Finite Group DatabasebetaFinite Group DatabasebetaOrder 2592.
3466 conjugacy classes of subgroups.
The subgroup lattice has 760 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13049721 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#10620152 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13049685 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C3×#89028 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C32×#3811 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13049523 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13049513 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13049502 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#6291 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11724588 | — | 3 | 2 | no | maximal |
| 11 | #11724420 | — | 3 | 4 | no | maximal |
| 12 | C22×C3⋊(C3⋊(C3⋊D3)) | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | C22×C32×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C2×C3⋊#1113 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×D3×C3⋊(C3⋊D3) | C22 | 1 | 2 | yes | complemented |
| 16 | C2×C32×D32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C3×#6312 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×C32×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C33×#67 | C22 | 1 | 2 | yes | complemented |
| 20 | #10620157 | C22 | 1 | 2 | yes | complemented |
| 21 | #10620155 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #10620152 | C22 | 1 | 2 | yes | complemented |
| 23 | #10620152 | C22 | 1 | 2 | yes | complemented |
| 24 | #10620147 | C22 | 1 | 2 | yes | complemented |
| 25 | #10620146 | C22 | 1 | 2 | yes | complemented |
| 26 | #10620144 | C22 | 1 | 2 | yes | complemented |
| 27 | C3×#6293 | C22 | 1 | 2 | yes | complemented |
| 28 | C3×#6291 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×#6289 | C22 | 1 | 2 | yes | complemented |
| 30 | C3×D3×C3⋊Dic3 | C22 | 1 | 2 | yes | complemented |
| 31 | C32×#626 | C22 | 1 | 2 | yes | complemented |
| 32 | C32×#624 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | D4×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 34 | C3×#3830 | — | 3 | 2 | no | — |
| 35 | C32×D3×D4 | — | 3 | 2 | no | — |
| 36 | #89049 | — | 3 | 4 | no | — |
| 37 | #89039 | — | 3 | 2 | no | — |
| 38 | #89039 | — | 3 | 8 | no | — |
| 39 | #89039 | — | 3 | 2 | no | — |
| 40 | #89039 | — | 6 | 8 | no | — |
| 41 | D3×#638 | — | 3 | 2 | no | — |
| 42 | D3×#638 | — | 3 | 2 | no | — |
| 43 | C2×#6292 | — | 3 | 4 | no | — |
| 44 | C2×#6291 | — | 3 | 2 | no | — |
| 45 | C2×#6291 | — | 3 | 2 | no | — |
| 46 | C2×#6291 | — | 6 | 1 | no | — |
| 47 | #89028 | — | 3 | 2 | no | — |
| 48 | #89028 | D3 | 1 | 2 | yes | complemented |
| 49 | C3⋊D3×D12 | — | 3 | 2 | no | — |
| 50 | #89022 | — | 3 | 2 | no | — |
| 51 | #89020 | — | 3 | 2 | no | — |
| 52 | #89015 | — | 3 | 2 | no | — |
| 53 | C3×#3811 | D3 | 1 | 4 | yes | complemented |
| 54 | C3×#3804 | — | 3 | 8 | no | — |
| 55 | #88965 | — | 3 | 8 | no | — |
| 56 | #88962 | — | 3 | 8 | no | — |
| 57 | #88955 | — | 3 | 8 | no | — |
| 58 | D3×#626 | — | 3 | 8 | no | — |
| 59 | C22×C34 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C3⋊(C3⋊(C3⋊D3)) | — | 4 | 1 | no | — |
| 61 | C2×C3⋊(C3⋊(C3⋊D3)) | C23 | 1 | 2 | yes | — |
| 62 | C2×C3×C3⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 63 | C2×C32×C3⋊D3 | — | 4 | 1 | no | — |
| 64 | C2×C32×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C32×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C33×D3 | C23 | 1 | 2 | yes | — |
| 67 | C3⋊#1113 | — | 4 | 1 | no | — |
| 68 | D3×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 69 | C32×D32 | — | 4 | 1 | no | — |
| 70 | C3×C3⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 71 | C32×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 72 | C33×Dic3 | C23 | 1 | 2 | yes | — |
| 73 | #64361 | — | 9 | 1 | no | — |
| 74 | #64314 | — | 9 | 8 | no | — |
| 75 | #64308 | — | 9 | 1 | no | — |
| 76 | C22×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 77 | C22×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 78 | C22×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 79 | C22×C3⋊(C3⋊D3) | — | 6 | 1 | no | — |
| 80 | C22×C3⋊(C3⋊D3) | — | 6 | 8 | no | — |
| 81 | C22×C3⋊(C3⋊D3) | — | 12 | 4 | no | — |
| 82 | C22×C3×C3⋊D3 | C2×D3 | 1 | 4 | yes | complemented |
| 83 | C22×C32×D3 | — | 3 | 2 | no | — |
| 84 | C22×C32×D3 | — | 3 | 2 | no | — |
| 85 | C22×C32×D3 | — | 6 | 1 | no | — |
| 86 | C2×#1113 | — | 3 | 4 | no | — |
| 87 | C2×D3×C3⋊D3 | — | 3 | 2 | no | — |
| 88 | C2×D3×C3⋊D3 | — | 3 | 2 | no | — |
| 89 | C2×D3×C3⋊D3 | — | 3 | 8 | no | — |
| 90 | C2×D3×C3⋊D3 | — | 6 | 8 | no | — |
| 91 | C2×C3×D32 | C2×D3 | 1 | 4 | yes | complemented |
| 92 | C33×D4 | — | 3 | 2 | no | — |
| 93 | #6312 | — | 3 | 2 | no | — |
| 94 | #6312 | C2×D3 | 1 | 2 | yes | complemented |
| 95 | C4⋊(C3⋊(C3⋊D3)) | — | 3 | 2 | no | — |
| 96 | C4×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 97 | C3×#638 | — | 3 | 2 | no | — |
| 98 | C3×#638 | — | 3 | 8 | no | — |
| 99 | C3×#638 | — | 3 | 2 | no | — |
| 100 | C3×#638 | — | 6 | 8 | no | — |
| 101 | C2×C3×C3⋊Dic3 | — | 2 | 1 | no | — |
| 102 | C2×C3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 103 | C2×C3×C3⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 104 | C3×C4×C3⋊D3 | — | 3 | 2 | no | — |
| 105 | C3×#634 | — | 3 | 2 | no | — |
| 106 | C32×#67 | — | 2 | 8 | no | — |
| 107 | C32×#67 | — | 3 | 2 | no | — |
| 108 | C32×#67 | C2×D3 | 1 | 8 | yes | complemented |
| 109 | C32×#67 | C2×D3 | 1 | 2 | yes | complemented |
| 110 | C2×C32×Dic3 | — | 3 | 4 | no | — |
| 111 | C32×D12 | — | 3 | 2 | no | — |
| 112 | C32×C4×D3 | — | 3 | 2 | no | — |
| 113 | #6295 | — | 3 | 8 | no | — |
| 114 | #6294 | — | 3 | 4 | no | — |
| 115 | #6293 | C2×D3 | 1 | 2 | yes | complemented |
| 116 | #6292 | — | 3 | 8 | no | — |
| 117 | #6292 | — | 3 | 8 | no | — |
| 118 | #6292 | — | 3 | 2 | no | — |
| 119 | #6292 | — | 3 | 8 | no | — |
| 120 | #6292 | — | 6 | 8 | no | — |
| 121 | #6291 | — | 3 | 2 | no | — |
| 122 | #6291 | — | 3 | 2 | no | — |
| 123 | #6291 | — | 3 | 8 | no | — |
| 124 | #6291 | — | 3 | 2 | no | — |
| 125 | #6291 | — | 3 | 2 | no | — |
| 126 | #6291 | — | 3 | 2 | no | — |
| 127 | #6291 | — | 3 | 2 | no | — |
| 128 | #6291 | — | 6 | 2 | no | — |
| 129 | #6291 | — | 6 | 2 | no | — |
| 130 | #6291 | — | 6 | 8 | no | — |
| 131 | #6291 | C2×D3 | 1 | 2 | yes | complemented |
| 132 | #6290 | — | 3 | 2 | no | — |
| 133 | #6289 | — | 3 | 2 | no | — |
| 134 | #6289 | — | 3 | 8 | no | — |
| 135 | #6289 | — | 6 | 8 | no | — |
| 136 | #6289 | C2×D3 | 1 | 2 | yes | complemented |
| 137 | D3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 138 | D3×C3⋊Dic3 | C2×D3 | 1 | 2 | yes | complemented |
| 139 | C3×#627 | — | 3 | 8 | no | — |
| 140 | C3×#626 | — | 3 | 8 | no | — |
| 141 | C3×#626 | C2×D3 | 1 | 8 | yes | complemented |
| 142 | C3×#624 | — | 3 | 8 | no | — |
| 143 | C3×#624 | C2×D3 | 1 | 4 | yes | complemented |
| 144 | C3×D3×Dic3 | — | 3 | 8 | no | — |
| 145 | C2×C34 | — | 2 | 1 | no | — |
| 146 | C2×C34 | C24 | 1 | 1 | yes | characteristic |
| 147 | C3⋊(C3⋊(C3⋊D3)) | — | 2 | 2 | no | — |
| 148 | C3×C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 149 | C32×C3⋊D3 | — | 2 | 1 | no | — |
| 150 | C32×C3⋊D3 | — | 2 | 1 | no | — |
| 151 | C33×D3 | — | 2 | 2 | no | — |
| 152 | C2×C32×D4 | — | 9 | 1 | no | — |
| 153 | C2×#638 | — | 9 | 2 | no | — |
| 154 | C2×#638 | — | 9 | 1 | no | — |
| 155 | C2×#638 | — | 9 | 1 | no | — |
| 156 | #3830 | — | 3 | 2 | no | — |
| 157 | #3830 | — | 9 | 2 | no | — |
| 158 | D4×C3⋊D3 | — | 9 | 2 | no | — |
| 159 | D4×C3⋊D3 | — | 9 | 2 | no | — |
| 160 | D4×C3⋊D3 | — | 9 | 8 | no | — |
| 161 | D4×C3⋊D3 | — | 18 | 8 | no | — |
| 162 | #3828 | — | 9 | 2 | no | — |
| 163 | C2×C4⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 164 | C3×#237 | — | 9 | 8 | no | — |
| 165 | C3×D3×D4 | — | 3 | 8 | no | — |
| 166 | C3×#235 | — | 9 | 2 | no | — |
| 167 | #3811 | — | 9 | 8 | no | — |
| 168 | #3811 | — | 9 | 1 | no | — |
| 169 | #3811 | — | 9 | 8 | no | — |
| 170 | #3811 | — | 9 | 2 | no | — |
| 171 | #3811 | — | 18 | 8 | no | — |
| 172 | #3811 | C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 173 | D3×#67 | — | 9 | 8 | no | — |
| 174 | D3×#67 | — | 9 | 8 | no | — |
| 175 | C2×#626 | — | 9 | 8 | no | — |
| 176 | C2×#626 | — | 9 | 8 | no | — |
| 177 | C2×#626 | — | 18 | 4 | no | — |
| 178 | #3804 | — | 3 | 8 | no | — |
| 179 | #3804 | — | 9 | 8 | no | — |
| 180 | D3×D12 | — | 9 | 8 | no | — |
| 181 | D3×D12 | — | 9 | 2 | no | — |
| 182 | D3×D12 | — | 9 | 2 | no | — |
| 183 | #3799 | — | 9 | 8 | no | — |
| 184 | #3799 | — | 9 | 2 | no | — |
| 185 | #3799 | — | 9 | 2 | no | — |
| 186 | #3798 | — | 9 | 8 | no | — |
| 187 | #3796 | — | 9 | 8 | no | — |
| 188 | C22×C33 | — | 2 | 1 | no | — |
| 189 | C22×C33 | — | 2 | 8 | no | — |
| 190 | C22×C33 | — | 3 | 2 | no | — |
| 191 | C22×C33 | — | 4 | 4 | no | — |
| 192 | C22×C33 | C22×D3 | 1 | 2 | yes | — |
| 193 | C22×C33 | C22×D3 | 1 | 4 | yes | — |
| 194 | C2×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 195 | C2×C3⋊(C3⋊D3) | — | 3 | 2 | no | — |
| 196 | C2×C3⋊(C3⋊D3) | — | 3 | 8 | no | — |
| 197 | C2×C3⋊(C3⋊D3) | — | 6 | 8 | no | — |
| 198 | C2×C3⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 199 | C2×C3⋊(C3⋊D3) | — | 6 | 8 | no | — |
| 200 | C2×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 201 | C2×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 202 | C2×C3⋊(C3⋊D3) | — | 12 | 4 | no | — |
| 203 | C2×C3⋊(C3⋊D3) | — | 12 | 16 | no | — |
| 204 | C2×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 205 | C2×C3⋊(C3⋊D3) | — | 12 | 8 | no | — |
| 206 | C2×C3⋊(C3⋊D3) | — | 12 | 16 | no | — |
| 207 | C2×C3⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 208 | C2×C3×C3⋊D3 | — | 3 | 2 | no | — |
| 209 | C2×C3×C3⋊D3 | — | 3 | 8 | no | — |
| 210 | C2×C3×C3⋊D3 | — | 4 | 4 | no | — |
| 211 | C2×C3×C3⋊D3 | — | 6 | 8 | no | — |
| 212 | C2×C3×C3⋊D3 | C22×D3 | 1 | 4 | yes | — |
| 213 | C2×C3×C3⋊D3 | C22×D3 | 1 | 4 | yes | — |
| 214 | C2×C32×D3 | — | 2 | 8 | no | — |
| 215 | C2×C32×D3 | — | 3 | 2 | no | — |
| 216 | C2×C32×D3 | — | 3 | 2 | no | — |
| 217 | C2×C32×D3 | — | 6 | 1 | no | — |
| 218 | C2×C32×D3 | — | 6 | 1 | no | — |
| 219 | C2×C32×D3 | — | 12 | 2 | no | — |
| 220 | C2×C32×D3 | — | 12 | 2 | no | — |
| 221 | C2×C32×D3 | — | 12 | 2 | no | — |
| 222 | C2×C32×D3 | C22×D3 | 1 | 8 | yes | — |
| 223 | C2×C32×D3 | C22×D3 | 1 | 2 | yes | — |
| 224 | #1113 | — | 12 | 4 | no | — |
| 225 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 226 | D3×C3⋊D3 | — | 12 | 8 | no | — |
| 227 | D3×C3⋊D3 | — | 12 | 16 | no | — |
| 228 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 229 | C3×D32 | — | 4 | 4 | no | — |
| 230 | C33×C4 | — | 3 | 2 | no | — |
| 231 | C3⋊(C3⋊Dic3) | C22×D3 | 1 | 2 | yes | — |
| 232 | C3×C3⋊Dic3 | — | 2 | 2 | no | — |
| 233 | C3×C3⋊Dic3 | — | 3 | 2 | no | — |
| 234 | C3×C3⋊Dic3 | — | 3 | 8 | no | — |
| 235 | C3×C3⋊Dic3 | — | 6 | 8 | no | — |
| 236 | C3×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 237 | C3×C3⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 238 | C32×Dic3 | — | 2 | 8 | no | — |
| 239 | C32×Dic3 | — | 3 | 8 | no | — |
| 240 | C32×Dic3 | C22×D3 | 1 | 8 | yes | — |
| 241 | C32×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 242 | #1009 | — | 27 | 2 | no | — |
| 243 | #1004 | — | 27 | 4 | no | — |
| 244 | C34 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 245 | C23×C32 | — | 9 | 1 | no | — |
| 246 | C23×C32 | — | 9 | 1 | no | — |
| 247 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 248 | C22×C3⋊D3 | — | 9 | 2 | no | — |
| 249 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 250 | C22×C3⋊D3 | — | 9 | 8 | no | — |
| 251 | C22×C3⋊D3 | — | 9 | 8 | no | — |
| 252 | C22×C3⋊D3 | — | 9 | 1 | no | — |
| 253 | C22×C3⋊D3 | — | 18 | 8 | no | — |
| 254 | C22×C3⋊D3 | — | 18 | 8 | no | — |
| 255 | C22×C3⋊D3 | — | 18 | 8 | no | — |
| 256 | C22×C3⋊D3 | — | 18 | 4 | no | — |
| 257 | C22×C3⋊D3 | — | 36 | 4 | no | — |
| 258 | C22×C3⋊D3 | — | 36 | 4 | no | — |
| 259 | C22×C3⋊D3 | — | 36 | 12 | no | — |
| 260 | C22×C3⋊D3 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 261 | C22×C3×D3 | — | 3 | 8 | no | — |
| 262 | C22×C3×D3 | — | 3 | 8 | no | — |
| 263 | C22×C3×D3 | — | 6 | 4 | no | — |
| 264 | C2×D32 | — | 9 | 8 | no | — |
| 265 | C2×D32 | — | 9 | 1 | no | — |
| 266 | C2×D32 | — | 9 | 8 | no | — |
| 267 | C2×D32 | — | 9 | 2 | no | — |
| 268 | C2×D32 | — | 18 | 8 | no | — |
| 269 | C2×D32 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 270 | C32×D4 | — | 3 | 2 | no | — |
| 271 | C32×D4 | — | 3 | 8 | no | — |
| 272 | C32×D4 | — | 6 | 8 | no | — |
| 273 | C32×D4 | — | 9 | 2 | no | — |
| 274 | C2×C32×C4 | — | 9 | 1 | no | — |
| 275 | C2×C32×C4 | — | 9 | 1 | no | — |
| 276 | #638 | — | 3 | 2 | no | — |
| 277 | #638 | — | 3 | 2 | no | — |
| 278 | #638 | — | 3 | 8 | no | — |
| 279 | #638 | — | 6 | 8 | no | — |
| 280 | #638 | — | 9 | 2 | no | — |
| 281 | #638 | — | 9 | 2 | no | — |
| 282 | #638 | — | 9 | 2 | no | — |
| 283 | #638 | — | 9 | 2 | no | — |
| 284 | #638 | — | 9 | 8 | no | — |
| 285 | #638 | — | 18 | 8 | no | — |
| 286 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 287 | C2×C3⋊Dic3 | — | 9 | 1 | no | — |
| 288 | C2×C3⋊Dic3 | D32 | 1 | 1 | yes | characteristic, complemented |
| 289 | C4⋊(C3⋊D3) | — | 9 | 2 | no | — |
| 290 | C4⋊(C3⋊D3) | — | 9 | 8 | no | — |
| 291 | C4⋊(C3⋊D3) | — | 9 | 2 | no | — |
| 292 | C4⋊(C3⋊D3) | — | 9 | 2 | no | — |
| 293 | C4⋊(C3⋊D3) | — | 18 | 8 | no | — |
| 294 | C4×C3⋊D3 | — | 3 | 2 | no | — |
| 295 | C4×C3⋊D3 | — | 9 | 2 | no | — |
| 296 | C4×C3⋊D3 | — | 9 | 8 | no | — |
| 297 | C4×C3⋊D3 | — | 18 | 8 | no | — |
| 298 | #634 | — | 3 | 2 | no | — |
| 299 | C3×#67 | — | 2 | 8 | no | — |
| 300 | C3×#67 | — | 3 | 8 | no | — |
| 301 | C3×#67 | — | 9 | 8 | no | — |
| 302 | C3×#67 | — | 9 | 8 | no | — |
| 303 | C3×#67 | — | 9 | 2 | no | — |
| 304 | C3×#67 | — | 18 | 8 | no | — |
| 305 | C3×#67 | D32 | 1 | 8 | yes | complemented |
| 306 | C3×#67 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 307 | C2×C3×Dic3 | — | 3 | 8 | no | — |
| 308 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 309 | C2×C3×Dic3 | — | 9 | 8 | no | — |
| 310 | C3×D12 | — | 3 | 8 | no | — |
| 311 | C3×D12 | — | 9 | 2 | no | — |
| 312 | C3×C4×D3 | — | 3 | 8 | no | — |
| 313 | C3×C4×D3 | — | 9 | 8 | no | — |
| 314 | C3×C4×D3 | — | 9 | 2 | no | — |
| 315 | C3×C4×D3 | — | 9 | 2 | no | — |
| 316 | C3×Dic6 | — | 9 | 8 | no | — |
| 317 | C3×Dic6 | — | 9 | 2 | no | — |
| 318 | #627 | — | 3 | 8 | no | — |
| 319 | #626 | — | 3 | 8 | no | — |
| 320 | #626 | — | 9 | 8 | no | — |
| 321 | #626 | — | 9 | 8 | no | — |
| 322 | #626 | — | 9 | 8 | no | — |
| 323 | #626 | — | 9 | 8 | no | — |
| 324 | #626 | — | 9 | 8 | no | — |
| 325 | #626 | — | 9 | 2 | no | — |
| 326 | #626 | — | 9 | 8 | no | — |
| 327 | #626 | — | 9 | 2 | no | — |
| 328 | #626 | — | 9 | 8 | no | — |
| 329 | #626 | — | 9 | 2 | no | — |
| 330 | #626 | — | 18 | 8 | no | — |
| 331 | #626 | — | 18 | 8 | no | — |
| 332 | #626 | — | 18 | 8 | no | — |
| 333 | #626 | — | 18 | 8 | no | — |
| 334 | #626 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 335 | #625 | — | 9 | 8 | no | — |
| 336 | #624 | — | 3 | 8 | no | — |
| 337 | #624 | — | 9 | 1 | no | — |
| 338 | #624 | — | 9 | 8 | no | — |
| 339 | #624 | — | 9 | 2 | no | — |
| 340 | #624 | — | 18 | 8 | no | — |
| 341 | #624 | C2×C3⋊D3 | 1 | 1 | yes | characteristic, complemented |
| 342 | D3×Dic3 | — | 3 | 8 | no | — |
| 343 | D3×Dic3 | — | 9 | 8 | no | — |
| 344 | C2×C33 | — | 2 | 2 | no | — |
| 345 | C2×C33 | — | 2 | 4 | no | — |
| 346 | C2×C33 | — | 2 | 2 | no | — |
| 347 | C2×C33 | — | 2 | 8 | no | — |
| 348 | C2×C33 | — | 2 | 1 | no | — |
| 349 | C2×C33 | — | 4 | 4 | no | — |
| 350 | C2×C33 | — | 4 | 8 | no | — |
| 351 | C2×C33 | — | 4 | 8 | no | — |
| 352 | C2×C33 | — | 6 | 2 | no | — |
| 353 | C2×C33 | C23×D3 | 1 | 2 | yes | — |
| 354 | C2×C33 | C23×D3 | 1 | 4 | yes | — |
| 355 | C3⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 356 | C3⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 357 | C3⋊(C3⋊D3) | — | 6 | 16 | no | — |
| 358 | C3⋊(C3⋊D3) | — | 6 | 8 | no | — |
| 359 | C3⋊(C3⋊D3) | — | 6 | 2 | no | — |
| 360 | C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 361 | C3⋊(C3⋊D3) | — | 12 | 8 | no | — |
| 362 | C3⋊(C3⋊D3) | — | 12 | 16 | no | — |
| 363 | C3×C3⋊D3 | — | 2 | 4 | no | — |
| 364 | C3×C3⋊D3 | — | 2 | 4 | no | — |
| 365 | C3×C3⋊D3 | — | 6 | 2 | no | — |
| 366 | C3×C3⋊D3 | — | 6 | 8 | no | — |
| 367 | C3×C3⋊D3 | — | 12 | 8 | no | — |
| 368 | C32×D3 | — | 2 | 2 | no | — |
| 369 | C32×D3 | — | 2 | 8 | no | — |
| 370 | C32×D3 | — | 4 | 8 | no | — |
| 371 | C32×D3 | — | 6 | 2 | no | — |
| 372 | C32×D3 | — | 6 | 2 | no | — |
| 373 | C32×D3 | — | 12 | 1 | no | — |
| 374 | C32×D3 | — | 12 | 1 | no | — |
| 375 | C3×#41 | — | 27 | 2 | no | — |
| 376 | C2×C3×D4 | — | 9 | 4 | no | — |
| 377 | C2×#67 | — | 27 | 4 | no | — |
| 378 | C2×#67 | — | 27 | 8 | no | — |
| 379 | C2×#67 | — | 27 | 4 | no | — |
| 380 | #239 | — | 27 | 2 | no | — |
| 381 | #239 | — | 27 | 2 | no | — |
| 382 | #237 | — | 9 | 8 | no | — |
| 383 | #237 | — | 27 | 8 | no | — |
| 384 | D3×D4 | — | 3 | 2 | no | — |
| 385 | D3×D4 | — | 27 | 2 | no | — |
| 386 | D3×D4 | — | 27 | 8 | no | — |
| 387 | D3×D4 | — | 27 | 2 | no | — |
| 388 | D3×D4 | — | 27 | 8 | no | — |
| 389 | D3×D4 | — | 27 | 2 | no | — |
| 390 | D3×D4 | — | 27 | 2 | no | — |
| 391 | D3×D4 | — | 27 | 2 | no | — |
| 392 | D3×D4 | — | 54 | 8 | no | — |
| 393 | #235 | — | 9 | 2 | no | — |
| 394 | #235 | — | 27 | 2 | no | — |
| 395 | #235 | — | 27 | 8 | no | — |
| 396 | #235 | — | 27 | 2 | no | — |
| 397 | C2×D12 | — | 27 | 2 | no | — |
| 398 | C2×D12 | — | 27 | 2 | no | — |
| 399 | C2×D12 | — | 27 | 2 | no | — |
| 400 | C2×D12 | — | 54 | 1 | no | — |
| 401 | C22×C32 | — | 2 | 8 | no | — |
| 402 | C22×C32 | — | 2 | 4 | no | — |
| 403 | C22×C32 | — | 2 | 8 | no | — |
| 404 | C22×C32 | — | 3 | 2 | no | — |
| 405 | C22×C32 | — | 3 | 8 | no | — |
| 406 | C22×C32 | — | 4 | 4 | no | — |
| 407 | C22×C32 | — | 4 | 12 | no | — |
| 408 | C22×C32 | — | 4 | 4 | no | — |
| 409 | C22×C32 | — | 6 | 8 | no | — |
| 410 | C22×C32 | — | 9 | 1 | no | — |
| 411 | C22×C32 | — | 9 | 1 | no | — |
| 412 | C22×C32 | — | 36 | 1 | no | — |
| 413 | C22×C32 | — | 36 | 1 | no | — |
| 414 | C22×C32 | C2×D32 | 1 | 8 | yes | — |
| 415 | C22×C32 | C2×D32 | 1 | 1 | yes | characteristic |
| 416 | C22×C32 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 417 | C2×C3⋊D3 | — | 3 | 2 | no | — |
| 418 | C2×C3⋊D3 | — | 3 | 8 | no | — |
| 419 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 420 | C2×C3⋊D3 | — | 6 | 8 | no | — |
| 421 | C2×C3⋊D3 | — | 9 | 2 | no | — |
| 422 | C2×C3⋊D3 | — | 9 | 8 | no | — |
| 423 | C2×C3⋊D3 | — | 9 | 8 | no | — |
| 424 | C2×C3⋊D3 | — | 9 | 2 | no | — |
| 425 | C2×C3⋊D3 | — | 18 | 8 | no | — |
| 426 | C2×C3⋊D3 | — | 18 | 8 | no | — |
| 427 | C2×C3⋊D3 | — | 18 | 8 | no | — |
| 428 | C2×C3⋊D3 | — | 18 | 8 | no | — |
| 429 | C2×C3⋊D3 | — | 18 | 8 | no | — |
| 430 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 431 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 432 | C2×C3⋊D3 | — | 36 | 24 | no | — |
| 433 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 434 | C2×C3⋊D3 | — | 36 | 2 | no | — |
| 435 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 436 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 437 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 438 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 439 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 440 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 441 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 442 | C2×C3⋊D3 | — | 36 | 8 | no | — |
| 443 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 444 | C2×C3⋊D3 | — | 36 | 16 | no | — |
| 445 | C2×C3⋊D3 | — | 36 | 48 | no | — |
| 446 | C2×C3⋊D3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 447 | C2×C3⋊D3 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
| 448 | C2×C3×D3 | — | 2 | 8 | no | — |
| 449 | C2×C3×D3 | — | 3 | 8 | no | — |
| 450 | C2×C3×D3 | — | 3 | 8 | no | — |
| 451 | C2×C3×D3 | — | 6 | 4 | no | — |
| 452 | C2×C3×D3 | — | 6 | 4 | no | — |
| 453 | C2×C3×D3 | — | 9 | 8 | no | — |
| 454 | C2×C3×D3 | — | 9 | 2 | no | — |
| 455 | C2×C3×D3 | — | 12 | 8 | no | — |
| 456 | C2×C3×D3 | — | 12 | 8 | no | — |
| 457 | C2×C3×D3 | — | 12 | 8 | no | — |
| 458 | C2×C3×D3 | — | 18 | 8 | no | — |
| 459 | C2×C3×D3 | C2×D32 | 1 | 8 | yes | — |
| 460 | C2×C3×D3 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 461 | D32 | — | 4 | 1 | no | — |
| 462 | D32 | — | 36 | 8 | no | — |
| 463 | D32 | — | 36 | 2 | no | — |
| 464 | D32 | — | 36 | 16 | no | — |
| 465 | D32 | — | 36 | 8 | no | — |
| 466 | D32 | — | 36 | 1 | no | — |
| 467 | C32×C4 | — | 3 | 2 | no | — |
| 468 | C32×C4 | — | 3 | 8 | no | — |
| 469 | C32×C4 | — | 6 | 8 | no | — |
| 470 | C32×C4 | — | 9 | 2 | no | — |
| 471 | C3⋊Dic3 | — | 3 | 2 | no | — |
| 472 | C3⋊Dic3 | — | 3 | 8 | no | — |
| 473 | C3⋊Dic3 | — | 6 | 8 | no | — |
| 474 | C3⋊Dic3 | C2×D32 | 1 | 2 | yes | — |
| 475 | C3×Dic3 | — | 2 | 8 | no | — |
| 476 | C3×Dic3 | — | 3 | 8 | no | — |
| 477 | C3×Dic3 | — | 3 | 8 | no | — |
| 478 | C3×Dic3 | — | 6 | 8 | no | — |
| 479 | C3×Dic3 | — | 9 | 8 | no | — |
| 480 | C3×Dic3 | — | 9 | 2 | no | — |
| 481 | C3×Dic3 | — | 18 | 8 | no | — |
| 482 | C3×Dic3 | C2×D32 | 1 | 8 | yes | — |
| 483 | C3×Dic3 | C22×C3⋊D3 | 1 | 2 | yes | — |
| 484 | H(5,𝔽2) | — | 81 | 1 | no | Sylow |
| 485 | C33 | — | 2 | 1 | no | — |
| 486 | C33 | — | 2 | 8 | no | — |
| 487 | C33 | — | 4 | 4 | no | — |
| 488 | C33 | #1004 | 1 | 4 | yes | complemented |
| 489 | C33 | #1009 | 1 | 2 | yes | complemented |
| 490 | C23×C3 | — | 9 | 4 | no | — |
| 491 | C23×C3 | — | 9 | 4 | no | — |
| 492 | C22×D3 | — | 3 | 2 | no | — |
| 493 | C22×D3 | — | 3 | 2 | no | — |
| 494 | C22×D3 | — | 6 | 1 | no | — |
| 495 | C22×D3 | — | 27 | 2 | no | — |
| 496 | C22×D3 | — | 27 | 4 | no | — |
| 497 | C22×D3 | — | 27 | 2 | no | — |
| 498 | C22×D3 | — | 27 | 8 | no | — |
| 499 | C22×D3 | — | 27 | 4 | no | — |
| 500 | C22×D3 | — | 27 | 2 | no | — |
| 501 | C22×D3 | — | 27 | 2 | no | — |
| 502 | C22×D3 | — | 54 | 8 | no | — |
| 503 | C22×D3 | — | 54 | 1 | no | — |
| 504 | C22×D3 | — | 54 | 8 | no | — |
| 505 | C22×D3 | — | 108 | 4 | no | — |
| 506 | C3×Q8 | — | 27 | 2 | no | — |
| 507 | C3×D4 | — | 3 | 8 | no | — |
| 508 | C3×D4 | — | 3 | 2 | no | — |
| 509 | C3×D4 | — | 6 | 8 | no | — |
| 510 | C3×D4 | — | 9 | 8 | no | — |
| 511 | C3×D4 | — | 27 | 2 | no | — |
| 512 | C3×D4 | — | 27 | 2 | no | — |
| 513 | C2×C3×C4 | — | 9 | 4 | no | — |
| 514 | C2×C3×C4 | — | 9 | 2 | no | — |
| 515 | C2×C3×C4 | — | 18 | 1 | no | — |
| 516 | C2×C3×C4 | — | 27 | 2 | no | — |
| 517 | C2×C3×C4 | — | 27 | 2 | no | — |
| 518 | #67 | — | 3 | 2 | no | — |
| 519 | #67 | — | 9 | 8 | no | — |
| 520 | #67 | — | 9 | 8 | no | — |
| 521 | #67 | — | 9 | 2 | no | — |
| 522 | #67 | — | 18 | 8 | no | — |
| 523 | #67 | — | 27 | 8 | no | — |
| 524 | #67 | — | 27 | 8 | no | — |
| 525 | #67 | — | 27 | 2 | no | — |
| 526 | #67 | — | 27 | 8 | no | — |
| 527 | #67 | — | 27 | 2 | no | — |
| 528 | #67 | — | 27 | 8 | no | — |
| 529 | #67 | — | 27 | 2 | no | — |
| 530 | #67 | — | 54 | 8 | no | — |
| 531 | #67 | D3×C3⋊D3 | 1 | 2 | yes | complemented |
| 532 | C2×Dic3 | — | 3 | 4 | no | — |
| 533 | C2×Dic3 | — | 9 | 8 | no | — |
| 534 | C2×Dic3 | — | 27 | 4 | no | — |
| 535 | D12 | — | 3 | 2 | no | — |
| 536 | D12 | — | 9 | 2 | no | — |
| 537 | D12 | — | 27 | 2 | no | — |
| 538 | D12 | — | 27 | 8 | no | — |
| 539 | D12 | — | 27 | 2 | no | — |
| 540 | D12 | — | 27 | 2 | no | — |
| 541 | D12 | — | 27 | 2 | no | — |
| 542 | D12 | — | 27 | 2 | no | — |
| 543 | D12 | — | 27 | 2 | no | — |
| 544 | D12 | — | 27 | 2 | no | — |
| 545 | D12 | — | 54 | 8 | no | — |
| 546 | D12 | — | 54 | 2 | no | — |
| 547 | D12 | — | 54 | 2 | no | — |
| 548 | C4×D3 | — | 3 | 2 | no | — |
| 549 | C4×D3 | — | 9 | 8 | no | — |
| 550 | C4×D3 | — | 9 | 2 | no | — |
| 551 | C4×D3 | — | 9 | 2 | no | — |
| 552 | C4×D3 | — | 27 | 2 | no | — |
| 553 | C4×D3 | — | 27 | 8 | no | — |
| 554 | C4×D3 | — | 27 | 2 | no | — |
| 555 | C4×D3 | — | 27 | 2 | no | — |
| 556 | C4×D3 | — | 54 | 8 | no | — |
| 557 | Dic6 | — | 9 | 8 | no | — |
| 558 | Dic6 | — | 9 | 2 | no | — |
| 559 | C2×C32 | — | 2 | 1 | no | — |
| 560 | C2×C32 | — | 2 | 1 | no | — |
| 561 | C2×C32 | — | 2 | 8 | no | — |
| 562 | C2×C32 | — | 2 | 8 | no | — |
| 563 | C2×C32 | — | 2 | 8 | no | — |
| 564 | C2×C32 | — | 2 | 4 | no | — |
| 565 | C2×C32 | — | 2 | 8 | no | — |
| 566 | C2×C32 | — | 4 | 4 | no | — |
| 567 | C2×C32 | — | 4 | 12 | no | — |
| 568 | C2×C32 | — | 4 | 8 | no | — |
| 569 | C2×C32 | — | 4 | 8 | no | — |
| 570 | C2×C32 | — | 4 | 8 | no | — |
| 571 | C2×C32 | — | 4 | 8 | no | — |
| 572 | C2×C32 | — | 4 | 24 | no | — |
| 573 | C2×C32 | — | 4 | 4 | no | — |
| 574 | C2×C32 | — | 6 | 2 | no | — |
| 575 | C2×C32 | — | 6 | 8 | no | — |
| 576 | C2×C32 | — | 12 | 8 | no | — |
| 577 | C2×C32 | — | 18 | 1 | no | — |
| 578 | C2×C32 | — | 18 | 1 | no | — |
| 579 | C2×C32 | C22×D32 | 1 | 8 | yes | — |
| 580 | C2×C32 | C22×D32 | 1 | 1 | yes | characteristic |
| 581 | C2×C32 | C23×C3⋊D3 | 1 | 1 | yes | characteristic |
| 582 | C3⋊D3 | — | 2 | 1 | no | — |
| 583 | C3⋊D3 | — | 2 | 1 | no | — |
| 584 | C3⋊D3 | — | 6 | 2 | no | — |
| 585 | C3⋊D3 | — | 6 | 8 | no | — |
| 586 | C3⋊D3 | — | 12 | 8 | no | — |
| 587 | C3⋊D3 | — | 18 | 16 | no | — |
| 588 | C3⋊D3 | — | 18 | 2 | no | — |
| 589 | C3⋊D3 | — | 18 | 8 | no | — |
| 590 | C3⋊D3 | — | 18 | 16 | no | — |
| 591 | C3⋊D3 | — | 18 | 8 | no | — |
| 592 | C3⋊D3 | — | 18 | 2 | no | — |
| 593 | C3⋊D3 | — | 36 | 8 | no | — |
| 594 | C3⋊D3 | — | 36 | 8 | no | — |
| 595 | C3⋊D3 | — | 36 | 8 | no | — |
| 596 | C3⋊D3 | — | 36 | 16 | no | — |
| 597 | C3⋊D3 | — | 36 | 48 | no | — |
| 598 | C3⋊D3 | — | 36 | 16 | no | — |
| 599 | C3×D3 | — | 2 | 8 | no | — |
| 600 | C3×D3 | — | 2 | 2 | no | — |
| 601 | C3×D3 | — | 4 | 8 | no | — |
| 602 | C3×D3 | — | 6 | 8 | no | — |
| 603 | C3×D3 | — | 6 | 8 | no | — |
| 604 | C3×D3 | — | 12 | 4 | no | — |
| 605 | C3×D3 | — | 12 | 4 | no | — |
| 606 | C3×D3 | — | 18 | 8 | no | — |
| 607 | C3×D3 | — | 18 | 2 | no | — |
| 608 | C3×D3 | — | 36 | 8 | no | — |
| 609 | #41 | — | 27 | 2 | no | — |
| 610 | #41 | — | 81 | 2 | no | — |
| 611 | #41 | — | 81 | 2 | no | — |
| 612 | C2×D4 | — | 9 | 1 | no | — |
| 613 | C2×D4 | — | 81 | 1 | no | — |
| 614 | C2×D4 | — | 81 | 2 | no | — |
| 615 | C2×D4 | — | 81 | 2 | no | — |
| 616 | C2×D4 | — | 81 | 2 | no | — |
| 617 | C2×D4 | — | 81 | 1 | no | — |
| 618 | C22×C3 | — | 2 | 1 | no | — |
| 619 | C22×C3 | — | 2 | 8 | no | — |
| 620 | C22×C3 | — | 3 | 8 | no | — |
| 621 | C22×C3 | — | 3 | 2 | no | — |
| 622 | C22×C3 | — | 4 | 4 | no | — |
| 623 | C22×C3 | — | 6 | 8 | no | — |
| 624 | C22×C3 | — | 9 | 4 | no | — |
| 625 | C22×C3 | — | 9 | 4 | no | — |
| 626 | C22×C3 | — | 27 | 2 | no | — |
| 627 | C22×C3 | — | 36 | 4 | no | — |
| 628 | C22×C3 | — | 36 | 4 | no | — |
| 629 | C22×C3 | D33 | 1 | 4 | yes | — |
| 630 | C22×C3 | C2×D3×C3⋊D3 | 1 | 2 | yes | — |
| 631 | C2×D3 | — | 3 | 2 | no | — |
| 632 | C2×D3 | — | 3 | 2 | no | — |
| 633 | C2×D3 | — | 6 | 1 | no | — |
| 634 | C2×D3 | — | 6 | 1 | no | — |
| 635 | C2×D3 | — | 9 | 8 | no | — |
| 636 | C2×D3 | — | 9 | 2 | no | — |
| 637 | C2×D3 | — | 12 | 2 | no | — |
| 638 | C2×D3 | — | 12 | 2 | no | — |
| 639 | C2×D3 | — | 12 | 2 | no | — |
| 640 | C2×D3 | — | 18 | 8 | no | — |
| 641 | C2×D3 | — | 27 | 8 | no | — |
| 642 | C2×D3 | — | 27 | 2 | no | — |
| 643 | C2×D3 | — | 27 | 2 | no | — |
| 644 | C2×D3 | — | 54 | 8 | no | — |
| 645 | C2×D3 | — | 54 | 2 | no | — |
| 646 | C2×D3 | — | 54 | 8 | no | — |
| 647 | C2×D3 | — | 108 | 2 | no | — |
| 648 | C2×D3 | — | 108 | 2 | no | — |
| 649 | C2×D3 | — | 108 | 4 | no | — |
| 650 | C2×D3 | — | 108 | 2 | no | — |
| 651 | C2×D3 | — | 108 | 8 | no | — |
| 652 | C2×D3 | — | 108 | 16 | no | — |
| 653 | C2×D3 | — | 108 | 2 | no | — |
| 654 | C2×D3 | — | 108 | 4 | no | — |
| 655 | C2×D3 | — | 108 | 16 | no | — |
| 656 | C2×D3 | — | 108 | 2 | no | — |
| 657 | C2×D3 | — | 108 | 16 | no | — |
| 658 | C2×D3 | — | 108 | 8 | no | — |
| 659 | C2×D3 | C2×D3×C3⋊D3 | 1 | 2 | yes | — |
| 660 | C3×C4 | — | 3 | 8 | no | — |
| 661 | C3×C4 | — | 3 | 2 | no | — |
| 662 | C3×C4 | — | 6 | 8 | no | — |
| 663 | C3×C4 | — | 9 | 2 | no | — |
| 664 | C3×C4 | — | 9 | 2 | no | — |
| 665 | C3×C4 | — | 18 | 2 | no | — |
| 666 | C3×C4 | — | 27 | 2 | no | — |
| 667 | Dic3 | — | 3 | 8 | no | — |
| 668 | Dic3 | — | 9 | 8 | no | — |
| 669 | Dic3 | — | 9 | 2 | no | — |
| 670 | Dic3 | — | 18 | 8 | no | — |
| 671 | Dic3 | C2×D3×C3⋊D3 | 1 | 2 | yes | — |
| 672 | C32 | — | 2 | 8 | no | — |
| 673 | C32 | — | 2 | 8 | no | — |
| 674 | C32 | — | 2 | 4 | no | — |
| 675 | C32 | — | 4 | 4 | no | — |
| 676 | C32 | — | 4 | 12 | no | — |
| 677 | C32 | — | 4 | 4 | no | — |
| 678 | C32 | #64308 | 1 | 1 | yes | characteristic, complemented |
| 679 | C32 | #64314 | 1 | 8 | yes | complemented |
| 680 | C32 | #64361 | 1 | 1 | yes | characteristic, complemented |
| 681 | C23 | — | 9 | 1 | no | — |
| 682 | C23 | — | 9 | 1 | no | — |
| 683 | C23 | — | 81 | 2 | no | — |
| 684 | C23 | — | 81 | 1 | no | — |
| 685 | C23 | — | 81 | 1 | no | — |
| 686 | Q8 | — | 27 | 2 | no | — |
| 687 | D4 | — | 3 | 2 | no | — |
| 688 | D4 | — | 9 | 2 | no | — |
| 689 | D4 | — | 27 | 2 | no | — |
| 690 | D4 | — | 27 | 2 | no | — |
| 691 | D4 | — | 81 | 2 | no | — |
| 692 | D4 | — | 81 | 2 | no | — |
| 693 | D4 | — | 81 | 2 | no | — |
| 694 | D4 | — | 81 | 2 | no | — |
| 695 | D4 | — | 81 | 2 | no | — |
| 696 | C2×C4 | — | 9 | 1 | no | — |
| 697 | C2×C4 | — | 9 | 1 | no | — |
| 698 | C2×C4 | — | 27 | 2 | no | — |
| 699 | C2×C4 | — | 27 | 2 | no | — |
| 700 | C2×C4 | — | 81 | 2 | no | — |
| 701 | C2×C4 | — | 81 | 1 | no | — |
| 702 | C2×C3 | — | 2 | 2 | no | — |
| 703 | C2×C3 | — | 2 | 2 | no | — |
| 704 | C2×C3 | — | 2 | 4 | no | — |
| 705 | C2×C3 | — | 2 | 8 | no | — |
| 706 | C2×C3 | — | 2 | 1 | no | — |
| 707 | C2×C3 | — | 4 | 8 | no | — |
| 708 | C2×C3 | — | 4 | 8 | no | — |
| 709 | C2×C3 | — | 4 | 4 | no | — |
| 710 | C2×C3 | — | 6 | 2 | no | — |
| 711 | C2×C3 | — | 6 | 8 | no | — |
| 712 | C2×C3 | — | 12 | 8 | no | — |
| 713 | C2×C3 | — | 18 | 4 | no | — |
| 714 | C2×C3 | — | 18 | 4 | no | — |
| 715 | C2×C3 | — | 54 | 2 | no | — |
| 716 | C2×C3 | C2×D33 | 1 | 4 | yes | — |
| 717 | C2×C3 | C22×D3×C3⋊D3 | 1 | 2 | yes | — |
| 718 | D3 | — | 2 | 2 | no | — |
| 719 | D3 | — | 6 | 2 | no | — |
| 720 | D3 | — | 6 | 2 | no | — |
| 721 | D3 | — | 12 | 1 | no | — |
| 722 | D3 | — | 12 | 1 | no | — |
| 723 | D3 | — | 18 | 2 | no | — |
| 724 | D3 | — | 18 | 8 | no | — |
| 725 | D3 | — | 36 | 8 | no | — |
| 726 | D3 | — | 54 | 16 | no | — |
| 727 | D3 | — | 54 | 2 | no | — |
| 728 | D3 | — | 54 | 2 | no | — |
| 729 | D3 | — | 54 | 8 | no | — |
| 730 | D3 | — | 108 | 2 | no | — |
| 731 | D3 | — | 108 | 8 | no | — |
| 732 | D3 | — | 108 | 16 | no | — |
| 733 | C22 | — | 3 | 2 | no | — |
| 734 | C22 | — | 9 | 1 | no | — |
| 735 | C22 | — | 9 | 1 | no | — |
| 736 | C22 | — | 27 | 2 | no | — |
| 737 | C22 | — | 36 | 1 | no | — |
| 738 | C22 | — | 36 | 1 | no | — |
| 739 | C22 | — | 324 | 1 | no | — |
| 740 | C22 | — | 324 | 2 | no | — |
| 741 | C22 | — | 324 | 1 | no | — |
| 742 | C22 | — | 81 | 2 | no | — |
| 743 | C22 | D32×C3⋊D3 | 1 | 1 | yes | characteristic |
| 744 | C4 | — | 3 | 2 | no | — |
| 745 | C4 | — | 9 | 2 | no | — |
| 746 | C4 | — | 27 | 2 | no | — |
| 747 | C3 | — | 2 | 1 | no | — |
| 748 | C3 | — | 2 | 8 | no | — |
| 749 | C3 | — | 4 | 4 | no | — |
| 750 | C3 | #11724420 | 1 | 4 | yes | complemented |
| 751 | C3 | #11724588 | 1 | 2 | yes | complemented |
| 752 | C2 | — | 2 | 1 | no | — |
| 753 | C2 | — | 6 | 2 | no | — |
| 754 | C2 | — | 18 | 1 | no | — |
| 755 | C2 | — | 18 | 1 | no | — |
| 756 | C2 | — | 54 | 2 | no | — |
| 757 | C2 | — | 162 | 2 | no | — |
| 758 | C2 | C2×D32×C3⋊D3 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D32×C3⋊D3 |
| commutator, socle, cosocle | C2×C34 | C24 |
| Fitting | C22×C34 | C23 |
| hypercenter | C22 | D32×C3⋊D3 |
| hypocenter | C34 | H(5,𝔽2) |
| LCS | G ▷ C2×C34 ▷ C34 | |
| UCS | C1 ◁ C2 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13049721 | C2 | semidirect |
| 2. C2×#10620152 | C2 | semidirect |
| 3. #13049685 | C2 | semidirect |
| 4. C3×#89028 | C2 | semidirect |
| 5. C32×#3811 | C2 | semidirect |
| 6. #13049523 | C2 | semidirect |
| 7. #13049513 | C2 | semidirect |
| 8. #13049502 | C2 | semidirect |
| 9. D3×#6291 | C2 | semidirect |
| 12. C22×C3⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 13. C22×C32×C3⋊D3 | C22 | semidirect |
| 14. C2×C3⋊#1113 | C22 | semidirect |
| 15. C2×D3×C3⋊(C3⋊D3) | C22 | semidirect |
| 16. C2×C32×D32 | C22 | semidirect |
| 17. C3×#6312 | C22 | semidirect |
| 18. C2×C32×C3⋊Dic3 | C22 | semidirect |
| 19. C33×#67 | C22 | semidirect |
| 20. #10620157 | C22 | semidirect |
| 21. #10620155 | C22 | semidirect |
| 22. #10620152 | C22 | semidirect |
| 23. #10620152 | C22 | semidirect |
| 24. #10620147 | C22 | semidirect |
| 25. #10620146 | C22 | semidirect |
| 26. #10620144 | C22 | semidirect |
| 27. C3×#6293 | C22 | semidirect |
| 28. C3×#6291 | C22 | semidirect |
| 29. C3×#6289 | C22 | semidirect |
| 30. C3×D3×C3⋊Dic3 | C22 | semidirect |
| 31. C32×#626 | C22 | semidirect |
| 32. C32×#624 | C22 | semidirect |
| 48. #89028 | D3 | semidirect |
| 53. C3×#3811 | D3 | semidirect |
| 82. C22×C3×C3⋊D3 | C2×D3 | semidirect |
| 91. C2×C3×D32 | C2×D3 | semidirect |
| 94. #6312 | C2×D3 | semidirect |
| 103. C2×C3×C3⋊Dic3 | C2×D3 | semidirect |
| 108. C32×#67 | C2×D3 | semidirect |
| 109. C32×#67 | C2×D3 | semidirect |
| 115. #6293 | C2×D3 | semidirect |
| 131. #6291 | C2×D3 | semidirect |
| 136. #6289 | C2×D3 | semidirect |
| 138. D3×C3⋊Dic3 | C2×D3 | semidirect |
| 141. C3×#626 | C2×D3 | semidirect |
| 143. C3×#624 | C2×D3 | semidirect |
| 172. #3811 | C3⋊D3 | semidirect |
| 244. C34 | H(5,𝔽2) | semidirect |
| 260. C22×C3⋊D3 | C2×C3⋊D3 | semidirect |
| 269. C2×D32 | C2×C3⋊D3 | semidirect |
| 288. C2×C3⋊Dic3 | D32 | semidirect |
| 305. C3×#67 | D32 | semidirect |
| 306. C3×#67 | C2×C3⋊D3 | semidirect |
| 334. #626 | C2×C3⋊D3 | semidirect |
| 341. #624 | C2×C3⋊D3 | semidirect |
| 488. C33 | #1004 | semidirect |
| 489. C33 | #1009 | semidirect |
| 531. #67 | D3×C3⋊D3 | semidirect |
| 678. C32 | #64308 | semidirect |
| 679. C32 | #64314 | semidirect |
| 680. C32 | #64361 | semidirect |
| 750. C3 | #11724420 | semidirect |
| 751. C3 | #11724588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13049721 | 2 |
| C2×#10620152 | 2 |
| #13049685 | 2 |
| C3×#89028 | 2 |
| C32×#3811 | 2 |
| #13049523 | 2 |
| #13049513 | 2 |
| #13049502 | 2 |
| D3×#6291 | 2 |
| #11724588 | 3 |
| #11724420 | 3 |