← #11895496
Subgroups — #11895496
Order 1152.
720 conjugacy classes of subgroups.
The subgroup lattice has 672 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10595338 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10594312 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10592492 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#4795 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×#4792 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #10591623 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #10591581 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10591574 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | Dic3×Dic12 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10590804 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #10590798 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10590644 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #10590567 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #10590489 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #10590476 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #81624 | — | 3 | 1 | no | maximal |
| 17 | #80462 | — | 3 | 1 | no | maximal |
| 18 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64097 | C22 | 1 | 1 | yes | characteristic |
| 20 | C3×#944 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#944 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C3×#216 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#888 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#887 | C22 | 1 | 1 | yes | characteristic |
| 26 | #63918 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×#627 | C22 | 1 | 1 | yes | characteristic |
| 28 | #63873 | C22 | 1 | 1 | yes | characteristic |
| 29 | #63870 | — | 2 | 1 | no | — |
| 30 | #63866 | — | 2 | 1 | no | — |
| 31 | #63845 | — | 2 | 1 | no | — |
| 32 | #63845 | — | 2 | 1 | no | — |
| 33 | #63843 | C22 | 1 | 1 | yes | characteristic |
| 34 | Dic3×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 35 | Dic3×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 36 | Dic3×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 37 | #63840 | — | 2 | 1 | no | — |
| 38 | #63839 | — | 2 | 1 | no | — |
| 39 | #63838 | — | 2 | 1 | no | — |
| 40 | #63837 | — | 2 | 1 | no | — |
| 41 | C2×#3718 | C22 | 1 | 1 | yes | characteristic |
| 42 | C32×#103 | C22 | 1 | 1 | yes | characteristic |
| 43 | #63662 | C22 | 1 | 1 | yes | characteristic |
| 44 | #63645 | C22 | 1 | 1 | yes | characteristic |
| 45 | #63641 | C22 | 1 | 1 | yes | characteristic |
| 46 | #63634 | C22 | 1 | 1 | yes | characteristic |
| 47 | C3×#835 | C22 | 1 | 1 | yes | characteristic |
| 48 | C3×#816 | C22 | 1 | 1 | yes | characteristic |
| 49 | C3×Dic3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 50 | C3×C8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 51 | C3×#810 | C22 | 1 | 1 | yes | characteristic |
| 52 | C3×#810 | C22 | 1 | 1 | yes | characteristic |
| 53 | #63575 | C22 | 1 | 1 | yes | characteristic |
| 54 | Dic3⋊(C3⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 55 | #63566 | C22 | 1 | 1 | yes | characteristic |
| 56 | #63566 | C22 | 1 | 1 | yes | characteristic |
| 57 | #63566 | C22 | 1 | 1 | yes | characteristic |
| 58 | #63565 | C22 | 1 | 1 | yes | characteristic |
| 59 | #63553 | C22 | 1 | 1 | yes | characteristic |
| 60 | Dic3×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | #5722 | — | 3 | 1 | no | — |
| 62 | #5721 | — | 3 | 1 | no | — |
| 63 | #5721 | — | 3 | 1 | no | — |
| 64 | Q8×Dic6 | — | 3 | 1 | no | — |
| 65 | C3×#487 | — | 3 | 1 | no | — |
| 66 | C3×#462 | — | 3 | 1 | no | — |
| 67 | #5182 | — | 3 | 1 | no | — |
| 68 | #5182 | — | 3 | 1 | no | — |
| 69 | Dic3×Q16 | — | 3 | 1 | no | — |
| 70 | Dic3×Q16 | — | 3 | 1 | no | — |
| 71 | #5091 | — | 3 | 1 | no | — |
| 72 | #5090 | — | 3 | 1 | no | — |
| 73 | #5079 | — | 3 | 1 | no | — |
| 74 | C4×#216 | — | 3 | 1 | no | — |
| 75 | #4850 | — | 3 | 1 | no | — |
| 76 | #4830 | — | 3 | 1 | no | — |
| 77 | #4795 | — | 3 | 1 | no | — |
| 78 | #4795 | D3 | 1 | 1 | yes | characteristic |
| 79 | #4793 | — | 3 | 1 | no | — |
| 80 | #4793 | — | 3 | 1 | no | — |
| 81 | #4793 | — | 3 | 1 | no | — |
| 82 | #4793 | — | 3 | 1 | no | — |
| 83 | #4793 | — | 6 | 1 | no | — |
| 84 | #4792 | — | 3 | 1 | no | — |
| 85 | #4792 | — | 3 | 1 | no | — |
| 86 | #4792 | — | 3 | 1 | no | — |
| 87 | #4792 | D3 | 1 | 1 | yes | characteristic |
| 88 | #4790 | — | 3 | 1 | no | — |
| 89 | #4790 | — | 3 | 1 | no | — |
| 90 | C4×Dic12 | — | 3 | 1 | no | — |
| 91 | C8×Dic6 | — | 3 | 1 | no | — |
| 92 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×#634 | — | 2 | 1 | no | — |
| 94 | C2×C3×Dic6 | — | 2 | 1 | no | — |
| 95 | C2×C3×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×#627 | — | 2 | 1 | no | — |
| 99 | C2×#627 | D4 | 1 | 1 | yes | characteristic |
| 100 | C2×C32×C8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C32×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 102 | C4⋊(C3⋊Dic3) | — | 2 | 1 | no | — |
| 103 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 104 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 105 | #3750 | — | 2 | 1 | no | — |
| 106 | C4×C3⋊Dic3 | — | 2 | 1 | no | — |
| 107 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C3⋊(C3⋊C8) | C23 | 1 | 1 | yes | characteristic |
| 109 | C3×#216 | — | 2 | 2 | no | — |
| 110 | C3×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 111 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 112 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 113 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 114 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 115 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 116 | C3×Dic3⋊C4 | — | 2 | 1 | no | — |
| 117 | C3×C4×Dic3 | — | 2 | 1 | no | — |
| 118 | C3×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 119 | C3×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 120 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 121 | C2×C3×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 122 | C3×Dic12 | — | 2 | 2 | no | — |
| 123 | #3724 | — | 2 | 1 | no | — |
| 124 | #3724 | — | 2 | 1 | no | — |
| 125 | #3724 | D4 | 1 | 1 | yes | characteristic |
| 126 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 127 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 128 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 129 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 130 | Dic3⋊Dic3 | — | 2 | 1 | no | — |
| 131 | Dic3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 132 | Dic3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 133 | Dic32 | — | 2 | 1 | no | — |
| 134 | Dic32 | — | 2 | 1 | no | — |
| 135 | Dic32 | — | 2 | 1 | no | — |
| 136 | Dic32 | — | 2 | 1 | no | — |
| 137 | #3718 | — | 2 | 2 | no | — |
| 138 | #3363 | — | 9 | 1 | no | Sylow |
| 139 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 140 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 141 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 142 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 143 | C3×C4⋊Q8 | — | 3 | 1 | no | — |
| 144 | C3×C4×Q8 | — | 3 | 1 | no | — |
| 145 | Q8×Dic3 | — | 3 | 1 | no | — |
| 146 | Q8×Dic3 | — | 3 | 1 | no | — |
| 147 | Q8×Dic3 | — | 3 | 1 | no | — |
| 148 | Q8×Dic3 | — | 3 | 1 | no | — |
| 149 | Q8×Dic3 | — | 3 | 1 | no | — |
| 150 | Q8×Dic3 | — | 3 | 1 | no | — |
| 151 | Q8×Dic3 | — | 6 | 1 | no | — |
| 152 | #944 | — | 3 | 1 | no | — |
| 153 | #944 | — | 3 | 1 | no | — |
| 154 | #944 | — | 6 | 1 | no | — |
| 155 | #944 | — | 6 | 1 | no | — |
| 156 | #944 | C2×D3 | 1 | 1 | yes | characteristic |
| 157 | #944 | C2×D3 | 1 | 1 | yes | characteristic |
| 158 | C2×#216 | — | 3 | 1 | no | — |
| 159 | C2×#216 | — | 3 | 1 | no | — |
| 160 | C2×#216 | C2×D3 | 1 | 1 | yes | characteristic |
| 161 | C2×Dic12 | C2×D3 | 1 | 1 | yes | characteristic |
| 162 | #890 | — | 6 | 1 | no | — |
| 163 | #890 | — | 6 | 1 | no | — |
| 164 | #889 | — | 6 | 1 | no | — |
| 165 | #889 | — | 6 | 1 | no | — |
| 166 | #889 | — | 6 | 1 | no | — |
| 167 | #889 | — | 6 | 1 | no | — |
| 168 | #888 | — | 3 | 1 | no | — |
| 169 | #888 | — | 3 | 1 | no | — |
| 170 | #888 | — | 3 | 1 | no | — |
| 171 | #888 | — | 6 | 1 | no | — |
| 172 | #888 | — | 6 | 1 | no | — |
| 173 | #888 | — | 6 | 1 | no | — |
| 174 | #888 | — | 6 | 1 | no | — |
| 175 | #888 | C2×D3 | 1 | 1 | yes | characteristic |
| 176 | #887 | — | 3 | 1 | no | — |
| 177 | #887 | — | 6 | 1 | no | — |
| 178 | #887 | — | 6 | 1 | no | — |
| 179 | #887 | — | 6 | 1 | no | — |
| 180 | #887 | C2×D3 | 1 | 1 | yes | characteristic |
| 181 | #869 | — | 3 | 1 | no | — |
| 182 | #869 | — | 6 | 1 | no | — |
| 183 | C4×Dic6 | — | 3 | 1 | no | — |
| 184 | C4×Dic6 | — | 3 | 1 | no | — |
| 185 | C4×Dic6 | — | 3 | 1 | no | — |
| 186 | C4×Dic6 | — | 3 | 1 | no | — |
| 187 | C4×Dic6 | — | 3 | 1 | no | — |
| 188 | C4×Dic6 | — | 6 | 1 | no | — |
| 189 | C3×C4⋊C8 | — | 3 | 1 | no | — |
| 190 | C3×#103 | — | 2 | 1 | no | — |
| 191 | C3×#103 | — | 3 | 1 | no | — |
| 192 | C3×#103 | — | 3 | 1 | no | — |
| 193 | C3×#103 | — | 3 | 1 | no | — |
| 194 | C3×#103 | — | 3 | 1 | no | — |
| 195 | C3×#103 | C2×D3 | 1 | 1 | yes | characteristic |
| 196 | C3×#103 | C2×D3 | 1 | 1 | yes | characteristic |
| 197 | C3×C4×C8 | — | 3 | 1 | no | — |
| 198 | #835 | — | 3 | 1 | no | — |
| 199 | #835 | — | 3 | 1 | no | — |
| 200 | #835 | — | 3 | 1 | no | — |
| 201 | #835 | — | 3 | 1 | no | — |
| 202 | #835 | — | 3 | 1 | no | — |
| 203 | #835 | — | 3 | 1 | no | — |
| 204 | #835 | — | 6 | 1 | no | — |
| 205 | #835 | C2×D3 | 1 | 1 | yes | characteristic |
| 206 | #818 | — | 3 | 1 | no | — |
| 207 | #818 | — | 3 | 1 | no | — |
| 208 | #818 | — | 3 | 1 | no | — |
| 209 | #818 | — | 6 | 1 | no | — |
| 210 | #816 | — | 3 | 1 | no | — |
| 211 | #816 | — | 3 | 1 | no | — |
| 212 | #816 | — | 3 | 1 | no | — |
| 213 | #816 | C2×D3 | 1 | 1 | yes | characteristic |
| 214 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 215 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 216 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 217 | Dic3⋊C8 | — | 6 | 1 | no | — |
| 218 | Dic3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 219 | C8×Dic3 | — | 3 | 1 | no | — |
| 220 | C8×Dic3 | — | 3 | 1 | no | — |
| 221 | C8×Dic3 | — | 3 | 1 | no | — |
| 222 | C8×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 223 | #810 | — | 3 | 1 | no | — |
| 224 | #810 | C2×D3 | 1 | 1 | yes | characteristic |
| 225 | #810 | C2×D3 | 1 | 1 | yes | characteristic |
| 226 | #807 | — | 3 | 1 | no | — |
| 227 | #807 | — | 3 | 1 | no | — |
| 228 | #807 | — | 3 | 1 | no | — |
| 229 | #807 | — | 6 | 1 | no | — |
| 230 | C4⋊(C3⋊C8) | — | 3 | 1 | no | — |
| 231 | C4×C3⋊C8 | — | 3 | 1 | no | — |
| 232 | C32×Q8 | — | 2 | 1 | no | — |
| 233 | C32×Q8 | — | 2 | 1 | no | — |
| 234 | C2×C32×C4 | — | 2 | 1 | no | — |
| 235 | C2×C32×C4 | — | 2 | 1 | no | — |
| 236 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 237 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 238 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 239 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C3⋊Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | #634 | — | 8 | 1 | no | — |
| 242 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 243 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 244 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 245 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 246 | C2×C3×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C3×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×C3×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C3×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C3×Dic6 | — | 2 | 1 | no | — |
| 251 | C3×Dic6 | — | 2 | 1 | no | — |
| 252 | C3×Dic6 | — | 2 | 1 | no | — |
| 253 | C3×Dic6 | — | 2 | 1 | no | — |
| 254 | C3×Dic6 | — | 2 | 1 | no | — |
| 255 | C3×Dic6 | — | 8 | 1 | no | — |
| 256 | C3×Dic6 | #41 | 1 | 2 | yes | — |
| 257 | #627 | — | 8 | 1 | no | — |
| 258 | #627 | Q16 | 1 | 4 | yes | complemented |
| 259 | C32×C8 | — | 2 | 1 | no | — |
| 260 | C3⋊(C3⋊C8) | — | 2 | 1 | no | — |
| 261 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 262 | C3×C3⋊C8 | — | 2 | 1 | no | — |
| 263 | Q82 | — | 9 | 1 | no | — |
| 264 | #557 | — | 9 | 1 | no | — |
| 265 | #487 | — | 3 | 1 | no | — |
| 266 | #487 | — | 9 | 1 | no | — |
| 267 | #487 | — | 9 | 1 | no | — |
| 268 | #477 | — | 9 | 1 | no | — |
| 269 | #477 | — | 9 | 1 | no | — |
| 270 | #477 | — | 9 | 1 | no | — |
| 271 | #462 | — | 3 | 1 | no | — |
| 272 | #462 | — | 9 | 1 | no | — |
| 273 | #462 | — | 9 | 1 | no | — |
| 274 | C8×Q8 | — | 9 | 1 | no | — |
| 275 | C4×Q16 | — | 9 | 1 | no | — |
| 276 | C4×Q16 | — | 9 | 1 | no | — |
| 277 | C4×Q16 | — | 9 | 1 | no | — |
| 278 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 279 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 280 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 281 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 282 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 283 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 284 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 285 | C2×Dic6 | — | 2 | 1 | no | — |
| 286 | C2×Dic6 | — | 3 | 1 | no | — |
| 287 | C2×Dic6 | — | 3 | 1 | no | — |
| 288 | C2×Dic6 | — | 6 | 1 | no | — |
| 289 | C2×Dic6 | — | 6 | 1 | no | — |
| 290 | C2×Dic6 | — | 6 | 1 | no | — |
| 291 | C2×Dic6 | — | 6 | 1 | no | — |
| 292 | C2×Dic6 | — | 12 | 1 | no | — |
| 293 | C2×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 294 | C2×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 295 | C2×Dic6 | C22×D3 | 1 | 1 | yes | characteristic |
| 296 | C3×Q16 | — | 6 | 2 | no | — |
| 297 | C3×Q16 | — | 6 | 2 | no | — |
| 298 | C2×C3×C8 | — | 2 | 1 | no | — |
| 299 | C2×C3×C8 | — | 3 | 1 | no | — |
| 300 | C2×C3×C8 | — | 3 | 1 | no | — |
| 301 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 302 | C2×C3×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 303 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 304 | C3×C4⋊C4 | — | 3 | 1 | no | — |
| 305 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 306 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 307 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 308 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 309 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 310 | C3×C4⋊C4 | — | 6 | 1 | no | — |
| 311 | C3×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 312 | C3×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 313 | C3×C42 | — | 3 | 1 | no | — |
| 314 | C3×C42 | — | 3 | 1 | no | — |
| 315 | C3×C42 | — | 6 | 1 | no | — |
| 316 | #216 | — | 2 | 2 | no | — |
| 317 | #216 | — | 6 | 2 | no | — |
| 318 | #216 | — | 6 | 2 | no | — |
| 319 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 320 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 321 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 322 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 323 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 324 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 325 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 326 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 327 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 328 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 329 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 330 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 331 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 332 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 333 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 334 | C4⋊Dic3 | — | 12 | 1 | no | — |
| 335 | C4⋊Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 336 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 337 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 338 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 339 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 340 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 341 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 342 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 343 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 344 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 345 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 346 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 347 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 348 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 349 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 350 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 351 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 352 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 353 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 354 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 355 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 356 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 357 | Dic3⋊C4 | — | 12 | 1 | no | — |
| 358 | C4×Dic3 | — | 2 | 1 | no | — |
| 359 | C4×Dic3 | — | 3 | 1 | no | — |
| 360 | C4×Dic3 | — | 3 | 1 | no | — |
| 361 | C4×Dic3 | — | 6 | 1 | no | — |
| 362 | C4×Dic3 | — | 6 | 1 | no | — |
| 363 | C4×Dic3 | — | 6 | 1 | no | — |
| 364 | C4×Dic3 | — | 6 | 1 | no | — |
| 365 | C4×Dic3 | — | 6 | 1 | no | — |
| 366 | C4×Dic3 | — | 6 | 1 | no | — |
| 367 | C4×Dic3 | — | 6 | 1 | no | — |
| 368 | C4×Dic3 | — | 6 | 1 | no | — |
| 369 | C4×Dic3 | — | 6 | 1 | no | — |
| 370 | C4×Dic3 | — | 6 | 1 | no | — |
| 371 | C4×Dic3 | — | 6 | 1 | no | — |
| 372 | C4×Dic3 | — | 12 | 1 | no | — |
| 373 | C4×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 374 | C4×Dic3 | C22×D3 | 1 | 1 | yes | characteristic |
| 375 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 376 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 377 | C2×C3⋊C8 | — | 6 | 1 | no | — |
| 378 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 379 | C2×C3⋊C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 380 | Dic12 | — | 2 | 2 | no | — |
| 381 | C22×C32 | C22×D4 | 1 | 1 | yes | characteristic |
| 382 | C32×C4 | — | 4 | 1 | no | — |
| 383 | C32×C4 | — | 4 | 1 | no | — |
| 384 | C32×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 385 | C32×C4 | 2−1+4 | 1 | 1 | yes | characteristic |
| 386 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 387 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 388 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 389 | C3⋊Dic3 | C2×Q16 | 1 | 2 | yes | — |
| 390 | C3×Dic3 | — | 2 | 2 | no | — |
| 391 | C3×Dic3 | — | 2 | 1 | no | — |
| 392 | C3×Dic3 | — | 2 | 1 | no | — |
| 393 | C3×Dic3 | — | 4 | 1 | no | — |
| 394 | C3×Dic3 | — | 4 | 1 | no | — |
| 395 | C3×Dic3 | — | 4 | 1 | no | — |
| 396 | C3×Dic3 | C2×Q16 | 1 | 2 | yes | — |
| 397 | C3×Dic3 | C2×Q16 | 1 | 2 | yes | — |
| 398 | C2×Q16 | — | 3 | 1 | no | — |
| 399 | C2×Q16 | — | 3 | 1 | no | — |
| 400 | C2×Q16 | — | 9 | 1 | no | — |
| 401 | C4⋊Q8 | — | 3 | 1 | no | — |
| 402 | C4⋊Q8 | — | 3 | 1 | no | — |
| 403 | C4⋊Q8 | — | 3 | 1 | no | — |
| 404 | C4⋊Q8 | — | 9 | 1 | no | — |
| 405 | C4⋊Q8 | — | 9 | 1 | no | — |
| 406 | C4⋊Q8 | — | 9 | 1 | no | — |
| 407 | C4⋊Q8 | — | 18 | 1 | no | — |
| 408 | C4⋊Q8 | — | 18 | 1 | no | — |
| 409 | C4⋊Q8 | — | 18 | 1 | no | — |
| 410 | #125 | — | 18 | 1 | no | — |
| 411 | #125 | — | 18 | 1 | no | — |
| 412 | #125 | — | 18 | 1 | no | — |
| 413 | C4×Q8 | — | 3 | 1 | no | — |
| 414 | C4×Q8 | — | 9 | 1 | no | — |
| 415 | C4×Q8 | — | 9 | 1 | no | — |
| 416 | C4×Q8 | — | 9 | 1 | no | — |
| 417 | C4×Q8 | — | 9 | 1 | no | — |
| 418 | C4×Q8 | — | 9 | 1 | no | — |
| 419 | C4×Q8 | — | 9 | 1 | no | — |
| 420 | C4×Q8 | — | 18 | 1 | no | — |
| 421 | C4×Q8 | — | 18 | 1 | no | — |
| 422 | #107 | — | 9 | 1 | no | — |
| 423 | #107 | — | 9 | 1 | no | — |
| 424 | #107 | — | 9 | 1 | no | — |
| 425 | C4⋊C8 | — | 3 | 1 | no | — |
| 426 | C4⋊C8 | — | 9 | 1 | no | — |
| 427 | C4⋊C8 | — | 9 | 1 | no | — |
| 428 | #103 | — | 3 | 1 | no | — |
| 429 | #103 | — | 3 | 1 | no | — |
| 430 | #103 | — | 3 | 1 | no | — |
| 431 | #103 | — | 3 | 1 | no | — |
| 432 | #103 | — | 9 | 1 | no | — |
| 433 | #103 | — | 9 | 1 | no | — |
| 434 | #103 | — | 9 | 1 | no | — |
| 435 | #103 | — | 9 | 1 | no | — |
| 436 | #103 | — | 9 | 1 | no | — |
| 437 | #103 | D32 | 1 | 1 | yes | characteristic |
| 438 | C4×C8 | — | 3 | 1 | no | — |
| 439 | C4×C8 | — | 9 | 1 | no | — |
| 440 | C4×C8 | — | 9 | 1 | no | — |
| 441 | C3×Q8 | — | 2 | 2 | no | — |
| 442 | C3×Q8 | — | 2 | 1 | no | — |
| 443 | C3×Q8 | — | 2 | 1 | no | — |
| 444 | C3×Q8 | — | 2 | 1 | no | — |
| 445 | C3×Q8 | — | 2 | 1 | no | — |
| 446 | C3×Q8 | — | 3 | 2 | no | — |
| 447 | C3×Q8 | — | 4 | 1 | no | — |
| 448 | C3×Q8 | — | 6 | 1 | no | — |
| 449 | C3×Q8 | — | 6 | 1 | no | — |
| 450 | C3×Q8 | — | 6 | 1 | no | — |
| 451 | C3×Q8 | — | 6 | 1 | no | — |
| 452 | C3×Q8 | — | 6 | 1 | no | — |
| 453 | C3×Q8 | — | 24 | 1 | no | — |
| 454 | C2×C3×C4 | — | 2 | 1 | no | — |
| 455 | C2×C3×C4 | — | 2 | 1 | no | — |
| 456 | C2×C3×C4 | — | 2 | 1 | no | — |
| 457 | C2×C3×C4 | — | 2 | 1 | no | — |
| 458 | C2×C3×C4 | — | 2 | 1 | no | — |
| 459 | C2×C3×C4 | — | 3 | 1 | no | — |
| 460 | C2×C3×C4 | — | 3 | 1 | no | — |
| 461 | C2×C3×C4 | — | 3 | 1 | no | — |
| 462 | C2×C3×C4 | — | 3 | 1 | no | — |
| 463 | C2×C3×C4 | — | 4 | 1 | no | — |
| 464 | C2×C3×C4 | — | 4 | 1 | no | — |
| 465 | C2×C3×C4 | — | 6 | 1 | no | — |
| 466 | C2×C3×C4 | — | 6 | 1 | no | — |
| 467 | C2×C3×C4 | — | 6 | 1 | no | — |
| 468 | C2×C3×C4 | — | 6 | 1 | no | — |
| 469 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 470 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 471 | C2×Dic3 | — | 2 | 1 | no | — |
| 472 | C2×Dic3 | — | 2 | 1 | no | — |
| 473 | C2×Dic3 | — | 2 | 1 | no | — |
| 474 | C2×Dic3 | — | 2 | 1 | no | — |
| 475 | C2×Dic3 | — | 3 | 1 | no | — |
| 476 | C2×Dic3 | — | 3 | 1 | no | — |
| 477 | C2×Dic3 | — | 3 | 1 | no | — |
| 478 | C2×Dic3 | — | 3 | 1 | no | — |
| 479 | C2×Dic3 | — | 6 | 1 | no | — |
| 480 | C2×Dic3 | — | 6 | 1 | no | — |
| 481 | C2×Dic3 | — | 6 | 1 | no | — |
| 482 | C2×Dic3 | — | 6 | 1 | no | — |
| 483 | C2×Dic3 | — | 6 | 1 | no | — |
| 484 | C2×Dic3 | — | 6 | 1 | no | — |
| 485 | C2×Dic3 | — | 12 | 1 | no | — |
| 486 | C2×Dic3 | — | 12 | 1 | no | — |
| 487 | C2×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 488 | C2×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 489 | C2×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 490 | C2×Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 491 | Dic6 | — | 2 | 1 | no | — |
| 492 | Dic6 | — | 2 | 1 | no | — |
| 493 | Dic6 | — | 2 | 1 | no | — |
| 494 | Dic6 | — | 2 | 1 | no | — |
| 495 | Dic6 | — | 2 | 1 | no | — |
| 496 | Dic6 | — | 3 | 4 | no | — |
| 497 | Dic6 | — | 3 | 4 | no | — |
| 498 | Dic6 | — | 8 | 1 | no | — |
| 499 | Dic6 | — | 24 | 1 | no | — |
| 500 | Dic6 | — | 24 | 1 | no | — |
| 501 | Dic6 | — | 24 | 1 | no | — |
| 502 | Dic6 | — | 24 | 1 | no | — |
| 503 | Dic6 | — | 24 | 2 | no | — |
| 504 | Dic6 | #237 | 1 | 2 | yes | — |
| 505 | C3×C8 | — | 2 | 1 | no | — |
| 506 | C3×C8 | — | 2 | 1 | no | — |
| 507 | C3×C8 | — | 4 | 1 | no | — |
| 508 | C3×C8 | — | 6 | 1 | no | — |
| 509 | C3×C8 | — | 6 | 1 | no | — |
| 510 | C3⋊C8 | — | 2 | 1 | no | — |
| 511 | C3⋊C8 | — | 2 | 1 | no | — |
| 512 | C3⋊C8 | — | 6 | 1 | no | — |
| 513 | C3⋊C8 | — | 6 | 1 | no | — |
| 514 | C3⋊C8 | — | 12 | 1 | no | — |
| 515 | C2×C32 | #548 | 1 | 1 | yes | characteristic |
| 516 | C2×C32 | C22×Q16 | 1 | 1 | yes | characteristic |
| 517 | C2×C32 | #577 | 1 | 1 | yes | characteristic |
| 518 | C2×Q8 | — | 3 | 1 | no | — |
| 519 | C2×Q8 | — | 3 | 1 | no | — |
| 520 | C2×Q8 | — | 3 | 1 | no | — |
| 521 | C2×Q8 | — | 6 | 1 | no | — |
| 522 | C2×Q8 | — | 9 | 1 | no | — |
| 523 | C2×Q8 | — | 18 | 1 | no | — |
| 524 | C2×Q8 | — | 18 | 1 | no | — |
| 525 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 526 | Q16 | — | 6 | 2 | no | — |
| 527 | Q16 | — | 6 | 2 | no | — |
| 528 | Q16 | — | 18 | 2 | no | — |
| 529 | C2×C8 | — | 3 | 1 | no | — |
| 530 | C2×C8 | — | 3 | 1 | no | — |
| 531 | C2×C8 | — | 9 | 1 | no | — |
| 532 | C2×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 533 | C4⋊C4 | — | 3 | 1 | no | — |
| 534 | C4⋊C4 | — | 6 | 1 | no | — |
| 535 | C4⋊C4 | — | 6 | 1 | no | — |
| 536 | C4⋊C4 | — | 6 | 1 | no | — |
| 537 | C4⋊C4 | — | 6 | 1 | no | — |
| 538 | C4⋊C4 | — | 6 | 1 | no | — |
| 539 | C4⋊C4 | — | 6 | 1 | no | — |
| 540 | C4⋊C4 | — | 9 | 1 | no | — |
| 541 | C4⋊C4 | — | 9 | 1 | no | — |
| 542 | C4⋊C4 | — | 9 | 1 | no | — |
| 543 | C4⋊C4 | — | 9 | 1 | no | — |
| 544 | C4⋊C4 | — | 9 | 1 | no | — |
| 545 | C4⋊C4 | — | 18 | 1 | no | — |
| 546 | C4⋊C4 | — | 18 | 1 | no | — |
| 547 | C4⋊C4 | — | 18 | 1 | no | — |
| 548 | C4⋊C4 | — | 18 | 1 | no | — |
| 549 | C4⋊C4 | — | 18 | 1 | no | — |
| 550 | C4⋊C4 | — | 18 | 1 | no | — |
| 551 | C4⋊C4 | — | 18 | 1 | no | — |
| 552 | C4⋊C4 | — | 18 | 1 | no | — |
| 553 | C4⋊C4 | — | 18 | 1 | no | — |
| 554 | C4⋊C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 555 | C42 | — | 3 | 1 | no | — |
| 556 | C42 | — | 3 | 1 | no | — |
| 557 | C42 | — | 6 | 1 | no | — |
| 558 | C42 | — | 9 | 1 | no | — |
| 559 | C42 | — | 18 | 1 | no | — |
| 560 | C42 | — | 18 | 1 | no | — |
| 561 | C42 | — | 18 | 1 | no | — |
| 562 | C42 | — | 18 | 1 | no | — |
| 563 | C42 | — | 18 | 1 | no | — |
| 564 | C22×C3 | — | 2 | 1 | no | — |
| 565 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 566 | C22×C3 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 567 | C3×C4 | — | 2 | 1 | no | — |
| 568 | C3×C4 | — | 2 | 1 | no | — |
| 569 | C3×C4 | — | 3 | 2 | no | — |
| 570 | C3×C4 | — | 3 | 2 | no | — |
| 571 | C3×C4 | — | 4 | 2 | no | — |
| 572 | C3×C4 | — | 4 | 1 | no | — |
| 573 | C3×C4 | — | 4 | 1 | no | — |
| 574 | C3×C4 | — | 4 | 1 | no | — |
| 575 | C3×C4 | — | 4 | 1 | no | — |
| 576 | C3×C4 | — | 6 | 2 | no | — |
| 577 | C3×C4 | — | 6 | 1 | no | — |
| 578 | C3×C4 | — | 6 | 1 | no | — |
| 579 | C3×C4 | — | 8 | 1 | no | — |
| 580 | C3×C4 | — | 12 | 1 | no | — |
| 581 | C3×C4 | — | 12 | 1 | no | — |
| 582 | C3×C4 | — | 12 | 1 | no | — |
| 583 | C3×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 584 | C3×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 585 | C3×C4 | #1010 | 1 | 1 | yes | characteristic |
| 586 | C3×C4 | #1010 | 1 | 1 | yes | characteristic |
| 587 | Dic3 | — | 2 | 1 | no | — |
| 588 | Dic3 | — | 2 | 1 | no | — |
| 589 | Dic3 | — | 2 | 2 | no | — |
| 590 | Dic3 | — | 3 | 2 | no | — |
| 591 | Dic3 | — | 3 | 2 | no | — |
| 592 | Dic3 | — | 4 | 1 | no | — |
| 593 | Dic3 | — | 4 | 1 | no | — |
| 594 | Dic3 | — | 4 | 1 | no | — |
| 595 | Dic3 | — | 6 | 2 | no | — |
| 596 | Dic3 | — | 6 | 1 | no | — |
| 597 | Dic3 | — | 6 | 1 | no | — |
| 598 | Dic3 | — | 12 | 1 | no | — |
| 599 | Dic3 | — | 12 | 1 | no | — |
| 600 | Dic3 | — | 12 | 1 | no | — |
| 601 | Dic3 | — | 12 | 1 | no | — |
| 602 | Dic3 | — | 12 | 1 | no | — |
| 603 | Dic3 | — | 24 | 1 | no | — |
| 604 | Dic3 | — | 24 | 1 | no | — |
| 605 | Dic3 | D3×Q16 | 1 | 2 | yes | — |
| 606 | Dic3 | D3×Q16 | 1 | 2 | yes | — |
| 607 | C32 | #3363 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 608 | Q8 | — | 2 | 1 | no | — |
| 609 | Q8 | — | 2 | 1 | no | — |
| 610 | Q8 | — | 3 | 2 | no | — |
| 611 | Q8 | — | 6 | 1 | no | — |
| 612 | Q8 | — | 6 | 1 | no | — |
| 613 | Q8 | — | 6 | 1 | no | — |
| 614 | Q8 | — | 6 | 1 | no | — |
| 615 | Q8 | — | 6 | 1 | no | — |
| 616 | Q8 | — | 9 | 4 | no | — |
| 617 | Q8 | — | 24 | 1 | no | — |
| 618 | Q8 | — | 72 | 1 | no | — |
| 619 | Q8 | — | 72 | 1 | no | — |
| 620 | C2×C4 | — | 2 | 1 | no | — |
| 621 | C2×C4 | — | 2 | 1 | no | — |
| 622 | C2×C4 | — | 3 | 1 | no | — |
| 623 | C2×C4 | — | 3 | 1 | no | — |
| 624 | C2×C4 | — | 3 | 1 | no | — |
| 625 | C2×C4 | — | 3 | 1 | no | — |
| 626 | C2×C4 | — | 6 | 1 | no | — |
| 627 | C2×C4 | — | 6 | 1 | no | — |
| 628 | C2×C4 | — | 6 | 1 | no | — |
| 629 | C2×C4 | — | 6 | 1 | no | — |
| 630 | C2×C4 | — | 9 | 1 | no | — |
| 631 | C2×C4 | — | 9 | 1 | no | — |
| 632 | C2×C4 | — | 18 | 1 | no | — |
| 633 | C2×C4 | — | 18 | 1 | no | — |
| 634 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 635 | C8 | — | 2 | 1 | no | — |
| 636 | C8 | — | 6 | 1 | no | — |
| 637 | C8 | — | 6 | 1 | no | — |
| 638 | C8 | — | 18 | 1 | no | — |
| 639 | C2×C3 | — | 2 | 1 | no | — |
| 640 | C2×C3 | — | 2 | 1 | no | — |
| 641 | C2×C3 | — | 2 | 1 | no | — |
| 642 | C2×C3 | #5598 | 1 | 1 | yes | characteristic |
| 643 | C2×C3 | #5677 | 1 | 1 | yes | characteristic |
| 644 | C2×C3 | #5762 | 1 | 1 | yes | characteristic |
| 645 | C2×C3 | C2×D3×Q16 | 1 | 1 | yes | characteristic |
| 646 | C2×C3 | C2×D3×Q16 | 1 | 1 | yes | characteristic |
| 647 | C2×C3 | #5778 | 1 | 1 | yes | characteristic |
| 648 | C22 | D32×D4 | 1 | 1 | yes | characteristic |
| 649 | C4 | — | 3 | 2 | no | — |
| 650 | C4 | — | 3 | 2 | no | — |
| 651 | C4 | — | 4 | 1 | no | — |
| 652 | C4 | — | 4 | 1 | no | — |
| 653 | C4 | — | 6 | 2 | no | — |
| 654 | C4 | — | 6 | 1 | no | — |
| 655 | C4 | — | 6 | 1 | no | — |
| 656 | C4 | — | 9 | 2 | no | — |
| 657 | C4 | — | 12 | 1 | no | — |
| 658 | C4 | — | 12 | 1 | no | — |
| 659 | C4 | — | 12 | 1 | no | — |
| 660 | C4 | — | 18 | 1 | no | — |
| 661 | C4 | — | 36 | 1 | no | — |
| 662 | C4 | — | 36 | 1 | no | — |
| 663 | C4 | #64298 | 1 | 1 | yes | characteristic |
| 664 | C4 | D3×#237 | 1 | 1 | yes | characteristic |
| 665 | C3 | — | 2 | 1 | no | — |
| 666 | C3 | #80462 | 1 | 1 | yes | characteristic, complemented |
| 667 | C3 | #81624 | 1 | 1 | yes | characteristic, complemented |
| 668 | C2 | #10594076 | 1 | 1 | yes | characteristic |
| 669 | C2 | #10594751 | 1 | 1 | yes | characteristic |
| 670 | C2 | D32×Q16 | 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