← #11675855
Subgroups — #11675855
Order 768.
1682 conjugacy classes of subgroups.
The subgroup lattice has 500 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #86258 | C2 | 1 | 2 | yes | maximal |
| 2 | C3×#3160 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #83367 | C2 | 1 | 2 | yes | maximal |
| 4 | #81957 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #81956 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #81932 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #81914 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #81906 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #79198 | C2 | 1 | 4 | yes | maximal |
| 10 | #79173 | C2 | 1 | 2 | yes | maximal |
| 11 | #79169 | C2 | 1 | 2 | yes | maximal |
| 12 | C2×C4×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #78445 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #61372 | — | 3 | 1 | no | maximal, Sylow |
| 15 | C3×#533 | C22 | 1 | 2 | yes | — |
| 16 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5722 | C22 | 1 | 4 | yes | — |
| 18 | #5721 | C22 | 1 | 4 | yes | — |
| 19 | #5685 | C22 | 1 | 8 | yes | — |
| 20 | #5623 | — | 2 | 4 | no | — |
| 21 | #5622 | — | 2 | 4 | no | — |
| 22 | #5567 | — | 2 | 4 | no | — |
| 23 | #5567 | — | 2 | 2 | no | — |
| 24 | Q8×Dic6 | — | 2 | 2 | no | — |
| 25 | #5519 | C22 | 1 | 4 | yes | — |
| 26 | #5516 | C22 | 1 | 4 | yes | — |
| 27 | #5470 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×C4×Dic6 | C22 | 1 | 2 | yes | — |
| 29 | C3×#500 | C22 | 1 | 1 | yes | characteristic |
| 30 | C3×#500 | C22 | 1 | 1 | yes | characteristic |
| 31 | C3×#499 | C22 | 1 | 2 | yes | — |
| 32 | C3×#499 | C22 | 1 | 2 | yes | — |
| 33 | C3×#498 | C22 | 1 | 2 | yes | — |
| 34 | C3×#427 | C22 | 1 | 2 | yes | — |
| 35 | C3×#427 | C22 | 1 | 2 | yes | — |
| 36 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#818 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#816 | C22 | 1 | 2 | yes | — |
| 39 | #5102 | C22 | 1 | 2 | yes | — |
| 40 | #5101 | C22 | 1 | 2 | yes | — |
| 41 | #5094 | C22 | 1 | 4 | yes | — |
| 42 | #5091 | C22 | 1 | 4 | yes | — |
| 43 | #5063 | C22 | 1 | 8 | yes | — |
| 44 | #5004 | C22 | 1 | 4 | yes | — |
| 45 | #4995 | C22 | 1 | 4 | yes | — |
| 46 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 47 | #4878 | C22 | 1 | 4 | yes | — |
| 48 | #4877 | C22 | 1 | 8 | yes | — |
| 49 | #4875 | C22 | 1 | 8 | yes | — |
| 50 | #4874 | C22 | 1 | 4 | yes | — |
| 51 | #4873 | C22 | 1 | 4 | yes | — |
| 52 | #4873 | C22 | 1 | 4 | yes | — |
| 53 | #4857 | C22 | 1 | 8 | yes | — |
| 54 | #4856 | C22 | 1 | 8 | yes | — |
| 55 | #4854 | C22 | 1 | 8 | yes | — |
| 56 | #4853 | C22 | 1 | 8 | yes | — |
| 57 | C4×Dic12 | C22 | 1 | 2 | yes | — |
| 58 | C4×Dic12 | C22 | 1 | 2 | yes | — |
| 59 | C4×Dic12 | C22 | 1 | 2 | yes | — |
| 60 | C4×Dic12 | C22 | 1 | 2 | yes | — |
| 61 | #4679 | C22 | 1 | 2 | yes | — |
| 62 | #4679 | C22 | 1 | 2 | yes | — |
| 63 | C8×Dic6 | C22 | 1 | 2 | yes | — |
| 64 | C8×Dic6 | C22 | 1 | 2 | yes | — |
| 65 | #3502 | — | 3 | 2 | no | — |
| 66 | #3390 | — | 3 | 4 | no | — |
| 67 | #3387 | — | 3 | 4 | no | — |
| 68 | #3383 | — | 3 | 2 | no | — |
| 69 | #3383 | — | 3 | 4 | no | — |
| 70 | Q8×Q16 | — | 3 | 2 | no | — |
| 71 | #3164 | — | 3 | 2 | no | — |
| 72 | #3160 | D3 | 1 | 1 | yes | characteristic |
| 73 | #3082 | — | 3 | 4 | no | — |
| 74 | #3078 | — | 3 | 2 | no | — |
| 75 | #2960 | — | 3 | 1 | no | — |
| 76 | #2950 | — | 3 | 2 | no | — |
| 77 | C2×C4×Q16 | — | 3 | 1 | no | — |
| 78 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 79 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 81 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 82 | C3×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 83 | C3×#125 | C23 | 1 | 4 | yes | — |
| 84 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 85 | C3×C22⋊Q8 | — | 2 | 2 | no | — |
| 86 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 87 | C3×C4×Q8 | — | 2 | 2 | no | — |
| 88 | C3×#117 | C23 | 1 | 4 | yes | — |
| 89 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 90 | Q8×Dic3 | — | 2 | 4 | no | — |
| 91 | #944 | — | 2 | 4 | no | — |
| 92 | #944 | — | 2 | 8 | no | — |
| 93 | #926 | C23 | 1 | 2 | yes | — |
| 94 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 95 | #924 | D4 | 1 | 2 | yes | — |
| 96 | #924 | D4 | 1 | 2 | yes | — |
| 97 | C2×Dic3⋊C4 | — | 2 | 2 | no | — |
| 98 | C2×C4×Dic3 | — | 2 | 2 | no | — |
| 99 | C2×#208 | C23 | 1 | 2 | yes | — |
| 100 | C2×Dic12 | Q8 | 1 | 8 | yes | complemented |
| 101 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 102 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 103 | #890 | C23 | 1 | 8 | yes | — |
| 104 | #889 | — | 2 | 8 | no | — |
| 105 | #889 | — | 2 | 8 | no | — |
| 106 | #889 | — | 2 | 8 | no | — |
| 107 | #888 | — | 2 | 8 | no | — |
| 108 | #888 | — | 2 | 4 | no | — |
| 109 | #888 | C23 | 1 | 8 | yes | — |
| 110 | #887 | — | 2 | 4 | no | — |
| 111 | #887 | — | 2 | 8 | no | — |
| 112 | #887 | C23 | 1 | 8 | yes | — |
| 113 | #887 | C23 | 1 | 8 | yes | — |
| 114 | #878 | — | 2 | 8 | no | — |
| 115 | #877 | — | 2 | 8 | no | — |
| 116 | #870 | — | 2 | 4 | no | — |
| 117 | #870 | D4 | 1 | 2 | yes | — |
| 118 | #869 | — | 2 | 4 | no | — |
| 119 | #869 | D4 | 1 | 1 | yes | characteristic |
| 120 | #869 | D4 | 1 | 1 | yes | characteristic |
| 121 | C4×Dic6 | — | 2 | 2 | no | — |
| 122 | C4×Dic6 | — | 2 | 2 | no | — |
| 123 | C4×Dic6 | — | 2 | 4 | no | — |
| 124 | C4×Dic6 | — | 2 | 4 | no | — |
| 125 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 126 | C4×Dic6 | C23 | 1 | 4 | yes | — |
| 127 | C4×Dic6 | C23 | 1 | 2 | yes | — |
| 128 | C4×Dic6 | C23 | 1 | 2 | yes | — |
| 129 | C3×#107 | C23 | 1 | 2 | yes | — |
| 130 | C3×#107 | C23 | 1 | 2 | yes | — |
| 131 | C3×#107 | C23 | 1 | 2 | yes | — |
| 132 | C3×#107 | C23 | 1 | 2 | yes | — |
| 133 | C3×#106 | C23 | 1 | 4 | yes | — |
| 134 | C3×#106 | C23 | 1 | 4 | yes | — |
| 135 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 136 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 137 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 138 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 139 | #818 | C23 | 1 | 2 | yes | — |
| 140 | #818 | C23 | 1 | 2 | yes | — |
| 141 | #816 | C23 | 1 | 4 | yes | — |
| 142 | #816 | C23 | 1 | 4 | yes | — |
| 143 | #815 | C23 | 1 | 4 | yes | — |
| 144 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 145 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 146 | C8×Dic3 | C23 | 1 | 4 | yes | — |
| 147 | #810 | C23 | 1 | 8 | yes | — |
| 148 | #810 | C23 | 1 | 8 | yes | — |
| 149 | #808 | C23 | 1 | 8 | yes | — |
| 150 | #807 | C23 | 1 | 8 | yes | — |
| 151 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 152 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 153 | C22×Q16 | — | 3 | 1 | no | — |
| 154 | Q82 | — | 3 | 4 | no | — |
| 155 | Q82 | — | 6 | 2 | no | — |
| 156 | #557 | — | 3 | 4 | no | — |
| 157 | #557 | — | 3 | 8 | no | — |
| 158 | #557 | — | 6 | 4 | no | — |
| 159 | #557 | — | 6 | 2 | no | — |
| 160 | #544 | — | 3 | 4 | no | — |
| 161 | #544 | — | 6 | 4 | no | — |
| 162 | #533 | — | 3 | 1 | no | — |
| 163 | #533 | — | 6 | 4 | no | — |
| 164 | #533 | C2×D3 | 1 | 2 | yes | — |
| 165 | #519 | — | 3 | 4 | no | — |
| 166 | C2×C4×Q8 | — | 3 | 2 | no | — |
| 167 | #501 | — | 3 | 8 | no | — |
| 168 | #500 | — | 3 | 4 | no | — |
| 169 | #500 | C2×D3 | 1 | 1 | yes | characteristic |
| 170 | #500 | C2×D3 | 1 | 1 | yes | characteristic |
| 171 | #499 | — | 3 | 4 | no | — |
| 172 | #499 | C2×D3 | 1 | 2 | yes | — |
| 173 | #499 | C2×D3 | 1 | 2 | yes | — |
| 174 | #498 | C2×D3 | 1 | 2 | yes | — |
| 175 | #479 | — | 3 | 8 | no | — |
| 176 | #479 | — | 3 | 8 | no | — |
| 177 | #479 | — | 3 | 8 | no | — |
| 178 | #477 | — | 3 | 4 | no | — |
| 179 | #477 | — | 3 | 8 | no | — |
| 180 | #475 | — | 3 | 4 | no | — |
| 181 | #475 | — | 3 | 8 | no | — |
| 182 | #446 | — | 3 | 2 | no | — |
| 183 | #446 | — | 3 | 2 | no | — |
| 184 | C8×Q8 | — | 3 | 2 | no | — |
| 185 | C8×Q8 | — | 3 | 2 | no | — |
| 186 | #441 | — | 3 | 8 | no | — |
| 187 | C4×Q16 | — | 3 | 4 | no | — |
| 188 | C4×Q16 | — | 3 | 4 | no | — |
| 189 | C4×Q16 | — | 3 | 2 | no | — |
| 190 | C4×Q16 | — | 3 | 2 | no | — |
| 191 | C4×Q16 | — | 3 | 2 | no | — |
| 192 | C4×Q16 | — | 3 | 2 | no | — |
| 193 | #428 | — | 3 | 4 | no | — |
| 194 | #427 | C2×D3 | 1 | 2 | yes | — |
| 195 | #427 | C2×D3 | 1 | 2 | yes | — |
| 196 | C2×#107 | — | 3 | 1 | no | — |
| 197 | #424 | — | 3 | 2 | no | — |
| 198 | #423 | — | 3 | 1 | no | — |
| 199 | #419 | — | 3 | 4 | no | — |
| 200 | C2×#103 | — | 3 | 2 | no | — |
| 201 | #405 | — | 3 | 2 | no | — |
| 202 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 203 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 204 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 205 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 208 | C22×Dic3 | — | 2 | 2 | no | — |
| 209 | C22×Dic3 | — | 2 | 2 | no | — |
| 210 | C2×Dic6 | — | 2 | 2 | no | — |
| 211 | C2×Dic6 | — | 2 | 4 | no | — |
| 212 | C2×Dic6 | — | 2 | 8 | no | — |
| 213 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 214 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 215 | C2×Dic6 | C2×Q8 | 1 | 8 | yes | — |
| 216 | C2×Dic6 | C24 | 1 | 4 | yes | — |
| 217 | C2×C3×C8 | — | 2 | 2 | no | — |
| 218 | C2×C3×C8 | C2×Q8 | 1 | 4 | yes | — |
| 219 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 220 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 221 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 222 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 223 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 224 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 225 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 226 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 227 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 228 | C3×C4⋊C4 | C24 | 1 | 4 | yes | — |
| 229 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 230 | C3×C42 | — | 2 | 4 | no | — |
| 231 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 234 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 235 | #217 | C2×D4 | 1 | 4 | yes | — |
| 236 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 237 | C4⋊Dic3 | — | 2 | 8 | no | — |
| 238 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 239 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 240 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 241 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 242 | C4⋊Dic3 | C24 | 1 | 4 | yes | — |
| 243 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 244 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 245 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 246 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 247 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 248 | Dic3⋊C4 | — | 2 | 8 | no | — |
| 249 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 250 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 251 | C4×Dic3 | — | 2 | 4 | no | — |
| 252 | C4×Dic3 | — | 2 | 4 | no | — |
| 253 | C4×Dic3 | — | 2 | 8 | no | — |
| 254 | C4×Dic3 | — | 2 | 8 | no | — |
| 255 | C4×Dic3 | C24 | 1 | 4 | yes | — |
| 256 | #208 | — | 2 | 4 | no | — |
| 257 | C2×C3⋊C8 | C24 | 1 | 4 | yes | — |
| 258 | Dic12 | C2×Q8 | 1 | 8 | yes | — |
| 259 | Dic12 | C2×Q8 | 1 | 8 | yes | — |
| 260 | C22×Q8 | — | 3 | 2 | no | — |
| 261 | C2×Q16 | — | 3 | 8 | no | — |
| 262 | C2×Q16 | — | 3 | 2 | no | — |
| 263 | C2×Q16 | — | 3 | 2 | no | — |
| 264 | C2×M16 | — | 3 | 2 | no | — |
| 265 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 266 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 267 | C4⋊Q8 | — | 3 | 8 | no | — |
| 268 | C4⋊Q8 | — | 3 | 1 | no | — |
| 269 | C4⋊Q8 | — | 3 | 1 | no | — |
| 270 | C4⋊Q8 | — | 6 | 4 | no | — |
| 271 | C4⋊Q8 | — | 6 | 4 | no | — |
| 272 | C4⋊Q8 | — | 6 | 8 | no | — |
| 273 | C4⋊Q8 | — | 6 | 8 | no | — |
| 274 | C4⋊Q8 | — | 6 | 4 | no | — |
| 275 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 276 | C4⋊Q8 | C22×D3 | 1 | 2 | yes | — |
| 277 | #125 | — | 3 | 8 | no | — |
| 278 | #125 | — | 3 | 2 | no | — |
| 279 | #125 | — | 6 | 4 | no | — |
| 280 | #125 | — | 6 | 8 | no | — |
| 281 | #125 | — | 6 | 8 | no | — |
| 282 | #125 | — | 6 | 8 | no | — |
| 283 | #125 | C22×D3 | 1 | 4 | yes | — |
| 284 | C22⋊Q8 | — | 2 | 2 | no | — |
| 285 | C22⋊Q8 | — | 2 | 2 | no | — |
| 286 | C22⋊Q8 | — | 3 | 2 | no | — |
| 287 | C22⋊Q8 | — | 3 | 2 | no | — |
| 288 | C22⋊Q8 | — | 6 | 8 | no | — |
| 289 | C4×Q8 | — | 2 | 2 | no | — |
| 290 | C4×Q8 | — | 2 | 2 | no | — |
| 291 | C4×Q8 | — | 3 | 2 | no | — |
| 292 | C4×Q8 | — | 3 | 2 | no | — |
| 293 | C4×Q8 | — | 3 | 8 | no | — |
| 294 | C4×Q8 | — | 3 | 8 | no | — |
| 295 | C4×Q8 | — | 3 | 4 | no | — |
| 296 | C4×Q8 | — | 3 | 4 | no | — |
| 297 | C4×Q8 | — | 6 | 4 | no | — |
| 298 | C4×Q8 | — | 6 | 4 | no | — |
| 299 | C4×Q8 | — | 6 | 8 | no | — |
| 300 | C4×Q8 | — | 6 | 4 | no | — |
| 301 | C4×Q8 | — | 6 | 4 | no | — |
| 302 | C4×Q8 | — | 6 | 2 | no | — |
| 303 | C4×Q8 | — | 6 | 2 | no | — |
| 304 | #117 | — | 3 | 2 | no | — |
| 305 | #117 | — | 6 | 8 | no | — |
| 306 | #117 | C22×D3 | 1 | 4 | yes | — |
| 307 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 308 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 309 | C2×C42 | — | 6 | 2 | no | — |
| 310 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 311 | #107 | — | 3 | 2 | no | — |
| 312 | #107 | — | 3 | 2 | no | — |
| 313 | #107 | — | 3 | 8 | no | — |
| 314 | #107 | C22×D3 | 1 | 2 | yes | — |
| 315 | #107 | C22×D3 | 1 | 2 | yes | — |
| 316 | #107 | C22×D3 | 1 | 2 | yes | — |
| 317 | #107 | C22×D3 | 1 | 2 | yes | — |
| 318 | #106 | — | 3 | 8 | no | — |
| 319 | #106 | C22×D3 | 1 | 4 | yes | — |
| 320 | #106 | C22×D3 | 1 | 4 | yes | — |
| 321 | C4⋊C8 | — | 3 | 4 | no | — |
| 322 | C4⋊C8 | — | 3 | 4 | no | — |
| 323 | C4⋊C8 | — | 3 | 2 | no | — |
| 324 | C4⋊C8 | — | 3 | 2 | no | — |
| 325 | #103 | — | 3 | 4 | no | — |
| 326 | #103 | — | 3 | 4 | no | — |
| 327 | #103 | — | 3 | 8 | no | — |
| 328 | #103 | — | 3 | 8 | no | — |
| 329 | #97 | — | 3 | 4 | no | — |
| 330 | C4×C8 | — | 3 | 4 | no | — |
| 331 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 332 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 333 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 334 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 335 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 336 | C3×Q8 | — | 4 | 4 | no | — |
| 337 | C3×Q8 | — | 8 | 2 | no | — |
| 338 | C2×C3×C4 | — | 2 | 2 | no | — |
| 339 | C2×C3×C4 | — | 2 | 4 | no | — |
| 340 | C2×C3×C4 | — | 2 | 4 | no | — |
| 341 | C2×C3×C4 | — | 4 | 1 | no | — |
| 342 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 343 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 344 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 345 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 346 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 347 | C2×C3×C4 | C22×Q8 | 1 | 2 | yes | — |
| 348 | C2×C3×C4 | 2−1+4 | 1 | 2 | yes | — |
| 349 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 350 | C2×Dic3 | — | 2 | 8 | no | — |
| 351 | C2×Dic3 | — | 2 | 4 | no | — |
| 352 | C2×Dic3 | — | 2 | 4 | no | — |
| 353 | C2×Dic3 | — | 8 | 2 | no | — |
| 354 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 355 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 356 | Dic6 | — | 2 | 8 | no | — |
| 357 | Dic6 | — | 2 | 4 | no | — |
| 358 | Dic6 | — | 2 | 4 | no | — |
| 359 | Dic6 | — | 4 | 2 | no | — |
| 360 | Dic6 | — | 8 | 8 | no | — |
| 361 | Dic6 | C22×Q8 | 1 | 8 | yes | — |
| 362 | C3×C8 | — | 2 | 1 | no | — |
| 363 | C3×C8 | — | 2 | 1 | no | — |
| 364 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 365 | C3×C8 | C22×Q8 | 1 | 2 | yes | — |
| 366 | C3⋊C8 | — | 2 | 4 | no | — |
| 367 | C2×Q8 | — | 2 | 2 | no | — |
| 368 | C2×Q8 | — | 2 | 2 | no | — |
| 369 | C2×Q8 | — | 3 | 2 | no | — |
| 370 | C2×Q8 | — | 3 | 2 | no | — |
| 371 | C2×Q8 | — | 3 | 8 | no | — |
| 372 | C2×Q8 | — | 3 | 4 | no | — |
| 373 | C2×Q8 | — | 6 | 8 | no | — |
| 374 | C2×Q8 | — | 6 | 2 | no | — |
| 375 | C2×Q8 | — | 6 | 4 | no | — |
| 376 | C22×C4 | — | 6 | 2 | no | — |
| 377 | C22×C4 | — | 6 | 2 | no | — |
| 378 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 379 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 380 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 381 | Q16 | — | 3 | 8 | no | — |
| 382 | Q16 | — | 3 | 8 | no | — |
| 383 | M16 | — | 6 | 4 | no | — |
| 384 | C2×C8 | — | 2 | 2 | no | — |
| 385 | C2×C8 | — | 3 | 4 | no | — |
| 386 | C2×C8 | D3×Q8 | 1 | 4 | yes | — |
| 387 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 388 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 389 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 390 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 391 | C4⋊C4 | — | 2 | 4 | no | — |
| 392 | C4⋊C4 | — | 2 | 2 | no | — |
| 393 | C4⋊C4 | — | 2 | 2 | no | — |
| 394 | C4⋊C4 | — | 2 | 4 | no | — |
| 395 | C4⋊C4 | — | 3 | 2 | no | — |
| 396 | C4⋊C4 | — | 3 | 2 | no | — |
| 397 | C4⋊C4 | — | 3 | 4 | no | — |
| 398 | C4⋊C4 | — | 3 | 2 | no | — |
| 399 | C4⋊C4 | — | 3 | 4 | no | — |
| 400 | C4⋊C4 | — | 3 | 2 | no | — |
| 401 | C4⋊C4 | — | 3 | 4 | no | — |
| 402 | C4⋊C4 | — | 6 | 8 | no | — |
| 403 | C4⋊C4 | — | 6 | 8 | no | — |
| 404 | C4⋊C4 | — | 6 | 8 | no | — |
| 405 | C4⋊C4 | — | 6 | 8 | no | — |
| 406 | C4⋊C4 | — | 6 | 8 | no | — |
| 407 | C4⋊C4 | — | 6 | 2 | no | — |
| 408 | C4⋊C4 | — | 6 | 4 | no | — |
| 409 | C4⋊C4 | — | 6 | 4 | no | — |
| 410 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 411 | C4⋊C4 | C23×D3 | 1 | 4 | yes | — |
| 412 | C22⋊C4 | — | 2 | 4 | no | — |
| 413 | C22⋊C4 | — | 3 | 4 | no | — |
| 414 | C42 | — | 2 | 4 | no | — |
| 415 | C42 | — | 3 | 4 | no | — |
| 416 | C42 | — | 6 | 8 | no | — |
| 417 | C42 | — | 6 | 8 | no | — |
| 418 | C42 | — | 6 | 4 | no | — |
| 419 | C42 | — | 6 | 4 | no | — |
| 420 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 421 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 422 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 423 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 424 | C22×C3 | — | 2 | 1 | no | — |
| 425 | C22×C3 | — | 2 | 1 | no | — |
| 426 | C22×C3 | D4×Q8 | 1 | 2 | yes | — |
| 427 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 428 | C3×C4 | — | 2 | 1 | no | — |
| 429 | C3×C4 | — | 2 | 1 | no | — |
| 430 | C3×C4 | — | 2 | 1 | no | — |
| 431 | C3×C4 | — | 4 | 4 | no | — |
| 432 | C3×C4 | — | 4 | 4 | no | — |
| 433 | C3×C4 | D4×Q8 | 1 | 2 | yes | — |
| 434 | C3×C4 | #578 | 1 | 2 | yes | — |
| 435 | C3×C4 | C23×Q8 | 1 | 1 | yes | characteristic |
| 436 | C3×C4 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 437 | Dic3 | — | 2 | 4 | no | — |
| 438 | Dic3 | — | 2 | 8 | no | — |
| 439 | Dic3 | — | 2 | 4 | no | — |
| 440 | Dic3 | — | 4 | 4 | no | — |
| 441 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 442 | Q8 | — | 3 | 8 | no | — |
| 443 | Q8 | — | 4 | 4 | no | — |
| 444 | Q8 | — | 6 | 4 | no | — |
| 445 | Q8 | — | 6 | 8 | no | — |
| 446 | Q8 | — | 6 | 4 | no | — |
| 447 | Q8 | — | 8 | 2 | no | — |
| 448 | Q8 | — | 12 | 2 | no | — |
| 449 | Q8 | — | 24 | 8 | no | — |
| 450 | C2×C4 | — | 2 | 2 | no | — |
| 451 | C2×C4 | — | 2 | 4 | no | — |
| 452 | C2×C4 | — | 2 | 4 | no | — |
| 453 | C2×C4 | — | 3 | 4 | no | — |
| 454 | C2×C4 | — | 3 | 4 | no | — |
| 455 | C2×C4 | — | 4 | 1 | no | — |
| 456 | C2×C4 | — | 6 | 4 | no | — |
| 457 | C2×C4 | — | 6 | 8 | no | — |
| 458 | C2×C4 | — | 6 | 4 | no | — |
| 459 | C2×C4 | — | 24 | 2 | no | — |
| 460 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 461 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 463 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 464 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | C2×D3×Q8 | 1 | 2 | yes | — |
| 466 | C2×C4 | #1007 | 1 | 2 | yes | — |
| 467 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 468 | C8 | — | 2 | 1 | no | — |
| 469 | C8 | — | 2 | 1 | no | — |
| 470 | C8 | — | 6 | 4 | no | — |
| 471 | C8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 472 | C8 | C2×D3×Q8 | 1 | 2 | yes | — |
| 473 | C2×C3 | — | 2 | 2 | no | — |
| 474 | C2×C3 | C2×D4×Q8 | 1 | 1 | yes | characteristic |
| 475 | C2×C3 | C2×#578 | 1 | 1 | yes | characteristic |
| 476 | C2×C3 | #3584 | 1 | 1 | yes | characteristic |
| 477 | C22 | — | 2 | 1 | no | — |
| 478 | C22 | — | 2 | 1 | no | — |
| 479 | C22 | #5727 | 1 | 2 | yes | — |
| 480 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 481 | C4 | — | 2 | 1 | no | — |
| 482 | C4 | — | 2 | 1 | no | — |
| 483 | C4 | — | 2 | 1 | no | — |
| 484 | C4 | — | 4 | 4 | no | — |
| 485 | C4 | — | 4 | 4 | no | — |
| 486 | C4 | — | 6 | 4 | no | — |
| 487 | C4 | — | 6 | 4 | no | — |
| 488 | C4 | — | 6 | 8 | no | — |
| 489 | C4 | — | 12 | 4 | no | — |
| 490 | C4 | #5727 | 1 | 2 | yes | — |
| 491 | C4 | #5771 | 1 | 2 | yes | — |
| 492 | C4 | C22×D3×Q8 | 1 | 1 | yes | characteristic |
| 493 | C4 | C2×#1007 | 1 | 1 | yes | characteristic |
| 494 | C3 | #61372 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 495 | C2 | — | 2 | 2 | no | — |
| 496 | C2 | C2×#5727 | 1 | 1 | yes | characteristic |
| 497 | C2 | C2×#5771 | 1 | 1 | yes | characteristic |
| 498 | C2 | #87187 | 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