Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
171156 conjugacy classes of subgroups.
The subgroup lattice has 828 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#7266798 | C2 | 1 | 42 | yes | maximal, complemented |
| 2 | C2×#6499874 | C2 | 1 | 14 | yes | maximal, complemented |
| 3 | C2×#6499867 | C2 | 1 | 7 | yes | maximal, complemented |
| 4 | #72216292 | C2 | 1 | 64 | yes | maximal, direct product factor |
| 5 | C2×#62817 | C22 | 1 | 7 | yes | complemented |
| 6 | C2×#60399 | C22 | 1 | 14 | yes | complemented |
| 7 | C22×#2846 | C22 | 1 | 7 | yes | complemented |
| 8 | C2×#32700 | C22 | 1 | 168 | yes | complemented |
| 9 | #7266798 | C22 | 1 | 1344 | yes | complemented |
| 10 | C2×#32873 | C22 | 1 | 14 | yes | complemented |
| 11 | #6499874 | C22 | 1 | 448 | yes | complemented |
| 12 | #6499867 | C22 | 1 | 224 | yes | complemented |
| 13 | C2×#23984 | C22 | 1 | 84 | yes | complemented |
| 14 | C2×#23996 | C22 | 1 | 168 | yes | complemented |
| 15 | C2×#23895 | C22 | 1 | 42 | yes | complemented |
| 16 | C2×#23900 | C22 | 1 | 84 | yes | complemented |
| 17 | C2×#21776 | C22 | 1 | 42 | yes | complemented |
| 18 | C2×#21746 | C22 | 1 | 21 | yes | complemented |
| 19 | C28 | C23 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×H(7,𝔽2) | C23 | 1 | 2 | yes | complemented |
| 21 | #62817 | — | 4 | 84 | no | — |
| 22 | #62817 | C23 | 1 | 112 | yes | complemented |
| 23 | C2×#3490 | — | 4 | 21 | no | — |
| 24 | C2×#3490 | C23 | 1 | 42 | yes | — |
| 25 | C2×#3484 | — | 4 | 21 | no | — |
| 26 | C2×#3484 | C23 | 1 | 42 | yes | — |
| 27 | C2×#3532 | — | 4 | 42 | no | — |
| 28 | C23×#120 | — | 4 | 7 | no | — |
| 29 | C23×#120 | C23 | 1 | 21 | yes | — |
| 30 | #60399 | — | 4 | 56 | no | — |
| 31 | #60399 | C23 | 1 | 224 | yes | complemented |
| 32 | C2×#3027 | — | 4 | 14 | no | — |
| 33 | C2×#3026 | — | 4 | 14 | no | — |
| 34 | C2×#3026 | C23 | 1 | 56 | yes | complemented |
| 35 | C2×#3025 | — | 4 | 14 | no | — |
| 36 | C22×B(4,𝔽2) | — | 4 | 14 | no | — |
| 37 | C22×B(4,𝔽2) | C23 | 1 | 56 | yes | complemented |
| 38 | C2×#2883 | C23 | 1 | 42 | yes | complemented |
| 39 | C2×#2846 | — | 4 | 28 | no | — |
| 40 | C2×#2846 | — | 4 | 14 | no | — |
| 41 | C2×#2846 | C23 | 1 | 56 | yes | complemented |
| 42 | C2×#2846 | C23 | 1 | 112 | yes | complemented |
| 43 | C22×#379 | — | 4 | 7 | no | — |
| 44 | C22×#379 | C23 | 1 | 21 | yes | complemented |
| 45 | #32873 | C23 | 1 | 224 | yes | complemented |
| 46 | #32700 | C23 | 1 | 2688 | yes | complemented |
| 47 | #23996 | C23 | 1 | 2688 | yes | complemented |
| 48 | #23984 | C23 | 1 | 1344 | yes | complemented |
| 49 | #23900 | C23 | 1 | 1344 | yes | complemented |
| 50 | #23895 | C23 | 1 | 672 | yes | complemented |
| 51 | C2×#2104 | C23 | 1 | 48 | yes | complemented |
| 52 | C2×#2032 | C23 | 1 | 112 | yes | complemented |
| 53 | C2×#2029 | C23 | 1 | 56 | yes | complemented |
| 54 | C2×#2021 | C23 | 1 | 168 | yes | — |
| 55 | #21776 | C23 | 1 | 672 | yes | complemented |
| 56 | #21746 | C23 | 1 | 336 | yes | complemented |
| 57 | C2×#1913 | C23 | 1 | 168 | yes | complemented |
| 58 | C2×#1898 | C23 | 1 | 168 | yes | complemented |
| 59 | C2×#1889 | C23 | 1 | 168 | yes | complemented |
| 60 | C2×#1828 | C23 | 1 | 84 | yes | complemented |
| 61 | C2×#1819 | C23 | 1 | 42 | yes | complemented |
| 62 | C2×#1781 | C23 | 1 | 42 | yes | — |
| 63 | C27 | — | 4 | 7 | no | — |
| 64 | C27 | — | 4 | 7 | no | — |
| 65 | C27 | — | 4 | 14 | no | — |
| 66 | C27 | — | 8 | 16 | no | — |
| 67 | C27 | C24 | 1 | 7 | yes | — |
| 68 | C27 | C24 | 1 | 8 | yes | complemented |
| 69 | H(7,𝔽2) | — | 4 | 28 | no | — |
| 70 | H(7,𝔽2) | C24 | 1 | 16 | yes | complemented |
| 71 | C2×#585 | — | 4 | 14 | no | — |
| 72 | C22×H(5,𝔽2) | — | 4 | 14 | no | — |
| 73 | C22×H(5,𝔽2) | — | 4 | 7 | no | — |
| 74 | C22×H(5,𝔽2) | C24 | 1 | 14 | yes | — |
| 75 | C24×D4 | — | 2 | 21 | no | — |
| 76 | C24×D4 | C24 | 1 | 7 | yes | — |
| 77 | #3532 | — | 4 | 672 | no | — |
| 78 | #3532 | — | 4 | 672 | no | — |
| 79 | C2×H(3,𝔽4) | — | 4 | 14 | no | — |
| 80 | C2×#560 | — | 4 | 42 | no | — |
| 81 | #3490 | — | 4 | 84 | no | — |
| 82 | #3490 | — | 4 | 336 | no | — |
| 83 | #3490 | — | 4 | 168 | no | — |
| 84 | #3490 | — | 4 | 336 | no | — |
| 85 | #3490 | C24 | 1 | 336 | yes | — |
| 86 | #3484 | — | 2 | 168 | no | — |
| 87 | #3484 | — | 4 | 336 | no | — |
| 88 | #3484 | — | 4 | 168 | no | — |
| 89 | #3484 | — | 4 | 336 | no | — |
| 90 | #3484 | C24 | 1 | 336 | yes | — |
| 91 | C2×#551 | — | 4 | 84 | no | — |
| 92 | C2×#551 | — | 4 | 42 | no | — |
| 93 | C2×#546 | — | 4 | 84 | no | — |
| 94 | C2×#546 | — | 4 | 84 | no | — |
| 95 | C2×#546 | — | 4 | 84 | no | — |
| 96 | C2×D42 | — | 4 | 84 | no | — |
| 97 | C2×D42 | — | 4 | 42 | no | — |
| 98 | C2×#543 | — | 4 | 7 | no | — |
| 99 | C2×#543 | C24 | 1 | 14 | yes | — |
| 100 | C2×#538 | — | 4 | 42 | no | — |
| 101 | C2×#538 | — | 4 | 42 | no | — |
| 102 | C2×#538 | — | 4 | 42 | no | — |
| 103 | C2×#535 | — | 2 | 42 | no | — |
| 104 | C2×#535 | — | 4 | 42 | no | — |
| 105 | C2×#534 | — | 2 | 42 | no | — |
| 106 | C2×#534 | — | 4 | 21 | no | — |
| 107 | C2×#534 | — | 4 | 42 | no | — |
| 108 | C2×#534 | C24 | 1 | 42 | yes | — |
| 109 | C2×#525 | — | 2 | 42 | no | — |
| 110 | C2×#525 | — | 4 | 42 | no | — |
| 111 | C22×#120 | — | 2 | 84 | no | — |
| 112 | C22×#120 | — | 2 | 42 | no | — |
| 113 | C22×#120 | — | 2 | 42 | no | — |
| 114 | C22×#120 | — | 4 | 42 | no | — |
| 115 | C22×#120 | — | 4 | 84 | no | — |
| 116 | C22×#120 | — | 4 | 42 | no | — |
| 117 | C22×#120 | — | 4 | 56 | no | — |
| 118 | C22×#120 | — | 4 | 112 | no | — |
| 119 | C22×#120 | — | 8 | 112 | no | — |
| 120 | C22×#120 | C24 | 1 | 84 | yes | — |
| 121 | C22×#120 | C24 | 1 | 168 | yes | — |
| 122 | C2×#518 | — | 4 | 21 | no | — |
| 123 | C2×#518 | C24 | 1 | 42 | yes | — |
| 124 | C23×C22⋊C4 | — | 2 | 21 | no | — |
| 125 | C23×C22⋊C4 | — | 4 | 21 | no | — |
| 126 | C23×C22⋊C4 | C24 | 1 | 21 | yes | — |
| 127 | #3027 | — | 4 | 224 | no | — |
| 128 | #3026 | — | 4 | 224 | no | — |
| 129 | #3026 | — | 4 | 112 | no | — |
| 130 | #3026 | C24 | 1 | 448 | yes | complemented |
| 131 | #3025 | — | 4 | 224 | no | — |
| 132 | C2×#458 | — | 4 | 56 | no | — |
| 133 | C2×B(4,𝔽2) | — | 4 | 56 | no | — |
| 134 | C2×B(4,𝔽2) | — | 4 | 56 | no | — |
| 135 | C2×B(4,𝔽2) | — | 4 | 224 | no | — |
| 136 | C2×B(4,𝔽2) | — | 4 | 56 | no | — |
| 137 | C2×B(4,𝔽2) | — | 4 | 112 | no | — |
| 138 | C2×B(4,𝔽2) | C24 | 1 | 448 | yes | complemented |
| 139 | #2883 | — | 4 | 84 | no | — |
| 140 | #2883 | C24 | 1 | 336 | yes | complemented |
| 141 | C2×#410 | — | 4 | 42 | no | — |
| 142 | C22×#99 | — | 4 | 42 | no | — |
| 143 | C22×#99 | C24 | 1 | 168 | yes | — |
| 144 | #2846 | — | 4 | 112 | no | — |
| 145 | #2846 | — | 4 | 224 | no | — |
| 146 | #2846 | C24 | 1 | 448 | yes | complemented |
| 147 | C2×#379 | — | 4 | 56 | no | — |
| 148 | C2×#379 | — | 4 | 112 | no | — |
| 149 | C2×#379 | — | 4 | 21 | no | — |
| 150 | C2×#379 | — | 4 | 42 | no | — |
| 151 | C2×#379 | C24 | 1 | 84 | yes | — |
| 152 | C2×#379 | C24 | 1 | 168 | yes | complemented |
| 153 | #2104 | C24 | 1 | 384 | yes | complemented |
| 154 | #2032 | C24 | 1 | 896 | yes | complemented |
| 155 | #2029 | C24 | 1 | 448 | yes | complemented |
| 156 | #2021 | C24 | 1 | 1344 | yes | — |
| 157 | #1913 | C24 | 1 | 1344 | yes | complemented |
| 158 | #1898 | C24 | 1 | 1344 | yes | complemented |
| 159 | #1889 | C24 | 1 | 1344 | yes | complemented |
| 160 | #1828 | C24 | 1 | 672 | yes | complemented |
| 161 | #1819 | C24 | 1 | 336 | yes | complemented |
| 162 | #1781 | C24 | 1 | 336 | yes | — |
| 163 | C2×#342 | C24 | 1 | 168 | yes | — |
| 164 | C26 | — | 2 | 21 | no | — |
| 165 | C26 | — | 2 | 21 | no | — |
| 166 | C26 | — | 2 | 42 | no | — |
| 167 | C26 | — | 4 | 28 | no | — |
| 168 | C26 | — | 4 | 56 | no | — |
| 169 | C26 | — | 4 | 28 | no | — |
| 170 | C26 | — | 4 | 56 | no | — |
| 171 | C26 | — | 4 | 112 | no | — |
| 172 | C26 | — | 8 | 7 | no | — |
| 173 | C26 | — | 8 | 21 | no | — |
| 174 | C26 | — | 8 | 84 | no | — |
| 175 | C26 | — | 8 | 21 | no | — |
| 176 | C26 | — | 8 | 84 | no | — |
| 177 | C26 | — | 8 | 7 | no | — |
| 178 | C26 | — | 8 | 56 | no | — |
| 179 | C26 | — | 8 | 64 | no | — |
| 180 | C26 | — | 8 | 168 | no | — |
| 181 | C26 | — | 8 | 224 | no | — |
| 182 | C26 | — | 8 | 448 | no | — |
| 183 | C26 | H(5,𝔽2) | 1 | 7 | yes | complemented |
| 184 | C26 | C25 | 1 | 7 | yes | — |
| 185 | C26 | C25 | 1 | 28 | yes | — |
| 186 | #585 | — | 4 | 112 | no | — |
| 187 | #585 | — | 8 | 168 | no | — |
| 188 | C2×2−1+4 | — | 8 | 14 | no | — |
| 189 | C2×H(5,𝔽2) | — | 2 | 84 | no | — |
| 190 | C2×H(5,𝔽2) | — | 4 | 56 | no | — |
| 191 | C2×H(5,𝔽2) | — | 4 | 112 | no | — |
| 192 | C2×H(5,𝔽2) | — | 4 | 56 | no | — |
| 193 | C2×H(5,𝔽2) | — | 4 | 112 | no | — |
| 194 | C2×H(5,𝔽2) | — | 8 | 42 | no | — |
| 195 | C2×H(5,𝔽2) | — | 8 | 168 | no | — |
| 196 | C2×H(5,𝔽2) | — | 16 | 56 | no | — |
| 197 | C2×H(5,𝔽2) | C25 | 1 | 56 | yes | — |
| 198 | C22×#41 | — | 2 | 42 | no | — |
| 199 | C22×#41 | — | 4 | 42 | no | — |
| 200 | C22×#41 | — | 8 | 42 | no | — |
| 201 | C23×D4 | — | 2 | 42 | no | — |
| 202 | C23×D4 | — | 2 | 84 | no | — |
| 203 | C23×D4 | — | 2 | 168 | no | — |
| 204 | C23×D4 | — | 4 | 42 | no | — |
| 205 | C23×D4 | — | 4 | 42 | no | — |
| 206 | C23×D4 | — | 4 | 21 | no | — |
| 207 | C23×D4 | — | 4 | 21 | no | — |
| 208 | C23×D4 | — | 4 | 42 | no | — |
| 209 | C23×D4 | — | 4 | 84 | no | — |
| 210 | C23×D4 | — | 4 | 42 | no | — |
| 211 | C23×D4 | — | 8 | 14 | no | — |
| 212 | C23×D4 | — | 8 | 168 | no | — |
| 213 | C23×D4 | H(5,𝔽2) | 1 | 14 | yes | complemented |
| 214 | C23×D4 | H(5,𝔽2) | 1 | 28 | yes | complemented |
| 215 | C23×D4 | C25 | 1 | 14 | yes | — |
| 216 | C23×D4 | C25 | 1 | 28 | yes | — |
| 217 | C24×C4 | — | 2 | 21 | no | — |
| 218 | C24×C4 | H(5,𝔽2) | 1 | 7 | yes | complemented |
| 219 | H(3,𝔽4) | — | 4 | 224 | no | — |
| 220 | #560 | — | 4 | 672 | no | — |
| 221 | #551 | — | 4 | 672 | no | — |
| 222 | #551 | — | 4 | 672 | no | — |
| 223 | #551 | — | 4 | 672 | no | — |
| 224 | #546 | — | 4 | 672 | no | — |
| 225 | #546 | — | 4 | 672 | no | — |
| 226 | #546 | — | 4 | 672 | no | — |
| 227 | #546 | — | 4 | 1344 | no | — |
| 228 | #546 | — | 4 | 672 | no | — |
| 229 | D42 | — | 4 | 672 | no | — |
| 230 | D42 | — | 4 | 672 | no | — |
| 231 | D42 | — | 4 | 672 | no | — |
| 232 | #543 | — | 4 | 42 | no | — |
| 233 | #543 | — | 4 | 112 | no | — |
| 234 | #543 | C25 | 1 | 56 | yes | — |
| 235 | #538 | — | 4 | 336 | no | — |
| 236 | #538 | — | 4 | 672 | no | — |
| 237 | #538 | — | 4 | 336 | no | — |
| 238 | #538 | — | 4 | 672 | no | — |
| 239 | #535 | — | 2 | 336 | no | — |
| 240 | #535 | — | 4 | 168 | no | — |
| 241 | #535 | — | 4 | 672 | no | — |
| 242 | #534 | — | 2 | 168 | no | — |
| 243 | #534 | — | 2 | 336 | no | — |
| 244 | #534 | — | 4 | 42 | no | — |
| 245 | #534 | — | 4 | 168 | no | — |
| 246 | #534 | — | 4 | 336 | no | — |
| 247 | #534 | — | 4 | 672 | no | — |
| 248 | #534 | C25 | 1 | 168 | yes | — |
| 249 | C2×#127 | — | 4 | 42 | no | — |
| 250 | C2×#126 | — | 4 | 84 | no | — |
| 251 | C2×#124 | — | 4 | 42 | no | — |
| 252 | C2×#124 | — | 4 | 84 | no | — |
| 253 | #525 | — | 2 | 336 | no | — |
| 254 | #525 | — | 4 | 336 | no | — |
| 255 | #525 | — | 4 | 168 | no | — |
| 256 | #525 | — | 4 | 336 | no | — |
| 257 | C2×#123 | — | 2 | 84 | no | — |
| 258 | C2×#123 | — | 4 | 42 | no | — |
| 259 | C2×#123 | — | 4 | 84 | no | — |
| 260 | C2×#123 | — | 4 | 84 | no | — |
| 261 | C2×C22⋊Q8 | — | 4 | 42 | no | — |
| 262 | C2×C22⋊Q8 | — | 4 | 42 | no | — |
| 263 | C2×C22⋊Q8 | — | 4 | 42 | no | — |
| 264 | C2×#121 | — | 4 | 42 | no | — |
| 265 | C2×#121 | — | 4 | 84 | no | — |
| 266 | C2×#121 | — | 4 | 42 | no | — |
| 267 | C2×#121 | — | 4 | 84 | no | — |
| 268 | C2×#121 | — | 4 | 42 | no | — |
| 269 | C2×#121 | — | 4 | 84 | no | — |
| 270 | C2×#120 | — | 2 | 168 | no | — |
| 271 | C2×#120 | — | 2 | 336 | no | — |
| 272 | C2×#120 | — | 2 | 84 | no | — |
| 273 | C2×#120 | — | 2 | 84 | no | — |
| 274 | C2×#120 | — | 2 | 84 | no | — |
| 275 | C2×#120 | — | 2 | 168 | no | — |
| 276 | C2×#120 | — | 2 | 336 | no | — |
| 277 | C2×#120 | — | 4 | 84 | no | — |
| 278 | C2×#120 | — | 4 | 84 | no | — |
| 279 | C2×#120 | — | 4 | 336 | no | — |
| 280 | C2×#120 | — | 4 | 336 | no | — |
| 281 | C2×#120 | — | 4 | 84 | no | — |
| 282 | C2×#120 | — | 4 | 168 | no | — |
| 283 | C2×#120 | — | 4 | 84 | no | — |
| 284 | C2×#120 | — | 4 | 42 | no | — |
| 285 | C2×#120 | — | 4 | 336 | no | — |
| 286 | C2×#120 | — | 4 | 42 | no | — |
| 287 | C2×#120 | — | 4 | 168 | no | — |
| 288 | C2×#120 | — | 4 | 336 | no | — |
| 289 | C2×#120 | — | 4 | 42 | no | — |
| 290 | C2×#120 | — | 4 | 448 | no | — |
| 291 | C2×#120 | — | 8 | 448 | no | — |
| 292 | C2×#120 | — | 8 | 896 | no | — |
| 293 | C2×#120 | C25 | 1 | 336 | yes | — |
| 294 | #518 | — | 2 | 84 | no | — |
| 295 | #518 | — | 4 | 84 | no | — |
| 296 | #518 | — | 4 | 336 | no | — |
| 297 | #518 | C25 | 1 | 168 | yes | — |
| 298 | C2×C4×D4 | — | 4 | 84 | no | — |
| 299 | C2×C4×D4 | — | 4 | 84 | no | — |
| 300 | C2×C4×D4 | — | 4 | 84 | no | — |
| 301 | C2×#117 | — | 2 | 42 | no | — |
| 302 | C2×#117 | — | 4 | 42 | no | — |
| 303 | C22×C22⋊C4 | — | 2 | 42 | no | — |
| 304 | C22×C22⋊C4 | — | 2 | 21 | no | — |
| 305 | C22×C22⋊C4 | — | 2 | 42 | no | — |
| 306 | C22×C22⋊C4 | — | 2 | 84 | no | — |
| 307 | C22×C22⋊C4 | — | 2 | 168 | no | — |
| 308 | C22×C22⋊C4 | — | 4 | 42 | no | — |
| 309 | C22×C22⋊C4 | — | 4 | 42 | no | — |
| 310 | C22×C22⋊C4 | — | 4 | 42 | no | — |
| 311 | C22×C22⋊C4 | — | 4 | 21 | no | — |
| 312 | C22×C22⋊C4 | — | 4 | 21 | no | — |
| 313 | C22×C22⋊C4 | — | 4 | 42 | no | — |
| 314 | C22×C22⋊C4 | — | 4 | 84 | no | — |
| 315 | C22×C22⋊C4 | — | 4 | 84 | no | — |
| 316 | C22×C22⋊C4 | — | 4 | 168 | no | — |
| 317 | C22×C22⋊C4 | — | 8 | 168 | no | — |
| 318 | C22×C22⋊C4 | C25 | 1 | 42 | yes | — |
| 319 | C22×C22⋊C4 | C25 | 1 | 84 | yes | — |
| 320 | #458 | — | 4 | 448 | no | — |
| 321 | B(4,𝔽2) | — | 4 | 448 | no | — |
| 322 | B(4,𝔽2) | — | 4 | 448 | no | — |
| 323 | B(4,𝔽2) | — | 4 | 448 | no | — |
| 324 | #410 | — | 4 | 336 | no | — |
| 325 | C2×#99 | — | 4 | 168 | no | — |
| 326 | C2×#99 | — | 4 | 336 | no | — |
| 327 | C2×#99 | — | 4 | 168 | no | — |
| 328 | C2×#99 | C25 | 1 | 672 | yes | — |
| 329 | #379 | — | 4 | 448 | no | — |
| 330 | #379 | — | 4 | 84 | no | — |
| 331 | #379 | — | 4 | 168 | no | — |
| 332 | #379 | C25 | 1 | 336 | yes | — |
| 333 | #342 | C25 | 1 | 672 | yes | — |
| 334 | C25 | — | 2 | 7 | no | — |
| 335 | C25 | — | 2 | 21 | no | — |
| 336 | C25 | — | 2 | 84 | no | — |
| 337 | C25 | — | 2 | 21 | no | — |
| 338 | C25 | — | 2 | 84 | no | — |
| 339 | C25 | — | 2 | 7 | no | — |
| 340 | C25 | — | 2 | 14 | no | — |
| 341 | C25 | — | 2 | 42 | no | — |
| 342 | C25 | — | 2 | 84 | no | — |
| 343 | C25 | — | 2 | 42 | no | — |
| 344 | C25 | — | 2 | 84 | no | — |
| 345 | C25 | — | 4 | 112 | no | — |
| 346 | C25 | — | 4 | 21 | no | — |
| 347 | C25 | — | 4 | 21 | no | — |
| 348 | C25 | — | 4 | 168 | no | — |
| 349 | C25 | — | 4 | 224 | no | — |
| 350 | C25 | — | 4 | 448 | no | — |
| 351 | C25 | — | 8 | 42 | no | — |
| 352 | C25 | — | 8 | 42 | no | — |
| 353 | C25 | — | 8 | 42 | no | — |
| 354 | C25 | — | 8 | 168 | no | — |
| 355 | C25 | — | 8 | 42 | no | — |
| 356 | C25 | — | 8 | 56 | no | — |
| 357 | C25 | — | 8 | 112 | no | — |
| 358 | C25 | — | 8 | 168 | no | — |
| 359 | C25 | — | 8 | 168 | no | — |
| 360 | C25 | — | 8 | 56 | no | — |
| 361 | C25 | — | 8 | 28 | no | — |
| 362 | C25 | — | 8 | 112 | no | — |
| 363 | C25 | — | 8 | 84 | no | — |
| 364 | C25 | — | 8 | 168 | no | — |
| 365 | C25 | — | 8 | 336 | no | — |
| 366 | C25 | — | 8 | 336 | no | — |
| 367 | C25 | — | 8 | 672 | no | — |
| 368 | C25 | — | 8 | 672 | no | — |
| 369 | C25 | — | 8 | 336 | no | — |
| 370 | C25 | — | 8 | 1344 | no | — |
| 371 | C25 | — | 8 | 448 | no | — |
| 372 | C25 | — | 8 | 896 | no | — |
| 373 | C25 | — | 8 | 28 | no | — |
| 374 | C25 | — | 8 | 56 | no | — |
| 375 | C25 | — | 8 | 168 | no | — |
| 376 | C25 | — | 8 | 168 | no | — |
| 377 | C25 | — | 8 | 7 | no | — |
| 378 | C25 | — | 8 | 28 | no | — |
| 379 | C25 | — | 8 | 7 | no | — |
| 380 | C25 | — | 8 | 21 | no | — |
| 381 | C25 | — | 8 | 56 | no | — |
| 382 | C25 | — | 8 | 1 | no | — |
| 383 | C25 | — | 8 | 112 | no | — |
| 384 | C25 | — | 8 | 336 | no | — |
| 385 | C25 | — | 8 | 1344 | no | — |
| 386 | C25 | — | 8 | 224 | no | — |
| 387 | C25 | — | 8 | 2688 | no | — |
| 388 | C25 | — | 8 | 2 | no | — |
| 389 | C25 | C2×H(5,𝔽2) | 1 | 7 | yes | — |
| 390 | C25 | C2×H(5,𝔽2) | 1 | 7 | yes | — |
| 391 | C25 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 392 | C25 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 393 | C25 | C2×H(5,𝔽2) | 1 | 28 | yes | complemented |
| 394 | C25 | C26 | 1 | 14 | yes | — |
| 395 | C25 | C26 | 1 | 1 | yes | characteristic |
| 396 | 2−1+4 | — | 8 | 112 | no | — |
| 397 | 2−1+4 | — | 8 | 112 | no | — |
| 398 | H(5,𝔽2) | — | 4 | 224 | no | — |
| 399 | H(5,𝔽2) | — | 8 | 336 | no | — |
| 400 | H(5,𝔽2) | — | 8 | 336 | no | — |
| 401 | H(5,𝔽2) | — | 8 | 336 | no | — |
| 402 | H(5,𝔽2) | — | 16 | 448 | no | — |
| 403 | C2×#41 | — | 2 | 168 | no | — |
| 404 | C2×#41 | — | 2 | 168 | no | — |
| 405 | C2×#41 | — | 4 | 336 | no | — |
| 406 | C2×#41 | — | 8 | 84 | no | — |
| 407 | C2×#41 | — | 8 | 84 | no | — |
| 408 | C2×#41 | — | 8 | 336 | no | — |
| 409 | C2×#41 | — | 8 | 56 | no | — |
| 410 | C2×#41 | — | 8 | 336 | no | — |
| 411 | C2×#41 | — | 16 | 168 | no | — |
| 412 | C22×Q8 | — | 2 | 14 | no | — |
| 413 | C22×Q8 | — | 4 | 14 | no | — |
| 414 | C22×Q8 | — | 8 | 14 | no | — |
| 415 | C22×D4 | — | 2 | 84 | no | — |
| 416 | C22×D4 | — | 2 | 84 | no | — |
| 417 | C22×D4 | — | 2 | 42 | no | — |
| 418 | C22×D4 | — | 2 | 168 | no | — |
| 419 | C22×D4 | — | 2 | 168 | no | — |
| 420 | C22×D4 | — | 2 | 336 | no | — |
| 421 | C22×D4 | — | 4 | 42 | no | — |
| 422 | C22×D4 | — | 4 | 42 | no | — |
| 423 | C22×D4 | — | 4 | 168 | no | — |
| 424 | C22×D4 | — | 4 | 168 | no | — |
| 425 | C22×D4 | — | 4 | 84 | no | — |
| 426 | C22×D4 | — | 4 | 168 | no | — |
| 427 | C22×D4 | — | 4 | 42 | no | — |
| 428 | C22×D4 | — | 4 | 84 | no | — |
| 429 | C22×D4 | — | 4 | 168 | no | — |
| 430 | C22×D4 | — | 4 | 336 | no | — |
| 431 | C22×D4 | — | 4 | 168 | no | — |
| 432 | C22×D4 | — | 4 | 336 | no | — |
| 433 | C22×D4 | — | 8 | 84 | no | — |
| 434 | C22×D4 | — | 8 | 84 | no | — |
| 435 | C22×D4 | — | 8 | 168 | no | — |
| 436 | C22×D4 | — | 8 | 112 | no | — |
| 437 | C22×D4 | — | 8 | 42 | no | — |
| 438 | C22×D4 | — | 8 | 112 | no | — |
| 439 | C22×D4 | — | 8 | 336 | no | — |
| 440 | C22×D4 | — | 8 | 672 | no | — |
| 441 | C22×D4 | — | 16 | 84 | no | — |
| 442 | C22×D4 | — | 16 | 28 | no | — |
| 443 | C22×D4 | — | 16 | 84 | no | — |
| 444 | C22×D4 | — | 16 | 168 | no | — |
| 445 | C22×D4 | — | 16 | 336 | no | — |
| 446 | C22×D4 | — | 16 | 168 | no | — |
| 447 | C22×D4 | C2×H(5,𝔽2) | 1 | 28 | yes | — |
| 448 | C22×D4 | C2×H(5,𝔽2) | 1 | 56 | yes | complemented |
| 449 | C22×D4 | C26 | 1 | 28 | yes | — |
| 450 | C23×C4 | — | 2 | 42 | no | — |
| 451 | C23×C4 | — | 2 | 42 | no | — |
| 452 | C23×C4 | — | 2 | 84 | no | — |
| 453 | C23×C4 | — | 4 | 21 | no | — |
| 454 | C23×C4 | — | 4 | 21 | no | — |
| 455 | C23×C4 | — | 4 | 21 | no | — |
| 456 | C23×C4 | — | 4 | 42 | no | — |
| 457 | C23×C4 | — | 4 | 21 | no | — |
| 458 | C23×C4 | — | 4 | 42 | no | — |
| 459 | C23×C4 | — | 8 | 14 | no | — |
| 460 | C23×C4 | — | 8 | 84 | no | — |
| 461 | C23×C4 | C2×H(5,𝔽2) | 1 | 14 | yes | — |
| 462 | C23×C4 | C2×H(5,𝔽2) | 1 | 28 | yes | complemented |
| 463 | #127 | — | 4 | 336 | no | — |
| 464 | #126 | — | 4 | 672 | no | — |
| 465 | #124 | — | 4 | 336 | no | — |
| 466 | #124 | — | 4 | 672 | no | — |
| 467 | #123 | — | 2 | 336 | no | — |
| 468 | #123 | — | 4 | 168 | no | — |
| 469 | #123 | — | 4 | 336 | no | — |
| 470 | #123 | — | 4 | 672 | no | — |
| 471 | #123 | — | 4 | 672 | no | — |
| 472 | C22⋊Q8 | — | 4 | 168 | no | — |
| 473 | C22⋊Q8 | — | 4 | 336 | no | — |
| 474 | C22⋊Q8 | — | 4 | 336 | no | — |
| 475 | C22⋊Q8 | — | 4 | 168 | no | — |
| 476 | #121 | — | 4 | 168 | no | — |
| 477 | #121 | — | 4 | 672 | no | — |
| 478 | #121 | — | 4 | 168 | no | — |
| 479 | #121 | — | 4 | 336 | no | — |
| 480 | #121 | — | 4 | 672 | no | — |
| 481 | #121 | — | 4 | 336 | no | — |
| 482 | #121 | — | 4 | 672 | no | — |
| 483 | #120 | — | 2 | 336 | no | — |
| 484 | #120 | — | 2 | 336 | no | — |
| 485 | #120 | — | 2 | 336 | no | — |
| 486 | #120 | — | 4 | 336 | no | — |
| 487 | #120 | — | 4 | 168 | no | — |
| 488 | #120 | — | 4 | 168 | no | — |
| 489 | #120 | — | 4 | 336 | no | — |
| 490 | #120 | — | 4 | 168 | no | — |
| 491 | #120 | — | 4 | 672 | no | — |
| 492 | #120 | — | 4 | 672 | no | — |
| 493 | #120 | — | 4 | 336 | no | — |
| 494 | #120 | — | 4 | 336 | no | — |
| 495 | #120 | — | 4 | 336 | no | — |
| 496 | #120 | — | 8 | 1792 | no | — |
| 497 | C4×D4 | — | 4 | 336 | no | — |
| 498 | C4×D4 | — | 4 | 672 | no | — |
| 499 | C4×D4 | — | 4 | 336 | no | — |
| 500 | C4×D4 | — | 4 | 672 | no | — |
| 501 | #117 | — | 2 | 168 | no | — |
| 502 | #117 | — | 4 | 84 | no | — |
| 503 | #117 | — | 4 | 336 | no | — |
| 504 | C2×C4⋊C4 | — | 4 | 42 | no | — |
| 505 | C2×C4⋊C4 | — | 4 | 42 | no | — |
| 506 | C2×C4⋊C4 | — | 4 | 42 | no | — |
| 507 | C2×C22⋊C4 | — | 2 | 84 | no | — |
| 508 | C2×C22⋊C4 | — | 2 | 168 | no | — |
| 509 | C2×C22⋊C4 | — | 2 | 84 | no | — |
| 510 | C2×C22⋊C4 | — | 2 | 42 | no | — |
| 511 | C2×C22⋊C4 | — | 2 | 84 | no | — |
| 512 | C2×C22⋊C4 | — | 2 | 336 | no | — |
| 513 | C2×C22⋊C4 | — | 4 | 168 | no | — |
| 514 | C2×C22⋊C4 | — | 4 | 84 | no | — |
| 515 | C2×C22⋊C4 | — | 4 | 84 | no | — |
| 516 | C2×C22⋊C4 | — | 4 | 168 | no | — |
| 517 | C2×C22⋊C4 | — | 4 | 84 | no | — |
| 518 | C2×C22⋊C4 | — | 4 | 336 | no | — |
| 519 | C2×C22⋊C4 | — | 4 | 168 | no | — |
| 520 | C2×C22⋊C4 | — | 4 | 42 | no | — |
| 521 | C2×C22⋊C4 | — | 4 | 168 | no | — |
| 522 | C2×C22⋊C4 | — | 4 | 42 | no | — |
| 523 | C2×C22⋊C4 | — | 4 | 336 | no | — |
| 524 | C2×C22⋊C4 | — | 4 | 168 | no | — |
| 525 | C2×C22⋊C4 | — | 4 | 42 | no | — |
| 526 | C2×C22⋊C4 | — | 4 | 84 | no | — |
| 527 | C2×C22⋊C4 | — | 4 | 336 | no | — |
| 528 | C2×C22⋊C4 | — | 8 | 336 | no | — |
| 529 | C2×C22⋊C4 | — | 8 | 672 | no | — |
| 530 | C2×C22⋊C4 | C26 | 1 | 84 | yes | — |
| 531 | C2×C42 | — | 4 | 42 | no | — |
| 532 | #99 | — | 4 | 672 | no | — |
| 533 | C24 | — | 2 | 28 | no | — |
| 534 | C24 | — | 2 | 56 | no | — |
| 535 | C24 | — | 2 | 21 | no | — |
| 536 | C24 | — | 2 | 84 | no | — |
| 537 | C24 | — | 2 | 84 | no | — |
| 538 | C24 | — | 2 | 28 | no | — |
| 539 | C24 | — | 2 | 56 | no | — |
| 540 | C24 | — | 2 | 21 | no | — |
| 541 | C24 | — | 2 | 21 | no | — |
| 542 | C24 | — | 2 | 84 | no | — |
| 543 | C24 | — | 2 | 84 | no | — |
| 544 | C24 | — | 2 | 42 | no | — |
| 545 | C24 | — | 2 | 21 | no | — |
| 546 | C24 | — | 2 | 42 | no | — |
| 547 | C24 | — | 4 | 28 | no | — |
| 548 | C24 | — | 4 | 84 | no | — |
| 549 | C24 | — | 4 | 168 | no | — |
| 550 | C24 | — | 4 | 336 | no | — |
| 551 | C24 | — | 4 | 168 | no | — |
| 552 | C24 | — | 4 | 84 | no | — |
| 553 | C24 | — | 4 | 336 | no | — |
| 554 | C24 | — | 4 | 84 | no | — |
| 555 | C24 | — | 4 | 28 | no | — |
| 556 | C24 | — | 4 | 448 | no | — |
| 557 | C24 | — | 8 | 168 | no | — |
| 558 | C24 | — | 8 | 168 | no | — |
| 559 | C24 | — | 8 | 336 | no | — |
| 560 | C24 | — | 8 | 448 | no | — |
| 561 | C24 | — | 8 | 84 | no | — |
| 562 | C24 | — | 8 | 14 | no | — |
| 563 | C24 | — | 8 | 28 | no | — |
| 564 | C24 | — | 8 | 28 | no | — |
| 565 | C24 | — | 8 | 2 | no | — |
| 566 | C24 | — | 8 | 84 | no | — |
| 567 | C24 | — | 8 | 168 | no | — |
| 568 | C24 | — | 8 | 14 | no | — |
| 569 | C24 | — | 8 | 168 | no | — |
| 570 | C24 | — | 8 | 42 | no | — |
| 571 | C24 | — | 8 | 168 | no | — |
| 572 | C24 | — | 8 | 336 | no | — |
| 573 | C24 | — | 8 | 28 | no | — |
| 574 | C24 | — | 8 | 336 | no | — |
| 575 | C24 | — | 8 | 7 | no | — |
| 576 | C24 | — | 8 | 21 | no | — |
| 577 | C24 | — | 8 | 168 | no | — |
| 578 | C24 | — | 8 | 21 | no | — |
| 579 | C24 | — | 8 | 7 | no | — |
| 580 | C24 | — | 8 | 21 | no | — |
| 581 | C24 | — | 8 | 21 | no | — |
| 582 | C24 | — | 8 | 168 | no | — |
| 583 | C24 | — | 8 | 7 | no | — |
| 584 | C24 | — | 8 | 7 | no | — |
| 585 | C24 | — | 8 | 14 | no | — |
| 586 | C24 | — | 8 | 14 | no | — |
| 587 | C24 | — | 8 | 336 | no | — |
| 588 | C24 | — | 8 | 672 | no | — |
| 589 | C24 | — | 8 | 672 | no | — |
| 590 | C24 | — | 8 | 672 | no | — |
| 591 | C24 | — | 8 | 1344 | no | — |
| 592 | C24 | — | 8 | 2688 | no | — |
| 593 | C24 | — | 8 | 1344 | no | — |
| 594 | C24 | — | 8 | 28 | no | — |
| 595 | C24 | — | 8 | 56 | no | — |
| 596 | C24 | — | 8 | 56 | no | — |
| 597 | C24 | — | 8 | 224 | no | — |
| 598 | C24 | — | 8 | 56 | no | — |
| 599 | C24 | — | 8 | 168 | no | — |
| 600 | C24 | — | 8 | 8 | no | — |
| 601 | C24 | — | 8 | 112 | no | — |
| 602 | C24 | — | 8 | 672 | no | — |
| 603 | C24 | — | 8 | 448 | no | — |
| 604 | C24 | — | 8 | 1344 | no | — |
| 605 | C24 | — | 8 | 448 | no | — |
| 606 | C24 | — | 8 | 1344 | no | — |
| 607 | C24 | — | 8 | 896 | no | — |
| 608 | C24 | — | 8 | 896 | no | — |
| 609 | C24 | — | 8 | 112 | no | — |
| 610 | C24 | — | 8 | 2688 | no | — |
| 611 | C24 | — | 8 | 336 | no | — |
| 612 | C24 | — | 8 | 2688 | no | — |
| 613 | C24 | — | 8 | 896 | no | — |
| 614 | C24 | — | 8 | 16 | no | — |
| 615 | C24 | — | 8 | 16 | no | — |
| 616 | C24 | — | 16 | 21 | no | — |
| 617 | C24 | — | 16 | 7 | no | — |
| 618 | C24 | — | 16 | 42 | no | — |
| 619 | C24 | — | 16 | 84 | no | — |
| 620 | C24 | — | 16 | 28 | no | — |
| 621 | C24 | — | 64 | 4 | no | — |
| 622 | C24 | C22×H(5,𝔽2) | 1 | 14 | yes | — |
| 623 | C24 | C22×H(5,𝔽2) | 1 | 14 | yes | — |
| 624 | C24 | C22×H(5,𝔽2) | 1 | 28 | yes | — |
| 625 | C24 | C22×H(5,𝔽2) | 1 | 7 | yes | — |
| 626 | C24 | C22×H(5,𝔽2) | 1 | 7 | yes | — |
| 627 | C24 | C27 | 1 | 1 | yes | characteristic |
| 628 | #41 | — | 8 | 336 | no | — |
| 629 | #41 | — | 8 | 336 | no | — |
| 630 | #41 | — | 8 | 448 | no | — |
| 631 | #41 | — | 16 | 672 | no | — |
| 632 | C2×Q8 | — | 2 | 56 | no | — |
| 633 | C2×Q8 | — | 4 | 56 | no | — |
| 634 | C2×Q8 | — | 8 | 14 | no | — |
| 635 | C2×Q8 | — | 8 | 14 | no | — |
| 636 | C2×Q8 | — | 8 | 112 | no | — |
| 637 | C2×Q8 | — | 16 | 28 | no | — |
| 638 | C2×D4 | — | 2 | 168 | no | — |
| 639 | C2×D4 | — | 2 | 168 | no | — |
| 640 | C2×D4 | — | 2 | 168 | no | — |
| 641 | C2×D4 | — | 4 | 168 | no | — |
| 642 | C2×D4 | — | 4 | 56 | no | — |
| 643 | C2×D4 | — | 4 | 168 | no | — |
| 644 | C2×D4 | — | 4 | 336 | no | — |
| 645 | C2×D4 | — | 4 | 168 | no | — |
| 646 | C2×D4 | — | 4 | 336 | no | — |
| 647 | C2×D4 | — | 8 | 42 | no | — |
| 648 | C2×D4 | — | 8 | 42 | no | — |
| 649 | C2×D4 | — | 8 | 336 | no | — |
| 650 | C2×D4 | — | 8 | 336 | no | — |
| 651 | C2×D4 | — | 8 | 336 | no | — |
| 652 | C2×D4 | — | 8 | 672 | no | — |
| 653 | C2×D4 | — | 8 | 336 | no | — |
| 654 | C2×D4 | — | 8 | 672 | no | — |
| 655 | C2×D4 | — | 16 | 42 | no | — |
| 656 | C2×D4 | — | 16 | 14 | no | — |
| 657 | C2×D4 | — | 16 | 168 | no | — |
| 658 | C2×D4 | — | 16 | 336 | no | — |
| 659 | C2×D4 | — | 16 | 84 | no | — |
| 660 | C2×D4 | — | 16 | 112 | no | — |
| 661 | C2×D4 | — | 16 | 112 | no | — |
| 662 | C2×D4 | — | 16 | 336 | no | — |
| 663 | C2×D4 | — | 16 | 672 | no | — |
| 664 | C2×D4 | — | 16 | 672 | no | — |
| 665 | C22×C4 | — | 2 | 42 | no | — |
| 666 | C22×C4 | — | 2 | 42 | no | — |
| 667 | C22×C4 | — | 2 | 168 | no | — |
| 668 | C22×C4 | — | 2 | 84 | no | — |
| 669 | C22×C4 | — | 4 | 84 | no | — |
| 670 | C22×C4 | — | 4 | 84 | no | — |
| 671 | C22×C4 | — | 4 | 42 | no | — |
| 672 | C22×C4 | — | 4 | 168 | no | — |
| 673 | C22×C4 | — | 4 | 84 | no | — |
| 674 | C22×C4 | — | 4 | 42 | no | — |
| 675 | C22×C4 | — | 8 | 42 | no | — |
| 676 | C22×C4 | — | 8 | 42 | no | — |
| 677 | C22×C4 | — | 8 | 84 | no | — |
| 678 | C22×C4 | — | 8 | 112 | no | — |
| 679 | C22×C4 | — | 8 | 84 | no | — |
| 680 | C22×C4 | — | 8 | 168 | no | — |
| 681 | C22×C4 | — | 16 | 21 | no | — |
| 682 | C22×C4 | — | 16 | 7 | no | — |
| 683 | C22×C4 | — | 16 | 42 | no | — |
| 684 | C22×C4 | — | 16 | 84 | no | — |
| 685 | C22×C4 | — | 16 | 84 | no | — |
| 686 | C22×C4 | C22×H(5,𝔽2) | 1 | 28 | yes | — |
| 687 | C4⋊C4 | — | 4 | 168 | no | — |
| 688 | C4⋊C4 | — | 4 | 168 | no | — |
| 689 | C4⋊C4 | — | 4 | 168 | no | — |
| 690 | C22⋊C4 | — | 2 | 168 | no | — |
| 691 | C22⋊C4 | — | 4 | 336 | no | — |
| 692 | C22⋊C4 | — | 4 | 336 | no | — |
| 693 | C22⋊C4 | — | 4 | 336 | no | — |
| 694 | C22⋊C4 | — | 4 | 168 | no | — |
| 695 | C22⋊C4 | — | 4 | 168 | no | — |
| 696 | C22⋊C4 | — | 4 | 84 | no | — |
| 697 | C22⋊C4 | — | 8 | 672 | no | — |
| 698 | C42 | — | 4 | 168 | no | — |
| 699 | C23 | — | 2 | 84 | no | — |
| 700 | C23 | — | 2 | 112 | no | — |
| 701 | C23 | — | 2 | 42 | no | — |
| 702 | C23 | — | 2 | 42 | no | — |
| 703 | C23 | — | 2 | 84 | no | — |
| 704 | C23 | — | 4 | 14 | no | — |
| 705 | C23 | — | 4 | 28 | no | — |
| 706 | C23 | — | 4 | 42 | no | — |
| 707 | C23 | — | 4 | 84 | no | — |
| 708 | C23 | — | 4 | 168 | no | — |
| 709 | C23 | — | 4 | 84 | no | — |
| 710 | C23 | — | 4 | 168 | no | — |
| 711 | C23 | — | 4 | 336 | no | — |
| 712 | C23 | — | 4 | 168 | no | — |
| 713 | C23 | — | 4 | 21 | no | — |
| 714 | C23 | — | 4 | 7 | no | — |
| 715 | C23 | — | 4 | 56 | no | — |
| 716 | C23 | — | 4 | 21 | no | — |
| 717 | C23 | — | 4 | 14 | no | — |
| 718 | C23 | — | 4 | 7 | no | — |
| 719 | C23 | — | 4 | 56 | no | — |
| 720 | C23 | — | 4 | 42 | no | — |
| 721 | C23 | — | 8 | 112 | no | — |
| 722 | C23 | — | 8 | 672 | no | — |
| 723 | C23 | — | 8 | 84 | no | — |
| 724 | C23 | — | 8 | 168 | no | — |
| 725 | C23 | — | 8 | 7 | no | — |
| 726 | C23 | — | 8 | 14 | no | — |
| 727 | C23 | — | 8 | 1 | no | — |
| 728 | C23 | — | 8 | 84 | no | — |
| 729 | C23 | — | 8 | 84 | no | — |
| 730 | C23 | — | 8 | 42 | no | — |
| 731 | C23 | — | 8 | 28 | no | — |
| 732 | C23 | — | 8 | 84 | no | — |
| 733 | C23 | — | 8 | 56 | no | — |
| 734 | C23 | — | 8 | 56 | no | — |
| 735 | C23 | — | 8 | 28 | no | — |
| 736 | C23 | — | 8 | 84 | no | — |
| 737 | C23 | — | 8 | 84 | no | — |
| 738 | C23 | — | 8 | 56 | no | — |
| 739 | C23 | — | 8 | 28 | no | — |
| 740 | C23 | — | 8 | 56 | no | — |
| 741 | C23 | — | 8 | 336 | no | — |
| 742 | C23 | — | 8 | 168 | no | — |
| 743 | C23 | — | 8 | 168 | no | — |
| 744 | C23 | — | 8 | 28 | no | — |
| 745 | C23 | — | 8 | 672 | no | — |
| 746 | C23 | — | 8 | 1344 | no | — |
| 747 | C23 | — | 8 | 168 | no | — |
| 748 | C23 | — | 8 | 1344 | no | — |
| 749 | C23 | — | 8 | 168 | no | — |
| 750 | C23 | — | 8 | 1344 | no | — |
| 751 | C23 | — | 8 | 56 | no | — |
| 752 | C23 | — | 8 | 448 | no | — |
| 753 | C23 | — | 8 | 1792 | no | — |
| 754 | C23 | — | 8 | 448 | no | — |
| 755 | C23 | — | 8 | 1344 | no | — |
| 756 | C23 | — | 8 | 64 | no | — |
| 757 | C23 | — | 8 | 56 | no | — |
| 758 | C23 | — | 16 | 28 | no | — |
| 759 | C23 | — | 16 | 42 | no | — |
| 760 | C23 | — | 16 | 84 | no | — |
| 761 | C23 | — | 16 | 56 | no | — |
| 762 | C23 | — | 32 | 28 | no | — |
| 763 | C23 | — | 32 | 84 | no | — |
| 764 | C23 | — | 32 | 28 | no | — |
| 765 | C23 | — | 64 | 14 | no | — |
| 766 | C23 | — | 64 | 16 | no | — |
| 767 | C23 | #62817 | 1 | 7 | yes | — |
| 768 | C23 | #62817 | 1 | 21 | yes | — |
| 769 | C23 | C23×H(5,𝔽2) | 1 | 7 | yes | — |
| 770 | Q8 | — | 8 | 56 | no | — |
| 771 | Q8 | — | 16 | 56 | no | — |
| 772 | D4 | — | 4 | 112 | no | — |
| 773 | D4 | — | 4 | 112 | no | — |
| 774 | D4 | — | 8 | 168 | no | — |
| 775 | D4 | — | 8 | 672 | no | — |
| 776 | D4 | — | 16 | 56 | no | — |
| 777 | D4 | — | 16 | 336 | no | — |
| 778 | D4 | — | 16 | 168 | no | — |
| 779 | C2×C4 | — | 2 | 84 | no | — |
| 780 | C2×C4 | — | 4 | 42 | no | — |
| 781 | C2×C4 | — | 4 | 14 | no | — |
| 782 | C2×C4 | — | 4 | 84 | no | — |
| 783 | C2×C4 | — | 8 | 168 | no | — |
| 784 | C2×C4 | — | 8 | 84 | no | — |
| 785 | C2×C4 | — | 8 | 168 | no | — |
| 786 | C2×C4 | — | 8 | 84 | no | — |
| 787 | C2×C4 | — | 16 | 28 | no | — |
| 788 | C2×C4 | — | 16 | 42 | no | — |
| 789 | C2×C4 | — | 16 | 84 | no | — |
| 790 | C2×C4 | — | 16 | 168 | no | — |
| 791 | C22 | — | 2 | 14 | no | — |
| 792 | C22 | — | 2 | 84 | no | — |
| 793 | C22 | — | 4 | 7 | no | — |
| 794 | C22 | — | 4 | 21 | no | — |
| 795 | C22 | — | 4 | 42 | no | — |
| 796 | C22 | — | 4 | 84 | no | — |
| 797 | C22 | — | 4 | 84 | no | — |
| 798 | C22 | — | 4 | 14 | no | — |
| 799 | C22 | — | 4 | 28 | no | — |
| 800 | C22 | — | 4 | 28 | no | — |
| 801 | C22 | — | 4 | 14 | no | — |
| 802 | C22 | — | 8 | 112 | no | — |
| 803 | C22 | — | 8 | 112 | no | — |
| 804 | C22 | — | 8 | 84 | no | — |
| 805 | C22 | — | 8 | 42 | no | — |
| 806 | C22 | — | 8 | 112 | no | — |
| 807 | C22 | — | 8 | 336 | no | — |
| 808 | C22 | — | 8 | 336 | no | — |
| 809 | C22 | — | 8 | 112 | no | — |
| 810 | C22 | — | 8 | 14 | no | — |
| 811 | C22 | — | 8 | 28 | no | — |
| 812 | C22 | — | 16 | 42 | no | — |
| 813 | C22 | — | 32 | 56 | no | — |
| 814 | C22 | — | 32 | 56 | no | — |
| 815 | C22 | #8932885 | 1 | 7 | yes | — |
| 816 | C22 | #8932885 | 1 | 1 | yes | characteristic |
| 817 | C22 | C2×#62817 | 1 | 7 | yes | — |
| 818 | C4 | — | 4 | 28 | no | — |
| 819 | C4 | — | 8 | 84 | no | — |
| 820 | C2 | — | 2 | 7 | no | — |
| 821 | C2 | — | 2 | 7 | no | — |
| 822 | C2 | — | 4 | 28 | no | — |
| 823 | C2 | — | 8 | 14 | no | — |
| 824 | C2 | — | 8 | 28 | no | — |
| 825 | C2 | #72216292 | 1 | 2 | yes | direct product factor |
| 826 | C2 | C2×#8932885 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #8932885 |
| commutator, Frattini, cosocle | C24 | C27 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C25 ◁ G | |
| LECS | G ▷ C24 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#7266798 | C2 | semidirect |
| 2. C2×#6499874 | C2 | semidirect |
| 3. C2×#6499867 | C2 | semidirect |
| 4. #72216292 | C2 | direct (N × H) |
| 5. C2×#62817 | C22 | semidirect |
| 6. C2×#60399 | C22 | semidirect |
| 7. C22×#2846 | C22 | semidirect |
| 8. C2×#32700 | C22 | semidirect |
| 9. #7266798 | C22 | semidirect |
| 10. C2×#32873 | C22 | semidirect |
| 11. #6499874 | C22 | semidirect |
| 12. #6499867 | C22 | semidirect |
| 13. C2×#23984 | C22 | semidirect |
| 14. C2×#23996 | C22 | semidirect |
| 15. C2×#23895 | C22 | semidirect |
| 16. C2×#23900 | C22 | semidirect |
| 17. C2×#21776 | C22 | semidirect |
| 18. C2×#21746 | C22 | semidirect |
| 19. C28 | C23 | semidirect |
| 20. C2×H(7,𝔽2) | C23 | semidirect |
| 22. #62817 | C23 | semidirect |
| 31. #60399 | C23 | semidirect |
| 34. C2×#3026 | C23 | semidirect |
| 37. C22×B(4,𝔽2) | C23 | semidirect |
| 38. C2×#2883 | C23 | semidirect |
| 41. C2×#2846 | C23 | semidirect |
| 42. C2×#2846 | C23 | semidirect |
| 44. C22×#379 | C23 | semidirect |
| 45. #32873 | C23 | semidirect |
| 46. #32700 | C23 | semidirect |
| 47. #23996 | C23 | semidirect |
| 48. #23984 | C23 | semidirect |
| 49. #23900 | C23 | semidirect |
| 50. #23895 | C23 | semidirect |
| 51. C2×#2104 | C23 | semidirect |
| 52. C2×#2032 | C23 | semidirect |
| 53. C2×#2029 | C23 | semidirect |
| 55. #21776 | C23 | semidirect |
| 56. #21746 | C23 | semidirect |
| 57. C2×#1913 | C23 | semidirect |
| 58. C2×#1898 | C23 | semidirect |
| 59. C2×#1889 | C23 | semidirect |
| 60. C2×#1828 | C23 | semidirect |
| 61. C2×#1819 | C23 | semidirect |
| 68. C27 | C24 | semidirect |
| 70. H(7,𝔽2) | C24 | semidirect |
| 130. #3026 | C24 | semidirect |
| 138. C2×B(4,𝔽2) | C24 | semidirect |
| 140. #2883 | C24 | semidirect |
| 146. #2846 | C24 | semidirect |
| 152. C2×#379 | C24 | semidirect |
| 153. #2104 | C24 | semidirect |
| 154. #2032 | C24 | semidirect |
| 155. #2029 | C24 | semidirect |
| 157. #1913 | C24 | semidirect |
| 158. #1898 | C24 | semidirect |
| 159. #1889 | C24 | semidirect |
| 160. #1828 | C24 | semidirect |
| 161. #1819 | C24 | semidirect |
| 183. C26 | H(5,𝔽2) | semidirect |
| 213. C23×D4 | H(5,𝔽2) | semidirect |
| 214. C23×D4 | H(5,𝔽2) | semidirect |
| 218. C24×C4 | H(5,𝔽2) | semidirect |
| 393. C25 | C2×H(5,𝔽2) | semidirect |
| 448. C22×D4 | C2×H(5,𝔽2) | semidirect |
| 462. C23×C4 | C2×H(5,𝔽2) | semidirect |
| 825. C2 | #72216292 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#7266798 | 2 |
| C2×#6499874 | 2 |
| C2×#6499867 | 2 |
| #72216292 | 2 |