Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1418 conjugacy classes of subgroups.
The subgroup lattice has 1036 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86356 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #83981 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #83269 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#5095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×D3×#104 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #78962 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#2005 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72110 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71863 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70348 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #70121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #70115 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68756 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #24466 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×D3×#41 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#1007 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C3×#137 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#536 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #5833 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#946 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#946 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#942 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#942 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×D3×M16 | C22 | 1 | 1 | yes | characteristic |
| 28 | #5727 | — | 2 | 1 | no | — |
| 29 | #5726 | — | 2 | 1 | no | — |
| 30 | #5677 | — | 2 | 1 | no | — |
| 31 | #5676 | — | 2 | 1 | no | — |
| 32 | #5655 | — | 2 | 2 | no | — |
| 33 | #5654 | — | 2 | 2 | no | — |
| 34 | #5629 | — | 2 | 1 | no | — |
| 35 | #5628 | — | 2 | 1 | no | — |
| 36 | #5627 | — | 2 | 1 | no | — |
| 37 | D3×C22⋊Q8 | — | 2 | 1 | no | — |
| 38 | #5524 | C22 | 1 | 1 | yes | characteristic |
| 39 | #5523 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C3×#104 | C22 | 1 | 1 | yes | characteristic |
| 42 | C3×#419 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×C3×#101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C2×#837 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5232 | C22 | 1 | 1 | yes | characteristic |
| 46 | #5229 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #5229 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×#836 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #5187 | — | 2 | 1 | no | — |
| 50 | #5186 | — | 2 | 1 | no | — |
| 51 | #5173 | — | 2 | 1 | no | — |
| 52 | #5169 | — | 2 | 1 | no | — |
| 53 | C2×#825 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#825 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #5133 | C22 | 1 | 1 | yes | characteristic |
| 56 | #5133 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #5126 | C22 | 1 | 1 | yes | characteristic |
| 58 | #5095 | — | 2 | 4 | no | — |
| 59 | #4995 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #4987 | — | 2 | 2 | no | — |
| 61 | #4972 | — | 2 | 2 | no | — |
| 62 | #4935 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C2×#805 | C22 | 1 | 1 | yes | characteristic |
| 64 | C2×#805 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | D3×#104 | — | 2 | 4 | no | — |
| 66 | #4816 | — | 2 | 1 | no | — |
| 67 | #4813 | — | 2 | 1 | no | — |
| 68 | #4812 | — | 2 | 1 | no | — |
| 69 | #4807 | — | 2 | 1 | no | — |
| 70 | C3×#339 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #4554 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | #4554 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #4532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | #3489 | — | 3 | 1 | no | — |
| 75 | #3056 | — | 3 | 1 | no | — |
| 76 | C2×#456 | — | 3 | 1 | no | — |
| 77 | #3007 | — | 3 | 1 | no | — |
| 78 | C22×#104 | — | 3 | 1 | no | — |
| 79 | #2857 | — | 3 | 1 | no | — |
| 80 | #2039 | — | 3 | 1 | no | — |
| 81 | #2038 | — | 3 | 1 | no | — |
| 82 | #2007 | — | 3 | 1 | no | — |
| 83 | #2005 | D3 | 1 | 1 | yes | characteristic, complemented |
| 84 | #1901 | — | 3 | 1 | no | — |
| 85 | #1896 | — | 3 | 1 | no | — |
| 86 | #1882 | — | 3 | 1 | no | — |
| 87 | #1859 | — | 3 | 1 | no | — |
| 88 | #1793 | — | 3 | 1 | no | — |
| 89 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 92 | D3×#41 | — | 2 | 2 | no | — |
| 93 | D3×#41 | — | 2 | 2 | no | — |
| 94 | D3×#41 | — | 4 | 1 | no | — |
| 95 | D3×#41 | — | 4 | 1 | no | — |
| 96 | #1007 | — | 2 | 2 | no | — |
| 97 | #1007 | — | 2 | 2 | no | — |
| 98 | #1007 | — | 4 | 1 | no | — |
| 99 | #1007 | — | 4 | 1 | no | — |
| 100 | C2×#239 | — | 2 | 1 | no | — |
| 101 | C2×#239 | — | 2 | 1 | no | — |
| 102 | C2×#239 | D4 | 1 | 1 | yes | characteristic |
| 103 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 104 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 105 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#237 | — | 2 | 1 | no | — |
| 107 | C2×#237 | D4 | 1 | 1 | yes | characteristic |
| 108 | C2×D3×D4 | — | 2 | 1 | no | — |
| 109 | C2×D3×D4 | D4 | 1 | 1 | yes | characteristic |
| 110 | C2×#235 | — | 2 | 2 | no | — |
| 111 | C2×#235 | — | 2 | 1 | no | — |
| 112 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 114 | C22×C4×D3 | — | 2 | 1 | no | — |
| 115 | C22×C4×D3 | — | 2 | 1 | no | — |
| 116 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 117 | C3×#137 | — | 4 | 1 | no | — |
| 118 | C3×#137 | — | 4 | 1 | no | — |
| 119 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 120 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 121 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 122 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 123 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 124 | C3×C4⋊Q8 | — | 2 | 2 | no | — |
| 125 | C3×C4⋊Q8 | — | 4 | 1 | no | — |
| 126 | C3×#124 | — | 2 | 1 | no | — |
| 127 | C3×#123 | — | 2 | 2 | no | — |
| 128 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 129 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 130 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 131 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 132 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 133 | #946 | — | 2 | 1 | no | — |
| 134 | #946 | — | 2 | 1 | no | — |
| 135 | #946 | — | 2 | 1 | no | — |
| 136 | #946 | — | 2 | 1 | no | — |
| 137 | #946 | — | 2 | 1 | no | — |
| 138 | #946 | — | 2 | 1 | no | — |
| 139 | #946 | — | 2 | 1 | no | — |
| 140 | #946 | — | 2 | 1 | no | — |
| 141 | #946 | — | 2 | 1 | no | — |
| 142 | C2×#216 | — | 2 | 1 | no | — |
| 143 | C2×#216 | — | 2 | 1 | no | — |
| 144 | #942 | — | 2 | 2 | no | — |
| 145 | #942 | — | 2 | 2 | no | — |
| 146 | #942 | — | 2 | 2 | no | — |
| 147 | #942 | — | 4 | 1 | no | — |
| 148 | C2×#215 | — | 2 | 1 | no | — |
| 149 | C2×#215 | — | 2 | 1 | no | — |
| 150 | #939 | — | 2 | 2 | no | — |
| 151 | #938 | — | 2 | 1 | no | — |
| 152 | #930 | — | 2 | 1 | no | — |
| 153 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 154 | C2×(C2×D3)⋊C4 | D4 | 1 | 2 | yes | — |
| 155 | C2×C4⋊Dic3 | — | 2 | 2 | no | — |
| 156 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 157 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 158 | #924 | — | 2 | 1 | no | — |
| 159 | C2×Dic3⋊C4 | — | 2 | 1 | no | — |
| 160 | C2×Dic3⋊C4 | D4 | 1 | 2 | yes | — |
| 161 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 162 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 164 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 165 | D3×M16 | — | 2 | 2 | no | — |
| 166 | D3×M16 | — | 4 | 1 | no | — |
| 167 | C2×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 168 | C2×D3×C8 | — | 2 | 1 | no | — |
| 169 | #897 | D4 | 1 | 1 | yes | characteristic |
| 170 | #897 | D4 | 1 | 1 | yes | characteristic |
| 171 | #896 | — | 2 | 2 | no | — |
| 172 | #896 | — | 2 | 2 | no | — |
| 173 | #895 | — | 2 | 2 | no | — |
| 174 | #895 | D4 | 1 | 1 | yes | characteristic |
| 175 | #895 | D4 | 1 | 1 | yes | characteristic |
| 176 | #894 | — | 2 | 2 | no | — |
| 177 | #894 | — | 2 | 2 | no | — |
| 178 | #893 | — | 2 | 2 | no | — |
| 179 | #892 | — | 2 | 1 | no | — |
| 180 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 181 | D3×C4⋊C4 | — | 2 | 1 | no | — |
| 182 | #888 | — | 2 | 2 | no | — |
| 183 | #886 | — | 2 | 1 | no | — |
| 184 | #885 | — | 2 | 2 | no | — |
| 185 | #884 | — | 2 | 2 | no | — |
| 186 | #884 | — | 2 | 2 | no | — |
| 187 | #883 | — | 2 | 2 | no | — |
| 188 | #882 | — | 2 | 2 | no | — |
| 189 | #882 | — | 2 | 1 | no | — |
| 190 | #67⋊C4 | — | 2 | 2 | no | — |
| 191 | #67⋊C4 | — | 2 | 2 | no | — |
| 192 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 193 | #878 | — | 2 | 2 | no | — |
| 194 | C4×D12 | — | 2 | 1 | no | — |
| 195 | C4×D12 | — | 2 | 1 | no | — |
| 196 | C4×D12 | — | 2 | 1 | no | — |
| 197 | C42×D3 | — | 2 | 2 | no | — |
| 198 | C42×D3 | — | 4 | 1 | no | — |
| 199 | C4×Dic6 | — | 2 | 1 | no | — |
| 200 | C3×#104 | — | 2 | 2 | no | — |
| 201 | C3×#103 | — | 2 | 1 | no | — |
| 202 | C3×#103 | — | 2 | 1 | no | — |
| 203 | C3×#101 | — | 4 | 1 | no | — |
| 204 | #837 | — | 2 | 2 | no | — |
| 205 | #836 | — | 2 | 2 | no | — |
| 206 | #835 | — | 2 | 1 | no | — |
| 207 | #832 | — | 2 | 1 | no | — |
| 208 | C3⋊#95 | — | 2 | 2 | no | — |
| 209 | C3⋊#95 | — | 2 | 2 | no | — |
| 210 | #825 | — | 2 | 2 | no | — |
| 211 | #825 | — | 4 | 1 | no | — |
| 212 | #821 | — | 2 | 1 | no | — |
| 213 | #821 | — | 2 | 1 | no | — |
| 214 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 215 | (C2×D3)⋊C8 | — | 2 | 1 | no | — |
| 216 | #816 | — | 2 | 1 | no | — |
| 217 | #816 | — | 2 | 1 | no | — |
| 218 | #808 | — | 2 | 1 | no | — |
| 219 | #807 | — | 2 | 1 | no | — |
| 220 | #805 | — | 2 | 2 | no | — |
| 221 | #805 | D4 | 1 | 4 | yes | complemented |
| 222 | C2×2−1+4 | — | 3 | 1 | no | — |
| 223 | C22×#41 | — | 3 | 1 | no | — |
| 224 | C2×#137 | — | 3 | 1 | no | — |
| 225 | C2×#137 | — | 3 | 1 | no | — |
| 226 | C2×#137 | C2×D3 | 1 | 1 | yes | characteristic |
| 227 | C22×M16 | — | 3 | 1 | no | — |
| 228 | D4×Q8 | — | 6 | 1 | no | — |
| 229 | #548 | — | 6 | 1 | no | — |
| 230 | #547 | — | 6 | 2 | no | — |
| 231 | #547 | — | 6 | 1 | no | — |
| 232 | #546 | — | 6 | 2 | no | — |
| 233 | #546 | — | 6 | 1 | no | — |
| 234 | #537 | — | 3 | 1 | no | — |
| 235 | #537 | — | 6 | 1 | no | — |
| 236 | #536 | — | 6 | 1 | no | — |
| 237 | #536 | C2×D3 | 1 | 1 | yes | characteristic |
| 238 | C2×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 239 | #525 | — | 3 | 1 | no | — |
| 240 | #525 | — | 6 | 1 | no | — |
| 241 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 242 | C2×C22⋊Q8 | — | 3 | 1 | no | — |
| 243 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 244 | #520 | — | 3 | 1 | no | — |
| 245 | C22×C42 | — | 3 | 1 | no | — |
| 246 | #470 | — | 6 | 1 | no | — |
| 247 | #468 | — | 6 | 1 | no | — |
| 248 | #467 | — | 6 | 1 | no | — |
| 249 | #465 | — | 6 | 1 | no | — |
| 250 | #456 | — | 6 | 4 | no | — |
| 251 | #452 | — | 6 | 1 | no | — |
| 252 | #452 | — | 6 | 1 | no | — |
| 253 | #451 | — | 6 | 1 | no | — |
| 254 | #450 | — | 6 | 1 | no | — |
| 255 | #428 | — | 3 | 1 | no | — |
| 256 | C2×#104 | — | 3 | 1 | no | — |
| 257 | C2×#104 | — | 3 | 1 | no | — |
| 258 | C2×#104 | — | 3 | 1 | no | — |
| 259 | C2×#104 | — | 3 | 1 | no | — |
| 260 | C2×#104 | — | 3 | 1 | no | — |
| 261 | C2×#104 | — | 6 | 4 | no | — |
| 262 | C2×#104 | C2×D3 | 1 | 1 | yes | characteristic |
| 263 | #419 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 264 | #417 | — | 3 | 1 | no | — |
| 265 | #417 | — | 3 | 1 | no | — |
| 266 | #417 | — | 3 | 1 | no | — |
| 267 | C2×#101 | — | 3 | 1 | no | — |
| 268 | C2×#101 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 269 | #407 | — | 3 | 1 | no | — |
| 270 | #391 | — | 3 | 1 | no | — |
| 271 | #391 | — | 3 | 1 | no | — |
| 272 | #389 | — | 6 | 2 | no | — |
| 273 | #384 | — | 3 | 1 | no | — |
| 274 | #380 | — | 6 | 2 | no | — |
| 275 | #343 | — | 3 | 1 | no | — |
| 276 | #343 | — | 3 | 1 | no | — |
| 277 | #339 | — | 3 | 1 | no | — |
| 278 | #339 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 279 | C23×D3 | — | 2 | 1 | no | — |
| 280 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C3×#41 | — | 2 | 1 | no | — |
| 282 | C3×#41 | — | 2 | 1 | no | — |
| 283 | C3×#41 | — | 2 | 1 | no | — |
| 284 | C3×#41 | — | 2 | 1 | no | — |
| 285 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 286 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 287 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 288 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 289 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 290 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 291 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 292 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 293 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 294 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 295 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 296 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 297 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×C3×D4 | — | 2 | 1 | no | — |
| 299 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C22×C3×C4 | — | 2 | 1 | no | — |
| 301 | C22×C3×C4 | — | 2 | 1 | no | — |
| 302 | C22×C3×C4 | — | 2 | 1 | no | — |
| 303 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 304 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 305 | C2×#67 | — | 2 | 1 | no | — |
| 306 | C2×#67 | — | 2 | 1 | no | — |
| 307 | C2×#67 | — | 2 | 1 | no | — |
| 308 | C2×#67 | — | 2 | 2 | no | — |
| 309 | C2×#67 | — | 2 | 1 | no | — |
| 310 | C22×Dic3 | — | 2 | 1 | no | — |
| 311 | C22×Dic3 | — | 2 | 1 | no | — |
| 312 | C22×Dic3 | — | 2 | 1 | no | — |
| 313 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 314 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 315 | #239 | — | 2 | 2 | no | — |
| 316 | #239 | — | 4 | 1 | no | — |
| 317 | #239 | — | 4 | 2 | no | — |
| 318 | #239 | — | 4 | 2 | no | — |
| 319 | #239 | — | 4 | 2 | no | — |
| 320 | #239 | — | 4 | 2 | no | — |
| 321 | D3×Q8 | — | 2 | 2 | no | — |
| 322 | D3×Q8 | — | 4 | 1 | no | — |
| 323 | D3×Q8 | — | 4 | 2 | no | — |
| 324 | D3×Q8 | — | 4 | 2 | no | — |
| 325 | D3×Q8 | — | 4 | 2 | no | — |
| 326 | D3×Q8 | — | 4 | 2 | no | — |
| 327 | #237 | — | 2 | 2 | no | — |
| 328 | #237 | — | 4 | 1 | no | — |
| 329 | #237 | — | 4 | 2 | no | — |
| 330 | #237 | — | 4 | 2 | no | — |
| 331 | D3×D4 | — | 2 | 2 | no | — |
| 332 | D3×D4 | — | 4 | 1 | no | — |
| 333 | D3×D4 | — | 4 | 2 | no | — |
| 334 | D3×D4 | — | 4 | 2 | no | — |
| 335 | #235 | — | 2 | 1 | no | — |
| 336 | #235 | — | 2 | 1 | no | — |
| 337 | #235 | — | 2 | 1 | no | — |
| 338 | #235 | — | 2 | 1 | no | — |
| 339 | #235 | — | 2 | 1 | no | — |
| 340 | #235 | — | 2 | 1 | no | — |
| 341 | #235 | — | 4 | 2 | no | — |
| 342 | #235 | — | 4 | 2 | no | — |
| 343 | #235 | — | 4 | 4 | no | — |
| 344 | #235 | — | 4 | 4 | no | — |
| 345 | #235 | C2×D4 | 1 | 2 | yes | — |
| 346 | #235 | #41 | 1 | 2 | yes | — |
| 347 | C2×D12 | — | 2 | 2 | no | — |
| 348 | C2×D12 | — | 2 | 1 | no | — |
| 349 | C2×D12 | — | 2 | 1 | no | — |
| 350 | C2×D12 | — | 2 | 1 | no | — |
| 351 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 352 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×C4×D3 | — | 2 | 1 | no | — |
| 354 | C2×C4×D3 | — | 2 | 1 | no | — |
| 355 | C2×C4×D3 | — | 2 | 1 | no | — |
| 356 | C2×C4×D3 | — | 2 | 1 | no | — |
| 357 | C2×C4×D3 | — | 2 | 1 | no | — |
| 358 | C2×C4×D3 | — | 2 | 2 | no | — |
| 359 | C2×C4×D3 | — | 2 | 2 | no | — |
| 360 | C2×C4×D3 | — | 2 | 4 | no | — |
| 361 | C2×C4×D3 | — | 2 | 1 | no | — |
| 362 | C2×C4×D3 | — | 2 | 1 | no | — |
| 363 | C2×C4×D3 | — | 2 | 1 | no | — |
| 364 | C2×C4×D3 | — | 2 | 2 | no | — |
| 365 | C2×C4×D3 | — | 4 | 2 | no | — |
| 366 | C2×C4×D3 | — | 4 | 2 | no | — |
| 367 | C2×C4×D3 | — | 4 | 2 | no | — |
| 368 | C2×C4×D3 | — | 4 | 2 | no | — |
| 369 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 370 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 371 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 372 | C2×C4×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 373 | C2×Dic6 | — | 2 | 2 | no | — |
| 374 | C2×Dic6 | — | 2 | 1 | no | — |
| 375 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 376 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 377 | C3×Q16 | — | 4 | 2 | no | — |
| 378 | C3×SD16 | — | 4 | 2 | no | — |
| 379 | C3×M16 | — | 2 | 1 | no | — |
| 380 | C3×M16 | — | 2 | 1 | no | — |
| 381 | C3×M16 | — | 2 | 1 | no | — |
| 382 | C3×M16 | — | 2 | 1 | no | — |
| 383 | C2×C3×C8 | — | 2 | 1 | no | — |
| 384 | C2×C3×C8 | — | 2 | 1 | no | — |
| 385 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 386 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 387 | C3×C4⋊C4 | — | 4 | 4 | no | — |
| 388 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 389 | C3×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 390 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 391 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 392 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 393 | C3×C42 | — | 2 | 1 | no | — |
| 394 | C3×C42 | — | 2 | 1 | no | — |
| 395 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 396 | #217 | — | 2 | 2 | no | — |
| 397 | #216 | — | 4 | 2 | no | — |
| 398 | #216 | — | 4 | 2 | no | — |
| 399 | #215 | — | 4 | 2 | no | — |
| 400 | #215 | — | 4 | 2 | no | — |
| 401 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 402 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 403 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 404 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 405 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 406 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 407 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 408 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 409 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 410 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 411 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 412 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 413 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 414 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 415 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 416 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 417 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 418 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 419 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 420 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 421 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 422 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 423 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 424 | C4×Dic3 | — | 2 | 2 | no | — |
| 425 | C4×Dic3 | — | 2 | 1 | no | — |
| 426 | C4×Dic3 | — | 2 | 1 | no | — |
| 427 | C4×Dic3 | — | 4 | 2 | no | — |
| 428 | #208 | — | 2 | 1 | no | — |
| 429 | #208 | — | 2 | 1 | no | — |
| 430 | #208 | — | 2 | 1 | no | — |
| 431 | #208 | C2×D4 | 1 | 2 | yes | — |
| 432 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 433 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 434 | ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 435 | D3×C8 | — | 4 | 2 | no | — |
| 436 | 2−1+4 | — | 6 | 2 | no | — |
| 437 | 2−1+4 | — | 6 | 2 | no | — |
| 438 | 2−1+4 | — | 12 | 1 | no | — |
| 439 | 2−1+4 | — | 12 | 1 | no | — |
| 440 | C2×#41 | — | 3 | 1 | no | — |
| 441 | C2×#41 | — | 3 | 1 | no | — |
| 442 | C2×#41 | — | 3 | 1 | no | — |
| 443 | C2×#41 | — | 3 | 1 | no | — |
| 444 | C2×#41 | — | 6 | 1 | no | — |
| 445 | C2×#41 | — | 6 | 1 | no | — |
| 446 | C2×#41 | — | 6 | 1 | no | — |
| 447 | C2×#41 | — | 6 | 1 | no | — |
| 448 | C2×#41 | — | 6 | 2 | no | — |
| 449 | C2×#41 | — | 6 | 2 | no | — |
| 450 | C2×#41 | — | 6 | 2 | no | — |
| 451 | C2×#41 | — | 12 | 1 | no | — |
| 452 | C2×#41 | — | 12 | 1 | no | — |
| 453 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 454 | C22×Q8 | — | 3 | 1 | no | — |
| 455 | C22×Q8 | — | 6 | 1 | no | — |
| 456 | C22×Q8 | — | 6 | 1 | no | — |
| 457 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 458 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 459 | C22×D4 | — | 3 | 1 | no | — |
| 460 | C22×D4 | — | 6 | 1 | no | — |
| 461 | C23×C4 | — | 3 | 1 | no | — |
| 462 | C23×C4 | — | 6 | 1 | no | — |
| 463 | C23×C4 | — | 6 | 1 | no | — |
| 464 | #137 | — | 4 | 1 | no | — |
| 465 | #137 | — | 4 | 1 | no | — |
| 466 | #137 | — | 6 | 2 | no | — |
| 467 | #137 | — | 6 | 2 | no | — |
| 468 | #137 | — | 6 | 2 | no | — |
| 469 | #137 | — | 12 | 1 | no | — |
| 470 | C2×Q16 | — | 2 | 1 | no | — |
| 471 | C2×Q16 | — | 6 | 1 | no | — |
| 472 | C2×Q16 | — | 6 | 1 | no | — |
| 473 | C2×SD16 | — | 2 | 1 | no | — |
| 474 | C2×SD16 | — | 6 | 1 | no | — |
| 475 | C2×SD16 | — | 6 | 1 | no | — |
| 476 | C2×M16 | — | 3 | 1 | no | — |
| 477 | C2×M16 | — | 3 | 1 | no | — |
| 478 | C2×M16 | — | 6 | 1 | no | — |
| 479 | C2×M16 | — | 6 | 2 | no | — |
| 480 | C2×M16 | — | 12 | 1 | no | — |
| 481 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 482 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 483 | C22×C8 | — | 6 | 1 | no | — |
| 484 | C4⋊Q8 | — | 2 | 1 | no | — |
| 485 | C4⋊Q8 | — | 2 | 2 | no | — |
| 486 | C4⋊Q8 | — | 4 | 1 | no | — |
| 487 | C4⋊Q8 | — | 6 | 2 | no | — |
| 488 | #124 | — | 2 | 1 | no | — |
| 489 | #124 | — | 6 | 2 | no | — |
| 490 | #123 | — | 2 | 2 | no | — |
| 491 | #123 | — | 6 | 1 | no | — |
| 492 | #123 | — | 6 | 2 | no | — |
| 493 | #123 | — | 6 | 2 | no | — |
| 494 | #123 | — | 6 | 2 | no | — |
| 495 | C22⋊Q8 | — | 2 | 1 | no | — |
| 496 | C22⋊Q8 | — | 2 | 1 | no | — |
| 497 | C22⋊Q8 | — | 3 | 1 | no | — |
| 498 | C22⋊Q8 | — | 3 | 1 | no | — |
| 499 | C22⋊Q8 | — | 6 | 2 | no | — |
| 500 | C22⋊Q8 | — | 6 | 2 | no | — |
| 501 | C22⋊Q8 | — | 6 | 2 | no | — |
| 502 | C22⋊Q8 | — | 6 | 1 | no | — |
| 503 | C22⋊Q8 | — | 6 | 1 | no | — |
| 504 | C22⋊Q8 | — | 6 | 1 | no | — |
| 505 | C22⋊Q8 | — | 6 | 1 | no | — |
| 506 | C22⋊Q8 | — | 6 | 1 | no | — |
| 507 | C22⋊Q8 | — | 6 | 1 | no | — |
| 508 | C22⋊Q8 | — | 6 | 1 | no | — |
| 509 | C22⋊Q8 | — | 6 | 1 | no | — |
| 510 | C22⋊Q8 | — | 6 | 1 | no | — |
| 511 | C22⋊Q8 | — | 6 | 1 | no | — |
| 512 | #121 | — | 3 | 1 | no | — |
| 513 | #121 | — | 3 | 1 | no | — |
| 514 | #121 | — | 6 | 2 | no | — |
| 515 | #121 | — | 6 | 2 | no | — |
| 516 | #121 | — | 6 | 2 | no | — |
| 517 | #121 | — | 6 | 1 | no | — |
| 518 | #121 | — | 6 | 2 | no | — |
| 519 | #121 | — | 6 | 1 | no | — |
| 520 | #120 | — | 6 | 1 | no | — |
| 521 | #120 | — | 6 | 2 | no | — |
| 522 | C4×Q8 | — | 6 | 1 | no | — |
| 523 | C4×D4 | — | 6 | 1 | no | — |
| 524 | C4×D4 | — | 6 | 1 | no | — |
| 525 | C4×D4 | — | 6 | 1 | no | — |
| 526 | C4×D4 | — | 6 | 2 | no | — |
| 527 | C4×D4 | — | 6 | 2 | no | — |
| 528 | C4×D4 | — | 6 | 2 | no | — |
| 529 | #117 | — | 6 | 1 | no | — |
| 530 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 531 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 532 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 533 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 534 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 535 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 536 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 537 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 538 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 539 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 540 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 541 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 542 | C2×C42 | — | 3 | 1 | no | — |
| 543 | C2×C42 | — | 6 | 2 | no | — |
| 544 | C2×C42 | — | 6 | 1 | no | — |
| 545 | C2×C42 | — | 12 | 1 | no | — |
| 546 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 547 | #107 | — | 6 | 1 | no | — |
| 548 | #106 | — | 6 | 1 | no | — |
| 549 | #104 | — | 2 | 2 | no | — |
| 550 | #104 | — | 3 | 4 | no | — |
| 551 | #104 | — | 6 | 2 | no | — |
| 552 | #104 | — | 6 | 2 | no | — |
| 553 | #104 | — | 6 | 2 | no | — |
| 554 | #104 | — | 12 | 1 | no | — |
| 555 | #103 | — | 2 | 1 | no | — |
| 556 | #103 | — | 2 | 1 | no | — |
| 557 | #103 | — | 6 | 1 | no | — |
| 558 | #103 | — | 6 | 1 | no | — |
| 559 | #103 | — | 6 | 1 | no | — |
| 560 | #102 | — | 6 | 1 | no | — |
| 561 | #102 | — | 6 | 1 | no | — |
| 562 | #102 | — | 6 | 1 | no | — |
| 563 | #101 | — | 4 | 1 | no | — |
| 564 | #101 | — | 6 | 2 | no | — |
| 565 | C22⋊C8 | — | 6 | 1 | no | — |
| 566 | C22⋊C8 | — | 6 | 1 | no | — |
| 567 | #95 | — | 6 | 2 | no | — |
| 568 | #95 | — | 6 | 2 | no | — |
| 569 | C23×C3 | — | 2 | 1 | no | — |
| 570 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 571 | C22×D3 | — | 2 | 1 | no | — |
| 572 | C22×D3 | — | 2 | 1 | no | — |
| 573 | C22×D3 | — | 2 | 1 | no | — |
| 574 | C22×D3 | — | 2 | 2 | no | — |
| 575 | C22×D3 | — | 2 | 1 | no | — |
| 576 | C22×D3 | — | 4 | 1 | no | — |
| 577 | C22×D3 | — | 4 | 2 | no | — |
| 578 | C22×D3 | — | 4 | 2 | no | — |
| 579 | C22×D3 | — | 8 | 1 | no | — |
| 580 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 581 | C22×D3 | #120 | 1 | 1 | yes | characteristic |
| 582 | C3×Q8 | — | 2 | 1 | no | — |
| 583 | C3×Q8 | — | 2 | 1 | no | — |
| 584 | C3×Q8 | — | 4 | 1 | no | — |
| 585 | C3×Q8 | — | 4 | 1 | no | — |
| 586 | C3×Q8 | — | 4 | 1 | no | — |
| 587 | C3×Q8 | — | 4 | 1 | no | — |
| 588 | C3×Q8 | — | 4 | 1 | no | — |
| 589 | C3×Q8 | — | 4 | 1 | no | — |
| 590 | C3×Q8 | — | 4 | 1 | no | — |
| 591 | C3×Q8 | — | 4 | 1 | no | — |
| 592 | C3×D4 | — | 2 | 1 | no | — |
| 593 | C3×D4 | — | 2 | 1 | no | — |
| 594 | C3×D4 | — | 4 | 1 | no | — |
| 595 | C3×D4 | — | 4 | 1 | no | — |
| 596 | C2×C3×C4 | — | 2 | 2 | no | — |
| 597 | C2×C3×C4 | — | 2 | 2 | no | — |
| 598 | C2×C3×C4 | — | 2 | 2 | no | — |
| 599 | C2×C3×C4 | — | 2 | 1 | no | — |
| 600 | C2×C3×C4 | — | 2 | 1 | no | — |
| 601 | C2×C3×C4 | — | 2 | 2 | no | — |
| 602 | C2×C3×C4 | — | 2 | 1 | no | — |
| 603 | C2×C3×C4 | — | 2 | 2 | no | — |
| 604 | C2×C3×C4 | — | 2 | 2 | no | — |
| 605 | C2×C3×C4 | — | 4 | 1 | no | — |
| 606 | C2×C3×C4 | — | 4 | 1 | no | — |
| 607 | C2×C3×C4 | — | 4 | 1 | no | — |
| 608 | C2×C3×C4 | — | 4 | 1 | no | — |
| 609 | C2×C3×C4 | — | 4 | 1 | no | — |
| 610 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 611 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 612 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 613 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 614 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 615 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 616 | #67 | — | 2 | 2 | no | — |
| 617 | #67 | — | 2 | 2 | no | — |
| 618 | #67 | — | 4 | 2 | no | — |
| 619 | #67 | — | 4 | 2 | no | — |
| 620 | #67 | — | 4 | 1 | no | — |
| 621 | #67 | — | 4 | 1 | no | — |
| 622 | #67 | — | 8 | 2 | no | — |
| 623 | C2×Dic3 | — | 2 | 1 | no | — |
| 624 | C2×Dic3 | — | 2 | 1 | no | — |
| 625 | C2×Dic3 | — | 2 | 1 | no | — |
| 626 | C2×Dic3 | — | 2 | 2 | no | — |
| 627 | C2×Dic3 | — | 2 | 2 | no | — |
| 628 | C2×Dic3 | — | 2 | 1 | no | — |
| 629 | C2×Dic3 | — | 4 | 2 | no | — |
| 630 | C2×Dic3 | — | 4 | 1 | no | — |
| 631 | C2×Dic3 | — | 4 | 1 | no | — |
| 632 | C2×Dic3 | — | 4 | 2 | no | — |
| 633 | C2×Dic3 | — | 4 | 2 | no | — |
| 634 | C2×Dic3 | — | 4 | 1 | no | — |
| 635 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 636 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 637 | D12 | — | 2 | 1 | no | — |
| 638 | D12 | — | 2 | 1 | no | — |
| 639 | D12 | — | 2 | 1 | no | — |
| 640 | D12 | — | 4 | 2 | no | — |
| 641 | D12 | — | 4 | 4 | no | — |
| 642 | D12 | — | 4 | 2 | no | — |
| 643 | D12 | — | 8 | 1 | no | — |
| 644 | D12 | #121 | 1 | 2 | yes | — |
| 645 | C4×D3 | — | 2 | 1 | no | — |
| 646 | C4×D3 | — | 2 | 1 | no | — |
| 647 | C4×D3 | — | 2 | 1 | no | — |
| 648 | C4×D3 | — | 2 | 1 | no | — |
| 649 | C4×D3 | — | 2 | 1 | no | — |
| 650 | C4×D3 | — | 2 | 1 | no | — |
| 651 | C4×D3 | — | 2 | 2 | no | — |
| 652 | C4×D3 | — | 2 | 1 | no | — |
| 653 | C4×D3 | — | 2 | 1 | no | — |
| 654 | C4×D3 | — | 2 | 2 | no | — |
| 655 | C4×D3 | — | 4 | 2 | no | — |
| 656 | C4×D3 | — | 4 | 2 | no | — |
| 657 | C4×D3 | — | 4 | 4 | no | — |
| 658 | C4×D3 | — | 4 | 8 | no | — |
| 659 | C4×D3 | — | 4 | 4 | no | — |
| 660 | C4×D3 | — | 4 | 1 | no | — |
| 661 | C4×D3 | — | 4 | 1 | no | — |
| 662 | C4×D3 | — | 8 | 2 | no | — |
| 663 | Dic6 | — | 2 | 1 | no | — |
| 664 | Dic6 | — | 2 | 1 | no | — |
| 665 | Dic6 | — | 2 | 1 | no | — |
| 666 | Dic6 | — | 4 | 2 | no | — |
| 667 | Dic6 | — | 4 | 4 | no | — |
| 668 | Dic6 | #121 | 1 | 2 | yes | — |
| 669 | C3×C8 | — | 4 | 1 | no | — |
| 670 | C3×C8 | — | 4 | 1 | no | — |
| 671 | C3⋊C8 | — | 2 | 2 | no | — |
| 672 | C3⋊C8 | — | 4 | 1 | no | — |
| 673 | C24 | — | 3 | 1 | no | — |
| 674 | C24 | — | 6 | 1 | no | — |
| 675 | #41 | — | 2 | 1 | no | — |
| 676 | #41 | — | 2 | 1 | no | — |
| 677 | #41 | — | 2 | 1 | no | — |
| 678 | #41 | — | 2 | 1 | no | — |
| 679 | #41 | — | 3 | 2 | no | — |
| 680 | #41 | — | 3 | 2 | no | — |
| 681 | #41 | — | 6 | 1 | no | — |
| 682 | #41 | — | 6 | 1 | no | — |
| 683 | #41 | — | 6 | 2 | no | — |
| 684 | #41 | — | 6 | 2 | no | — |
| 685 | #41 | — | 6 | 1 | no | — |
| 686 | #41 | — | 6 | 1 | no | — |
| 687 | #41 | — | 6 | 1 | no | — |
| 688 | #41 | — | 6 | 1 | no | — |
| 689 | #41 | — | 12 | 4 | no | — |
| 690 | #41 | — | 12 | 4 | no | — |
| 691 | #41 | — | 12 | 2 | no | — |
| 692 | #41 | — | 12 | 2 | no | — |
| 693 | #41 | — | 12 | 1 | no | — |
| 694 | #41 | — | 12 | 2 | no | — |
| 695 | #41 | — | 12 | 2 | no | — |
| 696 | #41 | — | 12 | 1 | no | — |
| 697 | #41 | — | 12 | 2 | no | — |
| 698 | #41 | — | 12 | 2 | no | — |
| 699 | #41 | — | 12 | 2 | no | — |
| 700 | #41 | — | 12 | 2 | no | — |
| 701 | C2×Q8 | — | 2 | 1 | no | — |
| 702 | C2×Q8 | — | 2 | 1 | no | — |
| 703 | C2×Q8 | — | 2 | 1 | no | — |
| 704 | C2×Q8 | — | 2 | 1 | no | — |
| 705 | C2×Q8 | — | 2 | 1 | no | — |
| 706 | C2×Q8 | — | 2 | 1 | no | — |
| 707 | C2×Q8 | — | 2 | 1 | no | — |
| 708 | C2×Q8 | — | 2 | 1 | no | — |
| 709 | C2×Q8 | — | 2 | 1 | no | — |
| 710 | C2×Q8 | — | 2 | 1 | no | — |
| 711 | C2×Q8 | — | 2 | 1 | no | — |
| 712 | C2×Q8 | — | 2 | 1 | no | — |
| 713 | C2×Q8 | — | 3 | 1 | no | — |
| 714 | C2×Q8 | — | 3 | 1 | no | — |
| 715 | C2×Q8 | — | 6 | 1 | no | — |
| 716 | C2×Q8 | — | 6 | 2 | no | — |
| 717 | C2×Q8 | — | 6 | 2 | no | — |
| 718 | C2×Q8 | — | 12 | 1 | no | — |
| 719 | C2×Q8 | — | 12 | 2 | no | — |
| 720 | C2×Q8 | — | 12 | 2 | no | — |
| 721 | C2×Q8 | — | 12 | 2 | no | — |
| 722 | C2×Q8 | — | 12 | 2 | no | — |
| 723 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 724 | C2×D4 | — | 2 | 1 | no | — |
| 725 | C2×D4 | — | 3 | 1 | no | — |
| 726 | C2×D4 | — | 3 | 1 | no | — |
| 727 | C2×D4 | — | 6 | 1 | no | — |
| 728 | C2×D4 | — | 6 | 1 | no | — |
| 729 | C2×D4 | — | 6 | 2 | no | — |
| 730 | C2×D4 | — | 6 | 1 | no | — |
| 731 | C2×D4 | — | 6 | 1 | no | — |
| 732 | C2×D4 | — | 6 | 2 | no | — |
| 733 | C2×D4 | — | 6 | 1 | no | — |
| 734 | C2×D4 | — | 6 | 1 | no | — |
| 735 | C2×D4 | — | 6 | 1 | no | — |
| 736 | C2×D4 | — | 6 | 2 | no | — |
| 737 | C2×D4 | — | 12 | 1 | no | — |
| 738 | C2×D4 | — | 12 | 2 | no | — |
| 739 | C2×D4 | — | 12 | 2 | no | — |
| 740 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 741 | C22×C4 | — | 2 | 1 | no | — |
| 742 | C22×C4 | — | 2 | 1 | no | — |
| 743 | C22×C4 | — | 2 | 1 | no | — |
| 744 | C22×C4 | — | 3 | 1 | no | — |
| 745 | C22×C4 | — | 3 | 1 | no | — |
| 746 | C22×C4 | — | 3 | 1 | no | — |
| 747 | C22×C4 | — | 3 | 1 | no | — |
| 748 | C22×C4 | — | 3 | 1 | no | — |
| 749 | C22×C4 | — | 3 | 2 | no | — |
| 750 | C22×C4 | — | 6 | 1 | no | — |
| 751 | C22×C4 | — | 6 | 1 | no | — |
| 752 | C22×C4 | — | 6 | 2 | no | — |
| 753 | C22×C4 | — | 6 | 2 | no | — |
| 754 | C22×C4 | — | 6 | 4 | no | — |
| 755 | C22×C4 | — | 6 | 2 | no | — |
| 756 | C22×C4 | — | 6 | 1 | no | — |
| 757 | C22×C4 | — | 6 | 1 | no | — |
| 758 | C22×C4 | — | 6 | 1 | no | — |
| 759 | C22×C4 | — | 6 | 1 | no | — |
| 760 | C22×C4 | — | 6 | 1 | no | — |
| 761 | C22×C4 | — | 6 | 1 | no | — |
| 762 | C22×C4 | — | 6 | 1 | no | — |
| 763 | C22×C4 | — | 6 | 1 | no | — |
| 764 | C22×C4 | — | 6 | 1 | no | — |
| 765 | C22×C4 | — | 12 | 2 | no | — |
| 766 | C22×C4 | — | 12 | 2 | no | — |
| 767 | C22×C4 | — | 12 | 2 | no | — |
| 768 | C22×C4 | — | 12 | 2 | no | — |
| 769 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 770 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 771 | Q16 | — | 4 | 2 | no | — |
| 772 | Q16 | — | 12 | 2 | no | — |
| 773 | Q16 | — | 12 | 2 | no | — |
| 774 | SD16 | — | 4 | 2 | no | — |
| 775 | SD16 | — | 12 | 2 | no | — |
| 776 | SD16 | — | 12 | 2 | no | — |
| 777 | M16 | — | 2 | 1 | no | — |
| 778 | M16 | — | 2 | 1 | no | — |
| 779 | M16 | — | 2 | 1 | no | — |
| 780 | M16 | — | 2 | 1 | no | — |
| 781 | M16 | — | 3 | 2 | no | — |
| 782 | M16 | — | 6 | 1 | no | — |
| 783 | M16 | — | 6 | 1 | no | — |
| 784 | M16 | — | 6 | 1 | no | — |
| 785 | M16 | — | 12 | 2 | no | — |
| 786 | C2×C8 | — | 2 | 1 | no | — |
| 787 | C2×C8 | — | 2 | 1 | no | — |
| 788 | C2×C8 | — | 6 | 1 | no | — |
| 789 | C2×C8 | — | 6 | 1 | no | — |
| 790 | C2×C8 | — | 12 | 2 | no | — |
| 791 | C4⋊C4 | — | 2 | 2 | no | — |
| 792 | C4⋊C4 | — | 2 | 2 | no | — |
| 793 | C4⋊C4 | — | 4 | 4 | no | — |
| 794 | C4⋊C4 | — | 6 | 2 | no | — |
| 795 | C4⋊C4 | — | 6 | 2 | no | — |
| 796 | C4⋊C4 | — | 6 | 1 | no | — |
| 797 | C4⋊C4 | — | 6 | 1 | no | — |
| 798 | C4⋊C4 | — | 6 | 2 | no | — |
| 799 | C4⋊C4 | — | 6 | 2 | no | — |
| 800 | C4⋊C4 | — | 6 | 1 | no | — |
| 801 | C4⋊C4 | — | 6 | 1 | no | — |
| 802 | C4⋊C4 | — | 6 | 1 | no | — |
| 803 | C4⋊C4 | — | 6 | 1 | no | — |
| 804 | C4⋊C4 | — | 12 | 4 | no | — |
| 805 | C4⋊C4 | — | 12 | 1 | no | — |
| 806 | C4⋊C4 | — | 12 | 1 | no | — |
| 807 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 808 | C4⋊C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 809 | C22⋊C4 | — | 2 | 2 | no | — |
| 810 | C22⋊C4 | — | 2 | 2 | no | — |
| 811 | C22⋊C4 | — | 2 | 1 | no | — |
| 812 | C22⋊C4 | — | 6 | 1 | no | — |
| 813 | C22⋊C4 | — | 6 | 1 | no | — |
| 814 | C22⋊C4 | — | 6 | 2 | no | — |
| 815 | C22⋊C4 | — | 6 | 2 | no | — |
| 816 | C22⋊C4 | — | 6 | 1 | no | — |
| 817 | C22⋊C4 | — | 6 | 1 | no | — |
| 818 | C22⋊C4 | — | 6 | 2 | no | — |
| 819 | C22⋊C4 | — | 6 | 2 | no | — |
| 820 | C22⋊C4 | — | 6 | 2 | no | — |
| 821 | C22⋊C4 | — | 12 | 1 | no | — |
| 822 | C22⋊C4 | — | 12 | 1 | no | — |
| 823 | C42 | — | 2 | 1 | no | — |
| 824 | C42 | — | 2 | 1 | no | — |
| 825 | C42 | — | 6 | 2 | no | — |
| 826 | C42 | — | 6 | 1 | no | — |
| 827 | C42 | — | 6 | 1 | no | — |
| 828 | C42 | — | 12 | 2 | no | — |
| 829 | C42 | D3×D4 | 1 | 2 | yes | — |
| 830 | C22×C3 | — | 2 | 1 | no | — |
| 831 | C22×C3 | — | 2 | 1 | no | — |
| 832 | C22×C3 | — | 4 | 1 | no | — |
| 833 | C22×C3 | — | 4 | 1 | no | — |
| 834 | C22×C3 | — | 4 | 1 | no | — |
| 835 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 836 | C22×C3 | D42 | 1 | 1 | yes | characteristic |
| 837 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 838 | C2×D3 | — | 2 | 1 | no | — |
| 839 | C2×D3 | — | 2 | 1 | no | — |
| 840 | C2×D3 | — | 2 | 1 | no | — |
| 841 | C2×D3 | — | 2 | 2 | no | — |
| 842 | C2×D3 | — | 2 | 1 | no | — |
| 843 | C2×D3 | — | 2 | 1 | no | — |
| 844 | C2×D3 | — | 4 | 2 | no | — |
| 845 | C2×D3 | — | 4 | 2 | no | — |
| 846 | C2×D3 | — | 4 | 1 | no | — |
| 847 | C2×D3 | — | 4 | 1 | no | — |
| 848 | C2×D3 | — | 4 | 1 | no | — |
| 849 | C2×D3 | — | 4 | 1 | no | — |
| 850 | C2×D3 | — | 4 | 1 | no | — |
| 851 | C2×D3 | — | 8 | 4 | no | — |
| 852 | C2×D3 | #456 | 1 | 2 | yes | complemented |
| 853 | C3×C4 | — | 2 | 4 | no | — |
| 854 | C3×C4 | — | 4 | 2 | no | — |
| 855 | C3×C4 | — | 4 | 1 | no | — |
| 856 | C3×C4 | — | 4 | 1 | no | — |
| 857 | C3×C4 | — | 4 | 1 | no | — |
| 858 | C3×C4 | — | 8 | 1 | no | — |
| 859 | C3×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 860 | C3×C4 | #534 | 1 | 1 | yes | characteristic |
| 861 | C3×C4 | D42 | 1 | 1 | yes | characteristic |
| 862 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 863 | Dic3 | — | 2 | 2 | no | — |
| 864 | Dic3 | — | 2 | 1 | no | — |
| 865 | Dic3 | — | 2 | 1 | no | — |
| 866 | Dic3 | — | 4 | 2 | no | — |
| 867 | Dic3 | — | 4 | 1 | no | — |
| 868 | Dic3 | — | 4 | 2 | no | — |
| 869 | Dic3 | — | 8 | 1 | no | — |
| 870 | C23 | — | 2 | 1 | no | — |
| 871 | C23 | — | 3 | 1 | no | — |
| 872 | C23 | — | 3 | 1 | no | — |
| 873 | C23 | — | 6 | 2 | no | — |
| 874 | C23 | — | 6 | 1 | no | — |
| 875 | C23 | — | 6 | 1 | no | — |
| 876 | C23 | — | 6 | 1 | no | — |
| 877 | C23 | — | 6 | 1 | no | — |
| 878 | C23 | — | 12 | 1 | no | — |
| 879 | C23 | — | 12 | 2 | no | — |
| 880 | C23 | — | 12 | 2 | no | — |
| 881 | C23 | — | 24 | 1 | no | — |
| 882 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 883 | Q8 | — | 2 | 1 | no | — |
| 884 | Q8 | — | 2 | 1 | no | — |
| 885 | Q8 | — | 3 | 2 | no | — |
| 886 | Q8 | — | 4 | 1 | no | — |
| 887 | Q8 | — | 4 | 1 | no | — |
| 888 | Q8 | — | 4 | 1 | no | — |
| 889 | Q8 | — | 4 | 1 | no | — |
| 890 | Q8 | — | 4 | 1 | no | — |
| 891 | Q8 | — | 4 | 1 | no | — |
| 892 | Q8 | — | 4 | 1 | no | — |
| 893 | Q8 | — | 4 | 1 | no | — |
| 894 | Q8 | — | 6 | 1 | no | — |
| 895 | Q8 | — | 6 | 1 | no | — |
| 896 | Q8 | — | 6 | 1 | no | — |
| 897 | Q8 | — | 12 | 2 | no | — |
| 898 | Q8 | — | 12 | 4 | no | — |
| 899 | D4 | — | 2 | 1 | no | — |
| 900 | D4 | — | 2 | 1 | no | — |
| 901 | D4 | — | 3 | 2 | no | — |
| 902 | D4 | — | 4 | 1 | no | — |
| 903 | D4 | — | 4 | 1 | no | — |
| 904 | D4 | — | 6 | 2 | no | — |
| 905 | D4 | — | 6 | 2 | no | — |
| 906 | D4 | — | 6 | 1 | no | — |
| 907 | D4 | — | 6 | 1 | no | — |
| 908 | D4 | — | 6 | 1 | no | — |
| 909 | D4 | — | 12 | 2 | no | — |
| 910 | D4 | — | 12 | 2 | no | — |
| 911 | D4 | — | 12 | 4 | no | — |
| 912 | D4 | — | 12 | 2 | no | — |
| 913 | D4 | — | 12 | 2 | no | — |
| 914 | D4 | — | 12 | 1 | no | — |
| 915 | D4 | — | 12 | 1 | no | — |
| 916 | D4 | — | 24 | 1 | no | — |
| 917 | D4 | — | 24 | 2 | no | — |
| 918 | C2×C4 | — | 2 | 2 | no | — |
| 919 | C2×C4 | — | 2 | 2 | no | — |
| 920 | C2×C4 | — | 2 | 2 | no | — |
| 921 | C2×C4 | — | 2 | 1 | no | — |
| 922 | C2×C4 | — | 2 | 1 | no | — |
| 923 | C2×C4 | — | 2 | 2 | no | — |
| 924 | C2×C4 | — | 2 | 1 | no | — |
| 925 | C2×C4 | — | 2 | 2 | no | — |
| 926 | C2×C4 | — | 2 | 2 | no | — |
| 927 | C2×C4 | — | 3 | 1 | no | — |
| 928 | C2×C4 | — | 3 | 1 | no | — |
| 929 | C2×C4 | — | 4 | 1 | no | — |
| 930 | C2×C4 | — | 4 | 1 | no | — |
| 931 | C2×C4 | — | 4 | 1 | no | — |
| 932 | C2×C4 | — | 4 | 1 | no | — |
| 933 | C2×C4 | — | 4 | 1 | no | — |
| 934 | C2×C4 | — | 6 | 1 | no | — |
| 935 | C2×C4 | — | 6 | 1 | no | — |
| 936 | C2×C4 | — | 6 | 1 | no | — |
| 937 | C2×C4 | — | 6 | 1 | no | — |
| 938 | C2×C4 | — | 6 | 1 | no | — |
| 939 | C2×C4 | — | 6 | 2 | no | — |
| 940 | C2×C4 | — | 6 | 1 | no | — |
| 941 | C2×C4 | — | 6 | 1 | no | — |
| 942 | C2×C4 | — | 6 | 1 | no | — |
| 943 | C2×C4 | — | 6 | 1 | no | — |
| 944 | C2×C4 | — | 6 | 1 | no | — |
| 945 | C2×C4 | — | 6 | 1 | no | — |
| 946 | C2×C4 | — | 6 | 2 | no | — |
| 947 | C2×C4 | — | 6 | 2 | no | — |
| 948 | C2×C4 | — | 6 | 2 | no | — |
| 949 | C2×C4 | — | 6 | 1 | no | — |
| 950 | C2×C4 | — | 12 | 8 | no | — |
| 951 | C2×C4 | — | 12 | 2 | no | — |
| 952 | C2×C4 | — | 12 | 2 | no | — |
| 953 | C2×C4 | — | 12 | 4 | no | — |
| 954 | C2×C4 | — | 12 | 4 | no | — |
| 955 | C2×C4 | — | 12 | 2 | no | — |
| 956 | C2×C4 | — | 12 | 1 | no | — |
| 957 | C2×C4 | — | 12 | 1 | no | — |
| 958 | C2×C4 | — | 12 | 1 | no | — |
| 959 | C2×C4 | — | 12 | 1 | no | — |
| 960 | C2×C4 | — | 12 | 2 | no | — |
| 961 | C2×C4 | — | 12 | 2 | no | — |
| 962 | C2×C4 | — | 12 | 1 | no | — |
| 963 | C2×C4 | — | 24 | 2 | no | — |
| 964 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 965 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 966 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 967 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 968 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 969 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 970 | C8 | — | 4 | 1 | no | — |
| 971 | C8 | — | 4 | 1 | no | — |
| 972 | C8 | — | 6 | 2 | no | — |
| 973 | C8 | — | 12 | 1 | no | — |
| 974 | C2×C3 | — | 2 | 1 | no | — |
| 975 | C2×C3 | — | 2 | 1 | no | — |
| 976 | C2×C3 | — | 8 | 1 | no | — |
| 977 | C2×C3 | #2410 | 1 | 1 | yes | characteristic |
| 978 | C2×C3 | C2×#456 | 1 | 1 | yes | characteristic |
| 979 | C2×C3 | #3018 | 1 | 1 | yes | characteristic |
| 980 | D3 | — | 2 | 2 | no | — |
| 981 | D3 | — | 4 | 1 | no | — |
| 982 | D3 | — | 4 | 2 | no | — |
| 983 | D3 | — | 8 | 1 | no | — |
| 984 | C22 | — | 2 | 1 | no | — |
| 985 | C22 | — | 2 | 1 | no | — |
| 986 | C22 | — | 3 | 2 | no | — |
| 987 | C22 | — | 4 | 1 | no | — |
| 988 | C22 | — | 4 | 1 | no | — |
| 989 | C22 | — | 4 | 1 | no | — |
| 990 | C22 | — | 6 | 1 | no | — |
| 991 | C22 | — | 6 | 1 | no | — |
| 992 | C22 | — | 6 | 1 | no | — |
| 993 | C22 | — | 6 | 1 | no | — |
| 994 | C22 | — | 6 | 1 | no | — |
| 995 | C22 | — | 6 | 2 | no | — |
| 996 | C22 | — | 12 | 2 | no | — |
| 997 | C22 | — | 12 | 2 | no | — |
| 998 | C22 | — | 12 | 1 | no | — |
| 999 | C22 | — | 12 | 1 | no | — |
| 1000 | C22 | — | 12 | 1 | no | — |
| 1001 | C22 | — | 12 | 1 | no | — |
| 1002 | C22 | — | 12 | 1 | no | — |
| 1003 | C22 | — | 24 | 4 | no | — |
| 1004 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 1005 | C22 | #5590 | 1 | 1 | yes | characteristic |
| 1006 | C22 | #5610 | 1 | 1 | yes | characteristic |
| 1007 | C4 | — | 2 | 4 | no | — |
| 1008 | C4 | — | 4 | 1 | no | — |
| 1009 | C4 | — | 4 | 1 | no | — |
| 1010 | C4 | — | 4 | 2 | no | — |
| 1011 | C4 | — | 4 | 1 | no | — |
| 1012 | C4 | — | 6 | 1 | no | — |
| 1013 | C4 | — | 6 | 1 | no | — |
| 1014 | C4 | — | 6 | 2 | no | — |
| 1015 | C4 | — | 8 | 1 | no | — |
| 1016 | C4 | — | 12 | 2 | no | — |
| 1017 | C4 | — | 12 | 2 | no | — |
| 1018 | C4 | — | 12 | 1 | no | — |
| 1019 | C4 | — | 24 | 1 | no | — |
| 1020 | C4 | #5589 | 1 | 1 | yes | characteristic |
| 1021 | C4 | D3×#121 | 1 | 1 | yes | characteristic |
| 1022 | C4 | #5612 | 1 | 1 | yes | characteristic |
| 1023 | C4 | #5717 | 1 | 1 | yes | characteristic |
| 1024 | C3 | #24466 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 1025 | C2 | — | 2 | 1 | no | — |
| 1026 | C2 | — | 2 | 1 | no | — |
| 1027 | C2 | — | 6 | 2 | no | — |
| 1028 | C2 | — | 8 | 1 | no | — |
| 1029 | C2 | — | 12 | 1 | no | — |
| 1030 | C2 | — | 12 | 2 | no | — |
| 1031 | C2 | — | 24 | 1 | no | — |
| 1032 | C2 | #76755 | 1 | 1 | yes | characteristic |
| 1033 | C2 | D3×#456 | 1 | 1 | yes | characteristic |
| 1034 | C2 | #80298 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #83981 | C2 | semidirect |
| 3. #83269 | C2 | semidirect |
| 4. C2×#5095 | C2 | semidirect |
| 5. C2×D3×#104 | C2 | semidirect |
| 6. #78962 | C2 | semidirect |
| 7. C3×#2005 | C2 | semidirect |
| 8. #72110 | C2 | semidirect |
| 9. #71863 | C2 | semidirect |
| 10. #70361 | C2 | semidirect |
| 11. #70348 | C2 | semidirect |
| 12. #70121 | C2 | semidirect |
| 13. #70115 | C2 | semidirect |
| 14. #68771 | C2 | semidirect |
| 15. #68756 | C2 | semidirect |
| 21. C2×C3×C4⋊Q8 | C22 | semidirect |
| 26. C2×#942 | C22 | semidirect |
| 42. C3×#419 | C22 | semidirect |
| 43. C2×C3×#101 | C22 | semidirect |
| 46. #5229 | C22 | semidirect |
| 47. #5229 | C22 | semidirect |
| 48. C2×#836 | C22 | semidirect |
| 54. C2×#825 | C22 | semidirect |
| 56. #5133 | C22 | semidirect |
| 59. #4995 | C22 | semidirect |
| 62. #4935 | C22 | semidirect |
| 64. C2×#805 | C22 | semidirect |
| 70. C3×#339 | C22 | semidirect |
| 71. #4554 | C22 | semidirect |
| 72. #4554 | C22 | semidirect |
| 73. #4532 | C22 | semidirect |
| 83. #2005 | D3 | semidirect |
| 221. #805 | D4 | semidirect |
| 238. C2×C4⋊Q8 | C2×D3 | semidirect |
| 263. #419 | C2×D3 | semidirect |
| 268. C2×#101 | C2×D3 | semidirect |
| 278. #339 | C2×D3 | semidirect |
| 852. C2×D3 | #456 | semidirect |
| 1024. C3 | #24466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86356 | 2 |
| #83981 | 2 |
| #83269 | 2 |
| C2×#5095 | 2 |
| C2×D3×#104 | 2 |
| #78962 | 2 |
| C3×#2005 | 2 |
| #72110 | 2 |
| #71863 | 2 |
| #70361 | 2 |
| #70348 | 2 |
| #70121 | 2 |
| #70115 | 2 |
| #68771 | 2 |
| #68756 | 2 |
| #24466 | 3 |