← #16860482
Subgroups — #16860482
Order 3968.
1424 conjugacy classes of subgroups.
The subgroup lattice has 258 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14521885 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14521864 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #14521860 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #14521857 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #14521852 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #14521847 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#11758527 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#11758525 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C31×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C31×2−1+4 | — | 2 | 1 | no | — |
| 11 | C31×2−1+4 | C22 | 1 | 4 | yes | complemented |
| 12 | C31×H(5,𝔽2) | — | 2 | 3 | no | — |
| 13 | C31×H(5,𝔽2) | C22 | 1 | 4 | yes | complemented |
| 14 | C2×#41×C31 | — | 2 | 4 | no | — |
| 15 | C2×#41×C31 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#41×C31 | C22 | 1 | 6 | yes | complemented |
| 17 | #11758567 | C22 | 1 | 4 | yes | complemented |
| 18 | #11758566 | C22 | 1 | 4 | yes | complemented |
| 19 | #41×D31 | — | 2 | 4 | no | — |
| 20 | #11758564 | — | 2 | 1 | no | — |
| 21 | #11758561 | — | 2 | 3 | no | — |
| 22 | C2×#92495 | C22 | 1 | 6 | yes | complemented |
| 23 | #11758528 | C22 | 1 | 12 | yes | complemented |
| 24 | #11758527 | C22 | 1 | 12 | yes | complemented |
| 25 | #11758527 | C22 | 1 | 12 | yes | complemented |
| 26 | #11758527 | C22 | 1 | 4 | yes | complemented |
| 27 | #11758527 | C22 | 1 | 12 | yes | complemented |
| 28 | #11758526 | C22 | 1 | 12 | yes | complemented |
| 29 | #11758525 | C22 | 1 | 4 | yes | complemented |
| 30 | #11758525 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#92482 | C22 | 1 | 6 | yes | complemented |
| 32 | #11758519 | C22 | 1 | 12 | yes | complemented |
| 33 | C2×#92481 | C22 | 1 | 6 | yes | complemented |
| 34 | C2×#92480 | C22 | 1 | 6 | yes | complemented |
| 35 | #11758509 | C22 | 1 | 12 | yes | complemented |
| 36 | C2×#92479 | C22 | 1 | 6 | yes | complemented |
| 37 | C2×#92474 | C22 | 1 | 3 | yes | complemented |
| 38 | C22×C31⋊C8 | C22 | 1 | 3 | yes | complemented |
| 39 | #41×C31 | — | 2 | 4 | no | — |
| 40 | #41×C31 | — | 2 | 12 | no | — |
| 41 | #41×C31 | — | 2 | 6 | no | — |
| 42 | #41×C31 | — | 2 | 6 | no | — |
| 43 | #41×C31 | D4 | 1 | 4 | yes | — |
| 44 | #41×C31 | C23 | 1 | 12 | yes | — |
| 45 | #41×C31 | C23 | 1 | 4 | yes | — |
| 46 | #41×C31 | C23 | 1 | 4 | yes | — |
| 47 | C2×Q8×C31 | — | 2 | 4 | no | — |
| 48 | C2×Q8×C31 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×Q8×C31 | C23 | 1 | 6 | yes | — |
| 50 | C2×D4×C31 | — | 2 | 6 | no | — |
| 51 | C2×D4×C31 | — | 2 | 12 | no | — |
| 52 | C2×D4×C31 | D4 | 1 | 3 | yes | — |
| 53 | C2×D4×C31 | C23 | 1 | 6 | yes | — |
| 54 | C22×C4×C31 | — | 2 | 6 | no | — |
| 55 | C22×C4×C31 | C23 | 1 | 3 | yes | — |
| 56 | C2×C22⋊D31 | — | 2 | 6 | no | — |
| 57 | #92499 | — | 2 | 4 | no | — |
| 58 | Q8×D31 | — | 2 | 4 | no | — |
| 59 | #92497 | — | 2 | 12 | no | — |
| 60 | D4×D31 | — | 2 | 12 | no | — |
| 61 | #92495 | — | 2 | 6 | no | — |
| 62 | #92495 | — | 2 | 6 | no | — |
| 63 | #92495 | C23 | 1 | 12 | yes | — |
| 64 | #92495 | C23 | 1 | 4 | yes | — |
| 65 | C2×D124 | C23 | 1 | 6 | yes | — |
| 66 | C2×C4×D31 | — | 2 | 6 | no | — |
| 67 | C2×Dic62 | C23 | 1 | 6 | yes | — |
| 68 | #92482 | C23 | 1 | 12 | yes | — |
| 69 | #92482 | C23 | 1 | 4 | yes | — |
| 70 | #92481 | C23 | 1 | 4 | yes | — |
| 71 | #92481 | C23 | 1 | 12 | yes | — |
| 72 | #92480 | C23 | 1 | 12 | yes | — |
| 73 | #92480 | C23 | 1 | 4 | yes | — |
| 74 | #92479 | C23 | 1 | 4 | yes | — |
| 75 | #92479 | C23 | 1 | 12 | yes | — |
| 76 | #92474 | C23 | 1 | 12 | yes | — |
| 77 | C2×C31⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C31⋊C8 | C23 | 1 | 3 | yes | — |
| 79 | C2×C31⋊C8 | C23 | 1 | 6 | yes | — |
| 80 | C2×C31⋊C8 | C23 | 1 | 6 | yes | — |
| 81 | C23×C31 | — | 2 | 6 | no | — |
| 82 | C23×C31 | C2×D4 | 1 | 3 | yes | — |
| 83 | C22×D31 | — | 2 | 6 | no | — |
| 84 | Q8×C31 | — | 2 | 6 | no | — |
| 85 | Q8×C31 | C2×D4 | 1 | 4 | yes | — |
| 86 | Q8×C31 | C24 | 1 | 4 | yes | — |
| 87 | D4×C31 | — | 2 | 12 | no | — |
| 88 | D4×C31 | — | 2 | 4 | no | — |
| 89 | D4×C31 | — | 2 | 6 | no | — |
| 90 | D4×C31 | C2×D4 | 1 | 12 | yes | — |
| 91 | D4×C31 | C24 | 1 | 4 | yes | — |
| 92 | C2×C4×C31 | — | 2 | 6 | no | — |
| 93 | C2×C4×C31 | — | 2 | 4 | no | — |
| 94 | C2×C4×C31 | — | 2 | 12 | no | — |
| 95 | C2×C4×C31 | C2×D4 | 1 | 6 | yes | — |
| 96 | C2×C4×C31 | C2×D4 | 1 | 3 | yes | — |
| 97 | C2×C4×C31 | C24 | 1 | 1 | yes | characteristic |
| 98 | C2×C4×C31 | C24 | 1 | 6 | yes | — |
| 99 | C22⋊D31 | — | 2 | 4 | no | — |
| 100 | C22⋊D31 | — | 2 | 12 | no | — |
| 101 | C2×Dic31 | — | 2 | 6 | no | — |
| 102 | D124 | — | 2 | 6 | no | — |
| 103 | D124 | C24 | 1 | 4 | yes | — |
| 104 | C4×D31 | — | 2 | 4 | no | — |
| 105 | C4×D31 | — | 2 | 12 | no | — |
| 106 | Dic62 | — | 2 | 6 | no | — |
| 107 | Dic62 | C24 | 1 | 4 | yes | — |
| 108 | C31⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 109 | C31⋊C8 | C24 | 1 | 1 | yes | characteristic |
| 110 | C31⋊C8 | C24 | 1 | 6 | yes | — |
| 111 | #3584 | — | 31 | 1 | no | maximal, Sylow |
| 112 | C22×C31 | — | 2 | 4 | no | — |
| 113 | C22×C31 | — | 4 | 3 | no | — |
| 114 | C22×C31 | — | 8 | 6 | no | — |
| 115 | C22×C31 | C22×D4 | 1 | 6 | yes | — |
| 116 | C22×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 117 | C2×D31 | — | 2 | 4 | no | — |
| 118 | C2×D31 | — | 8 | 6 | no | — |
| 119 | C4×C31 | — | 2 | 4 | no | — |
| 120 | C4×C31 | C22×D4 | 1 | 6 | yes | — |
| 121 | C4×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 122 | C4×C31 | C25 | 1 | 1 | yes | characteristic |
| 123 | Dic31 | — | 2 | 4 | no | — |
| 124 | #585 | — | 31 | 1 | no | — |
| 125 | #585 | D31 | 1 | 1 | yes | characteristic, complemented |
| 126 | #578 | — | 31 | 4 | no | — |
| 127 | #577 | — | 31 | 4 | no | — |
| 128 | #577 | — | 31 | 4 | no | — |
| 129 | #576 | — | 31 | 4 | no | — |
| 130 | #575 | — | 31 | 6 | no | — |
| 131 | C2×#135 | — | 31 | 6 | no | — |
| 132 | C2×#131 | — | 31 | 1 | no | — |
| 133 | C2×C31 | — | 2 | 6 | no | — |
| 134 | C2×C31 | — | 2 | 1 | no | — |
| 135 | C2×C31 | — | 4 | 4 | no | — |
| 136 | C2×C31 | C23×D4 | 1 | 1 | yes | characteristic |
| 137 | D31 | — | 4 | 4 | no | — |
| 138 | 2−1+4 | — | 2 | 1 | no | — |
| 139 | 2−1+4 | — | 31 | 4 | no | — |
| 140 | 2−1+4 | — | 62 | 1 | no | — |
| 141 | 2−1+4 | C2×D31 | 1 | 4 | yes | complemented |
| 142 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 143 | H(5,𝔽2) | — | 31 | 4 | no | — |
| 144 | H(5,𝔽2) | — | 62 | 3 | no | — |
| 145 | H(5,𝔽2) | C2×D31 | 1 | 4 | yes | complemented |
| 146 | C2×#41 | — | 2 | 4 | no | — |
| 147 | C2×#41 | — | 31 | 6 | no | — |
| 148 | C2×#41 | — | 62 | 4 | no | — |
| 149 | C2×#41 | C2×D31 | 1 | 1 | yes | characteristic |
| 150 | C2×#41 | C2×D31 | 1 | 6 | yes | complemented |
| 151 | #137 | — | 31 | 12 | no | — |
| 152 | #137 | — | 31 | 12 | no | — |
| 153 | AGL(1,ℤ/8) | — | 31 | 12 | no | — |
| 154 | AGL(1,ℤ/8) | — | 31 | 12 | no | — |
| 155 | #135 | — | 31 | 4 | no | — |
| 156 | #135 | — | 31 | 12 | no | — |
| 157 | #135 | — | 31 | 12 | no | — |
| 158 | #135 | — | 31 | 12 | no | — |
| 159 | C2×Q16 | — | 31 | 6 | no | — |
| 160 | C2×SD16 | — | 31 | 6 | no | — |
| 161 | C2×SD16 | — | 31 | 6 | no | — |
| 162 | C2×D8 | — | 31 | 6 | no | — |
| 163 | #131 | — | 31 | 4 | no | — |
| 164 | #131 | — | 31 | 4 | no | — |
| 165 | C2×M16 | — | 31 | 3 | no | — |
| 166 | C22×C8 | — | 31 | 3 | no | — |
| 167 | C31 | #3584 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 168 | #41 | — | 2 | 4 | no | — |
| 169 | #41 | — | 2 | 12 | no | — |
| 170 | #41 | — | 2 | 6 | no | — |
| 171 | #41 | — | 2 | 6 | no | — |
| 172 | #41 | — | 31 | 4 | no | — |
| 173 | #41 | — | 31 | 12 | no | — |
| 174 | #41 | — | 62 | 4 | no | — |
| 175 | #41 | — | 62 | 12 | no | — |
| 176 | #41 | — | 62 | 6 | no | — |
| 177 | #41 | — | 62 | 6 | no | — |
| 178 | #41 | C22⋊D31 | 1 | 4 | yes | — |
| 179 | #41 | C22×D31 | 1 | 4 | yes | — |
| 180 | #41 | C22×D31 | 1 | 12 | yes | — |
| 181 | #41 | C22×D31 | 1 | 4 | yes | — |
| 182 | C2×Q8 | — | 2 | 4 | no | — |
| 183 | C2×Q8 | — | 31 | 6 | no | — |
| 184 | C2×Q8 | — | 62 | 4 | no | — |
| 185 | C2×Q8 | C22⋊D31 | 1 | 1 | yes | characteristic |
| 186 | C2×Q8 | C22×D31 | 1 | 6 | yes | — |
| 187 | C2×D4 | — | 2 | 6 | no | — |
| 188 | C2×D4 | — | 2 | 12 | no | — |
| 189 | C2×D4 | — | 31 | 6 | no | — |
| 190 | C2×D4 | — | 62 | 6 | no | — |
| 191 | C2×D4 | — | 62 | 12 | no | — |
| 192 | C2×D4 | C22⋊D31 | 1 | 3 | yes | — |
| 193 | C2×D4 | C22×D31 | 1 | 6 | yes | — |
| 194 | C22×C4 | — | 2 | 6 | no | — |
| 195 | C22×C4 | — | 62 | 6 | no | — |
| 196 | C22×C4 | C22×D31 | 1 | 3 | yes | — |
| 197 | Q16 | — | 31 | 4 | no | — |
| 198 | Q16 | — | 31 | 12 | no | — |
| 199 | SD16 | — | 31 | 4 | no | — |
| 200 | SD16 | — | 31 | 12 | no | — |
| 201 | SD16 | — | 31 | 4 | no | — |
| 202 | SD16 | — | 31 | 12 | no | — |
| 203 | D8 | — | 31 | 4 | no | — |
| 204 | D8 | — | 31 | 12 | no | — |
| 205 | M16 | — | 31 | 12 | no | — |
| 206 | C2×C8 | — | 31 | 1 | no | — |
| 207 | C2×C8 | — | 31 | 3 | no | — |
| 208 | C2×C8 | — | 31 | 6 | no | — |
| 209 | C2×C8 | — | 31 | 6 | no | — |
| 210 | C23 | — | 2 | 6 | no | — |
| 211 | C23 | — | 62 | 6 | no | — |
| 212 | C23 | C2×C22⋊D31 | 1 | 3 | yes | — |
| 213 | Q8 | — | 2 | 6 | no | — |
| 214 | Q8 | — | 31 | 4 | no | — |
| 215 | Q8 | — | 62 | 6 | no | — |
| 216 | Q8 | C2×C22⋊D31 | 1 | 4 | yes | — |
| 217 | Q8 | C23×D31 | 1 | 4 | yes | — |
| 218 | D4 | — | 2 | 12 | no | — |
| 219 | D4 | — | 2 | 4 | no | — |
| 220 | D4 | — | 2 | 6 | no | — |
| 221 | D4 | — | 31 | 4 | no | — |
| 222 | D4 | — | 62 | 12 | no | — |
| 223 | D4 | — | 62 | 4 | no | — |
| 224 | D4 | — | 62 | 6 | no | — |
| 225 | D4 | C2×C22⋊D31 | 1 | 12 | yes | — |
| 226 | D4 | C23×D31 | 1 | 4 | yes | — |
| 227 | C2×C4 | — | 2 | 6 | no | — |
| 228 | C2×C4 | — | 2 | 12 | no | — |
| 229 | C2×C4 | — | 2 | 4 | no | — |
| 230 | C2×C4 | — | 62 | 6 | no | — |
| 231 | C2×C4 | — | 62 | 12 | no | — |
| 232 | C2×C4 | — | 62 | 4 | no | — |
| 233 | C2×C4 | C2×C22⋊D31 | 1 | 3 | yes | — |
| 234 | C2×C4 | C2×C22⋊D31 | 1 | 6 | yes | — |
| 235 | C2×C4 | C23×D31 | 1 | 6 | yes | — |
| 236 | C2×C4 | C23×D31 | 1 | 1 | yes | characteristic |
| 237 | C8 | — | 31 | 1 | no | — |
| 238 | C8 | — | 31 | 1 | no | — |
| 239 | C8 | — | 31 | 6 | no | — |
| 240 | C22 | — | 2 | 4 | no | — |
| 241 | C22 | — | 4 | 3 | no | — |
| 242 | C22 | — | 8 | 6 | no | — |
| 243 | C22 | — | 62 | 4 | no | — |
| 244 | C22 | — | 248 | 6 | no | — |
| 245 | C22 | C22×C22⋊D31 | 1 | 6 | yes | — |
| 246 | C22 | C22×C22⋊D31 | 1 | 1 | yes | characteristic |
| 247 | C4 | — | 2 | 4 | no | — |
| 248 | C4 | — | 62 | 4 | no | — |
| 249 | C4 | C22×C22⋊D31 | 1 | 6 | yes | — |
| 250 | C4 | C22×C22⋊D31 | 1 | 1 | yes | characteristic |
| 251 | C4 | C24×D31 | 1 | 1 | yes | characteristic |
| 252 | C2 | — | 2 | 1 | no | — |
| 253 | C2 | — | 2 | 6 | no | — |
| 254 | C2 | — | 4 | 4 | no | — |
| 255 | C2 | — | 124 | 4 | no | — |
| 256 | C2 | C23×C22⋊D31 | 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