← C2×#20291105 #28328343
Subgroups — C2×#20291105 #28328343
Order 13568.
654 conjugacy classes of subgroups.
The subgroup lattice has 268 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#16811681 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #20291105 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 3 | C2×#16811545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#16811521 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#16811512 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#16810740 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #16811681 | — | 2 | 4 | no | — |
| 8 | #16811681 | C22 | 1 | 8 | yes | complemented |
| 9 | C2×#13133291 | — | 2 | 2 | no | — |
| 10 | C2×#13133291 | C22 | 1 | 2 | yes | — |
| 11 | C22×#11719910 | — | 2 | 2 | no | — |
| 12 | C22×#11719910 | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×#11719910 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16811545 | C22 | 1 | 4 | yes | complemented |
| 15 | #16811521 | C22 | 1 | 8 | yes | complemented |
| 16 | #16811512 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×#13133224 | C22 | 1 | 2 | yes | — |
| 18 | #16810740 | C4 | 1 | 4 | yes | — |
| 19 | #16810740 | C22 | 1 | 4 | yes | — |
| 20 | C2×#13133153 | C4 | 1 | 1 | yes | characteristic |
| 21 | C2×#13133144 | C4 | 1 | 2 | yes | — |
| 22 | C2×C8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#135×C53 | C4 | 1 | 1 | yes | characteristic |
| 24 | #13133291 | — | 2 | 2 | no | — |
| 25 | #13133291 | — | 2 | 8 | no | — |
| 26 | #13133291 | C23 | 1 | 4 | yes | — |
| 27 | C2×#11719910 | — | 2 | 2 | no | — |
| 28 | C2×#11719910 | — | 2 | 1 | no | — |
| 29 | C2×#11719910 | — | 2 | 1 | no | — |
| 30 | C2×#11719910 | — | 2 | 8 | no | — |
| 31 | C2×#11719910 | D4 | 1 | 2 | yes | — |
| 32 | C2×#11719910 | D4 | 1 | 2 | yes | — |
| 33 | C2×#11719910 | C23 | 1 | 2 | yes | — |
| 34 | C2×#11719910 | C23 | 1 | 2 | yes | — |
| 35 | #13133224 | — | 2 | 2 | no | — |
| 36 | #13133224 | — | 2 | 2 | no | — |
| 37 | #13133224 | C2×C4 | 1 | 4 | yes | — |
| 38 | #13133224 | C23 | 1 | 4 | yes | — |
| 39 | C2×#11719917 | — | 2 | 2 | no | — |
| 40 | C2×#11719917 | C2×C4 | 1 | 2 | yes | — |
| 41 | C22×#88322 | — | 2 | 2 | no | — |
| 42 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×C4×Dic53 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | #13133153 | C2×C4 | 1 | 4 | yes | — |
| 45 | #13133144 | C2×C4 | 1 | 8 | yes | — |
| 46 | C8×Dic53 | C2×C4 | 1 | 2 | yes | — |
| 47 | C8×Dic53 | C23 | 1 | 2 | yes | — |
| 48 | C2×#41×C53 | C2×C4 | 1 | 2 | yes | — |
| 49 | #135×C53 | C8 | 1 | 4 | yes | — |
| 50 | #135×C53 | C2×C4 | 1 | 4 | yes | — |
| 51 | C2×Q16×C53 | C8 | 1 | 1 | yes | characteristic |
| 52 | C2×SD16×C53 | C8 | 1 | 2 | yes | — |
| 53 | C2×D8×C53 | C8 | 1 | 1 | yes | characteristic |
| 54 | C22×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | #41×C53 | — | 2 | 2 | no | — |
| 56 | #41×C53 | — | 2 | 2 | no | — |
| 57 | #41×C53 | C2×C8 | 1 | 4 | yes | — |
| 58 | #41×C53 | C22×C4 | 1 | 4 | yes | — |
| 59 | C2×Q8×C53 | C2×C8 | 1 | 2 | yes | — |
| 60 | C2×D4×C53 | — | 2 | 2 | no | — |
| 61 | C2×D4×C53 | C2×C8 | 1 | 2 | yes | — |
| 62 | C22×C4×C53 | — | 2 | 2 | no | — |
| 63 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 64 | C22×Dic53 | — | 2 | 1 | no | — |
| 65 | Q16×C53 | C2×C8 | 1 | 4 | yes | — |
| 66 | SD16×C53 | C2×C8 | 1 | 8 | yes | — |
| 67 | D8×C53 | C2×C8 | 1 | 4 | yes | — |
| 68 | C2×C8×C53 | C2×C8 | 1 | 1 | yes | characteristic |
| 69 | C2×C8×C53 | C2×C8 | 1 | 1 | yes | characteristic |
| 70 | C2×C8×C53 | C2×C8 | 1 | 2 | yes | — |
| 71 | C2×C8×C53 | C22×C4 | 1 | 2 | yes | — |
| 72 | C4×Dic53 | — | 2 | 1 | no | — |
| 73 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 74 | #11719917 | — | 2 | 2 | no | — |
| 75 | #11719917 | — | 2 | 4 | no | — |
| 76 | #11719917 | — | 2 | 4 | no | — |
| 77 | #11719917 | C22×C4 | 1 | 4 | yes | — |
| 78 | C2×#88322 | — | 2 | 2 | no | — |
| 79 | C2×#88322 | — | 2 | 4 | no | — |
| 80 | C2×#88322 | — | 2 | 4 | no | — |
| 81 | C2×#88322 | C22×C4 | 1 | 1 | yes | characteristic |
| 82 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 83 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×#88322 | #41 | 1 | 1 | yes | characteristic |
| 85 | C2×#88322 | #41 | 1 | 1 | yes | characteristic |
| 86 | C2×#88322 | C24 | 1 | 1 | yes | characteristic |
| 87 | #11719910 | — | 2 | 4 | no | — |
| 88 | #11719910 | — | 2 | 2 | no | — |
| 89 | #11719910 | C2×D4 | 1 | 4 | yes | — |
| 90 | C23×C53 | — | 2 | 2 | no | — |
| 91 | C23×C53 | #131 | 1 | 1 | yes | characteristic |
| 92 | Q8×C53 | — | 2 | 2 | no | — |
| 93 | Q8×C53 | C22×C8 | 1 | 4 | yes | — |
| 94 | D4×C53 | — | 2 | 4 | no | — |
| 95 | D4×C53 | — | 2 | 4 | no | — |
| 96 | D4×C53 | — | 2 | 2 | no | — |
| 97 | D4×C53 | C22×C8 | 1 | 4 | yes | — |
| 98 | C2×C4×C53 | — | 2 | 2 | no | — |
| 99 | C2×C4×C53 | — | 2 | 4 | no | — |
| 100 | C2×C4×C53 | — | 2 | 4 | no | — |
| 101 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C53 | C22×C8 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C53 | C22×C8 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×C53 | #131 | 1 | 1 | yes | characteristic |
| 106 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 107 | C2×Dic53 | — | 2 | 2 | no | — |
| 108 | C2×Dic53 | — | 4 | 2 | no | — |
| 109 | C8×C53 | C22×C8 | 1 | 2 | yes | — |
| 110 | C8×C53 | C22×C8 | 1 | 2 | yes | — |
| 111 | #88322 | — | 2 | 4 | no | — |
| 112 | #88322 | C4×D4 | 1 | 1 | yes | characteristic |
| 113 | #88322 | C4×D4 | 1 | 1 | yes | characteristic |
| 114 | #88322 | C22×D4 | 1 | 1 | yes | characteristic |
| 115 | #88322 | C2×#41 | 1 | 1 | yes | characteristic |
| 116 | C2×#2171 | — | 53 | 1 | no | maximal, Sylow |
| 117 | C22×C53 | — | 2 | 2 | no | — |
| 118 | C22×C53 | — | 2 | 4 | no | — |
| 119 | C22×C53 | — | 4 | 4 | no | — |
| 120 | C22×C53 | C8×D4 | 1 | 1 | yes | characteristic |
| 121 | C22×C53 | C8×D4 | 1 | 1 | yes | characteristic |
| 122 | C22×C53 | C2×#131 | 1 | 1 | yes | characteristic |
| 123 | C4×C53 | — | 2 | 4 | no | — |
| 124 | C4×C53 | C8×D4 | 1 | 1 | yes | characteristic |
| 125 | C4×C53 | C8×D4 | 1 | 1 | yes | characteristic |
| 126 | C4×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 127 | C4×C53 | C23×C8 | 1 | 1 | yes | characteristic |
| 128 | Dic53 | — | 4 | 2 | no | — |
| 129 | C2×#504 | — | 53 | 2 | no | — |
| 130 | C2×#443 | — | 53 | 1 | no | — |
| 131 | #2171 | — | 53 | 8 | no | — |
| 132 | C2×#364 | — | 53 | 1 | no | — |
| 133 | C2×#350 | — | 53 | 2 | no | — |
| 134 | C2×#346 | — | 53 | 1 | no | — |
| 135 | C2×C53 | — | 2 | 1 | no | — |
| 136 | C2×C53 | — | 2 | 1 | no | — |
| 137 | C2×C53 | — | 4 | 4 | no | — |
| 138 | C2×C53 | #2171 | 1 | 2 | yes | complemented |
| 139 | C2×C53 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 140 | C2×#135 | #6157 | 1 | 1 | yes | characteristic |
| 141 | C2×#131 | — | 53 | 2 | no | — |
| 142 | #504 | — | 53 | 8 | no | — |
| 143 | #504 | — | 106 | 4 | no | — |
| 144 | C2×M32 | — | 53 | 2 | no | — |
| 145 | C2×M32 | — | 106 | 2 | no | — |
| 146 | C22×C16 | — | 53 | 1 | no | — |
| 147 | C22×C16 | — | 53 | 1 | no | — |
| 148 | C22×C16 | — | 106 | 2 | no | — |
| 149 | #443 | — | 53 | 4 | no | — |
| 150 | #443 | — | 53 | 4 | no | — |
| 151 | C2×#108 | — | 53 | 1 | no | — |
| 152 | C2×#104 | — | 53 | 2 | no | — |
| 153 | C2×C4×C8 | — | 53 | 1 | no | — |
| 154 | #364 | — | 53 | 4 | no | — |
| 155 | #350 | — | 53 | 8 | no | — |
| 156 | #346 | — | 53 | 4 | no | — |
| 157 | C53 | C2×#2171 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 158 | C2×#41 | C2×#6157 | 1 | 2 | yes | — |
| 159 | #135 | #88324 | 1 | 4 | yes | — |
| 160 | #135 | C2×#6157 | 1 | 4 | yes | — |
| 161 | C2×Q16 | #88324 | 1 | 1 | yes | characteristic |
| 162 | C2×SD16 | #88324 | 1 | 2 | yes | — |
| 163 | C2×D8 | #88324 | 1 | 1 | yes | characteristic |
| 164 | #131 | — | 53 | 4 | no | — |
| 165 | #131 | — | 53 | 4 | no | — |
| 166 | #131 | — | 106 | 2 | no | — |
| 167 | #131 | — | 106 | 2 | no | — |
| 168 | C2×M16 | — | 53 | 2 | no | — |
| 169 | C2×M16 | — | 106 | 2 | no | — |
| 170 | C22×C8 | — | 53 | 1 | no | — |
| 171 | C22×C8 | — | 106 | 2 | no | — |
| 172 | C22×C8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 173 | C2×C42 | — | 53 | 1 | no | — |
| 174 | M32 | — | 53 | 4 | no | — |
| 175 | M32 | — | 106 | 8 | no | — |
| 176 | M32 | — | 106 | 2 | no | — |
| 177 | C2×C16 | — | 53 | 2 | no | — |
| 178 | C2×C16 | — | 53 | 2 | no | — |
| 179 | C2×C16 | — | 53 | 2 | no | — |
| 180 | C2×C16 | — | 53 | 2 | no | — |
| 181 | C2×C16 | — | 106 | 8 | no | — |
| 182 | C2×C16 | — | 106 | 1 | no | — |
| 183 | C2×C16 | — | 106 | 1 | no | — |
| 184 | C2×C16 | — | 106 | 2 | no | — |
| 185 | #108 | — | 53 | 4 | no | — |
| 186 | #104 | — | 53 | 8 | no | — |
| 187 | C4×C8 | — | 53 | 2 | no | — |
| 188 | C4×C8 | — | 53 | 2 | no | — |
| 189 | #41 | — | 2 | 2 | no | — |
| 190 | #41 | — | 2 | 2 | no | — |
| 191 | #41 | C2×#88324 | 1 | 4 | yes | — |
| 192 | #41 | C22×#6157 | 1 | 4 | yes | — |
| 193 | C2×Q8 | C2×#88324 | 1 | 2 | yes | — |
| 194 | C2×D4 | — | 2 | 2 | no | — |
| 195 | C2×D4 | C2×#88324 | 1 | 2 | yes | — |
| 196 | C22×C4 | — | 2 | 2 | no | — |
| 197 | C22×C4 | — | 106 | 1 | no | — |
| 198 | C22×C4 | C22×#6157 | 1 | 1 | yes | characteristic |
| 199 | Q16 | C2×#88324 | 1 | 4 | yes | — |
| 200 | SD16 | C2×#88324 | 1 | 8 | yes | — |
| 201 | D8 | C2×#88324 | 1 | 4 | yes | — |
| 202 | M16 | — | 53 | 4 | no | — |
| 203 | M16 | — | 106 | 4 | no | — |
| 204 | M16 | — | 106 | 4 | no | — |
| 205 | M16 | — | 106 | 2 | no | — |
| 206 | C2×C8 | — | 53 | 1 | no | — |
| 207 | C2×C8 | — | 53 | 1 | no | — |
| 208 | C2×C8 | — | 53 | 1 | no | — |
| 209 | C2×C8 | — | 53 | 1 | no | — |
| 210 | C2×C8 | — | 53 | 1 | no | — |
| 211 | C2×C8 | — | 53 | 1 | no | — |
| 212 | C2×C8 | — | 106 | 4 | no | — |
| 213 | C2×C8 | — | 106 | 4 | no | — |
| 214 | C2×C8 | — | 106 | 2 | no | — |
| 215 | C2×C8 | C2×#88324 | 1 | 1 | yes | characteristic |
| 216 | C2×C8 | C2×#88324 | 1 | 1 | yes | characteristic |
| 217 | C2×C8 | C2×#88324 | 1 | 2 | yes | — |
| 218 | C2×C8 | C22×#6157 | 1 | 2 | yes | — |
| 219 | C42 | — | 53 | 2 | no | — |
| 220 | C42 | — | 106 | 1 | no | — |
| 221 | C16 | — | 53 | 4 | no | — |
| 222 | C16 | — | 106 | 2 | no | — |
| 223 | C16 | — | 106 | 4 | no | — |
| 224 | C23 | — | 2 | 2 | no | — |
| 225 | C23 | #13133304 | 1 | 1 | yes | characteristic |
| 226 | Q8 | — | 2 | 2 | no | — |
| 227 | Q8 | C22×#88324 | 1 | 4 | yes | — |
| 228 | D4 | — | 2 | 4 | no | — |
| 229 | D4 | — | 2 | 4 | no | — |
| 230 | D4 | — | 2 | 2 | no | — |
| 231 | D4 | C22×#88324 | 1 | 4 | yes | — |
| 232 | C2×C4 | — | 2 | 2 | no | — |
| 233 | C2×C4 | — | 2 | 4 | no | — |
| 234 | C2×C4 | — | 2 | 4 | no | — |
| 235 | C2×C4 | — | 106 | 2 | no | — |
| 236 | C2×C4 | — | 212 | 2 | no | — |
| 237 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 238 | C2×C4 | D4×#6157 | 1 | 1 | yes | characteristic |
| 239 | C2×C4 | C22×#88324 | 1 | 1 | yes | characteristic |
| 240 | C2×C4 | C22×#88324 | 1 | 1 | yes | characteristic |
| 241 | C2×C4 | #13133304 | 1 | 1 | yes | characteristic |
| 242 | C2×C4 | C23×#6157 | 1 | 1 | yes | characteristic |
| 243 | C8 | — | 53 | 1 | no | — |
| 244 | C8 | — | 53 | 1 | no | — |
| 245 | C8 | — | 53 | 1 | no | — |
| 246 | C8 | — | 53 | 1 | no | — |
| 247 | C8 | — | 106 | 4 | no | — |
| 248 | C8 | C22×#88324 | 1 | 2 | yes | — |
| 249 | C8 | C22×#88324 | 1 | 2 | yes | — |
| 250 | C22 | — | 2 | 2 | no | — |
| 251 | C22 | — | 2 | 4 | no | — |
| 252 | C22 | — | 4 | 4 | no | — |
| 253 | C22 | D4×#88324 | 1 | 1 | yes | characteristic |
| 254 | C22 | D4×#88324 | 1 | 1 | yes | characteristic |
| 255 | C22 | C2×#13133304 | 1 | 1 | yes | characteristic |
| 256 | C4 | — | 2 | 4 | no | — |
| 257 | C4 | — | 212 | 2 | no | — |
| 258 | C4 | D4×#88324 | 1 | 1 | yes | characteristic |
| 259 | C4 | D4×#88324 | 1 | 1 | yes | characteristic |
| 260 | C4 | C2×D4×#6157 | 1 | 1 | yes | characteristic |
| 261 | C4 | C23×#88324 | 1 | 1 | yes | characteristic |
| 262 | C2 | — | 2 | 1 | no | — |
| 263 | C2 | — | 2 | 1 | no | — |
| 264 | C2 | — | 4 | 4 | no | — |
| 265 | C2 | #20291105 | 1 | 2 | yes | direct product factor |
| 266 | C2 | C2×D4×#88324 | 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