Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
208897 conjugacy classes of subgroups.
The subgroup lattice has 912 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×H(3,𝔽4) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C24×#120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#45439 | C2 | 1 | 96 | yes | maximal, direct product factor |
| 4 | C22×#2670 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C22×#2679 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C22×#2684 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C22×#2812 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C22×#2846 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C22×#2435 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C22×#2472 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | C22×#2403 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C22×#2375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C28 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C25×D4 | C22 | 1 | 3 | yes | — |
| 15 | C25×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C22×H(3,𝔽4) | — | 2 | 32 | no | — |
| 17 | C22×H(3,𝔽4) | C22 | 1 | 48 | yes | complemented |
| 18 | C23×#124 | C22 | 1 | 3 | yes | complemented |
| 19 | C23×#124 | C22 | 1 | 6 | yes | complemented |
| 20 | C23×#124 | C22 | 1 | 3 | yes | complemented |
| 21 | C23×C22⋊Q8 | C22 | 1 | 3 | yes | complemented |
| 22 | C23×#120 | — | 2 | 32 | no | — |
| 23 | C23×#120 | C22 | 1 | 3 | yes | — |
| 24 | C23×#120 | C22 | 1 | 6 | yes | — |
| 25 | C23×#120 | C22 | 1 | 1 | yes | characteristic |
| 26 | C23×#120 | C22 | 1 | 3 | yes | complemented |
| 27 | C23×#120 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C23×#120 | C22 | 1 | 2 | yes | complemented |
| 29 | C23×#120 | C22 | 1 | 6 | yes | complemented |
| 30 | C23×#120 | C22 | 1 | 48 | yes | complemented |
| 31 | C23×#120 | C22 | 1 | 3 | yes | complemented |
| 32 | C23×#120 | C22 | 1 | 3 | yes | complemented |
| 33 | C24×C22⋊C4 | C22 | 1 | 3 | yes | complemented |
| 34 | C2×#2684 | C22 | 1 | 144 | yes | complemented |
| 35 | C2×#2679 | C22 | 1 | 144 | yes | complemented |
| 36 | C2×#2670 | C22 | 1 | 288 | yes | complemented |
| 37 | #45439 | C22 | 1 | 1024 | yes | direct product factor |
| 38 | C2×#2812 | C22 | 1 | 96 | yes | complemented |
| 39 | C2×#2846 | C22 | 1 | 96 | yes | complemented |
| 40 | C2×#2435 | C22 | 1 | 144 | yes | complemented |
| 41 | C2×#2472 | C22 | 1 | 288 | yes | complemented |
| 42 | C2×#2403 | C22 | 1 | 144 | yes | complemented |
| 43 | C22×#397 | C22 | 1 | 6 | yes | complemented |
| 44 | C22×#394 | C22 | 1 | 6 | yes | complemented |
| 45 | C22×#394 | C22 | 1 | 6 | yes | complemented |
| 46 | C22×#394 | C22 | 1 | 6 | yes | complemented |
| 47 | C22×#394 | C22 | 1 | 6 | yes | complemented |
| 48 | C22×#393 | C22 | 1 | 6 | yes | complemented |
| 49 | C22×#392 | C22 | 1 | 6 | yes | complemented |
| 50 | C22×#392 | C22 | 1 | 6 | yes | complemented |
| 51 | C2×#2375 | C22 | 1 | 48 | yes | complemented |
| 52 | C22×#390 | C22 | 1 | 6 | yes | complemented |
| 53 | C22×#390 | C22 | 1 | 3 | yes | complemented |
| 54 | C22×#390 | C22 | 1 | 3 | yes | complemented |
| 55 | C22×#388 | C22 | 1 | 6 | yes | complemented |
| 56 | C22×#388 | C22 | 1 | 6 | yes | complemented |
| 57 | C22×#386 | C22 | 1 | 6 | yes | complemented |
| 58 | C22×#386 | C22 | 1 | 3 | yes | complemented |
| 59 | C22×#386 | C22 | 1 | 3 | yes | complemented |
| 60 | C22×#379 | C22 | 1 | 6 | yes | complemented |
| 61 | C22×#379 | C22 | 1 | 6 | yes | complemented |
| 62 | C22×#379 | C22 | 1 | 2 | yes | complemented |
| 63 | C22×#379 | C22 | 1 | 3 | yes | complemented |
| 64 | C22×C4×C22⋊C4 | C22 | 1 | 3 | yes | complemented |
| 65 | C27 | — | 2 | 16 | no | — |
| 66 | C27 | — | 4 | 24 | no | — |
| 67 | C27 | — | 4 | 24 | no | — |
| 68 | C27 | C23 | 1 | 3 | yes | — |
| 69 | C27 | C23 | 1 | 1 | yes | characteristic |
| 70 | C27 | C23 | 1 | 3 | yes | — |
| 71 | C27 | C23 | 1 | 1 | yes | characteristic |
| 72 | C27 | C23 | 1 | 24 | yes | complemented |
| 73 | C27 | C23 | 1 | 1 | yes | characteristic, complemented |
| 74 | C24×Q8 | C23 | 1 | 3 | yes | complemented |
| 75 | C24×D4 | — | 2 | 48 | no | — |
| 76 | C24×D4 | — | 4 | 24 | no | — |
| 77 | C24×D4 | — | 4 | 24 | no | — |
| 78 | C24×D4 | — | 4 | 24 | no | — |
| 79 | C24×D4 | C23 | 1 | 2 | yes | — |
| 80 | C24×D4 | C23 | 1 | 3 | yes | — |
| 81 | C24×D4 | C23 | 1 | 3 | yes | — |
| 82 | C24×D4 | C23 | 1 | 72 | yes | — |
| 83 | C24×D4 | C23 | 1 | 3 | yes | — |
| 84 | C24×D4 | C23 | 1 | 6 | yes | — |
| 85 | C24×D4 | C23 | 1 | 6 | yes | — |
| 86 | C24×D4 | C23 | 1 | 3 | yes | — |
| 87 | C24×D4 | C23 | 1 | 2 | yes | complemented |
| 88 | C24×D4 | C23 | 1 | 24 | yes | complemented |
| 89 | C25×C4 | C23 | 1 | 3 | yes | — |
| 90 | C25×C4 | C23 | 1 | 1 | yes | characteristic, complemented |
| 91 | C2×H(3,𝔽4) | — | 2 | 768 | no | — |
| 92 | C2×H(3,𝔽4) | C23 | 1 | 256 | yes | complemented |
| 93 | C22×#124 | — | 2 | 48 | no | — |
| 94 | C22×#124 | — | 2 | 96 | no | — |
| 95 | C22×#124 | — | 4 | 24 | no | — |
| 96 | C22×#124 | C23 | 1 | 144 | yes | complemented |
| 97 | C22×#124 | C23 | 1 | 72 | yes | complemented |
| 98 | C22×#124 | C23 | 1 | 72 | yes | complemented |
| 99 | C22×C22⋊Q8 | — | 4 | 24 | no | — |
| 100 | C22×C22⋊Q8 | C23 | 1 | 72 | yes | complemented |
| 101 | C22×#120 | — | 2 | 16 | no | — |
| 102 | C22×#120 | — | 2 | 32 | no | — |
| 103 | C22×#120 | — | 2 | 48 | no | — |
| 104 | C22×#120 | — | 2 | 48 | no | — |
| 105 | C22×#120 | — | 2 | 768 | no | — |
| 106 | C22×#120 | — | 2 | 48 | no | — |
| 107 | C22×#120 | — | 4 | 48 | no | — |
| 108 | C22×#120 | — | 4 | 48 | no | — |
| 109 | C22×#120 | — | 4 | 24 | no | — |
| 110 | C22×#120 | D4 | 1 | 32 | yes | complemented |
| 111 | C22×#120 | C23 | 1 | 72 | yes | — |
| 112 | C22×#120 | C23 | 1 | 144 | yes | — |
| 113 | C22×#120 | C23 | 1 | 24 | yes | — |
| 114 | C22×#120 | C23 | 1 | 48 | yes | complemented |
| 115 | C22×#120 | C23 | 1 | 24 | yes | complemented |
| 116 | C22×#120 | C23 | 1 | 72 | yes | complemented |
| 117 | C22×#120 | C23 | 1 | 144 | yes | complemented |
| 118 | C22×#120 | C23 | 1 | 256 | yes | complemented |
| 119 | C22×#120 | C23 | 1 | 72 | yes | complemented |
| 120 | C22×#120 | C23 | 1 | 72 | yes | complemented |
| 121 | C23×C4⋊C4 | C23 | 1 | 3 | yes | complemented |
| 122 | C23×C4⋊C4 | C23 | 1 | 6 | yes | complemented |
| 123 | C23×C22⋊C4 | — | 2 | 48 | no | — |
| 124 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 125 | C23×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 126 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 127 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 128 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 129 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 130 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 131 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 132 | C23×C22⋊C4 | C23 | 1 | 6 | yes | — |
| 133 | C23×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 134 | C23×C22⋊C4 | C23 | 1 | 72 | yes | complemented |
| 135 | C23×C22⋊C4 | C23 | 1 | 3 | yes | complemented |
| 136 | C23×C22⋊C4 | C23 | 1 | 6 | yes | complemented |
| 137 | C23×C22⋊C4 | C23 | 1 | 3 | yes | complemented |
| 138 | C23×C22⋊C4 | C23 | 1 | 6 | yes | complemented |
| 139 | C23×C22⋊C4 | C23 | 1 | 6 | yes | complemented |
| 140 | C23×C42 | C23 | 1 | 3 | yes | complemented |
| 141 | C23×C42 | C23 | 1 | 3 | yes | complemented |
| 142 | #2846 | C23 | 1 | 512 | yes | complemented |
| 143 | #2812 | C23 | 1 | 512 | yes | complemented |
| 144 | #2684 | C23 | 1 | 768 | yes | complemented |
| 145 | #2679 | C23 | 1 | 768 | yes | complemented |
| 146 | #2670 | C23 | 1 | 1536 | yes | complemented |
| 147 | #2472 | C23 | 1 | 1536 | yes | complemented |
| 148 | #2435 | C23 | 1 | 768 | yes | complemented |
| 149 | #2403 | C23 | 1 | 768 | yes | complemented |
| 150 | C2×#397 | C23 | 1 | 144 | yes | complemented |
| 151 | C2×#394 | C23 | 1 | 144 | yes | complemented |
| 152 | C2×#394 | C23 | 1 | 144 | yes | complemented |
| 153 | C2×#394 | C23 | 1 | 144 | yes | complemented |
| 154 | C2×#394 | C23 | 1 | 144 | yes | complemented |
| 155 | C2×#393 | C23 | 1 | 144 | yes | complemented |
| 156 | C2×#392 | C23 | 1 | 144 | yes | complemented |
| 157 | C2×#392 | C23 | 1 | 144 | yes | complemented |
| 158 | #2375 | C23 | 1 | 256 | yes | complemented |
| 159 | C2×#390 | C23 | 1 | 72 | yes | complemented |
| 160 | C2×#390 | C23 | 1 | 144 | yes | complemented |
| 161 | C2×#390 | C23 | 1 | 72 | yes | complemented |
| 162 | C2×#388 | C23 | 1 | 144 | yes | complemented |
| 163 | C2×#388 | C23 | 1 | 144 | yes | complemented |
| 164 | C2×#386 | C23 | 1 | 72 | yes | complemented |
| 165 | C2×#386 | C23 | 1 | 72 | yes | complemented |
| 166 | C2×#386 | C23 | 1 | 144 | yes | complemented |
| 167 | C2×#379 | C23 | 1 | 48 | yes | complemented |
| 168 | C2×#379 | C23 | 1 | 144 | yes | complemented |
| 169 | C2×#379 | C23 | 1 | 144 | yes | complemented |
| 170 | C2×#379 | C23 | 1 | 72 | yes | complemented |
| 171 | C2×C4×C22⋊C4 | C23 | 1 | 72 | yes | complemented |
| 172 | C22×#95 | C23 | 1 | 6 | yes | complemented |
| 173 | C22×#95 | C23 | 1 | 6 | yes | complemented |
| 174 | C22×#95 | C23 | 1 | 6 | yes | complemented |
| 175 | C26 | — | 2 | 24 | no | — |
| 176 | C26 | — | 2 | 24 | no | — |
| 177 | C26 | — | 2 | 24 | no | — |
| 178 | C26 | — | 2 | 8 | no | — |
| 179 | C26 | — | 2 | 24 | no | — |
| 180 | C26 | — | 2 | 192 | no | — |
| 181 | C26 | — | 2 | 48 | no | — |
| 182 | C26 | — | 2 | 48 | no | — |
| 183 | C26 | — | 2 | 24 | no | — |
| 184 | C26 | — | 2 | 8 | no | — |
| 185 | C26 | — | 4 | 24 | no | — |
| 186 | C26 | — | 4 | 12 | no | — |
| 187 | C26 | — | 4 | 12 | no | — |
| 188 | C26 | — | 4 | 24 | no | — |
| 189 | C26 | — | 4 | 12 | no | — |
| 190 | C26 | — | 4 | 12 | no | — |
| 191 | C26 | — | 4 | 288 | no | — |
| 192 | C26 | — | 4 | 288 | no | — |
| 193 | C26 | — | 4 | 12 | no | — |
| 194 | C26 | — | 4 | 12 | no | — |
| 195 | C26 | — | 4 | 12 | no | — |
| 196 | C26 | — | 4 | 768 | no | — |
| 197 | C26 | — | 4 | 768 | no | — |
| 198 | C26 | — | 4 | 256 | no | — |
| 199 | C26 | C2×D4 | 1 | 16 | yes | complemented |
| 200 | C26 | C24 | 1 | 2 | yes | — |
| 201 | C26 | C24 | 1 | 1 | yes | characteristic |
| 202 | C26 | C24 | 1 | 1 | yes | characteristic |
| 203 | C26 | C24 | 1 | 3 | yes | — |
| 204 | C26 | C24 | 1 | 3 | yes | — |
| 205 | C26 | C24 | 1 | 36 | yes | — |
| 206 | C26 | C24 | 1 | 12 | yes | — |
| 207 | C26 | C24 | 1 | 1 | yes | characteristic |
| 208 | C26 | C24 | 1 | 36 | yes | — |
| 209 | C26 | C24 | 1 | 12 | yes | — |
| 210 | C26 | C24 | 1 | 64 | yes | complemented |
| 211 | C26 | C24 | 1 | 12 | yes | complemented |
| 212 | C23×Q8 | — | 2 | 24 | no | — |
| 213 | C23×Q8 | — | 4 | 12 | no | — |
| 214 | C23×Q8 | — | 4 | 12 | no | — |
| 215 | C23×Q8 | C24 | 1 | 36 | yes | complemented |
| 216 | C23×D4 | — | 2 | 24 | no | — |
| 217 | C23×D4 | — | 2 | 24 | no | — |
| 218 | C23×D4 | — | 2 | 24 | no | — |
| 219 | C23×D4 | — | 2 | 48 | no | — |
| 220 | C23×D4 | — | 2 | 24 | no | — |
| 221 | C23×D4 | — | 2 | 48 | no | — |
| 222 | C23×D4 | — | 2 | 48 | no | — |
| 223 | C23×D4 | — | 2 | 576 | no | — |
| 224 | C23×D4 | — | 2 | 24 | no | — |
| 225 | C23×D4 | — | 4 | 12 | no | — |
| 226 | C23×D4 | — | 4 | 12 | no | — |
| 227 | C23×D4 | — | 4 | 12 | no | — |
| 228 | C23×D4 | — | 4 | 12 | no | — |
| 229 | C23×D4 | — | 4 | 12 | no | — |
| 230 | C23×D4 | — | 4 | 12 | no | — |
| 231 | C23×D4 | — | 4 | 288 | no | — |
| 232 | C23×D4 | — | 4 | 24 | no | — |
| 233 | C23×D4 | — | 4 | 24 | no | — |
| 234 | C23×D4 | — | 4 | 24 | no | — |
| 235 | C23×D4 | — | 4 | 24 | no | — |
| 236 | C23×D4 | — | 4 | 24 | no | — |
| 237 | C23×D4 | — | 4 | 288 | no | — |
| 238 | C23×D4 | — | 4 | 288 | no | — |
| 239 | C23×D4 | — | 4 | 768 | no | — |
| 240 | C23×D4 | — | 4 | 256 | no | — |
| 241 | C23×D4 | C2×D4 | 1 | 48 | yes | — |
| 242 | C23×D4 | C24 | 1 | 24 | yes | — |
| 243 | C23×D4 | C24 | 1 | 36 | yes | — |
| 244 | C23×D4 | C24 | 1 | 36 | yes | — |
| 245 | C23×D4 | C24 | 1 | 36 | yes | — |
| 246 | C23×D4 | C24 | 1 | 192 | yes | — |
| 247 | C23×D4 | C24 | 1 | 72 | yes | — |
| 248 | C23×D4 | C24 | 1 | 72 | yes | — |
| 249 | C23×D4 | C24 | 1 | 36 | yes | — |
| 250 | C23×D4 | C24 | 1 | 24 | yes | complemented |
| 251 | C23×D4 | C24 | 1 | 64 | yes | complemented |
| 252 | C24×C4 | — | 2 | 24 | no | — |
| 253 | C24×C4 | — | 2 | 24 | no | — |
| 254 | C24×C4 | — | 4 | 12 | no | — |
| 255 | C24×C4 | — | 4 | 12 | no | — |
| 256 | C24×C4 | C24 | 1 | 3 | yes | — |
| 257 | C24×C4 | C24 | 1 | 2 | yes | — |
| 258 | C24×C4 | C24 | 1 | 6 | yes | — |
| 259 | C24×C4 | C24 | 1 | 6 | yes | — |
| 260 | C24×C4 | C24 | 1 | 36 | yes | — |
| 261 | C24×C4 | C24 | 1 | 3 | yes | — |
| 262 | C24×C4 | C24 | 1 | 12 | yes | complemented |
| 263 | H(3,𝔽4) | — | 2 | 2048 | no | — |
| 264 | C2×#124 | — | 2 | 576 | no | — |
| 265 | C2×#124 | — | 2 | 1152 | no | — |
| 266 | C2×#124 | — | 4 | 288 | no | — |
| 267 | C2×#124 | C24 | 1 | 384 | yes | complemented |
| 268 | C2×#124 | C24 | 1 | 192 | yes | complemented |
| 269 | C2×#124 | C24 | 1 | 192 | yes | complemented |
| 270 | C2×C22⋊Q8 | — | 4 | 288 | no | — |
| 271 | C2×C22⋊Q8 | C24 | 1 | 192 | yes | complemented |
| 272 | C2×#120 | — | 2 | 192 | no | — |
| 273 | C2×#120 | — | 2 | 384 | no | — |
| 274 | C2×#120 | — | 2 | 576 | no | — |
| 275 | C2×#120 | — | 2 | 576 | no | — |
| 276 | C2×#120 | — | 2 | 2048 | no | — |
| 277 | C2×#120 | — | 2 | 576 | no | — |
| 278 | C2×#120 | — | 4 | 576 | no | — |
| 279 | C2×#120 | — | 4 | 576 | no | — |
| 280 | C2×#120 | — | 4 | 288 | no | — |
| 281 | C2×#120 | C2×D4 | 1 | 384 | yes | complemented |
| 282 | C2×#120 | C24 | 1 | 192 | yes | — |
| 283 | C2×#120 | C24 | 1 | 384 | yes | — |
| 284 | C2×#120 | C24 | 1 | 64 | yes | — |
| 285 | C2×#120 | C24 | 1 | 128 | yes | complemented |
| 286 | C2×#120 | C24 | 1 | 192 | yes | complemented |
| 287 | C2×#120 | C24 | 1 | 64 | yes | complemented |
| 288 | C2×#120 | C24 | 1 | 384 | yes | complemented |
| 289 | C2×#120 | C24 | 1 | 192 | yes | complemented |
| 290 | C2×#120 | C24 | 1 | 192 | yes | complemented |
| 291 | C22×C4⋊C4 | — | 4 | 12 | no | — |
| 292 | C22×C4⋊C4 | — | 4 | 24 | no | — |
| 293 | C22×C4⋊C4 | C24 | 1 | 72 | yes | complemented |
| 294 | C22×C4⋊C4 | C24 | 1 | 36 | yes | complemented |
| 295 | C22×C22⋊C4 | — | 2 | 24 | no | — |
| 296 | C22×C22⋊C4 | — | 2 | 48 | no | — |
| 297 | C22×C22⋊C4 | — | 2 | 24 | no | — |
| 298 | C22×C22⋊C4 | — | 2 | 48 | no | — |
| 299 | C22×C22⋊C4 | — | 2 | 48 | no | — |
| 300 | C22×C22⋊C4 | — | 2 | 48 | no | — |
| 301 | C22×C22⋊C4 | — | 2 | 48 | no | — |
| 302 | C22×C22⋊C4 | — | 2 | 576 | no | — |
| 303 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 304 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 305 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 306 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 307 | C22×C22⋊C4 | — | 4 | 12 | no | — |
| 308 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 309 | C22×C22⋊C4 | — | 4 | 24 | no | — |
| 310 | C22×C22⋊C4 | C2×D4 | 1 | 48 | yes | complemented |
| 311 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 312 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 313 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 314 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 315 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 316 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 317 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 318 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 319 | C22×C22⋊C4 | C24 | 1 | 72 | yes | — |
| 320 | C22×C22⋊C4 | C24 | 1 | 36 | yes | — |
| 321 | C22×C22⋊C4 | C24 | 1 | 192 | yes | complemented |
| 322 | C22×C22⋊C4 | C24 | 1 | 72 | yes | complemented |
| 323 | C22×C22⋊C4 | C24 | 1 | 36 | yes | complemented |
| 324 | C22×C22⋊C4 | C24 | 1 | 72 | yes | complemented |
| 325 | C22×C22⋊C4 | C24 | 1 | 72 | yes | complemented |
| 326 | C22×C22⋊C4 | C24 | 1 | 36 | yes | complemented |
| 327 | C22×C42 | — | 2 | 24 | no | — |
| 328 | C22×C42 | — | 4 | 12 | no | — |
| 329 | C22×C42 | C24 | 1 | 36 | yes | complemented |
| 330 | C22×C42 | C24 | 1 | 36 | yes | complemented |
| 331 | #397 | C24 | 1 | 384 | yes | complemented |
| 332 | #394 | C24 | 1 | 384 | yes | complemented |
| 333 | #394 | C24 | 1 | 384 | yes | complemented |
| 334 | #394 | C24 | 1 | 384 | yes | complemented |
| 335 | #394 | C24 | 1 | 384 | yes | complemented |
| 336 | #393 | C24 | 1 | 384 | yes | complemented |
| 337 | #392 | C24 | 1 | 384 | yes | complemented |
| 338 | #392 | C24 | 1 | 384 | yes | complemented |
| 339 | #390 | C24 | 1 | 192 | yes | complemented |
| 340 | #390 | C24 | 1 | 192 | yes | complemented |
| 341 | #390 | C24 | 1 | 384 | yes | complemented |
| 342 | #388 | C24 | 1 | 384 | yes | complemented |
| 343 | #388 | C24 | 1 | 384 | yes | complemented |
| 344 | #386 | C24 | 1 | 192 | yes | complemented |
| 345 | #386 | C24 | 1 | 192 | yes | complemented |
| 346 | #386 | C24 | 1 | 384 | yes | complemented |
| 347 | #379 | C24 | 1 | 128 | yes | complemented |
| 348 | #379 | C24 | 1 | 384 | yes | complemented |
| 349 | #379 | C24 | 1 | 384 | yes | complemented |
| 350 | #379 | C24 | 1 | 192 | yes | complemented |
| 351 | C4×C22⋊C4 | C24 | 1 | 192 | yes | complemented |
| 352 | C2×#95 | C24 | 1 | 72 | yes | complemented |
| 353 | C2×#95 | C24 | 1 | 72 | yes | complemented |
| 354 | C2×#95 | C24 | 1 | 72 | yes | complemented |
| 355 | C25 | — | 2 | 4 | no | — |
| 356 | C25 | — | 2 | 12 | no | — |
| 357 | C25 | — | 2 | 384 | no | — |
| 358 | C25 | — | 2 | 144 | no | — |
| 359 | C25 | — | 2 | 12 | no | — |
| 360 | C25 | — | 2 | 12 | no | — |
| 361 | C25 | — | 2 | 24 | no | — |
| 362 | C25 | — | 2 | 24 | no | — |
| 363 | C25 | — | 2 | 24 | no | — |
| 364 | C25 | — | 2 | 24 | no | — |
| 365 | C25 | — | 2 | 12 | no | — |
| 366 | C25 | — | 2 | 144 | no | — |
| 367 | C25 | — | 2 | 144 | no | — |
| 368 | C25 | — | 2 | 12 | no | — |
| 369 | C25 | — | 2 | 12 | no | — |
| 370 | C25 | — | 2 | 12 | no | — |
| 371 | C25 | — | 2 | 8 | no | — |
| 372 | C25 | — | 2 | 144 | no | — |
| 373 | C25 | — | 2 | 48 | no | — |
| 374 | C25 | — | 2 | 4 | no | — |
| 375 | C25 | — | 2 | 256 | no | — |
| 376 | C25 | — | 2 | 12 | no | — |
| 377 | C25 | — | 2 | 24 | no | — |
| 378 | C25 | — | 2 | 288 | no | — |
| 379 | C25 | — | 2 | 288 | no | — |
| 380 | C25 | — | 2 | 24 | no | — |
| 381 | C25 | — | 2 | 12 | no | — |
| 382 | C25 | — | 2 | 144 | no | — |
| 383 | C25 | — | 2 | 48 | no | — |
| 384 | C25 | — | 4 | 192 | no | — |
| 385 | C25 | — | 4 | 144 | no | — |
| 386 | C25 | — | 4 | 72 | no | — |
| 387 | C25 | — | 4 | 72 | no | — |
| 388 | C25 | — | 4 | 144 | no | — |
| 389 | C25 | — | 4 | 72 | no | — |
| 390 | C25 | — | 4 | 72 | no | — |
| 391 | C25 | — | 4 | 384 | no | — |
| 392 | C25 | — | 4 | 384 | no | — |
| 393 | C25 | — | 4 | 72 | no | — |
| 394 | C25 | — | 4 | 72 | no | — |
| 395 | C25 | — | 4 | 72 | no | — |
| 396 | C25 | — | 4 | 384 | no | — |
| 397 | C25 | — | 4 | 384 | no | — |
| 398 | C25 | — | 4 | 384 | no | — |
| 399 | C25 | — | 4 | 192 | no | — |
| 400 | C25 | — | 4 | 192 | no | — |
| 401 | C25 | — | 4 | 192 | no | — |
| 402 | C25 | — | 4 | 4608 | no | — |
| 403 | C25 | — | 4 | 192 | no | — |
| 404 | C25 | — | 4 | 384 | no | — |
| 405 | C25 | — | 4 | 4608 | no | — |
| 406 | C25 | — | 4 | 8192 | no | — |
| 407 | C25 | — | 4 | 64 | no | — |
| 408 | C25 | — | 4 | 192 | no | — |
| 409 | C25 | — | 4 | 1536 | no | — |
| 410 | C25 | — | 4 | 192 | no | — |
| 411 | C25 | — | 4 | 192 | no | — |
| 412 | C25 | — | 4 | 64 | no | — |
| 413 | C25 | — | 4 | 64 | no | — |
| 414 | C25 | — | 8 | 96 | no | — |
| 415 | C25 | — | 8 | 96 | no | — |
| 416 | C25 | — | 8 | 96 | no | — |
| 417 | C25 | C22×D4 | 1 | 24 | yes | — |
| 418 | C25 | C22×D4 | 1 | 8 | yes | — |
| 419 | C25 | C22×D4 | 1 | 96 | yes | complemented |
| 420 | C25 | H(5,𝔽2) | 1 | 24 | yes | — |
| 421 | C25 | H(5,𝔽2) | 1 | 24 | yes | — |
| 422 | C25 | C25 | 1 | 12 | yes | — |
| 423 | C25 | C25 | 1 | 6 | yes | — |
| 424 | C25 | C25 | 1 | 18 | yes | — |
| 425 | C25 | C25 | 1 | 6 | yes | — |
| 426 | C25 | C25 | 1 | 18 | yes | — |
| 427 | C25 | C25 | 1 | 48 | yes | — |
| 428 | C25 | C25 | 1 | 16 | yes | — |
| 429 | C25 | C25 | 1 | 6 | yes | — |
| 430 | C25 | C25 | 1 | 48 | yes | — |
| 431 | C25 | C25 | 1 | 16 | yes | — |
| 432 | C25 | C25 | 1 | 1 | yes | characteristic |
| 433 | C25 | C25 | 1 | 16 | yes | complemented |
| 434 | C22×Q8 | — | 2 | 144 | no | — |
| 435 | C22×Q8 | — | 4 | 72 | no | — |
| 436 | C22×Q8 | — | 4 | 72 | no | — |
| 437 | C22×Q8 | — | 8 | 96 | no | — |
| 438 | C22×Q8 | C25 | 1 | 48 | yes | complemented |
| 439 | C22×D4 | — | 2 | 144 | no | — |
| 440 | C22×D4 | — | 2 | 144 | no | — |
| 441 | C22×D4 | — | 2 | 144 | no | — |
| 442 | C22×D4 | — | 2 | 288 | no | — |
| 443 | C22×D4 | — | 2 | 144 | no | — |
| 444 | C22×D4 | — | 2 | 288 | no | — |
| 445 | C22×D4 | — | 2 | 288 | no | — |
| 446 | C22×D4 | — | 2 | 768 | no | — |
| 447 | C22×D4 | — | 2 | 144 | no | — |
| 448 | C22×D4 | — | 4 | 192 | no | — |
| 449 | C22×D4 | — | 4 | 72 | no | — |
| 450 | C22×D4 | — | 4 | 72 | no | — |
| 451 | C22×D4 | — | 4 | 72 | no | — |
| 452 | C22×D4 | — | 4 | 72 | no | — |
| 453 | C22×D4 | — | 4 | 72 | no | — |
| 454 | C22×D4 | — | 4 | 72 | no | — |
| 455 | C22×D4 | — | 4 | 384 | no | — |
| 456 | C22×D4 | — | 4 | 144 | no | — |
| 457 | C22×D4 | — | 4 | 192 | no | — |
| 458 | C22×D4 | — | 4 | 144 | no | — |
| 459 | C22×D4 | — | 4 | 144 | no | — |
| 460 | C22×D4 | — | 4 | 144 | no | — |
| 461 | C22×D4 | — | 4 | 144 | no | — |
| 462 | C22×D4 | — | 4 | 384 | no | — |
| 463 | C22×D4 | — | 4 | 384 | no | — |
| 464 | C22×D4 | — | 4 | 192 | no | — |
| 465 | C22×D4 | — | 4 | 4608 | no | — |
| 466 | C22×D4 | — | 4 | 192 | no | — |
| 467 | C22×D4 | — | 4 | 1536 | no | — |
| 468 | C22×D4 | — | 4 | 128 | no | — |
| 469 | C22×D4 | — | 4 | 128 | no | — |
| 470 | C22×D4 | — | 8 | 192 | no | — |
| 471 | C22×D4 | — | 8 | 192 | no | — |
| 472 | C22×D4 | C22×D4 | 1 | 288 | yes | — |
| 473 | C22×D4 | C25 | 1 | 32 | yes | — |
| 474 | C22×D4 | C25 | 1 | 48 | yes | — |
| 475 | C22×D4 | C25 | 1 | 48 | yes | — |
| 476 | C22×D4 | C25 | 1 | 96 | yes | — |
| 477 | C22×D4 | C25 | 1 | 96 | yes | — |
| 478 | C22×D4 | C25 | 1 | 48 | yes | — |
| 479 | C22×D4 | C25 | 1 | 48 | yes | — |
| 480 | C22×D4 | C25 | 1 | 32 | yes | complemented |
| 481 | C23×C4 | — | 2 | 12 | no | — |
| 482 | C23×C4 | — | 2 | 12 | no | — |
| 483 | C23×C4 | — | 2 | 12 | no | — |
| 484 | C23×C4 | — | 2 | 24 | no | — |
| 485 | C23×C4 | — | 2 | 24 | no | — |
| 486 | C23×C4 | — | 2 | 24 | no | — |
| 487 | C23×C4 | — | 2 | 24 | no | — |
| 488 | C23×C4 | — | 2 | 24 | no | — |
| 489 | C23×C4 | — | 2 | 24 | no | — |
| 490 | C23×C4 | — | 2 | 12 | no | — |
| 491 | C23×C4 | — | 2 | 24 | no | — |
| 492 | C23×C4 | — | 2 | 12 | no | — |
| 493 | C23×C4 | — | 2 | 144 | no | — |
| 494 | C23×C4 | — | 2 | 144 | no | — |
| 495 | C23×C4 | — | 4 | 72 | no | — |
| 496 | C23×C4 | — | 4 | 72 | no | — |
| 497 | C23×C4 | — | 4 | 192 | no | — |
| 498 | C23×C4 | — | 4 | 64 | no | — |
| 499 | C23×C4 | C22×D4 | 1 | 24 | yes | — |
| 500 | C23×C4 | C25 | 1 | 36 | yes | — |
| 501 | C23×C4 | C25 | 1 | 36 | yes | — |
| 502 | C23×C4 | C25 | 1 | 12 | yes | — |
| 503 | C23×C4 | C25 | 1 | 18 | yes | — |
| 504 | C23×C4 | C25 | 1 | 48 | yes | — |
| 505 | C23×C4 | C25 | 1 | 18 | yes | — |
| 506 | C23×C4 | C25 | 1 | 16 | yes | complemented |
| 507 | #124 | — | 2 | 768 | no | — |
| 508 | #124 | — | 2 | 1536 | no | — |
| 509 | #124 | — | 4 | 384 | no | — |
| 510 | C22⋊Q8 | — | 4 | 384 | no | — |
| 511 | #120 | — | 2 | 256 | no | — |
| 512 | #120 | — | 2 | 512 | no | — |
| 513 | #120 | — | 2 | 768 | no | — |
| 514 | #120 | — | 2 | 768 | no | — |
| 515 | #120 | — | 2 | 768 | no | — |
| 516 | #120 | — | 4 | 768 | no | — |
| 517 | #120 | — | 4 | 768 | no | — |
| 518 | #120 | — | 4 | 384 | no | — |
| 519 | #120 | C22×D4 | 1 | 512 | yes | complemented |
| 520 | C2×C4⋊C4 | — | 4 | 72 | no | — |
| 521 | C2×C4⋊C4 | — | 4 | 144 | no | — |
| 522 | C2×C4⋊C4 | C25 | 1 | 48 | yes | complemented |
| 523 | C2×C4⋊C4 | C25 | 1 | 96 | yes | complemented |
| 524 | C2×C22⋊C4 | — | 2 | 144 | no | — |
| 525 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 526 | C2×C22⋊C4 | — | 2 | 144 | no | — |
| 527 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 528 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 529 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 530 | C2×C22⋊C4 | — | 2 | 288 | no | — |
| 531 | C2×C22⋊C4 | — | 2 | 768 | no | — |
| 532 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 533 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 534 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 535 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 536 | C2×C22⋊C4 | — | 4 | 72 | no | — |
| 537 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 538 | C2×C22⋊C4 | — | 4 | 144 | no | — |
| 539 | C2×C22⋊C4 | C22×D4 | 1 | 288 | yes | complemented |
| 540 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 541 | C2×C22⋊C4 | C25 | 1 | 48 | yes | — |
| 542 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 543 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 544 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 545 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 546 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 547 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 548 | C2×C22⋊C4 | C25 | 1 | 96 | yes | — |
| 549 | C2×C22⋊C4 | C25 | 1 | 48 | yes | — |
| 550 | C2×C22⋊C4 | C25 | 1 | 48 | yes | complemented |
| 551 | C2×C22⋊C4 | C25 | 1 | 96 | yes | complemented |
| 552 | C2×C22⋊C4 | C25 | 1 | 48 | yes | complemented |
| 553 | C2×C22⋊C4 | C25 | 1 | 96 | yes | complemented |
| 554 | C2×C22⋊C4 | C25 | 1 | 96 | yes | complemented |
| 555 | C2×C42 | — | 2 | 144 | no | — |
| 556 | C2×C42 | — | 4 | 72 | no | — |
| 557 | C2×C42 | C25 | 1 | 48 | yes | complemented |
| 558 | C2×C42 | C25 | 1 | 48 | yes | complemented |
| 559 | #95 | C25 | 1 | 96 | yes | complemented |
| 560 | #95 | C25 | 1 | 96 | yes | complemented |
| 561 | #95 | C25 | 1 | 96 | yes | complemented |
| 562 | C24 | — | 2 | 12 | no | — |
| 563 | C24 | — | 2 | 36 | no | — |
| 564 | C24 | — | 2 | 96 | no | — |
| 565 | C24 | — | 2 | 96 | no | — |
| 566 | C24 | — | 2 | 1152 | no | — |
| 567 | C24 | — | 2 | 96 | no | — |
| 568 | C24 | — | 2 | 36 | no | — |
| 569 | C24 | — | 2 | 36 | no | — |
| 570 | C24 | — | 2 | 72 | no | — |
| 571 | C24 | — | 2 | 72 | no | — |
| 572 | C24 | — | 2 | 72 | no | — |
| 573 | C24 | — | 2 | 72 | no | — |
| 574 | C24 | — | 2 | 36 | no | — |
| 575 | C24 | — | 2 | 96 | no | — |
| 576 | C24 | — | 2 | 96 | no | — |
| 577 | C24 | — | 2 | 36 | no | — |
| 578 | C24 | — | 2 | 36 | no | — |
| 579 | C24 | — | 2 | 36 | no | — |
| 580 | C24 | — | 2 | 96 | no | — |
| 581 | C24 | — | 2 | 96 | no | — |
| 582 | C24 | — | 2 | 96 | no | — |
| 583 | C24 | — | 2 | 192 | no | — |
| 584 | C24 | — | 2 | 192 | no | — |
| 585 | C24 | — | 2 | 24 | no | — |
| 586 | C24 | — | 2 | 96 | no | — |
| 587 | C24 | — | 2 | 32 | no | — |
| 588 | C24 | — | 2 | 12 | no | — |
| 589 | C24 | — | 2 | 36 | no | — |
| 590 | C24 | — | 2 | 72 | no | — |
| 591 | C24 | — | 2 | 192 | no | — |
| 592 | C24 | — | 2 | 192 | no | — |
| 593 | C24 | — | 2 | 72 | no | — |
| 594 | C24 | — | 2 | 36 | no | — |
| 595 | C24 | — | 2 | 96 | no | — |
| 596 | C24 | — | 2 | 32 | no | — |
| 597 | C24 | — | 4 | 576 | no | — |
| 598 | C24 | — | 4 | 96 | no | — |
| 599 | C24 | — | 4 | 48 | no | — |
| 600 | C24 | — | 4 | 48 | no | — |
| 601 | C24 | — | 4 | 48 | no | — |
| 602 | C24 | — | 4 | 96 | no | — |
| 603 | C24 | — | 4 | 48 | no | — |
| 604 | C24 | — | 4 | 48 | no | — |
| 605 | C24 | — | 4 | 48 | no | — |
| 606 | C24 | — | 4 | 48 | no | — |
| 607 | C24 | — | 4 | 1152 | no | — |
| 608 | C24 | — | 4 | 1152 | no | — |
| 609 | C24 | — | 4 | 1152 | no | — |
| 610 | C24 | — | 4 | 576 | no | — |
| 611 | C24 | — | 4 | 576 | no | — |
| 612 | C24 | — | 4 | 3072 | no | — |
| 613 | C24 | — | 4 | 576 | no | — |
| 614 | C24 | — | 4 | 3072 | no | — |
| 615 | C24 | — | 4 | 576 | no | — |
| 616 | C24 | — | 4 | 1152 | no | — |
| 617 | C24 | — | 4 | 3072 | no | — |
| 618 | C24 | — | 4 | 24576 | no | — |
| 619 | C24 | — | 4 | 1024 | no | — |
| 620 | C24 | — | 4 | 3072 | no | — |
| 621 | C24 | — | 4 | 192 | no | — |
| 622 | C24 | — | 4 | 576 | no | — |
| 623 | C24 | — | 4 | 1024 | no | — |
| 624 | C24 | — | 4 | 576 | no | — |
| 625 | C24 | — | 4 | 96 | no | — |
| 626 | C24 | — | 4 | 16 | no | — |
| 627 | C24 | — | 4 | 48 | no | — |
| 628 | C24 | — | 4 | 48 | no | — |
| 629 | C24 | — | 4 | 576 | no | — |
| 630 | C24 | — | 4 | 96 | no | — |
| 631 | C24 | — | 4 | 48 | no | — |
| 632 | C24 | — | 4 | 48 | no | — |
| 633 | C24 | — | 4 | 48 | no | — |
| 634 | C24 | — | 4 | 192 | no | — |
| 635 | C24 | — | 4 | 48 | no | — |
| 636 | C24 | — | 4 | 96 | no | — |
| 637 | C24 | — | 4 | 16 | no | — |
| 638 | C24 | — | 4 | 32 | no | — |
| 639 | C24 | — | 4 | 192 | no | — |
| 640 | C24 | — | 4 | 96 | no | — |
| 641 | C24 | — | 4 | 48 | no | — |
| 642 | C24 | — | 8 | 288 | no | — |
| 643 | C24 | — | 8 | 288 | no | — |
| 644 | C24 | — | 8 | 512 | no | — |
| 645 | C24 | — | 8 | 288 | no | — |
| 646 | C24 | — | 8 | 512 | no | — |
| 647 | C24 | H(3,𝔽4) | 1 | 64 | yes | complemented |
| 648 | C24 | C23×D4 | 1 | 72 | yes | — |
| 649 | C24 | C23×D4 | 1 | 24 | yes | — |
| 650 | C24 | C23×D4 | 1 | 4 | yes | — |
| 651 | C24 | C23×D4 | 1 | 64 | yes | complemented |
| 652 | C24 | C2×H(5,𝔽2) | 1 | 72 | yes | — |
| 653 | C24 | C2×H(5,𝔽2) | 1 | 72 | yes | — |
| 654 | C24 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 655 | C24 | C2×H(5,𝔽2) | 1 | 12 | yes | — |
| 656 | C24 | C26 | 1 | 8 | yes | — |
| 657 | C24 | C26 | 1 | 4 | yes | — |
| 658 | C24 | C26 | 1 | 12 | yes | — |
| 659 | C24 | C26 | 1 | 4 | yes | — |
| 660 | C24 | C26 | 1 | 12 | yes | — |
| 661 | C24 | C26 | 1 | 4 | yes | — |
| 662 | C24 | C26 | 1 | 3 | yes | — |
| 663 | C2×Q8 | — | 2 | 96 | no | — |
| 664 | C2×Q8 | — | 4 | 48 | no | — |
| 665 | C2×Q8 | — | 4 | 48 | no | — |
| 666 | C2×Q8 | — | 8 | 288 | no | — |
| 667 | C2×D4 | — | 2 | 96 | no | — |
| 668 | C2×D4 | — | 2 | 96 | no | — |
| 669 | C2×D4 | — | 2 | 96 | no | — |
| 670 | C2×D4 | — | 2 | 192 | no | — |
| 671 | C2×D4 | — | 2 | 96 | no | — |
| 672 | C2×D4 | — | 2 | 192 | no | — |
| 673 | C2×D4 | — | 2 | 192 | no | — |
| 674 | C2×D4 | — | 2 | 96 | no | — |
| 675 | C2×D4 | — | 4 | 576 | no | — |
| 676 | C2×D4 | — | 4 | 48 | no | — |
| 677 | C2×D4 | — | 4 | 48 | no | — |
| 678 | C2×D4 | — | 4 | 48 | no | — |
| 679 | C2×D4 | — | 4 | 48 | no | — |
| 680 | C2×D4 | — | 4 | 48 | no | — |
| 681 | C2×D4 | — | 4 | 48 | no | — |
| 682 | C2×D4 | — | 4 | 96 | no | — |
| 683 | C2×D4 | — | 4 | 576 | no | — |
| 684 | C2×D4 | — | 4 | 96 | no | — |
| 685 | C2×D4 | — | 4 | 96 | no | — |
| 686 | C2×D4 | — | 4 | 96 | no | — |
| 687 | C2×D4 | — | 4 | 96 | no | — |
| 688 | C2×D4 | — | 4 | 576 | no | — |
| 689 | C2×D4 | — | 4 | 3072 | no | — |
| 690 | C2×D4 | — | 4 | 576 | no | — |
| 691 | C2×D4 | — | 4 | 1024 | no | — |
| 692 | C2×D4 | — | 4 | 384 | no | — |
| 693 | C2×D4 | — | 4 | 384 | no | — |
| 694 | C2×D4 | — | 8 | 576 | no | — |
| 695 | C2×D4 | — | 8 | 576 | no | — |
| 696 | C2×D4 | C23×D4 | 1 | 192 | yes | — |
| 697 | C22×C4 | — | 2 | 36 | no | — |
| 698 | C22×C4 | — | 2 | 36 | no | — |
| 699 | C22×C4 | — | 2 | 96 | no | — |
| 700 | C22×C4 | — | 2 | 72 | no | — |
| 701 | C22×C4 | — | 2 | 36 | no | — |
| 702 | C22×C4 | — | 2 | 72 | no | — |
| 703 | C22×C4 | — | 2 | 72 | no | — |
| 704 | C22×C4 | — | 2 | 72 | no | — |
| 705 | C22×C4 | — | 2 | 72 | no | — |
| 706 | C22×C4 | — | 2 | 72 | no | — |
| 707 | C22×C4 | — | 2 | 36 | no | — |
| 708 | C22×C4 | — | 2 | 72 | no | — |
| 709 | C22×C4 | — | 2 | 36 | no | — |
| 710 | C22×C4 | — | 2 | 96 | no | — |
| 711 | C22×C4 | — | 2 | 96 | no | — |
| 712 | C22×C4 | — | 4 | 48 | no | — |
| 713 | C22×C4 | — | 4 | 48 | no | — |
| 714 | C22×C4 | — | 4 | 576 | no | — |
| 715 | C22×C4 | — | 4 | 192 | no | — |
| 716 | C22×C4 | — | 4 | 48 | no | — |
| 717 | C22×C4 | — | 4 | 96 | no | — |
| 718 | C22×C4 | — | 4 | 32 | no | — |
| 719 | C22×C4 | — | 4 | 96 | no | — |
| 720 | C22×C4 | C23×D4 | 1 | 72 | yes | — |
| 721 | C22×C4 | C26 | 1 | 8 | yes | — |
| 722 | C22×C4 | C26 | 1 | 12 | yes | — |
| 723 | C22×C4 | C26 | 1 | 24 | yes | — |
| 724 | C22×C4 | C26 | 1 | 24 | yes | — |
| 725 | C22×C4 | C26 | 1 | 12 | yes | — |
| 726 | C4⋊C4 | — | 4 | 48 | no | — |
| 727 | C4⋊C4 | — | 4 | 96 | no | — |
| 728 | C22⋊C4 | — | 2 | 96 | no | — |
| 729 | C22⋊C4 | — | 2 | 192 | no | — |
| 730 | C22⋊C4 | — | 2 | 96 | no | — |
| 731 | C22⋊C4 | — | 2 | 192 | no | — |
| 732 | C22⋊C4 | — | 2 | 192 | no | — |
| 733 | C22⋊C4 | — | 2 | 192 | no | — |
| 734 | C22⋊C4 | — | 2 | 192 | no | — |
| 735 | C22⋊C4 | — | 4 | 96 | no | — |
| 736 | C22⋊C4 | — | 4 | 96 | no | — |
| 737 | C22⋊C4 | — | 4 | 96 | no | — |
| 738 | C22⋊C4 | — | 4 | 96 | no | — |
| 739 | C22⋊C4 | — | 4 | 48 | no | — |
| 740 | C22⋊C4 | — | 4 | 96 | no | — |
| 741 | C22⋊C4 | — | 4 | 96 | no | — |
| 742 | C22⋊C4 | C23×D4 | 1 | 192 | yes | complemented |
| 743 | C42 | — | 2 | 96 | no | — |
| 744 | C42 | — | 4 | 48 | no | — |
| 745 | C23 | — | 2 | 144 | no | — |
| 746 | C23 | — | 2 | 4 | no | — |
| 747 | C23 | — | 2 | 12 | no | — |
| 748 | C23 | — | 2 | 256 | no | — |
| 749 | C23 | — | 2 | 144 | no | — |
| 750 | C23 | — | 2 | 384 | no | — |
| 751 | C23 | — | 2 | 144 | no | — |
| 752 | C23 | — | 2 | 144 | no | — |
| 753 | C23 | — | 2 | 144 | no | — |
| 754 | C23 | — | 2 | 288 | no | — |
| 755 | C23 | — | 2 | 12 | no | — |
| 756 | C23 | — | 2 | 12 | no | — |
| 757 | C23 | — | 2 | 24 | no | — |
| 758 | C23 | — | 2 | 24 | no | — |
| 759 | C23 | — | 2 | 24 | no | — |
| 760 | C23 | — | 2 | 24 | no | — |
| 761 | C23 | — | 2 | 12 | no | — |
| 762 | C23 | — | 2 | 12 | no | — |
| 763 | C23 | — | 2 | 12 | no | — |
| 764 | C23 | — | 2 | 12 | no | — |
| 765 | C23 | — | 2 | 288 | no | — |
| 766 | C23 | — | 2 | 8 | no | — |
| 767 | C23 | — | 2 | 4 | no | — |
| 768 | C23 | — | 2 | 12 | no | — |
| 769 | C23 | — | 2 | 24 | no | — |
| 770 | C23 | — | 2 | 24 | no | — |
| 771 | C23 | — | 2 | 12 | no | — |
| 772 | C23 | — | 4 | 192 | no | — |
| 773 | C23 | — | 4 | 384 | no | — |
| 774 | C23 | — | 4 | 384 | no | — |
| 775 | C23 | — | 4 | 192 | no | — |
| 776 | C23 | — | 4 | 384 | no | — |
| 777 | C23 | — | 4 | 192 | no | — |
| 778 | C23 | — | 4 | 192 | no | — |
| 779 | C23 | — | 4 | 4608 | no | — |
| 780 | C23 | — | 4 | 384 | no | — |
| 781 | C23 | — | 4 | 192 | no | — |
| 782 | C23 | — | 4 | 8192 | no | — |
| 783 | C23 | — | 4 | 192 | no | — |
| 784 | C23 | — | 4 | 1536 | no | — |
| 785 | C23 | — | 4 | 4608 | no | — |
| 786 | C23 | — | 4 | 64 | no | — |
| 787 | C23 | — | 4 | 192 | no | — |
| 788 | C23 | — | 4 | 144 | no | — |
| 789 | C23 | — | 4 | 384 | no | — |
| 790 | C23 | — | 4 | 384 | no | — |
| 791 | C23 | — | 4 | 128 | no | — |
| 792 | C23 | — | 4 | 24 | no | — |
| 793 | C23 | — | 4 | 72 | no | — |
| 794 | C23 | — | 4 | 72 | no | — |
| 795 | C23 | — | 4 | 192 | no | — |
| 796 | C23 | — | 4 | 144 | no | — |
| 797 | C23 | — | 4 | 72 | no | — |
| 798 | C23 | — | 4 | 72 | no | — |
| 799 | C23 | — | 4 | 72 | no | — |
| 800 | C23 | — | 4 | 64 | no | — |
| 801 | C23 | — | 4 | 72 | no | — |
| 802 | C23 | — | 4 | 144 | no | — |
| 803 | C23 | — | 4 | 24 | no | — |
| 804 | C23 | — | 4 | 48 | no | — |
| 805 | C23 | — | 4 | 64 | no | — |
| 806 | C23 | — | 4 | 144 | no | — |
| 807 | C23 | — | 4 | 72 | no | — |
| 808 | C23 | — | 8 | 96 | no | — |
| 809 | C23 | — | 8 | 96 | no | — |
| 810 | C23 | — | 8 | 768 | no | — |
| 811 | C23 | — | 8 | 96 | no | — |
| 812 | C23 | — | 8 | 768 | no | — |
| 813 | C23 | — | 8 | 64 | no | — |
| 814 | C23 | — | 8 | 128 | no | — |
| 815 | C23 | #3484 | 1 | 48 | yes | — |
| 816 | C23 | C2×H(3,𝔽4) | 1 | 16 | yes | — |
| 817 | C23 | C2×H(3,𝔽4) | 1 | 96 | yes | complemented |
| 818 | C23 | #3532 | 1 | 48 | yes | — |
| 819 | C23 | C24×D4 | 1 | 24 | yes | — |
| 820 | C23 | C24×D4 | 1 | 8 | yes | — |
| 821 | C23 | C24×D4 | 1 | 6 | yes | — |
| 822 | C23 | C22×H(5,𝔽2) | 1 | 24 | yes | — |
| 823 | C23 | C22×H(5,𝔽2) | 1 | 24 | yes | — |
| 824 | C23 | C22×H(5,𝔽2) | 1 | 18 | yes | — |
| 825 | C23 | C22×H(5,𝔽2) | 1 | 18 | yes | — |
| 826 | C23 | C27 | 1 | 1 | yes | characteristic |
| 827 | Q8 | — | 8 | 96 | no | — |
| 828 | D4 | — | 4 | 192 | no | — |
| 829 | D4 | — | 4 | 192 | no | — |
| 830 | D4 | — | 4 | 192 | no | — |
| 831 | D4 | — | 4 | 192 | no | — |
| 832 | D4 | — | 4 | 128 | no | — |
| 833 | D4 | — | 4 | 128 | no | — |
| 834 | D4 | — | 8 | 192 | no | — |
| 835 | D4 | — | 8 | 192 | no | — |
| 836 | C2×C4 | — | 2 | 144 | no | — |
| 837 | C2×C4 | — | 2 | 12 | no | — |
| 838 | C2×C4 | — | 2 | 12 | no | — |
| 839 | C2×C4 | — | 2 | 24 | no | — |
| 840 | C2×C4 | — | 2 | 12 | no | — |
| 841 | C2×C4 | — | 2 | 24 | no | — |
| 842 | C2×C4 | — | 2 | 24 | no | — |
| 843 | C2×C4 | — | 2 | 24 | no | — |
| 844 | C2×C4 | — | 2 | 24 | no | — |
| 845 | C2×C4 | — | 2 | 24 | no | — |
| 846 | C2×C4 | — | 2 | 12 | no | — |
| 847 | C2×C4 | — | 2 | 24 | no | — |
| 848 | C2×C4 | — | 2 | 12 | no | — |
| 849 | C2×C4 | — | 4 | 192 | no | — |
| 850 | C2×C4 | — | 4 | 64 | no | — |
| 851 | C2×C4 | — | 4 | 72 | no | — |
| 852 | C2×C4 | — | 4 | 144 | no | — |
| 853 | C2×C4 | — | 4 | 48 | no | — |
| 854 | C2×C4 | — | 4 | 144 | no | — |
| 855 | C2×C4 | C24×D4 | 1 | 24 | yes | — |
| 856 | C22 | — | 2 | 24 | no | — |
| 857 | C22 | — | 2 | 24 | no | — |
| 858 | C22 | — | 2 | 192 | no | — |
| 859 | C22 | — | 2 | 48 | no | — |
| 860 | C22 | — | 2 | 24 | no | — |
| 861 | C22 | — | 2 | 24 | no | — |
| 862 | C22 | — | 2 | 24 | no | — |
| 863 | C22 | — | 2 | 48 | no | — |
| 864 | C22 | — | 4 | 768 | no | — |
| 865 | C22 | — | 4 | 256 | no | — |
| 866 | C22 | — | 4 | 768 | no | — |
| 867 | C22 | — | 4 | 12 | no | — |
| 868 | C22 | — | 4 | 24 | no | — |
| 869 | C22 | — | 4 | 12 | no | — |
| 870 | C22 | — | 4 | 12 | no | — |
| 871 | C22 | — | 4 | 24 | no | — |
| 872 | C22 | — | 4 | 288 | no | — |
| 873 | C22 | — | 4 | 288 | no | — |
| 874 | C22 | — | 4 | 96 | no | — |
| 875 | C22 | — | 4 | 4 | no | — |
| 876 | C22 | — | 4 | 12 | no | — |
| 877 | C22 | — | 4 | 12 | no | — |
| 878 | C22 | — | 4 | 24 | no | — |
| 879 | C22 | — | 4 | 12 | no | — |
| 880 | C22 | — | 4 | 12 | no | — |
| 881 | C22 | — | 4 | 24 | no | — |
| 882 | C22 | — | 4 | 4 | no | — |
| 883 | C22 | — | 4 | 8 | no | — |
| 884 | C22 | — | 8 | 128 | no | — |
| 885 | C22 | — | 8 | 128 | no | — |
| 886 | C22 | — | 8 | 48 | no | — |
| 887 | C22 | — | 8 | 96 | no | — |
| 888 | C22 | #45439 | 1 | 64 | yes | direct product factor |
| 889 | C22 | C22×H(3,𝔽4) | 1 | 12 | yes | — |
| 890 | C22 | C22×H(3,𝔽4) | 1 | 16 | yes | complemented |
| 891 | C22 | C2×#3532 | 1 | 36 | yes | — |
| 892 | C22 | C2×#3484 | 1 | 36 | yes | — |
| 893 | C22 | C25×D4 | 1 | 1 | yes | characteristic |
| 894 | C22 | C23×H(5,𝔽2) | 1 | 3 | yes | — |
| 895 | C22 | C23×H(5,𝔽2) | 1 | 3 | yes | — |
| 896 | C4 | — | 2 | 24 | no | — |
| 897 | C4 | — | 4 | 24 | no | — |
| 898 | C4 | — | 4 | 12 | no | — |
| 899 | C4 | — | 4 | 24 | no | — |
| 900 | C4 | — | 4 | 8 | no | — |
| 901 | C2 | — | 2 | 16 | no | — |
| 902 | C2 | — | 4 | 24 | no | — |
| 903 | C2 | — | 4 | 24 | no | — |
| 904 | C2 | — | 4 | 8 | no | — |
| 905 | C2 | — | 8 | 8 | no | — |
| 906 | C2 | — | 8 | 4 | no | — |
| 907 | C2 | C2×#45439 | 1 | 24 | yes | direct product factor |
| 908 | C2 | C22×#3484 | 1 | 3 | yes | — |
| 909 | C2 | C23×H(3,𝔽4) | 1 | 1 | yes | characteristic |
| 910 | C2 | C22×#3532 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, socle | C25 | C25 |
| commutator, Frattini, cosocle | C23 | C27 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C25 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×H(3,𝔽4) | C2 | semidirect |
| 2. C24×#120 | C2 | semidirect |
| 3. C2×#45439 | C2 | direct (N × H) |
| 4. C22×#2670 | C2 | semidirect |
| 5. C22×#2679 | C2 | semidirect |
| 6. C22×#2684 | C2 | semidirect |
| 7. C22×#2812 | C2 | semidirect |
| 8. C22×#2846 | C2 | semidirect |
| 9. C22×#2435 | C2 | semidirect |
| 10. C22×#2472 | C2 | semidirect |
| 11. C22×#2403 | C2 | semidirect |
| 12. C22×#2375 | C2 | semidirect |
| 13. C28 | C22 | semidirect |
| 15. C25×D4 | C22 | semidirect |
| 17. C22×H(3,𝔽4) | C22 | semidirect |
| 18. C23×#124 | C22 | semidirect |
| 19. C23×#124 | C22 | semidirect |
| 20. C23×#124 | C22 | semidirect |
| 21. C23×C22⋊Q8 | C22 | semidirect |
| 26. C23×#120 | C22 | semidirect |
| 27. C23×#120 | C22 | semidirect |
| 28. C23×#120 | C22 | semidirect |
| 29. C23×#120 | C22 | semidirect |
| 30. C23×#120 | C22 | semidirect |
| 31. C23×#120 | C22 | semidirect |
| 32. C23×#120 | C22 | semidirect |
| 33. C24×C22⋊C4 | C22 | semidirect |
| 34. C2×#2684 | C22 | semidirect |
| 35. C2×#2679 | C22 | semidirect |
| 36. C2×#2670 | C22 | semidirect |
| 37. #45439 | C22 | direct (N × H) |
| 38. C2×#2812 | C22 | semidirect |
| 39. C2×#2846 | C22 | semidirect |
| 40. C2×#2435 | C22 | semidirect |
| 41. C2×#2472 | C22 | semidirect |
| 42. C2×#2403 | C22 | semidirect |
| 43. C22×#397 | C22 | semidirect |
| 44. C22×#394 | C22 | semidirect |
| 45. C22×#394 | C22 | semidirect |
| 46. C22×#394 | C22 | semidirect |
| 47. C22×#394 | C22 | semidirect |
| 48. C22×#393 | C22 | semidirect |
| 49. C22×#392 | C22 | semidirect |
| 50. C22×#392 | C22 | semidirect |
| 51. C2×#2375 | C22 | semidirect |
| 52. C22×#390 | C22 | semidirect |
| 53. C22×#390 | C22 | semidirect |
| 54. C22×#390 | C22 | semidirect |
| 55. C22×#388 | C22 | semidirect |
| 56. C22×#388 | C22 | semidirect |
| 57. C22×#386 | C22 | semidirect |
| 58. C22×#386 | C22 | semidirect |
| 59. C22×#386 | C22 | semidirect |
| 60. C22×#379 | C22 | semidirect |
| 61. C22×#379 | C22 | semidirect |
| 62. C22×#379 | C22 | semidirect |
| 63. C22×#379 | C22 | semidirect |
| 64. C22×C4×C22⋊C4 | C22 | semidirect |
| 72. C27 | C23 | semidirect |
| 73. C27 | C23 | semidirect |
| 74. C24×Q8 | C23 | semidirect |
| 87. C24×D4 | C23 | semidirect |
| 88. C24×D4 | C23 | semidirect |
| 90. C25×C4 | C23 | semidirect |
| 92. C2×H(3,𝔽4) | C23 | semidirect |
| 96. C22×#124 | C23 | semidirect |
| 97. C22×#124 | C23 | semidirect |
| 98. C22×#124 | C23 | semidirect |
| 100. C22×C22⋊Q8 | C23 | semidirect |
| 110. C22×#120 | D4 | semidirect |
| 114. C22×#120 | C23 | semidirect |
| 115. C22×#120 | C23 | semidirect |
| 116. C22×#120 | C23 | semidirect |
| 117. C22×#120 | C23 | semidirect |
| 118. C22×#120 | C23 | semidirect |
| 119. C22×#120 | C23 | semidirect |
| 120. C22×#120 | C23 | semidirect |
| 121. C23×C4⋊C4 | C23 | semidirect |
| 122. C23×C4⋊C4 | C23 | semidirect |
| 134. C23×C22⋊C4 | C23 | semidirect |
| 135. C23×C22⋊C4 | C23 | semidirect |
| 136. C23×C22⋊C4 | C23 | semidirect |
| 137. C23×C22⋊C4 | C23 | semidirect |
| 138. C23×C22⋊C4 | C23 | semidirect |
| 139. C23×C22⋊C4 | C23 | semidirect |
| 140. C23×C42 | C23 | semidirect |
| 141. C23×C42 | C23 | semidirect |
| 142. #2846 | C23 | semidirect |
| 143. #2812 | C23 | semidirect |
| 144. #2684 | C23 | semidirect |
| 145. #2679 | C23 | semidirect |
| 146. #2670 | C23 | semidirect |
| 147. #2472 | C23 | semidirect |
| 148. #2435 | C23 | semidirect |
| 149. #2403 | C23 | semidirect |
| 150. C2×#397 | C23 | semidirect |
| 151. C2×#394 | C23 | semidirect |
| 152. C2×#394 | C23 | semidirect |
| 153. C2×#394 | C23 | semidirect |
| 154. C2×#394 | C23 | semidirect |
| 155. C2×#393 | C23 | semidirect |
| 156. C2×#392 | C23 | semidirect |
| 157. C2×#392 | C23 | semidirect |
| 158. #2375 | C23 | semidirect |
| 159. C2×#390 | C23 | semidirect |
| 160. C2×#390 | C23 | semidirect |
| 161. C2×#390 | C23 | semidirect |
| 162. C2×#388 | C23 | semidirect |
| 163. C2×#388 | C23 | semidirect |
| 164. C2×#386 | C23 | semidirect |
| 165. C2×#386 | C23 | semidirect |
| 166. C2×#386 | C23 | semidirect |
| 167. C2×#379 | C23 | semidirect |
| 168. C2×#379 | C23 | semidirect |
| 169. C2×#379 | C23 | semidirect |
| 170. C2×#379 | C23 | semidirect |
| 171. C2×C4×C22⋊C4 | C23 | semidirect |
| 172. C22×#95 | C23 | semidirect |
| 173. C22×#95 | C23 | semidirect |
| 174. C22×#95 | C23 | semidirect |
| 199. C26 | C2×D4 | semidirect |
| 210. C26 | C24 | semidirect |
| 211. C26 | C24 | semidirect |
| 215. C23×Q8 | C24 | semidirect |
| 250. C23×D4 | C24 | semidirect |
| 251. C23×D4 | C24 | semidirect |
| 262. C24×C4 | C24 | semidirect |
| 267. C2×#124 | C24 | semidirect |
| 268. C2×#124 | C24 | semidirect |
| 269. C2×#124 | C24 | semidirect |
| 271. C2×C22⋊Q8 | C24 | semidirect |
| 281. C2×#120 | C2×D4 | semidirect |
| 285. C2×#120 | C24 | semidirect |
| 286. C2×#120 | C24 | semidirect |
| 287. C2×#120 | C24 | semidirect |
| 288. C2×#120 | C24 | semidirect |
| 289. C2×#120 | C24 | semidirect |
| 290. C2×#120 | C24 | semidirect |
| 293. C22×C4⋊C4 | C24 | semidirect |
| 294. C22×C4⋊C4 | C24 | semidirect |
| 310. C22×C22⋊C4 | C2×D4 | semidirect |
| 321. C22×C22⋊C4 | C24 | semidirect |
| 322. C22×C22⋊C4 | C24 | semidirect |
| 323. C22×C22⋊C4 | C24 | semidirect |
| 324. C22×C22⋊C4 | C24 | semidirect |
| 325. C22×C22⋊C4 | C24 | semidirect |
| 326. C22×C22⋊C4 | C24 | semidirect |
| 329. C22×C42 | C24 | semidirect |
| 330. C22×C42 | C24 | semidirect |
| 331. #397 | C24 | semidirect |
| 332. #394 | C24 | semidirect |
| 333. #394 | C24 | semidirect |
| 334. #394 | C24 | semidirect |
| 335. #394 | C24 | semidirect |
| 336. #393 | C24 | semidirect |
| 337. #392 | C24 | semidirect |
| 338. #392 | C24 | semidirect |
| 339. #390 | C24 | semidirect |
| 340. #390 | C24 | semidirect |
| 341. #390 | C24 | semidirect |
| 342. #388 | C24 | semidirect |
| 343. #388 | C24 | semidirect |
| 344. #386 | C24 | semidirect |
| 345. #386 | C24 | semidirect |
| 346. #386 | C24 | semidirect |
| 347. #379 | C24 | semidirect |
| 348. #379 | C24 | semidirect |
| 349. #379 | C24 | semidirect |
| 350. #379 | C24 | semidirect |
| 351. C4×C22⋊C4 | C24 | semidirect |
| 352. C2×#95 | C24 | semidirect |
| 353. C2×#95 | C24 | semidirect |
| 354. C2×#95 | C24 | semidirect |
| 419. C25 | C22×D4 | semidirect |
| 433. C25 | C25 | semidirect |
| 438. C22×Q8 | C25 | semidirect |
| 480. C22×D4 | C25 | semidirect |
| 506. C23×C4 | C25 | semidirect |
| 519. #120 | C22×D4 | semidirect |
| 522. C2×C4⋊C4 | C25 | semidirect |
| 523. C2×C4⋊C4 | C25 | semidirect |
| 539. C2×C22⋊C4 | C22×D4 | semidirect |
| 550. C2×C22⋊C4 | C25 | semidirect |
| 551. C2×C22⋊C4 | C25 | semidirect |
| 552. C2×C22⋊C4 | C25 | semidirect |
| 553. C2×C22⋊C4 | C25 | semidirect |
| 554. C2×C22⋊C4 | C25 | semidirect |
| 557. C2×C42 | C25 | semidirect |
| 558. C2×C42 | C25 | semidirect |
| 559. #95 | C25 | semidirect |
| 560. #95 | C25 | semidirect |
| 561. #95 | C25 | semidirect |
| 647. C24 | H(3,𝔽4) | semidirect |
| 651. C24 | C23×D4 | semidirect |
| 742. C22⋊C4 | C23×D4 | semidirect |
| 817. C23 | C2×H(3,𝔽4) | semidirect |
| 888. C22 | #45439 | direct (N × H) |
| 890. C22 | C22×H(3,𝔽4) | semidirect |
| 907. C2 | C2×#45439 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×H(3,𝔽4) | 2 |
| C24×#120 | 2 |
| C2×#45439 | 2 |
| C22×#2670 | 2 |
| C22×#2679 | 2 |
| C22×#2684 | 2 |
| C22×#2812 | 2 |
| C22×#2846 | 2 |
| C22×#2435 | 2 |
| C22×#2472 | 2 |
| C22×#2403 | 2 |
| C22×#2375 | 2 |