Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
784584 conjugacy classes of subgroups.
The subgroup lattice has 684 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×#2804 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C23×C4×C4⋊Q8 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C23×#2571 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C22×#59864 | C2 | 1 | 224 | yes | maximal, direct product factor |
| 5 | C23×#2563 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C23×#2487 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C23×#2580 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | C23×#2366 | C2 | 1 | 2 | yes | maximal |
| 9 | C23×C4×#127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C23×D4×C4⋊C4 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C24×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 12 | C24×#127 | C22 | 1 | 1 | yes | characteristic |
| 13 | C24×C4×Q8 | C22 | 1 | 4 | yes | — |
| 14 | C24×C4×D4 | C22 | 1 | 4 | yes | — |
| 15 | C24×C4×D4 | C22 | 1 | 8 | yes | — |
| 16 | C24×C4×D4 | C22 | 1 | 2 | yes | — |
| 17 | C25×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 18 | C2×#59864 | C22 | 1 | 7168 | yes | direct product factor |
| 19 | C22×#2804 | C22 | 1 | 448 | yes | complemented |
| 20 | C22×#2571 | C22 | 1 | 224 | yes | complemented |
| 21 | C22×#2563 | C22 | 1 | 448 | yes | complemented |
| 22 | C22×#2580 | C22 | 1 | 896 | yes | complemented |
| 23 | C22×#2487 | C22 | 1 | 448 | yes | complemented |
| 24 | C23×#400 | C22 | 1 | 8 | yes | — |
| 25 | C23×#399 | C22 | 1 | 8 | yes | — |
| 26 | C23×#393 | C22 | 1 | 16 | yes | — |
| 27 | C22×#2366 | C22 | 1 | 224 | yes | — |
| 28 | C22×D4×C4⋊C4 | C22 | 1 | 448 | yes | complemented |
| 29 | C22×C4×C4⋊Q8 | C22 | 1 | 224 | yes | complemented |
| 30 | C22×C4×#127 | C22 | 1 | 112 | yes | — |
| 31 | C23×#391 | C22 | 1 | 4 | yes | — |
| 32 | C23×#390 | C22 | 1 | 2 | yes | — |
| 33 | C23×#390 | C22 | 1 | 4 | yes | — |
| 34 | C23×#390 | C22 | 1 | 8 | yes | — |
| 35 | C23×#389 | C22 | 1 | 8 | yes | — |
| 36 | C23×#389 | C22 | 1 | 4 | yes | — |
| 37 | C23×#389 | C22 | 1 | 4 | yes | — |
| 38 | C23×#386 | C22 | 1 | 8 | yes | — |
| 39 | C23×#385 | C22 | 1 | 16 | yes | — |
| 40 | C23×#385 | C22 | 1 | 8 | yes | — |
| 41 | C23×#384 | C22 | 1 | 2 | yes | — |
| 42 | C23×#384 | C22 | 1 | 1 | yes | characteristic |
| 43 | C23×#382 | C22 | 1 | 8 | yes | — |
| 44 | C23×#380 | C22 | 1 | 8 | yes | — |
| 45 | C23×#380 | C22 | 1 | 4 | yes | — |
| 46 | C23×C4×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 47 | C23×C4×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 48 | C23×C43 | C22 | 1 | 1 | yes | characteristic |
| 49 | C25×Q8 | C23 | 1 | 4 | yes | — |
| 50 | C25×D4 | C23 | 1 | 4 | yes | — |
| 51 | C25×D4 | C23 | 1 | 2 | yes | — |
| 52 | C26×C4 | C23 | 1 | 4 | yes | — |
| 53 | C26×C4 | C23 | 1 | 8 | yes | — |
| 54 | C23×C4⋊Q8 | — | 2 | 64 | no | — |
| 55 | C23×C4⋊Q8 | C23 | 1 | 112 | yes | — |
| 56 | C23×#127 | Q8 | 1 | 64 | yes | complemented |
| 57 | C23×#127 | C23 | 1 | 56 | yes | — |
| 58 | C23×C4×Q8 | — | 4 | 64 | no | — |
| 59 | C23×C4×Q8 | C23 | 1 | 224 | yes | — |
| 60 | C23×C4×D4 | — | 2 | 128 | no | — |
| 61 | C23×C4×D4 | — | 4 | 32 | no | — |
| 62 | C23×C4×D4 | — | 4 | 128 | no | — |
| 63 | C23×C4×D4 | C23 | 1 | 224 | yes | — |
| 64 | C23×C4×D4 | C23 | 1 | 448 | yes | — |
| 65 | C23×C4×D4 | C23 | 1 | 112 | yes | — |
| 66 | C24×C4⋊C4 | — | 4 | 64 | no | — |
| 67 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 68 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 69 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 70 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 71 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 72 | C24×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 73 | C24×C4⋊C4 | C23 | 1 | 224 | yes | — |
| 74 | C24×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 75 | C24×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 76 | C24×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 77 | C24×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 78 | C24×C22⋊C4 | C23 | 1 | 16 | yes | — |
| 79 | C24×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 80 | C24×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 81 | C24×C42 | C23 | 1 | 8 | yes | — |
| 82 | C24×C42 | C23 | 1 | 1 | yes | characteristic |
| 83 | C24×C42 | C23 | 1 | 2 | yes | — |
| 84 | C24×C42 | C23 | 1 | 1 | yes | characteristic |
| 85 | C24×C42 | C23 | 1 | 1 | yes | characteristic |
| 86 | C24×C42 | C23 | 1 | 2 | yes | — |
| 87 | #59864 | C23 | 1 | 32768 | yes | direct product factor |
| 88 | C2×#2804 | C23 | 1 | 7168 | yes | complemented |
| 89 | C2×#2571 | C23 | 1 | 3584 | yes | complemented |
| 90 | C2×#2563 | C23 | 1 | 7168 | yes | complemented |
| 91 | C2×#2580 | C23 | 1 | 14336 | yes | complemented |
| 92 | C2×#2487 | C23 | 1 | 7168 | yes | complemented |
| 93 | C22×#400 | C23 | 1 | 448 | yes | — |
| 94 | C22×#399 | C23 | 1 | 448 | yes | — |
| 95 | C22×#393 | C23 | 1 | 896 | yes | — |
| 96 | C2×#2366 | C23 | 1 | 3584 | yes | — |
| 97 | C2×D4×C4⋊C4 | C23 | 1 | 7168 | yes | complemented |
| 98 | C2×C4×C4⋊Q8 | C23 | 1 | 3584 | yes | complemented |
| 99 | C2×C4×#127 | C23 | 1 | 1792 | yes | — |
| 100 | C22×#391 | C23 | 1 | 224 | yes | — |
| 101 | C22×#390 | C23 | 1 | 224 | yes | — |
| 102 | C22×#390 | C23 | 1 | 448 | yes | — |
| 103 | C22×#390 | C23 | 1 | 112 | yes | — |
| 104 | C22×#389 | C23 | 1 | 224 | yes | — |
| 105 | C22×#389 | C23 | 1 | 448 | yes | — |
| 106 | C22×#389 | C23 | 1 | 224 | yes | — |
| 107 | C22×#386 | C23 | 1 | 448 | yes | — |
| 108 | C22×#385 | C23 | 1 | 448 | yes | — |
| 109 | C22×#385 | C23 | 1 | 896 | yes | — |
| 110 | C22×#384 | C23 | 1 | 56 | yes | — |
| 111 | C22×#384 | C23 | 1 | 112 | yes | — |
| 112 | C22×#382 | C23 | 1 | 448 | yes | — |
| 113 | C22×#380 | C23 | 1 | 224 | yes | — |
| 114 | C22×#380 | C23 | 1 | 448 | yes | — |
| 115 | C22×C4×C4⋊C4 | C23 | 1 | 224 | yes | — |
| 116 | C22×C4×C4⋊C4 | C23 | 1 | 224 | yes | — |
| 117 | C23×#95 | C23 | 1 | 8 | yes | — |
| 118 | C23×#95 | C23 | 1 | 16 | yes | — |
| 119 | C23×#95 | C23 | 1 | 8 | yes | — |
| 120 | C23×#95 | C23 | 1 | 8 | yes | — |
| 121 | C22×C43 | C23 | 1 | 56 | yes | — |
| 122 | C27 | C24 | 1 | 4 | yes | — |
| 123 | C24×Q8 | — | 2 | 64 | no | — |
| 124 | C24×Q8 | — | 4 | 32 | no | — |
| 125 | C24×Q8 | — | 4 | 32 | no | — |
| 126 | C24×Q8 | C24 | 1 | 112 | yes | — |
| 127 | C24×D4 | — | 2 | 64 | no | — |
| 128 | C24×D4 | — | 2 | 64 | no | — |
| 129 | C24×D4 | — | 4 | 16 | no | — |
| 130 | C24×D4 | — | 4 | 16 | no | — |
| 131 | C24×D4 | C2×Q8 | 1 | 128 | yes | — |
| 132 | C24×D4 | C2×Q8 | 1 | 64 | yes | — |
| 133 | C24×D4 | C24 | 1 | 112 | yes | — |
| 134 | C24×D4 | C24 | 1 | 56 | yes | — |
| 135 | C25×C4 | — | 2 | 128 | no | — |
| 136 | C25×C4 | — | 2 | 64 | no | — |
| 137 | C25×C4 | — | 4 | 64 | no | — |
| 138 | C25×C4 | — | 4 | 128 | no | — |
| 139 | C25×C4 | C24 | 1 | 112 | yes | — |
| 140 | C25×C4 | C24 | 1 | 8 | yes | — |
| 141 | C25×C4 | C24 | 1 | 4 | yes | — |
| 142 | C25×C4 | C24 | 1 | 8 | yes | — |
| 143 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 144 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 145 | C25×C4 | C24 | 1 | 2 | yes | — |
| 146 | C25×C4 | C24 | 1 | 224 | yes | — |
| 147 | C25×C4 | C24 | 1 | 2 | yes | — |
| 148 | C25×C4 | C24 | 1 | 1 | yes | characteristic |
| 149 | C22×C4⋊Q8 | — | 2 | 1792 | no | — |
| 150 | C22×C4⋊Q8 | C24 | 1 | 896 | yes | — |
| 151 | C22×#127 | C2×Q8 | 1 | 1792 | yes | complemented |
| 152 | C22×#127 | C24 | 1 | 448 | yes | — |
| 153 | C22×C4×Q8 | — | 4 | 1792 | no | — |
| 154 | C22×C4×Q8 | C24 | 1 | 1792 | yes | — |
| 155 | C22×C4×D4 | — | 2 | 3584 | no | — |
| 156 | C22×C4×D4 | — | 4 | 3584 | no | — |
| 157 | C22×C4×D4 | — | 4 | 896 | no | — |
| 158 | C22×C4×D4 | C24 | 1 | 1792 | yes | — |
| 159 | C22×C4×D4 | C24 | 1 | 3584 | yes | — |
| 160 | C22×C4×D4 | C24 | 1 | 896 | yes | — |
| 161 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 162 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 163 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 164 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 165 | C23×C4⋊C4 | — | 2 | 64 | no | — |
| 166 | C23×C4⋊C4 | — | 4 | 1792 | no | — |
| 167 | C23×C4⋊C4 | — | 4 | 64 | no | — |
| 168 | C23×C4⋊C4 | — | 4 | 16 | no | — |
| 169 | C23×C4⋊C4 | — | 4 | 32 | no | — |
| 170 | C23×C4⋊C4 | — | 4 | 64 | no | — |
| 171 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 172 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 173 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 174 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 175 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 176 | C23×C4⋊C4 | C24 | 1 | 1792 | yes | — |
| 177 | C23×C4⋊C4 | C24 | 1 | 224 | yes | — |
| 178 | C23×C4⋊C4 | C24 | 1 | 56 | yes | — |
| 179 | C23×C4⋊C4 | C24 | 1 | 112 | yes | — |
| 180 | C23×C4⋊C4 | C24 | 1 | 224 | yes | — |
| 181 | C23×C22⋊C4 | — | 2 | 128 | no | — |
| 182 | C23×C22⋊C4 | — | 4 | 64 | no | — |
| 183 | C23×C22⋊C4 | — | 4 | 32 | no | — |
| 184 | C23×C22⋊C4 | — | 4 | 128 | no | — |
| 185 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 186 | C23×C22⋊C4 | C24 | 1 | 448 | yes | — |
| 187 | C23×C22⋊C4 | C24 | 1 | 112 | yes | — |
| 188 | C23×C22⋊C4 | C24 | 1 | 224 | yes | — |
| 189 | C23×C42 | — | 2 | 16 | no | — |
| 190 | C23×C42 | — | 2 | 128 | no | — |
| 191 | C23×C42 | — | 2 | 32 | no | — |
| 192 | C23×C42 | — | 4 | 8 | no | — |
| 193 | C23×C42 | C2×Q8 | 1 | 32 | yes | — |
| 194 | C23×C42 | #41 | 1 | 64 | yes | — |
| 195 | C23×C42 | C24 | 1 | 28 | yes | — |
| 196 | C23×C42 | C24 | 1 | 224 | yes | — |
| 197 | C23×C42 | C24 | 1 | 56 | yes | — |
| 198 | C23×C42 | C24 | 1 | 28 | yes | — |
| 199 | C23×C42 | C24 | 1 | 28 | yes | — |
| 200 | C23×C42 | C24 | 1 | 56 | yes | — |
| 201 | #2804 | C24 | 1 | 16384 | yes | complemented |
| 202 | #2580 | C24 | 1 | 32768 | yes | complemented |
| 203 | #2571 | C24 | 1 | 8192 | yes | complemented |
| 204 | #2563 | C24 | 1 | 16384 | yes | complemented |
| 205 | #2487 | C24 | 1 | 16384 | yes | complemented |
| 206 | C2×#400 | C24 | 1 | 3584 | yes | — |
| 207 | C2×#399 | C24 | 1 | 3584 | yes | — |
| 208 | C2×#393 | C24 | 1 | 7168 | yes | — |
| 209 | #2366 | C24 | 1 | 8192 | yes | — |
| 210 | D4×C4⋊C4 | C24 | 1 | 16384 | yes | complemented |
| 211 | C4×C4⋊Q8 | C24 | 1 | 8192 | yes | complemented |
| 212 | C4×#127 | C24 | 1 | 4096 | yes | — |
| 213 | C2×#391 | C24 | 1 | 1792 | yes | — |
| 214 | C2×#390 | C24 | 1 | 896 | yes | — |
| 215 | C2×#390 | C24 | 1 | 1792 | yes | — |
| 216 | C2×#390 | C24 | 1 | 3584 | yes | — |
| 217 | C2×#389 | C24 | 1 | 3584 | yes | — |
| 218 | C2×#389 | C24 | 1 | 1792 | yes | — |
| 219 | C2×#389 | C24 | 1 | 1792 | yes | — |
| 220 | C2×#386 | C24 | 1 | 3584 | yes | — |
| 221 | C2×#385 | C24 | 1 | 7168 | yes | — |
| 222 | C2×#385 | C24 | 1 | 3584 | yes | — |
| 223 | C2×#384 | C24 | 1 | 896 | yes | — |
| 224 | C2×#384 | C24 | 1 | 448 | yes | — |
| 225 | C2×#382 | C24 | 1 | 3584 | yes | — |
| 226 | C2×#380 | C24 | 1 | 3584 | yes | — |
| 227 | C2×#380 | C24 | 1 | 1792 | yes | — |
| 228 | C2×C4×C4⋊C4 | C24 | 1 | 1792 | yes | — |
| 229 | C2×C4×C4⋊C4 | C24 | 1 | 1792 | yes | — |
| 230 | C22×#95 | C24 | 1 | 224 | yes | — |
| 231 | C22×#95 | C24 | 1 | 224 | yes | — |
| 232 | C22×#95 | C24 | 1 | 224 | yes | — |
| 233 | C22×#95 | C24 | 1 | 448 | yes | — |
| 234 | C2×C43 | C24 | 1 | 448 | yes | — |
| 235 | C26 | — | 2 | 64 | no | — |
| 236 | C26 | — | 2 | 32 | no | — |
| 237 | C26 | — | 2 | 64 | no | — |
| 238 | C26 | — | 2 | 32 | no | — |
| 239 | C26 | C22×Q8 | 1 | 64 | yes | — |
| 240 | C26 | C25 | 1 | 56 | yes | — |
| 241 | C26 | C25 | 1 | 1 | yes | characteristic |
| 242 | C23×Q8 | — | 2 | 896 | no | — |
| 243 | C23×Q8 | — | 4 | 448 | no | — |
| 244 | C23×Q8 | — | 4 | 448 | no | — |
| 245 | C23×Q8 | — | 4 | 1024 | no | — |
| 246 | C23×Q8 | C25 | 1 | 448 | yes | — |
| 247 | C23×D4 | — | 2 | 2048 | no | — |
| 248 | C23×D4 | — | 2 | 896 | no | — |
| 249 | C23×D4 | — | 2 | 896 | no | — |
| 250 | C23×D4 | — | 4 | 512 | no | — |
| 251 | C23×D4 | — | 4 | 224 | no | — |
| 252 | C23×D4 | — | 4 | 224 | no | — |
| 253 | C23×D4 | C22×Q8 | 1 | 1792 | yes | — |
| 254 | C23×D4 | C22×Q8 | 1 | 896 | yes | — |
| 255 | C23×D4 | C25 | 1 | 448 | yes | — |
| 256 | C23×D4 | C25 | 1 | 224 | yes | — |
| 257 | C24×C4 | — | 2 | 8 | no | — |
| 258 | C24×C4 | — | 2 | 16 | no | — |
| 259 | C24×C4 | — | 2 | 8 | no | — |
| 260 | C24×C4 | — | 2 | 16 | no | — |
| 261 | C24×C4 | — | 2 | 64 | no | — |
| 262 | C24×C4 | — | 2 | 64 | no | — |
| 263 | C24×C4 | — | 2 | 32 | no | — |
| 264 | C24×C4 | — | 2 | 64 | no | — |
| 265 | C24×C4 | — | 2 | 64 | no | — |
| 266 | C24×C4 | — | 2 | 64 | no | — |
| 267 | C24×C4 | — | 2 | 64 | no | — |
| 268 | C24×C4 | — | 2 | 8 | no | — |
| 269 | C24×C4 | — | 2 | 16 | no | — |
| 270 | C24×C4 | — | 2 | 64 | no | — |
| 271 | C24×C4 | — | 2 | 1792 | no | — |
| 272 | C24×C4 | — | 2 | 896 | no | — |
| 273 | C24×C4 | — | 4 | 896 | no | — |
| 274 | C24×C4 | — | 4 | 1792 | no | — |
| 275 | C24×C4 | — | 4 | 1024 | no | — |
| 276 | C24×C4 | — | 8 | 1024 | no | — |
| 277 | C24×C4 | C22×Q8 | 1 | 16 | yes | — |
| 278 | C24×C4 | C22×Q8 | 1 | 32 | yes | — |
| 279 | C24×C4 | C2×#41 | 1 | 32 | yes | — |
| 280 | C24×C4 | C2×#41 | 1 | 32 | yes | — |
| 281 | C24×C4 | C2×#41 | 1 | 32 | yes | — |
| 282 | C24×C4 | H(5,𝔽2) | 1 | 32 | yes | — |
| 283 | C24×C4 | H(5,𝔽2) | 1 | 16 | yes | — |
| 284 | C24×C4 | C25 | 1 | 112 | yes | — |
| 285 | C24×C4 | C25 | 1 | 56 | yes | — |
| 286 | C24×C4 | C25 | 1 | 448 | yes | — |
| 287 | C24×C4 | C25 | 1 | 112 | yes | — |
| 288 | C24×C4 | C25 | 1 | 14 | yes | — |
| 289 | C24×C4 | C25 | 1 | 14 | yes | — |
| 290 | C24×C4 | C25 | 1 | 28 | yes | — |
| 291 | C24×C4 | C25 | 1 | 896 | yes | — |
| 292 | C24×C4 | C25 | 1 | 28 | yes | — |
| 293 | C24×C4 | C25 | 1 | 14 | yes | — |
| 294 | C2×C4⋊Q8 | — | 2 | 7168 | no | — |
| 295 | C2×C4⋊Q8 | C25 | 1 | 1024 | yes | — |
| 296 | C2×#127 | C22×Q8 | 1 | 7168 | yes | complemented |
| 297 | C2×#127 | C25 | 1 | 512 | yes | — |
| 298 | C2×C4×Q8 | — | 4 | 7168 | no | — |
| 299 | C2×C4×Q8 | C25 | 1 | 2048 | yes | — |
| 300 | C2×C4×D4 | — | 2 | 14336 | no | — |
| 301 | C2×C4×D4 | — | 4 | 14336 | no | — |
| 302 | C2×C4×D4 | — | 4 | 3584 | no | — |
| 303 | C2×C4×D4 | C25 | 1 | 2048 | yes | — |
| 304 | C2×C4×D4 | C25 | 1 | 1024 | yes | — |
| 305 | C2×C4×D4 | C25 | 1 | 4096 | yes | — |
| 306 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 307 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 308 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 309 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 310 | C22×C4⋊C4 | — | 2 | 896 | no | — |
| 311 | C22×C4⋊C4 | — | 4 | 7168 | no | — |
| 312 | C22×C4⋊C4 | — | 4 | 896 | no | — |
| 313 | C22×C4⋊C4 | — | 4 | 224 | no | — |
| 314 | C22×C4⋊C4 | — | 4 | 448 | no | — |
| 315 | C22×C4⋊C4 | — | 4 | 896 | no | — |
| 316 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 317 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 318 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 319 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 320 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 321 | C22×C4⋊C4 | C25 | 1 | 2048 | yes | — |
| 322 | C22×C4⋊C4 | C25 | 1 | 896 | yes | — |
| 323 | C22×C4⋊C4 | C25 | 1 | 896 | yes | — |
| 324 | C22×C4⋊C4 | C25 | 1 | 224 | yes | — |
| 325 | C22×C4⋊C4 | C25 | 1 | 448 | yes | — |
| 326 | C22×C22⋊C4 | — | 2 | 1792 | no | — |
| 327 | C22×C22⋊C4 | — | 4 | 896 | no | — |
| 328 | C22×C22⋊C4 | — | 4 | 448 | no | — |
| 329 | C22×C22⋊C4 | — | 4 | 1792 | no | — |
| 330 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 331 | C22×C22⋊C4 | C25 | 1 | 896 | yes | — |
| 332 | C22×C22⋊C4 | C25 | 1 | 1792 | yes | — |
| 333 | C22×C22⋊C4 | C25 | 1 | 448 | yes | — |
| 334 | C22×C42 | — | 2 | 224 | no | — |
| 335 | C22×C42 | — | 2 | 1792 | no | — |
| 336 | C22×C42 | — | 2 | 448 | no | — |
| 337 | C22×C42 | — | 4 | 112 | no | — |
| 338 | C22×C42 | C22×Q8 | 1 | 448 | yes | — |
| 339 | C22×C42 | C2×#41 | 1 | 896 | yes | — |
| 340 | C22×C42 | C25 | 1 | 112 | yes | — |
| 341 | C22×C42 | C25 | 1 | 896 | yes | — |
| 342 | C22×C42 | C25 | 1 | 224 | yes | — |
| 343 | C22×C42 | C25 | 1 | 112 | yes | — |
| 344 | C22×C42 | C25 | 1 | 112 | yes | — |
| 345 | C22×C42 | C25 | 1 | 224 | yes | — |
| 346 | #400 | C25 | 1 | 4096 | yes | — |
| 347 | #399 | C25 | 1 | 4096 | yes | — |
| 348 | #393 | C25 | 1 | 8192 | yes | — |
| 349 | #391 | C25 | 1 | 2048 | yes | — |
| 350 | #390 | C25 | 1 | 2048 | yes | — |
| 351 | #390 | C25 | 1 | 1024 | yes | — |
| 352 | #390 | C25 | 1 | 4096 | yes | — |
| 353 | #389 | C25 | 1 | 2048 | yes | — |
| 354 | #389 | C25 | 1 | 2048 | yes | — |
| 355 | #389 | C25 | 1 | 4096 | yes | — |
| 356 | #386 | C25 | 1 | 4096 | yes | — |
| 357 | #385 | C25 | 1 | 4096 | yes | — |
| 358 | #385 | C25 | 1 | 8192 | yes | — |
| 359 | #384 | C25 | 1 | 512 | yes | — |
| 360 | #384 | C25 | 1 | 1024 | yes | — |
| 361 | #382 | C25 | 1 | 4096 | yes | — |
| 362 | #380 | C25 | 1 | 2048 | yes | — |
| 363 | #380 | C25 | 1 | 4096 | yes | — |
| 364 | C4×C4⋊C4 | C25 | 1 | 2048 | yes | — |
| 365 | C4×C4⋊C4 | C25 | 1 | 2048 | yes | — |
| 366 | C2×#95 | C25 | 1 | 896 | yes | — |
| 367 | C2×#95 | C25 | 1 | 896 | yes | — |
| 368 | C2×#95 | C25 | 1 | 1792 | yes | — |
| 369 | C2×#95 | C25 | 1 | 896 | yes | — |
| 370 | C43 | C25 | 1 | 512 | yes | — |
| 371 | C25 | — | 2 | 448 | no | — |
| 372 | C25 | — | 2 | 448 | no | — |
| 373 | C25 | — | 2 | 224 | no | — |
| 374 | C25 | — | 2 | 224 | no | — |
| 375 | C25 | — | 2 | 1024 | no | — |
| 376 | C25 | — | 2 | 512 | no | — |
| 377 | C25 | — | 4 | 256 | no | — |
| 378 | C25 | — | 4 | 512 | no | — |
| 379 | C25 | — | 4 | 256 | no | — |
| 380 | C25 | C23×Q8 | 1 | 448 | yes | — |
| 381 | C25 | C23×Q8 | 1 | 8 | yes | — |
| 382 | C25 | C22×#41 | 1 | 16 | yes | — |
| 383 | C25 | C2×H(5,𝔽2) | 1 | 16 | yes | — |
| 384 | C25 | C2×H(5,𝔽2) | 1 | 8 | yes | — |
| 385 | C25 | #585 | 1 | 8 | yes | — |
| 386 | C25 | C26 | 1 | 112 | yes | — |
| 387 | C25 | C26 | 1 | 7 | yes | — |
| 388 | C22×Q8 | — | 2 | 1792 | no | — |
| 389 | C22×Q8 | — | 4 | 896 | no | — |
| 390 | C22×Q8 | — | 4 | 896 | no | — |
| 391 | C22×Q8 | — | 4 | 7168 | no | — |
| 392 | C22×Q8 | C26 | 1 | 256 | yes | — |
| 393 | C22×D4 | — | 2 | 1792 | no | — |
| 394 | C22×D4 | — | 2 | 1792 | no | — |
| 395 | C22×D4 | — | 2 | 14336 | no | — |
| 396 | C22×D4 | — | 4 | 448 | no | — |
| 397 | C22×D4 | — | 4 | 3584 | no | — |
| 398 | C22×D4 | — | 4 | 448 | no | — |
| 399 | C22×D4 | C23×Q8 | 1 | 3584 | yes | — |
| 400 | C22×D4 | C23×Q8 | 1 | 1792 | yes | — |
| 401 | C22×D4 | C26 | 1 | 256 | yes | — |
| 402 | C22×D4 | C26 | 1 | 128 | yes | — |
| 403 | C23×C4 | — | 2 | 56 | no | — |
| 404 | C23×C4 | — | 2 | 112 | no | — |
| 405 | C23×C4 | — | 2 | 56 | no | — |
| 406 | C23×C4 | — | 2 | 112 | no | — |
| 407 | C23×C4 | — | 2 | 128 | no | — |
| 408 | C23×C4 | — | 2 | 256 | no | — |
| 409 | C23×C4 | — | 2 | 448 | no | — |
| 410 | C23×C4 | — | 2 | 448 | no | — |
| 411 | C23×C4 | — | 2 | 56 | no | — |
| 412 | C23×C4 | — | 2 | 448 | no | — |
| 413 | C23×C4 | — | 2 | 448 | no | — |
| 414 | C23×C4 | — | 2 | 224 | no | — |
| 415 | C23×C4 | — | 2 | 448 | no | — |
| 416 | C23×C4 | — | 2 | 112 | no | — |
| 417 | C23×C4 | — | 2 | 448 | no | — |
| 418 | C23×C4 | — | 2 | 448 | no | — |
| 419 | C23×C4 | — | 2 | 3584 | no | — |
| 420 | C23×C4 | — | 2 | 1792 | no | — |
| 421 | C23×C4 | — | 4 | 1792 | no | — |
| 422 | C23×C4 | — | 4 | 3584 | no | — |
| 423 | C23×C4 | — | 4 | 256 | no | — |
| 424 | C23×C4 | — | 4 | 512 | no | — |
| 425 | C23×C4 | — | 4 | 64 | no | — |
| 426 | C23×C4 | — | 4 | 512 | no | — |
| 427 | C23×C4 | — | 4 | 7168 | no | — |
| 428 | C23×C4 | — | 8 | 7168 | no | — |
| 429 | C23×C4 | #554 | 1 | 512 | yes | — |
| 430 | C23×C4 | #559 | 1 | 256 | yes | — |
| 431 | C23×C4 | C23×Q8 | 1 | 112 | yes | — |
| 432 | C23×C4 | C23×Q8 | 1 | 224 | yes | — |
| 433 | C23×C4 | C22×#41 | 1 | 224 | yes | — |
| 434 | C23×C4 | C22×#41 | 1 | 224 | yes | — |
| 435 | C23×C4 | C22×#41 | 1 | 224 | yes | — |
| 436 | C23×C4 | C2×H(5,𝔽2) | 1 | 224 | yes | — |
| 437 | C23×C4 | C2×H(5,𝔽2) | 1 | 112 | yes | — |
| 438 | C23×C4 | C26 | 1 | 28 | yes | — |
| 439 | C23×C4 | C26 | 1 | 224 | yes | — |
| 440 | C23×C4 | C26 | 1 | 112 | yes | — |
| 441 | C23×C4 | C26 | 1 | 224 | yes | — |
| 442 | C23×C4 | C26 | 1 | 256 | yes | — |
| 443 | C23×C4 | C26 | 1 | 28 | yes | — |
| 444 | C23×C4 | C26 | 1 | 56 | yes | — |
| 445 | C23×C4 | C26 | 1 | 512 | yes | — |
| 446 | C23×C4 | C26 | 1 | 56 | yes | — |
| 447 | C23×C4 | C26 | 1 | 28 | yes | — |
| 448 | C4⋊Q8 | — | 2 | 4096 | no | — |
| 449 | #127 | C23×Q8 | 1 | 4096 | yes | complemented |
| 450 | C4×Q8 | — | 4 | 4096 | no | — |
| 451 | C4×D4 | — | 2 | 8192 | no | — |
| 452 | C4×D4 | — | 4 | 8192 | no | — |
| 453 | C4×D4 | — | 4 | 2048 | no | — |
| 454 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 455 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 456 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 457 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 458 | C2×C4⋊C4 | — | 2 | 1792 | no | — |
| 459 | C2×C4⋊C4 | — | 4 | 4096 | no | — |
| 460 | C2×C4⋊C4 | — | 4 | 1792 | no | — |
| 461 | C2×C4⋊C4 | — | 4 | 448 | no | — |
| 462 | C2×C4⋊C4 | — | 4 | 896 | no | — |
| 463 | C2×C4⋊C4 | — | 4 | 1792 | no | — |
| 464 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 465 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 466 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 467 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 468 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 469 | C2×C4⋊C4 | C26 | 1 | 512 | yes | — |
| 470 | C2×C4⋊C4 | C26 | 1 | 128 | yes | — |
| 471 | C2×C4⋊C4 | C26 | 1 | 256 | yes | — |
| 472 | C2×C4⋊C4 | C26 | 1 | 512 | yes | — |
| 473 | C2×C22⋊C4 | — | 2 | 3584 | no | — |
| 474 | C2×C22⋊C4 | — | 4 | 1792 | no | — |
| 475 | C2×C22⋊C4 | — | 4 | 896 | no | — |
| 476 | C2×C22⋊C4 | — | 4 | 3584 | no | — |
| 477 | C2×C22⋊C4 | C26 | 1 | 512 | yes | — |
| 478 | C2×C22⋊C4 | C26 | 1 | 1024 | yes | — |
| 479 | C2×C22⋊C4 | C26 | 1 | 256 | yes | — |
| 480 | C2×C22⋊C4 | C26 | 1 | 512 | yes | — |
| 481 | C2×C42 | — | 2 | 448 | no | — |
| 482 | C2×C42 | — | 2 | 3584 | no | — |
| 483 | C2×C42 | — | 2 | 896 | no | — |
| 484 | C2×C42 | — | 4 | 224 | no | — |
| 485 | C2×C42 | C23×Q8 | 1 | 896 | yes | — |
| 486 | C2×C42 | C22×#41 | 1 | 1792 | yes | — |
| 487 | C2×C42 | C26 | 1 | 64 | yes | — |
| 488 | C2×C42 | C26 | 1 | 512 | yes | — |
| 489 | C2×C42 | C26 | 1 | 128 | yes | — |
| 490 | C2×C42 | C26 | 1 | 64 | yes | — |
| 491 | C2×C42 | C26 | 1 | 64 | yes | — |
| 492 | C2×C42 | C26 | 1 | 128 | yes | — |
| 493 | #95 | C26 | 1 | 512 | yes | — |
| 494 | #95 | C26 | 1 | 512 | yes | — |
| 495 | #95 | C26 | 1 | 512 | yes | — |
| 496 | #95 | C26 | 1 | 1024 | yes | — |
| 497 | C24 | — | 2 | 1792 | no | — |
| 498 | C24 | — | 2 | 448 | no | — |
| 499 | C24 | — | 2 | 448 | no | — |
| 500 | C24 | — | 2 | 224 | no | — |
| 501 | C24 | — | 2 | 224 | no | — |
| 502 | C24 | — | 2 | 3584 | no | — |
| 503 | C24 | — | 4 | 896 | no | — |
| 504 | C24 | — | 4 | 1792 | no | — |
| 505 | C24 | — | 4 | 4096 | no | — |
| 506 | C24 | — | 4 | 896 | no | — |
| 507 | C24 | C2×#554 | 1 | 128 | yes | — |
| 508 | C24 | C2×#559 | 1 | 64 | yes | — |
| 509 | C24 | #3501 | 1 | 64 | yes | — |
| 510 | C24 | #3506 | 1 | 128 | yes | — |
| 511 | C24 | #3549 | 1 | 64 | yes | — |
| 512 | C24 | C24×Q8 | 1 | 448 | yes | — |
| 513 | C24 | C24×Q8 | 1 | 28 | yes | — |
| 514 | C24 | C23×#41 | 1 | 56 | yes | — |
| 515 | C24 | C22×H(5,𝔽2) | 1 | 28 | yes | — |
| 516 | C24 | C22×H(5,𝔽2) | 1 | 56 | yes | — |
| 517 | C24 | C2×#585 | 1 | 28 | yes | — |
| 518 | C24 | C27 | 1 | 32 | yes | — |
| 519 | C24 | C27 | 1 | 7 | yes | — |
| 520 | C2×Q8 | — | 2 | 512 | no | — |
| 521 | C2×Q8 | — | 4 | 256 | no | — |
| 522 | C2×Q8 | — | 4 | 256 | no | — |
| 523 | C2×Q8 | — | 4 | 7168 | no | — |
| 524 | C2×D4 | — | 2 | 512 | no | — |
| 525 | C2×D4 | — | 2 | 512 | no | — |
| 526 | C2×D4 | — | 2 | 14336 | no | — |
| 527 | C2×D4 | — | 4 | 128 | no | — |
| 528 | C2×D4 | — | 4 | 3584 | no | — |
| 529 | C2×D4 | — | 4 | 128 | no | — |
| 530 | C2×D4 | C24×Q8 | 1 | 1024 | yes | — |
| 531 | C2×D4 | C24×Q8 | 1 | 512 | yes | — |
| 532 | C22×C4 | — | 2 | 448 | no | — |
| 533 | C22×C4 | — | 2 | 896 | no | — |
| 534 | C22×C4 | — | 2 | 56 | no | — |
| 535 | C22×C4 | — | 2 | 112 | no | — |
| 536 | C22×C4 | — | 2 | 56 | no | — |
| 537 | C22×C4 | — | 2 | 112 | no | — |
| 538 | C22×C4 | — | 2 | 448 | no | — |
| 539 | C22×C4 | — | 2 | 448 | no | — |
| 540 | C22×C4 | — | 2 | 56 | no | — |
| 541 | C22×C4 | — | 2 | 448 | no | — |
| 542 | C22×C4 | — | 2 | 112 | no | — |
| 543 | C22×C4 | — | 2 | 448 | no | — |
| 544 | C22×C4 | — | 2 | 448 | no | — |
| 545 | C22×C4 | — | 2 | 224 | no | — |
| 546 | C22×C4 | — | 2 | 448 | no | — |
| 547 | C22×C4 | — | 2 | 448 | no | — |
| 548 | C22×C4 | — | 2 | 1024 | no | — |
| 549 | C22×C4 | — | 2 | 512 | no | — |
| 550 | C22×C4 | — | 4 | 512 | no | — |
| 551 | C22×C4 | — | 4 | 1024 | no | — |
| 552 | C22×C4 | — | 4 | 224 | no | — |
| 553 | C22×C4 | — | 4 | 1792 | no | — |
| 554 | C22×C4 | — | 4 | 1792 | no | — |
| 555 | C22×C4 | — | 4 | 896 | no | — |
| 556 | C22×C4 | — | 4 | 7168 | no | — |
| 557 | C22×C4 | — | 8 | 7168 | no | — |
| 558 | C22×C4 | C2×#554 | 1 | 1792 | yes | — |
| 559 | C22×C4 | C2×#559 | 1 | 896 | yes | — |
| 560 | C22×C4 | C24×Q8 | 1 | 112 | yes | — |
| 561 | C22×C4 | C24×Q8 | 1 | 224 | yes | — |
| 562 | C22×C4 | C23×#41 | 1 | 224 | yes | — |
| 563 | C22×C4 | C23×#41 | 1 | 224 | yes | — |
| 564 | C22×C4 | C23×#41 | 1 | 224 | yes | — |
| 565 | C22×C4 | C22×H(5,𝔽2) | 1 | 224 | yes | — |
| 566 | C22×C4 | C22×H(5,𝔽2) | 1 | 112 | yes | — |
| 567 | C22×C4 | C27 | 1 | 64 | yes | — |
| 568 | C22×C4 | C27 | 1 | 32 | yes | — |
| 569 | C22×C4 | C27 | 1 | 64 | yes | — |
| 570 | C22×C4 | C27 | 1 | 8 | yes | — |
| 571 | C22×C4 | C27 | 1 | 8 | yes | — |
| 572 | C22×C4 | C27 | 1 | 16 | yes | — |
| 573 | C22×C4 | C27 | 1 | 16 | yes | — |
| 574 | C22×C4 | C27 | 1 | 8 | yes | — |
| 575 | C4⋊C4 | — | 2 | 512 | no | — |
| 576 | C4⋊C4 | — | 2 | 512 | no | — |
| 577 | C4⋊C4 | — | 2 | 512 | no | — |
| 578 | C4⋊C4 | — | 2 | 512 | no | — |
| 579 | C4⋊C4 | — | 2 | 512 | no | — |
| 580 | C4⋊C4 | — | 4 | 512 | no | — |
| 581 | C4⋊C4 | — | 4 | 128 | no | — |
| 582 | C4⋊C4 | — | 4 | 256 | no | — |
| 583 | C4⋊C4 | — | 4 | 512 | no | — |
| 584 | C22⋊C4 | — | 2 | 1024 | no | — |
| 585 | C22⋊C4 | — | 4 | 512 | no | — |
| 586 | C22⋊C4 | — | 4 | 256 | no | — |
| 587 | C22⋊C4 | — | 4 | 1024 | no | — |
| 588 | C42 | — | 2 | 128 | no | — |
| 589 | C42 | — | 2 | 1024 | no | — |
| 590 | C42 | — | 2 | 256 | no | — |
| 591 | C42 | — | 4 | 64 | no | — |
| 592 | C42 | C24×Q8 | 1 | 256 | yes | — |
| 593 | C42 | C23×#41 | 1 | 512 | yes | — |
| 594 | C23 | — | 2 | 1792 | no | — |
| 595 | C23 | — | 2 | 896 | no | — |
| 596 | C23 | — | 2 | 64 | no | — |
| 597 | C23 | — | 2 | 64 | no | — |
| 598 | C23 | — | 2 | 32 | no | — |
| 599 | C23 | — | 2 | 32 | no | — |
| 600 | C23 | — | 4 | 7168 | no | — |
| 601 | C23 | — | 4 | 448 | no | — |
| 602 | C23 | — | 4 | 448 | no | — |
| 603 | C23 | — | 4 | 896 | no | — |
| 604 | C23 | #59864 | 1 | 512 | yes | direct product factor |
| 605 | C23 | C22×#554 | 1 | 224 | yes | — |
| 606 | C23 | C22×#559 | 1 | 112 | yes | — |
| 607 | C23 | C2×#3549 | 1 | 112 | yes | — |
| 608 | C23 | C2×#3501 | 1 | 112 | yes | — |
| 609 | C23 | C2×#3506 | 1 | 224 | yes | — |
| 610 | C23 | C25×Q8 | 1 | 64 | yes | — |
| 611 | C23 | C25×Q8 | 1 | 14 | yes | — |
| 612 | C23 | C24×#41 | 1 | 28 | yes | — |
| 613 | C23 | C23×H(5,𝔽2) | 1 | 28 | yes | — |
| 614 | C23 | C23×H(5,𝔽2) | 1 | 14 | yes | — |
| 615 | C23 | C22×#585 | 1 | 14 | yes | — |
| 616 | C23 | C28 | 1 | 1 | yes | characteristic |
| 617 | Q8 | — | 4 | 1024 | no | — |
| 618 | D4 | — | 2 | 2048 | no | — |
| 619 | D4 | — | 4 | 512 | no | — |
| 620 | C2×C4 | — | 2 | 224 | no | — |
| 621 | C2×C4 | — | 2 | 448 | no | — |
| 622 | C2×C4 | — | 2 | 8 | no | — |
| 623 | C2×C4 | — | 2 | 16 | no | — |
| 624 | C2×C4 | — | 2 | 8 | no | — |
| 625 | C2×C4 | — | 2 | 16 | no | — |
| 626 | C2×C4 | — | 2 | 64 | no | — |
| 627 | C2×C4 | — | 2 | 64 | no | — |
| 628 | C2×C4 | — | 2 | 8 | no | — |
| 629 | C2×C4 | — | 2 | 64 | no | — |
| 630 | C2×C4 | — | 2 | 16 | no | — |
| 631 | C2×C4 | — | 2 | 64 | no | — |
| 632 | C2×C4 | — | 2 | 64 | no | — |
| 633 | C2×C4 | — | 2 | 32 | no | — |
| 634 | C2×C4 | — | 2 | 64 | no | — |
| 635 | C2×C4 | — | 2 | 64 | no | — |
| 636 | C2×C4 | — | 4 | 112 | no | — |
| 637 | C2×C4 | — | 4 | 896 | no | — |
| 638 | C2×C4 | — | 4 | 448 | no | — |
| 639 | C2×C4 | — | 4 | 896 | no | — |
| 640 | C2×C4 | — | 4 | 1024 | no | — |
| 641 | C2×C4 | — | 8 | 1024 | no | — |
| 642 | C2×C4 | C22×#554 | 1 | 896 | yes | — |
| 643 | C2×C4 | C22×#559 | 1 | 448 | yes | — |
| 644 | C2×C4 | C25×Q8 | 1 | 16 | yes | — |
| 645 | C2×C4 | C25×Q8 | 1 | 32 | yes | — |
| 646 | C2×C4 | C24×#41 | 1 | 32 | yes | — |
| 647 | C2×C4 | C24×#41 | 1 | 32 | yes | — |
| 648 | C2×C4 | C24×#41 | 1 | 32 | yes | — |
| 649 | C2×C4 | C23×H(5,𝔽2) | 1 | 32 | yes | — |
| 650 | C2×C4 | C23×H(5,𝔽2) | 1 | 16 | yes | — |
| 651 | C22 | — | 2 | 128 | no | — |
| 652 | C22 | — | 2 | 64 | no | — |
| 653 | C22 | — | 4 | 1792 | no | — |
| 654 | C22 | — | 4 | 32 | no | — |
| 655 | C22 | — | 4 | 64 | no | — |
| 656 | C22 | — | 4 | 32 | no | — |
| 657 | C22 | C2×#59864 | 1 | 448 | yes | direct product factor |
| 658 | C22 | C23×#554 | 1 | 56 | yes | — |
| 659 | C22 | C23×#559 | 1 | 28 | yes | — |
| 660 | C22 | C22×#3501 | 1 | 28 | yes | — |
| 661 | C22 | C22×#3506 | 1 | 56 | yes | — |
| 662 | C22 | C22×#3549 | 1 | 28 | yes | — |
| 663 | C22 | C26×Q8 | 1 | 1 | yes | characteristic |
| 664 | C22 | C25×#41 | 1 | 2 | yes | — |
| 665 | C22 | C24×H(5,𝔽2) | 1 | 2 | yes | — |
| 666 | C22 | C24×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 667 | C22 | C23×#585 | 1 | 1 | yes | characteristic |
| 668 | C4 | — | 2 | 16 | no | — |
| 669 | C4 | — | 2 | 32 | no | — |
| 670 | C4 | — | 4 | 32 | no | — |
| 671 | C4 | — | 4 | 64 | no | — |
| 672 | C4 | — | 4 | 8 | no | — |
| 673 | C4 | — | 4 | 64 | no | — |
| 674 | C4 | C23×#554 | 1 | 64 | yes | — |
| 675 | C4 | C23×#559 | 1 | 32 | yes | — |
| 676 | C2 | — | 4 | 64 | no | — |
| 677 | C2 | C23×#3549 | 1 | 1 | yes | characteristic |
| 678 | C2 | C24×#554 | 1 | 2 | yes | — |
| 679 | C2 | C24×#559 | 1 | 1 | yes | characteristic |
| 680 | C2 | C22×#59864 | 1 | 56 | yes | direct product factor |
| 681 | C2 | C23×#3501 | 1 | 1 | yes | characteristic |
| 682 | C2 | C23×#3506 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26 | C25 |
| commutator, Frattini, cosocle | C23 | C28 |
| prime radical | C24×#127 | 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. C23×#2804 | C2 | semidirect |
| 2. C23×C4×C4⋊Q8 | C2 | semidirect |
| 3. C23×#2571 | C2 | semidirect |
| 4. C22×#59864 | C2 | direct (N × H) |
| 5. C23×#2563 | C2 | semidirect |
| 6. C23×#2487 | C2 | semidirect |
| 7. C23×#2580 | C2 | semidirect |
| 10. C23×D4×C4⋊C4 | C2 | semidirect |
| 18. C2×#59864 | C22 | direct (N × H) |
| 19. C22×#2804 | C22 | semidirect |
| 20. C22×#2571 | C22 | semidirect |
| 21. C22×#2563 | C22 | semidirect |
| 22. C22×#2580 | C22 | semidirect |
| 23. C22×#2487 | C22 | semidirect |
| 28. C22×D4×C4⋊C4 | C22 | semidirect |
| 29. C22×C4×C4⋊Q8 | C22 | semidirect |
| 56. C23×#127 | Q8 | semidirect |
| 87. #59864 | C23 | direct (N × H) |
| 88. C2×#2804 | C23 | semidirect |
| 89. C2×#2571 | C23 | semidirect |
| 90. C2×#2563 | C23 | semidirect |
| 91. C2×#2580 | C23 | semidirect |
| 92. C2×#2487 | C23 | semidirect |
| 97. C2×D4×C4⋊C4 | C23 | semidirect |
| 98. C2×C4×C4⋊Q8 | C23 | semidirect |
| 151. C22×#127 | C2×Q8 | semidirect |
| 201. #2804 | C24 | semidirect |
| 202. #2580 | C24 | semidirect |
| 203. #2571 | C24 | semidirect |
| 204. #2563 | C24 | semidirect |
| 205. #2487 | C24 | semidirect |
| 210. D4×C4⋊C4 | C24 | semidirect |
| 211. C4×C4⋊Q8 | C24 | semidirect |
| 296. C2×#127 | C22×Q8 | semidirect |
| 449. #127 | C23×Q8 | semidirect |
| 604. C23 | #59864 | direct (N × H) |
| 657. C22 | C2×#59864 | direct (N × H) |
| 680. C2 | C22×#59864 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2804 | 2 |
| C23×C4×C4⋊Q8 | 2 |
| C23×#2571 | 2 |
| C22×#59864 | 2 |
| C23×#2563 | 2 |
| C23×#2487 | 2 |
| C23×#2580 | 2 |
| C23×#2366 | 2 |
| C23×C4×#127 | 2 |
| C23×D4×C4⋊C4 | 2 |