← C3×#34498 #10653105
Subgroups — C3×#34498 #10653105
Order 768.
2340 conjugacy classes of subgroups.
The subgroup lattice has 432 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C3×#559 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#2376 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C3×#2367 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C3×#2366 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×Q8×C4⋊C4 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C3×D4×C4⋊C4 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C3×#2326 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C3×#2322 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | C3×#2319 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | C3×C4×#127 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C3×#2295 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #34498 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 13 | C3×#559 | C4 | 1 | 16 | yes | complemented |
| 14 | C2×C3×#127 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×C3×#124 | C22 | 1 | 4 | yes | — |
| 16 | C2×C3×#123 | C22 | 1 | 4 | yes | — |
| 17 | C2×C3×C4×Q8 | C22 | 1 | 4 | yes | — |
| 18 | C2×C3×C4×Q8 | C22 | 1 | 2 | yes | — |
| 19 | C2×C3×C4×D4 | C22 | 1 | 4 | yes | — |
| 20 | C2×C3×C4×D4 | C22 | 1 | 4 | yes | — |
| 21 | C2×C3×C4×D4 | C22 | 1 | 2 | yes | — |
| 22 | C2×C3×C4×D4 | C22 | 1 | 4 | yes | — |
| 23 | C22×C3×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 24 | C3×#391 | C22 | 1 | 2 | yes | — |
| 25 | C3×#391 | C22 | 1 | 2 | yes | — |
| 26 | C3×#390 | C22 | 1 | 4 | yes | — |
| 27 | C3×#390 | C22 | 1 | 2 | yes | — |
| 28 | C3×#390 | C22 | 1 | 4 | yes | — |
| 29 | C3×#389 | C22 | 1 | 8 | yes | — |
| 30 | C3×#389 | C22 | 1 | 2 | yes | — |
| 31 | C3×#389 | C22 | 1 | 2 | yes | — |
| 32 | C3×#389 | C22 | 1 | 4 | yes | — |
| 33 | C3×#388 | C22 | 1 | 8 | yes | — |
| 34 | C3×#388 | C22 | 1 | 8 | yes | — |
| 35 | C3×#388 | C22 | 1 | 8 | yes | — |
| 36 | C3×#387 | C22 | 1 | 4 | yes | — |
| 37 | C3×#387 | C22 | 1 | 4 | yes | — |
| 38 | C3×#386 | C22 | 1 | 4 | yes | — |
| 39 | C3×#385 | C22 | 1 | 8 | yes | — |
| 40 | C3×#385 | C22 | 1 | 8 | yes | — |
| 41 | C3×#385 | C22 | 1 | 4 | yes | — |
| 42 | C3×#384 | C22 | 1 | 1 | yes | characteristic |
| 43 | C3×#384 | C22 | 1 | 4 | yes | — |
| 44 | C3×#381 | C22 | 1 | 4 | yes | — |
| 45 | C3×#380 | C22 | 1 | 8 | yes | — |
| 46 | C3×C4×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 47 | C3×C4×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 48 | C3×C4×C4⋊C4 | C22 | 1 | 4 | yes | — |
| 49 | C3×C4×C22⋊C4 | C22 | 1 | 4 | yes | — |
| 50 | C3×#376 | C22 | 1 | 4 | yes | — |
| 51 | C3×C43 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#559 | C2×C3 | 1 | 1 | yes | characteristic |
| 53 | #2376 | C2×C3 | 1 | 4 | yes | complemented |
| 54 | #2367 | C2×C3 | 1 | 4 | yes | complemented |
| 55 | #2366 | C2×C3 | 1 | 1 | yes | characteristic |
| 56 | Q8×C4⋊C4 | C2×C3 | 1 | 2 | yes | complemented |
| 57 | D4×C4⋊C4 | C2×C3 | 1 | 4 | yes | complemented |
| 58 | #2326 | C2×C3 | 1 | 4 | yes | complemented |
| 59 | #2322 | C2×C3 | 1 | 4 | yes | complemented |
| 60 | #2319 | C2×C3 | 1 | 4 | yes | complemented |
| 61 | C4×#127 | C2×C3 | 1 | 1 | yes | characteristic |
| 62 | #2295 | C2×C3 | 1 | 2 | yes | complemented |
| 63 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 64 | C22×C3×D4 | C23 | 1 | 4 | yes | — |
| 65 | C22×C3×D4 | C23 | 1 | 2 | yes | — |
| 66 | C23×C3×C4 | C23 | 1 | 4 | yes | — |
| 67 | C23×C3×C4 | C23 | 1 | 4 | yes | — |
| 68 | C23×C3×C4 | C23 | 1 | 4 | yes | — |
| 69 | C3×#127 | C2×C4 | 1 | 8 | yes | — |
| 70 | C3×#124 | C2×C4 | 1 | 32 | yes | complemented |
| 71 | C3×#123 | C2×C4 | 1 | 32 | yes | complemented |
| 72 | C3×C4×Q8 | — | 4 | 8 | no | — |
| 73 | C3×C4×Q8 | C2×C4 | 1 | 16 | yes | complemented |
| 74 | C3×C4×D4 | — | 4 | 8 | no | — |
| 75 | C3×C4×D4 | — | 4 | 8 | no | — |
| 76 | C3×C4×D4 | — | 4 | 4 | no | — |
| 77 | C3×C4×D4 | C2×C4 | 1 | 32 | yes | complemented |
| 78 | C2×C3×C4⋊C4 | — | 4 | 8 | no | — |
| 79 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 80 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 81 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 82 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 83 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 84 | C2×C3×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 85 | C2×C3×C4⋊C4 | C23 | 1 | 8 | yes | — |
| 86 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 87 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 88 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 89 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 90 | C2×C3×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 91 | C2×C3×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 92 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 93 | C2×C3×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 94 | C2×C3×C22⋊C4 | C23 | 1 | 8 | yes | — |
| 95 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 96 | C2×C3×C42 | C23 | 1 | 2 | yes | — |
| 97 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×C42 | C23 | 1 | 4 | yes | — |
| 99 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C3×C42 | C23 | 1 | 8 | yes | — |
| 101 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C3×C42 | C23 | 1 | 4 | yes | — |
| 103 | C3×#95 | C23 | 1 | 4 | yes | — |
| 104 | C3×#95 | C23 | 1 | 4 | yes | — |
| 105 | C3×#95 | C23 | 1 | 4 | yes | — |
| 106 | C3×#95 | C23 | 1 | 4 | yes | — |
| 107 | C3×#95 | C23 | 1 | 4 | yes | — |
| 108 | C3×#95 | C23 | 1 | 8 | yes | — |
| 109 | C3×#95 | C23 | 1 | 4 | yes | — |
| 110 | C3×#95 | C23 | 1 | 4 | yes | — |
| 111 | #559 | C3×C4 | 1 | 16 | yes | complemented |
| 112 | C2×#127 | C22×C3 | 1 | 1 | yes | characteristic |
| 113 | C2×#124 | C22×C3 | 1 | 4 | yes | — |
| 114 | C2×#123 | C22×C3 | 1 | 4 | yes | — |
| 115 | C2×C4×Q8 | C22×C3 | 1 | 4 | yes | — |
| 116 | C2×C4×Q8 | C22×C3 | 1 | 2 | yes | — |
| 117 | C2×C4×D4 | C22×C3 | 1 | 2 | yes | — |
| 118 | C2×C4×D4 | C22×C3 | 1 | 4 | yes | — |
| 119 | C2×C4×D4 | C22×C3 | 1 | 4 | yes | — |
| 120 | C2×C4×D4 | C22×C3 | 1 | 4 | yes | — |
| 121 | C22×C4⋊C4 | C22×C3 | 1 | 4 | yes | — |
| 122 | #391 | C22×C3 | 1 | 2 | yes | — |
| 123 | #391 | C22×C3 | 1 | 2 | yes | — |
| 124 | #390 | C22×C3 | 1 | 4 | yes | — |
| 125 | #390 | C22×C3 | 1 | 2 | yes | — |
| 126 | #390 | C22×C3 | 1 | 4 | yes | — |
| 127 | #389 | C22×C3 | 1 | 2 | yes | — |
| 128 | #389 | C22×C3 | 1 | 4 | yes | — |
| 129 | #389 | C22×C3 | 1 | 8 | yes | — |
| 130 | #389 | C22×C3 | 1 | 2 | yes | — |
| 131 | #388 | C22×C3 | 1 | 8 | yes | — |
| 132 | #388 | C22×C3 | 1 | 8 | yes | — |
| 133 | #388 | C22×C3 | 1 | 8 | yes | — |
| 134 | #387 | C22×C3 | 1 | 4 | yes | — |
| 135 | #387 | C22×C3 | 1 | 4 | yes | — |
| 136 | #386 | C22×C3 | 1 | 4 | yes | — |
| 137 | #385 | C22×C3 | 1 | 4 | yes | — |
| 138 | #385 | C22×C3 | 1 | 8 | yes | — |
| 139 | #385 | C22×C3 | 1 | 8 | yes | — |
| 140 | #384 | C22×C3 | 1 | 1 | yes | characteristic |
| 141 | #384 | C22×C3 | 1 | 4 | yes | — |
| 142 | #381 | C22×C3 | 1 | 4 | yes | — |
| 143 | #380 | C22×C3 | 1 | 8 | yes | — |
| 144 | C4×C4⋊C4 | C22×C3 | 1 | 4 | yes | — |
| 145 | C4×C4⋊C4 | C22×C3 | 1 | 4 | yes | — |
| 146 | C4×C4⋊C4 | C22×C3 | 1 | 2 | yes | — |
| 147 | C4×C22⋊C4 | C22×C3 | 1 | 4 | yes | — |
| 148 | #376 | C22×C3 | 1 | 4 | yes | — |
| 149 | C43 | C22×C3 | 1 | 1 | yes | characteristic |
| 150 | C24×C3 | C24 | 1 | 4 | yes | — |
| 151 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 152 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 153 | C2×C3×Q8 | C22×C4 | 1 | 8 | yes | — |
| 154 | C2×C3×D4 | — | 2 | 8 | no | — |
| 155 | C2×C3×D4 | — | 2 | 8 | no | — |
| 156 | C2×C3×D4 | — | 4 | 2 | no | — |
| 157 | C2×C3×D4 | — | 4 | 2 | no | — |
| 158 | C2×C3×D4 | C22×C4 | 1 | 16 | yes | — |
| 159 | C2×C3×D4 | C22×C4 | 1 | 8 | yes | — |
| 160 | C22×C3×C4 | — | 2 | 8 | no | — |
| 161 | C22×C3×C4 | — | 4 | 4 | no | — |
| 162 | C22×C3×C4 | — | 4 | 4 | no | — |
| 163 | C22×C3×C4 | — | 4 | 4 | no | — |
| 164 | C22×C3×C4 | — | 4 | 8 | no | — |
| 165 | C22×C3×C4 | — | 4 | 8 | no | — |
| 166 | C22×C3×C4 | C22×C4 | 1 | 16 | yes | — |
| 167 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 168 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 169 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 170 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 171 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 172 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 173 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 174 | C22×C3×C4 | C24 | 1 | 4 | yes | — |
| 175 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 176 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 177 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 178 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 179 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 180 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 181 | C3×C4⋊C4 | — | 4 | 8 | no | — |
| 182 | C3×C4⋊C4 | — | 4 | 4 | no | — |
| 183 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 184 | C3×C4⋊C4 | — | 4 | 8 | no | — |
| 185 | C3×C4⋊C4 | C22×C4 | 1 | 8 | yes | — |
| 186 | C3×C4⋊C4 | C22×C4 | 1 | 16 | yes | — |
| 187 | C3×C22⋊C4 | — | 4 | 4 | no | — |
| 188 | C3×C22⋊C4 | — | 4 | 8 | no | — |
| 189 | C3×C22⋊C4 | — | 4 | 8 | no | — |
| 190 | C3×C22⋊C4 | — | 4 | 4 | no | — |
| 191 | C3×C22⋊C4 | C22×C4 | 1 | 32 | yes | — |
| 192 | C3×C22⋊C4 | C22×C4 | 1 | 16 | yes | — |
| 193 | C3×C42 | — | 2 | 2 | no | — |
| 194 | C3×C42 | — | 2 | 4 | no | — |
| 195 | C3×C42 | — | 2 | 8 | no | — |
| 196 | C3×C42 | — | 2 | 4 | no | — |
| 197 | C3×C42 | — | 4 | 1 | no | — |
| 198 | C3×C42 | — | 4 | 8 | no | — |
| 199 | C3×C42 | C22×C4 | 1 | 16 | yes | — |
| 200 | C3×C42 | C22×C4 | 1 | 4 | yes | — |
| 201 | C22×Q8 | C23×C3 | 1 | 2 | yes | — |
| 202 | C22×D4 | C23×C3 | 1 | 4 | yes | — |
| 203 | C22×D4 | C23×C3 | 1 | 2 | yes | — |
| 204 | C23×C4 | C23×C3 | 1 | 4 | yes | — |
| 205 | C23×C4 | C23×C3 | 1 | 4 | yes | — |
| 206 | C23×C4 | C23×C3 | 1 | 4 | yes | — |
| 207 | #127 | C2×C3×C4 | 1 | 8 | yes | — |
| 208 | #124 | C2×C3×C4 | 1 | 32 | yes | complemented |
| 209 | #123 | C2×C3×C4 | 1 | 32 | yes | complemented |
| 210 | C4×Q8 | — | 4 | 8 | no | — |
| 211 | C4×Q8 | C2×C3×C4 | 1 | 16 | yes | complemented |
| 212 | C4×D4 | — | 4 | 8 | no | — |
| 213 | C4×D4 | — | 4 | 8 | no | — |
| 214 | C4×D4 | — | 4 | 4 | no | — |
| 215 | C4×D4 | C2×C3×C4 | 1 | 32 | yes | complemented |
| 216 | C2×C4⋊C4 | — | 4 | 8 | no | — |
| 217 | C2×C4⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 218 | C2×C4⋊C4 | C23×C3 | 1 | 2 | yes | — |
| 219 | C2×C4⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 220 | C2×C4⋊C4 | C23×C3 | 1 | 2 | yes | — |
| 221 | C2×C4⋊C4 | C23×C3 | 1 | 8 | yes | — |
| 222 | C2×C4⋊C4 | C23×C3 | 1 | 2 | yes | — |
| 223 | C2×C4⋊C4 | C23×C3 | 1 | 8 | yes | — |
| 224 | C2×C4⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 225 | C2×C4⋊C4 | C23×C3 | 1 | 2 | yes | — |
| 226 | C2×C4⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 227 | C2×C22⋊C4 | C23×C3 | 1 | 8 | yes | — |
| 228 | C2×C22⋊C4 | C23×C3 | 1 | 8 | yes | — |
| 229 | C2×C22⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 230 | C2×C22⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 231 | C2×C22⋊C4 | C23×C3 | 1 | 8 | yes | — |
| 232 | C2×C22⋊C4 | C23×C3 | 1 | 4 | yes | — |
| 233 | C2×C42 | C23×C3 | 1 | 2 | yes | — |
| 234 | C2×C42 | C23×C3 | 1 | 1 | yes | characteristic |
| 235 | C2×C42 | C23×C3 | 1 | 4 | yes | — |
| 236 | C2×C42 | C23×C3 | 1 | 2 | yes | — |
| 237 | C2×C42 | C23×C3 | 1 | 8 | yes | — |
| 238 | C2×C42 | C23×C3 | 1 | 1 | yes | characteristic |
| 239 | C2×C42 | C23×C3 | 1 | 4 | yes | — |
| 240 | C2×C42 | C23×C3 | 1 | 1 | yes | characteristic |
| 241 | #95 | C23×C3 | 1 | 4 | yes | — |
| 242 | #95 | C23×C3 | 1 | 4 | yes | — |
| 243 | #95 | C23×C3 | 1 | 4 | yes | — |
| 244 | #95 | C23×C3 | 1 | 4 | yes | — |
| 245 | #95 | C23×C3 | 1 | 4 | yes | — |
| 246 | #95 | C23×C3 | 1 | 8 | yes | — |
| 247 | #95 | C23×C3 | 1 | 4 | yes | — |
| 248 | #95 | C23×C3 | 1 | 4 | yes | — |
| 249 | C23×C3 | — | 2 | 8 | no | — |
| 250 | C23×C3 | — | 2 | 4 | no | — |
| 251 | C23×C3 | — | 2 | 8 | no | — |
| 252 | C23×C3 | — | 2 | 4 | no | — |
| 253 | C23×C3 | C23×C4 | 1 | 8 | yes | — |
| 254 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 255 | C3×Q8 | — | 2 | 16 | no | — |
| 256 | C3×D4 | — | 2 | 32 | no | — |
| 257 | C3×D4 | — | 4 | 8 | no | — |
| 258 | C2×C3×C4 | — | 2 | 1 | no | — |
| 259 | C2×C3×C4 | — | 2 | 2 | no | — |
| 260 | C2×C3×C4 | — | 2 | 4 | no | — |
| 261 | C2×C3×C4 | — | 2 | 4 | no | — |
| 262 | C2×C3×C4 | — | 2 | 4 | no | — |
| 263 | C2×C3×C4 | — | 2 | 1 | no | — |
| 264 | C2×C3×C4 | — | 2 | 4 | no | — |
| 265 | C2×C3×C4 | — | 2 | 4 | no | — |
| 266 | C2×C3×C4 | — | 2 | 1 | no | — |
| 267 | C2×C3×C4 | — | 2 | 2 | no | — |
| 268 | C2×C3×C4 | — | 2 | 4 | no | — |
| 269 | C2×C3×C4 | — | 2 | 8 | no | — |
| 270 | C2×C3×C4 | — | 2 | 4 | no | — |
| 271 | C2×C3×C4 | — | 2 | 4 | no | — |
| 272 | C2×C3×C4 | — | 2 | 4 | no | — |
| 273 | C2×C3×C4 | — | 2 | 2 | no | — |
| 274 | C2×C3×C4 | — | 2 | 2 | no | — |
| 275 | C2×C3×C4 | — | 2 | 4 | no | — |
| 276 | C2×C3×C4 | — | 2 | 2 | no | — |
| 277 | C2×C3×C4 | — | 2 | 4 | no | — |
| 278 | C2×C3×C4 | — | 4 | 16 | no | — |
| 279 | C2×C3×C4 | — | 8 | 8 | no | — |
| 280 | C2×C3×C4 | — | 8 | 8 | no | — |
| 281 | C2×C3×C4 | C23×C4 | 1 | 8 | yes | — |
| 282 | C2×C3×C4 | C23×C4 | 1 | 8 | yes | — |
| 283 | C2×C3×C4 | C23×C4 | 1 | 2 | yes | — |
| 284 | C2×C3×C4 | C23×C4 | 1 | 4 | yes | — |
| 285 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 286 | C2×C3×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 287 | C2×C3×C4 | 2−1+4 | 1 | 4 | yes | — |
| 288 | C24 | C24×C3 | 1 | 4 | yes | — |
| 289 | C2×Q8 | — | 2 | 4 | no | — |
| 290 | C2×Q8 | — | 2 | 4 | no | — |
| 291 | C2×Q8 | C22×C3×C4 | 1 | 8 | yes | — |
| 292 | C2×D4 | — | 2 | 8 | no | — |
| 293 | C2×D4 | — | 2 | 8 | no | — |
| 294 | C2×D4 | — | 4 | 2 | no | — |
| 295 | C2×D4 | — | 4 | 2 | no | — |
| 296 | C2×D4 | C22×C3×C4 | 1 | 16 | yes | — |
| 297 | C2×D4 | C22×C3×C4 | 1 | 8 | yes | — |
| 298 | C22×C4 | — | 2 | 8 | no | — |
| 299 | C22×C4 | — | 4 | 4 | no | — |
| 300 | C22×C4 | — | 4 | 4 | no | — |
| 301 | C22×C4 | — | 4 | 4 | no | — |
| 302 | C22×C4 | — | 4 | 8 | no | — |
| 303 | C22×C4 | — | 4 | 8 | no | — |
| 304 | C22×C4 | C22×C3×C4 | 1 | 16 | yes | — |
| 305 | C22×C4 | C24×C3 | 1 | 1 | yes | characteristic |
| 306 | C22×C4 | C24×C3 | 1 | 4 | yes | — |
| 307 | C22×C4 | C24×C3 | 1 | 2 | yes | — |
| 308 | C22×C4 | C24×C3 | 1 | 4 | yes | — |
| 309 | C22×C4 | C24×C3 | 1 | 4 | yes | — |
| 310 | C22×C4 | C24×C3 | 1 | 4 | yes | — |
| 311 | C22×C4 | C24×C3 | 1 | 1 | yes | characteristic |
| 312 | C22×C4 | C24×C3 | 1 | 4 | yes | — |
| 313 | C22×C4 | C24×C3 | 1 | 1 | yes | characteristic |
| 314 | C22×C4 | C24×C3 | 1 | 2 | yes | — |
| 315 | C4⋊C4 | — | 2 | 8 | no | — |
| 316 | C4⋊C4 | — | 2 | 4 | no | — |
| 317 | C4⋊C4 | — | 2 | 8 | no | — |
| 318 | C4⋊C4 | — | 2 | 4 | no | — |
| 319 | C4⋊C4 | — | 4 | 8 | no | — |
| 320 | C4⋊C4 | — | 4 | 2 | no | — |
| 321 | C4⋊C4 | — | 4 | 8 | no | — |
| 322 | C4⋊C4 | — | 4 | 4 | no | — |
| 323 | C4⋊C4 | C22×C3×C4 | 1 | 8 | yes | — |
| 324 | C4⋊C4 | C22×C3×C4 | 1 | 16 | yes | — |
| 325 | C22⋊C4 | — | 4 | 8 | no | — |
| 326 | C22⋊C4 | — | 4 | 8 | no | — |
| 327 | C22⋊C4 | — | 4 | 4 | no | — |
| 328 | C22⋊C4 | — | 4 | 4 | no | — |
| 329 | C22⋊C4 | C22×C3×C4 | 1 | 32 | yes | — |
| 330 | C22⋊C4 | C22×C3×C4 | 1 | 16 | yes | — |
| 331 | C42 | — | 2 | 2 | no | — |
| 332 | C42 | — | 2 | 4 | no | — |
| 333 | C42 | — | 2 | 8 | no | — |
| 334 | C42 | — | 2 | 4 | no | — |
| 335 | C42 | — | 4 | 8 | no | — |
| 336 | C42 | — | 4 | 1 | no | — |
| 337 | C42 | C22×C3×C4 | 1 | 16 | yes | — |
| 338 | C42 | C22×C3×C4 | 1 | 4 | yes | — |
| 339 | C22×C3 | — | 2 | 16 | no | — |
| 340 | C22×C3 | — | 2 | 8 | no | — |
| 341 | C22×C3 | — | 4 | 4 | no | — |
| 342 | C22×C3 | — | 4 | 4 | no | — |
| 343 | C22×C3 | — | 4 | 8 | no | — |
| 344 | C22×C3 | C24×C4 | 1 | 1 | yes | characteristic |
| 345 | C22×C3 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 346 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 347 | C22×C3 | C2×2−1+4 | 1 | 2 | yes | — |
| 348 | C22×C3 | #585 | 1 | 1 | yes | characteristic |
| 349 | C3×C4 | — | 2 | 8 | no | — |
| 350 | C3×C4 | — | 2 | 8 | no | — |
| 351 | C3×C4 | — | 2 | 2 | no | — |
| 352 | C3×C4 | — | 2 | 2 | no | — |
| 353 | C3×C4 | — | 4 | 4 | no | — |
| 354 | C3×C4 | — | 4 | 4 | no | — |
| 355 | C3×C4 | — | 4 | 1 | no | — |
| 356 | C3×C4 | — | 4 | 4 | no | — |
| 357 | C3×C4 | — | 4 | 2 | no | — |
| 358 | C3×C4 | #520 | 1 | 8 | yes | — |
| 359 | C23 | — | 2 | 8 | no | — |
| 360 | C23 | — | 2 | 4 | no | — |
| 361 | C23 | — | 2 | 8 | no | — |
| 362 | C23 | — | 2 | 4 | no | — |
| 363 | C23 | C23×C3×C4 | 1 | 8 | yes | — |
| 364 | C23 | C25×C3 | 1 | 1 | yes | characteristic |
| 365 | Q8 | — | 2 | 16 | no | — |
| 366 | D4 | — | 2 | 32 | no | — |
| 367 | D4 | — | 4 | 8 | no | — |
| 368 | C2×C4 | — | 2 | 1 | no | — |
| 369 | C2×C4 | — | 2 | 2 | no | — |
| 370 | C2×C4 | — | 2 | 4 | no | — |
| 371 | C2×C4 | — | 2 | 4 | no | — |
| 372 | C2×C4 | — | 2 | 4 | no | — |
| 373 | C2×C4 | — | 2 | 1 | no | — |
| 374 | C2×C4 | — | 2 | 4 | no | — |
| 375 | C2×C4 | — | 2 | 4 | no | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 2 | 4 | no | — |
| 379 | C2×C4 | — | 2 | 8 | no | — |
| 380 | C2×C4 | — | 2 | 4 | no | — |
| 381 | C2×C4 | — | 2 | 4 | no | — |
| 382 | C2×C4 | — | 2 | 4 | no | — |
| 383 | C2×C4 | — | 2 | 2 | no | — |
| 384 | C2×C4 | — | 2 | 2 | no | — |
| 385 | C2×C4 | — | 2 | 4 | no | — |
| 386 | C2×C4 | — | 2 | 2 | no | — |
| 387 | C2×C4 | — | 2 | 4 | no | — |
| 388 | C2×C4 | — | 4 | 16 | no | — |
| 389 | C2×C4 | — | 8 | 8 | no | — |
| 390 | C2×C4 | — | 8 | 8 | no | — |
| 391 | C2×C4 | C23×C3×C4 | 1 | 8 | yes | — |
| 392 | C2×C4 | C23×C3×C4 | 1 | 8 | yes | — |
| 393 | C2×C4 | C23×C3×C4 | 1 | 2 | yes | — |
| 394 | C2×C4 | C23×C3×C4 | 1 | 4 | yes | — |
| 395 | C2×C4 | C3×H(5,𝔽2) | 1 | 2 | yes | — |
| 396 | C2×C4 | C3×H(5,𝔽2) | 1 | 4 | yes | — |
| 397 | C2×C4 | C3×2−1+4 | 1 | 4 | yes | — |
| 398 | C2×C3 | — | 4 | 8 | no | — |
| 399 | C2×C3 | C2×#520 | 1 | 2 | yes | — |
| 400 | C2×C3 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 401 | C2×C3 | #3543 | 1 | 1 | yes | characteristic |
| 402 | C2×C3 | #3550 | 1 | 1 | yes | characteristic |
| 403 | C2×C3 | #3554 | 1 | 2 | yes | — |
| 404 | C22 | — | 2 | 16 | no | — |
| 405 | C22 | — | 2 | 8 | no | — |
| 406 | C22 | — | 4 | 4 | no | — |
| 407 | C22 | — | 4 | 4 | no | — |
| 408 | C22 | — | 4 | 8 | no | — |
| 409 | C22 | C24×C3×C4 | 1 | 1 | yes | characteristic |
| 410 | C22 | C2×C3×H(5,𝔽2) | 1 | 2 | yes | — |
| 411 | C22 | C2×C3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 412 | C22 | C2×C3×2−1+4 | 1 | 2 | yes | — |
| 413 | C22 | C3×#585 | 1 | 1 | yes | characteristic |
| 414 | C4 | — | 2 | 8 | no | — |
| 415 | C4 | — | 2 | 8 | no | — |
| 416 | C4 | — | 2 | 2 | no | — |
| 417 | C4 | — | 2 | 2 | no | — |
| 418 | C4 | — | 4 | 4 | no | — |
| 419 | C4 | — | 4 | 4 | no | — |
| 420 | C4 | — | 4 | 1 | no | — |
| 421 | C4 | — | 4 | 4 | no | — |
| 422 | C4 | — | 4 | 2 | no | — |
| 423 | C4 | C3×#520 | 1 | 8 | yes | — |
| 424 | C3 | #34498 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 425 | C2 | — | 4 | 8 | no | — |
| 426 | C2 | C2×C3×#520 | 1 | 2 | yes | — |
| 427 | C2 | C3×C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 428 | C2 | C3×#3543 | 1 | 1 | yes | characteristic |
| 429 | C2 | C3×#3550 | 1 | 1 | yes | characteristic |
| 430 | C2 | C3×#3554 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta