← #30571156
Subgroups — #30571156
Order 15616.
1698 conjugacy classes of subgroups.
The subgroup lattice has 616 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21459681 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16840487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #21458877 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #21458854 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #21458627 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #21458604 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #21456844 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #21456767 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #21455985 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #21455859 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #21455846 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #21454902 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C61×#3206 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #16840498 | C22 | 1 | 2 | yes | — |
| 15 | #16840487 | — | 2 | 2 | no | — |
| 16 | #16840487 | — | 2 | 2 | no | — |
| 17 | #16840487 | C22 | 1 | 4 | yes | — |
| 18 | #16840487 | C22 | 1 | 4 | yes | — |
| 19 | #16840487 | C22 | 1 | 2 | yes | — |
| 20 | #16840482 | C22 | 1 | 2 | yes | — |
| 21 | #16840481 | — | 2 | 2 | no | — |
| 22 | #16840469 | C22 | 1 | 2 | yes | — |
| 23 | #16840452 | — | 2 | 2 | no | — |
| 24 | #16840357 | — | 2 | 2 | no | — |
| 25 | #16840333 | — | 2 | 1 | no | — |
| 26 | #16840319 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#14519775 | C22 | 1 | 2 | yes | — |
| 28 | #16840293 | C22 | 1 | 4 | yes | — |
| 29 | C2×#14519768 | — | 2 | 1 | no | — |
| 30 | C2×#14519767 | — | 2 | 2 | no | — |
| 31 | #16840245 | — | 2 | 1 | no | — |
| 32 | C2×Q8×Dic61 | C22 | 1 | 2 | yes | — |
| 33 | C2×C4×Dic122 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×C4×Dic122 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#14519742 | — | 2 | 1 | no | — |
| 36 | #16840153 | C22 | 1 | 8 | yes | — |
| 37 | #16840141 | C22 | 1 | 2 | yes | — |
| 38 | #16840129 | C22 | 1 | 8 | yes | — |
| 39 | #16840112 | C22 | 1 | 2 | yes | — |
| 40 | #16840098 | C22 | 1 | 2 | yes | — |
| 41 | #16840078 | C22 | 1 | 2 | yes | — |
| 42 | #16840071 | C22 | 1 | 8 | yes | — |
| 43 | #16840058 | C22 | 1 | 2 | yes | — |
| 44 | #16840044 | C22 | 1 | 2 | yes | — |
| 45 | #16839982 | C22 | 1 | 8 | yes | — |
| 46 | #16839973 | C22 | 1 | 2 | yes | — |
| 47 | #16839971 | C22 | 1 | 8 | yes | — |
| 48 | #16839969 | C22 | 1 | 4 | yes | — |
| 49 | #16839965 | C22 | 1 | 8 | yes | — |
| 50 | #16839959 | C22 | 1 | 2 | yes | — |
| 51 | #16839920 | C22 | 1 | 2 | yes | — |
| 52 | #16839918 | C22 | 1 | 4 | yes | — |
| 53 | #16839900 | C22 | 1 | 2 | yes | — |
| 54 | #16839892 | C22 | 1 | 4 | yes | — |
| 55 | #16839889 | C22 | 1 | 4 | yes | — |
| 56 | #16839866 | C22 | 1 | 8 | yes | — |
| 57 | #16839863 | C22 | 1 | 8 | yes | — |
| 58 | C4×Dic244 | C22 | 1 | 4 | yes | — |
| 59 | C4×#11758200 | C22 | 1 | 4 | yes | — |
| 60 | #16839816 | C22 | 1 | 4 | yes | — |
| 61 | #16839815 | C22 | 1 | 1 | yes | characteristic |
| 62 | C61×#532 | C22 | 1 | 1 | yes | characteristic |
| 63 | C2×C4⋊Q8×C61 | C22 | 1 | 1 | yes | characteristic |
| 64 | C61×#492 | C22 | 1 | 2 | yes | — |
| 65 | C61×#487 | C22 | 1 | 2 | yes | — |
| 66 | C61×#461 | C22 | 1 | 4 | yes | — |
| 67 | C61×#448 | C22 | 1 | 4 | yes | — |
| 68 | C61×#431 | C22 | 1 | 1 | yes | characteristic |
| 69 | C22×Dic122 | D4 | 1 | 1 | yes | characteristic |
| 70 | C22×Dic122 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×Dic244 | C23 | 1 | 4 | yes | — |
| 72 | C2×#11758202 | C23 | 1 | 8 | yes | — |
| 73 | C2×#11758200 | C23 | 1 | 4 | yes | — |
| 74 | #14519777 | C23 | 1 | 1 | yes | characteristic |
| 75 | #14519777 | C23 | 1 | 1 | yes | characteristic |
| 76 | #14519775 | — | 2 | 2 | no | — |
| 77 | #14519775 | — | 2 | 4 | no | — |
| 78 | #14519775 | C23 | 1 | 8 | yes | — |
| 79 | #14519770 | — | 2 | 4 | no | — |
| 80 | #14519770 | — | 2 | 4 | no | — |
| 81 | #14519769 | — | 2 | 1 | no | — |
| 82 | #14519768 | — | 2 | 4 | no | — |
| 83 | #14519768 | — | 2 | 4 | no | — |
| 84 | #14519768 | C23 | 1 | 4 | yes | — |
| 85 | #14519767 | — | 2 | 4 | no | — |
| 86 | #14519767 | — | 2 | 8 | no | — |
| 87 | #14519767 | — | 2 | 8 | no | — |
| 88 | #14519764 | — | 2 | 2 | no | — |
| 89 | #14519764 | C23 | 1 | 4 | yes | — |
| 90 | #14519758 | — | 2 | 4 | no | — |
| 91 | #14519758 | — | 2 | 4 | no | — |
| 92 | #14519756 | — | 2 | 1 | no | — |
| 93 | #14519756 | — | 2 | 2 | no | — |
| 94 | #14519756 | — | 2 | 2 | no | — |
| 95 | #14519756 | C23 | 1 | 2 | yes | — |
| 96 | #14519754 | — | 2 | 4 | no | — |
| 97 | Q8×Dic61 | — | 2 | 2 | no | — |
| 98 | Q8×Dic61 | — | 2 | 4 | no | — |
| 99 | Q8×Dic61 | C23 | 1 | 8 | yes | — |
| 100 | C4×Dic122 | — | 2 | 1 | no | — |
| 101 | C4×Dic122 | — | 2 | 1 | no | — |
| 102 | C4×Dic122 | — | 2 | 1 | no | — |
| 103 | C4×Dic122 | D4 | 1 | 2 | yes | — |
| 104 | C4×Dic122 | D4 | 1 | 2 | yes | — |
| 105 | C4×Dic122 | C23 | 1 | 2 | yes | — |
| 106 | C4×Dic122 | C23 | 1 | 2 | yes | — |
| 107 | C4×Dic122 | C23 | 1 | 2 | yes | — |
| 108 | C4×Dic122 | C23 | 1 | 2 | yes | — |
| 109 | C4×Dic122 | C23 | 1 | 2 | yes | — |
| 110 | #14519742 | — | 2 | 4 | no | — |
| 111 | #14519742 | — | 2 | 4 | no | — |
| 112 | #14519742 | C23 | 1 | 4 | yes | — |
| 113 | D4×Dic61 | — | 2 | 4 | no | — |
| 114 | D4×Dic61 | — | 2 | 2 | no | — |
| 115 | D4×Dic61 | C23 | 1 | 4 | yes | — |
| 116 | #14519736 | — | 2 | 1 | no | — |
| 117 | #14519736 | — | 2 | 2 | no | — |
| 118 | #14519733 | — | 2 | 4 | no | — |
| 119 | C2×C4⋊Dic61 | — | 2 | 2 | no | — |
| 120 | C2×C4⋊Dic61 | — | 2 | 2 | no | — |
| 121 | C2×C4⋊Dic61 | D4 | 1 | 1 | yes | characteristic |
| 122 | C2×C4⋊Dic61 | C23 | 1 | 1 | yes | characteristic |
| 123 | C2×#11758196 | — | 2 | 1 | no | — |
| 124 | C2×#11758196 | — | 2 | 2 | no | — |
| 125 | C2×#11758196 | — | 2 | 2 | no | — |
| 126 | C2×#11758196 | D4 | 1 | 2 | yes | — |
| 127 | C2×C4×Dic61 | — | 2 | 1 | no | — |
| 128 | C2×C4×Dic61 | — | 2 | 2 | no | — |
| 129 | C2×C4×Dic61 | C23 | 1 | 2 | yes | — |
| 130 | #14519711 | C23 | 1 | 4 | yes | — |
| 131 | #14519708 | C23 | 1 | 4 | yes | — |
| 132 | C4⋊#92418 | C23 | 1 | 2 | yes | — |
| 133 | #14519706 | C23 | 1 | 8 | yes | — |
| 134 | #14519702 | C23 | 1 | 4 | yes | — |
| 135 | #14519702 | C23 | 1 | 4 | yes | — |
| 136 | #14519701 | C23 | 1 | 8 | yes | — |
| 137 | #14519700 | C23 | 1 | 4 | yes | — |
| 138 | #14519698 | C23 | 1 | 4 | yes | — |
| 139 | C22⋊#92418 | C23 | 1 | 2 | yes | — |
| 140 | #14519687 | C23 | 1 | 8 | yes | — |
| 141 | C4×#92418 | C23 | 1 | 2 | yes | — |
| 142 | C2×#41×C61 | — | 2 | 1 | no | — |
| 143 | C22×Q8×C61 | C23 | 1 | 2 | yes | — |
| 144 | C2×SD16×C61 | C23 | 1 | 8 | yes | — |
| 145 | C4⋊Q8×C61 | — | 2 | 1 | no | — |
| 146 | C4⋊Q8×C61 | — | 2 | 1 | no | — |
| 147 | C4⋊Q8×C61 | C23 | 1 | 2 | yes | — |
| 148 | C4⋊Q8×C61 | C23 | 1 | 2 | yes | — |
| 149 | C4⋊Q8×C61 | C23 | 1 | 1 | yes | characteristic |
| 150 | #127×C61 | C23 | 1 | 1 | yes | characteristic |
| 151 | #124×C61 | — | 2 | 1 | no | — |
| 152 | #121×C61 | — | 2 | 1 | no | — |
| 153 | #121×C61 | C23 | 1 | 2 | yes | — |
| 154 | C4×D4×C61 | — | 2 | 1 | no | — |
| 155 | C4×D4×C61 | C23 | 1 | 2 | yes | — |
| 156 | C2×C4⋊C4×C61 | — | 2 | 1 | no | — |
| 157 | C2×C4⋊C4×C61 | — | 2 | 1 | no | — |
| 158 | C2×C42×C61 | C23 | 1 | 1 | yes | characteristic |
| 159 | C4⋊C8×C61 | C23 | 1 | 2 | yes | — |
| 160 | #103×C61 | C23 | 1 | 8 | yes | — |
| 161 | C22⋊C8×C61 | C23 | 1 | 2 | yes | — |
| 162 | C4×C8×C61 | C23 | 1 | 2 | yes | — |
| 163 | #41×C61 | — | 4 | 4 | no | — |
| 164 | C2×Q8×C61 | — | 2 | 1 | no | — |
| 165 | C2×Q8×C61 | — | 2 | 2 | no | — |
| 166 | C2×Q8×C61 | — | 4 | 4 | no | — |
| 167 | C2×Q8×C61 | C24 | 1 | 4 | yes | — |
| 168 | C2×D4×C61 | — | 2 | 2 | no | — |
| 169 | C2×D4×C61 | — | 2 | 1 | no | — |
| 170 | C2×D4×C61 | — | 2 | 1 | no | — |
| 171 | C2×D4×C61 | C24 | 1 | 2 | yes | — |
| 172 | C22×C4×C61 | — | 2 | 2 | no | — |
| 173 | C22×C4×C61 | — | 2 | 2 | no | — |
| 174 | C22×C4×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C22×C4×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×C4×C61 | C24 | 1 | 1 | yes | characteristic |
| 177 | C22×Dic61 | — | 2 | 1 | no | — |
| 178 | C22×Dic61 | — | 2 | 1 | no | — |
| 179 | C22×Dic61 | — | 2 | 4 | no | — |
| 180 | C22×Dic61 | C2×D4 | 1 | 2 | yes | — |
| 181 | C22×Dic61 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×Dic122 | — | 2 | 4 | no | — |
| 183 | C2×Dic122 | — | 2 | 1 | no | — |
| 184 | C2×Dic122 | — | 2 | 1 | no | — |
| 185 | C2×Dic122 | — | 4 | 2 | no | — |
| 186 | C2×Dic122 | C2×D4 | 1 | 2 | yes | — |
| 187 | C2×Dic122 | C2×D4 | 1 | 2 | yes | — |
| 188 | C2×Dic122 | C24 | 1 | 2 | yes | — |
| 189 | C2×Dic122 | C24 | 1 | 2 | yes | — |
| 190 | SD16×C61 | — | 4 | 8 | no | — |
| 191 | C2×C8×C61 | C24 | 1 | 4 | yes | — |
| 192 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 193 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 194 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 195 | C4⋊C4×C61 | — | 2 | 2 | no | — |
| 196 | C4⋊C4×C61 | — | 2 | 1 | no | — |
| 197 | C4⋊C4×C61 | C24 | 1 | 2 | yes | — |
| 198 | C22⋊C4×C61 | — | 2 | 2 | no | — |
| 199 | C22⋊C4×C61 | — | 2 | 2 | no | — |
| 200 | C42×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C42×C61 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C42×C61 | C24 | 1 | 1 | yes | characteristic |
| 203 | C42×C61 | C24 | 1 | 1 | yes | characteristic |
| 204 | C22⋊Dic61 | — | 2 | 2 | no | — |
| 205 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 206 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 207 | C22⋊Dic61 | — | 2 | 4 | no | — |
| 208 | #11758202 | — | 4 | 8 | no | — |
| 209 | #11758200 | — | 4 | 4 | no | — |
| 210 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 211 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 212 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 213 | C4⋊Dic61 | — | 2 | 1 | no | — |
| 214 | C4⋊Dic61 | — | 2 | 4 | no | — |
| 215 | C4⋊Dic61 | — | 2 | 8 | no | — |
| 216 | C4⋊Dic61 | C2×D4 | 1 | 2 | yes | — |
| 217 | C4⋊Dic61 | C2×D4 | 1 | 2 | yes | — |
| 218 | C4⋊Dic61 | C24 | 1 | 2 | yes | — |
| 219 | C4⋊Dic61 | C24 | 1 | 2 | yes | — |
| 220 | #11758196 | — | 2 | 2 | no | — |
| 221 | #11758196 | — | 2 | 2 | no | — |
| 222 | #11758196 | — | 2 | 2 | no | — |
| 223 | #11758196 | — | 2 | 2 | no | — |
| 224 | #11758196 | — | 2 | 8 | no | — |
| 225 | #11758196 | — | 2 | 8 | no | — |
| 226 | #11758196 | — | 2 | 4 | no | — |
| 227 | #11758196 | — | 2 | 4 | no | — |
| 228 | #11758196 | C2×D4 | 1 | 4 | yes | — |
| 229 | #11758196 | C2×D4 | 1 | 4 | yes | — |
| 230 | C4×Dic61 | — | 2 | 2 | no | — |
| 231 | C4×Dic61 | — | 2 | 2 | no | — |
| 232 | C4×Dic61 | — | 2 | 2 | no | — |
| 233 | C4×Dic61 | — | 2 | 8 | no | — |
| 234 | C4×Dic61 | — | 2 | 4 | no | — |
| 235 | C4×Dic61 | C2×D4 | 1 | 4 | yes | — |
| 236 | C4×Dic61 | C24 | 1 | 4 | yes | — |
| 237 | C2×#92418 | C24 | 1 | 4 | yes | — |
| 238 | Dic244 | — | 4 | 4 | no | — |
| 239 | C23×C61 | — | 2 | 2 | no | — |
| 240 | C23×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 241 | Q8×C61 | — | 2 | 8 | no | — |
| 242 | Q8×C61 | — | 4 | 4 | no | — |
| 243 | Q8×C61 | — | 4 | 2 | no | — |
| 244 | D4×C61 | — | 2 | 4 | no | — |
| 245 | D4×C61 | — | 4 | 4 | no | — |
| 246 | D4×C61 | — | 4 | 2 | no | — |
| 247 | D4×C61 | — | 8 | 1 | no | — |
| 248 | C2×C4×C61 | — | 2 | 2 | no | — |
| 249 | C2×C4×C61 | — | 2 | 2 | no | — |
| 250 | C2×C4×C61 | — | 2 | 4 | no | — |
| 251 | C2×C4×C61 | — | 4 | 1 | no | — |
| 252 | C2×C4×C61 | — | 4 | 4 | no | — |
| 253 | C2×C4×C61 | — | 4 | 4 | no | — |
| 254 | C2×C4×C61 | #137 | 1 | 4 | yes | — |
| 255 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×C61 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×C4×C61 | C25 | 1 | 1 | yes | characteristic |
| 261 | C2×Dic61 | — | 2 | 4 | no | — |
| 262 | C2×Dic61 | — | 2 | 2 | no | — |
| 263 | C2×Dic61 | — | 2 | 2 | no | — |
| 264 | C2×Dic61 | — | 2 | 2 | no | — |
| 265 | C2×Dic61 | — | 2 | 2 | no | — |
| 266 | C2×Dic61 | — | 4 | 2 | no | — |
| 267 | C2×Dic61 | — | 4 | 2 | no | — |
| 268 | C2×Dic61 | — | 4 | 2 | no | — |
| 269 | C2×Dic61 | — | 8 | 4 | no | — |
| 270 | C2×Dic61 | C22×D4 | 1 | 4 | yes | — |
| 271 | C2×Dic61 | C22×D4 | 1 | 4 | yes | — |
| 272 | Dic122 | — | 2 | 4 | no | — |
| 273 | Dic122 | — | 2 | 4 | no | — |
| 274 | Dic122 | — | 2 | 2 | no | — |
| 275 | Dic122 | — | 2 | 4 | no | — |
| 276 | Dic122 | — | 2 | 2 | no | — |
| 277 | Dic122 | — | 4 | 2 | no | — |
| 278 | Dic122 | — | 8 | 1 | no | — |
| 279 | C8×C61 | — | 2 | 4 | no | — |
| 280 | #92418 | — | 2 | 4 | no | — |
| 281 | #61893 | — | 61 | 1 | no | maximal, Sylow |
| 282 | C22×C61 | — | 2 | 1 | no | — |
| 283 | C22×C61 | — | 2 | 1 | no | — |
| 284 | C22×C61 | — | 4 | 2 | no | — |
| 285 | C22×C61 | — | 4 | 2 | no | — |
| 286 | C22×C61 | — | 4 | 2 | no | — |
| 287 | C22×C61 | C2×#137 | 1 | 2 | yes | — |
| 288 | C22×C61 | C23×D4 | 1 | 1 | yes | characteristic |
| 289 | C4×C61 | — | 2 | 1 | no | — |
| 290 | C4×C61 | — | 2 | 1 | no | — |
| 291 | C4×C61 | — | 2 | 1 | no | — |
| 292 | C4×C61 | — | 4 | 4 | no | — |
| 293 | C4×C61 | — | 4 | 2 | no | — |
| 294 | C4×C61 | C2×#137 | 1 | 2 | yes | — |
| 295 | C4×C61 | C2×#137 | 1 | 2 | yes | — |
| 296 | C4×C61 | #585 | 1 | 2 | yes | — |
| 297 | Dic61 | — | 2 | 4 | no | — |
| 298 | Dic61 | — | 2 | 4 | no | — |
| 299 | Dic61 | — | 4 | 2 | no | — |
| 300 | Dic61 | — | 4 | 2 | no | — |
| 301 | Dic61 | — | 4 | 2 | no | — |
| 302 | Dic61 | — | 4 | 2 | no | — |
| 303 | #3507 | — | 61 | 1 | no | — |
| 304 | C2×#557 | — | 61 | 1 | no | — |
| 305 | #3400 | — | 61 | 4 | no | — |
| 306 | #3398 | — | 61 | 4 | no | — |
| 307 | #3374 | — | 61 | 4 | no | — |
| 308 | #3372 | — | 61 | 4 | no | — |
| 309 | #3218 | — | 61 | 4 | no | — |
| 310 | #3209 | — | 61 | 1 | no | — |
| 311 | #3206 | D61 | 1 | 1 | yes | characteristic |
| 312 | #3117 | — | 61 | 4 | no | — |
| 313 | #3104 | — | 61 | 1 | no | — |
| 314 | #3103 | — | 61 | 1 | no | — |
| 315 | #2983 | — | 61 | 1 | no | — |
| 316 | C2×C61 | — | 2 | 2 | no | — |
| 317 | C2×C61 | — | 8 | 2 | no | — |
| 318 | C2×C61 | #3487 | 1 | 1 | yes | characteristic |
| 319 | C2×C61 | C22×#137 | 1 | 1 | yes | characteristic |
| 320 | C2×C61 | #3586 | 1 | 1 | yes | characteristic |
| 321 | #559 | — | 61 | 2 | no | — |
| 322 | #557 | — | 61 | 2 | no | — |
| 323 | #557 | — | 61 | 4 | no | — |
| 324 | #557 | — | 61 | 4 | no | — |
| 325 | #557 | — | 122 | 2 | no | — |
| 326 | #557 | — | 122 | 2 | no | — |
| 327 | #556 | — | 61 | 2 | no | — |
| 328 | #556 | — | 122 | 2 | no | — |
| 329 | #554 | — | 61 | 2 | no | — |
| 330 | #552 | — | 122 | 2 | no | — |
| 331 | #539 | — | 122 | 2 | no | — |
| 332 | #536 | — | 122 | 1 | no | — |
| 333 | #533 | — | 61 | 1 | no | — |
| 334 | #532 | C2×D61 | 1 | 1 | yes | characteristic |
| 335 | C2×C4⋊Q8 | — | 61 | 2 | no | — |
| 336 | C2×C4⋊Q8 | C2×D61 | 1 | 1 | yes | characteristic |
| 337 | #529 | — | 61 | 4 | no | — |
| 338 | C2×#125 | — | 122 | 2 | no | — |
| 339 | C2×#125 | — | 122 | 1 | no | — |
| 340 | #520 | — | 122 | 1 | no | — |
| 341 | C2×C4×Q8 | — | 61 | 1 | no | — |
| 342 | C2×C4×Q8 | — | 61 | 2 | no | — |
| 343 | C2×C4×Q8 | — | 61 | 1 | no | — |
| 344 | C2×C4×Q8 | — | 122 | 1 | no | — |
| 345 | #497 | — | 61 | 8 | no | — |
| 346 | #494 | — | 61 | 2 | no | — |
| 347 | #492 | C2×D61 | 1 | 2 | yes | — |
| 348 | #491 | — | 61 | 8 | no | — |
| 349 | #487 | — | 61 | 2 | no | — |
| 350 | #487 | C2×D61 | 1 | 2 | yes | — |
| 351 | #484 | — | 61 | 2 | no | — |
| 352 | #481 | — | 61 | 2 | no | — |
| 353 | #479 | — | 61 | 8 | no | — |
| 354 | #477 | — | 61 | 2 | no | — |
| 355 | #475 | — | 61 | 2 | no | — |
| 356 | #464 | — | 61 | 8 | no | — |
| 357 | #462 | — | 61 | 4 | no | — |
| 358 | #462 | — | 61 | 2 | no | — |
| 359 | #462 | — | 61 | 8 | no | — |
| 360 | #461 | — | 61 | 8 | no | — |
| 361 | #461 | C2×D61 | 1 | 4 | yes | — |
| 362 | #460 | — | 61 | 2 | no | — |
| 363 | #451 | — | 61 | 4 | no | — |
| 364 | #451 | — | 61 | 2 | no | — |
| 365 | #448 | — | 61 | 2 | no | — |
| 366 | #448 | C2×D61 | 1 | 4 | yes | — |
| 367 | #446 | — | 61 | 4 | no | — |
| 368 | #446 | — | 61 | 4 | no | — |
| 369 | #441 | — | 61 | 8 | no | — |
| 370 | #440 | — | 61 | 8 | no | — |
| 371 | C4×Q16 | — | 61 | 4 | no | — |
| 372 | C4×SD16 | — | 61 | 4 | no | — |
| 373 | #432 | — | 61 | 4 | no | — |
| 374 | #431 | — | 61 | 1 | no | — |
| 375 | #431 | C2×D61 | 1 | 1 | yes | characteristic |
| 376 | C61 | #61893 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 377 | C2×#41 | — | 2 | 1 | no | — |
| 378 | C22×Q8 | — | 61 | 1 | no | — |
| 379 | C22×Q8 | — | 61 | 1 | no | — |
| 380 | C22×Q8 | C22×D61 | 1 | 2 | yes | — |
| 381 | C2×Q16 | — | 61 | 8 | no | — |
| 382 | C2×Q16 | — | 61 | 4 | no | — |
| 383 | C2×SD16 | — | 61 | 4 | no | — |
| 384 | C2×SD16 | C22×D61 | 1 | 8 | yes | — |
| 385 | C4⋊Q8 | — | 2 | 1 | no | — |
| 386 | C4⋊Q8 | — | 2 | 1 | no | — |
| 387 | C4⋊Q8 | — | 61 | 8 | no | — |
| 388 | C4⋊Q8 | — | 61 | 1 | no | — |
| 389 | C4⋊Q8 | — | 61 | 1 | no | — |
| 390 | C4⋊Q8 | — | 122 | 4 | no | — |
| 391 | C4⋊Q8 | — | 122 | 2 | no | — |
| 392 | C4⋊Q8 | C22×D61 | 1 | 2 | yes | — |
| 393 | C4⋊Q8 | C22×D61 | 1 | 2 | yes | — |
| 394 | C4⋊Q8 | C22×D61 | 1 | 1 | yes | characteristic |
| 395 | #127 | C22×D61 | 1 | 1 | yes | characteristic |
| 396 | #126 | — | 122 | 4 | no | — |
| 397 | #126 | — | 122 | 4 | no | — |
| 398 | #125 | — | 61 | 4 | no | — |
| 399 | #125 | — | 122 | 8 | no | — |
| 400 | #125 | — | 122 | 8 | no | — |
| 401 | #125 | — | 122 | 4 | no | — |
| 402 | #125 | — | 122 | 4 | no | — |
| 403 | #125 | — | 122 | 4 | no | — |
| 404 | #125 | — | 122 | 1 | no | — |
| 405 | #124 | — | 2 | 1 | no | — |
| 406 | #124 | — | 61 | 4 | no | — |
| 407 | #124 | — | 122 | 2 | no | — |
| 408 | #123 | — | 122 | 4 | no | — |
| 409 | #123 | — | 122 | 4 | no | — |
| 410 | C22⋊Q8 | — | 61 | 2 | no | — |
| 411 | C22⋊Q8 | — | 122 | 4 | no | — |
| 412 | C22⋊Q8 | — | 122 | 2 | no | — |
| 413 | C22⋊Q8 | — | 122 | 2 | no | — |
| 414 | C22⋊Q8 | — | 122 | 1 | no | — |
| 415 | #121 | — | 2 | 1 | no | — |
| 416 | #121 | C22×D61 | 1 | 2 | yes | — |
| 417 | C4×Q8 | — | 61 | 2 | no | — |
| 418 | C4×Q8 | — | 61 | 2 | no | — |
| 419 | C4×Q8 | — | 61 | 2 | no | — |
| 420 | C4×Q8 | — | 61 | 2 | no | — |
| 421 | C4×Q8 | — | 61 | 8 | no | — |
| 422 | C4×Q8 | — | 61 | 4 | no | — |
| 423 | C4×Q8 | — | 61 | 2 | no | — |
| 424 | C4×Q8 | — | 61 | 2 | no | — |
| 425 | C4×Q8 | — | 61 | 2 | no | — |
| 426 | C4×Q8 | — | 122 | 4 | no | — |
| 427 | C4×Q8 | — | 122 | 4 | no | — |
| 428 | C4×Q8 | — | 122 | 4 | no | — |
| 429 | C4×Q8 | — | 122 | 2 | no | — |
| 430 | C4×Q8 | — | 122 | 1 | no | — |
| 431 | C4×Q8 | — | 122 | 1 | no | — |
| 432 | C4×Q8 | — | 122 | 1 | no | — |
| 433 | C4×D4 | — | 2 | 1 | no | — |
| 434 | C4×D4 | — | 61 | 4 | no | — |
| 435 | C4×D4 | — | 122 | 2 | no | — |
| 436 | C4×D4 | — | 122 | 4 | no | — |
| 437 | C4×D4 | C22×D61 | 1 | 2 | yes | — |
| 438 | #117 | — | 122 | 4 | no | — |
| 439 | #117 | — | 122 | 2 | no | — |
| 440 | #117 | — | 122 | 1 | no | — |
| 441 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 442 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 443 | C2×C4⋊C4 | — | 61 | 1 | no | — |
| 444 | C2×C4⋊C4 | — | 61 | 2 | no | — |
| 445 | C2×C4⋊C4 | — | 61 | 1 | no | — |
| 446 | C2×C4⋊C4 | — | 122 | 2 | no | — |
| 447 | C2×C4⋊C4 | — | 122 | 2 | no | — |
| 448 | C2×C4⋊C4 | — | 122 | 2 | no | — |
| 449 | C2×C4⋊C4 | — | 122 | 2 | no | — |
| 450 | C2×C4⋊C4 | — | 122 | 1 | no | — |
| 451 | C2×C42 | — | 61 | 2 | no | — |
| 452 | C2×C42 | — | 122 | 2 | no | — |
| 453 | C2×C42 | — | 122 | 1 | no | — |
| 454 | C2×C42 | C22×D61 | 1 | 1 | yes | characteristic |
| 455 | #107 | — | 61 | 4 | no | — |
| 456 | #106 | — | 61 | 4 | no | — |
| 457 | C4⋊C8 | — | 61 | 8 | no | — |
| 458 | C4⋊C8 | — | 61 | 2 | no | — |
| 459 | C4⋊C8 | C22×D61 | 1 | 2 | yes | — |
| 460 | #103 | — | 61 | 8 | no | — |
| 461 | #103 | — | 61 | 4 | no | — |
| 462 | #103 | — | 61 | 4 | no | — |
| 463 | #103 | — | 61 | 4 | no | — |
| 464 | #103 | C22×D61 | 1 | 8 | yes | — |
| 465 | #102 | — | 61 | 4 | no | — |
| 466 | C22⋊C8 | — | 61 | 2 | no | — |
| 467 | C22⋊C8 | C22×D61 | 1 | 2 | yes | — |
| 468 | #97 | — | 61 | 8 | no | — |
| 469 | C4×C8 | — | 61 | 2 | no | — |
| 470 | C4×C8 | C22×D61 | 1 | 2 | yes | — |
| 471 | #41 | — | 4 | 4 | no | — |
| 472 | C2×Q8 | — | 2 | 1 | no | — |
| 473 | C2×Q8 | — | 2 | 2 | no | — |
| 474 | C2×Q8 | — | 4 | 4 | no | — |
| 475 | C2×Q8 | — | 61 | 2 | no | — |
| 476 | C2×Q8 | — | 61 | 2 | no | — |
| 477 | C2×Q8 | — | 61 | 2 | no | — |
| 478 | C2×Q8 | — | 61 | 2 | no | — |
| 479 | C2×Q8 | — | 122 | 1 | no | — |
| 480 | C2×Q8 | — | 122 | 1 | no | — |
| 481 | C2×Q8 | — | 122 | 4 | no | — |
| 482 | C2×Q8 | — | 244 | 2 | no | — |
| 483 | C2×Q8 | C23×D61 | 1 | 4 | yes | — |
| 484 | C2×D4 | — | 2 | 2 | no | — |
| 485 | C2×D4 | — | 2 | 1 | no | — |
| 486 | C2×D4 | — | 2 | 1 | no | — |
| 487 | C2×D4 | C23×D61 | 1 | 2 | yes | — |
| 488 | C22×C4 | — | 2 | 2 | no | — |
| 489 | C22×C4 | — | 2 | 2 | no | — |
| 490 | C22×C4 | — | 61 | 2 | no | — |
| 491 | C22×C4 | — | 61 | 2 | no | — |
| 492 | C22×C4 | — | 122 | 4 | no | — |
| 493 | C22×C4 | — | 122 | 1 | no | — |
| 494 | C22×C4 | — | 122 | 1 | no | — |
| 495 | C22×C4 | D4×D61 | 1 | 1 | yes | characteristic |
| 496 | C22×C4 | D4×D61 | 1 | 1 | yes | characteristic |
| 497 | C22×C4 | C23×D61 | 1 | 1 | yes | characteristic |
| 498 | Q16 | — | 244 | 4 | no | — |
| 499 | Q16 | — | 244 | 8 | no | — |
| 500 | SD16 | — | 4 | 8 | no | — |
| 501 | SD16 | — | 244 | 4 | no | — |
| 502 | C2×C8 | — | 61 | 4 | no | — |
| 503 | C2×C8 | C23×D61 | 1 | 4 | yes | — |
| 504 | C4⋊C4 | — | 2 | 2 | no | — |
| 505 | C4⋊C4 | — | 2 | 2 | no | — |
| 506 | C4⋊C4 | — | 2 | 2 | no | — |
| 507 | C4⋊C4 | — | 2 | 2 | no | — |
| 508 | C4⋊C4 | — | 2 | 1 | no | — |
| 509 | C4⋊C4 | — | 61 | 2 | no | — |
| 510 | C4⋊C4 | — | 61 | 4 | no | — |
| 511 | C4⋊C4 | — | 61 | 4 | no | — |
| 512 | C4⋊C4 | — | 61 | 2 | no | — |
| 513 | C4⋊C4 | — | 61 | 2 | no | — |
| 514 | C4⋊C4 | — | 61 | 2 | no | — |
| 515 | C4⋊C4 | — | 122 | 8 | no | — |
| 516 | C4⋊C4 | — | 122 | 8 | no | — |
| 517 | C4⋊C4 | — | 122 | 4 | no | — |
| 518 | C4⋊C4 | — | 122 | 8 | no | — |
| 519 | C4⋊C4 | — | 122 | 4 | no | — |
| 520 | C4⋊C4 | — | 122 | 4 | no | — |
| 521 | C4⋊C4 | — | 122 | 1 | no | — |
| 522 | C4⋊C4 | — | 122 | 1 | no | — |
| 523 | C4⋊C4 | — | 122 | 2 | no | — |
| 524 | C4⋊C4 | — | 122 | 2 | no | — |
| 525 | C4⋊C4 | — | 122 | 2 | no | — |
| 526 | C4⋊C4 | — | 122 | 2 | no | — |
| 527 | C4⋊C4 | — | 122 | 1 | no | — |
| 528 | C4⋊C4 | — | 122 | 1 | no | — |
| 529 | C4⋊C4 | C23×D61 | 1 | 2 | yes | — |
| 530 | C22⋊C4 | — | 2 | 2 | no | — |
| 531 | C22⋊C4 | — | 2 | 2 | no | — |
| 532 | C22⋊C4 | — | 122 | 4 | no | — |
| 533 | C22⋊C4 | — | 122 | 4 | no | — |
| 534 | C22⋊C4 | — | 122 | 4 | no | — |
| 535 | C22⋊C4 | — | 122 | 2 | no | — |
| 536 | C42 | — | 61 | 4 | no | — |
| 537 | C42 | — | 61 | 4 | no | — |
| 538 | C42 | — | 122 | 8 | no | — |
| 539 | C42 | — | 122 | 4 | no | — |
| 540 | C42 | — | 122 | 2 | no | — |
| 541 | C42 | — | 122 | 2 | no | — |
| 542 | C42 | — | 122 | 2 | no | — |
| 543 | C42 | D4×D61 | 1 | 1 | yes | characteristic |
| 544 | C42 | D4×D61 | 1 | 1 | yes | characteristic |
| 545 | C42 | C23×D61 | 1 | 1 | yes | characteristic |
| 546 | C42 | C23×D61 | 1 | 1 | yes | characteristic |
| 547 | C23 | — | 2 | 2 | no | — |
| 548 | C23 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 549 | Q8 | — | 2 | 8 | no | — |
| 550 | Q8 | — | 4 | 4 | no | — |
| 551 | Q8 | — | 4 | 2 | no | — |
| 552 | Q8 | — | 122 | 4 | no | — |
| 553 | Q8 | — | 122 | 4 | no | — |
| 554 | Q8 | — | 122 | 2 | no | — |
| 555 | Q8 | — | 122 | 4 | no | — |
| 556 | Q8 | — | 122 | 2 | no | — |
| 557 | Q8 | — | 488 | 1 | no | — |
| 558 | Q8 | — | 244 | 2 | no | — |
| 559 | D4 | — | 2 | 4 | no | — |
| 560 | D4 | — | 4 | 4 | no | — |
| 561 | D4 | — | 4 | 2 | no | — |
| 562 | D4 | — | 8 | 1 | no | — |
| 563 | C2×C4 | — | 2 | 2 | no | — |
| 564 | C2×C4 | — | 2 | 2 | no | — |
| 565 | C2×C4 | — | 2 | 4 | no | — |
| 566 | C2×C4 | — | 4 | 1 | no | — |
| 567 | C2×C4 | — | 4 | 4 | no | — |
| 568 | C2×C4 | — | 4 | 4 | no | — |
| 569 | C2×C4 | — | 61 | 4 | no | — |
| 570 | C2×C4 | — | 61 | 4 | no | — |
| 571 | C2×C4 | — | 122 | 4 | no | — |
| 572 | C2×C4 | — | 122 | 2 | no | — |
| 573 | C2×C4 | — | 122 | 2 | no | — |
| 574 | C2×C4 | — | 122 | 2 | no | — |
| 575 | C2×C4 | — | 122 | 2 | no | — |
| 576 | C2×C4 | — | 488 | 4 | no | — |
| 577 | C2×C4 | — | 244 | 2 | no | — |
| 578 | C2×C4 | — | 244 | 2 | no | — |
| 579 | C2×C4 | — | 244 | 2 | no | — |
| 580 | C2×C4 | #14519806 | 1 | 4 | yes | — |
| 581 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 582 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 583 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 584 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 585 | C2×C4 | C2×D4×D61 | 1 | 1 | yes | characteristic |
| 586 | C2×C4 | C24×D61 | 1 | 1 | yes | characteristic |
| 587 | C8 | — | 2 | 4 | no | — |
| 588 | C8 | — | 122 | 4 | no | — |
| 589 | C22 | — | 2 | 1 | no | — |
| 590 | C22 | — | 2 | 1 | no | — |
| 591 | C22 | — | 4 | 2 | no | — |
| 592 | C22 | — | 4 | 2 | no | — |
| 593 | C22 | — | 4 | 2 | no | — |
| 594 | C22 | C2×#14519806 | 1 | 2 | yes | — |
| 595 | C22 | C22×D4×D61 | 1 | 1 | yes | characteristic |
| 596 | C4 | — | 2 | 1 | no | — |
| 597 | C4 | — | 2 | 1 | no | — |
| 598 | C4 | — | 2 | 1 | no | — |
| 599 | C4 | — | 4 | 4 | no | — |
| 600 | C4 | — | 4 | 2 | no | — |
| 601 | C4 | — | 122 | 4 | no | — |
| 602 | C4 | — | 122 | 4 | no | — |
| 603 | C4 | — | 244 | 2 | no | — |
| 604 | C4 | — | 244 | 2 | no | — |
| 605 | C4 | — | 244 | 2 | no | — |
| 606 | C4 | — | 244 | 2 | no | — |
| 607 | C4 | C2×#14519806 | 1 | 2 | yes | — |
| 608 | C4 | C2×#14519806 | 1 | 2 | yes | — |
| 609 | C4 | #16840597 | 1 | 2 | yes | — |
| 610 | C2 | — | 2 | 2 | no | — |
| 611 | C2 | — | 8 | 2 | no | — |
| 612 | C2 | #21459475 | 1 | 1 | yes | characteristic |
| 613 | C2 | C22×#14519806 | 1 | 1 | yes | characteristic |
| 614 | C2 | #21460602 | 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