← D3×Q8×Q16 #11675632
Subgroups — D3×Q8×Q16 #11675632
Order 768.
1830 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D3×Q82 | C2 | 1 | 2 | yes | maximal |
| 2 | C3×Q8×Q16 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#216 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #81956 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D3×#500 | C2 | 1 | 3 | yes | maximal |
| 6 | D3×#477 | C2 | 1 | 6 | yes | maximal |
| 7 | #81102 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | Q8×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | D3×C8×Q8 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C4×D3×Q16 | C2 | 1 | 3 | yes | maximal |
| 11 | Q16×Dic6 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×Q8×Q16 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×Q82 | C22 | 1 | 2 | yes | — |
| 14 | C2×D3×Q16 | C22 | 1 | 1 | yes | characteristic |
| 15 | D3×C4⋊Q8 | — | 2 | 6 | no | — |
| 16 | D3×C4⋊Q8 | C22 | 1 | 6 | yes | — |
| 17 | #5722 | — | 2 | 6 | no | — |
| 18 | #5722 | C22 | 1 | 6 | yes | — |
| 19 | C4×D3×Q8 | — | 2 | 2 | no | — |
| 20 | C4×D3×Q8 | C22 | 1 | 6 | yes | — |
| 21 | C4×D3×Q8 | C22 | 1 | 1 | yes | characteristic |
| 22 | Q8×Dic6 | — | 2 | 2 | no | — |
| 23 | Q8×Dic6 | C22 | 1 | 6 | yes | — |
| 24 | Q8×Dic6 | C22 | 1 | 2 | yes | — |
| 25 | C3×#500 | C22 | 1 | 3 | yes | — |
| 26 | C3×#477 | C22 | 1 | 6 | yes | — |
| 27 | C3×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×C4×Q16 | C22 | 1 | 3 | yes | — |
| 29 | Dic3×Q16 | C22 | 1 | 3 | yes | — |
| 30 | #5091 | C22 | 1 | 6 | yes | — |
| 31 | #5078 | C22 | 1 | 6 | yes | — |
| 32 | C4×#216 | C22 | 1 | 6 | yes | — |
| 33 | Q8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 34 | #5021 | C22 | 1 | 6 | yes | — |
| 35 | D3×#107 | C22 | 1 | 3 | yes | — |
| 36 | D3×#107 | C22 | 1 | 6 | yes | — |
| 37 | #4875 | C22 | 1 | 12 | yes | — |
| 38 | #4874 | C22 | 1 | 6 | yes | — |
| 39 | #4874 | C22 | 1 | 6 | yes | — |
| 40 | #4873 | C22 | 1 | 3 | yes | — |
| 41 | #4850 | C22 | 1 | 6 | yes | — |
| 42 | D3×C4⋊C8 | C22 | 1 | 3 | yes | — |
| 43 | #4830 | C22 | 1 | 3 | yes | — |
| 44 | D3×#103 | C22 | 1 | 6 | yes | — |
| 45 | #4793 | C22 | 1 | 12 | yes | — |
| 46 | #4790 | C22 | 1 | 6 | yes | — |
| 47 | C4×Dic12 | C22 | 1 | 3 | yes | — |
| 48 | C4×D3×C8 | C22 | 1 | 3 | yes | — |
| 49 | #4682 | C22 | 1 | 3 | yes | — |
| 50 | C8×Dic6 | C22 | 1 | 3 | yes | — |
| 51 | C2×Q82 | — | 3 | 2 | no | — |
| 52 | Q8×Q16 | — | 3 | 3 | no | — |
| 53 | Q8×Q16 | — | 3 | 6 | no | — |
| 54 | Q8×Q16 | — | 3 | 1 | no | — |
| 55 | Q8×Q16 | — | 3 | 3 | no | — |
| 56 | Q8×Q16 | — | 3 | 2 | no | — |
| 57 | Q8×Q16 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 58 | C2×#500 | — | 3 | 3 | no | — |
| 59 | C2×#477 | — | 3 | 6 | no | — |
| 60 | C2×C8×Q8 | — | 3 | 1 | no | — |
| 61 | C2×C4×Q16 | — | 3 | 3 | no | — |
| 62 | C2×D3×Q8 | — | 2 | 6 | no | — |
| 63 | C2×D3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 64 | C2×D3×Q8 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 66 | C3×C4⋊Q8 | — | 2 | 6 | no | — |
| 67 | C3×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 68 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 69 | C3×C4×Q8 | C23 | 1 | 6 | yes | — |
| 70 | C3×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 71 | Q8×Dic3 | — | 2 | 2 | no | — |
| 72 | Q8×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 73 | Q8×Dic3 | C23 | 1 | 6 | yes | — |
| 74 | #944 | — | 2 | 12 | no | — |
| 75 | #944 | — | 2 | 6 | no | — |
| 76 | C2×#216 | C23 | 1 | 2 | yes | — |
| 77 | D3×Q16 | Q8 | 1 | 8 | yes | direct product factor |
| 78 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×D3×C8 | C23 | 1 | 3 | yes | — |
| 80 | C2×D3×C8 | C23 | 1 | 1 | yes | characteristic |
| 81 | D3×C4⋊C4 | — | 2 | 6 | no | — |
| 82 | D3×C4⋊C4 | — | 2 | 6 | no | — |
| 83 | D3×C4⋊C4 | D4 | 1 | 3 | yes | — |
| 84 | D3×C4⋊C4 | C23 | 1 | 6 | yes | — |
| 85 | #888 | — | 2 | 6 | no | — |
| 86 | #888 | — | 2 | 6 | no | — |
| 87 | #888 | — | 2 | 12 | no | — |
| 88 | #888 | — | 2 | 6 | no | — |
| 89 | #888 | C23 | 1 | 12 | yes | — |
| 90 | #887 | — | 2 | 6 | no | — |
| 91 | #887 | — | 2 | 6 | no | — |
| 92 | #887 | D4 | 1 | 3 | yes | — |
| 93 | #887 | C23 | 1 | 6 | yes | — |
| 94 | C42×D3 | — | 2 | 6 | no | — |
| 95 | C42×D3 | C23 | 1 | 3 | yes | — |
| 96 | #869 | — | 2 | 6 | no | — |
| 97 | #869 | C23 | 1 | 6 | yes | — |
| 98 | C4×Dic6 | — | 2 | 6 | no | — |
| 99 | C4×Dic6 | — | 2 | 6 | no | — |
| 100 | C4×Dic6 | C23 | 1 | 6 | yes | — |
| 101 | C4×Dic6 | C23 | 1 | 3 | yes | — |
| 102 | C3×#107 | C23 | 1 | 3 | yes | — |
| 103 | C3×#107 | C23 | 1 | 6 | yes | — |
| 104 | C3×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 105 | C3×#103 | C23 | 1 | 6 | yes | — |
| 106 | C3×C4×C8 | C23 | 1 | 3 | yes | — |
| 107 | #835 | C23 | 1 | 6 | yes | — |
| 108 | #818 | C23 | 1 | 3 | yes | — |
| 109 | #818 | C23 | 1 | 6 | yes | — |
| 110 | #816 | C23 | 1 | 6 | yes | — |
| 111 | Dic3⋊C8 | C23 | 1 | 6 | yes | — |
| 112 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 113 | C8×Dic3 | C23 | 1 | 3 | yes | — |
| 114 | #810 | C23 | 1 | 6 | yes | — |
| 115 | #807 | C23 | 1 | 6 | yes | — |
| 116 | #807 | C23 | 1 | 12 | yes | — |
| 117 | C4⋊(C3⋊C8) | C23 | 1 | 3 | yes | — |
| 118 | C4×C3⋊C8 | C23 | 1 | 3 | yes | — |
| 119 | C22×Q16 | — | 3 | 1 | no | — |
| 120 | Q82 | — | 3 | 6 | no | — |
| 121 | Q82 | — | 3 | 6 | no | — |
| 122 | Q82 | — | 3 | 2 | no | — |
| 123 | Q82 | — | 6 | 2 | no | — |
| 124 | Q82 | — | 6 | 6 | no | — |
| 125 | Q82 | C2×D3 | 1 | 2 | yes | — |
| 126 | C2×C4⋊Q8 | — | 3 | 6 | no | — |
| 127 | C2×C4⋊Q8 | — | 6 | 6 | no | — |
| 128 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 129 | C2×C4×Q8 | — | 3 | 6 | no | — |
| 130 | C2×C4×Q8 | — | 6 | 2 | no | — |
| 131 | #500 | — | 3 | 6 | no | — |
| 132 | #500 | — | 3 | 6 | no | — |
| 133 | #500 | — | 3 | 6 | no | — |
| 134 | #500 | — | 3 | 3 | no | — |
| 135 | #500 | C2×D3 | 1 | 3 | yes | — |
| 136 | #477 | — | 3 | 6 | no | — |
| 137 | #477 | — | 3 | 6 | no | — |
| 138 | #477 | — | 3 | 12 | no | — |
| 139 | #477 | — | 3 | 6 | no | — |
| 140 | #477 | — | 3 | 12 | no | — |
| 141 | #477 | C2×D3 | 1 | 6 | yes | — |
| 142 | C8×Q8 | — | 3 | 1 | no | — |
| 143 | C8×Q8 | — | 3 | 3 | no | — |
| 144 | C8×Q8 | — | 3 | 3 | no | — |
| 145 | C8×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 146 | C4×Q16 | — | 3 | 3 | no | — |
| 147 | C4×Q16 | — | 3 | 6 | no | — |
| 148 | C4×Q16 | — | 3 | 3 | no | — |
| 149 | C4×Q16 | — | 3 | 6 | no | — |
| 150 | C4×Q16 | — | 3 | 3 | no | — |
| 151 | C4×Q16 | C2×D3 | 1 | 3 | yes | — |
| 152 | C2×#107 | — | 3 | 6 | no | — |
| 153 | C2×#107 | — | 3 | 3 | no | — |
| 154 | C2×C4⋊C8 | — | 3 | 3 | no | — |
| 155 | C2×#103 | — | 3 | 6 | no | — |
| 156 | C2×C4×C8 | — | 3 | 3 | no | — |
| 157 | C2×C3×Q8 | — | 2 | 6 | no | — |
| 158 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 160 | D3×Q8 | — | 2 | 4 | no | — |
| 161 | D3×Q8 | — | 8 | 12 | no | — |
| 162 | D3×Q8 | Q16 | 1 | 8 | yes | direct product factor |
| 163 | D3×Q8 | C2×Q8 | 1 | 8 | yes | — |
| 164 | C2×C4×D3 | — | 2 | 2 | no | — |
| 165 | C2×C4×D3 | — | 2 | 6 | no | — |
| 166 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 167 | C2×C4×D3 | C2×D4 | 1 | 3 | yes | — |
| 168 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×Dic6 | — | 2 | 2 | no | — |
| 170 | C2×Dic6 | — | 2 | 6 | no | — |
| 171 | C2×Dic6 | — | 2 | 12 | no | — |
| 172 | C2×Dic6 | C2×D4 | 1 | 3 | yes | — |
| 173 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 174 | C3×Q16 | C2×Q8 | 1 | 4 | yes | complemented |
| 175 | C2×C3×C8 | C24 | 1 | 3 | yes | — |
| 176 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 177 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 178 | C3×C4⋊C4 | — | 2 | 6 | no | — |
| 179 | C3×C4⋊C4 | C2×D4 | 1 | 3 | yes | — |
| 180 | C3×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 181 | C3×C42 | — | 2 | 6 | no | — |
| 182 | C3×C42 | C24 | 1 | 3 | yes | — |
| 183 | #216 | C2×Q8 | 1 | 8 | yes | complemented |
| 184 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 185 | C4⋊Dic3 | — | 2 | 6 | no | — |
| 186 | C4⋊Dic3 | C2×D4 | 1 | 3 | yes | — |
| 187 | C4⋊Dic3 | C24 | 1 | 6 | yes | — |
| 188 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 189 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 190 | Dic3⋊C4 | — | 2 | 12 | no | — |
| 191 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 192 | Dic3⋊C4 | C2×D4 | 1 | 6 | yes | — |
| 193 | C4×Dic3 | — | 2 | 6 | no | — |
| 194 | C4×Dic3 | — | 2 | 6 | no | — |
| 195 | C4×Dic3 | — | 2 | 6 | no | — |
| 196 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 197 | C4×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 198 | C4×Dic3 | C24 | 1 | 3 | yes | — |
| 199 | C2×C3⋊C8 | C24 | 1 | 3 | yes | — |
| 200 | C2×C3⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 201 | Dic12 | C2×Q8 | 1 | 4 | yes | complemented |
| 202 | D3×C8 | — | 2 | 6 | no | — |
| 203 | D3×C8 | C2×Q8 | 1 | 4 | yes | — |
| 204 | C22×Q8 | — | 3 | 1 | no | — |
| 205 | C22×Q8 | — | 3 | 2 | no | — |
| 206 | C22×Q8 | — | 6 | 6 | no | — |
| 207 | C2×Q16 | — | 3 | 2 | no | — |
| 208 | C2×Q16 | — | 3 | 8 | no | — |
| 209 | C2×Q16 | — | 3 | 1 | no | — |
| 210 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 211 | C22×C8 | — | 3 | 1 | no | — |
| 212 | C22×C8 | — | 3 | 3 | no | — |
| 213 | C4⋊Q8 | — | 2 | 6 | no | — |
| 214 | C4⋊Q8 | — | 3 | 12 | no | — |
| 215 | C4⋊Q8 | — | 3 | 6 | no | — |
| 216 | C4⋊Q8 | — | 6 | 6 | no | — |
| 217 | C4⋊Q8 | — | 6 | 6 | no | — |
| 218 | C4⋊Q8 | — | 6 | 6 | no | — |
| 219 | C4⋊Q8 | — | 6 | 12 | no | — |
| 220 | C4⋊Q8 | — | 6 | 6 | no | — |
| 221 | C4⋊Q8 | — | 6 | 12 | no | — |
| 222 | C4⋊Q8 | — | 6 | 6 | no | — |
| 223 | C4⋊Q8 | C22×D3 | 1 | 6 | yes | — |
| 224 | C4×Q8 | — | 2 | 2 | no | — |
| 225 | C4×Q8 | — | 3 | 1 | no | — |
| 226 | C4×Q8 | — | 3 | 3 | no | — |
| 227 | C4×Q8 | — | 3 | 3 | no | — |
| 228 | C4×Q8 | — | 3 | 6 | no | — |
| 229 | C4×Q8 | — | 3 | 6 | no | — |
| 230 | C4×Q8 | — | 3 | 6 | no | — |
| 231 | C4×Q8 | — | 6 | 6 | no | — |
| 232 | C4×Q8 | — | 6 | 6 | no | — |
| 233 | C4×Q8 | — | 6 | 6 | no | — |
| 234 | C4×Q8 | — | 6 | 6 | no | — |
| 235 | C4×Q8 | — | 6 | 2 | no | — |
| 236 | C4×Q8 | C22×D3 | 1 | 6 | yes | — |
| 237 | C4×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 238 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 239 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 240 | C2×C4⋊C4 | — | 6 | 6 | no | — |
| 241 | C2×C4⋊C4 | — | 6 | 6 | no | — |
| 242 | C2×C42 | — | 3 | 3 | no | — |
| 243 | C2×C42 | — | 6 | 6 | no | — |
| 244 | #107 | — | 3 | 3 | no | — |
| 245 | #107 | — | 3 | 6 | no | — |
| 246 | #107 | — | 3 | 6 | no | — |
| 247 | #107 | — | 3 | 12 | no | — |
| 248 | #107 | C22×D3 | 1 | 3 | yes | — |
| 249 | #107 | C22×D3 | 1 | 6 | yes | — |
| 250 | C4⋊C8 | — | 3 | 6 | no | — |
| 251 | C4⋊C8 | — | 3 | 3 | no | — |
| 252 | C4⋊C8 | C22×D3 | 1 | 3 | yes | — |
| 253 | #103 | — | 3 | 6 | no | — |
| 254 | #103 | — | 3 | 6 | no | — |
| 255 | #103 | — | 3 | 6 | no | — |
| 256 | #103 | C22×D3 | 1 | 6 | yes | — |
| 257 | C4×C8 | — | 3 | 3 | no | — |
| 258 | C4×C8 | — | 3 | 3 | no | — |
| 259 | C4×C8 | — | 3 | 3 | no | — |
| 260 | C4×C8 | C22×D3 | 1 | 3 | yes | — |
| 261 | C22×D3 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | C3×Q8 | — | 2 | 2 | no | — |
| 263 | C3×Q8 | — | 8 | 6 | no | — |
| 264 | C3×Q8 | C2×Q16 | 1 | 4 | yes | complemented |
| 265 | C3×Q8 | C22×Q8 | 1 | 4 | yes | — |
| 266 | C2×C3×C4 | — | 2 | 2 | no | — |
| 267 | C2×C3×C4 | — | 2 | 6 | no | — |
| 268 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 269 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 270 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 271 | C2×Dic3 | — | 2 | 2 | no | — |
| 272 | C2×Dic3 | — | 2 | 6 | no | — |
| 273 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 274 | C2×Dic3 | C22×D4 | 1 | 1 | yes | characteristic |
| 275 | C2×Dic3 | C22×D4 | 1 | 3 | yes | — |
| 276 | C4×D3 | — | 2 | 8 | no | — |
| 277 | C4×D3 | — | 2 | 6 | no | — |
| 278 | C4×D3 | — | 4 | 12 | no | — |
| 279 | C4×D3 | C2×Q16 | 1 | 12 | yes | — |
| 280 | C4×D3 | C22×Q8 | 1 | 2 | yes | — |
| 281 | C4×D3 | 2−1+4 | 1 | 2 | yes | — |
| 282 | Dic6 | — | 2 | 2 | no | — |
| 283 | Dic6 | — | 2 | 8 | no | — |
| 284 | Dic6 | — | 8 | 12 | no | — |
| 285 | Dic6 | — | 8 | 6 | no | — |
| 286 | Dic6 | C2×Q16 | 1 | 12 | yes | complemented |
| 287 | Dic6 | C22×Q8 | 1 | 4 | yes | — |
| 288 | C3×C8 | — | 2 | 3 | no | — |
| 289 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 290 | C3⋊C8 | — | 2 | 3 | no | — |
| 291 | C3⋊C8 | C22×Q8 | 1 | 2 | yes | — |
| 292 | C2×Q8 | — | 2 | 6 | no | — |
| 293 | C2×Q8 | — | 3 | 8 | no | — |
| 294 | C2×Q8 | — | 3 | 3 | no | — |
| 295 | C2×Q8 | — | 3 | 8 | no | — |
| 296 | C2×Q8 | — | 3 | 2 | no | — |
| 297 | C2×Q8 | — | 6 | 2 | no | — |
| 298 | C2×Q8 | — | 6 | 12 | no | — |
| 299 | C2×Q8 | — | 6 | 4 | no | — |
| 300 | C2×Q8 | — | 6 | 6 | no | — |
| 301 | C2×Q8 | — | 24 | 12 | no | — |
| 302 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 303 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 304 | C22×C4 | — | 3 | 3 | no | — |
| 305 | C22×C4 | — | 3 | 1 | no | — |
| 306 | C22×C4 | — | 3 | 3 | no | — |
| 307 | C22×C4 | — | 6 | 2 | no | — |
| 308 | C22×C4 | — | 6 | 6 | no | — |
| 309 | Q16 | — | 3 | 8 | no | — |
| 310 | Q16 | — | 3 | 4 | no | — |
| 311 | Q16 | D3×Q8 | 1 | 4 | yes | direct product factor |
| 312 | C2×C8 | — | 3 | 1 | no | — |
| 313 | C2×C8 | — | 3 | 4 | no | — |
| 314 | C2×C8 | — | 3 | 3 | no | — |
| 315 | C2×C8 | — | 6 | 6 | no | — |
| 316 | C2×C8 | C23×D3 | 1 | 3 | yes | — |
| 317 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 318 | C4⋊C4 | — | 2 | 6 | no | — |
| 319 | C4⋊C4 | — | 2 | 6 | no | — |
| 320 | C4⋊C4 | — | 3 | 6 | no | — |
| 321 | C4⋊C4 | — | 3 | 3 | no | — |
| 322 | C4⋊C4 | — | 3 | 6 | no | — |
| 323 | C4⋊C4 | — | 6 | 6 | no | — |
| 324 | C4⋊C4 | — | 6 | 6 | no | — |
| 325 | C4⋊C4 | — | 6 | 6 | no | — |
| 326 | C4⋊C4 | — | 6 | 12 | no | — |
| 327 | C4⋊C4 | — | 6 | 6 | no | — |
| 328 | C4⋊C4 | — | 6 | 6 | no | — |
| 329 | C4⋊C4 | D3×D4 | 1 | 3 | yes | — |
| 330 | C4⋊C4 | C23×D3 | 1 | 6 | yes | — |
| 331 | C42 | — | 2 | 6 | no | — |
| 332 | C42 | — | 3 | 3 | no | — |
| 333 | C42 | — | 3 | 3 | no | — |
| 334 | C42 | — | 3 | 3 | no | — |
| 335 | C42 | — | 6 | 6 | no | — |
| 336 | C42 | — | 6 | 6 | no | — |
| 337 | C42 | — | 6 | 6 | no | — |
| 338 | C42 | C23×D3 | 1 | 3 | yes | — |
| 339 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 340 | C2×D3 | D4×Q8 | 1 | 2 | yes | — |
| 341 | C2×D3 | C22×Q16 | 1 | 2 | yes | — |
| 342 | C2×D3 | #576 | 1 | 2 | yes | — |
| 343 | C3×C4 | — | 2 | 4 | no | — |
| 344 | C3×C4 | — | 2 | 3 | no | — |
| 345 | C3×C4 | — | 4 | 6 | no | — |
| 346 | C3×C4 | C22×Q16 | 1 | 6 | yes | — |
| 347 | C3×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 348 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 349 | Dic3 | — | 2 | 4 | no | — |
| 350 | Dic3 | — | 2 | 3 | no | — |
| 351 | Dic3 | — | 4 | 6 | no | — |
| 352 | Dic3 | D4×Q8 | 1 | 2 | yes | — |
| 353 | Dic3 | C22×Q16 | 1 | 6 | yes | — |
| 354 | C23 | — | 3 | 1 | no | — |
| 355 | Q8 | — | 2 | 2 | no | — |
| 356 | Q8 | — | 3 | 12 | no | — |
| 357 | Q8 | — | 3 | 4 | no | — |
| 358 | Q8 | — | 6 | 8 | no | — |
| 359 | Q8 | — | 6 | 2 | no | — |
| 360 | Q8 | — | 8 | 6 | no | — |
| 361 | Q8 | — | 24 | 6 | no | — |
| 362 | Q8 | — | 24 | 12 | no | — |
| 363 | Q8 | D3×Q16 | 1 | 4 | yes | direct product factor |
| 364 | Q8 | C2×D3×Q8 | 1 | 4 | yes | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 2 | 6 | no | — |
| 367 | C2×C4 | — | 3 | 1 | no | — |
| 368 | C2×C4 | — | 3 | 3 | no | — |
| 369 | C2×C4 | — | 3 | 2 | no | — |
| 370 | C2×C4 | — | 3 | 2 | no | — |
| 371 | C2×C4 | — | 3 | 12 | no | — |
| 372 | C2×C4 | — | 3 | 3 | no | — |
| 373 | C2×C4 | — | 6 | 6 | no | — |
| 374 | C2×C4 | — | 6 | 8 | no | — |
| 375 | C2×C4 | — | 6 | 2 | no | — |
| 376 | C2×C4 | — | 6 | 6 | no | — |
| 377 | C2×C4 | — | 12 | 12 | no | — |
| 378 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 379 | C2×C4 | C2×D3×D4 | 1 | 3 | yes | — |
| 380 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 381 | C8 | — | 2 | 3 | no | — |
| 382 | C8 | — | 3 | 2 | no | — |
| 383 | C8 | — | 6 | 3 | no | — |
| 384 | C8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 385 | C2×C3 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 386 | C2×C3 | C23×Q16 | 1 | 1 | yes | characteristic |
| 387 | C2×C3 | C2×#576 | 1 | 1 | yes | characteristic |
| 388 | D3 | Q8×Q16 | 1 | 4 | yes | direct product factor |
| 389 | C22 | — | 3 | 2 | no | — |
| 390 | C22 | — | 3 | 2 | no | — |
| 391 | C22 | — | 3 | 2 | no | — |
| 392 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 2 | 3 | no | — |
| 394 | C4 | — | 2 | 4 | no | — |
| 395 | C4 | — | 3 | 6 | no | — |
| 396 | C4 | — | 3 | 2 | no | — |
| 397 | C4 | — | 4 | 6 | no | — |
| 398 | C4 | — | 6 | 3 | no | — |
| 399 | C4 | — | 6 | 4 | no | — |
| 400 | C4 | — | 12 | 6 | no | — |
| 401 | C4 | C2×D3×Q16 | 1 | 6 | yes | — |
| 402 | C4 | C22×D3×Q8 | 1 | 1 | yes | characteristic |
| 403 | C4 | D3×2−1+4 | 1 | 1 | yes | characteristic |
| 404 | C3 | C2×Q8×Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 405 | C2 | — | 3 | 4 | no | — |
| 406 | C2 | D3×D4×Q8 | 1 | 1 | yes | characteristic |
| 407 | C2 | C22×D3×Q16 | 1 | 1 | yes | characteristic |
| 408 | C2 | D3×#576 | 1 | 1 | yes | characteristic |
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