Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1790 conjugacy classes of subgroups.
The subgroup lattice has 814 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86215 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #86098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×C3×#501 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #83207 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83015 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #81977 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #81976 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #81975 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #81974 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #81973 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | D3×#501 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #79146 | C2 | 1 | 2 | yes | maximal |
| 13 | #79139 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #79116 | C2 | 1 | 2 | yes | maximal |
| 15 | #79110 | C2 | 1 | 2 | yes | maximal, complemented |
| 16 | #78486 | C2 | 1 | 1 | yes | maximal, characteristic |
| 17 | #78479 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #60668 | — | 3 | 1 | no | maximal, Sylow |
| 19 | C2×C3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C3×#125 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×#67 | — | 2 | 2 | no | — |
| 22 | C2×#901 | C22 | 1 | 2 | yes | — |
| 23 | #5730 | — | 2 | 1 | no | — |
| 24 | #5729 | C22 | 1 | 4 | yes | — |
| 25 | #5728 | C22 | 1 | 2 | yes | — |
| 26 | #5727 | — | 2 | 1 | no | — |
| 27 | D3×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 28 | #5722 | — | 2 | 1 | no | — |
| 29 | #5721 | — | 2 | 1 | no | — |
| 30 | #5690 | — | 2 | 1 | no | — |
| 31 | #5690 | — | 2 | 1 | no | — |
| 32 | #5689 | C22 | 1 | 2 | yes | — |
| 33 | #5689 | C22 | 1 | 2 | yes | — |
| 34 | #5688 | C22 | 1 | 2 | yes | — |
| 35 | D3×#125 | C22 | 1 | 2 | yes | — |
| 36 | #5685 | — | 2 | 1 | no | — |
| 37 | #5685 | — | 2 | 1 | no | — |
| 38 | #5511 | — | 2 | 2 | no | — |
| 39 | #5511 | — | 2 | 2 | no | — |
| 40 | #5511 | — | 2 | 2 | no | — |
| 41 | #5504 | C22 | 1 | 1 | yes | characteristic |
| 42 | #5504 | C22 | 1 | 2 | yes | — |
| 43 | #5504 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5500 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5500 | C22 | 1 | 2 | yes | — |
| 46 | #5500 | C22 | 1 | 1 | yes | characteristic |
| 47 | C4×#235 | C22 | 1 | 1 | yes | characteristic |
| 48 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 49 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 50 | C3×#501 | C22 | 1 | 2 | yes | — |
| 51 | C3×#501 | C22 | 1 | 4 | yes | — |
| 52 | C3×#501 | C22 | 1 | 2 | yes | — |
| 53 | C2×C3×#107 | C22 | 1 | 2 | yes | — |
| 54 | C2×C3×#106 | C22 | 1 | 2 | yes | — |
| 55 | C2×C3×#97 | C22 | 1 | 1 | yes | characteristic |
| 56 | #5106 | C22 | 1 | 2 | yes | — |
| 57 | #5106 | C22 | 1 | 2 | yes | — |
| 58 | #5101 | C22 | 1 | 2 | yes | — |
| 59 | #5081 | C22 | 1 | 2 | yes | — |
| 60 | #5081 | C22 | 1 | 2 | yes | — |
| 61 | #5080 | C22 | 1 | 2 | yes | — |
| 62 | #5078 | C22 | 1 | 2 | yes | — |
| 63 | #5065 | C22 | 1 | 4 | yes | — |
| 64 | #5064 | C22 | 1 | 2 | yes | — |
| 65 | #5064 | C22 | 1 | 2 | yes | — |
| 66 | #4964 | C22 | 1 | 2 | yes | — |
| 67 | #4964 | C22 | 1 | 2 | yes | — |
| 68 | #4964 | C22 | 1 | 2 | yes | — |
| 69 | #4964 | C22 | 1 | 2 | yes | — |
| 70 | C4×#208 | C22 | 1 | 1 | yes | characteristic |
| 71 | #4881 | C22 | 1 | 4 | yes | — |
| 72 | #4881 | C22 | 1 | 4 | yes | — |
| 73 | #4880 | C22 | 1 | 4 | yes | — |
| 74 | D3×#107 | C22 | 1 | 4 | yes | — |
| 75 | #4878 | C22 | 1 | 4 | yes | — |
| 76 | #4876 | C22 | 1 | 4 | yes | — |
| 77 | #4876 | C22 | 1 | 4 | yes | — |
| 78 | #4874 | C22 | 1 | 4 | yes | — |
| 79 | #4861 | C22 | 1 | 4 | yes | — |
| 80 | #4861 | C22 | 1 | 4 | yes | — |
| 81 | #4860 | C22 | 1 | 4 | yes | — |
| 82 | D3×#106 | C22 | 1 | 4 | yes | — |
| 83 | #4858 | C22 | 1 | 4 | yes | — |
| 84 | #4856 | C22 | 1 | 4 | yes | — |
| 85 | #4856 | C22 | 1 | 4 | yes | — |
| 86 | #4855 | C22 | 1 | 4 | yes | — |
| 87 | #4708 | C22 | 1 | 4 | yes | — |
| 88 | #4707 | C22 | 1 | 2 | yes | — |
| 89 | D3×#97 | C22 | 1 | 2 | yes | — |
| 90 | #4702 | C22 | 1 | 1 | yes | characteristic |
| 91 | #4702 | C22 | 1 | 1 | yes | characteristic |
| 92 | #4702 | C22 | 1 | 2 | yes | — |
| 93 | #4702 | C22 | 1 | 2 | yes | — |
| 94 | #4702 | C22 | 1 | 1 | yes | characteristic |
| 95 | #4702 | C22 | 1 | 1 | yes | characteristic |
| 96 | #3504 | — | 3 | 1 | no | — |
| 97 | #3503 | — | 3 | 1 | no | — |
| 98 | #3166 | — | 3 | 2 | no | — |
| 99 | #3166 | — | 3 | 1 | no | — |
| 100 | #3165 | — | 3 | 2 | no | — |
| 101 | #3165 | — | 3 | 1 | no | — |
| 102 | #3164 | — | 3 | 4 | no | — |
| 103 | #3164 | — | 3 | 2 | no | — |
| 104 | #3163 | — | 3 | 4 | no | — |
| 105 | #3163 | — | 3 | 2 | no | — |
| 106 | #3162 | — | 3 | 2 | no | — |
| 107 | #3162 | — | 3 | 1 | no | — |
| 108 | C2×#501 | — | 3 | 2 | no | — |
| 109 | C2×#501 | D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | #2913 | — | 3 | 2 | no | — |
| 111 | #2912 | — | 3 | 2 | no | — |
| 112 | #2875 | — | 3 | 1 | no | — |
| 113 | C22×C3×Q8 | — | 2 | 1 | no | — |
| 114 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 115 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 116 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 117 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 118 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 119 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 120 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 121 | C3×#125 | — | 2 | 1 | no | — |
| 122 | C3×#125 | — | 2 | 1 | no | — |
| 123 | C3×#125 | C23 | 1 | 2 | yes | — |
| 124 | C3×#125 | C23 | 1 | 2 | yes | — |
| 125 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 126 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 127 | C2×C3×C4⋊C4 | — | 2 | 1 | no | — |
| 128 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 130 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 131 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 132 | #946 | — | 2 | 2 | no | — |
| 133 | #946 | — | 2 | 4 | no | — |
| 134 | Q8×Dic3 | — | 2 | 2 | no | — |
| 135 | #944 | — | 2 | 4 | no | — |
| 136 | #944 | — | 2 | 2 | no | — |
| 137 | C4×#67 | — | 2 | 2 | no | — |
| 138 | C4×#67 | — | 2 | 2 | no | — |
| 139 | C4×#67 | — | 2 | 4 | no | — |
| 140 | C4×#67 | D4 | 1 | 2 | yes | — |
| 141 | C4×#67 | D4 | 1 | 2 | yes | — |
| 142 | #926 | C23 | 1 | 1 | yes | characteristic |
| 143 | #926 | C23 | 1 | 1 | yes | characteristic |
| 144 | #926 | C23 | 1 | 2 | yes | — |
| 145 | #926 | C23 | 1 | 1 | yes | characteristic |
| 146 | #924 | — | 2 | 1 | no | — |
| 147 | #924 | — | 2 | 1 | no | — |
| 148 | #924 | — | 2 | 1 | no | — |
| 149 | #924 | — | 2 | 1 | no | — |
| 150 | #924 | — | 2 | 2 | no | — |
| 151 | #924 | — | 2 | 2 | no | — |
| 152 | #924 | — | 2 | 4 | no | — |
| 153 | C2×#208 | C23 | 1 | 2 | yes | — |
| 154 | #901 | Q8 | 1 | 16 | yes | complemented |
| 155 | C2×ΓL(1,𝔽25) | C23 | 1 | 4 | yes | — |
| 156 | C2×D3×C8 | C23 | 1 | 4 | yes | — |
| 157 | #897 | — | 2 | 2 | no | — |
| 158 | #897 | — | 2 | 2 | no | — |
| 159 | #897 | — | 2 | 2 | no | — |
| 160 | #896 | — | 2 | 2 | no | — |
| 161 | #896 | — | 2 | 2 | no | — |
| 162 | #896 | — | 2 | 2 | no | — |
| 163 | #896 | — | 2 | 2 | no | — |
| 164 | #896 | — | 2 | 4 | no | — |
| 165 | #893 | — | 2 | 1 | no | — |
| 166 | #893 | — | 2 | 1 | no | — |
| 167 | #893 | — | 2 | 2 | no | — |
| 168 | #892 | C23 | 1 | 2 | yes | — |
| 169 | #892 | C23 | 1 | 4 | yes | — |
| 170 | #892 | C23 | 1 | 2 | yes | — |
| 171 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 172 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 173 | D3×C4⋊C4 | — | 2 | 2 | no | — |
| 174 | D3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 175 | D3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 176 | D3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 177 | #890 | — | 2 | 1 | no | — |
| 178 | #890 | — | 2 | 1 | no | — |
| 179 | #890 | — | 2 | 2 | no | — |
| 180 | #890 | C23 | 1 | 2 | yes | — |
| 181 | #890 | C23 | 1 | 4 | yes | — |
| 182 | #890 | C23 | 1 | 2 | yes | — |
| 183 | #889 | — | 2 | 2 | no | — |
| 184 | #889 | — | 2 | 2 | no | — |
| 185 | #889 | — | 2 | 4 | no | — |
| 186 | #889 | — | 2 | 2 | no | — |
| 187 | #889 | — | 2 | 2 | no | — |
| 188 | #888 | — | 2 | 1 | no | — |
| 189 | #888 | — | 2 | 1 | no | — |
| 190 | #888 | — | 2 | 2 | no | — |
| 191 | #888 | — | 2 | 2 | no | — |
| 192 | #888 | — | 2 | 2 | no | — |
| 193 | #888 | — | 2 | 2 | no | — |
| 194 | #888 | C23 | 1 | 2 | yes | — |
| 195 | #888 | C23 | 1 | 4 | yes | — |
| 196 | #888 | C23 | 1 | 2 | yes | — |
| 197 | #887 | — | 2 | 1 | no | — |
| 198 | #887 | — | 2 | 1 | no | — |
| 199 | #887 | — | 2 | 2 | no | — |
| 200 | #887 | — | 2 | 2 | no | — |
| 201 | #887 | — | 2 | 2 | no | — |
| 202 | #887 | — | 2 | 2 | no | — |
| 203 | C4×D12 | D4 | 1 | 1 | yes | characteristic |
| 204 | C4×D12 | D4 | 1 | 1 | yes | characteristic |
| 205 | #872 | C23 | 1 | 2 | yes | — |
| 206 | C42×D3 | C23 | 1 | 2 | yes | — |
| 207 | #870 | C23 | 1 | 1 | yes | characteristic |
| 208 | #870 | C23 | 1 | 1 | yes | characteristic |
| 209 | #870 | C23 | 1 | 2 | yes | — |
| 210 | #869 | C23 | 1 | 1 | yes | characteristic |
| 211 | #869 | C23 | 1 | 1 | yes | characteristic |
| 212 | #869 | C23 | 1 | 1 | yes | characteristic |
| 213 | #869 | C23 | 1 | 1 | yes | characteristic |
| 214 | C4×Dic6 | — | 2 | 1 | no | — |
| 215 | C4×Dic6 | — | 2 | 1 | no | — |
| 216 | C4×Dic6 | — | 2 | 1 | no | — |
| 217 | C4×Dic6 | — | 2 | 1 | no | — |
| 218 | C4×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 219 | C4×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 220 | C3×#107 | C23 | 1 | 4 | yes | — |
| 221 | C3×#107 | C23 | 1 | 4 | yes | — |
| 222 | C3×#106 | C23 | 1 | 4 | yes | — |
| 223 | C3×#106 | C23 | 1 | 4 | yes | — |
| 224 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 225 | C3×#97 | C23 | 1 | 1 | yes | characteristic |
| 226 | C3×#97 | C23 | 1 | 2 | yes | — |
| 227 | #818 | C23 | 1 | 2 | yes | — |
| 228 | #818 | C23 | 1 | 2 | yes | — |
| 229 | #818 | C23 | 1 | 2 | yes | — |
| 230 | #818 | C23 | 1 | 2 | yes | — |
| 231 | #817 | C23 | 1 | 2 | yes | — |
| 232 | #817 | C23 | 1 | 2 | yes | — |
| 233 | #817 | C23 | 1 | 2 | yes | — |
| 234 | #817 | C23 | 1 | 2 | yes | — |
| 235 | #815 | C23 | 1 | 4 | yes | — |
| 236 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 237 | #808 | C23 | 1 | 4 | yes | — |
| 238 | #808 | C23 | 1 | 4 | yes | — |
| 239 | #808 | C23 | 1 | 4 | yes | — |
| 240 | #808 | C23 | 1 | 4 | yes | — |
| 241 | #807 | C23 | 1 | 4 | yes | — |
| 242 | #807 | C23 | 1 | 4 | yes | — |
| 243 | #807 | C23 | 1 | 4 | yes | — |
| 244 | #807 | C23 | 1 | 4 | yes | — |
| 245 | #803 | C23 | 1 | 2 | yes | — |
| 246 | C4×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 247 | C2×#131 | — | 3 | 2 | no | — |
| 248 | Q82 | — | 6 | 1 | no | — |
| 249 | #557 | — | 6 | 1 | no | — |
| 250 | #557 | — | 6 | 1 | no | — |
| 251 | #557 | — | 6 | 1 | no | — |
| 252 | #554 | — | 6 | 2 | no | — |
| 253 | #554 | — | 6 | 2 | no | — |
| 254 | #554 | — | 6 | 2 | no | — |
| 255 | #554 | — | 6 | 1 | no | — |
| 256 | #554 | — | 6 | 1 | no | — |
| 257 | #554 | — | 6 | 1 | no | — |
| 258 | D4×Q8 | — | 6 | 1 | no | — |
| 259 | D4×Q8 | — | 6 | 2 | no | — |
| 260 | #544 | — | 3 | 4 | no | — |
| 261 | #544 | — | 3 | 2 | no | — |
| 262 | #544 | — | 3 | 2 | no | — |
| 263 | #544 | — | 3 | 1 | no | — |
| 264 | #544 | — | 3 | 2 | no | — |
| 265 | #544 | — | 3 | 1 | no | — |
| 266 | #533 | — | 3 | 2 | no | — |
| 267 | #533 | — | 3 | 2 | no | — |
| 268 | #533 | — | 3 | 1 | no | — |
| 269 | #533 | — | 3 | 1 | no | — |
| 270 | C2×C4⋊Q8 | — | 3 | 2 | no | — |
| 271 | C2×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 272 | C2×#125 | — | 3 | 2 | no | — |
| 273 | C2×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 274 | #520 | — | 3 | 1 | no | — |
| 275 | #520 | — | 3 | 2 | no | — |
| 276 | #520 | — | 3 | 1 | no | — |
| 277 | C4×#41 | — | 3 | 1 | no | — |
| 278 | #501 | — | 3 | 2 | no | — |
| 279 | #501 | — | 3 | 2 | no | — |
| 280 | #501 | — | 3 | 2 | no | — |
| 281 | #501 | — | 3 | 2 | no | — |
| 282 | #501 | — | 3 | 4 | no | — |
| 283 | #501 | — | 3 | 4 | no | — |
| 284 | #501 | — | 3 | 4 | no | — |
| 285 | #501 | — | 3 | 4 | no | — |
| 286 | #501 | — | 3 | 1 | no | — |
| 287 | #501 | — | 3 | 1 | no | — |
| 288 | #501 | — | 3 | 2 | no | — |
| 289 | #501 | — | 3 | 2 | no | — |
| 290 | #501 | — | 3 | 1 | no | — |
| 291 | #501 | — | 3 | 1 | no | — |
| 292 | #501 | C2×D3 | 1 | 2 | yes | — |
| 293 | #501 | C2×D3 | 1 | 4 | yes | — |
| 294 | #501 | C2×D3 | 1 | 2 | yes | — |
| 295 | #500 | — | 3 | 2 | no | — |
| 296 | #500 | — | 3 | 4 | no | — |
| 297 | #499 | — | 3 | 4 | no | — |
| 298 | #499 | — | 3 | 4 | no | — |
| 299 | #499 | — | 3 | 4 | no | — |
| 300 | #498 | — | 3 | 2 | no | — |
| 301 | #498 | — | 3 | 4 | no | — |
| 302 | #428 | — | 3 | 2 | no | — |
| 303 | #428 | — | 3 | 2 | no | — |
| 304 | #428 | — | 3 | 2 | no | — |
| 305 | #428 | — | 3 | 2 | no | — |
| 306 | #428 | — | 3 | 4 | no | — |
| 307 | #428 | — | 3 | 4 | no | — |
| 308 | #428 | — | 3 | 4 | no | — |
| 309 | #428 | — | 3 | 4 | no | — |
| 310 | #427 | — | 3 | 2 | no | — |
| 311 | #427 | — | 3 | 2 | no | — |
| 312 | #427 | — | 3 | 4 | no | — |
| 313 | #427 | — | 3 | 4 | no | — |
| 314 | C2×#107 | — | 3 | 4 | no | — |
| 315 | C2×#107 | C2×D3 | 1 | 2 | yes | — |
| 316 | C2×#106 | — | 3 | 4 | no | — |
| 317 | C2×#106 | C2×D3 | 1 | 2 | yes | — |
| 318 | #405 | — | 3 | 2 | no | — |
| 319 | #405 | — | 3 | 4 | no | — |
| 320 | C4×M16 | — | 3 | 1 | no | — |
| 321 | C4×M16 | — | 3 | 2 | no | — |
| 322 | C2×#97 | — | 3 | 2 | no | — |
| 323 | C2×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 324 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 325 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 326 | C2×C3×Q8 | — | 8 | 2 | no | — |
| 327 | C22×C3×C4 | — | 2 | 1 | no | — |
| 328 | C22×C3×C4 | — | 2 | 1 | no | — |
| 329 | C22×C3×C4 | — | 2 | 2 | no | — |
| 330 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 331 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 332 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 333 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 334 | D3×Q8 | — | 8 | 4 | no | — |
| 335 | #235 | C2×Q8 | 1 | 8 | yes | — |
| 336 | C2×D12 | C2×D4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4×D3 | — | 2 | 2 | no | — |
| 338 | C2×C4×D3 | — | 2 | 2 | no | — |
| 339 | C2×C4×D3 | — | 2 | 4 | no | — |
| 340 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 341 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 342 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 343 | C2×Dic6 | — | 2 | 1 | no | — |
| 344 | C2×Dic6 | — | 2 | 1 | no | — |
| 345 | C2×Dic6 | — | 2 | 1 | no | — |
| 346 | C2×Dic6 | — | 2 | 1 | no | — |
| 347 | C2×Dic6 | — | 2 | 2 | no | — |
| 348 | C2×Dic6 | — | 2 | 2 | no | — |
| 349 | C2×Dic6 | — | 2 | 4 | no | — |
| 350 | C2×Dic6 | C2×D4 | 1 | 1 | yes | characteristic |
| 351 | C2×C3×C8 | C2×Q8 | 1 | 8 | yes | complemented |
| 352 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 353 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 354 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 355 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 356 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 357 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 358 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 359 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 360 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 361 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 362 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 364 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 365 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 366 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 367 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 369 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 370 | #217 | — | 2 | 2 | no | — |
| 371 | #217 | — | 2 | 1 | no | — |
| 372 | #217 | — | 2 | 1 | no | — |
| 373 | #217 | C2×D4 | 1 | 2 | yes | — |
| 374 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 375 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 376 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 377 | (C2×D3)⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 378 | (C2×D3)⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 379 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 380 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 381 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 382 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 383 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 384 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 385 | C4⋊Dic3 | — | 2 | 4 | no | — |
| 386 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 387 | C4⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 388 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 389 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 390 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 391 | C4⋊Dic3 | C24 | 1 | 2 | yes | — |
| 392 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 393 | C4⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 394 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 395 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 396 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 397 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 398 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 399 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 400 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 401 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 402 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 403 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 404 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 405 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 406 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 407 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 408 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 409 | Dic3⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 410 | Dic3⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 411 | C4×Dic3 | — | 2 | 2 | no | — |
| 412 | C4×Dic3 | — | 2 | 1 | no | — |
| 413 | C4×Dic3 | — | 2 | 1 | no | — |
| 414 | C4×Dic3 | — | 2 | 2 | no | — |
| 415 | C4×Dic3 | — | 2 | 2 | no | — |
| 416 | C4×Dic3 | — | 2 | 4 | no | — |
| 417 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 418 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 419 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 420 | #208 | C2×Q8 | 1 | 8 | yes | complemented |
| 421 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 422 | ΓL(1,𝔽25) | C2×Q8 | 1 | 16 | yes | complemented |
| 423 | D3×C8 | C2×Q8 | 1 | 16 | yes | complemented |
| 424 | C2×#41 | — | 3 | 1 | no | — |
| 425 | C22×Q8 | — | 2 | 1 | no | — |
| 426 | C22×Q8 | — | 6 | 2 | no | — |
| 427 | #131 | — | 3 | 16 | no | — |
| 428 | C2×M16 | — | 3 | 2 | no | — |
| 429 | C2×M16 | — | 3 | 4 | no | — |
| 430 | C22×C8 | — | 3 | 4 | no | — |
| 431 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 432 | C4⋊Q8 | — | 2 | 1 | no | — |
| 433 | C4⋊Q8 | — | 2 | 1 | no | — |
| 434 | C4⋊Q8 | — | 3 | 4 | no | — |
| 435 | C4⋊Q8 | — | 3 | 2 | no | — |
| 436 | C4⋊Q8 | — | 3 | 2 | no | — |
| 437 | C4⋊Q8 | — | 3 | 1 | no | — |
| 438 | C4⋊Q8 | — | 3 | 1 | no | — |
| 439 | C4⋊Q8 | — | 3 | 1 | no | — |
| 440 | C4⋊Q8 | — | 3 | 1 | no | — |
| 441 | C4⋊Q8 | — | 6 | 2 | no | — |
| 442 | C4⋊Q8 | — | 6 | 2 | no | — |
| 443 | C4⋊Q8 | — | 6 | 2 | no | — |
| 444 | C4⋊Q8 | — | 6 | 2 | no | — |
| 445 | C4⋊Q8 | — | 6 | 2 | no | — |
| 446 | C4⋊Q8 | — | 6 | 1 | no | — |
| 447 | C4⋊Q8 | — | 6 | 1 | no | — |
| 448 | C4⋊Q8 | — | 6 | 4 | no | — |
| 449 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 450 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 451 | #125 | — | 2 | 1 | no | — |
| 452 | #125 | — | 2 | 1 | no | — |
| 453 | #125 | — | 3 | 2 | no | — |
| 454 | #125 | — | 3 | 2 | no | — |
| 455 | #125 | — | 3 | 4 | no | — |
| 456 | #125 | — | 3 | 1 | no | — |
| 457 | #125 | — | 3 | 1 | no | — |
| 458 | #125 | — | 3 | 2 | no | — |
| 459 | #125 | — | 6 | 2 | no | — |
| 460 | #125 | — | 6 | 2 | no | — |
| 461 | #125 | — | 6 | 2 | no | — |
| 462 | #125 | — | 6 | 2 | no | — |
| 463 | #125 | — | 6 | 4 | no | — |
| 464 | #125 | — | 6 | 1 | no | — |
| 465 | #125 | — | 6 | 1 | no | — |
| 466 | #125 | — | 6 | 2 | no | — |
| 467 | #125 | C22×D3 | 1 | 2 | yes | — |
| 468 | #125 | C22×D3 | 1 | 2 | yes | — |
| 469 | C22⋊Q8 | — | 6 | 4 | no | — |
| 470 | C22⋊Q8 | — | 6 | 2 | no | — |
| 471 | C22⋊Q8 | — | 6 | 2 | no | — |
| 472 | C22⋊Q8 | — | 6 | 2 | no | — |
| 473 | C22⋊Q8 | — | 6 | 2 | no | — |
| 474 | C22⋊Q8 | — | 6 | 4 | no | — |
| 475 | C22⋊Q8 | — | 6 | 2 | no | — |
| 476 | C22⋊Q8 | — | 6 | 2 | no | — |
| 477 | C22⋊Q8 | — | 6 | 4 | no | — |
| 478 | C22⋊Q8 | — | 6 | 2 | no | — |
| 479 | C22⋊Q8 | — | 6 | 2 | no | — |
| 480 | C22⋊Q8 | — | 6 | 2 | no | — |
| 481 | C22⋊Q8 | — | 6 | 2 | no | — |
| 482 | C22⋊Q8 | — | 6 | 1 | no | — |
| 483 | C22⋊Q8 | — | 6 | 1 | no | — |
| 484 | C22⋊Q8 | — | 6 | 1 | no | — |
| 485 | C22⋊Q8 | — | 6 | 1 | no | — |
| 486 | C4×Q8 | — | 3 | 1 | no | — |
| 487 | C4×Q8 | — | 3 | 1 | no | — |
| 488 | C4×Q8 | — | 6 | 2 | no | — |
| 489 | C4×Q8 | — | 6 | 2 | no | — |
| 490 | C4×Q8 | — | 6 | 2 | no | — |
| 491 | C4×Q8 | — | 6 | 2 | no | — |
| 492 | C4×Q8 | — | 6 | 1 | no | — |
| 493 | C4×Q8 | — | 6 | 1 | no | — |
| 494 | C4×Q8 | — | 6 | 2 | no | — |
| 495 | C4×Q8 | — | 6 | 1 | no | — |
| 496 | C4×Q8 | — | 6 | 1 | no | — |
| 497 | C4×Q8 | — | 6 | 1 | no | — |
| 498 | C4×Q8 | — | 6 | 1 | no | — |
| 499 | C4×D4 | — | 3 | 2 | no | — |
| 500 | C4×D4 | — | 3 | 2 | no | — |
| 501 | C4×D4 | — | 3 | 1 | no | — |
| 502 | C4×D4 | — | 3 | 1 | no | — |
| 503 | C4×D4 | — | 6 | 2 | no | — |
| 504 | C4×D4 | — | 6 | 1 | no | — |
| 505 | C4×D4 | — | 6 | 1 | no | — |
| 506 | C4×D4 | — | 6 | 4 | no | — |
| 507 | C4×D4 | — | 6 | 2 | no | — |
| 508 | C4×D4 | — | 6 | 2 | no | — |
| 509 | #117 | — | 3 | 1 | no | — |
| 510 | #117 | — | 3 | 2 | no | — |
| 511 | #117 | — | 3 | 1 | no | — |
| 512 | #117 | — | 3 | 1 | no | — |
| 513 | #117 | — | 3 | 2 | no | — |
| 514 | #117 | — | 3 | 2 | no | — |
| 515 | #117 | — | 3 | 4 | no | — |
| 516 | #117 | — | 3 | 2 | no | — |
| 517 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 518 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 519 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 520 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 521 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 522 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 523 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 524 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 525 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 526 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 527 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 528 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 529 | C2×C42 | — | 3 | 2 | no | — |
| 530 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 531 | #107 | — | 3 | 2 | no | — |
| 532 | #107 | — | 3 | 2 | no | — |
| 533 | #107 | — | 3 | 2 | no | — |
| 534 | #107 | — | 3 | 2 | no | — |
| 535 | #107 | — | 3 | 4 | no | — |
| 536 | #107 | — | 3 | 4 | no | — |
| 537 | #107 | — | 3 | 4 | no | — |
| 538 | #107 | — | 3 | 4 | no | — |
| 539 | #107 | C22×D3 | 1 | 4 | yes | — |
| 540 | #107 | C22×D3 | 1 | 4 | yes | — |
| 541 | #106 | — | 3 | 2 | no | — |
| 542 | #106 | — | 3 | 2 | no | — |
| 543 | #106 | — | 3 | 2 | no | — |
| 544 | #106 | — | 3 | 2 | no | — |
| 545 | #106 | — | 3 | 4 | no | — |
| 546 | #106 | — | 3 | 4 | no | — |
| 547 | #106 | — | 3 | 4 | no | — |
| 548 | #106 | — | 3 | 4 | no | — |
| 549 | #106 | C22×D3 | 1 | 4 | yes | — |
| 550 | #106 | C22×D3 | 1 | 4 | yes | — |
| 551 | #97 | — | 3 | 4 | no | — |
| 552 | #97 | — | 3 | 2 | no | — |
| 553 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 554 | #97 | C22×D3 | 1 | 1 | yes | characteristic |
| 555 | #97 | C22×D3 | 1 | 2 | yes | — |
| 556 | C4×C8 | — | 3 | 4 | no | — |
| 557 | C4×C8 | — | 3 | 2 | no | — |
| 558 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 559 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 560 | C3×Q8 | — | 4 | 4 | no | — |
| 561 | C3×Q8 | — | 8 | 2 | no | — |
| 562 | C2×C3×C4 | — | 2 | 2 | no | — |
| 563 | C2×C3×C4 | — | 2 | 2 | no | — |
| 564 | C2×C3×C4 | — | 2 | 4 | no | — |
| 565 | C2×C3×C4 | — | 4 | 1 | no | — |
| 566 | C2×C3×C4 | — | 4 | 1 | no | — |
| 567 | C2×C3×C4 | — | 8 | 1 | no | — |
| 568 | C2×C3×C4 | — | 8 | 1 | no | — |
| 569 | C2×C3×C4 | — | 8 | 2 | no | — |
| 570 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 571 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 572 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 573 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 574 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 575 | C2×C3×C4 | C22×Q8 | 1 | 4 | yes | — |
| 576 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 577 | #67 | C4⋊Q8 | 1 | 8 | yes | — |
| 578 | C2×Dic3 | — | 2 | 2 | no | — |
| 579 | C2×Dic3 | — | 2 | 1 | no | — |
| 580 | C2×Dic3 | — | 2 | 1 | no | — |
| 581 | C2×Dic3 | — | 2 | 1 | no | — |
| 582 | C2×Dic3 | — | 2 | 1 | no | — |
| 583 | C2×Dic3 | — | 2 | 2 | no | — |
| 584 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 585 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 586 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 587 | D12 | C4⋊Q8 | 1 | 4 | yes | — |
| 588 | C4×D3 | — | 4 | 2 | no | — |
| 589 | C4×D3 | — | 4 | 2 | no | — |
| 590 | C4×D3 | — | 8 | 2 | no | — |
| 591 | C4×D3 | — | 8 | 2 | no | — |
| 592 | C4×D3 | — | 8 | 4 | no | — |
| 593 | C4×D3 | C22×Q8 | 1 | 8 | yes | — |
| 594 | Dic6 | — | 4 | 2 | no | — |
| 595 | Dic6 | — | 4 | 2 | no | — |
| 596 | Dic6 | — | 8 | 2 | no | — |
| 597 | Dic6 | — | 8 | 2 | no | — |
| 598 | Dic6 | — | 8 | 4 | no | — |
| 599 | Dic6 | — | 8 | 1 | no | — |
| 600 | Dic6 | — | 8 | 1 | no | — |
| 601 | Dic6 | C4⋊Q8 | 1 | 4 | yes | — |
| 602 | C3×C8 | C22×Q8 | 1 | 4 | yes | — |
| 603 | C3×C8 | C22×Q8 | 1 | 4 | yes | — |
| 604 | C3⋊C8 | C22×Q8 | 1 | 8 | yes | — |
| 605 | #41 | — | 3 | 8 | no | — |
| 606 | C2×Q8 | — | 2 | 2 | no | — |
| 607 | C2×Q8 | — | 2 | 2 | no | — |
| 608 | C2×Q8 | — | 3 | 1 | no | — |
| 609 | C2×Q8 | — | 6 | 2 | no | — |
| 610 | C2×Q8 | — | 6 | 2 | no | — |
| 611 | C2×Q8 | — | 6 | 4 | no | — |
| 612 | C2×Q8 | — | 6 | 1 | no | — |
| 613 | C2×Q8 | — | 6 | 1 | no | — |
| 614 | C2×Q8 | — | 6 | 1 | no | — |
| 615 | C2×Q8 | — | 6 | 1 | no | — |
| 616 | C2×Q8 | — | 8 | 2 | no | — |
| 617 | C2×Q8 | — | 24 | 4 | no | — |
| 618 | C2×D4 | — | 3 | 2 | no | — |
| 619 | C2×D4 | — | 3 | 1 | no | — |
| 620 | C22×C4 | — | 2 | 1 | no | — |
| 621 | C22×C4 | — | 2 | 1 | no | — |
| 622 | C22×C4 | — | 2 | 2 | no | — |
| 623 | C22×C4 | — | 3 | 2 | no | — |
| 624 | C22×C4 | — | 3 | 2 | no | — |
| 625 | C22×C4 | — | 3 | 2 | no | — |
| 626 | C22×C4 | — | 6 | 2 | no | — |
| 627 | C22×C4 | — | 6 | 2 | no | — |
| 628 | C22×C4 | — | 6 | 4 | no | — |
| 629 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 630 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 631 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 632 | M16 | — | 3 | 8 | no | — |
| 633 | M16 | — | 3 | 16 | no | — |
| 634 | C2×C8 | — | 3 | 4 | no | — |
| 635 | C2×C8 | — | 3 | 16 | no | — |
| 636 | C2×C8 | D3×Q8 | 1 | 8 | yes | complemented |
| 637 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 638 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 639 | C4⋊C4 | — | 2 | 2 | no | — |
| 640 | C4⋊C4 | — | 2 | 2 | no | — |
| 641 | C4⋊C4 | — | 2 | 2 | no | — |
| 642 | C4⋊C4 | — | 2 | 2 | no | — |
| 643 | C4⋊C4 | — | 2 | 2 | no | — |
| 644 | C4⋊C4 | — | 2 | 2 | no | — |
| 645 | C4⋊C4 | — | 2 | 1 | no | — |
| 646 | C4⋊C4 | — | 2 | 1 | no | — |
| 647 | C4⋊C4 | — | 2 | 2 | no | — |
| 648 | C4⋊C4 | — | 3 | 2 | no | — |
| 649 | C4⋊C4 | — | 3 | 1 | no | — |
| 650 | C4⋊C4 | — | 3 | 2 | no | — |
| 651 | C4⋊C4 | — | 3 | 1 | no | — |
| 652 | C4⋊C4 | — | 3 | 1 | no | — |
| 653 | C4⋊C4 | — | 3 | 1 | no | — |
| 654 | C4⋊C4 | — | 3 | 2 | no | — |
| 655 | C4⋊C4 | — | 3 | 2 | no | — |
| 656 | C4⋊C4 | — | 3 | 1 | no | — |
| 657 | C4⋊C4 | — | 3 | 1 | no | — |
| 658 | C4⋊C4 | — | 6 | 2 | no | — |
| 659 | C4⋊C4 | — | 6 | 2 | no | — |
| 660 | C4⋊C4 | — | 6 | 4 | no | — |
| 661 | C4⋊C4 | — | 6 | 2 | no | — |
| 662 | C4⋊C4 | — | 6 | 2 | no | — |
| 663 | C4⋊C4 | — | 6 | 2 | no | — |
| 664 | C4⋊C4 | — | 6 | 2 | no | — |
| 665 | C4⋊C4 | — | 6 | 4 | no | — |
| 666 | C4⋊C4 | — | 6 | 4 | no | — |
| 667 | C4⋊C4 | — | 6 | 4 | no | — |
| 668 | C4⋊C4 | — | 6 | 2 | no | — |
| 669 | C4⋊C4 | — | 6 | 2 | no | — |
| 670 | C4⋊C4 | — | 6 | 1 | no | — |
| 671 | C4⋊C4 | — | 6 | 1 | no | — |
| 672 | C4⋊C4 | — | 6 | 1 | no | — |
| 673 | C4⋊C4 | — | 6 | 1 | no | — |
| 674 | C4⋊C4 | — | 6 | 1 | no | — |
| 675 | C4⋊C4 | — | 6 | 1 | no | — |
| 676 | C4⋊C4 | — | 6 | 2 | no | — |
| 677 | C4⋊C4 | — | 6 | 2 | no | — |
| 678 | C4⋊C4 | — | 6 | 1 | no | — |
| 679 | C4⋊C4 | — | 6 | 1 | no | — |
| 680 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 681 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 682 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 683 | C22⋊C4 | — | 3 | 2 | no | — |
| 684 | C22⋊C4 | — | 3 | 2 | no | — |
| 685 | C22⋊C4 | — | 3 | 2 | no | — |
| 686 | C22⋊C4 | — | 6 | 2 | no | — |
| 687 | C22⋊C4 | — | 6 | 2 | no | — |
| 688 | C22⋊C4 | — | 6 | 4 | no | — |
| 689 | C22⋊C4 | — | 6 | 2 | no | — |
| 690 | C22⋊C4 | — | 6 | 1 | no | — |
| 691 | C22⋊C4 | — | 6 | 1 | no | — |
| 692 | C42 | — | 3 | 2 | no | — |
| 693 | C42 | — | 3 | 2 | no | — |
| 694 | C42 | — | 3 | 2 | no | — |
| 695 | C42 | — | 6 | 2 | no | — |
| 696 | C42 | — | 6 | 2 | no | — |
| 697 | C42 | — | 6 | 4 | no | — |
| 698 | C42 | — | 6 | 2 | no | — |
| 699 | C42 | — | 6 | 1 | no | — |
| 700 | C42 | — | 6 | 1 | no | — |
| 701 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 702 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 703 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 704 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 705 | C22×C3 | — | 2 | 1 | no | — |
| 706 | C22×C3 | — | 2 | 1 | no | — |
| 707 | C22×C3 | C2×C4⋊Q8 | 1 | 2 | yes | — |
| 708 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 709 | C2×D3 | — | 2 | 2 | no | — |
| 710 | C2×D3 | — | 2 | 2 | no | — |
| 711 | C2×D3 | C2×C4⋊Q8 | 1 | 4 | yes | — |
| 712 | C3×C4 | — | 2 | 1 | no | — |
| 713 | C3×C4 | — | 2 | 1 | no | — |
| 714 | C3×C4 | — | 2 | 1 | no | — |
| 715 | C3×C4 | — | 2 | 1 | no | — |
| 716 | C3×C4 | — | 4 | 2 | no | — |
| 717 | C3×C4 | — | 4 | 4 | no | — |
| 718 | C3×C4 | — | 4 | 2 | no | — |
| 719 | C3×C4 | C2×C4⋊Q8 | 1 | 2 | yes | — |
| 720 | C3×C4 | C23×Q8 | 1 | 2 | yes | — |
| 721 | Dic3 | — | 2 | 2 | no | — |
| 722 | Dic3 | — | 2 | 2 | no | — |
| 723 | Dic3 | — | 4 | 2 | no | — |
| 724 | Dic3 | — | 4 | 1 | no | — |
| 725 | Dic3 | — | 4 | 1 | no | — |
| 726 | Dic3 | — | 4 | 2 | no | — |
| 727 | Dic3 | — | 4 | 1 | no | — |
| 728 | Dic3 | — | 4 | 1 | no | — |
| 729 | Dic3 | C2×C4⋊Q8 | 1 | 4 | yes | — |
| 730 | C23 | — | 3 | 2 | no | — |
| 731 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 732 | Q8 | — | 3 | 4 | no | — |
| 733 | Q8 | — | 4 | 4 | no | — |
| 734 | Q8 | — | 8 | 2 | no | — |
| 735 | Q8 | — | 12 | 2 | no | — |
| 736 | Q8 | — | 12 | 2 | no | — |
| 737 | Q8 | — | 24 | 1 | no | — |
| 738 | Q8 | — | 24 | 1 | no | — |
| 739 | Q8 | — | 24 | 4 | no | — |
| 740 | Q8 | — | 24 | 2 | no | — |
| 741 | Q8 | — | 24 | 2 | no | — |
| 742 | D4 | — | 3 | 8 | no | — |
| 743 | D4 | — | 3 | 4 | no | — |
| 744 | C2×C4 | — | 2 | 2 | no | — |
| 745 | C2×C4 | — | 2 | 2 | no | — |
| 746 | C2×C4 | — | 2 | 4 | no | — |
| 747 | C2×C4 | — | 3 | 2 | no | — |
| 748 | C2×C4 | — | 3 | 8 | no | — |
| 749 | C2×C4 | — | 3 | 2 | no | — |
| 750 | C2×C4 | — | 3 | 2 | no | — |
| 751 | C2×C4 | — | 4 | 1 | no | — |
| 752 | C2×C4 | — | 4 | 1 | no | — |
| 753 | C2×C4 | — | 6 | 2 | no | — |
| 754 | C2×C4 | — | 6 | 1 | no | — |
| 755 | C2×C4 | — | 6 | 1 | no | — |
| 756 | C2×C4 | — | 6 | 1 | no | — |
| 757 | C2×C4 | — | 6 | 1 | no | — |
| 758 | C2×C4 | — | 6 | 2 | no | — |
| 759 | C2×C4 | — | 8 | 2 | no | — |
| 760 | C2×C4 | — | 8 | 1 | no | — |
| 761 | C2×C4 | — | 8 | 1 | no | — |
| 762 | C2×C4 | — | 12 | 2 | no | — |
| 763 | C2×C4 | — | 12 | 2 | no | — |
| 764 | C2×C4 | — | 24 | 4 | no | — |
| 765 | C2×C4 | — | 24 | 2 | no | — |
| 766 | C2×C4 | — | 24 | 2 | no | — |
| 767 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 768 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 769 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 770 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 771 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 772 | C2×C4 | C2×D3×Q8 | 1 | 4 | yes | — |
| 773 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 774 | C8 | — | 3 | 8 | no | — |
| 775 | C8 | C2×D3×Q8 | 1 | 4 | yes | — |
| 776 | C8 | C2×D3×Q8 | 1 | 4 | yes | — |
| 777 | C2×C3 | — | 2 | 2 | no | — |
| 778 | C2×C3 | C22×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 779 | C2×C3 | #3585 | 1 | 1 | yes | characteristic |
| 780 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 781 | D3 | — | 2 | 4 | no | — |
| 782 | C22 | — | 2 | 1 | no | — |
| 783 | C22 | — | 2 | 1 | no | — |
| 784 | C22 | — | 3 | 4 | no | — |
| 785 | C22 | — | 6 | 2 | no | — |
| 786 | C22 | — | 6 | 2 | no | — |
| 787 | C22 | D3×C4⋊Q8 | 1 | 2 | yes | — |
| 788 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 789 | C4 | — | 2 | 1 | no | — |
| 790 | C4 | — | 2 | 1 | no | — |
| 791 | C4 | — | 2 | 1 | no | — |
| 792 | C4 | — | 2 | 1 | no | — |
| 793 | C4 | — | 3 | 4 | no | — |
| 794 | C4 | — | 4 | 4 | no | — |
| 795 | C4 | — | 4 | 2 | no | — |
| 796 | C4 | — | 4 | 2 | no | — |
| 797 | C4 | — | 6 | 2 | no | — |
| 798 | C4 | — | 6 | 2 | no | — |
| 799 | C4 | — | 12 | 2 | no | — |
| 800 | C4 | — | 12 | 1 | no | — |
| 801 | C4 | — | 12 | 1 | no | — |
| 802 | C4 | — | 12 | 1 | no | — |
| 803 | C4 | — | 12 | 2 | no | — |
| 804 | C4 | — | 12 | 1 | no | — |
| 805 | C4 | D3×C4⋊Q8 | 1 | 2 | yes | — |
| 806 | C4 | C22×D3×Q8 | 1 | 2 | yes | — |
| 807 | C3 | #60668 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 808 | C2 | — | 2 | 2 | no | — |
| 809 | C2 | — | 6 | 4 | no | — |
| 810 | C2 | C2×D3×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 811 | C2 | #87192 | 1 | 1 | yes | characteristic |
| 812 | C2 | #87197 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3×#501 | C2 | semidirect |
| 4. #83207 | C2 | semidirect |
| 5. #83015 | C2 | semidirect |
| 6. #81977 | C2 | semidirect |
| 7. #81976 | C2 | semidirect |
| 8. #81975 | C2 | semidirect |
| 9. #81974 | C2 | semidirect |
| 10. #81973 | C2 | semidirect |
| 11. D3×#501 | C2 | semidirect |
| 13. #79139 | C2 | semidirect |
| 15. #79110 | C2 | semidirect |
| 17. #78479 | C2 | semidirect |
| 109. C2×#501 | D3 | semidirect |
| 154. #901 | Q8 | semidirect |
| 351. C2×C3×C8 | C2×Q8 | semidirect |
| 420. #208 | C2×Q8 | semidirect |
| 422. ΓL(1,𝔽25) | C2×Q8 | semidirect |
| 423. D3×C8 | C2×Q8 | semidirect |
| 636. C2×C8 | D3×Q8 | semidirect |
| 807. C3 | #60668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86215 | 2 |
| #86098 | 2 |
| C2×C3×#501 | 2 |
| #83207 | 2 |
| #83015 | 2 |
| #81977 | 2 |
| #81976 | 2 |
| #81975 | 2 |
| #81974 | 2 |
| #81973 | 2 |
| D3×#501 | 2 |
| #79146 | 2 |
| #79139 | 2 |
| #79116 | 2 |
| #79110 | 2 |
| #78486 | 2 |
| #78479 | 2 |
| #60668 | 3 |