Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3756 conjugacy classes of subgroups.
The subgroup lattice has 992 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#64367 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#64366 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#41×C3⋊D3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11724626 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11724624 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11724623 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11724622 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11724619 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11724618 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11724614 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×#89041 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10596698 | — | 3 | 1 | no | maximal |
| 13 | #10596697 | — | 3 | 1 | no | maximal |
| 14 | #10596696 | — | 3 | 1 | no | maximal |
| 15 | C33×#41 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#3832 | C22 | 1 | 2 | yes | complemented |
| 17 | C3×#3832 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×Q8×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 20 | C3×#3830 | C22 | 1 | 3 | yes | complemented |
| 21 | C3×#3830 | C22 | 1 | 6 | yes | complemented |
| 22 | C3×D4×C3⋊D3 | C22 | 1 | 6 | yes | complemented |
| 23 | C3×D4×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 24 | C3×#3828 | C22 | 1 | 3 | yes | complemented |
| 25 | C3×#3828 | C22 | 1 | 3 | yes | complemented |
| 26 | C3×#3828 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×C3×C4⋊(C3⋊D3) | C22 | 1 | 3 | yes | complemented |
| 28 | C2×C3×C4×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 29 | C2×C3×#634 | C22 | 1 | 3 | yes | complemented |
| 30 | #89049 | C22 | 1 | 6 | yes | complemented |
| 31 | #89049 | C22 | 1 | 12 | yes | complemented |
| 32 | C2×#6295 | C22 | 1 | 6 | yes | complemented |
| 33 | #89046 | C22 | 1 | 12 | yes | complemented |
| 34 | #89046 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#6294 | C22 | 1 | 6 | yes | complemented |
| 36 | C4⋊#1113 | C22 | 1 | 3 | yes | complemented |
| 37 | C4⋊#1113 | C22 | 1 | 6 | yes | complemented |
| 38 | C4×#1113 | C22 | 1 | 6 | yes | complemented |
| 39 | #89042 | C22 | 1 | 6 | yes | complemented |
| 40 | #89041 | C22 | 1 | 3 | yes | complemented |
| 41 | #89041 | C22 | 1 | 6 | yes | complemented |
| 42 | #89041 | C22 | 1 | 6 | yes | complemented |
| 43 | #89041 | C22 | 1 | 6 | yes | complemented |
| 44 | #89041 | C22 | 1 | 6 | yes | complemented |
| 45 | #89041 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #89041 | C22 | 1 | 6 | yes | complemented |
| 47 | #89040 | C22 | 1 | 3 | yes | complemented |
| 48 | #89040 | C22 | 1 | 6 | yes | complemented |
| 49 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | #64366 | D3 | 1 | 1 | yes | characteristic, complemented |
| 51 | #41×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 52 | C3×#1010 | — | 3 | 1 | no | — |
| 53 | C3×#1010 | — | 3 | 1 | no | — |
| 54 | C3×#1010 | — | 6 | 1 | no | — |
| 55 | C3×#1009 | — | 3 | 1 | no | — |
| 56 | C3×#1009 | — | 3 | 1 | no | — |
| 57 | C3×#1009 | — | 6 | 1 | no | — |
| 58 | C3×D3×#41 | — | 3 | 1 | no | — |
| 59 | C3×D3×#41 | — | 3 | 1 | no | — |
| 60 | C3×D3×#41 | — | 6 | 1 | no | — |
| 61 | #64319 | — | 3 | 2 | no | — |
| 62 | D3×#239 | — | 3 | 2 | no | — |
| 63 | D3×#239 | — | 3 | 2 | no | — |
| 64 | #64316 | — | 3 | 2 | no | — |
| 65 | #64315 | — | 3 | 2 | no | — |
| 66 | #64315 | — | 3 | 2 | no | — |
| 67 | #64314 | — | 3 | 6 | no | — |
| 68 | #64314 | — | 3 | 6 | no | — |
| 69 | #64313 | — | 3 | 6 | no | — |
| 70 | #64312 | — | 3 | 6 | no | — |
| 71 | D3×#237 | — | 3 | 6 | no | — |
| 72 | D3×#237 | — | 3 | 6 | no | — |
| 73 | #64308 | — | 3 | 3 | no | — |
| 74 | #64307 | — | 3 | 3 | no | — |
| 75 | #64307 | — | 3 | 3 | no | — |
| 76 | #64306 | — | 3 | 3 | no | — |
| 77 | D3×#235 | — | 3 | 3 | no | — |
| 78 | D3×#235 | — | 3 | 3 | no | — |
| 79 | C2×#3799 | — | 3 | 3 | no | — |
| 80 | #64298 | — | 3 | 3 | no | — |
| 81 | #64297 | — | 3 | 3 | no | — |
| 82 | #64297 | — | 3 | 3 | no | — |
| 83 | C2×#3796 | — | 3 | 3 | no | — |
| 84 | C2×#3795 | — | 3 | 3 | no | — |
| 85 | C22×C3×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 86 | C22×C3×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 87 | C2×#1113 | C23 | 1 | 6 | yes | — |
| 88 | C33×Q8 | C23 | 1 | 1 | yes | characteristic |
| 89 | C33×D4 | C23 | 1 | 3 | yes | — |
| 90 | C2×C33×C4 | C23 | 1 | 3 | yes | — |
| 91 | C3×#638 | C23 | 1 | 6 | yes | — |
| 92 | C3×#638 | C23 | 1 | 6 | yes | — |
| 93 | C3×#638 | C23 | 1 | 6 | yes | — |
| 94 | C2×C3×C3⋊Dic3 | C23 | 1 | 3 | yes | — |
| 95 | C2×C3×C3⋊Dic3 | C23 | 1 | 6 | yes | — |
| 96 | C3×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 97 | C3×C4⋊(C3⋊D3) | C23 | 1 | 6 | yes | — |
| 98 | C3×C4⋊(C3⋊D3) | C23 | 1 | 3 | yes | — |
| 99 | C3×C4⋊(C3⋊D3) | C23 | 1 | 1 | yes | characteristic |
| 100 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 101 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 102 | C3×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 103 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 104 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 105 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | — |
| 106 | C3×#634 | C23 | 1 | 1 | yes | characteristic |
| 107 | C3×#634 | C23 | 1 | 3 | yes | — |
| 108 | C3×#634 | C23 | 1 | 3 | yes | — |
| 109 | C3×#634 | C23 | 1 | 6 | yes | — |
| 110 | #6296 | C23 | 1 | 6 | yes | — |
| 111 | #6295 | C23 | 1 | 6 | yes | — |
| 112 | #6295 | C23 | 1 | 12 | yes | — |
| 113 | #6295 | C23 | 1 | 6 | yes | — |
| 114 | #6295 | C23 | 1 | 2 | yes | — |
| 115 | #6294 | C23 | 1 | 12 | yes | — |
| 116 | #6294 | C23 | 1 | 6 | yes | — |
| 117 | #6294 | C23 | 1 | 6 | yes | — |
| 118 | #6294 | C23 | 1 | 2 | yes | — |
| 119 | #5968 | — | 9 | 1 | no | — |
| 120 | #5966 | — | 9 | 1 | no | — |
| 121 | #5964 | — | 9 | 1 | no | — |
| 122 | C32×#41 | — | 2 | 1 | no | — |
| 123 | C32×#41 | — | 2 | 1 | no | — |
| 124 | C32×#41 | — | 2 | 1 | no | — |
| 125 | C32×#41 | — | 4 | 1 | no | — |
| 126 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 127 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 128 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 129 | #3832 | C2×D3 | 1 | 2 | yes | complemented |
| 130 | #3832 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 131 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 132 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 133 | #3830 | C2×D3 | 1 | 3 | yes | complemented |
| 134 | #3830 | C2×D3 | 1 | 6 | yes | complemented |
| 135 | D4×C3⋊D3 | C2×D3 | 1 | 6 | yes | complemented |
| 136 | D4×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 137 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 138 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 139 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 140 | C2×C4⋊(C3⋊D3) | C2×D3 | 1 | 3 | yes | complemented |
| 141 | C2×C4×C3⋊D3 | C2×D3 | 1 | 3 | yes | complemented |
| 142 | C2×#634 | C2×D3 | 1 | 3 | yes | complemented |
| 143 | C3×#239 | — | 3 | 2 | no | — |
| 144 | C3×#239 | — | 3 | 2 | no | — |
| 145 | C3×#239 | — | 3 | 1 | no | — |
| 146 | C3×#239 | — | 3 | 1 | no | — |
| 147 | C3×#239 | — | 6 | 1 | no | — |
| 148 | C3×#239 | — | 6 | 2 | no | — |
| 149 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 150 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 151 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 152 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 153 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 154 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 155 | C3×#237 | — | 3 | 3 | no | — |
| 156 | C3×#237 | — | 3 | 6 | no | — |
| 157 | C3×#237 | — | 3 | 3 | no | — |
| 158 | C3×#237 | — | 3 | 6 | no | — |
| 159 | C3×#237 | — | 6 | 3 | no | — |
| 160 | C3×#237 | — | 6 | 6 | no | — |
| 161 | C3×D3×D4 | — | 3 | 6 | no | — |
| 162 | C3×D3×D4 | — | 3 | 6 | no | — |
| 163 | C3×D3×D4 | — | 3 | 3 | no | — |
| 164 | C3×D3×D4 | — | 3 | 3 | no | — |
| 165 | C3×D3×D4 | — | 6 | 3 | no | — |
| 166 | C3×D3×D4 | — | 6 | 6 | no | — |
| 167 | C3×#235 | — | 3 | 3 | no | — |
| 168 | C3×#235 | — | 3 | 3 | no | — |
| 169 | C3×#235 | — | 3 | 3 | no | — |
| 170 | C3×#235 | — | 3 | 3 | no | — |
| 171 | C3×#235 | — | 3 | 3 | no | — |
| 172 | C3×#235 | — | 3 | 3 | no | — |
| 173 | C3×#235 | — | 6 | 3 | no | — |
| 174 | C3×#235 | — | 6 | 3 | no | — |
| 175 | C3×#235 | — | 6 | 3 | no | — |
| 176 | C2×C3×D12 | — | 3 | 3 | no | — |
| 177 | C2×C3×D12 | — | 3 | 3 | no | — |
| 178 | C2×C3×D12 | — | 6 | 3 | no | — |
| 179 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 180 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 181 | C2×C3×C4×D3 | — | 6 | 3 | no | — |
| 182 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 183 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 184 | C2×C3×Dic6 | — | 6 | 3 | no | — |
| 185 | #3811 | — | 3 | 6 | no | — |
| 186 | #3811 | — | 3 | 12 | no | — |
| 187 | D3×#67 | — | 3 | 6 | no | — |
| 188 | D3×#67 | — | 3 | 6 | no | — |
| 189 | D3×#67 | — | 3 | 12 | no | — |
| 190 | D3×#67 | — | 3 | 12 | no | — |
| 191 | C2×#626 | — | 3 | 6 | no | — |
| 192 | C2×#626 | — | 3 | 6 | no | — |
| 193 | C2×#625 | — | 3 | 6 | no | — |
| 194 | C2×#624 | — | 3 | 6 | no | — |
| 195 | #3805 | — | 3 | 12 | no | — |
| 196 | #3805 | — | 3 | 6 | no | — |
| 197 | #3804 | — | 3 | 12 | no | — |
| 198 | #3804 | — | 3 | 12 | no | — |
| 199 | #3804 | — | 3 | 6 | no | — |
| 200 | #3804 | — | 3 | 6 | no | — |
| 201 | C2×D3×Dic3 | — | 3 | 6 | no | — |
| 202 | C2×D3×Dic3 | — | 3 | 6 | no | — |
| 203 | #3802 | — | 3 | 3 | no | — |
| 204 | #3802 | — | 3 | 6 | no | — |
| 205 | D3×D12 | — | 3 | 3 | no | — |
| 206 | D3×D12 | — | 3 | 3 | no | — |
| 207 | D3×D12 | — | 3 | 6 | no | — |
| 208 | D3×D12 | — | 3 | 6 | no | — |
| 209 | C4×D32 | — | 3 | 6 | no | — |
| 210 | C4×D32 | — | 3 | 6 | no | — |
| 211 | C4×D32 | — | 3 | 6 | no | — |
| 212 | #3799 | — | 3 | 6 | no | — |
| 213 | #3799 | — | 3 | 6 | no | — |
| 214 | #3799 | — | 3 | 3 | no | — |
| 215 | #3799 | — | 3 | 6 | no | — |
| 216 | #3799 | — | 3 | 6 | no | — |
| 217 | #3799 | — | 3 | 1 | no | — |
| 218 | #3799 | — | 3 | 6 | no | — |
| 219 | #3798 | — | 3 | 6 | no | — |
| 220 | #3798 | — | 3 | 6 | no | — |
| 221 | #3798 | — | 3 | 6 | no | — |
| 222 | #3797 | — | 3 | 3 | no | — |
| 223 | #3797 | — | 3 | 6 | no | — |
| 224 | #3796 | — | 3 | 3 | no | — |
| 225 | #3796 | — | 3 | 6 | no | — |
| 226 | #3796 | — | 3 | 6 | no | — |
| 227 | #3796 | — | 3 | 6 | no | — |
| 228 | #3796 | — | 3 | 6 | no | — |
| 229 | #3796 | — | 3 | 1 | no | — |
| 230 | #3796 | — | 3 | 6 | no | — |
| 231 | #3795 | — | 3 | 3 | no | — |
| 232 | #3795 | — | 3 | 6 | no | — |
| 233 | #3795 | — | 3 | 6 | no | — |
| 234 | #3795 | — | 3 | 6 | no | — |
| 235 | #3795 | — | 3 | 6 | no | — |
| 236 | #3795 | — | 3 | 1 | no | — |
| 237 | #3795 | — | 3 | 6 | no | — |
| 238 | D3×Dic6 | — | 3 | 3 | no | — |
| 239 | D3×Dic6 | — | 3 | 6 | no | — |
| 240 | D3×Dic6 | — | 3 | 3 | no | — |
| 241 | D3×Dic6 | — | 3 | 6 | no | — |
| 242 | C22×C33 | C24 | 1 | 3 | yes | — |
| 243 | C2×C3×C3⋊D3 | — | 4 | 3 | no | — |
| 244 | C2×C3×C3⋊D3 | — | 4 | 6 | no | — |
| 245 | C2×C3×C3⋊D3 | C24 | 1 | 6 | yes | — |
| 246 | C2×C3×C3⋊D3 | C24 | 1 | 3 | yes | — |
| 247 | C2×C3×C3⋊D3 | C24 | 1 | 2 | yes | — |
| 248 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 249 | #1113 | — | 4 | 6 | no | — |
| 250 | C33×C4 | C24 | 1 | 1 | yes | characteristic |
| 251 | C33×C4 | C24 | 1 | 3 | yes | — |
| 252 | C3×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 253 | C3×C3⋊Dic3 | C24 | 1 | 6 | yes | — |
| 254 | C3×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 255 | C3×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 256 | C3×2−1+4 | — | 9 | 1 | no | — |
| 257 | C3×H(5,𝔽2) | — | 9 | 1 | no | — |
| 258 | C2×C3×#41 | — | 9 | 1 | no | — |
| 259 | #1010 | — | 3 | 1 | no | — |
| 260 | #1010 | — | 3 | 1 | no | — |
| 261 | #1010 | — | 6 | 1 | no | — |
| 262 | #1010 | — | 9 | 3 | no | — |
| 263 | #1010 | — | 9 | 3 | no | — |
| 264 | #1010 | — | 9 | 2 | no | — |
| 265 | #1009 | — | 3 | 1 | no | — |
| 266 | #1009 | — | 3 | 1 | no | — |
| 267 | #1009 | — | 6 | 1 | no | — |
| 268 | #1009 | — | 9 | 3 | no | — |
| 269 | #1009 | — | 9 | 3 | no | — |
| 270 | #1009 | — | 9 | 6 | no | — |
| 271 | D3×#41 | — | 3 | 1 | no | — |
| 272 | D3×#41 | — | 3 | 1 | no | — |
| 273 | D3×#41 | — | 6 | 1 | no | — |
| 274 | D3×#41 | — | 9 | 3 | no | — |
| 275 | D3×#41 | — | 9 | 3 | no | — |
| 276 | D3×#41 | — | 9 | 6 | no | — |
| 277 | D3×#41 | — | 9 | 6 | no | — |
| 278 | D3×#41 | — | 9 | 2 | no | — |
| 279 | D3×#41 | — | 9 | 2 | no | — |
| 280 | #1007 | — | 9 | 3 | no | — |
| 281 | #1007 | — | 9 | 2 | no | — |
| 282 | #1007 | — | 9 | 2 | no | — |
| 283 | C2×#239 | — | 9 | 3 | no | — |
| 284 | C2×#239 | — | 9 | 2 | no | — |
| 285 | #1004 | — | 9 | 3 | no | — |
| 286 | #1004 | — | 9 | 6 | no | — |
| 287 | #1004 | — | 9 | 6 | no | — |
| 288 | C2×#237 | — | 9 | 3 | no | — |
| 289 | C2×#237 | — | 9 | 6 | no | — |
| 290 | C2×#235 | — | 9 | 3 | no | — |
| 291 | C2×#235 | — | 9 | 3 | no | — |
| 292 | C22×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 293 | C22×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 294 | C22×C3×D3 | — | 3 | 6 | no | — |
| 295 | C22×C3×D3 | — | 3 | 6 | no | — |
| 296 | C22×C3×D3 | — | 3 | 3 | no | — |
| 297 | C22×C3×D3 | — | 3 | 3 | no | — |
| 298 | C22×C3×D3 | — | 6 | 3 | no | — |
| 299 | C22×C3×D3 | — | 6 | 6 | no | — |
| 300 | C2×D32 | — | 3 | 6 | no | — |
| 301 | C2×D32 | — | 3 | 6 | no | — |
| 302 | C2×D32 | — | 3 | 6 | no | — |
| 303 | C32×Q8 | — | 2 | 1 | no | — |
| 304 | C32×Q8 | — | 2 | 1 | no | — |
| 305 | C32×Q8 | — | 2 | 1 | no | — |
| 306 | C32×Q8 | — | 4 | 1 | no | — |
| 307 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 308 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 309 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 310 | C32×D4 | — | 2 | 3 | no | — |
| 311 | C32×D4 | — | 2 | 3 | no | — |
| 312 | C32×D4 | — | 2 | 3 | no | — |
| 313 | C32×D4 | — | 4 | 3 | no | — |
| 314 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 315 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 316 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 317 | C2×C32×C4 | — | 2 | 3 | no | — |
| 318 | C2×C32×C4 | — | 2 | 3 | no | — |
| 319 | C2×C32×C4 | — | 2 | 3 | no | — |
| 320 | C2×C32×C4 | — | 4 | 3 | no | — |
| 321 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 322 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 323 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 324 | #638 | C22×D3 | 1 | 6 | yes | — |
| 325 | #638 | C22×D3 | 1 | 6 | yes | — |
| 326 | #638 | C22×D3 | 1 | 6 | yes | — |
| 327 | C2×C3⋊Dic3 | C22×D3 | 1 | 3 | yes | — |
| 328 | C2×C3⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 329 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 330 | C4⋊(C3⋊D3) | C22×D3 | 1 | 6 | yes | — |
| 331 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 332 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 333 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 334 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 335 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 336 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 337 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 338 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 339 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 340 | #634 | C22×D3 | 1 | 3 | yes | — |
| 341 | #634 | C22×D3 | 1 | 3 | yes | — |
| 342 | #634 | C22×D3 | 1 | 6 | yes | — |
| 343 | C3×#67 | — | 3 | 6 | no | — |
| 344 | C3×#67 | — | 3 | 6 | no | — |
| 345 | C3×#67 | — | 3 | 6 | no | — |
| 346 | C3×#67 | — | 3 | 6 | no | — |
| 347 | C3×#67 | — | 3 | 6 | no | — |
| 348 | C3×#67 | — | 3 | 6 | no | — |
| 349 | C3×#67 | — | 6 | 6 | no | — |
| 350 | C3×#67 | — | 6 | 6 | no | — |
| 351 | C3×#67 | — | 6 | 6 | no | — |
| 352 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 353 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 354 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 355 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 356 | C2×C3×Dic3 | — | 6 | 6 | no | — |
| 357 | C2×C3×Dic3 | — | 6 | 3 | no | — |
| 358 | C3×D12 | — | 3 | 3 | no | — |
| 359 | C3×D12 | — | 3 | 6 | no | — |
| 360 | C3×D12 | — | 3 | 3 | no | — |
| 361 | C3×D12 | — | 3 | 6 | no | — |
| 362 | C3×D12 | — | 3 | 1 | no | — |
| 363 | C3×D12 | — | 3 | 3 | no | — |
| 364 | C3×D12 | — | 3 | 3 | no | — |
| 365 | C3×D12 | — | 3 | 1 | no | — |
| 366 | C3×D12 | — | 6 | 3 | no | — |
| 367 | C3×D12 | — | 6 | 6 | no | — |
| 368 | C3×D12 | — | 6 | 1 | no | — |
| 369 | C3×D12 | — | 6 | 3 | no | — |
| 370 | C3×C4×D3 | — | 3 | 3 | no | — |
| 371 | C3×C4×D3 | — | 3 | 6 | no | — |
| 372 | C3×C4×D3 | — | 3 | 6 | no | — |
| 373 | C3×C4×D3 | — | 3 | 3 | no | — |
| 374 | C3×C4×D3 | — | 3 | 1 | no | — |
| 375 | C3×C4×D3 | — | 3 | 3 | no | — |
| 376 | C3×C4×D3 | — | 3 | 3 | no | — |
| 377 | C3×C4×D3 | — | 3 | 6 | no | — |
| 378 | C3×C4×D3 | — | 3 | 1 | no | — |
| 379 | C3×C4×D3 | — | 3 | 3 | no | — |
| 380 | C3×C4×D3 | — | 3 | 6 | no | — |
| 381 | C3×C4×D3 | — | 3 | 3 | no | — |
| 382 | C3×C4×D3 | — | 6 | 1 | no | — |
| 383 | C3×C4×D3 | — | 6 | 3 | no | — |
| 384 | C3×C4×D3 | — | 6 | 3 | no | — |
| 385 | C3×C4×D3 | — | 6 | 3 | no | — |
| 386 | C3×C4×D3 | — | 6 | 6 | no | — |
| 387 | C3×C4×D3 | — | 6 | 6 | no | — |
| 388 | C3×Dic6 | — | 3 | 1 | no | — |
| 389 | C3×Dic6 | — | 3 | 3 | no | — |
| 390 | C3×Dic6 | — | 3 | 6 | no | — |
| 391 | C3×Dic6 | — | 3 | 3 | no | — |
| 392 | C3×Dic6 | — | 3 | 3 | no | — |
| 393 | C3×Dic6 | — | 3 | 1 | no | — |
| 394 | C3×Dic6 | — | 3 | 6 | no | — |
| 395 | C3×Dic6 | — | 3 | 3 | no | — |
| 396 | C3×Dic6 | — | 6 | 3 | no | — |
| 397 | C3×Dic6 | — | 6 | 6 | no | — |
| 398 | C3×Dic6 | — | 6 | 1 | no | — |
| 399 | C3×Dic6 | — | 6 | 3 | no | — |
| 400 | #627 | — | 3 | 6 | no | — |
| 401 | #627 | — | 3 | 6 | no | — |
| 402 | #627 | — | 3 | 6 | no | — |
| 403 | #626 | — | 3 | 6 | no | — |
| 404 | #626 | — | 3 | 6 | no | — |
| 405 | #626 | — | 3 | 12 | no | — |
| 406 | #626 | — | 3 | 2 | no | — |
| 407 | #626 | — | 3 | 12 | no | — |
| 408 | #626 | — | 3 | 2 | no | — |
| 409 | #626 | — | 3 | 6 | no | — |
| 410 | #626 | — | 3 | 6 | no | — |
| 411 | #625 | — | 3 | 6 | no | — |
| 412 | #625 | — | 3 | 12 | no | — |
| 413 | #625 | — | 3 | 6 | no | — |
| 414 | #625 | — | 3 | 2 | no | — |
| 415 | #624 | — | 3 | 12 | no | — |
| 416 | #624 | — | 3 | 6 | no | — |
| 417 | #624 | — | 3 | 6 | no | — |
| 418 | #624 | — | 3 | 2 | no | — |
| 419 | D3×Dic3 | — | 3 | 12 | no | — |
| 420 | D3×Dic3 | — | 3 | 6 | no | — |
| 421 | D3×Dic3 | — | 3 | 12 | no | — |
| 422 | D3×Dic3 | — | 3 | 6 | no | — |
| 423 | D3×Dic3 | — | 3 | 6 | no | — |
| 424 | D3×Dic3 | — | 3 | 2 | no | — |
| 425 | D3×Dic3 | — | 3 | 6 | no | — |
| 426 | D3×Dic3 | — | 3 | 2 | no | — |
| 427 | #585 | — | 27 | 1 | no | Sylow |
| 428 | C2×C33 | — | 2 | 3 | no | — |
| 429 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 430 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 431 | C3×C3⋊D3 | — | 2 | 2 | no | — |
| 432 | C3×C3⋊D3 | — | 2 | 3 | no | — |
| 433 | C3×C3⋊D3 | — | 2 | 6 | no | — |
| 434 | C3×#41 | — | 2 | 1 | no | — |
| 435 | C3×#41 | — | 2 | 1 | no | — |
| 436 | C3×#41 | — | 2 | 1 | no | — |
| 437 | C3×#41 | — | 4 | 1 | no | — |
| 438 | C3×#41 | — | 9 | 1 | no | — |
| 439 | C3×#41 | — | 9 | 2 | no | — |
| 440 | C3×#41 | — | 9 | 3 | no | — |
| 441 | C3×#41 | — | 9 | 6 | no | — |
| 442 | C3×#41 | — | 9 | 3 | no | — |
| 443 | C3×#41 | — | 9 | 3 | no | — |
| 444 | C3×#41 | — | 9 | 3 | no | — |
| 445 | C3×#41 | D32 | 1 | 1 | yes | characteristic, complemented |
| 446 | C3×#41 | D32 | 1 | 1 | yes | characteristic, complemented |
| 447 | C3×#41 | D32 | 1 | 1 | yes | characteristic, complemented |
| 448 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 449 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 450 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 451 | C2×C3×D4 | — | 9 | 6 | no | — |
| 452 | C2×C3×D4 | — | 9 | 3 | no | — |
| 453 | C2×C3×D4 | — | 9 | 3 | no | — |
| 454 | C22×C3×C4 | — | 9 | 3 | no | — |
| 455 | C2×#67 | — | 9 | 6 | no | — |
| 456 | C2×#67 | — | 9 | 6 | no | — |
| 457 | C2×#67 | — | 9 | 6 | no | — |
| 458 | C2×#67 | — | 9 | 12 | no | — |
| 459 | C22×Dic3 | — | 9 | 6 | no | — |
| 460 | #239 | — | 3 | 1 | no | — |
| 461 | #239 | — | 3 | 2 | no | — |
| 462 | #239 | — | 3 | 2 | no | — |
| 463 | #239 | — | 3 | 1 | no | — |
| 464 | #239 | — | 6 | 1 | no | — |
| 465 | #239 | — | 6 | 2 | no | — |
| 466 | #239 | — | 9 | 3 | no | — |
| 467 | #239 | — | 9 | 6 | no | — |
| 468 | #239 | — | 9 | 6 | no | — |
| 469 | #239 | — | 9 | 6 | no | — |
| 470 | #239 | — | 9 | 6 | no | — |
| 471 | #239 | — | 9 | 6 | no | — |
| 472 | #239 | — | 9 | 1 | no | — |
| 473 | D3×Q8 | — | 3 | 1 | no | — |
| 474 | D3×Q8 | — | 3 | 2 | no | — |
| 475 | D3×Q8 | — | 3 | 1 | no | — |
| 476 | D3×Q8 | — | 3 | 2 | no | — |
| 477 | D3×Q8 | — | 6 | 1 | no | — |
| 478 | D3×Q8 | — | 6 | 2 | no | — |
| 479 | D3×Q8 | — | 9 | 3 | no | — |
| 480 | D3×Q8 | — | 9 | 6 | no | — |
| 481 | D3×Q8 | — | 9 | 6 | no | — |
| 482 | D3×Q8 | — | 9 | 3 | no | — |
| 483 | #237 | — | 3 | 3 | no | — |
| 484 | #237 | — | 3 | 6 | no | — |
| 485 | #237 | — | 3 | 6 | no | — |
| 486 | #237 | — | 3 | 3 | no | — |
| 487 | #237 | — | 6 | 3 | no | — |
| 488 | #237 | — | 6 | 6 | no | — |
| 489 | #237 | — | 9 | 3 | no | — |
| 490 | #237 | — | 9 | 6 | no | — |
| 491 | #237 | — | 9 | 6 | no | — |
| 492 | #237 | — | 9 | 6 | no | — |
| 493 | #237 | — | 9 | 6 | no | — |
| 494 | #237 | — | 9 | 6 | no | — |
| 495 | #237 | — | 9 | 1 | no | — |
| 496 | #237 | — | 9 | 6 | no | — |
| 497 | #237 | — | 9 | 12 | no | — |
| 498 | #237 | — | 9 | 12 | no | — |
| 499 | #237 | — | 9 | 6 | no | — |
| 500 | D3×D4 | — | 3 | 3 | no | — |
| 501 | D3×D4 | — | 3 | 6 | no | — |
| 502 | D3×D4 | — | 3 | 3 | no | — |
| 503 | D3×D4 | — | 3 | 6 | no | — |
| 504 | D3×D4 | — | 6 | 3 | no | — |
| 505 | D3×D4 | — | 6 | 6 | no | — |
| 506 | D3×D4 | — | 9 | 3 | no | — |
| 507 | D3×D4 | — | 9 | 6 | no | — |
| 508 | D3×D4 | — | 9 | 6 | no | — |
| 509 | D3×D4 | — | 9 | 3 | no | — |
| 510 | D3×D4 | — | 9 | 6 | no | — |
| 511 | D3×D4 | — | 9 | 12 | no | — |
| 512 | D3×D4 | — | 9 | 6 | no | — |
| 513 | D3×D4 | — | 9 | 12 | no | — |
| 514 | #235 | — | 3 | 3 | no | — |
| 515 | #235 | — | 3 | 3 | no | — |
| 516 | #235 | — | 3 | 3 | no | — |
| 517 | #235 | — | 3 | 3 | no | — |
| 518 | #235 | — | 3 | 3 | no | — |
| 519 | #235 | — | 3 | 3 | no | — |
| 520 | #235 | — | 6 | 3 | no | — |
| 521 | #235 | — | 6 | 3 | no | — |
| 522 | #235 | — | 6 | 3 | no | — |
| 523 | #235 | — | 9 | 3 | no | — |
| 524 | #235 | — | 9 | 1 | no | — |
| 525 | #235 | — | 9 | 6 | no | — |
| 526 | #235 | — | 9 | 6 | no | — |
| 527 | #235 | — | 9 | 6 | no | — |
| 528 | #235 | — | 9 | 6 | no | — |
| 529 | #235 | — | 9 | 6 | no | — |
| 530 | #235 | — | 9 | 6 | no | — |
| 531 | #235 | — | 9 | 6 | no | — |
| 532 | #235 | — | 9 | 6 | no | — |
| 533 | #235 | — | 9 | 6 | no | — |
| 534 | #235 | — | 9 | 12 | no | — |
| 535 | C2×D12 | — | 3 | 3 | no | — |
| 536 | C2×D12 | — | 3 | 3 | no | — |
| 537 | C2×D12 | — | 6 | 3 | no | — |
| 538 | C2×D12 | — | 9 | 3 | no | — |
| 539 | C2×D12 | — | 9 | 6 | no | — |
| 540 | C2×D12 | — | 9 | 6 | no | — |
| 541 | C2×C4×D3 | — | 3 | 3 | no | — |
| 542 | C2×C4×D3 | — | 3 | 3 | no | — |
| 543 | C2×C4×D3 | — | 6 | 3 | no | — |
| 544 | C2×C4×D3 | — | 9 | 6 | no | — |
| 545 | C2×C4×D3 | — | 9 | 6 | no | — |
| 546 | C2×C4×D3 | — | 9 | 6 | no | — |
| 547 | C2×C4×D3 | — | 9 | 6 | no | — |
| 548 | C2×C4×D3 | — | 9 | 6 | no | — |
| 549 | C2×Dic6 | — | 3 | 3 | no | — |
| 550 | C2×Dic6 | — | 3 | 3 | no | — |
| 551 | C2×Dic6 | — | 6 | 3 | no | — |
| 552 | C2×Dic6 | — | 9 | 3 | no | — |
| 553 | C2×Dic6 | — | 9 | 6 | no | — |
| 554 | C22×C32 | — | 2 | 3 | no | — |
| 555 | C22×C32 | — | 2 | 3 | no | — |
| 556 | C22×C32 | — | 2 | 3 | no | — |
| 557 | C22×C32 | — | 4 | 3 | no | — |
| 558 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 559 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 560 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 561 | C2×C3⋊D3 | — | 4 | 3 | no | — |
| 562 | C2×C3⋊D3 | — | 4 | 6 | no | — |
| 563 | C2×C3⋊D3 | C23×D3 | 1 | 6 | yes | — |
| 564 | C2×C3⋊D3 | C23×D3 | 1 | 3 | yes | — |
| 565 | C2×C3⋊D3 | C23×D3 | 1 | 2 | yes | — |
| 566 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 567 | C2×C3×D3 | — | 3 | 6 | no | — |
| 568 | C2×C3×D3 | — | 3 | 6 | no | — |
| 569 | C2×C3×D3 | — | 3 | 3 | no | — |
| 570 | C2×C3×D3 | — | 3 | 3 | no | — |
| 571 | C2×C3×D3 | — | 3 | 2 | no | — |
| 572 | C2×C3×D3 | — | 3 | 2 | no | — |
| 573 | C2×C3×D3 | — | 3 | 1 | no | — |
| 574 | C2×C3×D3 | — | 3 | 1 | no | — |
| 575 | C2×C3×D3 | — | 6 | 1 | no | — |
| 576 | C2×C3×D3 | — | 6 | 2 | no | — |
| 577 | C2×C3×D3 | — | 6 | 3 | no | — |
| 578 | C2×C3×D3 | — | 6 | 6 | no | — |
| 579 | C2×C3×D3 | — | 12 | 3 | no | — |
| 580 | C2×C3×D3 | — | 12 | 3 | no | — |
| 581 | C2×C3×D3 | — | 12 | 6 | no | — |
| 582 | C2×C3×D3 | — | 12 | 6 | no | — |
| 583 | C2×C3×D3 | — | 12 | 6 | no | — |
| 584 | C2×C3×D3 | — | 24 | 6 | no | — |
| 585 | D32 | — | 12 | 6 | no | — |
| 586 | D32 | — | 12 | 6 | no | — |
| 587 | D32 | — | 12 | 6 | no | — |
| 588 | C32×C4 | — | 2 | 1 | no | — |
| 589 | C32×C4 | — | 2 | 3 | no | — |
| 590 | C32×C4 | — | 2 | 3 | no | — |
| 591 | C32×C4 | — | 2 | 1 | no | — |
| 592 | C32×C4 | — | 2 | 1 | no | — |
| 593 | C32×C4 | — | 2 | 3 | no | — |
| 594 | C32×C4 | — | 4 | 1 | no | — |
| 595 | C32×C4 | — | 4 | 3 | no | — |
| 596 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 597 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 598 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 599 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 600 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 601 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 602 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 603 | C3⋊Dic3 | C23×D3 | 1 | 6 | yes | — |
| 604 | C3⋊Dic3 | C23×D3 | 1 | 3 | yes | — |
| 605 | C3⋊Dic3 | C23×D3 | 1 | 2 | yes | — |
| 606 | C3×Dic3 | — | 3 | 1 | no | — |
| 607 | C3×Dic3 | — | 3 | 3 | no | — |
| 608 | C3×Dic3 | — | 3 | 6 | no | — |
| 609 | C3×Dic3 | — | 3 | 2 | no | — |
| 610 | C3×Dic3 | — | 3 | 1 | no | — |
| 611 | C3×Dic3 | — | 3 | 6 | no | — |
| 612 | C3×Dic3 | — | 3 | 2 | no | — |
| 613 | C3×Dic3 | — | 3 | 3 | no | — |
| 614 | C3×Dic3 | — | 6 | 6 | no | — |
| 615 | C3×Dic3 | — | 6 | 3 | no | — |
| 616 | C3×Dic3 | — | 6 | 2 | no | — |
| 617 | C3×Dic3 | — | 6 | 1 | no | — |
| 618 | 2−1+4 | — | 9 | 1 | no | — |
| 619 | 2−1+4 | — | 27 | 2 | no | — |
| 620 | 2−1+4 | — | 27 | 3 | no | — |
| 621 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 622 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 623 | H(5,𝔽2) | — | 27 | 3 | no | — |
| 624 | C2×#41 | — | 9 | 1 | no | — |
| 625 | C2×#41 | — | 27 | 3 | no | — |
| 626 | C2×#41 | — | 27 | 3 | no | — |
| 627 | C2×#41 | — | 27 | 6 | no | — |
| 628 | C2×#41 | — | 27 | 2 | no | — |
| 629 | C33 | #585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 630 | C23×C3 | — | 9 | 6 | no | — |
| 631 | C23×C3 | — | 9 | 3 | no | — |
| 632 | C22×D3 | — | 3 | 3 | no | — |
| 633 | C22×D3 | — | 3 | 3 | no | — |
| 634 | C22×D3 | — | 3 | 6 | no | — |
| 635 | C22×D3 | — | 3 | 6 | no | — |
| 636 | C22×D3 | — | 6 | 3 | no | — |
| 637 | C22×D3 | — | 6 | 6 | no | — |
| 638 | C22×D3 | — | 9 | 6 | no | — |
| 639 | C22×D3 | — | 9 | 6 | no | — |
| 640 | C22×D3 | — | 9 | 6 | no | — |
| 641 | C3×Q8 | — | 2 | 1 | no | — |
| 642 | C3×Q8 | — | 2 | 1 | no | — |
| 643 | C3×Q8 | — | 2 | 1 | no | — |
| 644 | C3×Q8 | — | 4 | 1 | no | — |
| 645 | C3×Q8 | — | 9 | 1 | no | — |
| 646 | C3×Q8 | — | 9 | 3 | no | — |
| 647 | C3×Q8 | — | 9 | 6 | no | — |
| 648 | C3×Q8 | — | 9 | 3 | no | — |
| 649 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 650 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 651 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 652 | C3×D4 | — | 2 | 3 | no | — |
| 653 | C3×D4 | — | 2 | 3 | no | — |
| 654 | C3×D4 | — | 2 | 3 | no | — |
| 655 | C3×D4 | — | 4 | 3 | no | — |
| 656 | C3×D4 | — | 9 | 6 | no | — |
| 657 | C3×D4 | — | 9 | 6 | no | — |
| 658 | C3×D4 | — | 9 | 6 | no | — |
| 659 | C3×D4 | — | 9 | 1 | no | — |
| 660 | C3×D4 | — | 9 | 3 | no | — |
| 661 | C3×D4 | — | 9 | 6 | no | — |
| 662 | C3×D4 | — | 9 | 3 | no | — |
| 663 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 664 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 665 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 666 | C2×C3×C4 | — | 2 | 3 | no | — |
| 667 | C2×C3×C4 | — | 2 | 3 | no | — |
| 668 | C2×C3×C4 | — | 2 | 3 | no | — |
| 669 | C2×C3×C4 | — | 4 | 3 | no | — |
| 670 | C2×C3×C4 | — | 9 | 3 | no | — |
| 671 | C2×C3×C4 | — | 9 | 6 | no | — |
| 672 | C2×C3×C4 | — | 9 | 6 | no | — |
| 673 | C2×C3×C4 | — | 9 | 3 | no | — |
| 674 | C2×C3×C4 | — | 9 | 3 | no | — |
| 675 | C2×C3×C4 | — | 9 | 6 | no | — |
| 676 | C2×C3×C4 | — | 9 | 1 | no | — |
| 677 | C2×C3×C4 | — | 9 | 3 | no | — |
| 678 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 679 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 680 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 681 | #67 | — | 3 | 6 | no | — |
| 682 | #67 | — | 3 | 6 | no | — |
| 683 | #67 | — | 3 | 6 | no | — |
| 684 | #67 | — | 3 | 6 | no | — |
| 685 | #67 | — | 3 | 6 | no | — |
| 686 | #67 | — | 3 | 6 | no | — |
| 687 | #67 | — | 6 | 6 | no | — |
| 688 | #67 | — | 6 | 6 | no | — |
| 689 | #67 | — | 6 | 6 | no | — |
| 690 | #67 | — | 9 | 6 | no | — |
| 691 | #67 | — | 9 | 2 | no | — |
| 692 | #67 | — | 9 | 6 | no | — |
| 693 | #67 | — | 9 | 2 | no | — |
| 694 | #67 | — | 9 | 12 | no | — |
| 695 | #67 | — | 9 | 6 | no | — |
| 696 | #67 | — | 9 | 12 | no | — |
| 697 | #67 | — | 9 | 6 | no | — |
| 698 | C2×Dic3 | — | 3 | 6 | no | — |
| 699 | C2×Dic3 | — | 3 | 6 | no | — |
| 700 | C2×Dic3 | — | 3 | 3 | no | — |
| 701 | C2×Dic3 | — | 3 | 3 | no | — |
| 702 | C2×Dic3 | — | 6 | 6 | no | — |
| 703 | C2×Dic3 | — | 6 | 3 | no | — |
| 704 | C2×Dic3 | — | 9 | 6 | no | — |
| 705 | C2×Dic3 | — | 9 | 12 | no | — |
| 706 | C2×Dic3 | — | 9 | 2 | no | — |
| 707 | C2×Dic3 | — | 9 | 6 | no | — |
| 708 | D12 | — | 3 | 3 | no | — |
| 709 | D12 | — | 3 | 3 | no | — |
| 710 | D12 | — | 3 | 6 | no | — |
| 711 | D12 | — | 3 | 6 | no | — |
| 712 | D12 | — | 3 | 1 | no | — |
| 713 | D12 | — | 3 | 3 | no | — |
| 714 | D12 | — | 3 | 1 | no | — |
| 715 | D12 | — | 3 | 3 | no | — |
| 716 | D12 | — | 6 | 3 | no | — |
| 717 | D12 | — | 6 | 6 | no | — |
| 718 | D12 | — | 6 | 1 | no | — |
| 719 | D12 | — | 6 | 3 | no | — |
| 720 | D12 | — | 9 | 6 | no | — |
| 721 | D12 | — | 9 | 12 | no | — |
| 722 | D12 | — | 9 | 6 | no | — |
| 723 | D12 | — | 9 | 2 | no | — |
| 724 | C4×D3 | — | 3 | 1 | no | — |
| 725 | C4×D3 | — | 3 | 1 | no | — |
| 726 | C4×D3 | — | 3 | 3 | no | — |
| 727 | C4×D3 | — | 3 | 3 | no | — |
| 728 | C4×D3 | — | 3 | 3 | no | — |
| 729 | C4×D3 | — | 3 | 3 | no | — |
| 730 | C4×D3 | — | 3 | 3 | no | — |
| 731 | C4×D3 | — | 3 | 3 | no | — |
| 732 | C4×D3 | — | 3 | 6 | no | — |
| 733 | C4×D3 | — | 3 | 6 | no | — |
| 734 | C4×D3 | — | 3 | 6 | no | — |
| 735 | C4×D3 | — | 3 | 6 | no | — |
| 736 | C4×D3 | — | 6 | 1 | no | — |
| 737 | C4×D3 | — | 6 | 3 | no | — |
| 738 | C4×D3 | — | 6 | 3 | no | — |
| 739 | C4×D3 | — | 6 | 3 | no | — |
| 740 | C4×D3 | — | 6 | 6 | no | — |
| 741 | C4×D3 | — | 6 | 6 | no | — |
| 742 | C4×D3 | — | 9 | 6 | no | — |
| 743 | C4×D3 | — | 9 | 2 | no | — |
| 744 | C4×D3 | — | 9 | 2 | no | — |
| 745 | C4×D3 | — | 9 | 6 | no | — |
| 746 | C4×D3 | — | 9 | 6 | no | — |
| 747 | C4×D3 | — | 9 | 12 | no | — |
| 748 | C4×D3 | — | 9 | 12 | no | — |
| 749 | C4×D3 | — | 9 | 6 | no | — |
| 750 | Dic6 | — | 3 | 3 | no | — |
| 751 | Dic6 | — | 3 | 3 | no | — |
| 752 | Dic6 | — | 3 | 6 | no | — |
| 753 | Dic6 | — | 3 | 6 | no | — |
| 754 | Dic6 | — | 3 | 1 | no | — |
| 755 | Dic6 | — | 3 | 3 | no | — |
| 756 | Dic6 | — | 3 | 1 | no | — |
| 757 | Dic6 | — | 3 | 3 | no | — |
| 758 | Dic6 | — | 6 | 3 | no | — |
| 759 | Dic6 | — | 6 | 6 | no | — |
| 760 | Dic6 | — | 6 | 1 | no | — |
| 761 | Dic6 | — | 6 | 3 | no | — |
| 762 | Dic6 | — | 9 | 6 | no | — |
| 763 | Dic6 | — | 9 | 6 | no | — |
| 764 | Dic6 | — | 9 | 6 | no | — |
| 765 | C2×C32 | — | 2 | 3 | no | — |
| 766 | C2×C32 | — | 2 | 3 | no | — |
| 767 | C2×C32 | — | 2 | 3 | no | — |
| 768 | C2×C32 | — | 2 | 1 | no | — |
| 769 | C2×C32 | — | 2 | 1 | no | — |
| 770 | C2×C32 | — | 2 | 1 | no | — |
| 771 | C2×C32 | — | 4 | 1 | no | — |
| 772 | C2×C32 | — | 4 | 3 | no | — |
| 773 | C2×C32 | — | 4 | 3 | no | — |
| 774 | C2×C32 | — | 4 | 3 | no | — |
| 775 | C2×C32 | — | 8 | 3 | no | — |
| 776 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 777 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 778 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 779 | C3⋊D3 | — | 2 | 1 | no | — |
| 780 | C3⋊D3 | — | 2 | 3 | no | — |
| 781 | C3⋊D3 | — | 2 | 6 | no | — |
| 782 | C3⋊D3 | — | 2 | 2 | no | — |
| 783 | C3×D3 | — | 6 | 2 | no | — |
| 784 | C3×D3 | — | 6 | 2 | no | — |
| 785 | C3×D3 | — | 6 | 6 | no | — |
| 786 | C3×D3 | — | 6 | 2 | no | — |
| 787 | C3×D3 | — | 6 | 3 | no | — |
| 788 | C3×D3 | — | 6 | 1 | no | — |
| 789 | C3×D3 | — | 6 | 3 | no | — |
| 790 | C3×D3 | — | 6 | 6 | no | — |
| 791 | C3×D3 | — | 6 | 1 | no | — |
| 792 | C3×D3 | — | 12 | 2 | no | — |
| 793 | C3×D3 | — | 12 | 3 | no | — |
| 794 | C3×D3 | — | 12 | 6 | no | — |
| 795 | #41 | — | 9 | 1 | no | — |
| 796 | #41 | — | 9 | 2 | no | — |
| 797 | #41 | — | 9 | 3 | no | — |
| 798 | #41 | — | 9 | 6 | no | — |
| 799 | #41 | — | 9 | 3 | no | — |
| 800 | #41 | — | 9 | 3 | no | — |
| 801 | #41 | — | 9 | 3 | no | — |
| 802 | #41 | — | 27 | 6 | no | — |
| 803 | #41 | — | 27 | 6 | no | — |
| 804 | #41 | — | 27 | 12 | no | — |
| 805 | #41 | — | 27 | 3 | no | — |
| 806 | #41 | — | 27 | 1 | no | — |
| 807 | #41 | — | 27 | 6 | no | — |
| 808 | #41 | — | 27 | 6 | no | — |
| 809 | #41 | — | 27 | 6 | no | — |
| 810 | #41 | — | 27 | 6 | no | — |
| 811 | #41 | — | 27 | 6 | no | — |
| 812 | #41 | #1113 | 1 | 1 | yes | characteristic, complemented |
| 813 | C2×Q8 | — | 9 | 1 | no | — |
| 814 | C2×Q8 | — | 9 | 2 | no | — |
| 815 | C2×Q8 | — | 9 | 3 | no | — |
| 816 | C2×Q8 | — | 27 | 3 | no | — |
| 817 | C2×Q8 | — | 27 | 6 | no | — |
| 818 | C2×D4 | — | 9 | 3 | no | — |
| 819 | C2×D4 | — | 9 | 6 | no | — |
| 820 | C2×D4 | — | 9 | 3 | no | — |
| 821 | C2×D4 | — | 27 | 3 | no | — |
| 822 | C2×D4 | — | 27 | 6 | no | — |
| 823 | C2×D4 | — | 27 | 6 | no | — |
| 824 | C2×D4 | — | 27 | 6 | no | — |
| 825 | C2×D4 | — | 27 | 12 | no | — |
| 826 | C22×C4 | — | 9 | 3 | no | — |
| 827 | C22×C4 | — | 27 | 6 | no | — |
| 828 | C22×C4 | — | 27 | 6 | no | — |
| 829 | C22×C3 | — | 2 | 3 | no | — |
| 830 | C22×C3 | — | 2 | 3 | no | — |
| 831 | C22×C3 | — | 2 | 3 | no | — |
| 832 | C22×C3 | — | 4 | 3 | no | — |
| 833 | C22×C3 | — | 9 | 6 | no | — |
| 834 | C22×C3 | — | 9 | 3 | no | — |
| 835 | C22×C3 | — | 9 | 2 | no | — |
| 836 | C22×C3 | — | 9 | 1 | no | — |
| 837 | C22×C3 | — | 36 | 3 | no | — |
| 838 | C22×C3 | — | 36 | 6 | no | — |
| 839 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 840 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 841 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 842 | C2×D3 | — | 3 | 1 | no | — |
| 843 | C2×D3 | — | 3 | 1 | no | — |
| 844 | C2×D3 | — | 3 | 2 | no | — |
| 845 | C2×D3 | — | 3 | 2 | no | — |
| 846 | C2×D3 | — | 3 | 3 | no | — |
| 847 | C2×D3 | — | 3 | 3 | no | — |
| 848 | C2×D3 | — | 3 | 6 | no | — |
| 849 | C2×D3 | — | 3 | 6 | no | — |
| 850 | C2×D3 | — | 6 | 1 | no | — |
| 851 | C2×D3 | — | 6 | 2 | no | — |
| 852 | C2×D3 | — | 6 | 3 | no | — |
| 853 | C2×D3 | — | 6 | 6 | no | — |
| 854 | C2×D3 | — | 12 | 3 | no | — |
| 855 | C2×D3 | — | 12 | 3 | no | — |
| 856 | C2×D3 | — | 12 | 6 | no | — |
| 857 | C2×D3 | — | 12 | 6 | no | — |
| 858 | C2×D3 | — | 12 | 6 | no | — |
| 859 | C2×D3 | — | 24 | 6 | no | — |
| 860 | C2×D3 | — | 36 | 6 | no | — |
| 861 | C2×D3 | — | 36 | 6 | no | — |
| 862 | C2×D3 | — | 36 | 6 | no | — |
| 863 | C3×C4 | — | 2 | 1 | no | — |
| 864 | C3×C4 | — | 2 | 3 | no | — |
| 865 | C3×C4 | — | 2 | 3 | no | — |
| 866 | C3×C4 | — | 2 | 1 | no | — |
| 867 | C3×C4 | — | 2 | 1 | no | — |
| 868 | C3×C4 | — | 2 | 3 | no | — |
| 869 | C3×C4 | — | 4 | 1 | no | — |
| 870 | C3×C4 | — | 4 | 3 | no | — |
| 871 | C3×C4 | — | 9 | 2 | no | — |
| 872 | C3×C4 | — | 9 | 3 | no | — |
| 873 | C3×C4 | — | 9 | 6 | no | — |
| 874 | C3×C4 | — | 9 | 1 | no | — |
| 875 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 876 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 877 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 878 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 879 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 880 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 881 | Dic3 | — | 3 | 6 | no | — |
| 882 | Dic3 | — | 3 | 6 | no | — |
| 883 | Dic3 | — | 3 | 3 | no | — |
| 884 | Dic3 | — | 3 | 3 | no | — |
| 885 | Dic3 | — | 3 | 2 | no | — |
| 886 | Dic3 | — | 3 | 2 | no | — |
| 887 | Dic3 | — | 3 | 1 | no | — |
| 888 | Dic3 | — | 3 | 1 | no | — |
| 889 | Dic3 | — | 6 | 6 | no | — |
| 890 | Dic3 | — | 6 | 3 | no | — |
| 891 | Dic3 | — | 6 | 2 | no | — |
| 892 | Dic3 | — | 6 | 1 | no | — |
| 893 | C32 | — | 2 | 1 | no | — |
| 894 | C32 | — | 2 | 1 | no | — |
| 895 | C32 | — | 2 | 1 | no | — |
| 896 | C32 | — | 4 | 1 | no | — |
| 897 | C32 | #5964 | 1 | 1 | yes | characteristic, complemented |
| 898 | C32 | #5966 | 1 | 1 | yes | characteristic, complemented |
| 899 | C32 | #5968 | 1 | 1 | yes | characteristic, complemented |
| 900 | C23 | — | 9 | 3 | no | — |
| 901 | C23 | — | 9 | 6 | no | — |
| 902 | C23 | — | 27 | 6 | no | — |
| 903 | Q8 | — | 9 | 6 | no | — |
| 904 | Q8 | — | 9 | 3 | no | — |
| 905 | Q8 | — | 9 | 3 | no | — |
| 906 | Q8 | — | 9 | 1 | no | — |
| 907 | Q8 | — | 27 | 6 | no | — |
| 908 | Q8 | C2×#1113 | 1 | 1 | yes | characteristic |
| 909 | D4 | — | 9 | 6 | no | — |
| 910 | D4 | — | 9 | 6 | no | — |
| 911 | D4 | — | 9 | 6 | no | — |
| 912 | D4 | — | 9 | 6 | no | — |
| 913 | D4 | — | 9 | 3 | no | — |
| 914 | D4 | — | 9 | 3 | no | — |
| 915 | D4 | — | 9 | 1 | no | — |
| 916 | D4 | — | 27 | 2 | no | — |
| 917 | D4 | — | 27 | 6 | no | — |
| 918 | D4 | — | 27 | 6 | no | — |
| 919 | D4 | — | 27 | 12 | no | — |
| 920 | D4 | C2×#1113 | 1 | 3 | yes | — |
| 921 | C2×C4 | — | 9 | 3 | no | — |
| 922 | C2×C4 | — | 9 | 6 | no | — |
| 923 | C2×C4 | — | 9 | 1 | no | — |
| 924 | C2×C4 | — | 9 | 3 | no | — |
| 925 | C2×C4 | — | 9 | 3 | no | — |
| 926 | C2×C4 | — | 9 | 3 | no | — |
| 927 | C2×C4 | — | 9 | 6 | no | — |
| 928 | C2×C4 | — | 9 | 6 | no | — |
| 929 | C2×C4 | — | 27 | 2 | no | — |
| 930 | C2×C4 | — | 27 | 6 | no | — |
| 931 | C2×C4 | — | 27 | 6 | no | — |
| 932 | C2×C4 | — | 27 | 12 | no | — |
| 933 | C2×C4 | C2×#1113 | 1 | 3 | yes | — |
| 934 | C2×C3 | — | 2 | 3 | no | — |
| 935 | C2×C3 | — | 2 | 3 | no | — |
| 936 | C2×C3 | — | 2 | 3 | no | — |
| 937 | C2×C3 | — | 2 | 1 | no | — |
| 938 | C2×C3 | — | 2 | 1 | no | — |
| 939 | C2×C3 | — | 2 | 1 | no | — |
| 940 | C2×C3 | — | 4 | 3 | no | — |
| 941 | C2×C3 | — | 4 | 3 | no | — |
| 942 | C2×C3 | — | 4 | 3 | no | — |
| 943 | C2×C3 | — | 4 | 1 | no | — |
| 944 | C2×C3 | — | 8 | 3 | no | — |
| 945 | C2×C3 | — | 18 | 2 | no | — |
| 946 | C2×C3 | — | 18 | 6 | no | — |
| 947 | C2×C3 | — | 18 | 3 | no | — |
| 948 | C2×C3 | — | 18 | 1 | no | — |
| 949 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 950 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 951 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 952 | D3 | — | 6 | 2 | no | — |
| 953 | D3 | — | 6 | 1 | no | — |
| 954 | D3 | — | 6 | 6 | no | — |
| 955 | D3 | — | 6 | 3 | no | — |
| 956 | D3 | — | 6 | 1 | no | — |
| 957 | D3 | — | 6 | 3 | no | — |
| 958 | D3 | — | 6 | 2 | no | — |
| 959 | D3 | — | 6 | 6 | no | — |
| 960 | D3 | — | 6 | 2 | no | — |
| 961 | D3 | — | 12 | 3 | no | — |
| 962 | D3 | — | 12 | 6 | no | — |
| 963 | D3 | — | 12 | 2 | no | — |
| 964 | C22 | — | 9 | 1 | no | — |
| 965 | C22 | — | 9 | 2 | no | — |
| 966 | C22 | — | 9 | 3 | no | — |
| 967 | C22 | — | 9 | 6 | no | — |
| 968 | C22 | — | 36 | 3 | no | — |
| 969 | C22 | — | 36 | 6 | no | — |
| 970 | C22 | — | 108 | 6 | no | — |
| 971 | C22 | C22×#1113 | 1 | 3 | yes | — |
| 972 | C4 | — | 9 | 1 | no | — |
| 973 | C4 | — | 9 | 2 | no | — |
| 974 | C4 | — | 9 | 3 | no | — |
| 975 | C4 | — | 9 | 6 | no | — |
| 976 | C4 | C22×#1113 | 1 | 3 | yes | — |
| 977 | C4 | C22×#1113 | 1 | 1 | yes | characteristic |
| 978 | C3 | — | 2 | 1 | no | — |
| 979 | C3 | — | 2 | 1 | no | — |
| 980 | C3 | — | 2 | 1 | no | — |
| 981 | C3 | — | 4 | 1 | no | — |
| 982 | C3 | #10596696 | 1 | 1 | yes | characteristic, complemented |
| 983 | C3 | #10596697 | 1 | 1 | yes | characteristic, complemented |
| 984 | C3 | #10596698 | 1 | 1 | yes | characteristic, complemented |
| 985 | C2 | — | 2 | 3 | no | — |
| 986 | C2 | — | 18 | 1 | no | — |
| 987 | C2 | — | 18 | 6 | no | — |
| 988 | C2 | — | 18 | 3 | no | — |
| 989 | C2 | — | 18 | 2 | no | — |
| 990 | C2 | C23×#1113 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#1113 |
| commutator, socle, cosocle | C2×C33 | C25 |
| Fitting | C33×#41 | C22 |
| hypercenter | #41 | #1113 |
| hypocenter | C33 | #585 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#64367 | C2 | semidirect |
| 2. C3×#64366 | C2 | semidirect |
| 3. C3×#41×C3⋊D3 | C2 | semidirect |
| 4. #11724626 | C2 | semidirect |
| 5. #11724624 | C2 | semidirect |
| 6. #11724623 | C2 | semidirect |
| 7. #11724622 | C2 | semidirect |
| 8. #11724619 | C2 | semidirect |
| 9. #11724618 | C2 | semidirect |
| 10. #11724614 | C2 | semidirect |
| 11. C2×#89041 | C2 | semidirect |
| 15. C33×#41 | C22 | semidirect |
| 16. C3×#3832 | C22 | semidirect |
| 17. C3×#3832 | C22 | semidirect |
| 18. C3×Q8×C3⋊D3 | C22 | semidirect |
| 19. C3×Q8×C3⋊D3 | C22 | semidirect |
| 20. C3×#3830 | C22 | semidirect |
| 21. C3×#3830 | C22 | semidirect |
| 22. C3×D4×C3⋊D3 | C22 | semidirect |
| 23. C3×D4×C3⋊D3 | C22 | semidirect |
| 24. C3×#3828 | C22 | semidirect |
| 25. C3×#3828 | C22 | semidirect |
| 26. C3×#3828 | C22 | semidirect |
| 27. C2×C3×C4⋊(C3⋊D3) | C22 | semidirect |
| 28. C2×C3×C4×C3⋊D3 | C22 | semidirect |
| 29. C2×C3×#634 | C22 | semidirect |
| 30. #89049 | C22 | semidirect |
| 31. #89049 | C22 | semidirect |
| 32. C2×#6295 | C22 | semidirect |
| 33. #89046 | C22 | semidirect |
| 34. #89046 | C22 | semidirect |
| 35. C2×#6294 | C22 | semidirect |
| 36. C4⋊#1113 | C22 | semidirect |
| 37. C4⋊#1113 | C22 | semidirect |
| 38. C4×#1113 | C22 | semidirect |
| 39. #89042 | C22 | semidirect |
| 40. #89041 | C22 | semidirect |
| 41. #89041 | C22 | semidirect |
| 42. #89041 | C22 | semidirect |
| 43. #89041 | C22 | semidirect |
| 44. #89041 | C22 | semidirect |
| 45. #89041 | C22 | semidirect |
| 46. #89041 | C22 | semidirect |
| 47. #89040 | C22 | semidirect |
| 48. #89040 | C22 | semidirect |
| 49. #64367 | D3 | semidirect |
| 50. #64366 | D3 | semidirect |
| 51. #41×C3⋊D3 | D3 | semidirect |
| 126. C32×#41 | C2×D3 | semidirect |
| 127. C32×#41 | C2×D3 | semidirect |
| 128. C32×#41 | C2×D3 | semidirect |
| 129. #3832 | C2×D3 | semidirect |
| 130. #3832 | C2×D3 | semidirect |
| 131. Q8×C3⋊D3 | C2×D3 | semidirect |
| 132. Q8×C3⋊D3 | C2×D3 | semidirect |
| 133. #3830 | C2×D3 | semidirect |
| 134. #3830 | C2×D3 | semidirect |
| 135. D4×C3⋊D3 | C2×D3 | semidirect |
| 136. D4×C3⋊D3 | C2×D3 | semidirect |
| 137. #3828 | C2×D3 | semidirect |
| 138. #3828 | C2×D3 | semidirect |
| 139. #3828 | C2×D3 | semidirect |
| 140. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 141. C2×C4×C3⋊D3 | C2×D3 | semidirect |
| 142. C2×#634 | C2×D3 | semidirect |
| 445. C3×#41 | D32 | semidirect |
| 446. C3×#41 | D32 | semidirect |
| 447. C3×#41 | D32 | semidirect |
| 629. C33 | #585 | semidirect |
| 812. #41 | #1113 | semidirect |
| 897. C32 | #5964 | semidirect |
| 898. C32 | #5966 | semidirect |
| 899. C32 | #5968 | semidirect |
| 982. C3 | #10596696 | semidirect |
| 983. C3 | #10596697 | semidirect |
| 984. C3 | #10596698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64367 | 2 |
| C3×#64366 | 2 |
| C3×#41×C3⋊D3 | 2 |
| #11724626 | 2 |
| #11724624 | 2 |
| #11724623 | 2 |
| #11724622 | 2 |
| #11724619 | 2 |
| #11724618 | 2 |
| #11724614 | 2 |
| C2×#89041 | 2 |
| #10596698 | 3 |
| #10596697 | 3 |
| #10596696 | 3 |