |
| 174 | C22×#127 | C24 | 1 | 1792 | yes | complemented |
| 175 | C22×#121 | — | 2 | 3584 | no | — |
| 176 | C22×#121 | — | 2 | 3584 | no | — |
| 177 | C22×#121 | — | 2 | 3584 | no | — |
| 178 | C22×#121 | — | 2 | 3584 | no | — |
| 179 | C22×#121 | — | 2 | 57344 | no | — |
| 180 | C22×#121 | C24 | 1 | 1792 | yes | — |
| 181 | C22×#121 | C24 | 1 | 1792 | yes | — |
| 182 | C22×#121 | C24 | 1 | 1792 | yes | complemented |
| 183 | C22×#121 | C24 | 1 | 1792 | yes | complemented |
| 184 | C22×#121 | C24 | 1 | 8192 | yes | complemented |
| 185 | C22×#120 | — | 4 | 7168 | no | — |
| 186 | C22×#120 | C24 | 1 | 7168 | yes | complemented |
| 187 | C22×#117 | — | 4 | 896 | no | — |
| 188 | C22×#117 | C24 | 1 | 896 | yes | complemented |
| 189 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 190 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 191 | C23×C4⋊C4 | — | 2 | 1792 | no | — |
| 192 | C23×C4⋊C4 | — | 4 | 32 | no | — |
| 193 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 194 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 195 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 196 | C23×C4⋊C4 | C24 | 1 | 896 | yes | complemented |
| 197 | C23×C22⋊C4 | — | 2 | 128 | no | — |
| 198 | C23×C22⋊C4 | — | 2 | 128 | no | — |
| 199 | C23×C22⋊C4 | — | 2 | 128 | no | — |
| 200 | C23×C22⋊C4 | — | 2 | 3584 | no | — |
| 201 | C23×C22⋊C4 | — | 4 | 32 | no | — |
| 202 | C23×C22⋊C4 | — | 4 | 256 | no | — |
| 203 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 204 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 205 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 206 | C23×C22⋊C4 | C24 | 1 | 112 | yes | — |
| 207 | C23×C22⋊C4 | C24 | 1 | 896 | yes | — |
| 208 | C23×C22⋊C4 | C24 | 1 | 1792 | yes | complemented |
| 209 | C23×C42 | — | 2 | 64 | no | — |
| 210 | C23×C42 | C24 | 1 | 112 | yes | — |
| 211 | #2815 | C24 | 1 | 16384 | yes | complemented |
| 212 | #2619 | C24 | 1 | 16384 | yes | complemented |
| 213 | #2617 | C24 | 1 | 32768 | yes | complemented |
| 214 | #2504 | C24 | 1 | 16384 | yes | complemented |
| 215 | #2433 | C24 | 1 | 16384 | yes | complemented |
| 216 | #2403 | C24 | 1 | 16384 | yes | complemented |
| 217 | C2×#397 | C24 | 1 | 7168 | yes | complemented |
| 218 | C2×#394 | C24 | 1 | 7168 | yes | complemented |
| 219 | C2×#392 | C24 | 1 | 7168 | yes | complemented |
| 220 | C2×#392 | C24 | 1 | 7168 | yes | complemented |
| 221 | C2×#390 | C24 | 1 | 3584 | yes | complemented |
| 222 | C2×#386 | C24 | 1 | 7168 | yes | complemented |
| 223 | C2×#382 | C24 | 1 | 1792 | yes | complemented |
| 224 | #2280 | C24 | 1 | 4096 | yes | complemented |
| 225 | C2×#381 | C24 | 1 | 896 | yes | complemented |
| 226 | C2×#380 | C24 | 1 | 1792 | yes | complemented |
| 227 | C2×#379 | C24 | 1 | 896 | yes | — |
| 228 | C2×C4×C22⋊C4 | C24 | 1 | 1792 | yes | complemented |
| 229 | C22×#95 | C24 | 1 | 224 | yes | — |
| 230 | C22×#95 | C24 | 1 | 448 | yes | — |
| 231 | C26 | — | 2 | 32 | no | — |
| 232 | C26 | — | 2 | 32 | no | — |
| 233 | C26 | — | 2 | 1024 | no | — |
| 234 | C26 | — | 2 | 16 | no | — |
| 235 | C26 | — | 2 | 896 | no | — |
| 236 | C26 | — | 2 | 32 | no | — |
| 237 | C26 | — | 2 | 896 | no | — |
| 238 | C26 | — | 2 | 64 | no | — |
| 239 | C26 | — | 2 | 128 | no | — |
| 240 | C26 | — | 2 | 128 | no | — |
| 241 | C26 | — | 2 | 128 | no | — |
| 242 | C26 | — | 2 | 1792 | no | — |
| 243 | C26 | — | 4 | 256 | no | — |
| 244 | C26 | — | 4 | 224 | no | — |
| 245 | C26 | — | 4 | 896 | no | — |
| 246 | C26 | — | 4 | 896 | no | — |
| 247 | C26 | — | 4 | 1024 | no | — |
| 248 | C26 | — | 4 | 1024 | no | — |
| 249 | C26 | — | 4 | 1024 | no | — |
| 250 | C26 | — | 4 | 1024 | no | — |
| 251 | C26 | — | 8 | 2048 | no | — |
| 252 | C26 | C22×D4 | 1 | 16 | yes | — |
| 253 | C26 | C22×D4 | 1 | 448 | yes | — |
| 254 | C26 | C22×D4 | 1 | 32 | yes | — |
| 255 | C26 | H(5,𝔽2) | 1 | 64 | yes | — |
| 256 | C26 | C25 | 1 | 112 | yes | — |
| 257 | C26 | C25 | 1 | 14 | yes | — |
| 258 | C26 | C25 | 1 | 112 | yes | — |
| 259 | C26 | C25 | 1 | 28 | yes | — |
| 260 | C26 | C25 | 1 | 448 | yes | — |
| 261 | C26 | C25 | 1 | 1 | yes | characteristic |
| 262 | C23×D4 | — | 2 | 1792 | no | — |
| 263 | C23×D4 | — | 2 | 14336 | no | — |
| 264 | C23×D4 | — | 2 | 1792 | no | — |
| 265 | C23×D4 | — | 2 | 3584 | no | — |
| 266 | C23×D4 | — | 2 | 896 | no | — |
| 267 | C23×D4 | — | 2 | 896 | no | — |
| 268 | C23×D4 | — | 2 | 7168 | no | — |
| 269 | C23×D4 | — | 2 | 1792 | no | — |
| 270 | C23×D4 | — | 4 | 7168 | no | — |
| 271 | C23×D4 | — | 4 | 896 | no | — |
| 272 | C23×D4 | — | 4 | 1792 | no | — |
| 273 | C23×D4 | — | 4 | 1024 | no | — |
| 274 | C23×D4 | — | 4 | 28672 | no | — |
| 275 | C23×D4 | — | 4 | 3584 | no | — |
| 276 | C23×D4 | — | 4 | 1792 | no | — |
| 277 | C23×D4 | — | 4 | 14336 | no | — |
| 278 | C23×D4 | — | 4 | 57344 | no | — |
| 279 | C23×D4 | — | 4 | 2048 | no | — |
| 280 | C23×D4 | — | 4 | 2048 | no | — |
| 281 | C23×D4 | — | 4 | 1024 | no | — |
| 282 | C23×D4 | — | 8 | 2048 | no | — |
| 283 | C23×D4 | C25 | 1 | 896 | yes | — |
| 284 | C23×D4 | C25 | 1 | 448 | yes | — |
| 285 | C23×D4 | C25 | 1 | 896 | yes | — |
| 286 | C23×D4 | C25 | 1 | 2048 | yes | — |
| 287 | C23×D4 | C25 | 1 | 448 | yes | — |
| 288 | C23×D4 | C25 | 1 | 1792 | yes | — |
| 289 | C23×D4 | C25 | 1 | 1024 | yes | complemented |
| 290 | C24×C4 | — | 2 | 32 | no | — |
| 291 | C24×C4 | — | 2 | 16 | no | — |
| 292 | C24×C4 | — | 2 | 512 | no | — |
| 293 | C24×C4 | — | 2 | 1024 | no | — |
| 294 | C24×C4 | — | 2 | 896 | no | — |
| 295 | C24×C4 | — | 2 | 448 | no | — |
| 296 | C24×C4 | — | 2 | 896 | no | — |
| 297 | C24×C4 | — | 2 | 64 | no | — |
| 298 | C24×C4 | — | 2 | 128 | no | — |
| 299 | C24×C4 | — | 2 | 64 | no | — |
| 300 | C24×C4 | — | 2 | 128 | no | — |
| 301 | C24×C4 | — | 4 | 14336 | no | — |
| 302 | C24×C4 | — | 4 | 3584 | no | — |
| 303 | C24×C4 | — | 4 | 512 | no | — |
| 304 | C24×C4 | — | 4 | 256 | no | — |
| 305 | C24×C4 | — | 4 | 448 | no | — |
| 306 | C24×C4 | — | 4 | 224 | no | — |
| 307 | C24×C4 | — | 4 | 896 | no | — |
| 308 | C24×C4 | — | 4 | 1024 | no | — |
| 309 | C24×C4 | C22×D4 | 1 | 32 | yes | — |
| 310 | C24×C4 | C22×D4 | 1 | 16 | yes | — |
| 311 | C24×C4 | C22×D4 | 1 | 896 | yes | — |
| 312 | C24×C4 | C22×D4 | 1 | 448 | yes | — |
| 313 | C24×C4 | C22×D4 | 1 | 896 | yes | — |
| 314 | C24×C4 | C22×D4 | 1 | 448 | yes | — |
| 315 | C24×C4 | C22×D4 | 1 | 16 | yes | — |
| 316 | C24×C4 | C22×D4 | 1 | 7168 | yes | complemented |
| 317 | C24×C4 | H(5,𝔽2) | 1 | 32 | yes | — |
| 318 | C24×C4 | C25 | 1 | 112 | yes | — |
| 319 | C24×C4 | C25 | 1 | 112 | yes | — |
| 320 | C24×C4 | C25 | 1 | 28 | yes | — |
| 321 | C24×C4 | C25 | 1 | 224 | yes | — |
| 322 | C24×C4 | C25 | 1 | 14 | yes | — |
| 323 | C24×C4 | C25 | 1 | 112 | yes | — |
| 324 | C24×C4 | C25 | 1 | 448 | yes | — |
| 325 | C24×C4 | C25 | 1 | 224 | yes | — |
| 326 | C24×C4 | C25 | 1 | 112 | yes | — |
| 327 | C24×C4 | C25 | 1 | 512 | yes | — |
| 328 | C24×C4 | C25 | 1 | 14 | yes | — |
| 329 | C2×#127 | — | 4 | 7168 | no | — |
| 330 | C2×#127 | C25 | 1 | 2048 | yes | complemented |
| 331 | C2×#121 | — | 2 | 14336 | no | — |
| 332 | C2×#121 | — | 2 | 14336 | no | — |
| 333 | C2×#121 | — | 2 | 14336 | no | — |
| 334 | C2×#121 | — | 2 | 14336 | no | — |
| 335 | C2×#121 | — | 2 | 65536 | no | — |
| 336 | C2×#121 | C25 | 1 | 2048 | yes | — |
| 337 | C2×#121 | C25 | 1 | 2048 | yes | — |
| 338 | C2×#121 | C25 | 1 | 2048 | yes | complemented |
| 339 | C2×#121 | C25 | 1 | 2048 | yes | complemented |
| 340 | C2×#120 | — | 4 | 28672 | no | — |
| 341 | C2×#120 | C25 | 1 | 8192 | yes | complemented |
| 342 | C2×#117 | — | 4 | 3584 | no | — |
| 343 | C2×#117 | C25 | 1 | 1024 | yes | complemented |
| 344 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 345 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 346 | C22×C4⋊C4 | — | 2 | 7168 | no | — |
| 347 | C22×C4⋊C4 | — | 4 | 448 | no | — |
| 348 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 349 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 350 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 351 | C22×C4⋊C4 | C25 | 1 | 1024 | yes | complemented |
| 352 | C22×C22⋊C4 | — | 2 | 1792 | no | — |
| 353 | C22×C22⋊C4 | — | 2 | 1792 | no | — |
| 354 | C22×C22⋊C4 | — | 2 | 1792 | no | — |
| 355 | C22×C22⋊C4 | — | 2 | 14336 | no | — |
| 356 | C22×C22⋊C4 | — | 4 | 448 | no | — |
| 357 | C22×C22⋊C4 | — | 4 | 3584 | no | — |
| 358 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 359 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 360 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 361 | C22×C22⋊C4 | C25 | 1 | 448 | yes | — |
| 362 | C22×C22⋊C4 | C25 | 1 | 3584 | yes | — |
| 363 | C22×C22⋊C4 | C25 | 1 | 2048 | yes | complemented |
| 364 | C22×C42 | — | 2 | 896 | no | — |
| 365 | C22×C42 | C25 | 1 | 448 | yes | — |
| 366 | #397 | C25 | 1 | 8192 | yes | complemented |
| 367 | #394 | C25 | 1 | 8192 | yes | complemented |
| 368 | #392 | C25 | 1 | 8192 | yes | complemented |
| 369 | #392 | C25 | 1 | 8192 | yes | complemented |
| 370 | #390 | C25 | 1 | 4096 | yes | complemented |
| 371 | #386 | C25 | 1 | 8192 | yes | complemented |
| 372 | #382 | C25 | 1 | 2048 | yes | complemented |
| 373 | #381 | C25 | 1 | 1024 | yes | complemented |
| 374 | #380 | C25 | 1 | 2048 | yes | complemented |
| 375 | #379 | C25 | 1 | 1024 | yes | — |
| 376 | C4×C22⋊C4 | C25 | 1 | 2048 | yes | complemented |
| 377 | C2×#95 | C25 | 1 | 896 | yes | — |
| 378 | C2×#95 | C25 | 1 | 1792 | yes | — |
| 379 | C25 | — | 2 | 224 | no | — |
| 380 | C25 | — | 2 | 224 | no | — |
| 381 | C25 | — | 2 | 256 | no | — |
| 382 | C25 | — | 2 | 256 | no | — |
| 383 | C25 | — | 2 | 1024 | no | — |
| 384 | C25 | — | 2 | 112 | no | — |
| 385 | C25 | — | 2 | 1792 | no | — |
| 386 | C25 | — | 2 | 224 | no | — |
| 387 | C25 | — | 2 | 128 | no | — |
| 388 | C25 | — | 2 | 7168 | no | — |
| 389 | C25 | — | 2 | 256 | no | — |
| 390 | C25 | — | 2 | 1792 | no | — |
| 391 | C25 | — | 2 | 448 | no | — |
| 392 | C25 | — | 2 | 896 | no | — |
| 393 | C25 | — | 2 | 896 | no | — |
| 394 | C25 | — | 2 | 896 | no | — |
| 395 | C25 | — | 2 | 3584 | no | — |
| 396 | C25 | — | 4 | 1792 | no | — |
| 397 | C25 | — | 4 | 448 | no | — |
| 398 | C25 | — | 4 | 1792 | no | — |
| 399 | C25 | — | 4 | 1792 | no | — |
| 400 | C25 | — | 4 | 7168 | no | — |
| 401 | C25 | — | 4 | 8192 | no | — |
| 402 | C25 | — | 4 | 7168 | no | — |
| 403 | C25 | — | 4 | 7168 | no | — |
| 404 | C25 | — | 4 | 256 | no | — |
| 405 | C25 | — | 4 | 512 | no | — |
| 406 | C25 | — | 4 | 512 | no | — |
| 407 | C25 | — | 4 | 7168 | no | — |
| 408 | C25 | — | 4 | 512 | no | — |
| 409 | C25 | — | 4 | 2048 | no | — |
| 410 | C25 | — | 8 | 14336 | no | — |
| 411 | C25 | — | 8 | 16384 | no | — |
| 412 | C25 | #535 | 1 | 512 | yes | — |
| 413 | C25 | C23×D4 | 1 | 112 | yes | — |
| 414 | C25 | C23×D4 | 1 | 896 | yes | — |
| 415 | C25 | C23×D4 | 1 | 224 | yes | — |
| 416 | C25 | C23×D4 | 1 | 8 | yes | — |
| 417 | C25 | C2×H(5,𝔽2) | 1 | 448 | yes | — |
| 418 | C25 | C2×H(5,𝔽2) | 1 | 16 | yes | — |
| 419 | C25 | C2×H(5,𝔽2) | 1 | 32 | yes | — |
| 420 | C25 | C26 | 1 | 224 | yes | — |
| 421 | C25 | C26 | 1 | 28 | yes | — |
| 422 | C25 | C26 | 1 | 64 | yes | — |
| 423 | C25 | C26 | 1 | 56 | yes | — |
| 424 | C25 | C26 | 1 | 256 | yes | — |
| 425 | C25 | C26 | 1 | 7 | yes | — |
| 426 | C22×D4 | — | 2 | 3584 | no | — |
| 427 | C22×D4 | — | 2 | 8192 | no | — |
| 428 | C22×D4 | — | 2 | 3584 | no | — |
| 429 | C22×D4 | — | 2 | 7168 | no | — |
| 430 | C22×D4 | — | 2 | 1792 | no | — |
| 431 | C22×D4 | — | 2 | 1792 | no | — |
| 432 | C22×D4 | — | 2 | 4096 | no | — |
| 433 | C22×D4 | — | 2 | 3584 | no | — |
| 434 | C22×D4 | — | 4 | 4096 | no | — |
| 435 | C22×D4 | — | 4 | 1792 | no | — |
| 436 | C22×D4 | — | 4 | 3584 | no | — |
| 437 | C22×D4 | — | 4 | 7168 | no | — |
| 438 | C22×D4 | — | 4 | 57344 | no | — |
| 439 | C22×D4 | — | 4 | 7168 | no | — |
| 440 | C22×D4 | — | 4 | 3584 | no | — |
| 441 | C22×D4 | — | 4 | 8192 | no | — |
| 442 | C22×D4 | — | 4 | 114688 | no | — |
| 443 | C22×D4 | — | 4 | 14336 | no | — |
| 444 | C22×D4 | — | 4 | 14336 | no | — |
| 445 | C22×D4 | — | 4 | 7168 | no | — |
| 446 | C22×D4 | — | 8 | 14336 | no | — |
| 447 | C22×D4 | C26 | 1 | 512 | yes | — |
| 448 | C22×D4 | C26 | 1 | 256 | yes | — |
| 449 | C22×D4 | C26 | 1 | 256 | yes | — |
| 450 | C22×D4 | C26 | 1 | 512 | yes | — |
| 451 | C22×D4 | C26 | 1 | 1024 | yes | — |
| 452 | C23×C4 | — | 2 | 112 | no | — |
| 453 | C23×C4 | — | 2 | 224 | no | — |
| 454 | C23×C4 | — | 2 | 128 | no | — |
| 455 | C23×C4 | — | 2 | 256 | no | — |
| 456 | C23×C4 | — | 2 | 896 | no | — |
| 457 | C23×C4 | — | 2 | 1792 | no | — |
| 458 | C23×C4 | — | 2 | 3584 | no | — |
| 459 | C23×C4 | — | 2 | 7168 | no | — |
| 460 | C23×C4 | — | 2 | 1792 | no | — |
| 461 | C23×C4 | — | 2 | 448 | no | — |
| 462 | C23×C4 | — | 2 | 896 | no | — |
| 463 | C23×C4 | — | 2 | 896 | no | — |
| 464 | C23×C4 | — | 2 | 448 | no | — |
| 465 | C23×C4 | — | 4 | 28672 | no | — |
| 466 | C23×C4 | — | 4 | 2048 | no | — |
| 467 | C23×C4 | — | 4 | 3584 | no | — |
| 468 | C23×C4 | — | 4 | 1792 | no | — |
| 469 | C23×C4 | — | 4 | 896 | no | — |
| 470 | C23×C4 | — | 4 | 448 | no | — |
| 471 | C23×C4 | — | 4 | 1792 | no | — |
| 472 | C23×C4 | — | 4 | 7168 | no | — |
| 473 | C23×C4 | — | 4 | 512 | no | — |
| 474 | C23×C4 | — | 4 | 512 | no | — |
| 475 | C23×C4 | #534 | 1 | 256 | yes | — |
| 476 | C23×C4 | C23×D4 | 1 | 112 | yes | — |
| 477 | C23×C4 | C23×D4 | 1 | 224 | yes | — |
| 478 | C23×C4 | C23×D4 | 1 | 1792 | yes | — |
| 479 | C23×C4 | C23×D4 | 1 | 896 | yes | — |
| 480 | C23×C4 | C23×D4 | 1 | 1792 | yes | — |
| 481 | C23×C4 | C23×D4 | 1 | 896 | yes | — |
| 482 | C23×C4 | C23×D4 | 1 | 112 | yes | — |
| 483 | C23×C4 | C23×D4 | 1 | 4096 | yes | complemented |
| 484 | C23×C4 | C2×H(5,𝔽2) | 1 | 224 | yes | — |
| 485 | C23×C4 | C26 | 1 | 224 | yes | — |
| 486 | C23×C4 | C26 | 1 | 224 | yes | — |
| 487 | C23×C4 | C26 | 1 | 28 | yes | — |
| 488 | C23×C4 | C26 | 1 | 56 | yes | — |
| 489 | C23×C4 | C26 | 1 | 128 | yes | — |
| 490 | C23×C4 | C26 | 1 | 64 | yes | — |
| 491 | C23×C4 | C26 | 1 | 256 | yes | — |
| 492 | C23×C4 | C26 | 1 | 128 | yes | — |
| 493 | C23×C4 | C26 | 1 | 64 | yes | — |
| 494 | C23×C4 | C26 | 1 | 28 | yes | — |
| 495 | #127 | — | 4 | 4096 | no | — |
| 496 | #121 | — | 2 | 8192 | no | — |
| 497 | #121 | — | 2 | 8192 | no | — |
| 498 | #121 | — | 2 | 8192 | no | — |
| 499 | #121 | — | 2 | 8192 | no | — |
| 500 | #120 | — | 4 | 16384 | no | — |
| 501 | #117 | — | 4 | 2048 | no | — |
| 502 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 503 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 504 | C2×C4⋊C4 | — | 2 | 4096 | no | — |
| 505 | C2×C4⋊C4 | — | 4 | 896 | no | — |
| 506 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 507 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 508 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 509 | C2×C22⋊C4 | — | 2 | 3584 | no | — |
| 510 | C2×C22⋊C4 | — | 2 | 3584 | no | — |
| 511 | C2×C22⋊C4 | — | 2 | 3584 | no | — |
| 512 | C2×C22⋊C4 | — | 2 | 8192 | no | — |
| 513 | C2×C22⋊C4 | — | 4 | 896 | no | — |
| 514 | C2×C22⋊C4 | — | 4 | 7168 | no | — |
| 515 | C2×C22⋊C4 | C26 | 1 | 512 | yes | — |
| 516 | C2×C22⋊C4 | C26 | 1 | 512 | yes | — |
| 517 | C2×C22⋊C4 | C26 | 1 | 512 | yes | — |
| 518 | C2×C22⋊C4 | C26 | 1 | 256 | yes | — |
| 519 | C2×C22⋊C4 | C26 | 1 | 2048 | yes | — |
| 520 | C2×C42 | — | 2 | 1792 | no | — |
| 521 | C2×C42 | C26 | 1 | 256 | yes | — |
| 522 | #95 | C26 | 1 | 512 | yes | — |
| 523 | #95 | C26 | 1 | 1024 | yes | — |
| 524 | C24 | — | 2 | 3584 | no | — |
| 525 | C24 | — | 2 | 4096 | no | — |
| 526 | C24 | — | 2 | 224 | no | — |
| 527 | C24 | — | 2 | 224 | no | — |
| 528 | C24 | — | 2 | 896 | no | — |
| 529 | C24 | — | 2 | 896 | no | — |
| 530 | C24 | — | 2 | 112 | no | — |
| 531 | C24 | — | 2 | 512 | no | — |
| 532 | C24 | — | 2 | 224 | no | — |
| 533 | C24 | — | 2 | 448 | no | — |
| 534 | C24 | — | 2 | 7168 | no | — |
| 535 | C24 | — | 2 | 896 | no | — |
| 536 | C24 | — | 2 | 512 | no | — |
| 537 | C24 | — | 2 | 448 | no | — |
| 538 | C24 | — | 2 | 896 | no | — |
| 539 | C24 | — | 2 | 896 | no | — |
| 540 | C24 | — | 2 | 896 | no | — |
| 541 | C24 | — | 2 | 1024 | no | — |
| 542 | C24 | — | 4 | 1792 | no | — |
| 543 | C24 | — | 4 | 128 | no | — |
| 544 | C24 | — | 4 | 512 | no | — |
| 545 | C24 | — | 4 | 512 | no | — |
| 546 | C24 | — | 4 | 7168 | no | — |
| 547 | C24 | — | 4 | 28672 | no | — |
| 548 | C24 | — | 4 | 7168 | no | — |
| 549 | C24 | — | 4 | 7168 | no | — |
| 550 | C24 | — | 4 | 896 | no | — |
| 551 | C24 | — | 4 | 1024 | no | — |
| 552 | C24 | — | 4 | 7168 | no | — |
| 553 | C24 | — | 4 | 1792 | no | — |
| 554 | C24 | — | 4 | 1792 | no | — |
| 555 | C24 | — | 4 | 7168 | no | — |
| 556 | C24 | — | 4 | 1792 | no | — |
| 557 | C24 | — | 8 | 14336 | no | — |
| 558 | C24 | — | 8 | 57344 | no | — |
| 559 | C24 | — | 8 | 4096 | no | — |
| 560 | C24 | C2×#534 | 1 | 64 | yes | — |
| 561 | C24 | C2×#535 | 1 | 1792 | yes | — |
| 562 | C24 | C2×#535 | 1 | 128 | yes | — |
| 563 | C24 | #3537 | 1 | 256 | yes | — |
| 564 | C24 | C24×D4 | 1 | 112 | yes | — |
| 565 | C24 | C24×D4 | 1 | 256 | yes | — |
| 566 | C24 | C24×D4 | 1 | 224 | yes | — |
| 567 | C24 | C24×D4 | 1 | 28 | yes | — |
| 568 | C24 | C22×H(5,𝔽2) | 1 | 448 | yes | — |
| 569 | C24 | C22×H(5,𝔽2) | 1 | 56 | yes | — |
| 570 | C24 | C22×H(5,𝔽2) | 1 | 112 | yes | — |
| 571 | C24 | C27 | 1 | 64 | yes | — |
| 572 | C24 | C27 | 1 | 8 | yes | — |
| 573 | C24 | C27 | 1 | 16 | yes | — |
| 574 | C24 | C27 | 1 | 7 | yes | — |
| 575 | C2×D4 | — | 2 | 1024 | no | — |
| 576 | C2×D4 | — | 2 | 1024 | no | — |
| 577 | C2×D4 | — | 2 | 2048 | no | — |
| 578 | C2×D4 | — | 2 | 512 | no | — |
| 579 | C2×D4 | — | 2 | 512 | no | — |
| 580 | C2×D4 | — | 2 | 1024 | no | — |
| 581 | C2×D4 | — | 4 | 512 | no | — |
| 582 | C2×D4 | — | 4 | 1024 | no | — |
| 583 | C2×D4 | — | 4 | 7168 | no | — |
| 584 | C2×D4 | — | 4 | 16384 | no | — |
| 585 | C2×D4 | — | 4 | 2048 | no | — |
| 586 | C2×D4 | — | 4 | 1024 | no | — |
| 587 | C2×D4 | — | 4 | 32768 | no | — |
| 588 | C2×D4 | — | 4 | 14336 | no | — |
| 589 | C2×D4 | — | 4 | 14336 | no | — |
| 590 | C2×D4 | — | 4 | 7168 | no | — |
| 591 | C2×D4 | — | 8 | 14336 | no | — |
| 592 | C22×C4 | — | 2 | 112 | no | — |
| 593 | C22×C4 | — | 2 | 224 | no | — |
| 594 | C22×C4 | — | 2 | 448 | no | — |
| 595 | C22×C4 | — | 2 | 896 | no | — |
| 596 | C22×C4 | — | 2 | 256 | no | — |
| 597 | C22×C4 | — | 2 | 512 | no | — |
| 598 | C22×C4 | — | 2 | 3584 | no | — |
| 599 | C22×C4 | — | 2 | 7168 | no | — |
| 600 | C22×C4 | — | 2 | 512 | no | — |
| 601 | C22×C4 | — | 2 | 448 | no | — |
| 602 | C22×C4 | — | 2 | 448 | no | — |
| 603 | C22×C4 | — | 2 | 896 | no | — |
| 604 | C22×C4 | — | 2 | 896 | no | — |
| 605 | C22×C4 | — | 4 | 8192 | no | — |
| 606 | C22×C4 | — | 4 | 3584 | no | — |
| 607 | C22×C4 | — | 4 | 1792 | no | — |
| 608 | C22×C4 | — | 4 | 256 | no | — |
| 609 | C22×C4 | — | 4 | 128 | no | — |
| 610 | C22×C4 | — | 4 | 512 | no | — |
| 611 | C22×C4 | — | 4 | 7168 | no | — |
| 612 | C22×C4 | — | 4 | 1792 | no | — |
| 613 | C22×C4 | — | 4 | 1792 | no | — |
| 614 | C22×C4 | C2×#534 | 1 | 896 | yes | — |
| 615 | C22×C4 | C24×D4 | 1 | 112 | yes | — |
| 616 | C22×C4 | C24×D4 | 1 | 224 | yes | — |
| 617 | C22×C4 | C24×D4 | 1 | 512 | yes | — |
| 618 | C22×C4 | C24×D4 | 1 | 256 | yes | — |
| 619 | C22×C4 | C24×D4 | 1 | 512 | yes | — |
| 620 | C22×C4 | C24×D4 | 1 | 256 | yes | — |
| 621 | C22×C4 | C24×D4 | 1 | 112 | yes | — |
| 622 | C22×C4 | C22×H(5,𝔽2) | 1 | 224 | yes | — |
| 623 | C22×C4 | C27 | 1 | 64 | yes | — |
| 624 | C22×C4 | C27 | 1 | 64 | yes | — |
| 625 | C22×C4 | C27 | 1 | 16 | yes | — |
| 626 | C22×C4 | C27 | 1 | 8 | yes | — |
| 627 | C22×C4 | C27 | 1 | 8 | yes | — |
| 628 | C4⋊C4 | — | 2 | 512 | no | — |
| 629 | C4⋊C4 | — | 2 | 512 | no | — |
| 630 | C4⋊C4 | — | 4 | 256 | no | — |
| 631 | C22⋊C4 | — | 2 | 1024 | no | — |
| 632 | C22⋊C4 | — | 2 | 1024 | no | — |
| 633 | C22⋊C4 | — | 2 | 1024 | no | — |
| 634 | C22⋊C4 | — | 4 | 256 | no | — |
| 635 | C22⋊C4 | — | 4 | 2048 | no | — |
| 636 | C42 | — | 2 | 512 | no | — |
| 637 | C23 | — | 2 | 1792 | no | — |
| 638 | C23 | — | 2 | 7168 | no | — |
| 639 | C23 | — | 2 | 448 | no | — |
| 640 | C23 | — | 2 | 448 | no | — |
| 641 | C23 | — | 2 | 32 | no | — |
| 642 | C23 | — | 2 | 32 | no | — |
| 643 | C23 | — | 2 | 224 | no | — |
| 644 | C23 | — | 2 | 1024 | no | — |
| 645 | C23 | — | 2 | 448 | no | — |
| 646 | C23 | — | 2 | 16 | no | — |
| 647 | C23 | — | 2 | 32 | no | — |
| 648 | C23 | — | 2 | 64 | no | — |
| 649 | C23 | — | 2 | 128 | no | — |
| 650 | C23 | — | 2 | 128 | no | — |
| 651 | C23 | — | 2 | 128 | no | — |
| 652 | C23 | — | 4 | 256 | no | — |
| 653 | C23 | — | 4 | 14336 | no | — |
| 654 | C23 | — | 4 | 1024 | no | — |
| 655 | C23 | — | 4 | 1024 | no | — |
| 656 | C23 | — | 4 | 1024 | no | — |
| 657 | C23 | — | 4 | 448 | no | — |
| 658 | C23 | — | 4 | 1792 | no | — |
| 659 | C23 | — | 4 | 3584 | no | — |
| 660 | C23 | — | 4 | 896 | no | — |
| 661 | C23 | — | 4 | 896 | no | — |
| 662 | C23 | — | 4 | 1024 | no | — |
| 663 | C23 | — | 4 | 896 | no | — |
| 664 | C23 | — | 8 | 2048 | no | — |
| 665 | C23 | — | 8 | 28672 | no | — |
| 666 | C23 | — | 8 | 7168 | no | — |
| 667 | C23 | #37450 | 1 | 512 | yes | direct product factor |
| 668 | C23 | C22×#534 | 1 | 112 | yes | — |
| 669 | C23 | C22×#535 | 1 | 896 | yes | — |
| 670 | C23 | C22×#535 | 1 | 224 | yes | — |
| 671 | C23 | C2×#3537 | 1 | 448 | yes | — |
| 672 | C23 | C25×D4 | 1 | 16 | yes | — |
| 673 | C23 | C25×D4 | 1 | 32 | yes | — |
| 674 | C23 | C25×D4 | 1 | 14 | yes | — |
| 675 | C23 | C23×H(5,𝔽2) | 1 | 64 | yes | — |
| 676 | C23 | C23×H(5,𝔽2) | 1 | 28 | yes | — |
| 677 | C23 | C23×H(5,𝔽2) | 1 | 56 | yes | — |
| 678 | C23 | C28 | 1 | 1 | yes | characteristic |
| 679 | D4 | — | 4 | 1024 | no | — |
| 680 | D4 | — | 4 | 2048 | no | — |
| 681 | D4 | — | 4 | 2048 | no | — |
| 682 | D4 | — | 4 | 1024 | no | — |
| 683 | D4 | — | 8 | 2048 | no | — |
| 684 | C2×C4 | — | 2 | 224 | no | — |
| 685 | C2×C4 | — | 2 | 448 | no | — |
| 686 | C2×C4 | — | 2 | 16 | no | — |
| 687 | C2×C4 | — | 2 | 32 | no | — |
| 688 | C2×C4 | — | 2 | 512 | no | — |
| 689 | C2×C4 | — | 2 | 1024 | no | — |
| 690 | C2×C4 | — | 2 | 64 | no | — |
| 691 | C2×C4 | — | 2 | 64 | no | — |
| 692 | C2×C4 | — | 2 | 128 | no | — |
| 693 | C2×C4 | — | 2 | 128 | no | — |
| 694 | C2×C4 | — | 4 | 512 | no | — |
| 695 | C2×C4 | — | 4 | 256 | no | — |
| 696 | C2×C4 | — | 4 | 1024 | no | — |
| 697 | C2×C4 | — | 4 | 896 | no | — |
| 698 | C2×C4 | — | 4 | 896 | no | — |
| 699 | C2×C4 | C22×#534 | 1 | 448 | yes | — |
| 700 | C2×C4 | C25×D4 | 1 | 16 | yes | — |
| 701 | C2×C4 | C25×D4 | 1 | 32 | yes | — |
| 702 | C2×C4 | C25×D4 | 1 | 16 | yes | — |
| 703 | C2×C4 | C23×H(5,𝔽2) | 1 | 32 | yes | — |
| 704 | C22 | — | 2 | 32 | no | — |
| 705 | C22 | — | 2 | 1792 | no | — |
| 706 | C22 | — | 2 | 32 | no | — |
| 707 | C22 | — | 2 | 128 | no | — |
| 708 | C22 | — | 2 | 32 | no | — |
| 709 | C22 | — | 2 | 16 | no | — |
| 710 | C22 | — | 4 | 1024 | no | — |
| 711 | C22 | — | 4 | 448 | no | — |
| 712 | C22 | — | 4 | 32 | no | — |
| 713 | C22 | — | 4 | 64 | no | — |
| 714 | C22 | — | 4 | 64 | no | — |
| 715 | C22 | — | 4 | 64 | no | — |
| 716 | C22 | — | 4 | 256 | no | — |
| 717 | C22 | — | 8 | 2048 | no | — |
| 718 | C22 | — | 8 | 1792 | no | — |
| 719 | C22 | C2×#37450 | 1 | 448 | yes | direct product factor |
| 720 | C22 | C23×#534 | 1 | 28 | yes | — |
| 721 | C22 | C23×#535 | 1 | 64 | yes | — |
| 722 | C22 | C23×#535 | 1 | 56 | yes | — |
| 723 | C22 | C22×#3537 | 1 | 112 | yes | — |
| 724 | C22 | C26×D4 | 1 | 1 | yes | characteristic |
| 725 | C22 | C24×H(5,𝔽2) | 1 | 4 | yes | — |
| 726 | C22 | C24×H(5,𝔽2) | 1 | 2 | yes | — |
| 727 | C4 | — | 2 | 16 | no | — |
| 728 | C4 | — | 2 | 32 | no | — |
| 729 | C4 | — | 4 | 64 | no | — |
| 730 | C4 | — | 4 | 64 | no | — |
| 731 | C4 | C23×#534 | 1 | 32 | yes | — |
| 732 | C2 | — | 2 | 64 | no | — |
| 733 | C2 | — | 4 | 16 | no | — |
| 734 | C2 | — | 8 | 64 | no | — |
| 735 | C2 | C23×#3537 | 1 | 4 | yes | — |
| 736 | C2 | C24×#534 | 1 | 1 | yes | characteristic |
| 737 | C2 | C24×#535 | 1 | 2 | yes | — |
| 738 | C2 | C22×#37450 | 1 | 56 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C25 |
| commutator, Frattini, cosocle | C23 | C28 |
| 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. C22×#37450 | C2 | direct (N × H) |
| 2. C23×#2815 | C2 | semidirect |
| 3. C23×#2504 | C2 | semidirect |
| 4. C23×#2280 | C2 | semidirect |
| 5. C23×#2619 | C2 | semidirect |
| 6. C23×#2617 | C2 | semidirect |
| 7. C25×#121 | C2 | semidirect |
| 8. C23×#2433 | C2 | semidirect |
| 9. C23×#2403 | C2 | semidirect |
| 11. C26×D4 | C22 | semidirect |
| 13. C24×#127 | C22 | semidirect |
| 17. C24×#121 | C22 | semidirect |
| 18. C24×#121 | C22 | semidirect |
| 19. C24×#121 | C22 | semidirect |
| 20. C24×#120 | C22 | semidirect |
| 21. C24×#117 | C22 | semidirect |
| 22. C25×C4⋊C4 | C22 | semidirect |
| 23. C25×C22⋊C4 | C22 | semidirect |
| 24. C2×#37450 | C22 | direct (N × H) |
| 25. C22×#2815 | C22 | semidirect |
| 26. C22×#2504 | C22 | semidirect |
| 27. C22×#2433 | C22 | semidirect |
| 28. C22×#2403 | C22 | semidirect |
| 29. C22×#2619 | C22 | semidirect |
| 30. C22×#2617 | C22 | semidirect |
| 31. C23×#397 | C22 | semidirect |
| 32. C23×#394 | C22 | semidirect |
| 33. C23×#392 | C22 | semidirect |
| 34. C23×#392 | C22 | semidirect |
| 35. C23×#390 | C22 | semidirect |
| 36. C23×#386 | C22 | semidirect |
| 37. C23×#382 | C22 | semidirect |
| 38. C22×#2280 | C22 | semidirect |
| 39. C23×#381 | C22 | semidirect |
| 40. C23×#380 | C22 | semidirect |
| 42. C23×C4×C22⋊C4 | C22 | semidirect |
| 55. C25×D4 | C23 | semidirect |
| 57. C26×C4 | D4 | semidirect |
| 65. C23×#127 | C23 | semidirect |
| 73. C23×#121 | C23 | semidirect |
| 74. C23×#121 | C23 | semidirect |
| 75. C23×#121 | C23 | semidirect |
| 77. C23×#120 | C23 | semidirect |
| 79. C23×#117 | C23 | semidirect |
| 84. C24×C4⋊C4 | C23 | semidirect |
| 91. C24×C22⋊C4 | C23 | semidirect |
| 93. #37450 | C23 | direct (N × H) |
| 94. C2×#2815 | C23 | semidirect |
| 95. C2×#2504 | C23 | semidirect |
| 96. C2×#2433 | C23 | semidirect |
| 97. C2×#2403 | C23 | semidirect |
| 98. C2×#2619 | C23 | semidirect |
| 99. C2×#2617 | C23 | semidirect |
| 100. C22×#397 | C23 | semidirect |
| 101. C22×#394 | C23 | semidirect |
| 102. C22×#392 | C23 | semidirect |
| 103. C22×#392 | C23 | semidirect |
| 104. C22×#390 | C23 | semidirect |
| 105. C22×#386 | C23 | semidirect |
| 106. C22×#382 | C23 | semidirect |
| 107. C2×#2280 | C23 | semidirect |
| 108. C22×#381 | C23 | semidirect |
| 109. C22×#380 | C23 | semidirect |
| 111. C22×C4×C22⋊C4 | C23 | semidirect |
| 148. C24×D4 | C24 | semidirect |
| 161. C25×C4 | C2×D4 | semidirect |
| 174. C22×#127 | C24 | semidirect |
| 182. C22×#121 | C24 | semidirect |
| 183. C22×#121 | C24 | semidirect |
| 184. C22×#121 | C24 | semidirect |
| 186. C22×#120 | C24 | semidirect |
| 188. C22×#117 | C24 | semidirect |
| 196. C23×C4⋊C4 | C24 | semidirect |
| 208. C23×C22⋊C4 | C24 | semidirect |
| 211. #2815 | C24 | semidirect |
| 212. #2619 | C24 | semidirect |
| 213. #2617 | C24 | semidirect |
| 214. #2504 | C24 | semidirect |
| 215. #2433 | C24 | semidirect |
| 216. #2403 | C24 | semidirect |
| 217. C2×#397 | C24 | semidirect |
| 218. C2×#394 | C24 | semidirect |
| 219. C2×#392 | C24 | semidirect |
| 220. C2×#392 | C24 | semidirect |
| 221. C2×#390 | C24 | semidirect |
| 222. C2×#386 | C24 | semidirect |
| 223. C2×#382 | C24 | semidirect |
| 224. #2280 | C24 | semidirect |
| 225. C2×#381 | C24 | semidirect |
| 226. C2×#380 | C24 | semidirect |
| 228. C2×C4×C22⋊C4 | C24 | semidirect |
| 289. C23×D4 | C25 | semidirect |
| 316. C24×C4 | C22×D4 | semidirect |
| 330. C2×#127 | C25 | semidirect |
| 338. C2×#121 | C25 | semidirect |
| 339. C2×#121 | C25 | semidirect |
| 341. C2×#120 | C25 | semidirect |
| 343. C2×#117 | C25 | semidirect |
| 351. C22×C4⋊C4 | C25 | semidirect |
| 363. C22×C22⋊C4 | C25 | semidirect |
| 366. #397 | C25 | semidirect |
| 367. #394 | C25 | semidirect |
| 368. #392 | C25 | semidirect |
| 369. #392 | C25 | semidirect |
| 370. #390 | C25 | semidirect |
| 371. #386 | C25 | semidirect |
| 372. #382 | C25 | semidirect |
| 373. #381 | C25 | semidirect |
| 374. #380 | C25 | semidirect |
| 376. C4×C22⋊C4 | C25 | semidirect |
| 483. C23×C4 | C23×D4 | semidirect |
| 667. C23 | #37450 | direct (N × H) |
| 719. C22 | C2×#37450 | direct (N × H) |
| 738. C2 | C22×#37450 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#37450 | 2 |
| C23×#2815 | 2 |
| C23×#2504 | 2 |
| C23×#2280 | 2 |
| C23×#2619 | 2 |
| C23×#2617 | 2 |
| C25×#121 | 2 |
| C23×#2433 | 2 |
| C23×#2403 | 2 |