Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
5782 conjugacy classes of subgroups.
The subgroup lattice has 828 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×#239 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5674 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×D3×#121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#2436 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #84066 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #82958 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #82653 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #76863 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #76809 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #76626 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #76482 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #74935 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #74884 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #73587 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #73561 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #35250 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C23×C3×Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | C22×#239 | — | 2 | 16 | no | — |
| 19 | C22×#239 | — | 2 | 8 | no | — |
| 20 | C22×#239 | C22 | 1 | 2 | yes | — |
| 21 | C22×#239 | C22 | 1 | 2 | yes | — |
| 22 | C22×#239 | C22 | 1 | 2 | yes | complemented |
| 23 | C22×#239 | C22 | 1 | 2 | yes | complemented |
| 24 | C22×D3×D4 | C22 | 1 | 2 | yes | — |
| 25 | C22×D3×D4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C23×D12 | C22 | 1 | 2 | yes | — |
| 27 | C23×D12 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C23×C4×D3 | C22 | 1 | 1 | yes | characteristic |
| 29 | C23×C4×D3 | C22 | 1 | 2 | yes | complemented |
| 30 | C2×C3×#124 | C22 | 1 | 2 | yes | complemented |
| 31 | C2×C3×#121 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#947 | C22 | 1 | 2 | yes | complemented |
| 33 | C2×#940 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#939 | C22 | 1 | 2 | yes | — |
| 35 | C2×#938 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#937 | C22 | 1 | 4 | yes | complemented |
| 37 | C2×#930 | C22 | 1 | 1 | yes | characteristic |
| 38 | #5674 | — | 2 | 16 | no | — |
| 39 | D3×#121 | — | 2 | 8 | no | — |
| 40 | C2×#895 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×D3×C4⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×#884 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#884 | C22 | 1 | 8 | yes | complemented |
| 44 | C2×#882 | C22 | 1 | 8 | yes | complemented |
| 45 | C2×#882 | C22 | 1 | 4 | yes | complemented |
| 46 | C2×D3×C22⋊C4 | C22 | 1 | 2 | yes | complemented |
| 47 | C2×#874 | C22 | 1 | 2 | yes | complemented |
| 48 | C2×#872 | C22 | 1 | 2 | yes | complemented |
| 49 | C3×#393 | C22 | 1 | 4 | yes | complemented |
| 50 | C3×#391 | C22 | 1 | 2 | yes | complemented |
| 51 | C3×#386 | C22 | 1 | 4 | yes | complemented |
| 52 | C3×C4×C22⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #5231 | C22 | 1 | 4 | yes | complemented |
| 54 | #5229 | C22 | 1 | 2 | yes | complemented |
| 55 | #5213 | C22 | 1 | 4 | yes | complemented |
| 56 | C4×#217 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #4988 | C22 | 1 | 2 | yes | complemented |
| 58 | #4960 | C22 | 1 | 8 | yes | complemented |
| 59 | #4960 | C22 | 1 | 4 | yes | complemented |
| 60 | #4956 | C22 | 1 | 8 | yes | complemented |
| 61 | #4955 | C22 | 1 | 2 | yes | — |
| 62 | #4942 | C22 | 1 | 2 | yes | complemented |
| 63 | #4939 | C22 | 1 | 2 | yes | complemented |
| 64 | C4×(C2×D3)⋊C4 | C22 | 1 | 2 | yes | complemented |
| 65 | #4671 | C22 | 1 | 4 | yes | complemented |
| 66 | #4671 | C22 | 1 | 8 | yes | complemented |
| 67 | #4667 | C22 | 1 | 2 | yes | complemented |
| 68 | #4667 | C22 | 1 | 8 | yes | complemented |
| 69 | #4665 | C22 | 1 | 8 | yes | complemented |
| 70 | #4665 | C22 | 1 | 8 | yes | complemented |
| 71 | #4664 | C22 | 1 | 2 | yes | complemented |
| 72 | C23×#41 | — | 3 | 1 | no | — |
| 73 | C2×#535 | — | 3 | 2 | no | — |
| 74 | C22×#121 | — | 3 | 1 | no | — |
| 75 | #2847 | — | 3 | 4 | no | — |
| 76 | #2615 | — | 3 | 4 | no | — |
| 77 | #2436 | — | 3 | 1 | no | — |
| 78 | #2436 | D3 | 1 | 1 | yes | characteristic, complemented |
| 79 | #2433 | — | 3 | 1 | no | — |
| 80 | #2433 | — | 3 | 1 | no | — |
| 81 | #2431 | — | 3 | 2 | no | — |
| 82 | #2431 | — | 3 | 2 | no | — |
| 83 | #2404 | — | 3 | 4 | no | — |
| 84 | #2403 | — | 3 | 4 | no | — |
| 85 | #2311 | — | 3 | 2 | no | — |
| 86 | #2280 | — | 3 | 1 | no | — |
| 87 | C24×D3 | C23 | 1 | 2 | yes | — |
| 88 | C24×D3 | C23 | 1 | 1 | yes | characteristic |
| 89 | C24×D3 | C23 | 1 | 2 | yes | — |
| 90 | C22×C3×Q8 | — | 2 | 8 | no | — |
| 91 | C22×C3×Q8 | — | 2 | 4 | no | — |
| 92 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 93 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 94 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 95 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 96 | C23×C3×C4 | C23 | 1 | 2 | yes | — |
| 97 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×#67 | C23 | 1 | 2 | yes | — |
| 99 | C22×#67 | C23 | 1 | 2 | yes | — |
| 100 | C22×#67 | C23 | 1 | 2 | yes | — |
| 101 | C22×#67 | C23 | 1 | 8 | yes | — |
| 102 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#239 | — | 2 | 128 | no | — |
| 104 | C2×#239 | — | 2 | 8 | no | — |
| 105 | C2×#239 | — | 2 | 16 | no | — |
| 106 | C2×#239 | — | 2 | 8 | no | — |
| 107 | C2×#239 | — | 2 | 8 | no | — |
| 108 | C2×#239 | — | 2 | 8 | no | — |
| 109 | C2×#239 | — | 2 | 8 | no | — |
| 110 | C2×#239 | — | 2 | 8 | no | — |
| 111 | C2×#239 | — | 2 | 8 | no | — |
| 112 | C2×#239 | — | 2 | 16 | no | — |
| 113 | C2×#239 | D4 | 1 | 16 | yes | complemented |
| 114 | C2×D3×D4 | — | 2 | 8 | no | — |
| 115 | C2×D3×D4 | — | 2 | 8 | no | — |
| 116 | C2×D3×D4 | — | 2 | 4 | no | — |
| 117 | C2×D3×D4 | — | 4 | 8 | no | — |
| 118 | C22×D12 | — | 2 | 8 | no | — |
| 119 | C22×D12 | — | 2 | 4 | no | — |
| 120 | C22×D12 | — | 2 | 16 | no | — |
| 121 | C22×D12 | — | 2 | 8 | no | — |
| 122 | C22×D12 | C23 | 1 | 4 | yes | — |
| 123 | C22×D12 | C23 | 1 | 2 | yes | — |
| 124 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 125 | C22×D12 | C23 | 1 | 4 | yes | — |
| 126 | C22×D12 | C23 | 1 | 2 | yes | — |
| 127 | C22×D12 | C23 | 1 | 8 | yes | — |
| 128 | C22×D12 | C23 | 1 | 2 | yes | — |
| 129 | C22×C4×D3 | — | 2 | 8 | no | — |
| 130 | C22×C4×D3 | — | 2 | 8 | no | — |
| 131 | C22×C4×D3 | — | 2 | 16 | no | — |
| 132 | C22×C4×D3 | D4 | 1 | 8 | yes | complemented |
| 133 | C22×C4×D3 | C23 | 1 | 4 | yes | — |
| 134 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 136 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×D3 | C23 | 1 | 4 | yes | — |
| 138 | C22×C4×D3 | C23 | 1 | 2 | yes | — |
| 139 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 140 | C3×#124 | — | 2 | 8 | no | — |
| 141 | C3×#121 | — | 2 | 4 | no | — |
| 142 | C2×C3×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 143 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 144 | C2×C3×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 145 | C2×C3×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 146 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 147 | C2×#217 | C23 | 1 | 2 | yes | — |
| 148 | C2×#217 | C23 | 1 | 2 | yes | — |
| 149 | #947 | — | 2 | 8 | no | — |
| 150 | #940 | — | 2 | 8 | no | — |
| 151 | #939 | — | 2 | 8 | no | — |
| 152 | #938 | — | 2 | 4 | no | — |
| 153 | #937 | — | 4 | 8 | no | — |
| 154 | #930 | — | 2 | 4 | no | — |
| 155 | C2×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 156 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 157 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 158 | C2×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 159 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 160 | C2×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 161 | C2×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 162 | C2×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 163 | C2×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 164 | C2×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 165 | C2×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 166 | #895 | — | 2 | 4 | no | — |
| 167 | D3×C4⋊C4 | — | 2 | 4 | no | — |
| 168 | #884 | — | 2 | 8 | no | — |
| 169 | #884 | — | 2 | 32 | no | — |
| 170 | #882 | — | 2 | 32 | no | — |
| 171 | #882 | — | 4 | 8 | no | — |
| 172 | D3×C22⋊C4 | — | 2 | 8 | no | — |
| 173 | #874 | — | 2 | 8 | no | — |
| 174 | #872 | — | 2 | 8 | no | — |
| 175 | C3×#95 | C23 | 1 | 2 | yes | — |
| 176 | C3×#95 | C23 | 1 | 8 | yes | — |
| 177 | C3⋊#95 | C23 | 1 | 4 | yes | — |
| 178 | C3⋊#95 | C23 | 1 | 2 | yes | — |
| 179 | C3⋊#95 | C23 | 1 | 8 | yes | — |
| 180 | C22×#41 | — | 3 | 2 | no | — |
| 181 | C22×#41 | — | 3 | 2 | no | — |
| 182 | C22×#41 | — | 3 | 2 | no | — |
| 183 | C22×#41 | — | 3 | 2 | no | — |
| 184 | C22×#41 | — | 6 | 8 | no | — |
| 185 | C22×#41 | — | 6 | 16 | no | — |
| 186 | C23×Q8 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 187 | C23×D4 | — | 3 | 1 | no | — |
| 188 | C23×D4 | — | 3 | 2 | no | — |
| 189 | C23×D4 | — | 3 | 2 | no | — |
| 190 | C23×D4 | — | 3 | 1 | no | — |
| 191 | C24×C4 | — | 3 | 1 | no | — |
| 192 | C24×C4 | — | 3 | 2 | no | — |
| 193 | #535 | — | 6 | 16 | no | — |
| 194 | C2×#127 | — | 3 | 2 | no | — |
| 195 | C2×#127 | — | 3 | 2 | no | — |
| 196 | C2×#124 | — | 3 | 2 | no | — |
| 197 | C2×#124 | C2×D3 | 1 | 2 | yes | complemented |
| 198 | C2×#121 | — | 3 | 2 | no | — |
| 199 | C2×#121 | — | 3 | 1 | no | — |
| 200 | C2×#121 | — | 3 | 1 | no | — |
| 201 | C2×#121 | — | 3 | 1 | no | — |
| 202 | C2×#121 | — | 3 | 8 | no | — |
| 203 | C2×#121 | — | 3 | 2 | no | — |
| 204 | C2×#121 | — | 6 | 8 | no | — |
| 205 | C2×#121 | C2×D3 | 1 | 1 | yes | characteristic |
| 206 | C2×#120 | — | 3 | 4 | no | — |
| 207 | C2×#120 | — | 3 | 8 | no | — |
| 208 | C2×#120 | — | 3 | 4 | no | — |
| 209 | C2×#117 | — | 3 | 2 | no | — |
| 210 | C22×C4⋊C4 | — | 3 | 1 | no | — |
| 211 | C22×C22⋊C4 | — | 3 | 2 | no | — |
| 212 | #393 | — | 3 | 4 | no | — |
| 213 | #393 | C2×D3 | 1 | 4 | yes | complemented |
| 214 | #392 | — | 3 | 8 | no | — |
| 215 | #392 | — | 3 | 4 | no | — |
| 216 | #392 | — | 3 | 8 | no | — |
| 217 | #392 | — | 3 | 4 | no | — |
| 218 | #391 | — | 3 | 2 | no | — |
| 219 | #391 | C2×D3 | 1 | 2 | yes | complemented |
| 220 | #390 | — | 3 | 2 | no | — |
| 221 | #390 | — | 3 | 2 | no | — |
| 222 | #386 | — | 3 | 4 | no | — |
| 223 | #386 | — | 3 | 8 | no | — |
| 224 | #386 | — | 3 | 8 | no | — |
| 225 | #386 | — | 3 | 8 | no | — |
| 226 | #386 | C2×D3 | 1 | 4 | yes | complemented |
| 227 | #381 | — | 3 | 2 | no | — |
| 228 | #380 | — | 3 | 2 | no | — |
| 229 | #380 | — | 3 | 8 | no | — |
| 230 | #380 | — | 3 | 2 | no | — |
| 231 | #379 | — | 3 | 2 | no | — |
| 232 | C4×C22⋊C4 | — | 3 | 1 | no | — |
| 233 | C4×C22⋊C4 | — | 3 | 2 | no | — |
| 234 | C4×C22⋊C4 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 235 | C24×C3 | C24 | 1 | 2 | yes | — |
| 236 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 237 | C23×D3 | — | 2 | 4 | no | — |
| 238 | C23×D3 | — | 2 | 4 | no | — |
| 239 | C23×D3 | — | 2 | 8 | no | — |
| 240 | C23×D3 | — | 2 | 4 | no | — |
| 241 | C23×D3 | — | 2 | 8 | no | — |
| 242 | C23×D3 | — | 2 | 4 | no | — |
| 243 | C23×D3 | — | 2 | 8 | no | — |
| 244 | C23×D3 | — | 4 | 2 | no | — |
| 245 | C23×D3 | — | 4 | 4 | no | — |
| 246 | C23×D3 | — | 4 | 4 | no | — |
| 247 | C23×D3 | — | 4 | 4 | no | — |
| 248 | C23×D3 | C2×D4 | 1 | 4 | yes | — |
| 249 | C23×D3 | C24 | 1 | 2 | yes | — |
| 250 | C23×D3 | C24 | 1 | 4 | yes | — |
| 251 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 252 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 253 | C2×C3×Q8 | — | 2 | 32 | no | — |
| 254 | C2×C3×Q8 | — | 2 | 8 | no | — |
| 255 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 256 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 257 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 258 | C2×C3×Q8 | C2×D4 | 1 | 8 | yes | complemented |
| 259 | C2×C3×D4 | — | 2 | 4 | no | — |
| 260 | C2×C3×D4 | — | 2 | 8 | no | — |
| 261 | C2×C3×D4 | — | 2 | 2 | no | — |
| 262 | C2×C3×D4 | — | 2 | 4 | no | — |
| 263 | C22×C3×C4 | — | 2 | 4 | no | — |
| 264 | C22×C3×C4 | — | 2 | 8 | no | — |
| 265 | C22×C3×C4 | — | 2 | 4 | no | — |
| 266 | C22×C3×C4 | C2×D4 | 1 | 4 | yes | — |
| 267 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 268 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 269 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 270 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 271 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×#67 | — | 2 | 4 | no | — |
| 273 | C2×#67 | — | 2 | 8 | no | — |
| 274 | C2×#67 | — | 2 | 4 | no | — |
| 275 | C2×#67 | — | 2 | 16 | no | — |
| 276 | C2×#67 | — | 2 | 8 | no | — |
| 277 | C2×#67 | — | 2 | 4 | no | — |
| 278 | C2×#67 | — | 4 | 4 | no | — |
| 279 | C2×#67 | — | 4 | 8 | no | — |
| 280 | C2×#67 | — | 4 | 8 | no | — |
| 281 | C22×Dic3 | — | 2 | 4 | no | — |
| 282 | C22×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 283 | C22×Dic3 | C24 | 1 | 4 | yes | — |
| 284 | C22×Dic3 | C24 | 1 | 2 | yes | — |
| 285 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 286 | C22×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 287 | #239 | — | 2 | 64 | no | — |
| 288 | #239 | — | 2 | 64 | no | — |
| 289 | #239 | — | 2 | 64 | no | — |
| 290 | #239 | — | 2 | 64 | no | — |
| 291 | D3×D4 | — | 4 | 32 | no | — |
| 292 | D3×D4 | — | 4 | 16 | no | — |
| 293 | C2×D12 | — | 2 | 64 | no | — |
| 294 | C2×D12 | — | 2 | 32 | no | — |
| 295 | C2×D12 | — | 2 | 8 | no | — |
| 296 | C2×D12 | — | 2 | 8 | no | — |
| 297 | C2×D12 | — | 2 | 8 | no | — |
| 298 | C2×D12 | — | 2 | 8 | no | — |
| 299 | C2×D12 | — | 2 | 8 | no | — |
| 300 | C2×D12 | — | 2 | 8 | no | — |
| 301 | C2×D12 | — | 2 | 4 | no | — |
| 302 | C2×D12 | — | 2 | 4 | no | — |
| 303 | C2×D12 | — | 2 | 4 | no | — |
| 304 | C2×D12 | — | 2 | 4 | no | — |
| 305 | C2×D12 | — | 2 | 4 | no | — |
| 306 | C2×D12 | — | 2 | 2 | no | — |
| 307 | C2×D12 | — | 2 | 16 | no | — |
| 308 | C2×D12 | — | 4 | 4 | no | — |
| 309 | C2×D12 | — | 4 | 8 | no | — |
| 310 | C2×D12 | — | 4 | 8 | no | — |
| 311 | C2×D12 | C2×D4 | 1 | 16 | yes | — |
| 312 | C2×D12 | C2×D4 | 1 | 8 | yes | complemented |
| 313 | C2×C4×D3 | — | 2 | 64 | no | — |
| 314 | C2×C4×D3 | — | 2 | 8 | no | — |
| 315 | C2×C4×D3 | — | 2 | 4 | no | — |
| 316 | C2×C4×D3 | — | 2 | 8 | no | — |
| 317 | C2×C4×D3 | — | 2 | 4 | no | — |
| 318 | C2×C4×D3 | — | 2 | 8 | no | — |
| 319 | C2×C4×D3 | — | 2 | 4 | no | — |
| 320 | C2×C4×D3 | — | 2 | 8 | no | — |
| 321 | C2×C4×D3 | — | 2 | 8 | no | — |
| 322 | C2×C4×D3 | — | 2 | 32 | no | — |
| 323 | C2×C4×D3 | — | 2 | 4 | no | — |
| 324 | C2×C4×D3 | — | 4 | 4 | no | — |
| 325 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 326 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 327 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 328 | C2×C4×D3 | C2×D4 | 1 | 8 | yes | — |
| 329 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 330 | C2×C4×D3 | C2×D4 | 1 | 16 | yes | complemented |
| 331 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 332 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 333 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 334 | C3×C22⋊C4 | — | 2 | 16 | no | — |
| 335 | C3×C42 | — | 2 | 4 | no | — |
| 336 | #217 | — | 2 | 4 | no | — |
| 337 | #217 | — | 2 | 4 | no | — |
| 338 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 339 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 340 | (C2×D3)⋊C4 | — | 2 | 16 | no | — |
| 341 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 342 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 343 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 344 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 345 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 346 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 347 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 348 | C4×Dic3 | — | 2 | 4 | no | — |
| 349 | C25 | — | 3 | 1 | no | — |
| 350 | C25 | — | 3 | 2 | no | — |
| 351 | C25 | — | 3 | 2 | no | — |
| 352 | C2×#41 | — | 3 | 16 | no | — |
| 353 | C2×#41 | — | 6 | 8 | no | — |
| 354 | C2×#41 | — | 6 | 8 | no | — |
| 355 | C2×#41 | — | 6 | 8 | no | — |
| 356 | C2×#41 | — | 6 | 8 | no | — |
| 357 | C2×#41 | — | 6 | 8 | no | — |
| 358 | C2×#41 | — | 6 | 16 | no | — |
| 359 | C2×#41 | — | 6 | 16 | no | — |
| 360 | C2×#41 | — | 6 | 8 | no | — |
| 361 | C2×#41 | — | 6 | 128 | no | — |
| 362 | C2×#41 | — | 6 | 8 | no | — |
| 363 | C22×Q8 | — | 2 | 8 | no | — |
| 364 | C22×Q8 | — | 2 | 4 | no | — |
| 365 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 366 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 367 | C22×D4 | — | 3 | 2 | no | — |
| 368 | C22×D4 | — | 3 | 2 | no | — |
| 369 | C22×D4 | — | 3 | 8 | no | — |
| 370 | C22×D4 | — | 3 | 2 | no | — |
| 371 | C22×D4 | — | 3 | 4 | no | — |
| 372 | C22×D4 | — | 3 | 2 | no | — |
| 373 | C22×D4 | — | 3 | 1 | no | — |
| 374 | C22×D4 | — | 3 | 4 | no | — |
| 375 | C22×D4 | — | 3 | 2 | no | — |
| 376 | C22×D4 | — | 3 | 8 | no | — |
| 377 | C22×D4 | — | 3 | 2 | no | — |
| 378 | C22×D4 | — | 6 | 16 | no | — |
| 379 | C22×D4 | — | 6 | 8 | no | — |
| 380 | C22×D4 | — | 6 | 8 | no | — |
| 381 | C22×D4 | — | 6 | 4 | no | — |
| 382 | C22×D4 | — | 6 | 8 | no | — |
| 383 | C22×D4 | — | 6 | 8 | no | — |
| 384 | C22×D4 | — | 6 | 4 | no | — |
| 385 | C22×D4 | — | 12 | 8 | no | — |
| 386 | C22×D4 | C22×D3 | 1 | 2 | yes | — |
| 387 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 388 | C23×C4 | — | 3 | 1 | no | — |
| 389 | C23×C4 | — | 3 | 1 | no | — |
| 390 | C23×C4 | — | 3 | 8 | no | — |
| 391 | C23×C4 | — | 3 | 1 | no | — |
| 392 | C23×C4 | — | 3 | 1 | no | — |
| 393 | C23×C4 | — | 3 | 1 | no | — |
| 394 | C23×C4 | — | 3 | 4 | no | — |
| 395 | C23×C4 | — | 3 | 4 | no | — |
| 396 | C23×C4 | — | 3 | 2 | no | — |
| 397 | C23×C4 | — | 6 | 8 | no | — |
| 398 | C23×C4 | — | 6 | 8 | no | — |
| 399 | C23×C4 | — | 6 | 16 | no | — |
| 400 | C23×C4 | C22×D3 | 1 | 2 | yes | — |
| 401 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 402 | #127 | — | 6 | 8 | no | — |
| 403 | #127 | — | 6 | 8 | no | — |
| 404 | #124 | — | 2 | 8 | no | — |
| 405 | #124 | — | 6 | 8 | no | — |
| 406 | #121 | — | 2 | 4 | no | — |
| 407 | #121 | — | 6 | 8 | no | — |
| 408 | #121 | — | 6 | 32 | no | — |
| 409 | #121 | — | 6 | 4 | no | — |
| 410 | #121 | — | 6 | 4 | no | — |
| 411 | #121 | — | 6 | 8 | no | — |
| 412 | #121 | — | 6 | 4 | no | — |
| 413 | #120 | — | 6 | 32 | no | — |
| 414 | #120 | — | 12 | 8 | no | — |
| 415 | #120 | — | 12 | 8 | no | — |
| 416 | #117 | — | 6 | 8 | no | — |
| 417 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 418 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 419 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 420 | C2×C4⋊C4 | — | 6 | 4 | no | — |
| 421 | C2×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 422 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 423 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 424 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 425 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 426 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 427 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 428 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 429 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 430 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 431 | C2×C22⋊C4 | — | 6 | 8 | no | — |
| 432 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 433 | C2×C22⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 434 | C2×C22⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 435 | C2×C42 | — | 3 | 2 | no | — |
| 436 | C2×C42 | C22×D3 | 1 | 2 | yes | — |
| 437 | #95 | — | 3 | 4 | no | — |
| 438 | #95 | — | 3 | 2 | no | — |
| 439 | #95 | — | 3 | 8 | no | — |
| 440 | #95 | C22×D3 | 1 | 2 | yes | — |
| 441 | #95 | C22×D3 | 1 | 8 | yes | — |
| 442 | C23×C3 | — | 2 | 2 | no | — |
| 443 | C23×C3 | — | 2 | 2 | no | — |
| 444 | C23×C3 | — | 2 | 2 | no | — |
| 445 | C23×C3 | — | 2 | 4 | no | — |
| 446 | C23×C3 | — | 2 | 4 | no | — |
| 447 | C23×C3 | — | 2 | 4 | no | — |
| 448 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 449 | C23×C3 | H(5,𝔽2) | 1 | 4 | yes | — |
| 450 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 451 | C22×D3 | — | 2 | 2 | no | — |
| 452 | C22×D3 | — | 2 | 2 | no | — |
| 453 | C22×D3 | — | 2 | 16 | no | — |
| 454 | C22×D3 | — | 2 | 8 | no | — |
| 455 | C22×D3 | — | 2 | 4 | no | — |
| 456 | C22×D3 | — | 2 | 4 | no | — |
| 457 | C22×D3 | — | 2 | 2 | no | — |
| 458 | C22×D3 | — | 2 | 8 | no | — |
| 459 | C22×D3 | — | 2 | 2 | no | — |
| 460 | C22×D3 | — | 2 | 2 | no | — |
| 461 | C22×D3 | — | 2 | 8 | no | — |
| 462 | C22×D3 | — | 2 | 8 | no | — |
| 463 | C22×D3 | — | 2 | 4 | no | — |
| 464 | C22×D3 | — | 2 | 2 | no | — |
| 465 | C22×D3 | — | 2 | 4 | no | — |
| 466 | C22×D3 | — | 2 | 4 | no | — |
| 467 | C22×D3 | — | 4 | 4 | no | — |
| 468 | C22×D3 | — | 4 | 16 | no | — |
| 469 | C22×D3 | — | 4 | 32 | no | — |
| 470 | C22×D3 | — | 4 | 8 | no | — |
| 471 | C22×D3 | — | 4 | 8 | no | — |
| 472 | C22×D3 | — | 4 | 8 | no | — |
| 473 | C22×D3 | — | 4 | 8 | no | — |
| 474 | C22×D3 | — | 4 | 8 | no | — |
| 475 | C22×D3 | — | 8 | 16 | no | — |
| 476 | C22×D3 | C22×D4 | 1 | 8 | yes | — |
| 477 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 478 | C22×D3 | C22×D4 | 1 | 4 | yes | — |
| 479 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 480 | C3×Q8 | — | 2 | 16 | no | — |
| 481 | C3×Q8 | — | 2 | 16 | no | — |
| 482 | C3×D4 | — | 4 | 8 | no | — |
| 483 | C3×D4 | — | 4 | 4 | no | — |
| 484 | C2×C3×C4 | — | 2 | 16 | no | — |
| 485 | C2×C3×C4 | — | 2 | 4 | no | — |
| 486 | C2×C3×C4 | — | 2 | 4 | no | — |
| 487 | C2×C3×C4 | — | 2 | 2 | no | — |
| 488 | C2×C3×C4 | — | 2 | 8 | no | — |
| 489 | C2×C3×C4 | — | 2 | 4 | no | — |
| 490 | C2×C3×C4 | — | 2 | 2 | no | — |
| 491 | C2×C3×C4 | — | 2 | 4 | no | — |
| 492 | C2×C3×C4 | — | 2 | 4 | no | — |
| 493 | C2×C3×C4 | — | 2 | 4 | no | — |
| 494 | C2×C3×C4 | C22×D4 | 1 | 8 | yes | — |
| 495 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 496 | C2×C3×C4 | C22×D4 | 1 | 4 | yes | — |
| 497 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 498 | #67 | — | 4 | 8 | no | — |
| 499 | #67 | — | 4 | 8 | no | — |
| 500 | #67 | — | 4 | 8 | no | — |
| 501 | #67 | — | 8 | 16 | no | — |
| 502 | C2×Dic3 | — | 2 | 2 | no | — |
| 503 | C2×Dic3 | — | 2 | 8 | no | — |
| 504 | C2×Dic3 | — | 2 | 4 | no | — |
| 505 | C2×Dic3 | — | 2 | 2 | no | — |
| 506 | C2×Dic3 | — | 2 | 4 | no | — |
| 507 | C2×Dic3 | — | 2 | 4 | no | — |
| 508 | C2×Dic3 | — | 2 | 4 | no | — |
| 509 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 510 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 511 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 512 | D12 | — | 2 | 32 | no | — |
| 513 | D12 | — | 2 | 16 | no | — |
| 514 | D12 | — | 2 | 32 | no | — |
| 515 | D12 | — | 2 | 16 | no | — |
| 516 | D12 | — | 4 | 8 | no | — |
| 517 | D12 | — | 4 | 4 | no | — |
| 518 | D12 | — | 8 | 16 | no | — |
| 519 | C4×D3 | — | 2 | 32 | no | — |
| 520 | C4×D3 | — | 2 | 8 | no | — |
| 521 | C4×D3 | — | 2 | 8 | no | — |
| 522 | C4×D3 | — | 2 | 8 | no | — |
| 523 | C4×D3 | — | 2 | 32 | no | — |
| 524 | C4×D3 | — | 4 | 8 | no | — |
| 525 | C4×D3 | #120 | 1 | 16 | yes | complemented |
| 526 | C24 | — | 3 | 1 | no | — |
| 527 | C24 | — | 3 | 1 | no | — |
| 528 | C24 | — | 3 | 4 | no | — |
| 529 | C24 | — | 3 | 4 | no | — |
| 530 | C24 | — | 3 | 2 | no | — |
| 531 | C24 | — | 6 | 4 | no | — |
| 532 | C24 | — | 6 | 8 | no | — |
| 533 | C24 | — | 6 | 4 | no | — |
| 534 | C24 | — | 6 | 8 | no | — |
| 535 | C24 | — | 6 | 4 | no | — |
| 536 | C24 | — | 6 | 4 | no | — |
| 537 | C24 | — | 6 | 8 | no | — |
| 538 | C24 | — | 12 | 2 | no | — |
| 539 | C24 | — | 12 | 4 | no | — |
| 540 | C24 | — | 12 | 4 | no | — |
| 541 | C24 | — | 12 | 4 | no | — |
| 542 | C24 | C23×D3 | 1 | 2 | yes | — |
| 543 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 544 | #41 | — | 6 | 64 | no | — |
| 545 | #41 | — | 6 | 64 | no | — |
| 546 | #41 | — | 6 | 64 | no | — |
| 547 | #41 | — | 6 | 64 | no | — |
| 548 | C2×Q8 | — | 2 | 32 | no | — |
| 549 | C2×Q8 | — | 2 | 8 | no | — |
| 550 | C2×Q8 | — | 2 | 4 | no | — |
| 551 | C2×Q8 | — | 2 | 4 | no | — |
| 552 | C2×Q8 | — | 2 | 4 | no | — |
| 553 | C2×Q8 | D3×D4 | 1 | 8 | yes | complemented |
| 554 | C2×D4 | — | 2 | 4 | no | — |
| 555 | C2×D4 | — | 2 | 8 | no | — |
| 556 | C2×D4 | — | 2 | 2 | no | — |
| 557 | C2×D4 | — | 2 | 4 | no | — |
| 558 | C2×D4 | — | 3 | 16 | no | — |
| 559 | C2×D4 | — | 3 | 8 | no | — |
| 560 | C2×D4 | — | 6 | 8 | no | — |
| 561 | C2×D4 | — | 6 | 8 | no | — |
| 562 | C2×D4 | — | 6 | 8 | no | — |
| 563 | C2×D4 | — | 6 | 8 | no | — |
| 564 | C2×D4 | — | 6 | 8 | no | — |
| 565 | C2×D4 | — | 6 | 64 | no | — |
| 566 | C2×D4 | — | 6 | 32 | no | — |
| 567 | C2×D4 | — | 6 | 4 | no | — |
| 568 | C2×D4 | — | 6 | 16 | no | — |
| 569 | C2×D4 | — | 6 | 8 | no | — |
| 570 | C2×D4 | — | 6 | 4 | no | — |
| 571 | C2×D4 | — | 6 | 4 | no | — |
| 572 | C2×D4 | — | 6 | 4 | no | — |
| 573 | C2×D4 | — | 6 | 8 | no | — |
| 574 | C2×D4 | — | 6 | 16 | no | — |
| 575 | C2×D4 | — | 6 | 8 | no | — |
| 576 | C2×D4 | — | 6 | 4 | no | — |
| 577 | C2×D4 | — | 6 | 4 | no | — |
| 578 | C2×D4 | — | 6 | 4 | no | — |
| 579 | C2×D4 | — | 6 | 2 | no | — |
| 580 | C2×D4 | — | 6 | 4 | no | — |
| 581 | C2×D4 | — | 12 | 4 | no | — |
| 582 | C2×D4 | — | 12 | 8 | no | — |
| 583 | C2×D4 | — | 12 | 8 | no | — |
| 584 | C2×D4 | — | 12 | 16 | no | — |
| 585 | C2×D4 | — | 12 | 4 | no | — |
| 586 | C2×D4 | — | 12 | 8 | no | — |
| 587 | C2×D4 | — | 12 | 8 | no | — |
| 588 | C2×D4 | — | 12 | 32 | no | — |
| 589 | C22×C4 | — | 2 | 4 | no | — |
| 590 | C22×C4 | — | 2 | 8 | no | — |
| 591 | C22×C4 | — | 2 | 4 | no | — |
| 592 | C22×C4 | — | 3 | 1 | no | — |
| 593 | C22×C4 | — | 3 | 4 | no | — |
| 594 | C22×C4 | — | 3 | 8 | no | — |
| 595 | C22×C4 | — | 3 | 4 | no | — |
| 596 | C22×C4 | — | 3 | 1 | no | — |
| 597 | C22×C4 | — | 3 | 4 | no | — |
| 598 | C22×C4 | — | 3 | 4 | no | — |
| 599 | C22×C4 | — | 3 | 4 | no | — |
| 600 | C22×C4 | — | 3 | 16 | no | — |
| 601 | C22×C4 | — | 3 | 4 | no | — |
| 602 | C22×C4 | — | 3 | 2 | no | — |
| 603 | C22×C4 | — | 6 | 8 | no | — |
| 604 | C22×C4 | — | 6 | 4 | no | — |
| 605 | C22×C4 | — | 6 | 8 | no | — |
| 606 | C22×C4 | — | 6 | 8 | no | — |
| 607 | C22×C4 | — | 6 | 32 | no | — |
| 608 | C22×C4 | — | 6 | 4 | no | — |
| 609 | C22×C4 | — | 6 | 8 | no | — |
| 610 | C22×C4 | — | 6 | 64 | no | — |
| 611 | C22×C4 | — | 6 | 4 | no | — |
| 612 | C22×C4 | — | 6 | 4 | no | — |
| 613 | C22×C4 | — | 6 | 8 | no | — |
| 614 | C22×C4 | — | 6 | 4 | no | — |
| 615 | C22×C4 | — | 12 | 4 | no | — |
| 616 | C22×C4 | D3×D4 | 1 | 4 | yes | — |
| 617 | C22×C4 | C23×D3 | 1 | 4 | yes | — |
| 618 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 619 | C22×C4 | C23×D3 | 1 | 4 | yes | — |
| 620 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 621 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 622 | C4⋊C4 | — | 2 | 2 | no | — |
| 623 | C4⋊C4 | — | 6 | 4 | no | — |
| 624 | C4⋊C4 | — | 6 | 8 | no | — |
| 625 | C4⋊C4 | — | 6 | 2 | no | — |
| 626 | C22⋊C4 | — | 2 | 4 | no | — |
| 627 | C22⋊C4 | — | 2 | 4 | no | — |
| 628 | C22⋊C4 | — | 2 | 16 | no | — |
| 629 | C22⋊C4 | — | 6 | 4 | no | — |
| 630 | C22⋊C4 | — | 6 | 8 | no | — |
| 631 | C22⋊C4 | — | 6 | 4 | no | — |
| 632 | C22⋊C4 | — | 6 | 4 | no | — |
| 633 | C22⋊C4 | — | 6 | 4 | no | — |
| 634 | C22⋊C4 | — | 6 | 16 | no | — |
| 635 | C22⋊C4 | — | 12 | 8 | no | — |
| 636 | C22⋊C4 | — | 12 | 8 | no | — |
| 637 | C22⋊C4 | — | 12 | 4 | no | — |
| 638 | C42 | — | 2 | 4 | no | — |
| 639 | C42 | — | 6 | 4 | no | — |
| 640 | C22×C3 | — | 2 | 2 | no | — |
| 641 | C22×C3 | — | 2 | 2 | no | — |
| 642 | C22×C3 | — | 2 | 8 | no | — |
| 643 | C22×C3 | — | 4 | 2 | no | — |
| 644 | C22×C3 | — | 4 | 2 | no | — |
| 645 | C22×C3 | — | 4 | 2 | no | — |
| 646 | C22×C3 | — | 4 | 8 | no | — |
| 647 | C22×C3 | #535 | 1 | 4 | yes | complemented |
| 648 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 649 | C22×C3 | C23×D4 | 1 | 2 | yes | — |
| 650 | C22×C3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 651 | C22×C3 | #585 | 1 | 2 | yes | — |
| 652 | C2×D3 | — | 2 | 2 | no | — |
| 653 | C2×D3 | — | 2 | 2 | no | — |
| 654 | C2×D3 | — | 2 | 8 | no | — |
| 655 | C2×D3 | — | 2 | 8 | no | — |
| 656 | C2×D3 | — | 2 | 2 | no | — |
| 657 | C2×D3 | — | 2 | 2 | no | — |
| 658 | C2×D3 | — | 2 | 2 | no | — |
| 659 | C2×D3 | — | 2 | 16 | no | — |
| 660 | C2×D3 | — | 4 | 16 | no | — |
| 661 | C2×D3 | — | 4 | 32 | no | — |
| 662 | C2×D3 | — | 4 | 4 | no | — |
| 663 | C2×D3 | — | 4 | 4 | no | — |
| 664 | C2×D3 | — | 4 | 8 | no | — |
| 665 | C2×D3 | — | 4 | 4 | no | — |
| 666 | C2×D3 | — | 4 | 2 | no | — |
| 667 | C2×D3 | — | 4 | 2 | no | — |
| 668 | C2×D3 | — | 4 | 2 | no | — |
| 669 | C2×D3 | — | 4 | 8 | no | — |
| 670 | C2×D3 | — | 8 | 16 | no | — |
| 671 | C2×D3 | C2×#120 | 1 | 4 | yes | — |
| 672 | C3×C4 | — | 2 | 8 | no | — |
| 673 | C3×C4 | — | 2 | 2 | no | — |
| 674 | C3×C4 | — | 4 | 2 | no | — |
| 675 | C3×C4 | — | 4 | 4 | no | — |
| 676 | C3×C4 | C2×#120 | 1 | 4 | yes | — |
| 677 | Dic3 | — | 2 | 2 | no | — |
| 678 | Dic3 | — | 4 | 2 | no | — |
| 679 | Dic3 | — | 4 | 4 | no | — |
| 680 | Dic3 | C2×#120 | 1 | 4 | yes | — |
| 681 | C23 | — | 2 | 2 | no | — |
| 682 | C23 | — | 2 | 2 | no | — |
| 683 | C23 | — | 2 | 4 | no | — |
| 684 | C23 | — | 2 | 2 | no | — |
| 685 | C23 | — | 2 | 4 | no | — |
| 686 | C23 | — | 2 | 4 | no | — |
| 687 | C23 | — | 3 | 4 | no | — |
| 688 | C23 | — | 3 | 2 | no | — |
| 689 | C23 | — | 3 | 2 | no | — |
| 690 | C23 | — | 3 | 8 | no | — |
| 691 | C23 | — | 6 | 8 | no | — |
| 692 | C23 | — | 6 | 16 | no | — |
| 693 | C23 | — | 6 | 2 | no | — |
| 694 | C23 | — | 6 | 2 | no | — |
| 695 | C23 | — | 6 | 8 | no | — |
| 696 | C23 | — | 6 | 4 | no | — |
| 697 | C23 | — | 6 | 4 | no | — |
| 698 | C23 | — | 6 | 2 | no | — |
| 699 | C23 | — | 6 | 8 | no | — |
| 700 | C23 | — | 6 | 2 | no | — |
| 701 | C23 | — | 6 | 2 | no | — |
| 702 | C23 | — | 6 | 8 | no | — |
| 703 | C23 | — | 6 | 2 | no | — |
| 704 | C23 | — | 6 | 4 | no | — |
| 705 | C23 | — | 6 | 4 | no | — |
| 706 | C23 | — | 6 | 4 | no | — |
| 707 | C23 | — | 12 | 4 | no | — |
| 708 | C23 | — | 12 | 16 | no | — |
| 709 | C23 | — | 12 | 32 | no | — |
| 710 | C23 | — | 12 | 8 | no | — |
| 711 | C23 | — | 12 | 8 | no | — |
| 712 | C23 | — | 12 | 8 | no | — |
| 713 | C23 | — | 12 | 8 | no | — |
| 714 | C23 | — | 12 | 8 | no | — |
| 715 | C23 | — | 24 | 16 | no | — |
| 716 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 717 | C23 | #1009 | 1 | 4 | yes | — |
| 718 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 719 | Q8 | — | 2 | 16 | no | — |
| 720 | Q8 | — | 2 | 16 | no | — |
| 721 | D4 | — | 4 | 8 | no | — |
| 722 | D4 | — | 4 | 4 | no | — |
| 723 | D4 | — | 6 | 32 | no | — |
| 724 | D4 | — | 6 | 32 | no | — |
| 725 | D4 | — | 6 | 16 | no | — |
| 726 | D4 | — | 6 | 16 | no | — |
| 727 | D4 | — | 12 | 8 | no | — |
| 728 | D4 | — | 12 | 8 | no | — |
| 729 | D4 | — | 12 | 8 | no | — |
| 730 | D4 | — | 12 | 8 | no | — |
| 731 | D4 | — | 12 | 4 | no | — |
| 732 | D4 | — | 24 | 16 | no | — |
| 733 | D4 | — | 24 | 16 | no | — |
| 734 | C2×C4 | — | 2 | 16 | no | — |
| 735 | C2×C4 | — | 2 | 4 | no | — |
| 736 | C2×C4 | — | 2 | 4 | no | — |
| 737 | C2×C4 | — | 2 | 2 | no | — |
| 738 | C2×C4 | — | 2 | 8 | no | — |
| 739 | C2×C4 | — | 2 | 4 | no | — |
| 740 | C2×C4 | — | 2 | 2 | no | — |
| 741 | C2×C4 | — | 2 | 4 | no | — |
| 742 | C2×C4 | — | 2 | 4 | no | — |
| 743 | C2×C4 | — | 2 | 4 | no | — |
| 744 | C2×C4 | — | 3 | 2 | no | — |
| 745 | C2×C4 | — | 3 | 4 | no | — |
| 746 | C2×C4 | — | 3 | 16 | no | — |
| 747 | C2×C4 | — | 3 | 2 | no | — |
| 748 | C2×C4 | — | 6 | 8 | no | — |
| 749 | C2×C4 | — | 6 | 32 | no | — |
| 750 | C2×C4 | — | 6 | 8 | no | — |
| 751 | C2×C4 | — | 6 | 32 | no | — |
| 752 | C2×C4 | — | 6 | 8 | no | — |
| 753 | C2×C4 | — | 6 | 2 | no | — |
| 754 | C2×C4 | — | 6 | 8 | no | — |
| 755 | C2×C4 | — | 6 | 4 | no | — |
| 756 | C2×C4 | — | 6 | 2 | no | — |
| 757 | C2×C4 | — | 6 | 4 | no | — |
| 758 | C2×C4 | — | 6 | 4 | no | — |
| 759 | C2×C4 | — | 6 | 4 | no | — |
| 760 | C2×C4 | — | 12 | 8 | no | — |
| 761 | C2×C4 | C2×D3×D4 | 1 | 8 | yes | — |
| 762 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 763 | C2×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 764 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 765 | C2×C3 | — | 2 | 4 | no | — |
| 766 | C2×C3 | — | 8 | 2 | no | — |
| 767 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 768 | C2×C3 | C2×#535 | 1 | 1 | yes | characteristic |
| 769 | C2×C3 | #3449 | 1 | 1 | yes | characteristic |
| 770 | C2×C3 | #3488 | 1 | 4 | yes | — |
| 771 | D3 | — | 2 | 4 | no | — |
| 772 | D3 | — | 4 | 2 | no | — |
| 773 | D3 | — | 4 | 8 | no | — |
| 774 | D3 | — | 8 | 2 | no | — |
| 775 | C22 | — | 2 | 2 | no | — |
| 776 | C22 | — | 2 | 2 | no | — |
| 777 | C22 | — | 2 | 8 | no | — |
| 778 | C22 | — | 3 | 4 | no | — |
| 779 | C22 | — | 4 | 2 | no | — |
| 780 | C22 | — | 4 | 2 | no | — |
| 781 | C22 | — | 4 | 2 | no | — |
| 782 | C22 | — | 4 | 8 | no | — |
| 783 | C22 | — | 6 | 2 | no | — |
| 784 | C22 | — | 6 | 2 | no | — |
| 785 | C22 | — | 6 | 8 | no | — |
| 786 | C22 | — | 6 | 2 | no | — |
| 787 | C22 | — | 6 | 2 | no | — |
| 788 | C22 | — | 6 | 8 | no | — |
| 789 | C22 | — | 6 | 2 | no | — |
| 790 | C22 | — | 6 | 16 | no | — |
| 791 | C22 | — | 12 | 16 | no | — |
| 792 | C22 | — | 12 | 32 | no | — |
| 793 | C22 | — | 12 | 4 | no | — |
| 794 | C22 | — | 12 | 4 | no | — |
| 795 | C22 | — | 12 | 8 | no | — |
| 796 | C22 | — | 12 | 4 | no | — |
| 797 | C22 | — | 12 | 2 | no | — |
| 798 | C22 | — | 12 | 2 | no | — |
| 799 | C22 | — | 12 | 2 | no | — |
| 800 | C22 | — | 12 | 8 | no | — |
| 801 | C22 | — | 24 | 16 | no | — |
| 802 | C22 | #5674 | 1 | 4 | yes | complemented |
| 803 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 804 | C22 | C22×D3×D4 | 1 | 2 | yes | — |
| 805 | C22 | C2×#1009 | 1 | 2 | yes | — |
| 806 | C22 | #5968 | 1 | 2 | yes | — |
| 807 | C4 | — | 2 | 8 | no | — |
| 808 | C4 | — | 2 | 2 | no | — |
| 809 | C4 | — | 3 | 4 | no | — |
| 810 | C4 | — | 4 | 2 | no | — |
| 811 | C4 | — | 4 | 4 | no | — |
| 812 | C4 | — | 6 | 2 | no | — |
| 813 | C4 | — | 12 | 2 | no | — |
| 814 | C4 | — | 12 | 4 | no | — |
| 815 | C4 | D3×#120 | 1 | 4 | yes | — |
| 816 | C3 | #35250 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 817 | C2 | — | 2 | 4 | no | — |
| 818 | C2 | — | 6 | 4 | no | — |
| 819 | C2 | — | 8 | 2 | no | — |
| 820 | C2 | — | 12 | 2 | no | — |
| 821 | C2 | — | 12 | 8 | no | — |
| 822 | C2 | — | 24 | 2 | no | — |
| 823 | C2 | C2×D3×#120 | 1 | 1 | yes | characteristic |
| 824 | C2 | C2×#5674 | 1 | 1 | yes | characteristic |
| 825 | C2 | #86338 | 1 | 1 | yes | characteristic |
| 826 | C2 | #86713 | 1 | 4 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D3 |
| commutator, socle, cosocle | C23×C3 | C25 |
| Fitting | C3×#2436 | C2 |
| hypercenter | #2436 | D3 |
| hypocenter | C3 | #35250 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #2436 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#239 | C2 | semidirect |
| 2. C2×#5674 | C2 | semidirect |
| 3. C2×D3×#121 | C2 | semidirect |
| 4. C3×#2436 | C2 | semidirect |
| 5. #84066 | C2 | semidirect |
| 6. #82958 | C2 | semidirect |
| 7. #82653 | C2 | semidirect |
| 8. #76863 | C2 | semidirect |
| 9. #76809 | C2 | semidirect |
| 10. #76626 | C2 | semidirect |
| 11. #76482 | C2 | semidirect |
| 12. #74935 | C2 | semidirect |
| 13. #74884 | C2 | semidirect |
| 14. #73587 | C2 | semidirect |
| 15. #73561 | C2 | semidirect |
| 17. C23×C3×Q8 | C22 | semidirect |
| 22. C22×#239 | C22 | semidirect |
| 23. C22×#239 | C22 | semidirect |
| 25. C22×D3×D4 | C22 | semidirect |
| 27. C23×D12 | C22 | semidirect |
| 29. C23×C4×D3 | C22 | semidirect |
| 30. C2×C3×#124 | C22 | semidirect |
| 32. C2×#947 | C22 | semidirect |
| 33. C2×#940 | C22 | semidirect |
| 35. C2×#938 | C22 | semidirect |
| 36. C2×#937 | C22 | semidirect |
| 40. C2×#895 | C22 | semidirect |
| 41. C2×D3×C4⋊C4 | C22 | semidirect |
| 42. C2×#884 | C22 | semidirect |
| 43. C2×#884 | C22 | semidirect |
| 44. C2×#882 | C22 | semidirect |
| 45. C2×#882 | C22 | semidirect |
| 46. C2×D3×C22⋊C4 | C22 | semidirect |
| 47. C2×#874 | C22 | semidirect |
| 48. C2×#872 | C22 | semidirect |
| 49. C3×#393 | C22 | semidirect |
| 50. C3×#391 | C22 | semidirect |
| 51. C3×#386 | C22 | semidirect |
| 52. C3×C4×C22⋊C4 | C22 | semidirect |
| 53. #5231 | C22 | semidirect |
| 54. #5229 | C22 | semidirect |
| 55. #5213 | C22 | semidirect |
| 56. C4×#217 | C22 | semidirect |
| 57. #4988 | C22 | semidirect |
| 58. #4960 | C22 | semidirect |
| 59. #4960 | C22 | semidirect |
| 60. #4956 | C22 | semidirect |
| 62. #4942 | C22 | semidirect |
| 63. #4939 | C22 | semidirect |
| 64. C4×(C2×D3)⋊C4 | C22 | semidirect |
| 65. #4671 | C22 | semidirect |
| 66. #4671 | C22 | semidirect |
| 67. #4667 | C22 | semidirect |
| 68. #4667 | C22 | semidirect |
| 69. #4665 | C22 | semidirect |
| 70. #4665 | C22 | semidirect |
| 71. #4664 | C22 | semidirect |
| 78. #2436 | D3 | semidirect |
| 113. C2×#239 | D4 | semidirect |
| 132. C22×C4×D3 | D4 | semidirect |
| 186. C23×Q8 | C2×D3 | semidirect |
| 197. C2×#124 | C2×D3 | semidirect |
| 213. #393 | C2×D3 | semidirect |
| 219. #391 | C2×D3 | semidirect |
| 226. #386 | C2×D3 | semidirect |
| 234. C4×C22⋊C4 | C2×D3 | semidirect |
| 258. C2×C3×Q8 | C2×D4 | semidirect |
| 312. C2×D12 | C2×D4 | semidirect |
| 330. C2×C4×D3 | C2×D4 | semidirect |
| 525. C4×D3 | #120 | semidirect |
| 553. C2×Q8 | D3×D4 | semidirect |
| 647. C22×C3 | #535 | semidirect |
| 802. C22 | #5674 | semidirect |
| 816. C3 | #35250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#239 | 2 |
| C2×#5674 | 2 |
| C2×D3×#121 | 2 |
| C3×#2436 | 2 |
| #84066 | 2 |
| #82958 | 2 |
| #82653 | 2 |
| #76863 | 2 |
| #76809 | 2 |
| #76626 | 2 |
| #76482 | 2 |
| #74935 | 2 |
| #74884 | 2 |
| #73587 | 2 |
| #73561 | 2 |
| #35250 | 3 |