← #16807423
Subgroups — #16807423
Order 3328.
484 conjugacy classes of subgroups.
The subgroup lattice has 326 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #13131251 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #13131220 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #13131216 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #13131216 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #13131201 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13131197 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13131171 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #13131168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13123812 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C13×#529 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#88106 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#88106 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#88106 | C22 | 1 | 2 | yes | — |
| 14 | C22×#6092 | C22 | 1 | 2 | yes | — |
| 15 | #11718685 | C4 | 1 | 1 | yes | characteristic |
| 16 | Q8×#1055 | C22 | 1 | 1 | yes | characteristic |
| 17 | #11718673 | C4 | 1 | 1 | yes | characteristic |
| 18 | #11718672 | C4 | 1 | 2 | yes | — |
| 19 | D4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 20 | D4×#1055 | C22 | 1 | 2 | yes | — |
| 21 | #11718661 | C4 | 1 | 2 | yes | — |
| 22 | #11718658 | C22 | 1 | 2 | yes | — |
| 23 | #11718587 | C4 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×#1055 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22⋊#6092 | C22 | 1 | 2 | yes | — |
| 26 | C22⋊#6092 | C22 | 1 | 2 | yes | — |
| 27 | C22⋊#6092 | C22 | 1 | 2 | yes | — |
| 28 | #11718231 | C22 | 1 | 2 | yes | — |
| 29 | #11718231 | C22 | 1 | 2 | yes | — |
| 30 | C4⋊#6092 | C22 | 1 | 2 | yes | — |
| 31 | C4⋊#6092 | C22 | 1 | 2 | yes | — |
| 32 | C4⋊#6092 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4⋊#6092 | C22 | 1 | 2 | yes | — |
| 34 | C4⋊#6092 | C22 | 1 | 2 | yes | — |
| 35 | C4⋊#6092 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×#6092 | C22 | 1 | 2 | yes | — |
| 37 | C13×#126 | C8 | 1 | 2 | yes | — |
| 38 | C13×#125 | C8 | 1 | 1 | yes | characteristic |
| 39 | C13×#124 | C8 | 1 | 1 | yes | characteristic |
| 40 | C13×#123 | C8 | 1 | 2 | yes | — |
| 41 | C13×C22⋊Q8 | C8 | 1 | 1 | yes | characteristic |
| 42 | C13×#121 | C8 | 1 | 1 | yes | characteristic |
| 43 | C4×Q8×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C4×D4×C13 | C2×C4 | 1 | 2 | yes | — |
| 45 | C4×D4×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C13×#117 | C2×C4 | 1 | 2 | yes | — |
| 47 | C2×C42×C13 | C2×C4 | 1 | 1 | yes | characteristic |
| 48 | C2×#6099 | C2×C4 | 1 | 2 | yes | — |
| 49 | C22×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C22×#1055 | C23 | 1 | 2 | yes | — |
| 51 | C22×#1055 | C23 | 1 | 1 | yes | characteristic |
| 52 | #88106 | — | 4 | 1 | no | — |
| 53 | #88106 | — | 4 | 2 | no | — |
| 54 | #88106 | — | 4 | 1 | no | — |
| 55 | C2×#6092 | — | 4 | 2 | no | — |
| 56 | C2×#6092 | C23 | 1 | 2 | yes | — |
| 57 | C2×#6092 | C23 | 1 | 2 | yes | — |
| 58 | C2×#6092 | C23 | 1 | 2 | yes | — |
| 59 | C2×#6092 | C23 | 1 | 2 | yes | — |
| 60 | C22⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 61 | C22⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 62 | C22⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 63 | C4⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 64 | C4⋊#1055 | C2×C4 | 1 | 2 | yes | — |
| 65 | C4⋊#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C4⋊#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 67 | #88043 | C2×C4 | 1 | 2 | yes | — |
| 68 | #88043 | C2×C4 | 1 | 2 | yes | — |
| 69 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C4×#1055 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 72 | C4×#1055 | C23 | 1 | 2 | yes | — |
| 73 | C4×#1055 | C23 | 1 | 1 | yes | characteristic |
| 74 | #33509 | — | 13 | 1 | no | maximal, Sylow |
| 75 | C2×Q8×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 76 | C2×D4×C13 | C2×C8 | 1 | 2 | yes | — |
| 77 | C2×D4×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 79 | C22×C4×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 80 | C22×C4×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 81 | C22×C4×C13 | C22×C4 | 1 | 2 | yes | — |
| 82 | C13×C4⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 83 | C13×C4⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 84 | C13×C4⋊C4 | C2×C8 | 1 | 1 | yes | characteristic |
| 85 | C13×C4⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 86 | C13×C4⋊C4 | C2×C8 | 1 | 1 | yes | characteristic |
| 87 | C13×C4⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 88 | C13×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 89 | C13×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 90 | C13×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 91 | C13×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 92 | C13×C22⋊C4 | C2×C8 | 1 | 2 | yes | — |
| 93 | C42×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 94 | C42×C13 | C2×C8 | 1 | 1 | yes | characteristic |
| 95 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 96 | C42×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 97 | C42×C13 | C22×C4 | 1 | 2 | yes | — |
| 98 | #6099 | — | 4 | 2 | no | — |
| 99 | C2×#1055 | — | 2 | 2 | no | — |
| 100 | C2×#1055 | — | 2 | 1 | no | — |
| 101 | C2×#1055 | — | 2 | 2 | no | — |
| 102 | C2×#1055 | — | 2 | 1 | no | — |
| 103 | C2×#1055 | — | 4 | 1 | no | — |
| 104 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C2×#1055 | C22×C4 | 1 | 2 | yes | — |
| 107 | C2×#1055 | C22×C4 | 1 | 2 | yes | — |
| 108 | C2×#1055 | C22×C4 | 1 | 1 | yes | characteristic |
| 109 | C2×#1055 | C24 | 1 | 1 | yes | characteristic |
| 110 | #6092 | — | 2 | 2 | no | — |
| 111 | #6092 | — | 2 | 2 | no | — |
| 112 | #6092 | — | 2 | 2 | no | — |
| 113 | #6092 | — | 2 | 2 | no | — |
| 114 | #2966 | — | 13 | 1 | no | — |
| 115 | #2183 | — | 13 | 2 | no | — |
| 116 | #2169 | — | 13 | 2 | no | — |
| 117 | #2168 | — | 13 | 2 | no | — |
| 118 | #2168 | — | 13 | 2 | no | — |
| 119 | #2164 | — | 13 | 2 | no | — |
| 120 | #2163 | — | 13 | 1 | no | — |
| 121 | #2151 | — | 13 | 2 | no | — |
| 122 | #2150 | — | 13 | 1 | no | — |
| 123 | C23×C13 | C22×C8 | 1 | 2 | yes | — |
| 124 | C23×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 125 | Q8×C13 | — | 4 | 1 | no | — |
| 126 | D4×C13 | — | 4 | 1 | no | — |
| 127 | D4×C13 | — | 4 | 2 | no | — |
| 128 | C2×C4×C13 | — | 2 | 2 | no | — |
| 129 | C2×C4×C13 | — | 2 | 1 | no | — |
| 130 | C2×C4×C13 | — | 2 | 1 | no | — |
| 131 | C2×C4×C13 | — | 2 | 2 | no | — |
| 132 | C2×C4×C13 | — | 4 | 1 | no | — |
| 133 | C2×C4×C13 | — | 4 | 1 | no | — |
| 134 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 136 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 137 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 138 | C2×C4×C13 | C22×C8 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C13 | C22×C8 | 1 | 2 | yes | — |
| 140 | C2×C4×C13 | C22×C8 | 1 | 2 | yes | — |
| 141 | C2×C4×C13 | C22×C8 | 1 | 2 | yes | — |
| 142 | C2×C4×C13 | C23×C4 | 1 | 1 | yes | characteristic |
| 143 | #1055 | — | 2 | 2 | no | — |
| 144 | #1055 | — | 2 | 1 | no | — |
| 145 | #1055 | — | 2 | 1 | no | — |
| 146 | #1055 | — | 2 | 1 | no | — |
| 147 | #1055 | — | 2 | 2 | no | — |
| 148 | #1055 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 149 | #1055 | 2−1+4 | 1 | 1 | yes | characteristic |
| 150 | #529 | #261 | 1 | 1 | yes | characteristic |
| 151 | C2×M32 | — | 13 | 1 | no | — |
| 152 | C2×M32 | — | 13 | 1 | no | — |
| 153 | C2×M32 | — | 13 | 2 | no | — |
| 154 | C22×C16 | — | 13 | 2 | no | — |
| 155 | #446 | — | 13 | 1 | no | — |
| 156 | C8×Q8 | — | 13 | 1 | no | — |
| 157 | #436 | — | 13 | 1 | no | — |
| 158 | #435 | — | 13 | 2 | no | — |
| 159 | C8×D4 | — | 13 | 1 | no | — |
| 160 | C8×D4 | — | 13 | 2 | no | — |
| 161 | #433 | — | 13 | 2 | no | — |
| 162 | #432 | — | 13 | 1 | no | — |
| 163 | #405 | — | 13 | 2 | no | — |
| 164 | C2×C4×C8 | — | 13 | 1 | no | — |
| 165 | C4⋊C16 | — | 13 | 2 | no | — |
| 166 | C4⋊C16 | — | 13 | 2 | no | — |
| 167 | C4⋊C16 | — | 13 | 1 | no | — |
| 168 | C4⋊C16 | — | 13 | 2 | no | — |
| 169 | C4⋊C16 | — | 13 | 2 | no | — |
| 170 | C4⋊C16 | — | 13 | 1 | no | — |
| 171 | C22⋊C16 | — | 13 | 2 | no | — |
| 172 | C22⋊C16 | — | 13 | 2 | no | — |
| 173 | C22⋊C16 | — | 13 | 2 | no | — |
| 174 | #346 | — | 13 | 2 | no | — |
| 175 | #346 | — | 13 | 2 | no | — |
| 176 | C4×C16 | — | 13 | 2 | no | — |
| 177 | C22×C13 | — | 2 | 1 | no | — |
| 178 | C22×C13 | — | 2 | 1 | no | — |
| 179 | C22×C13 | — | 2 | 2 | no | — |
| 180 | C22×C13 | — | 2 | 2 | no | — |
| 181 | C22×C13 | — | 2 | 1 | no | — |
| 182 | C22×C13 | — | 2 | 2 | no | — |
| 183 | C22×C13 | C23×C8 | 1 | 1 | yes | characteristic |
| 184 | C4×C13 | — | 2 | 1 | no | — |
| 185 | C4×C13 | — | 2 | 1 | no | — |
| 186 | C4×C13 | — | 2 | 1 | no | — |
| 187 | C4×C13 | — | 2 | 1 | no | — |
| 188 | C4×C13 | — | 2 | 2 | no | — |
| 189 | C4×C13 | — | 2 | 2 | no | — |
| 190 | C4×C13 | — | 2 | 1 | no | — |
| 191 | C4×C13 | — | 2 | 2 | no | — |
| 192 | C4×C13 | #520 | 1 | 1 | yes | characteristic |
| 193 | C4×C13 | #568 | 1 | 1 | yes | characteristic |
| 194 | C2×M16 | — | 13 | 2 | no | — |
| 195 | C22×C8 | — | 13 | 1 | no | — |
| 196 | C22×C8 | — | 13 | 2 | no | — |
| 197 | C22×C8 | — | 13 | 1 | no | — |
| 198 | #126 | #1057 | 1 | 2 | yes | — |
| 199 | #125 | #1057 | 1 | 1 | yes | characteristic |
| 200 | #124 | #1057 | 1 | 1 | yes | characteristic |
| 201 | #123 | #1057 | 1 | 2 | yes | — |
| 202 | C22⋊Q8 | #1057 | 1 | 1 | yes | characteristic |
| 203 | #121 | #1057 | 1 | 1 | yes | characteristic |
| 204 | C4×Q8 | C2×#261 | 1 | 1 | yes | characteristic |
| 205 | C4×D4 | C2×#261 | 1 | 2 | yes | — |
| 206 | C4×D4 | C2×#261 | 1 | 1 | yes | characteristic |
| 207 | #117 | C2×#261 | 1 | 2 | yes | — |
| 208 | C2×C42 | C2×#261 | 1 | 1 | yes | characteristic |
| 209 | M32 | — | 52 | 1 | no | — |
| 210 | M32 | — | 52 | 2 | no | — |
| 211 | M32 | — | 52 | 1 | no | — |
| 212 | C2×C16 | — | 13 | 2 | no | — |
| 213 | C2×C16 | — | 13 | 2 | no | — |
| 214 | C2×C16 | — | 13 | 2 | no | — |
| 215 | C2×C16 | — | 13 | 2 | no | — |
| 216 | C2×C16 | — | 52 | 2 | no | — |
| 217 | C4⋊C8 | — | 13 | 1 | no | — |
| 218 | C4⋊C8 | — | 13 | 1 | no | — |
| 219 | C4⋊C8 | — | 13 | 2 | no | — |
| 220 | C4⋊C8 | — | 13 | 2 | no | — |
| 221 | C22⋊C8 | — | 13 | 2 | no | — |
| 222 | C22⋊C8 | — | 13 | 2 | no | — |
| 223 | C22⋊C8 | — | 13 | 2 | no | — |
| 224 | #97 | — | 13 | 2 | no | — |
| 225 | #97 | — | 13 | 2 | no | — |
| 226 | C4×C8 | — | 13 | 2 | no | — |
| 227 | C4×C8 | — | 13 | 1 | no | — |
| 228 | C4×C8 | — | 13 | 1 | no | — |
| 229 | C4×C8 | — | 13 | 1 | no | — |
| 230 | C4×C8 | — | 13 | 1 | no | — |
| 231 | C2×C13 | — | 4 | 1 | no | — |
| 232 | C2×C13 | — | 4 | 2 | no | — |
| 233 | C2×C13 | #2988 | 1 | 1 | yes | characteristic |
| 234 | C2×C13 | #3407 | 1 | 1 | yes | characteristic |
| 235 | C2×C13 | #3407 | 1 | 1 | yes | characteristic |
| 236 | C2×Q8 | C2×#1057 | 1 | 1 | yes | characteristic |
| 237 | C2×D4 | C2×#1057 | 1 | 2 | yes | — |
| 238 | C2×D4 | C2×#1057 | 1 | 1 | yes | characteristic |
| 239 | C22×C4 | C2×#1057 | 1 | 1 | yes | characteristic |
| 240 | C22×C4 | C2×#1057 | 1 | 1 | yes | characteristic |
| 241 | C22×C4 | C22×#261 | 1 | 1 | yes | characteristic |
| 242 | C22×C4 | C22×#261 | 1 | 2 | yes | — |
| 243 | M16 | — | 52 | 2 | no | — |
| 244 | C2×C8 | — | 13 | 1 | no | — |
| 245 | C2×C8 | — | 13 | 1 | no | — |
| 246 | C2×C8 | — | 13 | 1 | no | — |
| 247 | C2×C8 | — | 13 | 1 | no | — |
| 248 | C2×C8 | — | 13 | 2 | no | — |
| 249 | C2×C8 | — | 13 | 2 | no | — |
| 250 | C2×C8 | — | 26 | 2 | no | — |
| 251 | C2×C8 | — | 26 | 1 | no | — |
| 252 | C2×C8 | — | 26 | 1 | no | — |
| 253 | C2×C8 | — | 26 | 2 | no | — |
| 254 | C2×C8 | — | 52 | 1 | no | — |
| 255 | C4⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 256 | C4⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 257 | C4⋊C4 | C2×#1057 | 1 | 1 | yes | characteristic |
| 258 | C4⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 259 | C4⋊C4 | C2×#1057 | 1 | 1 | yes | characteristic |
| 260 | C4⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 261 | C22⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 262 | C22⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 263 | C22⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 264 | C22⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 265 | C22⋊C4 | C2×#1057 | 1 | 2 | yes | — |
| 266 | C42 | C2×#1057 | 1 | 1 | yes | characteristic |
| 267 | C42 | C2×#1057 | 1 | 1 | yes | characteristic |
| 268 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 269 | C42 | C22×#261 | 1 | 1 | yes | characteristic |
| 270 | C42 | C22×#261 | 1 | 2 | yes | — |
| 271 | C16 | — | 26 | 2 | no | — |
| 272 | C16 | — | 26 | 2 | no | — |
| 273 | C16 | — | 26 | 2 | no | — |
| 274 | C16 | — | 26 | 2 | no | — |
| 275 | C13 | #33509 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 276 | C23 | C22×#1057 | 1 | 2 | yes | — |
| 277 | C23 | C22×#1057 | 1 | 1 | yes | characteristic |
| 278 | Q8 | — | 4 | 1 | no | — |
| 279 | D4 | — | 4 | 1 | no | — |
| 280 | D4 | — | 4 | 2 | no | — |
| 281 | C2×C4 | — | 2 | 1 | no | — |
| 282 | C2×C4 | — | 2 | 2 | no | — |
| 283 | C2×C4 | — | 2 | 2 | no | — |
| 284 | C2×C4 | — | 2 | 1 | no | — |
| 285 | C2×C4 | — | 4 | 1 | no | — |
| 286 | C2×C4 | — | 4 | 1 | no | — |
| 287 | C2×C4 | C22×#1057 | 1 | 1 | yes | characteristic |
| 288 | C2×C4 | C22×#1057 | 1 | 1 | yes | characteristic |
| 289 | C2×C4 | C22×#1057 | 1 | 1 | yes | characteristic |
| 290 | C2×C4 | C22×#1057 | 1 | 1 | yes | characteristic |
| 291 | C2×C4 | C22×#1057 | 1 | 1 | yes | characteristic |
| 292 | C2×C4 | C22×#1057 | 1 | 2 | yes | — |
| 293 | C2×C4 | C22×#1057 | 1 | 2 | yes | — |
| 294 | C2×C4 | C22×#1057 | 1 | 2 | yes | — |
| 295 | C2×C4 | C23×#261 | 1 | 1 | yes | characteristic |
| 296 | C8 | — | 13 | 1 | no | — |
| 297 | C8 | — | 13 | 1 | no | — |
| 298 | C8 | — | 26 | 1 | no | — |
| 299 | C8 | — | 26 | 1 | no | — |
| 300 | C8 | — | 26 | 2 | no | — |
| 301 | C8 | — | 26 | 1 | no | — |
| 302 | C8 | — | 26 | 2 | no | — |
| 303 | C22 | — | 2 | 1 | no | — |
| 304 | C22 | — | 2 | 1 | no | — |
| 305 | C22 | — | 2 | 2 | no | — |
| 306 | C22 | — | 2 | 2 | no | — |
| 307 | C22 | — | 2 | 1 | no | — |
| 308 | C22 | — | 2 | 2 | no | — |
| 309 | C22 | C23×#1057 | 1 | 1 | yes | characteristic |
| 310 | C4 | — | 2 | 1 | no | — |
| 311 | C4 | — | 2 | 1 | no | — |
| 312 | C4 | — | 2 | 1 | no | — |
| 313 | C4 | — | 2 | 1 | no | — |
| 314 | C4 | — | 2 | 2 | no | — |
| 315 | C4 | — | 2 | 2 | no | — |
| 316 | C4 | — | 2 | 1 | no | — |
| 317 | C4 | — | 2 | 2 | no | — |
| 318 | C4 | #11719629 | 1 | 1 | yes | characteristic |
| 319 | C4 | #11719631 | 1 | 1 | yes | characteristic |
| 320 | C2 | — | 4 | 1 | no | — |
| 321 | C2 | — | 4 | 2 | no | — |
| 322 | C2 | #13131751 | 1 | 1 | yes | characteristic |
| 323 | C2 | #13131803 | 1 | 1 | yes | characteristic |
| 324 | C2 | #13131803 | 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