Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1232 conjugacy classes of subgroups.
The subgroup lattice has 1232 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724396 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724380 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11723648 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11723340 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11723336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11723326 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#63804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C3×#63794 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C3×D3×#204 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11722884 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11722869 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #11722864 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #11722855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #11722843 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | D3×#3716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #10594749 | — | 3 | 1 | no | maximal |
| 17 | #10594713 | — | 3 | 1 | no | maximal |
| 18 | #10594677 | — | 3 | 1 | no | maximal |
| 19 | C4⋊#1113 | C22 | 1 | 1 | yes | characteristic |
| 20 | #89041 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | #89021 | C22 | 1 | 1 | yes | characteristic |
| 22 | #89021 | C22 | 1 | 1 | yes | characteristic |
| 23 | #89021 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3⋊D3×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #89014 | C22 | 1 | 1 | yes | characteristic |
| 26 | D3×#634 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C3×D3×D12 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×D3×D12 | C22 | 1 | 1 | yes | characteristic |
| 29 | C3×#3799 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×#3798 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×D3×Dic6 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #88964 | — | 2 | 1 | no | — |
| 33 | #88964 | — | 2 | 1 | no | — |
| 34 | #88961 | — | 2 | 1 | no | — |
| 35 | #88960 | — | 2 | 1 | no | — |
| 36 | #88957 | — | 2 | 1 | no | — |
| 37 | #88953 | — | 2 | 1 | no | — |
| 38 | #88953 | — | 2 | 1 | no | — |
| 39 | D3×#625 | — | 2 | 1 | no | — |
| 40 | #88853 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#3745 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×#3744 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C3×#3743 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C32×#204 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C32×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C32×D3×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | #88811 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #88810 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #88800 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #88799 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #88796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #88796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #88796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #88794 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×#3717 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C3×#3717 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C3×#3716 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C3×#3714 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C3×#3711 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | C3×#3710 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C3×D3×C3⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #64315 | — | 3 | 1 | no | — |
| 63 | #64313 | — | 3 | 1 | no | — |
| 64 | #64307 | — | 3 | 1 | no | — |
| 65 | #64307 | — | 3 | 1 | no | — |
| 66 | #64298 | — | 3 | 1 | no | — |
| 67 | #64297 | — | 3 | 1 | no | — |
| 68 | #64124 | — | 3 | 1 | no | — |
| 69 | #64118 | — | 3 | 1 | no | — |
| 70 | #64113 | — | 3 | 1 | no | — |
| 71 | C3×#914 | — | 3 | 1 | no | — |
| 72 | C3×D3×SD16 | — | 3 | 1 | no | — |
| 73 | C3×#908 | — | 3 | 1 | no | — |
| 74 | C3×#907 | — | 3 | 1 | no | — |
| 75 | C2×C3×#204 | — | 3 | 1 | no | — |
| 76 | C3×#901 | — | 3 | 1 | no | — |
| 77 | #63947 | — | 3 | 1 | no | — |
| 78 | #63946 | — | 3 | 1 | no | — |
| 79 | #63940 | — | 3 | 1 | no | — |
| 80 | #63936 | — | 3 | 1 | no | — |
| 81 | #63932 | — | 3 | 1 | no | — |
| 82 | D3×#214 | — | 3 | 1 | no | — |
| 83 | #63833 | — | 3 | 1 | no | — |
| 84 | #63830 | — | 3 | 1 | no | — |
| 85 | #63829 | — | 3 | 1 | no | — |
| 86 | C2×#3716 | — | 3 | 1 | no | — |
| 87 | #63807 | — | 3 | 1 | no | — |
| 88 | #63807 | — | 3 | 1 | no | — |
| 89 | #63807 | — | 3 | 1 | no | — |
| 90 | #63807 | — | 6 | 1 | no | — |
| 91 | #63806 | — | 3 | 1 | no | — |
| 92 | #63806 | — | 3 | 1 | no | — |
| 93 | #63804 | D3 | 1 | 1 | yes | characteristic, complemented |
| 94 | #63800 | — | 3 | 1 | no | — |
| 95 | #63800 | — | 3 | 1 | no | — |
| 96 | #63800 | — | 3 | 1 | no | — |
| 97 | #63800 | — | 3 | 1 | no | — |
| 98 | #63800 | — | 3 | 1 | no | — |
| 99 | #63800 | — | 6 | 1 | no | — |
| 100 | #63800 | — | 6 | 1 | no | — |
| 101 | #63798 | — | 3 | 1 | no | — |
| 102 | #63795 | — | 3 | 1 | no | — |
| 103 | #63795 | — | 3 | 1 | no | — |
| 104 | #63794 | — | 3 | 1 | no | — |
| 105 | #63794 | D3 | 1 | 1 | yes | characteristic, complemented |
| 106 | D3×#204 | — | 3 | 1 | no | — |
| 107 | D3×#204 | — | 3 | 1 | no | — |
| 108 | D3×#204 | — | 3 | 1 | no | — |
| 109 | D3×#204 | D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | C2×#1113 | — | 2 | 1 | no | — |
| 111 | C2×C3×D32 | — | 2 | 1 | no | — |
| 112 | C2×C3×D32 | — | 2 | 1 | no | — |
| 113 | #6308 | C23 | 1 | 1 | yes | characteristic |
| 114 | #6308 | C23 | 1 | 1 | yes | characteristic |
| 115 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 116 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 117 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 118 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 119 | C3×#634 | C23 | 1 | 1 | yes | characteristic |
| 120 | C32×D12 | C23 | 1 | 1 | yes | characteristic |
| 121 | C32×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 122 | C32×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 123 | C32×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 124 | #6295 | — | 2 | 1 | no | — |
| 125 | #6295 | — | 2 | 1 | no | — |
| 126 | #6294 | — | 2 | 1 | no | — |
| 127 | #6293 | — | 2 | 1 | no | — |
| 128 | #6293 | — | 2 | 1 | no | — |
| 129 | #6290 | — | 2 | 1 | no | — |
| 130 | #6290 | — | 2 | 1 | no | — |
| 131 | #6290 | — | 2 | 1 | no | — |
| 132 | #6290 | — | 2 | 1 | no | — |
| 133 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 134 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 135 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 136 | Dic3×C3⋊D3 | — | 2 | 1 | no | — |
| 137 | D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 138 | D3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 139 | C3×#627 | — | 2 | 1 | no | — |
| 140 | C3×#627 | D4 | 1 | 1 | yes | characteristic |
| 141 | C3×#626 | — | 2 | 1 | no | — |
| 142 | C3×#626 | — | 2 | 1 | no | — |
| 143 | C3×#626 | — | 2 | 1 | no | — |
| 144 | C3×#626 | D4 | 1 | 1 | yes | characteristic |
| 145 | C3×#626 | D4 | 1 | 1 | yes | characteristic |
| 146 | C3×#625 | D4 | 1 | 1 | yes | characteristic |
| 147 | C3×#624 | — | 2 | 1 | no | — |
| 148 | C3×D3×Dic3 | — | 2 | 1 | no | — |
| 149 | C33×C8 | C23 | 1 | 1 | yes | characteristic |
| 150 | C3×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 151 | C32×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 152 | C32×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 153 | #5775 | — | 9 | 1 | no | — |
| 154 | #5762 | — | 9 | 1 | no | — |
| 155 | #5751 | — | 9 | 1 | no | — |
| 156 | Q8×C3⋊D3 | — | 3 | 1 | no | — |
| 157 | #3830 | — | 3 | 1 | no | — |
| 158 | #3828 | — | 3 | 1 | no | — |
| 159 | #3828 | — | 3 | 1 | no | — |
| 160 | #3828 | — | 3 | 1 | no | — |
| 161 | C2×#634 | — | 3 | 1 | no | — |
| 162 | C3×#239 | — | 3 | 1 | no | — |
| 163 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 164 | C3×D3×D4 | — | 3 | 1 | no | — |
| 165 | C3×D3×D4 | — | 3 | 1 | no | — |
| 166 | C3×#235 | — | 3 | 1 | no | — |
| 167 | C3×#235 | — | 3 | 1 | no | — |
| 168 | C3×#235 | — | 3 | 1 | no | — |
| 169 | C2×C3×D12 | — | 3 | 1 | no | — |
| 170 | C2×C3×D12 | — | 3 | 1 | no | — |
| 171 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 172 | D3×#67 | — | 6 | 1 | no | — |
| 173 | D3×#67 | — | 6 | 1 | no | — |
| 174 | D3×#67 | — | 6 | 1 | no | — |
| 175 | D3×#67 | — | 6 | 1 | no | — |
| 176 | D3×#67 | — | 6 | 1 | no | — |
| 177 | D3×#67 | — | 6 | 1 | no | — |
| 178 | C2×#625 | — | 6 | 1 | no | — |
| 179 | #3805 | — | 6 | 1 | no | — |
| 180 | #3805 | — | 6 | 1 | no | — |
| 181 | #3805 | — | 6 | 1 | no | — |
| 182 | #3804 | — | 6 | 1 | no | — |
| 183 | #3804 | — | 6 | 1 | no | — |
| 184 | #3802 | — | 3 | 1 | no | — |
| 185 | #3802 | — | 6 | 1 | no | — |
| 186 | #3802 | — | 6 | 1 | no | — |
| 187 | D3×D12 | — | 3 | 1 | no | — |
| 188 | D3×D12 | — | 3 | 1 | no | — |
| 189 | D3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 190 | D3×D12 | C2×D3 | 1 | 1 | yes | characteristic |
| 191 | #3799 | — | 3 | 1 | no | — |
| 192 | #3799 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 193 | #3798 | — | 6 | 1 | no | — |
| 194 | #3798 | C2×D3 | 1 | 1 | yes | characteristic |
| 195 | #3797 | — | 6 | 1 | no | — |
| 196 | #3796 | — | 3 | 1 | no | — |
| 197 | #3796 | — | 6 | 1 | no | — |
| 198 | #3796 | — | 6 | 1 | no | — |
| 199 | #3796 | — | 6 | 1 | no | — |
| 200 | #3796 | — | 6 | 1 | no | — |
| 201 | #3795 | — | 3 | 1 | no | — |
| 202 | #3795 | — | 3 | 1 | no | — |
| 203 | #3795 | — | 3 | 1 | no | — |
| 204 | #3795 | — | 3 | 1 | no | — |
| 205 | #3795 | — | 3 | 1 | no | — |
| 206 | #3795 | — | 3 | 1 | no | — |
| 207 | #3795 | — | 3 | 1 | no | — |
| 208 | #3795 | — | 3 | 1 | no | — |
| 209 | #3795 | — | 3 | 1 | no | — |
| 210 | #3795 | — | 6 | 1 | no | — |
| 211 | #3795 | — | 6 | 1 | no | — |
| 212 | #3795 | — | 6 | 1 | no | — |
| 213 | #3795 | — | 6 | 1 | no | — |
| 214 | #3795 | — | 6 | 1 | no | — |
| 215 | #3795 | — | 6 | 1 | no | — |
| 216 | D3×Dic6 | — | 3 | 1 | no | — |
| 217 | D3×Dic6 | — | 3 | 1 | no | — |
| 218 | D3×Dic6 | — | 3 | 1 | no | — |
| 219 | D3×Dic6 | — | 3 | 1 | no | — |
| 220 | D3×Dic6 | — | 6 | 1 | no | — |
| 221 | D3×Dic6 | — | 6 | 1 | no | — |
| 222 | D3×Dic6 | — | 6 | 1 | no | — |
| 223 | D3×Dic6 | — | 6 | 1 | no | — |
| 224 | D3×Dic6 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 225 | C32×SD16 | — | 3 | 1 | no | — |
| 226 | C32×M16 | — | 3 | 1 | no | — |
| 227 | C2×C32×C8 | — | 3 | 1 | no | — |
| 228 | #3756 | — | 3 | 1 | no | — |
| 229 | #3754 | — | 3 | 1 | no | — |
| 230 | #3746 | — | 3 | 1 | no | — |
| 231 | #3746 | — | 3 | 1 | no | — |
| 232 | #3746 | — | 3 | 1 | no | — |
| 233 | #3746 | — | 3 | 1 | no | — |
| 234 | #3746 | — | 6 | 1 | no | — |
| 235 | #3746 | — | 6 | 1 | no | — |
| 236 | #3746 | — | 6 | 1 | no | — |
| 237 | #3746 | — | 12 | 1 | no | — |
| 238 | #3745 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 239 | #3744 | — | 3 | 1 | no | — |
| 240 | #3744 | — | 3 | 1 | no | — |
| 241 | #3744 | — | 3 | 1 | no | — |
| 242 | #3744 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 243 | #3743 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 244 | C3×#215 | — | 3 | 1 | no | — |
| 245 | C3×#215 | — | 3 | 1 | no | — |
| 246 | C3×#214 | — | 3 | 1 | no | — |
| 247 | C3×#213 | — | 3 | 1 | no | — |
| 248 | C3×#208 | — | 3 | 1 | no | — |
| 249 | C2×C3×C3⋊C8 | — | 3 | 1 | no | — |
| 250 | C3×D24 | — | 3 | 1 | no | — |
| 251 | C3×D24 | — | 3 | 1 | no | — |
| 252 | C3×D24 | — | 3 | 1 | no | — |
| 253 | C3×D24 | — | 6 | 1 | no | — |
| 254 | C3×#204 | — | 2 | 1 | no | — |
| 255 | C3×#204 | — | 3 | 1 | no | — |
| 256 | C3×#204 | — | 3 | 1 | no | — |
| 257 | C3×#204 | — | 3 | 1 | no | — |
| 258 | C3×#204 | — | 3 | 1 | no | — |
| 259 | C3×#204 | — | 3 | 1 | no | — |
| 260 | C3×#204 | — | 6 | 1 | no | — |
| 261 | C3×#204 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 262 | C3×#204 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 263 | C3×ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 264 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 265 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 266 | C3×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 267 | C3×ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 268 | C3×ΓL(1,𝔽25) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 269 | C3×ΓL(1,𝔽25) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 270 | C3×D3×C8 | — | 2 | 1 | no | — |
| 271 | C3×D3×C8 | — | 3 | 1 | no | — |
| 272 | C3×D3×C8 | — | 3 | 1 | no | — |
| 273 | C3×D3×C8 | — | 3 | 1 | no | — |
| 274 | C3×D3×C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 275 | C3×D3×C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 276 | #3719 | — | 3 | 1 | no | — |
| 277 | #3719 | — | 3 | 1 | no | — |
| 278 | #3719 | — | 3 | 1 | no | — |
| 279 | #3719 | — | 3 | 1 | no | — |
| 280 | #3719 | — | 6 | 1 | no | — |
| 281 | #3719 | — | 6 | 1 | no | — |
| 282 | #3717 | — | 3 | 1 | no | — |
| 283 | #3717 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 284 | #3717 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 285 | #3716 | — | 3 | 1 | no | — |
| 286 | #3716 | — | 3 | 1 | no | — |
| 287 | #3716 | — | 3 | 1 | no | — |
| 288 | #3716 | — | 3 | 1 | no | — |
| 289 | #3716 | — | 3 | 1 | no | — |
| 290 | #3716 | — | 3 | 1 | no | — |
| 291 | #3716 | — | 3 | 1 | no | — |
| 292 | #3716 | — | 3 | 1 | no | — |
| 293 | #3716 | — | 3 | 1 | no | — |
| 294 | #3716 | — | 6 | 1 | no | — |
| 295 | #3716 | — | 6 | 1 | no | — |
| 296 | #3716 | — | 6 | 1 | no | — |
| 297 | #3716 | — | 6 | 1 | no | — |
| 298 | #3716 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 299 | #3715 | — | 3 | 1 | no | — |
| 300 | #3714 | — | 3 | 1 | no | — |
| 301 | #3714 | — | 3 | 1 | no | — |
| 302 | #3714 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 303 | #3713 | — | 3 | 1 | no | — |
| 304 | #3711 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 305 | #3710 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 306 | D3×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 308 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 309 | C2×C3×C3⋊D3 | — | 2 | 1 | no | — |
| 310 | C2×C3×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×C32×D3 | — | 2 | 1 | no | — |
| 312 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×C32×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 314 | #1113 | — | 8 | 1 | no | — |
| 315 | C3×D32 | — | 8 | 1 | no | — |
| 316 | C3×D32 | — | 8 | 1 | no | — |
| 317 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 318 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 319 | C3⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 320 | C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 321 | C3×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 322 | C32×Dic3 | — | 2 | 1 | no | — |
| 323 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | C32×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | #1010 | — | 9 | 1 | no | — |
| 326 | #1010 | — | 9 | 1 | no | — |
| 327 | #1009 | — | 9 | 1 | no | — |
| 328 | #1007 | — | 9 | 1 | no | — |
| 329 | #1004 | — | 9 | 1 | no | — |
| 330 | #1004 | — | 9 | 1 | no | — |
| 331 | C3×AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 332 | C2×C3×SD16 | — | 9 | 1 | no | — |
| 333 | C3×#131 | — | 9 | 1 | no | — |
| 334 | #950 | — | 9 | 1 | no | — |
| 335 | #942 | — | 9 | 1 | no | — |
| 336 | C2×#214 | — | 9 | 1 | no | — |
| 337 | #932 | — | 9 | 1 | no | — |
| 338 | #916 | — | 9 | 1 | no | — |
| 339 | #916 | — | 9 | 1 | no | — |
| 340 | #915 | — | 9 | 1 | no | — |
| 341 | #915 | — | 9 | 1 | no | — |
| 342 | #915 | — | 9 | 1 | no | — |
| 343 | #915 | — | 9 | 1 | no | — |
| 344 | #915 | — | 18 | 1 | no | — |
| 345 | #914 | — | 3 | 1 | no | — |
| 346 | #914 | — | 9 | 1 | no | — |
| 347 | D3×SD16 | — | 3 | 1 | no | — |
| 348 | D3×SD16 | — | 9 | 1 | no | — |
| 349 | D3×SD16 | — | 9 | 1 | no | — |
| 350 | D3×SD16 | — | 9 | 1 | no | — |
| 351 | #912 | — | 9 | 1 | no | — |
| 352 | #912 | — | 9 | 1 | no | — |
| 353 | #911 | — | 9 | 1 | no | — |
| 354 | #911 | — | 9 | 1 | no | — |
| 355 | #909 | — | 9 | 1 | no | — |
| 356 | #909 | — | 9 | 1 | no | — |
| 357 | #909 | — | 9 | 1 | no | — |
| 358 | #909 | — | 9 | 1 | no | — |
| 359 | #909 | — | 18 | 1 | no | — |
| 360 | #908 | — | 3 | 1 | no | — |
| 361 | #908 | — | 9 | 1 | no | — |
| 362 | #908 | — | 9 | 1 | no | — |
| 363 | #907 | — | 3 | 1 | no | — |
| 364 | #904 | — | 9 | 1 | no | — |
| 365 | #904 | — | 9 | 1 | no | — |
| 366 | #904 | — | 9 | 1 | no | — |
| 367 | #904 | — | 9 | 1 | no | — |
| 368 | #904 | — | 18 | 1 | no | — |
| 369 | C2×#204 | — | 3 | 1 | no | — |
| 370 | C2×#204 | — | 9 | 1 | no | — |
| 371 | C2×#204 | — | 9 | 1 | no | — |
| 372 | #901 | — | 3 | 1 | no | — |
| 373 | C22×C3×D3 | — | 6 | 1 | no | — |
| 374 | C22×C3×D3 | — | 6 | 1 | no | — |
| 375 | C22×C3×D3 | — | 6 | 1 | no | — |
| 376 | C22×C3×D3 | — | 6 | 1 | no | — |
| 377 | C2×D32 | — | 2 | 1 | no | — |
| 378 | C2×D32 | — | 2 | 1 | no | — |
| 379 | C2×D32 | — | 6 | 1 | no | — |
| 380 | C2×D32 | — | 6 | 1 | no | — |
| 381 | C2×D32 | — | 6 | 1 | no | — |
| 382 | C32×Q8 | — | 3 | 1 | no | — |
| 383 | C32×D4 | — | 3 | 1 | no | — |
| 384 | C2×C32×C4 | — | 3 | 1 | no | — |
| 385 | C2×C32×C4 | — | 3 | 1 | no | — |
| 386 | #638 | — | 6 | 1 | no | — |
| 387 | #638 | — | 6 | 1 | no | — |
| 388 | #638 | — | 6 | 1 | no | — |
| 389 | #638 | — | 6 | 1 | no | — |
| 390 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 391 | C2×C3⋊Dic3 | — | 6 | 1 | no | — |
| 392 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 393 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 394 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 395 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 396 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 397 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 398 | C4×C3⋊D3 | — | 6 | 1 | no | — |
| 399 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 400 | #634 | — | 3 | 1 | no | — |
| 401 | #634 | — | 3 | 1 | no | — |
| 402 | #634 | — | 3 | 1 | no | — |
| 403 | #634 | — | 3 | 1 | no | — |
| 404 | #634 | — | 3 | 1 | no | — |
| 405 | #634 | — | 3 | 1 | no | — |
| 406 | #634 | — | 6 | 1 | no | — |
| 407 | #634 | — | 6 | 1 | no | — |
| 408 | #634 | — | 6 | 1 | no | — |
| 409 | #634 | — | 6 | 1 | no | — |
| 410 | #634 | — | 6 | 1 | no | — |
| 411 | #634 | — | 6 | 1 | no | — |
| 412 | #634 | — | 6 | 1 | no | — |
| 413 | #634 | — | 6 | 1 | no | — |
| 414 | #634 | — | 12 | 1 | no | — |
| 415 | #634 | — | 12 | 1 | no | — |
| 416 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 417 | C3×#67 | — | 3 | 1 | no | — |
| 418 | C3×#67 | — | 3 | 1 | no | — |
| 419 | C3×#67 | — | 3 | 1 | no | — |
| 420 | C3×#67 | — | 3 | 1 | no | — |
| 421 | C3×#67 | — | 6 | 1 | no | — |
| 422 | C3×#67 | — | 6 | 1 | no | — |
| 423 | C3×#67 | — | 6 | 1 | no | — |
| 424 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 425 | C3×D12 | — | 2 | 1 | no | — |
| 426 | C3×D12 | — | 3 | 1 | no | — |
| 427 | C3×D12 | — | 3 | 1 | no | — |
| 428 | C3×D12 | — | 3 | 1 | no | — |
| 429 | C3×D12 | — | 3 | 1 | no | — |
| 430 | C3×D12 | — | 3 | 1 | no | — |
| 431 | C3×D12 | — | 3 | 1 | no | — |
| 432 | C3×D12 | — | 3 | 1 | no | — |
| 433 | C3×D12 | — | 3 | 1 | no | — |
| 434 | C3×D12 | — | 6 | 1 | no | — |
| 435 | C3×D12 | — | 6 | 1 | no | — |
| 436 | C3×D12 | — | 6 | 1 | no | — |
| 437 | C3×D12 | — | 6 | 1 | no | — |
| 438 | C3×D12 | — | 6 | 1 | no | — |
| 439 | C3×D12 | — | 6 | 1 | no | — |
| 440 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 441 | C3×D12 | C22×D3 | 1 | 1 | yes | characteristic |
| 442 | C3×C4×D3 | — | 2 | 1 | no | — |
| 443 | C3×C4×D3 | — | 2 | 1 | no | — |
| 444 | C3×C4×D3 | — | 3 | 1 | no | — |
| 445 | C3×C4×D3 | — | 3 | 1 | no | — |
| 446 | C3×C4×D3 | — | 6 | 1 | no | — |
| 447 | C3×C4×D3 | — | 6 | 1 | no | — |
| 448 | C3×C4×D3 | — | 6 | 1 | no | — |
| 449 | C3×C4×D3 | — | 6 | 1 | no | — |
| 450 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 451 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 452 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 453 | C3×C4×D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 454 | C3×Dic6 | — | 2 | 1 | no | — |
| 455 | C3×Dic6 | — | 3 | 1 | no | — |
| 456 | C3×Dic6 | — | 3 | 1 | no | — |
| 457 | C3×Dic6 | — | 3 | 1 | no | — |
| 458 | C3×Dic6 | — | 3 | 1 | no | — |
| 459 | C3×Dic6 | — | 6 | 1 | no | — |
| 460 | C3×Dic6 | — | 6 | 1 | no | — |
| 461 | C3×Dic6 | — | 6 | 1 | no | — |
| 462 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 463 | C3×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 464 | #627 | — | 2 | 1 | no | — |
| 465 | #627 | — | 6 | 1 | no | — |
| 466 | #627 | — | 6 | 1 | no | — |
| 467 | #627 | — | 6 | 1 | no | — |
| 468 | #627 | — | 6 | 1 | no | — |
| 469 | #627 | — | 12 | 1 | no | — |
| 470 | #627 | — | 12 | 1 | no | — |
| 471 | #627 | D12 | 1 | 1 | yes | characteristic |
| 472 | #626 | — | 2 | 1 | no | — |
| 473 | #626 | — | 2 | 1 | no | — |
| 474 | #626 | — | 2 | 1 | no | — |
| 475 | #626 | — | 6 | 1 | no | — |
| 476 | #626 | — | 6 | 1 | no | — |
| 477 | #626 | — | 6 | 1 | no | — |
| 478 | #626 | — | 6 | 1 | no | — |
| 479 | #626 | D12 | 1 | 1 | yes | characteristic |
| 480 | #626 | D12 | 1 | 1 | yes | characteristic |
| 481 | #625 | — | 6 | 1 | no | — |
| 482 | #625 | — | 6 | 1 | no | — |
| 483 | #625 | — | 6 | 1 | no | — |
| 484 | #625 | — | 6 | 1 | no | — |
| 485 | #625 | — | 6 | 1 | no | — |
| 486 | #625 | — | 6 | 1 | no | — |
| 487 | #625 | — | 6 | 1 | no | — |
| 488 | #625 | — | 6 | 1 | no | — |
| 489 | #625 | — | 6 | 1 | no | — |
| 490 | #625 | — | 6 | 1 | no | — |
| 491 | #625 | — | 12 | 1 | no | — |
| 492 | #625 | — | 12 | 1 | no | — |
| 493 | #625 | — | 12 | 1 | no | — |
| 494 | #625 | — | 12 | 1 | no | — |
| 495 | #625 | D12 | 1 | 1 | yes | characteristic |
| 496 | #624 | — | 2 | 1 | no | — |
| 497 | #624 | — | 6 | 1 | no | — |
| 498 | D3×Dic3 | — | 2 | 1 | no | — |
| 499 | D3×Dic3 | — | 6 | 1 | no | — |
| 500 | D3×Dic3 | — | 6 | 1 | no | — |
| 501 | D3×Dic3 | — | 6 | 1 | no | — |
| 502 | D3×Dic3 | — | 6 | 1 | no | — |
| 503 | D3×Dic3 | — | 6 | 1 | no | — |
| 504 | D3×Dic3 | — | 6 | 1 | no | — |
| 505 | D3×Dic3 | — | 6 | 1 | no | — |
| 506 | D3×Dic3 | — | 6 | 1 | no | — |
| 507 | D3×Dic3 | — | 6 | 1 | no | — |
| 508 | D3×Dic3 | — | 6 | 1 | no | — |
| 509 | D3×Dic3 | — | 6 | 1 | no | — |
| 510 | D3×Dic3 | — | 6 | 1 | no | — |
| 511 | D3×Dic3 | — | 6 | 1 | no | — |
| 512 | D3×Dic3 | — | 6 | 1 | no | — |
| 513 | D3×Dic3 | — | 12 | 1 | no | — |
| 514 | D3×Dic3 | — | 12 | 1 | no | — |
| 515 | D3×Dic3 | — | 12 | 1 | no | — |
| 516 | D3×Dic3 | — | 12 | 1 | no | — |
| 517 | D3×Dic3 | — | 12 | 1 | no | — |
| 518 | D3×Dic3 | — | 12 | 1 | no | — |
| 519 | C32×C8 | — | 2 | 1 | no | — |
| 520 | C32×C8 | — | 2 | 1 | no | — |
| 521 | C32×C8 | — | 2 | 1 | no | — |
| 522 | C32×C8 | — | 3 | 1 | no | — |
| 523 | C32×C8 | — | 3 | 1 | no | — |
| 524 | C32×C8 | — | 4 | 1 | no | — |
| 525 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 526 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 527 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 528 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 529 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 530 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 531 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 532 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 533 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 534 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 535 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 536 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 537 | C3×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 538 | #577 | — | 27 | 1 | no | Sylow |
| 539 | C2×C33 | C22×D4 | 1 | 1 | yes | characteristic |
| 540 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 541 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 542 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 543 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 544 | C32×D3 | — | 2 | 1 | no | — |
| 545 | C32×D3 | — | 2 | 1 | no | — |
| 546 | C32×D3 | — | 4 | 1 | no | — |
| 547 | C3×#41 | — | 9 | 1 | no | — |
| 548 | C3×#41 | — | 9 | 1 | no | — |
| 549 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 550 | C2×C3×D4 | — | 9 | 1 | no | — |
| 551 | C2×C3×D4 | — | 9 | 1 | no | — |
| 552 | C2×#67 | — | 18 | 1 | no | — |
| 553 | C2×#67 | — | 18 | 1 | no | — |
| 554 | C2×#67 | — | 18 | 1 | no | — |
| 555 | C2×#67 | — | 18 | 1 | no | — |
| 556 | #239 | — | 3 | 1 | no | — |
| 557 | #239 | — | 9 | 1 | no | — |
| 558 | #239 | — | 18 | 1 | no | — |
| 559 | #239 | — | 18 | 1 | no | — |
| 560 | D3×Q8 | — | 3 | 1 | no | — |
| 561 | D3×Q8 | — | 9 | 1 | no | — |
| 562 | D3×Q8 | — | 9 | 1 | no | — |
| 563 | D3×Q8 | — | 9 | 1 | no | — |
| 564 | D3×Q8 | — | 18 | 1 | no | — |
| 565 | D3×Q8 | — | 18 | 1 | no | — |
| 566 | D3×Q8 | — | 18 | 1 | no | — |
| 567 | #237 | — | 9 | 1 | no | — |
| 568 | #237 | — | 9 | 1 | no | — |
| 569 | #237 | — | 9 | 1 | no | — |
| 570 | #237 | — | 9 | 1 | no | — |
| 571 | #237 | — | 9 | 1 | no | — |
| 572 | #237 | — | 9 | 1 | no | — |
| 573 | #237 | — | 18 | 1 | no | — |
| 574 | #237 | — | 18 | 1 | no | — |
| 575 | #237 | — | 18 | 1 | no | — |
| 576 | #237 | — | 18 | 1 | no | — |
| 577 | #237 | — | 18 | 1 | no | — |
| 578 | #237 | — | 18 | 1 | no | — |
| 579 | #237 | — | 18 | 1 | no | — |
| 580 | #237 | — | 18 | 1 | no | — |
| 581 | D3×D4 | — | 3 | 1 | no | — |
| 582 | D3×D4 | — | 3 | 1 | no | — |
| 583 | D3×D4 | — | 9 | 1 | no | — |
| 584 | D3×D4 | — | 9 | 1 | no | — |
| 585 | D3×D4 | — | 18 | 1 | no | — |
| 586 | D3×D4 | — | 18 | 1 | no | — |
| 587 | D3×D4 | — | 18 | 1 | no | — |
| 588 | D3×D4 | — | 18 | 1 | no | — |
| 589 | D3×D4 | — | 18 | 1 | no | — |
| 590 | #235 | — | 3 | 1 | no | — |
| 591 | #235 | — | 3 | 1 | no | — |
| 592 | #235 | — | 3 | 1 | no | — |
| 593 | #235 | — | 9 | 1 | no | — |
| 594 | #235 | — | 9 | 1 | no | — |
| 595 | #235 | — | 9 | 1 | no | — |
| 596 | #235 | — | 9 | 1 | no | — |
| 597 | #235 | — | 9 | 1 | no | — |
| 598 | #235 | — | 9 | 1 | no | — |
| 599 | #235 | — | 9 | 1 | no | — |
| 600 | #235 | — | 9 | 1 | no | — |
| 601 | #235 | — | 18 | 1 | no | — |
| 602 | #235 | — | 18 | 1 | no | — |
| 603 | #235 | — | 18 | 1 | no | — |
| 604 | #235 | — | 18 | 1 | no | — |
| 605 | #235 | — | 18 | 1 | no | — |
| 606 | #235 | — | 18 | 1 | no | — |
| 607 | C2×D12 | — | 3 | 1 | no | — |
| 608 | C2×D12 | — | 3 | 1 | no | — |
| 609 | C2×D12 | — | 9 | 1 | no | — |
| 610 | C2×Dic6 | — | 3 | 1 | no | — |
| 611 | C2×Dic6 | — | 9 | 1 | no | — |
| 612 | C2×Dic6 | — | 9 | 1 | no | — |
| 613 | C2×Dic6 | — | 9 | 1 | no | — |
| 614 | C2×Dic6 | — | 18 | 1 | no | — |
| 615 | C2×Dic6 | — | 18 | 1 | no | — |
| 616 | C3×SD16 | — | 3 | 1 | no | — |
| 617 | C3×SD16 | — | 3 | 1 | no | — |
| 618 | C3×SD16 | — | 6 | 1 | no | — |
| 619 | C3×SD16 | — | 9 | 1 | no | — |
| 620 | C3×SD16 | — | 9 | 1 | no | — |
| 621 | C3×SD16 | — | 9 | 1 | no | — |
| 622 | C3×SD16 | — | 9 | 1 | no | — |
| 623 | C3×D8 | — | 9 | 1 | no | — |
| 624 | C3×D8 | — | 9 | 1 | no | — |
| 625 | C3×M16 | — | 3 | 1 | no | — |
| 626 | C3×M16 | — | 3 | 1 | no | — |
| 627 | C3×M16 | — | 6 | 1 | no | — |
| 628 | C3×M16 | — | 9 | 1 | no | — |
| 629 | C3×M16 | — | 9 | 1 | no | — |
| 630 | C2×C3×C8 | — | 3 | 1 | no | — |
| 631 | C2×C3×C8 | — | 3 | 1 | no | — |
| 632 | C2×C3×C8 | — | 6 | 1 | no | — |
| 633 | C2×C3×C8 | — | 9 | 1 | no | — |
| 634 | C2×C3×C8 | — | 9 | 1 | no | — |
| 635 | #216 | — | 9 | 1 | no | — |
| 636 | #216 | — | 9 | 1 | no | — |
| 637 | #216 | — | 9 | 1 | no | — |
| 638 | #216 | — | 18 | 1 | no | — |
| 639 | #215 | — | 3 | 1 | no | — |
| 640 | #215 | — | 3 | 1 | no | — |
| 641 | #215 | — | 9 | 1 | no | — |
| 642 | #214 | — | 3 | 1 | no | — |
| 643 | #214 | — | 9 | 1 | no | — |
| 644 | #214 | — | 9 | 1 | no | — |
| 645 | #214 | — | 9 | 1 | no | — |
| 646 | #214 | — | 9 | 1 | no | — |
| 647 | #214 | — | 9 | 1 | no | — |
| 648 | #214 | — | 9 | 1 | no | — |
| 649 | #214 | — | 18 | 1 | no | — |
| 650 | #213 | — | 3 | 1 | no | — |
| 651 | #213 | — | 9 | 1 | no | — |
| 652 | #213 | — | 9 | 1 | no | — |
| 653 | #208 | — | 3 | 1 | no | — |
| 654 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 655 | Dic12 | — | 9 | 1 | no | — |
| 656 | Dic12 | — | 9 | 1 | no | — |
| 657 | Dic12 | — | 9 | 1 | no | — |
| 658 | Dic12 | — | 9 | 1 | no | — |
| 659 | Dic12 | — | 9 | 1 | no | — |
| 660 | Dic12 | — | 9 | 1 | no | — |
| 661 | Dic12 | — | 18 | 1 | no | — |
| 662 | Dic12 | — | 18 | 1 | no | — |
| 663 | Dic12 | — | 18 | 1 | no | — |
| 664 | Dic12 | — | 18 | 1 | no | — |
| 665 | Dic12 | — | 36 | 1 | no | — |
| 666 | D24 | — | 3 | 1 | no | — |
| 667 | D24 | — | 3 | 1 | no | — |
| 668 | D24 | — | 3 | 1 | no | — |
| 669 | D24 | — | 6 | 1 | no | — |
| 670 | D24 | — | 9 | 1 | no | — |
| 671 | #204 | — | 3 | 1 | no | — |
| 672 | #204 | — | 3 | 1 | no | — |
| 673 | #204 | — | 3 | 1 | no | — |
| 674 | #204 | — | 3 | 1 | no | — |
| 675 | #204 | — | 3 | 1 | no | — |
| 676 | #204 | — | 6 | 1 | no | — |
| 677 | #204 | — | 9 | 1 | no | — |
| 678 | #204 | — | 9 | 1 | no | — |
| 679 | #204 | — | 9 | 1 | no | — |
| 680 | #204 | — | 9 | 1 | no | — |
| 681 | #204 | — | 9 | 1 | no | — |
| 682 | #204 | — | 9 | 1 | no | — |
| 683 | #204 | — | 9 | 1 | no | — |
| 684 | #204 | — | 9 | 1 | no | — |
| 685 | #204 | — | 18 | 1 | no | — |
| 686 | #204 | — | 18 | 1 | no | — |
| 687 | #204 | — | 18 | 1 | no | — |
| 688 | #204 | D32 | 1 | 1 | yes | characteristic, complemented |
| 689 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 690 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 691 | ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 692 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 693 | ΓL(1,𝔽25) | D32 | 1 | 1 | yes | characteristic, complemented |
| 694 | D3×C8 | — | 3 | 1 | no | — |
| 695 | D3×C8 | — | 3 | 1 | no | — |
| 696 | D3×C8 | — | 3 | 1 | no | — |
| 697 | D3×C8 | D32 | 1 | 1 | yes | characteristic, complemented |
| 698 | C22×C32 | — | 3 | 1 | no | — |
| 699 | C22×C32 | — | 3 | 1 | no | — |
| 700 | C22×C32 | — | 6 | 1 | no | — |
| 701 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 702 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 703 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 704 | C2×C3⋊D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 705 | C2×C3×D3 | — | 2 | 1 | no | — |
| 706 | C2×C3×D3 | — | 2 | 1 | no | — |
| 707 | C2×C3×D3 | — | 2 | 1 | no | — |
| 708 | C2×C3×D3 | — | 2 | 1 | no | — |
| 709 | C2×C3×D3 | — | 3 | 1 | no | — |
| 710 | C2×C3×D3 | — | 3 | 1 | no | — |
| 711 | C2×C3×D3 | — | 4 | 1 | no | — |
| 712 | C2×C3×D3 | — | 6 | 1 | no | — |
| 713 | C2×C3×D3 | — | 6 | 1 | no | — |
| 714 | C2×C3×D3 | — | 6 | 1 | no | — |
| 715 | C2×C3×D3 | — | 6 | 1 | no | — |
| 716 | C2×C3×D3 | — | 6 | 1 | no | — |
| 717 | C2×C3×D3 | — | 6 | 1 | no | — |
| 718 | C2×C3×D3 | — | 6 | 1 | no | — |
| 719 | C2×C3×D3 | — | 12 | 1 | no | — |
| 720 | C2×C3×D3 | — | 12 | 1 | no | — |
| 721 | C2×C3×D3 | — | 12 | 1 | no | — |
| 722 | C2×C3×D3 | — | 24 | 1 | no | — |
| 723 | C2×C3×D3 | — | 24 | 1 | no | — |
| 724 | C2×C3×D3 | — | 24 | 1 | no | — |
| 725 | C2×C3×D3 | — | 24 | 1 | no | — |
| 726 | C2×C3×D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 727 | C2×C3×D3 | C2×D12 | 1 | 1 | yes | characteristic |
| 728 | C2×C3×D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 729 | C2×C3×D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 730 | D32 | — | 8 | 1 | no | — |
| 731 | D32 | — | 8 | 1 | no | — |
| 732 | D32 | — | 24 | 1 | no | — |
| 733 | D32 | — | 24 | 1 | no | — |
| 734 | D32 | — | 24 | 1 | no | — |
| 735 | C32×C4 | — | 2 | 1 | no | — |
| 736 | C32×C4 | — | 2 | 1 | no | — |
| 737 | C32×C4 | — | 2 | 1 | no | — |
| 738 | C32×C4 | — | 3 | 1 | no | — |
| 739 | C32×C4 | — | 3 | 1 | no | — |
| 740 | C32×C4 | — | 4 | 1 | no | — |
| 741 | C32×C4 | — | 6 | 1 | no | — |
| 742 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 743 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 744 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 745 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 746 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 747 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 748 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 749 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 750 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 751 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 752 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 753 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 754 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 755 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 756 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 757 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 758 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 759 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 760 | C3⋊Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 761 | C3×Dic3 | — | 2 | 1 | no | — |
| 762 | C3×Dic3 | — | 2 | 1 | no | — |
| 763 | C3×Dic3 | — | 2 | 1 | no | — |
| 764 | C3×Dic3 | — | 2 | 1 | no | — |
| 765 | C3×Dic3 | — | 3 | 1 | no | — |
| 766 | C3×Dic3 | — | 3 | 1 | no | — |
| 767 | C3×Dic3 | — | 4 | 1 | no | — |
| 768 | C3×Dic3 | — | 6 | 1 | no | — |
| 769 | C3×Dic3 | — | 6 | 1 | no | — |
| 770 | C3×Dic3 | — | 6 | 1 | no | — |
| 771 | C3×Dic3 | — | 12 | 1 | no | — |
| 772 | C3×Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 773 | C3×Dic3 | C2×D12 | 1 | 1 | yes | characteristic |
| 774 | C3×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 775 | C3×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 776 | 2−1+4 | — | 27 | 1 | no | — |
| 777 | H(5,𝔽2) | — | 27 | 1 | no | — |
| 778 | #137 | — | 27 | 1 | no | — |
| 779 | #137 | — | 27 | 1 | no | — |
| 780 | #137 | — | 27 | 1 | no | — |
| 781 | AGL(1,ℤ/8) | — | 9 | 1 | no | — |
| 782 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 783 | AGL(1,ℤ/8) | — | 27 | 1 | no | — |
| 784 | #135 | — | 27 | 1 | no | — |
| 785 | #135 | — | 27 | 1 | no | — |
| 786 | #135 | — | 27 | 1 | no | — |
| 787 | C2×SD16 | — | 9 | 1 | no | — |
| 788 | C2×SD16 | — | 27 | 1 | no | — |
| 789 | C2×SD16 | — | 27 | 1 | no | — |
| 790 | #131 | — | 9 | 1 | no | — |
| 791 | C33 | #577 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 792 | C23×C3 | — | 18 | 1 | no | — |
| 793 | C23×C3 | — | 18 | 1 | no | — |
| 794 | C22×D3 | — | 6 | 1 | no | — |
| 795 | C22×D3 | — | 6 | 1 | no | — |
| 796 | C22×D3 | — | 6 | 1 | no | — |
| 797 | C22×D3 | — | 6 | 1 | no | — |
| 798 | C22×D3 | — | 18 | 1 | no | — |
| 799 | C22×D3 | — | 18 | 1 | no | — |
| 800 | C22×D3 | — | 18 | 1 | no | — |
| 801 | C3×Q8 | — | 3 | 1 | no | — |
| 802 | C3×Q8 | — | 3 | 1 | no | — |
| 803 | C3×Q8 | — | 6 | 1 | no | — |
| 804 | C3×Q8 | — | 9 | 1 | no | — |
| 805 | C3×Q8 | — | 9 | 1 | no | — |
| 806 | C3×Q8 | — | 18 | 1 | no | — |
| 807 | C3×D4 | — | 3 | 1 | no | — |
| 808 | C3×D4 | — | 3 | 1 | no | — |
| 809 | C3×D4 | — | 6 | 1 | no | — |
| 810 | C3×D4 | — | 9 | 1 | no | — |
| 811 | C3×D4 | — | 9 | 1 | no | — |
| 812 | C3×D4 | — | 9 | 1 | no | — |
| 813 | C3×D4 | — | 9 | 1 | no | — |
| 814 | C3×D4 | — | 9 | 1 | no | — |
| 815 | C3×D4 | — | 9 | 1 | no | — |
| 816 | C3×D4 | — | 18 | 1 | no | — |
| 817 | C3×D4 | — | 18 | 1 | no | — |
| 818 | C3×D4 | — | 18 | 1 | no | — |
| 819 | C2×C3×C4 | — | 3 | 1 | no | — |
| 820 | C2×C3×C4 | — | 3 | 1 | no | — |
| 821 | C2×C3×C4 | — | 3 | 1 | no | — |
| 822 | C2×C3×C4 | — | 3 | 1 | no | — |
| 823 | C2×C3×C4 | — | 6 | 1 | no | — |
| 824 | C2×C3×C4 | — | 6 | 1 | no | — |
| 825 | C2×C3×C4 | — | 9 | 1 | no | — |
| 826 | C2×C3×C4 | — | 18 | 1 | no | — |
| 827 | C2×C3×C4 | — | 18 | 1 | no | — |
| 828 | #67 | — | 3 | 1 | no | — |
| 829 | #67 | — | 3 | 1 | no | — |
| 830 | #67 | — | 3 | 1 | no | — |
| 831 | #67 | — | 3 | 1 | no | — |
| 832 | #67 | — | 6 | 1 | no | — |
| 833 | #67 | — | 6 | 1 | no | — |
| 834 | #67 | — | 6 | 1 | no | — |
| 835 | #67 | — | 18 | 1 | no | — |
| 836 | #67 | — | 18 | 1 | no | — |
| 837 | #67 | — | 18 | 1 | no | — |
| 838 | #67 | — | 18 | 1 | no | — |
| 839 | #67 | — | 18 | 1 | no | — |
| 840 | #67 | — | 18 | 1 | no | — |
| 841 | #67 | — | 18 | 1 | no | — |
| 842 | #67 | — | 18 | 1 | no | — |
| 843 | #67 | — | 18 | 1 | no | — |
| 844 | #67 | — | 18 | 1 | no | — |
| 845 | #67 | — | 18 | 1 | no | — |
| 846 | #67 | — | 18 | 1 | no | — |
| 847 | #67 | — | 18 | 1 | no | — |
| 848 | #67 | — | 18 | 1 | no | — |
| 849 | #67 | — | 18 | 1 | no | — |
| 850 | #67 | — | 18 | 1 | no | — |
| 851 | #67 | — | 36 | 1 | no | — |
| 852 | #67 | — | 36 | 1 | no | — |
| 853 | #67 | — | 36 | 1 | no | — |
| 854 | #67 | — | 36 | 1 | no | — |
| 855 | C2×Dic3 | — | 6 | 1 | no | — |
| 856 | C2×Dic3 | — | 18 | 1 | no | — |
| 857 | C2×Dic3 | — | 18 | 1 | no | — |
| 858 | C2×Dic3 | — | 18 | 1 | no | — |
| 859 | C2×Dic3 | — | 18 | 1 | no | — |
| 860 | C2×Dic3 | — | 18 | 1 | no | — |
| 861 | C2×Dic3 | — | 18 | 1 | no | — |
| 862 | C2×Dic3 | — | 18 | 1 | no | — |
| 863 | C2×Dic3 | — | 18 | 1 | no | — |
| 864 | C2×Dic3 | — | 18 | 1 | no | — |
| 865 | C2×Dic3 | — | 36 | 1 | no | — |
| 866 | C2×Dic3 | — | 36 | 1 | no | — |
| 867 | D12 | — | 3 | 1 | no | — |
| 868 | D12 | — | 3 | 1 | no | — |
| 869 | D12 | — | 3 | 1 | no | — |
| 870 | D12 | — | 3 | 1 | no | — |
| 871 | D12 | — | 3 | 1 | no | — |
| 872 | D12 | — | 3 | 1 | no | — |
| 873 | D12 | — | 3 | 1 | no | — |
| 874 | D12 | — | 3 | 1 | no | — |
| 875 | D12 | — | 6 | 1 | no | — |
| 876 | D12 | — | 6 | 1 | no | — |
| 877 | D12 | — | 6 | 1 | no | — |
| 878 | D12 | — | 6 | 1 | no | — |
| 879 | D12 | — | 6 | 1 | no | — |
| 880 | D12 | — | 6 | 1 | no | — |
| 881 | D12 | — | 18 | 1 | no | — |
| 882 | D12 | — | 18 | 1 | no | — |
| 883 | D12 | C2×D32 | 1 | 1 | yes | characteristic |
| 884 | C4×D3 | — | 3 | 1 | no | — |
| 885 | C4×D3 | — | 3 | 1 | no | — |
| 886 | C4×D3 | — | 6 | 1 | no | — |
| 887 | C4×D3 | — | 6 | 1 | no | — |
| 888 | C4×D3 | — | 6 | 1 | no | — |
| 889 | C4×D3 | — | 6 | 1 | no | — |
| 890 | C4×D3 | — | 18 | 1 | no | — |
| 891 | C4×D3 | — | 18 | 1 | no | — |
| 892 | C4×D3 | — | 18 | 1 | no | — |
| 893 | C4×D3 | — | 18 | 1 | no | — |
| 894 | C4×D3 | — | 18 | 1 | no | — |
| 895 | C4×D3 | — | 18 | 1 | no | — |
| 896 | C4×D3 | — | 18 | 1 | no | — |
| 897 | C4×D3 | — | 18 | 1 | no | — |
| 898 | C4×D3 | — | 18 | 1 | no | — |
| 899 | C4×D3 | — | 18 | 1 | no | — |
| 900 | C4×D3 | — | 18 | 1 | no | — |
| 901 | C4×D3 | — | 18 | 1 | no | — |
| 902 | C4×D3 | — | 36 | 1 | no | — |
| 903 | C4×D3 | — | 36 | 1 | no | — |
| 904 | C4×D3 | — | 36 | 1 | no | — |
| 905 | C4×D3 | — | 36 | 1 | no | — |
| 906 | C4×D3 | C2×D32 | 1 | 1 | yes | characteristic |
| 907 | C4×D3 | C2×D32 | 1 | 1 | yes | characteristic |
| 908 | Dic6 | — | 3 | 1 | no | — |
| 909 | Dic6 | — | 3 | 1 | no | — |
| 910 | Dic6 | — | 3 | 1 | no | — |
| 911 | Dic6 | — | 3 | 1 | no | — |
| 912 | Dic6 | — | 6 | 1 | no | — |
| 913 | Dic6 | — | 6 | 1 | no | — |
| 914 | Dic6 | — | 6 | 1 | no | — |
| 915 | Dic6 | — | 9 | 1 | no | — |
| 916 | Dic6 | — | 9 | 1 | no | — |
| 917 | Dic6 | — | 9 | 1 | no | — |
| 918 | Dic6 | — | 9 | 1 | no | — |
| 919 | Dic6 | — | 9 | 1 | no | — |
| 920 | Dic6 | — | 9 | 1 | no | — |
| 921 | Dic6 | — | 18 | 1 | no | — |
| 922 | Dic6 | — | 18 | 1 | no | — |
| 923 | Dic6 | — | 18 | 1 | no | — |
| 924 | Dic6 | — | 18 | 1 | no | — |
| 925 | Dic6 | — | 18 | 1 | no | — |
| 926 | Dic6 | — | 18 | 1 | no | — |
| 927 | Dic6 | — | 18 | 1 | no | — |
| 928 | Dic6 | — | 18 | 1 | no | — |
| 929 | Dic6 | — | 18 | 1 | no | — |
| 930 | Dic6 | — | 18 | 1 | no | — |
| 931 | Dic6 | — | 18 | 1 | no | — |
| 932 | Dic6 | — | 18 | 1 | no | — |
| 933 | Dic6 | — | 36 | 1 | no | — |
| 934 | Dic6 | — | 36 | 1 | no | — |
| 935 | Dic6 | — | 36 | 1 | no | — |
| 936 | Dic6 | — | 36 | 1 | no | — |
| 937 | Dic6 | C2×D32 | 1 | 1 | yes | characteristic |
| 938 | C3×C8 | — | 2 | 1 | no | — |
| 939 | C3×C8 | — | 2 | 1 | no | — |
| 940 | C3×C8 | — | 2 | 1 | no | — |
| 941 | C3×C8 | — | 3 | 1 | no | — |
| 942 | C3×C8 | — | 3 | 1 | no | — |
| 943 | C3×C8 | — | 3 | 1 | no | — |
| 944 | C3×C8 | — | 3 | 1 | no | — |
| 945 | C3×C8 | — | 4 | 1 | no | — |
| 946 | C3×C8 | — | 6 | 1 | no | — |
| 947 | C3×C8 | — | 6 | 1 | no | — |
| 948 | C3×C8 | — | 9 | 1 | no | — |
| 949 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 950 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 951 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 952 | C3⋊C8 | — | 3 | 1 | no | — |
| 953 | C3⋊C8 | — | 3 | 1 | no | — |
| 954 | C3⋊C8 | — | 6 | 1 | no | — |
| 955 | C3⋊C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 956 | C3⋊C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 957 | C2×C32 | — | 2 | 1 | no | — |
| 958 | C2×C32 | — | 2 | 1 | no | — |
| 959 | C2×C32 | — | 2 | 1 | no | — |
| 960 | C2×C32 | — | 4 | 1 | no | — |
| 961 | C2×C32 | — | 6 | 1 | no | — |
| 962 | C2×C32 | — | 6 | 1 | no | — |
| 963 | C2×C32 | — | 12 | 1 | no | — |
| 964 | C2×C32 | C22×D12 | 1 | 1 | yes | characteristic |
| 965 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 966 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 967 | C3⋊D3 | — | 2 | 1 | no | — |
| 968 | C3⋊D3 | — | 4 | 1 | no | — |
| 969 | C3⋊D3 | — | 4 | 1 | no | — |
| 970 | C3⋊D3 | — | 4 | 1 | no | — |
| 971 | C3×D3 | — | 2 | 1 | no | — |
| 972 | C3×D3 | — | 2 | 1 | no | — |
| 973 | C3×D3 | — | 2 | 1 | no | — |
| 974 | C3×D3 | — | 2 | 1 | no | — |
| 975 | C3×D3 | — | 4 | 1 | no | — |
| 976 | C3×D3 | — | 4 | 1 | no | — |
| 977 | C3×D3 | — | 4 | 1 | no | — |
| 978 | C3×D3 | — | 4 | 1 | no | — |
| 979 | C3×D3 | — | 6 | 1 | no | — |
| 980 | C3×D3 | — | 6 | 1 | no | — |
| 981 | C3×D3 | — | 8 | 1 | no | — |
| 982 | C3×D3 | — | 12 | 1 | no | — |
| 983 | C3×D3 | — | 12 | 1 | no | — |
| 984 | C3×D3 | — | 12 | 1 | no | — |
| 985 | C3×D3 | — | 12 | 1 | no | — |
| 986 | C3×D3 | — | 12 | 1 | no | — |
| 987 | C3×D3 | — | 12 | 1 | no | — |
| 988 | C3×D3 | — | 12 | 1 | no | — |
| 989 | C3×D3 | — | 24 | 1 | no | — |
| 990 | C3×D3 | — | 24 | 1 | no | — |
| 991 | C3×D3 | — | 24 | 1 | no | — |
| 992 | #41 | — | 9 | 1 | no | — |
| 993 | #41 | — | 9 | 1 | no | — |
| 994 | #41 | — | 27 | 1 | no | — |
| 995 | #41 | — | 27 | 1 | no | — |
| 996 | #41 | — | 27 | 1 | no | — |
| 997 | #41 | — | 27 | 1 | no | — |
| 998 | #41 | — | 27 | 1 | no | — |
| 999 | #41 | — | 54 | 1 | no | — |
| 1000 | #41 | — | 54 | 1 | no | — |
| 1001 | #41 | — | 54 | 1 | no | — |
| 1002 | #41 | — | 54 | 1 | no | — |
| 1003 | C2×Q8 | — | 9 | 1 | no | — |
| 1004 | C2×Q8 | — | 27 | 1 | no | — |
| 1005 | C2×Q8 | — | 27 | 1 | no | — |
| 1006 | C2×Q8 | — | 54 | 1 | no | — |
| 1007 | C2×D4 | — | 9 | 1 | no | — |
| 1008 | C2×D4 | — | 9 | 1 | no | — |
| 1009 | C2×D4 | — | 27 | 1 | no | — |
| 1010 | C2×D4 | — | 54 | 1 | no | — |
| 1011 | C2×D4 | — | 54 | 1 | no | — |
| 1012 | C2×D4 | — | 54 | 1 | no | — |
| 1013 | Q16 | — | 27 | 1 | no | — |
| 1014 | Q16 | — | 27 | 1 | no | — |
| 1015 | Q16 | — | 27 | 1 | no | — |
| 1016 | SD16 | — | 3 | 1 | no | — |
| 1017 | SD16 | — | 9 | 1 | no | — |
| 1018 | SD16 | — | 9 | 1 | no | — |
| 1019 | SD16 | — | 9 | 1 | no | — |
| 1020 | SD16 | — | 9 | 1 | no | — |
| 1021 | SD16 | — | 27 | 1 | no | — |
| 1022 | SD16 | — | 27 | 1 | no | — |
| 1023 | SD16 | — | 27 | 1 | no | — |
| 1024 | SD16 | — | 27 | 1 | no | — |
| 1025 | SD16 | — | 27 | 1 | no | — |
| 1026 | D8 | — | 9 | 1 | no | — |
| 1027 | D8 | — | 9 | 1 | no | — |
| 1028 | D8 | — | 27 | 1 | no | — |
| 1029 | M16 | — | 3 | 1 | no | — |
| 1030 | M16 | — | 9 | 1 | no | — |
| 1031 | M16 | — | 9 | 1 | no | — |
| 1032 | C2×C8 | — | 3 | 1 | no | — |
| 1033 | C2×C8 | — | 9 | 1 | no | — |
| 1034 | C2×C8 | — | 9 | 1 | no | — |
| 1035 | C22×C3 | — | 3 | 1 | no | — |
| 1036 | C22×C3 | — | 3 | 1 | no | — |
| 1037 | C22×C3 | — | 3 | 1 | no | — |
| 1038 | C22×C3 | — | 3 | 1 | no | — |
| 1039 | C22×C3 | — | 6 | 1 | no | — |
| 1040 | C22×C3 | — | 6 | 1 | no | — |
| 1041 | C22×C3 | — | 6 | 1 | no | — |
| 1042 | C22×C3 | — | 6 | 1 | no | — |
| 1043 | C22×C3 | — | 9 | 1 | no | — |
| 1044 | C22×C3 | — | 12 | 1 | no | — |
| 1045 | C22×C3 | — | 18 | 1 | no | — |
| 1046 | C22×C3 | — | 18 | 1 | no | — |
| 1047 | C22×C3 | — | 18 | 1 | no | — |
| 1048 | C22×C3 | — | 72 | 1 | no | — |
| 1049 | C22×C3 | — | 72 | 1 | no | — |
| 1050 | C2×D3 | — | 2 | 1 | no | — |
| 1051 | C2×D3 | — | 3 | 1 | no | — |
| 1052 | C2×D3 | — | 3 | 1 | no | — |
| 1053 | C2×D3 | — | 6 | 1 | no | — |
| 1054 | C2×D3 | — | 6 | 1 | no | — |
| 1055 | C2×D3 | — | 6 | 1 | no | — |
| 1056 | C2×D3 | — | 6 | 1 | no | — |
| 1057 | C2×D3 | — | 6 | 1 | no | — |
| 1058 | C2×D3 | — | 6 | 1 | no | — |
| 1059 | C2×D3 | — | 6 | 1 | no | — |
| 1060 | C2×D3 | — | 12 | 1 | no | — |
| 1061 | C2×D3 | — | 12 | 1 | no | — |
| 1062 | C2×D3 | — | 12 | 1 | no | — |
| 1063 | C2×D3 | — | 24 | 1 | no | — |
| 1064 | C2×D3 | — | 24 | 1 | no | — |
| 1065 | C2×D3 | — | 24 | 1 | no | — |
| 1066 | C2×D3 | — | 24 | 1 | no | — |
| 1067 | C2×D3 | — | 72 | 1 | no | — |
| 1068 | C2×D3 | — | 72 | 1 | no | — |
| 1069 | C2×D3 | — | 72 | 1 | no | — |
| 1070 | C2×D3 | D3×D12 | 1 | 1 | yes | characteristic |
| 1071 | C2×D3 | D3×D12 | 1 | 1 | yes | characteristic |
| 1072 | C3×C4 | — | 2 | 1 | no | — |
| 1073 | C3×C4 | — | 2 | 1 | no | — |
| 1074 | C3×C4 | — | 2 | 1 | no | — |
| 1075 | C3×C4 | — | 3 | 1 | no | — |
| 1076 | C3×C4 | — | 3 | 1 | no | — |
| 1077 | C3×C4 | — | 3 | 1 | no | — |
| 1078 | C3×C4 | — | 3 | 1 | no | — |
| 1079 | C3×C4 | — | 4 | 1 | no | — |
| 1080 | C3×C4 | — | 6 | 1 | no | — |
| 1081 | C3×C4 | — | 6 | 1 | no | — |
| 1082 | C3×C4 | — | 6 | 1 | no | — |
| 1083 | C3×C4 | — | 6 | 1 | no | — |
| 1084 | C3×C4 | — | 9 | 1 | no | — |
| 1085 | C3×C4 | — | 12 | 1 | no | — |
| 1086 | C3×C4 | — | 18 | 1 | no | — |
| 1087 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 1088 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 1089 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 1090 | Dic3 | — | 2 | 1 | no | — |
| 1091 | Dic3 | — | 3 | 1 | no | — |
| 1092 | Dic3 | — | 3 | 1 | no | — |
| 1093 | Dic3 | — | 6 | 1 | no | — |
| 1094 | Dic3 | — | 6 | 1 | no | — |
| 1095 | Dic3 | — | 6 | 1 | no | — |
| 1096 | Dic3 | — | 12 | 1 | no | — |
| 1097 | Dic3 | — | 18 | 1 | no | — |
| 1098 | Dic3 | — | 18 | 1 | no | — |
| 1099 | Dic3 | — | 18 | 1 | no | — |
| 1100 | Dic3 | — | 18 | 1 | no | — |
| 1101 | Dic3 | — | 18 | 1 | no | — |
| 1102 | Dic3 | — | 18 | 1 | no | — |
| 1103 | Dic3 | — | 36 | 1 | no | — |
| 1104 | Dic3 | — | 36 | 1 | no | — |
| 1105 | Dic3 | — | 36 | 1 | no | — |
| 1106 | Dic3 | — | 36 | 1 | no | — |
| 1107 | Dic3 | — | 36 | 1 | no | — |
| 1108 | Dic3 | — | 36 | 1 | no | — |
| 1109 | Dic3 | — | 72 | 1 | no | — |
| 1110 | Dic3 | — | 72 | 1 | no | — |
| 1111 | Dic3 | D3×D12 | 1 | 1 | yes | characteristic |
| 1112 | Dic3 | D3×D12 | 1 | 1 | yes | characteristic |
| 1113 | C32 | — | 2 | 1 | no | — |
| 1114 | C32 | — | 2 | 1 | no | — |
| 1115 | C32 | — | 2 | 1 | no | — |
| 1116 | C32 | — | 4 | 1 | no | — |
| 1117 | C32 | #5751 | 1 | 1 | yes | characteristic, complemented |
| 1118 | C32 | #5762 | 1 | 1 | yes | characteristic, complemented |
| 1119 | C32 | #5775 | 1 | 1 | yes | characteristic, complemented |
| 1120 | C23 | — | 18 | 1 | no | — |
| 1121 | C23 | — | 18 | 1 | no | — |
| 1122 | C23 | — | 54 | 1 | no | — |
| 1123 | Q8 | — | 3 | 1 | no | — |
| 1124 | Q8 | — | 9 | 1 | no | — |
| 1125 | Q8 | — | 9 | 1 | no | — |
| 1126 | Q8 | — | 18 | 1 | no | — |
| 1127 | Q8 | — | 27 | 1 | no | — |
| 1128 | Q8 | — | 27 | 1 | no | — |
| 1129 | Q8 | — | 54 | 1 | no | — |
| 1130 | Q8 | — | 54 | 1 | no | — |
| 1131 | D4 | — | 3 | 1 | no | — |
| 1132 | D4 | — | 9 | 1 | no | — |
| 1133 | D4 | — | 9 | 1 | no | — |
| 1134 | D4 | — | 9 | 1 | no | — |
| 1135 | D4 | — | 9 | 1 | no | — |
| 1136 | D4 | — | 9 | 1 | no | — |
| 1137 | D4 | — | 9 | 1 | no | — |
| 1138 | D4 | — | 18 | 1 | no | — |
| 1139 | D4 | — | 18 | 1 | no | — |
| 1140 | D4 | — | 18 | 1 | no | — |
| 1141 | D4 | — | 54 | 1 | no | — |
| 1142 | D4 | — | 54 | 1 | no | — |
| 1143 | D4 | — | 54 | 1 | no | — |
| 1144 | D4 | — | 54 | 1 | no | — |
| 1145 | D4 | — | 54 | 1 | no | — |
| 1146 | D4 | — | 54 | 1 | no | — |
| 1147 | C2×C4 | — | 3 | 1 | no | — |
| 1148 | C2×C4 | — | 3 | 1 | no | — |
| 1149 | C2×C4 | — | 9 | 1 | no | — |
| 1150 | C2×C4 | — | 18 | 1 | no | — |
| 1151 | C2×C4 | — | 18 | 1 | no | — |
| 1152 | C2×C4 | — | 54 | 1 | no | — |
| 1153 | C2×C4 | — | 54 | 1 | no | — |
| 1154 | C2×C4 | — | 54 | 1 | no | — |
| 1155 | C2×C4 | — | 54 | 1 | no | — |
| 1156 | C2×C4 | — | 54 | 1 | no | — |
| 1157 | C2×C4 | — | 54 | 1 | no | — |
| 1158 | C2×C4 | — | 54 | 1 | no | — |
| 1159 | C8 | — | 3 | 1 | no | — |
| 1160 | C8 | — | 3 | 1 | no | — |
| 1161 | C8 | — | 9 | 1 | no | — |
| 1162 | C8 | D33 | 1 | 1 | yes | characteristic |
| 1163 | C2×C3 | — | 2 | 1 | no | — |
| 1164 | C2×C3 | — | 2 | 1 | no | — |
| 1165 | C2×C3 | — | 2 | 1 | no | — |
| 1166 | C2×C3 | — | 4 | 1 | no | — |
| 1167 | C2×C3 | — | 6 | 1 | no | — |
| 1168 | C2×C3 | — | 6 | 1 | no | — |
| 1169 | C2×C3 | — | 6 | 1 | no | — |
| 1170 | C2×C3 | — | 6 | 1 | no | — |
| 1171 | C2×C3 | — | 12 | 1 | no | — |
| 1172 | C2×C3 | — | 12 | 1 | no | — |
| 1173 | C2×C3 | — | 12 | 1 | no | — |
| 1174 | C2×C3 | — | 12 | 1 | no | — |
| 1175 | C2×C3 | — | 18 | 1 | no | — |
| 1176 | C2×C3 | — | 24 | 1 | no | — |
| 1177 | C2×C3 | — | 36 | 1 | no | — |
| 1178 | C2×C3 | — | 36 | 1 | no | — |
| 1179 | C2×C3 | — | 36 | 1 | no | — |
| 1180 | C2×C3 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 1181 | C2×C3 | C2×D3×D12 | 1 | 1 | yes | characteristic |
| 1182 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 1183 | D3 | — | 2 | 1 | no | — |
| 1184 | D3 | — | 2 | 1 | no | — |
| 1185 | D3 | — | 4 | 1 | no | — |
| 1186 | D3 | — | 6 | 1 | no | — |
| 1187 | D3 | — | 6 | 1 | no | — |
| 1188 | D3 | — | 12 | 1 | no | — |
| 1189 | D3 | — | 12 | 1 | no | — |
| 1190 | D3 | — | 12 | 1 | no | — |
| 1191 | D3 | — | 12 | 1 | no | — |
| 1192 | D3 | — | 12 | 1 | no | — |
| 1193 | D3 | — | 12 | 1 | no | — |
| 1194 | D3 | — | 12 | 1 | no | — |
| 1195 | D3 | — | 24 | 1 | no | — |
| 1196 | D3 | — | 24 | 1 | no | — |
| 1197 | D3 | — | 24 | 1 | no | — |
| 1198 | C22 | — | 3 | 1 | no | — |
| 1199 | C22 | — | 3 | 1 | no | — |
| 1200 | C22 | — | 6 | 1 | no | — |
| 1201 | C22 | — | 9 | 1 | no | — |
| 1202 | C22 | — | 18 | 1 | no | — |
| 1203 | C22 | — | 18 | 1 | no | — |
| 1204 | C22 | — | 18 | 1 | no | — |
| 1205 | C22 | — | 72 | 1 | no | — |
| 1206 | C22 | — | 72 | 1 | no | — |
| 1207 | C22 | — | 216 | 1 | no | — |
| 1208 | C4 | — | 3 | 1 | no | — |
| 1209 | C4 | — | 3 | 1 | no | — |
| 1210 | C4 | — | 6 | 1 | no | — |
| 1211 | C4 | — | 9 | 1 | no | — |
| 1212 | C4 | — | 18 | 1 | no | — |
| 1213 | C4 | — | 54 | 1 | no | — |
| 1214 | C4 | — | 54 | 1 | no | — |
| 1215 | C4 | C2×D33 | 1 | 1 | yes | characteristic |
| 1216 | C3 | — | 2 | 1 | no | — |
| 1217 | C3 | — | 2 | 1 | no | — |
| 1218 | C3 | — | 2 | 1 | no | — |
| 1219 | C3 | — | 4 | 1 | no | — |
| 1220 | C3 | #10594677 | 1 | 1 | yes | characteristic, complemented |
| 1221 | C3 | #10594713 | 1 | 1 | yes | characteristic, complemented |
| 1222 | C3 | #10594749 | 1 | 1 | yes | characteristic, complemented |
| 1223 | C2 | — | 6 | 1 | no | — |
| 1224 | C2 | — | 6 | 1 | no | — |
| 1225 | C2 | — | 12 | 1 | no | — |
| 1226 | C2 | — | 18 | 1 | no | — |
| 1227 | C2 | — | 36 | 1 | no | — |
| 1228 | C2 | — | 36 | 1 | no | — |
| 1229 | C2 | — | 36 | 1 | no | — |
| 1230 | C2 | D32×D12 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D32×D12 |
| commutator, cosocle | C33×C4 | C24 |
| Frattini | C4 | C2×D33 |
| Fitting | C33×C8 | C23 |
| socle | C2×C33 | C22×D4 |
| hypercenter | C8 | D33 |
| hypocenter | C33 | #577 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724396 | C2 | semidirect |
| 2. #11724380 | C2 | semidirect |
| 3. #11723648 | C2 | semidirect |
| 4. #11723340 | C2 | semidirect |
| 5. #11723336 | C2 | semidirect |
| 6. #11723326 | C2 | semidirect |
| 7. C3×#63804 | C2 | semidirect |
| 8. C3×#63794 | C2 | semidirect |
| 9. C3×D3×#204 | C2 | semidirect |
| 10. #11722884 | C2 | semidirect |
| 11. #11722869 | C2 | semidirect |
| 12. #11722864 | C2 | semidirect |
| 13. #11722855 | C2 | semidirect |
| 14. #11722843 | C2 | semidirect |
| 15. D3×#3716 | C2 | semidirect |
| 20. #89041 | C22 | semidirect |
| 23. #89021 | C22 | semidirect |
| 24. C3⋊D3×Dic6 | C22 | semidirect |
| 26. D3×#634 | C22 | semidirect |
| 29. C3×#3799 | C22 | semidirect |
| 31. C3×D3×Dic6 | C22 | semidirect |
| 40. #88853 | C22 | semidirect |
| 41. C3×#3745 | C22 | semidirect |
| 42. C3×#3744 | C22 | semidirect |
| 43. C3×#3743 | C22 | semidirect |
| 44. C32×#204 | C22 | semidirect |
| 45. C32×ΓL(1,𝔽25) | C22 | semidirect |
| 46. C32×D3×C8 | C22 | semidirect |
| 47. #88811 | C22 | semidirect |
| 48. #88810 | C22 | semidirect |
| 49. #88800 | C22 | semidirect |
| 50. #88799 | C22 | semidirect |
| 51. #88796 | C22 | semidirect |
| 52. #88796 | C22 | semidirect |
| 53. #88796 | C22 | semidirect |
| 54. #88794 | C22 | semidirect |
| 55. C3×#3717 | C22 | semidirect |
| 56. C3×#3717 | C22 | semidirect |
| 57. C3×#3716 | C22 | semidirect |
| 58. C3×#3714 | C22 | semidirect |
| 59. C3×#3711 | C22 | semidirect |
| 60. C3×#3710 | C22 | semidirect |
| 61. C3×D3×C3⋊C8 | C22 | semidirect |
| 93. #63804 | D3 | semidirect |
| 105. #63794 | D3 | semidirect |
| 109. D3×#204 | D3 | semidirect |
| 192. #3799 | C2×D3 | semidirect |
| 224. D3×Dic6 | C2×D3 | semidirect |
| 238. #3745 | C2×D3 | semidirect |
| 242. #3744 | C2×D3 | semidirect |
| 243. #3743 | C2×D3 | semidirect |
| 261. C3×#204 | C2×D3 | semidirect |
| 262. C3×#204 | C2×D3 | semidirect |
| 268. C3×ΓL(1,𝔽25) | C2×D3 | semidirect |
| 269. C3×ΓL(1,𝔽25) | C2×D3 | semidirect |
| 274. C3×D3×C8 | C2×D3 | semidirect |
| 275. C3×D3×C8 | C2×D3 | semidirect |
| 283. #3717 | C2×D3 | semidirect |
| 284. #3717 | C2×D3 | semidirect |
| 298. #3716 | C2×D3 | semidirect |
| 302. #3714 | C2×D3 | semidirect |
| 304. #3711 | C2×D3 | semidirect |
| 305. #3710 | C2×D3 | semidirect |
| 306. D3×C3⋊C8 | C2×D3 | semidirect |
| 688. #204 | D32 | semidirect |
| 693. ΓL(1,𝔽25) | D32 | semidirect |
| 697. D3×C8 | D32 | semidirect |
| 791. C33 | #577 | semidirect |
| 1117. C32 | #5751 | semidirect |
| 1118. C32 | #5762 | semidirect |
| 1119. C32 | #5775 | semidirect |
| 1220. C3 | #10594677 | semidirect |
| 1221. C3 | #10594713 | semidirect |
| 1222. C3 | #10594749 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724396 | 2 |
| #11724380 | 2 |
| #11723648 | 2 |
| #11723340 | 2 |
| #11723336 | 2 |
| #11723326 | 2 |
| C3×#63804 | 2 |
| C3×#63794 | 2 |
| C3×D3×#204 | 2 |
| #11722884 | 2 |
| #11722869 | 2 |
| #11722864 | 2 |
| #11722855 | 2 |
| #11722843 | 2 |
| D3×#3716 | 2 |
| #10594749 | 3 |
| #10594713 | 3 |
| #10594677 | 3 |