Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4128 conjugacy classes of subgroups.
The subgroup lattice has 864 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11724626 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11724597 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3⋊D3×#239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#64320 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#64319 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11724403 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | D3×#3802 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | D32×D12 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11724387 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11724384 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | #11724381 | C2 | 1 | 6 | yes | maximal, complemented |
| 12 | #10596692 | — | 3 | 1 | no | maximal |
| 13 | D3×#1009 | — | 3 | 2 | no | maximal |
| 14 | C2×D33 | C22 | 1 | 6 | yes | complemented |
| 15 | #89080 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3×#3832 | C22 | 1 | 2 | yes | complemented |
| 17 | C3×Q8×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32×#239 | C22 | 1 | 2 | yes | complemented |
| 19 | C32×#239 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C4⋊#1113 | C22 | 1 | 3 | yes | complemented |
| 21 | C4×#1113 | C22 | 1 | 3 | yes | complemented |
| 22 | #89041 | C22 | 1 | 6 | yes | complemented |
| 23 | #89026 | C22 | 1 | 6 | yes | complemented |
| 24 | C3⋊D3×D12 | C22 | 1 | 3 | yes | complemented |
| 25 | C3⋊D3×D12 | C22 | 1 | 6 | yes | complemented |
| 26 | D3×C4⋊(C3⋊D3) | C22 | 1 | 6 | yes | complemented |
| 27 | C4×D3×C3⋊D3 | C22 | 1 | 3 | yes | complemented |
| 28 | #89022 | C22 | 1 | 3 | yes | complemented |
| 29 | #89020 | C22 | 1 | 6 | yes | complemented |
| 30 | #89015 | C22 | 1 | 3 | yes | complemented |
| 31 | C3×#3802 | C22 | 1 | 3 | yes | complemented |
| 32 | C3×#3802 | C22 | 1 | 6 | yes | complemented |
| 33 | C3×D3×D12 | C22 | 1 | 6 | yes | complemented |
| 34 | C3×D3×D12 | C22 | 1 | 6 | yes | complemented |
| 35 | C3×C4×D32 | C22 | 1 | 3 | yes | complemented |
| 36 | C3×#3798 | C22 | 1 | 6 | yes | complemented |
| 37 | C3×#3795 | C22 | 1 | 6 | yes | complemented |
| 38 | #88962 | C22 | 1 | 6 | yes | complemented |
| 39 | #88961 | C22 | 1 | 6 | yes | complemented |
| 40 | #88957 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #88955 | C22 | 1 | 3 | yes | complemented |
| 42 | #88954 | C22 | 1 | 6 | yes | complemented |
| 43 | #88953 | C22 | 1 | 3 | yes | complemented |
| 44 | #88952 | C22 | 1 | 3 | yes | complemented |
| 45 | #88952 | C22 | 1 | 12 | yes | complemented |
| 46 | D3×#626 | C22 | 1 | 12 | yes | complemented |
| 47 | D3×#625 | C22 | 1 | 6 | yes | complemented |
| 48 | #64366 | — | 3 | 2 | no | — |
| 49 | #41×C3⋊D3 | — | 3 | 1 | no | — |
| 50 | C3×#1009 | — | 3 | 2 | no | — |
| 51 | C3×#1009 | — | 3 | 2 | no | — |
| 52 | C3×D3×#41 | — | 3 | 2 | no | — |
| 53 | #64320 | — | 3 | 2 | no | — |
| 54 | #64320 | — | 3 | 2 | no | — |
| 55 | #64320 | — | 6 | 2 | no | — |
| 56 | #64320 | D3 | 1 | 2 | yes | complemented |
| 57 | #64319 | — | 3 | 1 | no | — |
| 58 | #64319 | D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | D3×#239 | — | 3 | 2 | no | — |
| 60 | D3×#239 | — | 3 | 2 | no | — |
| 61 | D3×#239 | — | 6 | 1 | no | — |
| 62 | #64314 | — | 3 | 6 | no | — |
| 63 | #64314 | — | 3 | 6 | no | — |
| 64 | #64313 | — | 3 | 6 | no | — |
| 65 | D32×D4 | — | 3 | 6 | no | — |
| 66 | D32×D4 | — | 3 | 3 | no | — |
| 67 | D32×D4 | — | 3 | 6 | no | — |
| 68 | D32×D4 | — | 3 | 3 | no | — |
| 69 | #64308 | — | 3 | 6 | no | — |
| 70 | #64307 | — | 3 | 6 | no | — |
| 71 | #64307 | — | 3 | 6 | no | — |
| 72 | #64306 | — | 3 | 3 | no | — |
| 73 | D3×#235 | — | 3 | 6 | no | — |
| 74 | C2×#3802 | — | 3 | 3 | no | — |
| 75 | C2×D3×D12 | — | 3 | 6 | no | — |
| 76 | C2×#1113 | C23 | 1 | 3 | yes | — |
| 77 | C2×D3×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 78 | C2×D3×C3⋊D3 | C23 | 1 | 12 | yes | complemented |
| 79 | C2×C3×D32 | C23 | 1 | 3 | yes | — |
| 80 | C2×C3×D32 | C23 | 1 | 12 | yes | complemented |
| 81 | D33 | — | 4 | 12 | no | — |
| 82 | C33×Q8 | C23 | 1 | 1 | yes | characteristic, complemented |
| 83 | C4⋊(C3⋊(C3⋊D3)) | C23 | 1 | 3 | yes | complemented |
| 84 | C4×C3⋊(C3⋊D3) | C23 | 1 | 3 | yes | complemented |
| 85 | C3×C4⋊(C3⋊D3) | C23 | 1 | 6 | yes | complemented |
| 86 | C3×C4×C3⋊D3 | C23 | 1 | 3 | yes | — |
| 87 | C3×C4×C3⋊D3 | C23 | 1 | 6 | yes | complemented |
| 88 | C3×#634 | C23 | 1 | 3 | yes | complemented |
| 89 | C32×D12 | C23 | 1 | 6 | yes | complemented |
| 90 | C32×D12 | C23 | 1 | 3 | yes | complemented |
| 91 | C32×C4×D3 | C23 | 1 | 6 | yes | complemented |
| 92 | C32×C4×D3 | C23 | 1 | 3 | yes | complemented |
| 93 | #6295 | C23 | 1 | 6 | yes | complemented |
| 94 | #6294 | C23 | 1 | 1 | yes | characteristic |
| 95 | #6294 | C23 | 1 | 6 | yes | complemented |
| 96 | #6293 | C23 | 1 | 2 | yes | complemented |
| 97 | #6292 | C23 | 1 | 6 | yes | complemented |
| 98 | #6291 | C23 | 1 | 6 | yes | complemented |
| 99 | #6291 | C23 | 1 | 6 | yes | complemented |
| 100 | #6290 | C23 | 1 | 6 | yes | complemented |
| 101 | #6289 | C23 | 1 | 3 | yes | complemented |
| 102 | Dic3×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 103 | D3×C3⋊Dic3 | C23 | 1 | 3 | yes | complemented |
| 104 | C3×#627 | C23 | 1 | 2 | yes | complemented |
| 105 | C3×#626 | C23 | 1 | 6 | yes | complemented |
| 106 | C3×#626 | C23 | 1 | 6 | yes | complemented |
| 107 | C3×#625 | C23 | 1 | 6 | yes | complemented |
| 108 | C3×#625 | C23 | 1 | 6 | yes | complemented |
| 109 | C3×#624 | C23 | 1 | 1 | yes | characteristic |
| 110 | C3×D3×Dic3 | C23 | 1 | 6 | yes | complemented |
| 111 | D3×H(5,𝔽2) | — | 9 | 2 | no | — |
| 112 | C2×#1009 | — | 9 | 1 | no | — |
| 113 | C22×D32 | — | 3 | 6 | no | — |
| 114 | C22×D32 | — | 3 | 12 | no | — |
| 115 | C32×#41 | — | 3 | 2 | no | — |
| 116 | C32×#41 | — | 3 | 1 | no | — |
| 117 | #3832 | — | 3 | 2 | no | — |
| 118 | #3832 | — | 3 | 1 | no | — |
| 119 | #3832 | — | 6 | 1 | no | — |
| 120 | #3832 | — | 6 | 2 | no | — |
| 121 | #3832 | — | 12 | 1 | no | — |
| 122 | #3832 | C2×D3 | 1 | 2 | yes | complemented |
| 123 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 124 | #3830 | — | 3 | 3 | no | — |
| 125 | D4×C3⋊D3 | — | 3 | 6 | no | — |
| 126 | D4×C3⋊D3 | — | 3 | 3 | no | — |
| 127 | D4×C3⋊D3 | — | 3 | 6 | no | — |
| 128 | #3828 | — | 3 | 6 | no | — |
| 129 | #3828 | — | 3 | 3 | no | — |
| 130 | C2×C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 131 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 132 | C3×#239 | — | 2 | 1 | no | — |
| 133 | C3×#239 | — | 2 | 2 | no | — |
| 134 | C3×#239 | — | 3 | 2 | no | — |
| 135 | C3×#239 | — | 3 | 2 | no | — |
| 136 | C3×#239 | — | 6 | 2 | no | — |
| 137 | C3×#239 | C2×D3 | 1 | 2 | yes | complemented |
| 138 | C3×#239 | C2×D3 | 1 | 2 | yes | complemented |
| 139 | C3×#239 | C2×D3 | 1 | 2 | yes | complemented |
| 140 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 141 | C3×D3×Q8 | — | 6 | 1 | no | — |
| 142 | C3×#237 | — | 3 | 6 | no | — |
| 143 | C3×D3×D4 | — | 3 | 6 | no | — |
| 144 | C3×D3×D4 | — | 3 | 6 | no | — |
| 145 | C3×D3×D4 | — | 3 | 6 | no | — |
| 146 | C3×D3×D4 | — | 3 | 6 | no | — |
| 147 | C3×D3×D4 | — | 3 | 6 | no | — |
| 148 | C3×#235 | — | 3 | 6 | no | — |
| 149 | C3×#235 | — | 3 | 6 | no | — |
| 150 | C3×#235 | — | 3 | 6 | no | — |
| 151 | C2×C3×D12 | — | 3 | 6 | no | — |
| 152 | C2×C3×D12 | — | 3 | 6 | no | — |
| 153 | C2×C3×C4×D3 | — | 3 | 6 | no | — |
| 154 | #3811 | — | 3 | 3 | no | — |
| 155 | #3811 | — | 3 | 12 | no | — |
| 156 | #3811 | — | 3 | 12 | no | — |
| 157 | #3811 | — | 3 | 3 | no | — |
| 158 | D3×#67 | — | 3 | 12 | no | — |
| 159 | D3×#67 | — | 3 | 6 | no | — |
| 160 | D3×#67 | — | 3 | 6 | no | — |
| 161 | D3×#67 | — | 3 | 12 | no | — |
| 162 | D3×#67 | — | 3 | 12 | no | — |
| 163 | D3×#67 | — | 3 | 12 | no | — |
| 164 | C2×#626 | — | 3 | 12 | no | — |
| 165 | C2×#625 | — | 3 | 6 | no | — |
| 166 | #3805 | — | 3 | 6 | no | — |
| 167 | #3804 | — | 3 | 6 | no | — |
| 168 | #3804 | — | 3 | 6 | no | — |
| 169 | #3802 | — | 3 | 3 | no | — |
| 170 | #3802 | — | 3 | 3 | no | — |
| 171 | #3802 | — | 3 | 6 | no | — |
| 172 | #3802 | — | 3 | 6 | no | — |
| 173 | #3802 | — | 3 | 6 | no | — |
| 174 | #3802 | — | 6 | 6 | no | — |
| 175 | #3802 | C2×D3 | 1 | 3 | yes | complemented |
| 176 | #3802 | C2×D3 | 1 | 6 | yes | complemented |
| 177 | D3×D12 | — | 3 | 12 | no | — |
| 178 | D3×D12 | — | 3 | 6 | no | — |
| 179 | D3×D12 | — | 3 | 6 | no | — |
| 180 | D3×D12 | — | 3 | 6 | no | — |
| 181 | D3×D12 | — | 3 | 6 | no | — |
| 182 | D3×D12 | — | 3 | 6 | no | — |
| 183 | D3×D12 | — | 3 | 6 | no | — |
| 184 | D3×D12 | — | 3 | 6 | no | — |
| 185 | D3×D12 | — | 6 | 6 | no | — |
| 186 | D3×D12 | — | 6 | 3 | no | — |
| 187 | D3×D12 | — | 6 | 6 | no | — |
| 188 | D3×D12 | C2×D3 | 1 | 6 | yes | complemented |
| 189 | D3×D12 | C2×D3 | 1 | 6 | yes | complemented |
| 190 | C4×D32 | — | 3 | 3 | no | — |
| 191 | C4×D32 | — | 3 | 6 | no | — |
| 192 | C4×D32 | — | 3 | 6 | no | — |
| 193 | C4×D32 | — | 6 | 3 | no | — |
| 194 | C4×D32 | C2×D3 | 1 | 3 | yes | complemented |
| 195 | #3799 | — | 3 | 6 | no | — |
| 196 | #3799 | — | 3 | 6 | no | — |
| 197 | #3799 | — | 3 | 6 | no | — |
| 198 | #3799 | — | 6 | 3 | no | — |
| 199 | #3798 | — | 3 | 6 | no | — |
| 200 | #3798 | — | 3 | 6 | no | — |
| 201 | #3798 | — | 6 | 6 | no | — |
| 202 | #3798 | C2×D3 | 1 | 6 | yes | complemented |
| 203 | #3797 | — | 3 | 1 | no | — |
| 204 | #3796 | — | 3 | 6 | no | — |
| 205 | #3796 | — | 3 | 6 | no | — |
| 206 | #3796 | — | 3 | 6 | no | — |
| 207 | #3796 | — | 6 | 3 | no | — |
| 208 | #3795 | — | 3 | 6 | no | — |
| 209 | #3795 | — | 3 | 6 | no | — |
| 210 | #3795 | C2×D3 | 1 | 6 | yes | complemented |
| 211 | D3×Dic6 | — | 3 | 2 | no | — |
| 212 | C2×C3⋊(C3⋊D3) | C24 | 1 | 3 | yes | — |
| 213 | C2×C3×C3⋊D3 | C24 | 1 | 6 | yes | — |
| 214 | C2×C3×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 215 | C2×C32×D3 | C24 | 1 | 6 | yes | — |
| 216 | C2×C32×D3 | C24 | 1 | 3 | yes | — |
| 217 | #1113 | — | 2 | 6 | no | — |
| 218 | D3×C3⋊D3 | — | 2 | 6 | no | — |
| 219 | D3×C3⋊D3 | — | 4 | 12 | no | — |
| 220 | C3×D32 | — | 2 | 6 | no | — |
| 221 | C3×D32 | — | 4 | 12 | no | — |
| 222 | C33×C4 | C24 | 1 | 3 | yes | — |
| 223 | C3⋊(C3⋊Dic3) | C24 | 1 | 1 | yes | characteristic |
| 224 | C3×C3⋊Dic3 | C24 | 1 | 3 | yes | — |
| 225 | C3×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 226 | C32×Dic3 | C24 | 1 | 2 | yes | — |
| 227 | C32×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 228 | C3×H(5,𝔽2) | — | 9 | 2 | no | — |
| 229 | C2×C3×#41 | — | 9 | 1 | no | — |
| 230 | #1009 | — | 3 | 2 | no | — |
| 231 | #1009 | — | 3 | 2 | no | — |
| 232 | #1009 | — | 9 | 6 | no | — |
| 233 | #1009 | — | 9 | 6 | no | — |
| 234 | #1009 | — | 9 | 6 | no | — |
| 235 | #1009 | — | 9 | 2 | no | — |
| 236 | #1009 | — | 9 | 2 | no | — |
| 237 | #1009 | — | 9 | 2 | no | — |
| 238 | #1009 | — | 18 | 2 | no | — |
| 239 | D3×#41 | — | 3 | 2 | no | — |
| 240 | D3×#41 | — | 9 | 6 | no | — |
| 241 | D3×#41 | — | 9 | 2 | no | — |
| 242 | D3×#41 | — | 9 | 2 | no | — |
| 243 | D3×#41 | — | 18 | 1 | no | — |
| 244 | C2×#239 | — | 9 | 1 | no | — |
| 245 | C2×#239 | — | 9 | 1 | no | — |
| 246 | #1004 | — | 9 | 6 | no | — |
| 247 | #1004 | — | 9 | 6 | no | — |
| 248 | #1004 | — | 9 | 6 | no | — |
| 249 | C2×D3×D4 | — | 9 | 6 | no | — |
| 250 | C2×D3×D4 | — | 9 | 6 | no | — |
| 251 | C2×D3×D4 | — | 9 | 3 | no | — |
| 252 | C2×D3×D4 | — | 9 | 3 | no | — |
| 253 | C2×D3×D4 | — | 9 | 6 | no | — |
| 254 | C2×#235 | — | 9 | 3 | no | — |
| 255 | C22×D12 | — | 9 | 3 | no | — |
| 256 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 257 | C22×C3⋊D3 | — | 3 | 12 | no | — |
| 258 | C22×C3×D3 | — | 3 | 6 | no | — |
| 259 | C22×C3×D3 | — | 3 | 12 | no | — |
| 260 | C22×C3×D3 | — | 3 | 12 | no | — |
| 261 | C2×D32 | — | 3 | 6 | no | — |
| 262 | C2×D32 | — | 3 | 3 | no | — |
| 263 | C2×D32 | — | 3 | 6 | no | — |
| 264 | C2×D32 | — | 3 | 12 | no | — |
| 265 | C2×D32 | — | 3 | 12 | no | — |
| 266 | C2×D32 | — | 6 | 3 | no | — |
| 267 | C2×D32 | — | 6 | 12 | no | — |
| 268 | C2×D32 | — | 12 | 12 | no | — |
| 269 | C2×D32 | — | 12 | 24 | no | — |
| 270 | C2×D32 | C22×D3 | 1 | 3 | yes | — |
| 271 | C2×D32 | C22×D3 | 1 | 12 | yes | complemented |
| 272 | C32×Q8 | — | 2 | 1 | no | — |
| 273 | C32×Q8 | — | 2 | 2 | no | — |
| 274 | C32×Q8 | — | 4 | 1 | no | — |
| 275 | C32×Q8 | C22×D3 | 1 | 2 | yes | complemented |
| 276 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 277 | C32×D4 | — | 3 | 3 | no | — |
| 278 | C32×D4 | — | 3 | 6 | no | — |
| 279 | C2×C32×C4 | — | 3 | 6 | no | — |
| 280 | C2×C32×C4 | — | 3 | 3 | no | — |
| 281 | #638 | — | 3 | 6 | no | — |
| 282 | #638 | — | 3 | 6 | no | — |
| 283 | #638 | — | 3 | 6 | no | — |
| 284 | C2×C3⋊Dic3 | — | 3 | 3 | no | — |
| 285 | C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 286 | C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 287 | C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 288 | C4⋊(C3⋊D3) | — | 6 | 3 | no | — |
| 289 | C4⋊(C3⋊D3) | — | 6 | 6 | no | — |
| 290 | C4⋊(C3⋊D3) | — | 12 | 3 | no | — |
| 291 | C4⋊(C3⋊D3) | C22×D3 | 1 | 6 | yes | complemented |
| 292 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 293 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 294 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 295 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 296 | C4×C3⋊D3 | — | 6 | 3 | no | — |
| 297 | C4×C3⋊D3 | — | 6 | 6 | no | — |
| 298 | C4×C3⋊D3 | — | 12 | 3 | no | — |
| 299 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 300 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | complemented |
| 301 | #634 | — | 3 | 2 | no | — |
| 302 | #634 | C22×D3 | 1 | 3 | yes | complemented |
| 303 | C3×#67 | — | 3 | 6 | no | — |
| 304 | C3×#67 | — | 3 | 6 | no | — |
| 305 | C3×#67 | — | 3 | 12 | no | — |
| 306 | C3×#67 | — | 3 | 6 | no | — |
| 307 | C3×#67 | — | 3 | 6 | no | — |
| 308 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 309 | C3×D12 | — | 2 | 3 | no | — |
| 310 | C3×D12 | — | 2 | 6 | no | — |
| 311 | C3×D12 | — | 3 | 6 | no | — |
| 312 | C3×D12 | — | 3 | 6 | no | — |
| 313 | C3×D12 | — | 3 | 6 | no | — |
| 314 | C3×D12 | — | 3 | 6 | no | — |
| 315 | C3×D12 | — | 6 | 6 | no | — |
| 316 | C3×D12 | C22×D3 | 1 | 6 | yes | complemented |
| 317 | C3×D12 | C22×D3 | 1 | 6 | yes | complemented |
| 318 | C3×D12 | C22×D3 | 1 | 6 | yes | complemented |
| 319 | C3×C4×D3 | — | 2 | 6 | no | — |
| 320 | C3×C4×D3 | — | 2 | 3 | no | — |
| 321 | C3×C4×D3 | — | 3 | 6 | no | — |
| 322 | C3×C4×D3 | — | 3 | 6 | no | — |
| 323 | C3×C4×D3 | — | 3 | 6 | no | — |
| 324 | C3×C4×D3 | — | 3 | 6 | no | — |
| 325 | C3×C4×D3 | — | 3 | 2 | no | — |
| 326 | C3×C4×D3 | — | 6 | 3 | no | — |
| 327 | C3×C4×D3 | — | 6 | 6 | no | — |
| 328 | C3×C4×D3 | C22×D3 | 1 | 6 | yes | complemented |
| 329 | C3×C4×D3 | C22×D3 | 1 | 6 | yes | complemented |
| 330 | C3×C4×D3 | C22×D3 | 1 | 6 | yes | complemented |
| 331 | C3×Dic6 | — | 3 | 6 | no | — |
| 332 | C3×Dic6 | — | 3 | 2 | no | — |
| 333 | C3×Dic6 | — | 3 | 2 | no | — |
| 334 | C3×Dic6 | — | 6 | 3 | no | — |
| 335 | #627 | — | 3 | 2 | no | — |
| 336 | #627 | — | 3 | 2 | no | — |
| 337 | #627 | — | 6 | 2 | no | — |
| 338 | #627 | C22×D3 | 1 | 2 | yes | complemented |
| 339 | #626 | — | 3 | 12 | no | — |
| 340 | #626 | — | 3 | 6 | no | — |
| 341 | #626 | — | 3 | 12 | no | — |
| 342 | #626 | — | 3 | 6 | no | — |
| 343 | #626 | — | 3 | 6 | no | — |
| 344 | #626 | — | 3 | 6 | no | — |
| 345 | #626 | — | 6 | 6 | no | — |
| 346 | #626 | — | 6 | 6 | no | — |
| 347 | #626 | — | 6 | 6 | no | — |
| 348 | #626 | C22×D3 | 1 | 6 | yes | complemented |
| 349 | #626 | C22×D3 | 1 | 6 | yes | complemented |
| 350 | #625 | — | 3 | 6 | no | — |
| 351 | #625 | — | 3 | 6 | no | — |
| 352 | #625 | — | 3 | 6 | no | — |
| 353 | #625 | — | 6 | 6 | no | — |
| 354 | #625 | C22×D3 | 1 | 6 | yes | complemented |
| 355 | #625 | C22×D3 | 1 | 6 | yes | complemented |
| 356 | #624 | — | 3 | 1 | no | — |
| 357 | #624 | — | 3 | 6 | no | — |
| 358 | #624 | — | 3 | 6 | no | — |
| 359 | #624 | — | 6 | 3 | no | — |
| 360 | #624 | C22×D3 | 1 | 1 | yes | characteristic |
| 361 | D3×Dic3 | — | 3 | 6 | no | — |
| 362 | D3×Dic3 | — | 3 | 2 | no | — |
| 363 | D3×Dic3 | — | 3 | 6 | no | — |
| 364 | D3×Dic3 | — | 3 | 6 | no | — |
| 365 | D3×Dic3 | — | 3 | 2 | no | — |
| 366 | D3×Dic3 | — | 6 | 3 | no | — |
| 367 | D3×Dic3 | — | 6 | 1 | no | — |
| 368 | D3×Dic3 | C22×D3 | 1 | 6 | yes | complemented |
| 369 | C2×H(5,𝔽2) | — | 27 | 1 | no | Sylow |
| 370 | C2×C33 | C25 | 1 | 1 | yes | characteristic |
| 371 | C3⋊(C3⋊D3) | — | 2 | 3 | no | — |
| 372 | C3×C3⋊D3 | — | 2 | 6 | no | — |
| 373 | C3×C3⋊D3 | H(5,𝔽2) | 1 | 2 | yes | complemented |
| 374 | C32×D3 | — | 2 | 6 | no | — |
| 375 | C32×D3 | — | 2 | 3 | no | — |
| 376 | C23×D3 | — | 9 | 6 | no | — |
| 377 | C23×D3 | — | 9 | 12 | no | — |
| 378 | C3×#41 | — | 3 | 2 | no | — |
| 379 | C3×#41 | — | 3 | 2 | no | — |
| 380 | C3×#41 | — | 3 | 2 | no | — |
| 381 | C3×#41 | — | 6 | 1 | no | — |
| 382 | C3×#41 | — | 6 | 2 | no | — |
| 383 | C3×#41 | — | 9 | 6 | no | — |
| 384 | C3×#41 | — | 9 | 6 | no | — |
| 385 | C3×#41 | — | 9 | 2 | no | — |
| 386 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 387 | C2×C3×D4 | — | 9 | 6 | no | — |
| 388 | C2×C3×D4 | — | 9 | 6 | no | — |
| 389 | C2×C3×D4 | — | 9 | 3 | no | — |
| 390 | C2×C3×D4 | — | 9 | 6 | no | — |
| 391 | C22×C3×C4 | — | 9 | 3 | no | — |
| 392 | C2×#67 | — | 9 | 12 | no | — |
| 393 | C2×#67 | — | 9 | 3 | no | — |
| 394 | C2×#67 | — | 9 | 3 | no | — |
| 395 | C2×#67 | — | 9 | 12 | no | — |
| 396 | C2×#67 | — | 9 | 12 | no | — |
| 397 | #239 | — | 3 | 2 | no | — |
| 398 | #239 | — | 3 | 2 | no | — |
| 399 | #239 | — | 6 | 2 | no | — |
| 400 | #239 | — | 9 | 6 | no | — |
| 401 | #239 | — | 9 | 6 | no | — |
| 402 | #239 | — | 9 | 1 | no | — |
| 403 | #239 | — | 9 | 2 | no | — |
| 404 | #239 | — | 9 | 3 | no | — |
| 405 | #239 | — | 9 | 3 | no | — |
| 406 | #239 | — | 18 | 1 | no | — |
| 407 | #239 | — | 18 | 2 | no | — |
| 408 | #239 | — | 36 | 1 | no | — |
| 409 | #239 | D32 | 1 | 1 | yes | characteristic, complemented |
| 410 | #239 | D32 | 1 | 2 | yes | complemented |
| 411 | D3×Q8 | — | 3 | 2 | no | — |
| 412 | D3×Q8 | — | 6 | 1 | no | — |
| 413 | D3×Q8 | — | 9 | 2 | no | — |
| 414 | #237 | — | 3 | 6 | no | — |
| 415 | #237 | — | 9 | 6 | no | — |
| 416 | #237 | — | 9 | 6 | no | — |
| 417 | #237 | — | 9 | 6 | no | — |
| 418 | #237 | — | 9 | 6 | no | — |
| 419 | #237 | — | 9 | 6 | no | — |
| 420 | #237 | — | 18 | 3 | no | — |
| 421 | D3×D4 | — | 3 | 6 | no | — |
| 422 | D3×D4 | — | 3 | 6 | no | — |
| 423 | D3×D4 | — | 3 | 6 | no | — |
| 424 | D3×D4 | — | 3 | 6 | no | — |
| 425 | D3×D4 | — | 3 | 6 | no | — |
| 426 | D3×D4 | — | 9 | 6 | no | — |
| 427 | D3×D4 | — | 9 | 6 | no | — |
| 428 | D3×D4 | — | 9 | 6 | no | — |
| 429 | D3×D4 | — | 9 | 6 | no | — |
| 430 | D3×D4 | — | 9 | 6 | no | — |
| 431 | D3×D4 | — | 9 | 12 | no | — |
| 432 | D3×D4 | — | 9 | 12 | no | — |
| 433 | D3×D4 | — | 9 | 6 | no | — |
| 434 | D3×D4 | — | 9 | 6 | no | — |
| 435 | D3×D4 | — | 9 | 6 | no | — |
| 436 | D3×D4 | — | 9 | 6 | no | — |
| 437 | D3×D4 | — | 9 | 6 | no | — |
| 438 | D3×D4 | — | 9 | 12 | no | — |
| 439 | D3×D4 | — | 9 | 12 | no | — |
| 440 | D3×D4 | — | 9 | 6 | no | — |
| 441 | D3×D4 | — | 9 | 6 | no | — |
| 442 | D3×D4 | — | 9 | 6 | no | — |
| 443 | D3×D4 | — | 18 | 3 | no | — |
| 444 | D3×D4 | — | 18 | 6 | no | — |
| 445 | D3×D4 | — | 18 | 6 | no | — |
| 446 | #235 | — | 3 | 6 | no | — |
| 447 | #235 | — | 3 | 6 | no | — |
| 448 | #235 | — | 3 | 6 | no | — |
| 449 | #235 | — | 9 | 6 | no | — |
| 450 | #235 | — | 9 | 6 | no | — |
| 451 | #235 | — | 9 | 6 | no | — |
| 452 | #235 | — | 9 | 6 | no | — |
| 453 | #235 | — | 9 | 6 | no | — |
| 454 | #235 | — | 9 | 6 | no | — |
| 455 | #235 | — | 9 | 6 | no | — |
| 456 | #235 | — | 18 | 3 | no | — |
| 457 | #235 | — | 18 | 6 | no | — |
| 458 | C2×D12 | — | 3 | 6 | no | — |
| 459 | C2×D12 | — | 3 | 6 | no | — |
| 460 | C2×D12 | — | 9 | 3 | no | — |
| 461 | C2×D12 | — | 9 | 3 | no | — |
| 462 | C2×D12 | — | 9 | 6 | no | — |
| 463 | C2×D12 | — | 9 | 6 | no | — |
| 464 | C2×D12 | — | 9 | 12 | no | — |
| 465 | C2×D12 | — | 9 | 3 | no | — |
| 466 | C2×D12 | — | 9 | 6 | no | — |
| 467 | C2×D12 | — | 18 | 6 | no | — |
| 468 | C2×C4×D3 | — | 3 | 6 | no | — |
| 469 | C2×C4×D3 | — | 9 | 3 | no | — |
| 470 | C2×C4×D3 | — | 9 | 6 | no | — |
| 471 | C2×C4×D3 | — | 9 | 6 | no | — |
| 472 | C2×C4×D3 | — | 9 | 3 | no | — |
| 473 | C2×C4×D3 | — | 18 | 3 | no | — |
| 474 | C2×Dic6 | — | 9 | 1 | no | — |
| 475 | C22×C32 | — | 3 | 6 | no | — |
| 476 | C22×C32 | — | 3 | 3 | no | — |
| 477 | C2×C3⋊D3 | — | 3 | 6 | no | — |
| 478 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 479 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 480 | C2×C3⋊D3 | — | 6 | 6 | no | — |
| 481 | C2×C3⋊D3 | — | 6 | 6 | no | — |
| 482 | C2×C3⋊D3 | — | 12 | 3 | no | — |
| 483 | C2×C3⋊D3 | — | 12 | 12 | no | — |
| 484 | C2×C3⋊D3 | C23×D3 | 1 | 6 | yes | — |
| 485 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 486 | C2×C3×D3 | — | 2 | 3 | no | — |
| 487 | C2×C3×D3 | — | 2 | 6 | no | — |
| 488 | C2×C3×D3 | — | 3 | 2 | no | — |
| 489 | C2×C3×D3 | — | 3 | 6 | no | — |
| 490 | C2×C3×D3 | — | 3 | 6 | no | — |
| 491 | C2×C3×D3 | — | 6 | 1 | no | — |
| 492 | C2×C3×D3 | — | 6 | 6 | no | — |
| 493 | C2×C3×D3 | — | 6 | 12 | no | — |
| 494 | C2×C3×D3 | — | 12 | 12 | no | — |
| 495 | C2×C3×D3 | — | 12 | 12 | no | — |
| 496 | C2×C3×D3 | C23×D3 | 1 | 6 | yes | — |
| 497 | C2×C3×D3 | C23×D3 | 1 | 6 | yes | — |
| 498 | C2×C3×D3 | C23×D3 | 1 | 6 | yes | — |
| 499 | D32 | — | 2 | 6 | no | — |
| 500 | D32 | — | 4 | 12 | no | — |
| 501 | D32 | — | 6 | 12 | no | — |
| 502 | D32 | — | 6 | 12 | no | — |
| 503 | D32 | — | 6 | 6 | no | — |
| 504 | D32 | — | 12 | 6 | no | — |
| 505 | D32 | — | 12 | 12 | no | — |
| 506 | D32 | — | 12 | 12 | no | — |
| 507 | D32 | — | 24 | 12 | no | — |
| 508 | C32×C4 | — | 2 | 3 | no | — |
| 509 | C32×C4 | — | 2 | 6 | no | — |
| 510 | C32×C4 | — | 3 | 1 | no | — |
| 511 | C32×C4 | — | 3 | 2 | no | — |
| 512 | C32×C4 | — | 4 | 3 | no | — |
| 513 | C32×C4 | C23×D3 | 1 | 6 | yes | — |
| 514 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 515 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 516 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 517 | C3⋊Dic3 | — | 6 | 1 | no | — |
| 518 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 519 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 520 | C3⋊Dic3 | C23×D3 | 1 | 2 | yes | — |
| 521 | C3⋊Dic3 | C23×D3 | 1 | 3 | yes | — |
| 522 | C3×Dic3 | — | 2 | 1 | no | — |
| 523 | C3×Dic3 | — | 2 | 2 | no | — |
| 524 | C3×Dic3 | — | 3 | 2 | no | — |
| 525 | C3×Dic3 | — | 3 | 6 | no | — |
| 526 | C3×Dic3 | — | 3 | 2 | no | — |
| 527 | C3×Dic3 | — | 6 | 3 | no | — |
| 528 | C3×Dic3 | — | 6 | 2 | no | — |
| 529 | C3×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 530 | C3×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 531 | C3×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 532 | H(5,𝔽2) | — | 9 | 2 | no | — |
| 533 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 534 | H(5,𝔽2) | — | 27 | 6 | no | — |
| 535 | H(5,𝔽2) | — | 27 | 2 | no | — |
| 536 | C2×#41 | — | 9 | 1 | no | — |
| 537 | C2×#41 | — | 27 | 3 | no | — |
| 538 | C2×#41 | — | 27 | 1 | no | — |
| 539 | C2×#41 | — | 27 | 1 | no | — |
| 540 | C22×D4 | — | 27 | 3 | no | — |
| 541 | C22×D4 | — | 27 | 3 | no | — |
| 542 | C22×D4 | — | 27 | 3 | no | — |
| 543 | C33 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 544 | C23×C3 | — | 9 | 3 | no | — |
| 545 | C23×C3 | — | 9 | 12 | no | — |
| 546 | C22×D3 | — | 3 | 6 | no | — |
| 547 | C22×D3 | — | 3 | 12 | no | — |
| 548 | C22×D3 | — | 3 | 12 | no | — |
| 549 | C22×D3 | — | 9 | 3 | no | — |
| 550 | C22×D3 | — | 9 | 6 | no | — |
| 551 | C22×D3 | — | 9 | 6 | no | — |
| 552 | C22×D3 | — | 9 | 12 | no | — |
| 553 | C22×D3 | — | 9 | 12 | no | — |
| 554 | C22×D3 | — | 9 | 3 | no | — |
| 555 | C22×D3 | — | 9 | 12 | no | — |
| 556 | C22×D3 | — | 18 | 3 | no | — |
| 557 | C22×D3 | — | 18 | 12 | no | — |
| 558 | C22×D3 | — | 36 | 24 | no | — |
| 559 | C22×D3 | — | 36 | 12 | no | — |
| 560 | C3×Q8 | — | 2 | 1 | no | — |
| 561 | C3×Q8 | — | 2 | 2 | no | — |
| 562 | C3×Q8 | — | 4 | 1 | no | — |
| 563 | C3×Q8 | — | 9 | 2 | no | — |
| 564 | C3×Q8 | — | 9 | 3 | no | — |
| 565 | C3×Q8 | C2×D32 | 1 | 2 | yes | complemented |
| 566 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic, complemented |
| 567 | C3×D4 | — | 3 | 6 | no | — |
| 568 | C3×D4 | — | 3 | 6 | no | — |
| 569 | C3×D4 | — | 3 | 6 | no | — |
| 570 | C3×D4 | — | 6 | 6 | no | — |
| 571 | C3×D4 | — | 6 | 3 | no | — |
| 572 | C3×D4 | — | 9 | 6 | no | — |
| 573 | C3×D4 | — | 9 | 6 | no | — |
| 574 | C3×D4 | — | 9 | 6 | no | — |
| 575 | C3×D4 | — | 9 | 6 | no | — |
| 576 | C3×D4 | — | 9 | 6 | no | — |
| 577 | C2×C3×C4 | — | 3 | 6 | no | — |
| 578 | C2×C3×C4 | — | 3 | 6 | no | — |
| 579 | C2×C3×C4 | — | 3 | 6 | no | — |
| 580 | C2×C3×C4 | — | 6 | 3 | no | — |
| 581 | C2×C3×C4 | — | 6 | 6 | no | — |
| 582 | C2×C3×C4 | — | 9 | 1 | no | — |
| 583 | C2×C3×C4 | — | 9 | 6 | no | — |
| 584 | C2×C3×C4 | — | 9 | 3 | no | — |
| 585 | C2×C3×C4 | — | 9 | 6 | no | — |
| 586 | #67 | — | 3 | 6 | no | — |
| 587 | #67 | — | 3 | 6 | no | — |
| 588 | #67 | — | 3 | 12 | no | — |
| 589 | #67 | — | 3 | 6 | no | — |
| 590 | #67 | — | 3 | 6 | no | — |
| 591 | #67 | — | 9 | 12 | no | — |
| 592 | #67 | — | 9 | 6 | no | — |
| 593 | #67 | — | 9 | 12 | no | — |
| 594 | #67 | — | 9 | 6 | no | — |
| 595 | #67 | — | 9 | 6 | no | — |
| 596 | #67 | — | 9 | 6 | no | — |
| 597 | #67 | — | 9 | 6 | no | — |
| 598 | #67 | — | 9 | 6 | no | — |
| 599 | #67 | — | 18 | 6 | no | — |
| 600 | #67 | — | 18 | 6 | no | — |
| 601 | #67 | — | 18 | 6 | no | — |
| 602 | C2×Dic3 | — | 3 | 6 | no | — |
| 603 | C2×Dic3 | — | 9 | 1 | no | — |
| 604 | C2×Dic3 | — | 9 | 6 | no | — |
| 605 | C2×Dic3 | — | 9 | 6 | no | — |
| 606 | C2×Dic3 | — | 9 | 1 | no | — |
| 607 | C2×Dic3 | — | 18 | 3 | no | — |
| 608 | D12 | — | 3 | 6 | no | — |
| 609 | D12 | — | 3 | 6 | no | — |
| 610 | D12 | — | 3 | 6 | no | — |
| 611 | D12 | — | 3 | 6 | no | — |
| 612 | D12 | — | 6 | 6 | no | — |
| 613 | D12 | — | 9 | 6 | no | — |
| 614 | D12 | — | 9 | 6 | no | — |
| 615 | D12 | — | 9 | 6 | no | — |
| 616 | D12 | — | 9 | 6 | no | — |
| 617 | D12 | — | 9 | 6 | no | — |
| 618 | D12 | — | 9 | 3 | no | — |
| 619 | D12 | — | 9 | 6 | no | — |
| 620 | D12 | — | 18 | 6 | no | — |
| 621 | D12 | — | 18 | 3 | no | — |
| 622 | D12 | — | 18 | 6 | no | — |
| 623 | D12 | — | 36 | 3 | no | — |
| 624 | D12 | C2×D32 | 1 | 3 | yes | complemented |
| 625 | D12 | C2×D32 | 1 | 6 | yes | complemented |
| 626 | C4×D3 | — | 3 | 6 | no | — |
| 627 | C4×D3 | — | 3 | 6 | no | — |
| 628 | C4×D3 | — | 3 | 6 | no | — |
| 629 | C4×D3 | — | 3 | 6 | no | — |
| 630 | C4×D3 | — | 3 | 2 | no | — |
| 631 | C4×D3 | — | 6 | 3 | no | — |
| 632 | C4×D3 | — | 6 | 6 | no | — |
| 633 | C4×D3 | — | 9 | 6 | no | — |
| 634 | C4×D3 | — | 9 | 2 | no | — |
| 635 | C4×D3 | — | 9 | 6 | no | — |
| 636 | C4×D3 | — | 9 | 6 | no | — |
| 637 | C4×D3 | — | 9 | 2 | no | — |
| 638 | C4×D3 | — | 9 | 3 | no | — |
| 639 | C4×D3 | — | 9 | 6 | no | — |
| 640 | C4×D3 | — | 9 | 3 | no | — |
| 641 | C4×D3 | — | 9 | 3 | no | — |
| 642 | C4×D3 | — | 18 | 3 | no | — |
| 643 | C4×D3 | — | 18 | 3 | no | — |
| 644 | C4×D3 | — | 18 | 6 | no | — |
| 645 | C4×D3 | — | 18 | 1 | no | — |
| 646 | C4×D3 | — | 36 | 3 | no | — |
| 647 | C4×D3 | C2×D32 | 1 | 6 | yes | complemented |
| 648 | C4×D3 | C2×D32 | 1 | 3 | yes | complemented |
| 649 | Dic6 | — | 3 | 6 | no | — |
| 650 | Dic6 | — | 3 | 2 | no | — |
| 651 | Dic6 | — | 3 | 2 | no | — |
| 652 | Dic6 | — | 6 | 3 | no | — |
| 653 | Dic6 | — | 9 | 2 | no | — |
| 654 | Dic6 | — | 9 | 2 | no | — |
| 655 | Dic6 | — | 9 | 2 | no | — |
| 656 | Dic6 | — | 18 | 2 | no | — |
| 657 | C2×C32 | — | 2 | 1 | no | — |
| 658 | C2×C32 | — | 2 | 2 | no | — |
| 659 | C2×C32 | — | 4 | 1 | no | — |
| 660 | C2×C32 | — | 6 | 3 | no | — |
| 661 | C2×C32 | — | 6 | 6 | no | — |
| 662 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 663 | C2×C32 | C24×D3 | 1 | 2 | yes | — |
| 664 | C3⋊D3 | — | 2 | 6 | no | — |
| 665 | C3⋊D3 | — | 6 | 3 | no | — |
| 666 | C3⋊D3 | — | 6 | 6 | no | — |
| 667 | C3⋊D3 | — | 12 | 3 | no | — |
| 668 | C3⋊D3 | — | 12 | 6 | no | — |
| 669 | C3⋊D3 | — | 24 | 3 | no | — |
| 670 | C3⋊D3 | #1009 | 1 | 2 | yes | complemented |
| 671 | C3×D3 | — | 2 | 6 | no | — |
| 672 | C3×D3 | — | 2 | 6 | no | — |
| 673 | C3×D3 | — | 2 | 6 | no | — |
| 674 | C3×D3 | — | 3 | 4 | no | — |
| 675 | C3×D3 | — | 4 | 3 | no | — |
| 676 | C3×D3 | — | 4 | 6 | no | — |
| 677 | C3×D3 | — | 6 | 2 | no | — |
| 678 | C3×D3 | — | 6 | 6 | no | — |
| 679 | C3×D3 | — | 6 | 6 | no | — |
| 680 | C3×D3 | — | 12 | 6 | no | — |
| 681 | C24 | — | 27 | 6 | no | — |
| 682 | #41 | — | 3 | 2 | no | — |
| 683 | #41 | — | 3 | 1 | no | — |
| 684 | #41 | — | 9 | 6 | no | — |
| 685 | #41 | — | 9 | 6 | no | — |
| 686 | #41 | — | 9 | 2 | no | — |
| 687 | #41 | — | 27 | 6 | no | — |
| 688 | #41 | — | 27 | 3 | no | — |
| 689 | #41 | — | 27 | 6 | no | — |
| 690 | #41 | — | 27 | 6 | no | — |
| 691 | #41 | — | 27 | 6 | no | — |
| 692 | #41 | — | 27 | 3 | no | — |
| 693 | #41 | — | 27 | 1 | no | — |
| 694 | C2×Q8 | — | 9 | 1 | no | — |
| 695 | C2×Q8 | — | 27 | 1 | no | — |
| 696 | C2×D4 | — | 9 | 6 | no | — |
| 697 | C2×D4 | — | 9 | 6 | no | — |
| 698 | C2×D4 | — | 9 | 3 | no | — |
| 699 | C2×D4 | — | 9 | 6 | no | — |
| 700 | C2×D4 | — | 27 | 6 | no | — |
| 701 | C2×D4 | — | 27 | 3 | no | — |
| 702 | C2×D4 | — | 27 | 6 | no | — |
| 703 | C2×D4 | — | 27 | 3 | no | — |
| 704 | C2×D4 | — | 27 | 3 | no | — |
| 705 | C2×D4 | — | 27 | 12 | no | — |
| 706 | C2×D4 | — | 27 | 6 | no | — |
| 707 | C2×D4 | — | 27 | 6 | no | — |
| 708 | C2×D4 | — | 27 | 3 | no | — |
| 709 | C2×D4 | — | 27 | 3 | no | — |
| 710 | C2×D4 | — | 27 | 12 | no | — |
| 711 | C2×D4 | — | 27 | 6 | no | — |
| 712 | C22×C4 | — | 9 | 3 | no | — |
| 713 | C22×C4 | — | 27 | 3 | no | — |
| 714 | C22×C4 | — | 27 | 3 | no | — |
| 715 | C22×C3 | — | 3 | 6 | no | — |
| 716 | C22×C3 | — | 3 | 6 | no | — |
| 717 | C22×C3 | — | 3 | 6 | no | — |
| 718 | C22×C3 | — | 6 | 3 | no | — |
| 719 | C22×C3 | — | 6 | 6 | no | — |
| 720 | C22×C3 | — | 9 | 1 | no | — |
| 721 | C22×C3 | — | 9 | 6 | no | — |
| 722 | C22×C3 | — | 18 | 6 | no | — |
| 723 | C22×C3 | — | 36 | 12 | no | — |
| 724 | C2×D3 | — | 3 | 2 | no | — |
| 725 | C2×D3 | — | 3 | 6 | no | — |
| 726 | C2×D3 | — | 3 | 6 | no | — |
| 727 | C2×D3 | — | 6 | 1 | no | — |
| 728 | C2×D3 | — | 6 | 6 | no | — |
| 729 | C2×D3 | — | 6 | 12 | no | — |
| 730 | C2×D3 | — | 9 | 3 | no | — |
| 731 | C2×D3 | — | 9 | 6 | no | — |
| 732 | C2×D3 | — | 12 | 12 | no | — |
| 733 | C2×D3 | — | 12 | 12 | no | — |
| 734 | C2×D3 | — | 18 | 3 | no | — |
| 735 | C2×D3 | — | 18 | 6 | no | — |
| 736 | C2×D3 | — | 18 | 6 | no | — |
| 737 | C2×D3 | — | 18 | 12 | no | — |
| 738 | C2×D3 | — | 18 | 12 | no | — |
| 739 | C2×D3 | — | 18 | 6 | no | — |
| 740 | C2×D3 | — | 36 | 3 | no | — |
| 741 | C2×D3 | — | 36 | 6 | no | — |
| 742 | C2×D3 | — | 36 | 12 | no | — |
| 743 | C2×D3 | — | 36 | 12 | no | — |
| 744 | C2×D3 | — | 36 | 12 | no | — |
| 745 | C2×D3 | — | 72 | 12 | no | — |
| 746 | C2×D3 | C22×D32 | 1 | 6 | yes | — |
| 747 | C2×D3 | C22×D32 | 1 | 3 | yes | — |
| 748 | C3×C4 | — | 2 | 3 | no | — |
| 749 | C3×C4 | — | 2 | 6 | no | — |
| 750 | C3×C4 | — | 3 | 2 | no | — |
| 751 | C3×C4 | — | 3 | 2 | no | — |
| 752 | C3×C4 | — | 3 | 2 | no | — |
| 753 | C3×C4 | — | 4 | 3 | no | — |
| 754 | C3×C4 | — | 6 | 2 | no | — |
| 755 | C3×C4 | — | 6 | 1 | no | — |
| 756 | C3×C4 | — | 9 | 2 | no | — |
| 757 | C3×C4 | — | 9 | 3 | no | — |
| 758 | C3×C4 | C22×D32 | 1 | 6 | yes | — |
| 759 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 760 | Dic3 | — | 3 | 6 | no | — |
| 761 | Dic3 | — | 3 | 2 | no | — |
| 762 | Dic3 | — | 3 | 2 | no | — |
| 763 | Dic3 | — | 6 | 3 | no | — |
| 764 | Dic3 | — | 6 | 2 | no | — |
| 765 | Dic3 | — | 9 | 1 | no | — |
| 766 | Dic3 | — | 9 | 2 | no | — |
| 767 | Dic3 | — | 18 | 2 | no | — |
| 768 | Dic3 | — | 18 | 1 | no | — |
| 769 | Dic3 | — | 36 | 1 | no | — |
| 770 | Dic3 | C22×D32 | 1 | 1 | yes | characteristic |
| 771 | Dic3 | C22×D32 | 1 | 2 | yes | — |
| 772 | C32 | — | 2 | 2 | no | — |
| 773 | C32 | — | 2 | 1 | no | — |
| 774 | C32 | — | 4 | 1 | no | — |
| 775 | C32 | C2×#1009 | 1 | 1 | yes | characteristic, complemented |
| 776 | C32 | D3×H(5,𝔽2) | 1 | 2 | yes | complemented |
| 777 | C23 | — | 9 | 3 | no | — |
| 778 | C23 | — | 9 | 12 | no | — |
| 779 | C23 | — | 27 | 3 | no | — |
| 780 | C23 | — | 27 | 12 | no | — |
| 781 | C23 | — | 27 | 3 | no | — |
| 782 | C23 | — | 108 | 12 | no | — |
| 783 | Q8 | — | 9 | 2 | no | — |
| 784 | Q8 | — | 9 | 3 | no | — |
| 785 | Q8 | — | 27 | 2 | no | — |
| 786 | Q8 | D33 | 1 | 1 | yes | characteristic, complemented |
| 787 | D4 | — | 3 | 3 | no | — |
| 788 | D4 | — | 3 | 6 | no | — |
| 789 | D4 | — | 9 | 6 | no | — |
| 790 | D4 | — | 9 | 6 | no | — |
| 791 | D4 | — | 9 | 6 | no | — |
| 792 | D4 | — | 9 | 6 | no | — |
| 793 | D4 | — | 9 | 6 | no | — |
| 794 | D4 | — | 27 | 6 | no | — |
| 795 | D4 | — | 27 | 6 | no | — |
| 796 | D4 | — | 27 | 6 | no | — |
| 797 | D4 | — | 27 | 6 | no | — |
| 798 | D4 | — | 27 | 6 | no | — |
| 799 | D4 | — | 27 | 3 | no | — |
| 800 | C2×C4 | — | 3 | 6 | no | — |
| 801 | C2×C4 | — | 3 | 3 | no | — |
| 802 | C2×C4 | — | 9 | 1 | no | — |
| 803 | C2×C4 | — | 9 | 6 | no | — |
| 804 | C2×C4 | — | 9 | 3 | no | — |
| 805 | C2×C4 | — | 9 | 6 | no | — |
| 806 | C2×C4 | — | 27 | 3 | no | — |
| 807 | C2×C4 | — | 27 | 1 | no | — |
| 808 | C2×C4 | — | 27 | 1 | no | — |
| 809 | C2×C4 | — | 27 | 6 | no | — |
| 810 | C2×C4 | — | 27 | 3 | no | — |
| 811 | C2×C4 | — | 27 | 3 | no | — |
| 812 | C2×C3 | — | 2 | 1 | no | — |
| 813 | C2×C3 | — | 2 | 2 | no | — |
| 814 | C2×C3 | — | 4 | 1 | no | — |
| 815 | C2×C3 | — | 6 | 6 | no | — |
| 816 | C2×C3 | — | 6 | 6 | no | — |
| 817 | C2×C3 | — | 6 | 6 | no | — |
| 818 | C2×C3 | — | 9 | 2 | no | — |
| 819 | C2×C3 | — | 12 | 3 | no | — |
| 820 | C2×C3 | — | 12 | 6 | no | — |
| 821 | C2×C3 | — | 18 | 6 | no | — |
| 822 | C2×C3 | C23×D32 | 1 | 2 | yes | — |
| 823 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 824 | D3 | — | 2 | 6 | no | — |
| 825 | D3 | — | 2 | 3 | no | — |
| 826 | D3 | — | 3 | 4 | no | — |
| 827 | D3 | — | 6 | 2 | no | — |
| 828 | D3 | — | 6 | 6 | no | — |
| 829 | D3 | — | 6 | 6 | no | — |
| 830 | D3 | — | 12 | 6 | no | — |
| 831 | D3 | — | 18 | 6 | no | — |
| 832 | D3 | — | 18 | 3 | no | — |
| 833 | D3 | — | 36 | 3 | no | — |
| 834 | D3 | — | 36 | 6 | no | — |
| 835 | D3 | — | 72 | 3 | no | — |
| 836 | C22 | — | 3 | 6 | no | — |
| 837 | C22 | — | 3 | 3 | no | — |
| 838 | C22 | — | 9 | 1 | no | — |
| 839 | C22 | — | 9 | 6 | no | — |
| 840 | C22 | — | 18 | 6 | no | — |
| 841 | C22 | — | 27 | 3 | no | — |
| 842 | C22 | — | 36 | 12 | no | — |
| 843 | C22 | — | 54 | 6 | no | — |
| 844 | C22 | — | 54 | 6 | no | — |
| 845 | C22 | — | 108 | 12 | no | — |
| 846 | C4 | — | 3 | 2 | no | — |
| 847 | C4 | — | 3 | 1 | no | — |
| 848 | C4 | — | 9 | 2 | no | — |
| 849 | C4 | — | 9 | 3 | no | — |
| 850 | C4 | — | 27 | 1 | no | — |
| 851 | C4 | C2×D33 | 1 | 3 | yes | — |
| 852 | C3 | — | 2 | 1 | no | — |
| 853 | C3 | — | 2 | 2 | no | — |
| 854 | C3 | — | 4 | 1 | no | — |
| 855 | C3 | D3×#1009 | 1 | 2 | yes | complemented |
| 856 | C3 | #10596692 | 1 | 1 | yes | characteristic, complemented |
| 857 | C2 | — | 6 | 6 | no | — |
| 858 | C2 | — | 6 | 3 | no | — |
| 859 | C2 | — | 9 | 2 | no | — |
| 860 | C2 | — | 18 | 6 | no | — |
| 861 | C2 | — | 54 | 3 | no | — |
| 862 | C2 | C22×D33 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D33 |
| commutator, socle, cosocle | C2×C33 | C25 |
| Fitting | C33×Q8 | C23 |
| hypercenter | Q8 | D33 |
| hypocenter | C33 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11724626 | C2 | semidirect |
| 2. #11724597 | C2 | semidirect |
| 3. C3⋊D3×#239 | C2 | semidirect |
| 4. C3×#64320 | C2 | semidirect |
| 5. C3×#64319 | C2 | semidirect |
| 6. #11724403 | C2 | semidirect |
| 7. D3×#3802 | C2 | semidirect |
| 8. D32×D12 | C2 | semidirect |
| 9. #11724387 | C2 | semidirect |
| 10. #11724384 | C2 | semidirect |
| 11. #11724381 | C2 | semidirect |
| 14. C2×D33 | C22 | semidirect |
| 15. #89080 | C22 | semidirect |
| 16. C3×#3832 | C22 | semidirect |
| 17. C3×Q8×C3⋊D3 | C22 | semidirect |
| 18. C32×#239 | C22 | semidirect |
| 19. C32×#239 | C22 | semidirect |
| 20. C4⋊#1113 | C22 | semidirect |
| 21. C4×#1113 | C22 | semidirect |
| 22. #89041 | C22 | semidirect |
| 23. #89026 | C22 | semidirect |
| 24. C3⋊D3×D12 | C22 | semidirect |
| 25. C3⋊D3×D12 | C22 | semidirect |
| 26. D3×C4⋊(C3⋊D3) | C22 | semidirect |
| 27. C4×D3×C3⋊D3 | C22 | semidirect |
| 28. #89022 | C22 | semidirect |
| 29. #89020 | C22 | semidirect |
| 30. #89015 | C22 | semidirect |
| 31. C3×#3802 | C22 | semidirect |
| 32. C3×#3802 | C22 | semidirect |
| 33. C3×D3×D12 | C22 | semidirect |
| 34. C3×D3×D12 | C22 | semidirect |
| 35. C3×C4×D32 | C22 | semidirect |
| 36. C3×#3798 | C22 | semidirect |
| 37. C3×#3795 | C22 | semidirect |
| 38. #88962 | C22 | semidirect |
| 39. #88961 | C22 | semidirect |
| 40. #88957 | C22 | semidirect |
| 41. #88955 | C22 | semidirect |
| 42. #88954 | C22 | semidirect |
| 43. #88953 | C22 | semidirect |
| 44. #88952 | C22 | semidirect |
| 45. #88952 | C22 | semidirect |
| 46. D3×#626 | C22 | semidirect |
| 47. D3×#625 | C22 | semidirect |
| 56. #64320 | D3 | semidirect |
| 58. #64319 | D3 | semidirect |
| 78. C2×D3×C3⋊D3 | C23 | semidirect |
| 80. C2×C3×D32 | C23 | semidirect |
| 82. C33×Q8 | C23 | semidirect |
| 83. C4⋊(C3⋊(C3⋊D3)) | C23 | semidirect |
| 84. C4×C3⋊(C3⋊D3) | C23 | semidirect |
| 85. C3×C4⋊(C3⋊D3) | C23 | semidirect |
| 87. C3×C4×C3⋊D3 | C23 | semidirect |
| 88. C3×#634 | C23 | semidirect |
| 89. C32×D12 | C23 | semidirect |
| 90. C32×D12 | C23 | semidirect |
| 91. C32×C4×D3 | C23 | semidirect |
| 92. C32×C4×D3 | C23 | semidirect |
| 93. #6295 | C23 | semidirect |
| 95. #6294 | C23 | semidirect |
| 96. #6293 | C23 | semidirect |
| 97. #6292 | C23 | semidirect |
| 98. #6291 | C23 | semidirect |
| 99. #6291 | C23 | semidirect |
| 100. #6290 | C23 | semidirect |
| 101. #6289 | C23 | semidirect |
| 103. D3×C3⋊Dic3 | C23 | semidirect |
| 104. C3×#627 | C23 | semidirect |
| 105. C3×#626 | C23 | semidirect |
| 106. C3×#626 | C23 | semidirect |
| 107. C3×#625 | C23 | semidirect |
| 108. C3×#625 | C23 | semidirect |
| 110. C3×D3×Dic3 | C23 | semidirect |
| 122. #3832 | C2×D3 | semidirect |
| 123. Q8×C3⋊D3 | C2×D3 | semidirect |
| 137. C3×#239 | C2×D3 | semidirect |
| 138. C3×#239 | C2×D3 | semidirect |
| 139. C3×#239 | C2×D3 | semidirect |
| 175. #3802 | C2×D3 | semidirect |
| 176. #3802 | C2×D3 | semidirect |
| 188. D3×D12 | C2×D3 | semidirect |
| 189. D3×D12 | C2×D3 | semidirect |
| 194. C4×D32 | C2×D3 | semidirect |
| 202. #3798 | C2×D3 | semidirect |
| 210. #3795 | C2×D3 | semidirect |
| 271. C2×D32 | C22×D3 | semidirect |
| 275. C32×Q8 | C22×D3 | semidirect |
| 276. C32×Q8 | C22×D3 | semidirect |
| 291. C4⋊(C3⋊D3) | C22×D3 | semidirect |
| 300. C4×C3⋊D3 | C22×D3 | semidirect |
| 302. #634 | C22×D3 | semidirect |
| 316. C3×D12 | C22×D3 | semidirect |
| 317. C3×D12 | C22×D3 | semidirect |
| 318. C3×D12 | C22×D3 | semidirect |
| 328. C3×C4×D3 | C22×D3 | semidirect |
| 329. C3×C4×D3 | C22×D3 | semidirect |
| 330. C3×C4×D3 | C22×D3 | semidirect |
| 338. #627 | C22×D3 | semidirect |
| 348. #626 | C22×D3 | semidirect |
| 349. #626 | C22×D3 | semidirect |
| 354. #625 | C22×D3 | semidirect |
| 355. #625 | C22×D3 | semidirect |
| 368. D3×Dic3 | C22×D3 | semidirect |
| 373. C3×C3⋊D3 | H(5,𝔽2) | semidirect |
| 409. #239 | D32 | semidirect |
| 410. #239 | D32 | semidirect |
| 543. C33 | C2×H(5,𝔽2) | semidirect |
| 565. C3×Q8 | C2×D32 | semidirect |
| 566. C3×Q8 | C2×D32 | semidirect |
| 624. D12 | C2×D32 | semidirect |
| 625. D12 | C2×D32 | semidirect |
| 647. C4×D3 | C2×D32 | semidirect |
| 648. C4×D3 | C2×D32 | semidirect |
| 670. C3⋊D3 | #1009 | semidirect |
| 775. C32 | C2×#1009 | semidirect |
| 776. C32 | D3×H(5,𝔽2) | semidirect |
| 786. Q8 | D33 | semidirect |
| 855. C3 | D3×#1009 | semidirect |
| 856. C3 | #10596692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724626 | 2 |
| #11724597 | 2 |
| C3⋊D3×#239 | 2 |
| C3×#64320 | 2 |
| C3×#64319 | 2 |
| #11724403 | 2 |
| D3×#3802 | 2 |
| D32×D12 | 2 |
| #11724387 | 2 |
| #11724384 | 2 |
| #11724381 | 2 |
| #10596692 | 3 |
| D3×#1009 | 3 |