← #30624118
Subgroups — #30624118
Order 15616.
636 conjugacy classes of subgroups.
The subgroup lattice has 256 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #21462480 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #21462473 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #21462167 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #21462166 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D61⋊#365 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#16840686 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #21458920 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16840841 | — | 2 | 1 | no | — |
| 9 | #16840831 | — | 2 | 1 | no | — |
| 10 | #16840777 | — | 2 | 3 | no | — |
| 11 | D61⋊#108 | C22 | 1 | 3 | yes | — |
| 12 | C2×#14519847 | C22 | 1 | 3 | yes | — |
| 13 | #16840773 | — | 2 | 3 | no | — |
| 14 | #16840772 | C22 | 1 | 3 | yes | — |
| 15 | C2×#14519845 | C22 | 1 | 3 | yes | — |
| 16 | #16840687 | C22 | 1 | 3 | yes | — |
| 17 | #16840687 | C22 | 1 | 3 | yes | — |
| 18 | #16840686 | C22 | 1 | 3 | yes | — |
| 19 | #16840686 | C22 | 1 | 6 | yes | — |
| 20 | #16840686 | C22 | 1 | 1 | yes | characteristic |
| 21 | #131×D61 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16840180 | C4 | 1 | 3 | yes | complemented |
| 23 | #16840179 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #16840178 | C4 | 1 | 3 | yes | complemented |
| 25 | C2×#14519716 | C22 | 1 | 3 | yes | — |
| 26 | M32×D61 | C22 | 1 | 3 | yes | — |
| 27 | C61×#504 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #14519865 | — | 4 | 1 | no | — |
| 29 | #14519864 | — | 4 | 3 | no | — |
| 30 | C2×#11758213 | — | 2 | 3 | no | — |
| 31 | D61⋊M16 | — | 2 | 3 | no | — |
| 32 | Q8×#6923 | — | 4 | 1 | no | — |
| 33 | D4×#6923 | — | 4 | 3 | no | — |
| 34 | #14519856 | — | 2 | 3 | no | — |
| 35 | C2×C4⋊#6923 | — | 2 | 3 | no | — |
| 36 | #14519848 | — | 2 | 3 | no | — |
| 37 | #14519847 | — | 2 | 3 | no | — |
| 38 | #14519847 | C23 | 1 | 3 | yes | — |
| 39 | #14519847 | C23 | 1 | 1 | yes | characteristic |
| 40 | #14519846 | — | 2 | 3 | no | — |
| 41 | #14519845 | — | 2 | 3 | no | — |
| 42 | #14519845 | C23 | 1 | 3 | yes | — |
| 43 | #14519845 | C23 | 1 | 1 | yes | characteristic |
| 44 | #41×D61 | D4 | 1 | 1 | yes | characteristic |
| 45 | #14519785 | Q8 | 1 | 3 | yes | — |
| 46 | #14519784 | Q8 | 1 | 1 | yes | characteristic |
| 47 | #14519783 | C2×C4 | 1 | 3 | yes | — |
| 48 | M16×D61 | D4 | 1 | 3 | yes | — |
| 49 | C2×C8×D61 | C23 | 1 | 3 | yes | — |
| 50 | #14519717 | C2×C4 | 1 | 3 | yes | complemented |
| 51 | #14519716 | C2×C4 | 1 | 3 | yes | complemented |
| 52 | #14519716 | C2×C4 | 1 | 3 | yes | complemented |
| 53 | #14519716 | C23 | 1 | 1 | yes | characteristic |
| 54 | #14519716 | C23 | 1 | 3 | yes | — |
| 55 | C2×#11758185 | C2×C4 | 1 | 3 | yes | complemented |
| 56 | C16×D61 | C2×C4 | 1 | 6 | yes | complemented |
| 57 | #131×C61 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | M32×C61 | C2×C4 | 1 | 3 | yes | complemented |
| 59 | C2×C16×C61 | C2×C4 | 1 | 3 | yes | complemented |
| 60 | C22×#6923 | — | 4 | 3 | no | — |
| 61 | #41×C61 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 62 | #11758226 | SD16 | 1 | 1 | yes | characteristic |
| 63 | Q8×D61 | SD16 | 1 | 1 | yes | characteristic |
| 64 | #11758224 | SD16 | 1 | 3 | yes | — |
| 65 | D4×D61 | SD16 | 1 | 3 | yes | — |
| 66 | #11758222 | C4⋊C4 | 1 | 3 | yes | — |
| 67 | C2×C4×D61 | C2×D4 | 1 | 3 | yes | — |
| 68 | C22⋊#6923 | — | 4 | 3 | no | — |
| 69 | #11758217 | — | 4 | 3 | no | — |
| 70 | C2×#92420 | — | 4 | 3 | no | — |
| 71 | C4⋊#6923 | — | 2 | 3 | no | — |
| 72 | C4⋊#6923 | — | 2 | 1 | no | — |
| 73 | C4⋊#6923 | — | 4 | 3 | no | — |
| 74 | C4×#6923 | — | 4 | 3 | no | — |
| 75 | #11758213 | — | 2 | 3 | no | — |
| 76 | #11758213 | — | 2 | 1 | no | — |
| 77 | #11758213 | — | 4 | 3 | no | — |
| 78 | D61⋊C8 | — | 4 | 3 | no | — |
| 79 | M16×C61 | C4⋊C4 | 1 | 3 | yes | — |
| 80 | C2×C8×C61 | C22×C4 | 1 | 3 | yes | — |
| 81 | #11758194 | C4⋊C4 | 1 | 3 | yes | — |
| 82 | C2×#92418 | C2×Q8 | 1 | 3 | yes | — |
| 83 | #11758189 | C4⋊C4 | 1 | 6 | yes | — |
| 84 | C8×D61 | C22×C4 | 1 | 3 | yes | — |
| 85 | C8×D61 | C2×D4 | 1 | 3 | yes | — |
| 86 | C8×D61 | C2×Q8 | 1 | 3 | yes | — |
| 87 | C8×D61 | C24 | 1 | 1 | yes | characteristic |
| 88 | C16×C61 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C16×C61 | C22×C4 | 1 | 3 | yes | — |
| 90 | #11758185 | C22×C4 | 1 | 3 | yes | — |
| 91 | #11758185 | C22×C4 | 1 | 1 | yes | characteristic |
| 92 | C22×D61 | C2×SD16 | 1 | 3 | yes | — |
| 93 | C2×#6923 | — | 4 | 1 | no | — |
| 94 | C2×#6923 | — | 4 | 3 | no | — |
| 95 | C2×#6923 | — | 16 | 3 | no | — |
| 96 | Q8×C61 | #106 | 1 | 1 | yes | characteristic |
| 97 | D4×C61 | #106 | 1 | 3 | yes | — |
| 98 | C2×C4×C61 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 99 | C22⋊D61 | #106 | 1 | 6 | yes | — |
| 100 | C2×Dic61 | C2×SD16 | 1 | 3 | yes | — |
| 101 | D244 | #106 | 1 | 3 | yes | — |
| 102 | C4×D61 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 103 | C4×D61 | C2×SD16 | 1 | 3 | yes | — |
| 104 | C4×D61 | C2×SD16 | 1 | 3 | yes | — |
| 105 | C4×D61 | C22×D4 | 1 | 1 | yes | characteristic |
| 106 | Dic122 | #106 | 1 | 3 | yes | — |
| 107 | #92420 | — | 4 | 1 | no | — |
| 108 | #92420 | — | 4 | 3 | no | — |
| 109 | C8×C61 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 110 | C8×C61 | C23×C4 | 1 | 1 | yes | characteristic |
| 111 | #92418 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 112 | #92418 | C22×Q8 | 1 | 1 | yes | characteristic |
| 113 | #33404 | — | 61 | 1 | no | maximal, Sylow |
| 114 | C22×C61 | C2×#106 | 1 | 3 | yes | — |
| 115 | C2×D61 | — | 4 | 3 | no | — |
| 116 | C2×D61 | C2×#106 | 1 | 3 | yes | — |
| 117 | C2×D61 | C22×SD16 | 1 | 1 | yes | characteristic |
| 118 | #6923 | — | 8 | 1 | no | — |
| 119 | #6923 | — | 8 | 3 | no | — |
| 120 | C4×C61 | C2×#106 | 1 | 3 | yes | — |
| 121 | C4×C61 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 122 | Dic61 | C2×#106 | 1 | 3 | yes | — |
| 123 | Dic61 | C22×SD16 | 1 | 1 | yes | characteristic |
| 124 | #3407 | — | 61 | 1 | no | — |
| 125 | #2916 | — | 61 | 1 | no | — |
| 126 | #2912 | — | 61 | 1 | no | — |
| 127 | #2155 | — | 61 | 3 | no | — |
| 128 | #2155 | — | 61 | 3 | no | — |
| 129 | C2×#365 | — | 61 | 3 | no | — |
| 130 | C2×#365 | — | 61 | 3 | no | — |
| 131 | C2×C61 | — | 2 | 3 | no | — |
| 132 | C2×C61 | C22×#106 | 1 | 1 | yes | characteristic |
| 133 | D61 | — | 2 | 1 | no | — |
| 134 | D61 | — | 2 | 3 | no | — |
| 135 | #568 | — | 122 | 1 | no | — |
| 136 | C2×#131 | — | 61 | 1 | no | — |
| 137 | #520 | — | 122 | 1 | no | — |
| 138 | #504 | — | 61 | 1 | no | — |
| 139 | #504 | — | 61 | 3 | no | — |
| 140 | #504 | — | 61 | 3 | no | — |
| 141 | #504 | #6923 | 1 | 1 | yes | characteristic, complemented |
| 142 | C2×M32 | — | 61 | 3 | no | — |
| 143 | C2×M32 | — | 61 | 3 | no | — |
| 144 | #430 | — | 122 | 3 | no | — |
| 145 | C2×#108 | — | 61 | 3 | no | — |
| 146 | C2×#108 | — | 61 | 3 | no | — |
| 147 | #428 | — | 122 | 3 | no | — |
| 148 | #427 | — | 61 | 3 | no | — |
| 149 | C2×#106 | — | 61 | 3 | no | — |
| 150 | #365 | — | 61 | 3 | no | — |
| 151 | #365 | — | 61 | 6 | no | — |
| 152 | #365 | — | 61 | 3 | no | — |
| 153 | #365 | — | 61 | 1 | no | — |
| 154 | #365 | — | 61 | 3 | no | — |
| 155 | C61 | #33404 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 156 | C2×#41 | — | 61 | 1 | no | — |
| 157 | #131 | — | 61 | 1 | no | — |
| 158 | #131 | — | 61 | 3 | no | — |
| 159 | #131 | — | 61 | 3 | no | — |
| 160 | #131 | — | 244 | 3 | no | — |
| 161 | #131 | — | 244 | 1 | no | — |
| 162 | #131 | C2×#6923 | 1 | 1 | yes | characteristic |
| 163 | C2×M16 | — | 61 | 3 | no | — |
| 164 | C2×M16 | — | 122 | 3 | no | — |
| 165 | C2×M16 | — | 122 | 3 | no | — |
| 166 | C22×C8 | — | 61 | 3 | no | — |
| 167 | C4×Q8 | — | 244 | 1 | no | — |
| 168 | C4×D4 | — | 244 | 3 | no | — |
| 169 | #117 | — | 122 | 3 | no | — |
| 170 | C2×C4⋊C4 | — | 122 | 3 | no | — |
| 171 | M32 | — | 61 | 3 | no | — |
| 172 | M32 | — | 61 | 3 | no | — |
| 173 | M32 | — | 61 | 1 | no | — |
| 174 | M32 | — | 61 | 3 | no | — |
| 175 | M32 | — | 61 | 3 | no | — |
| 176 | M32 | C2×#6923 | 1 | 3 | yes | complemented |
| 177 | C2×C16 | — | 61 | 3 | no | — |
| 178 | C2×C16 | — | 61 | 6 | no | — |
| 179 | C2×C16 | C2×#6923 | 1 | 3 | yes | complemented |
| 180 | #108 | — | 61 | 3 | no | — |
| 181 | #108 | — | 61 | 1 | no | — |
| 182 | #108 | — | 122 | 3 | no | — |
| 183 | #108 | — | 122 | 3 | no | — |
| 184 | #107 | — | 122 | 3 | no | — |
| 185 | #106 | — | 61 | 3 | no | — |
| 186 | #106 | — | 61 | 1 | no | — |
| 187 | #106 | — | 122 | 3 | no | — |
| 188 | #41 | — | 61 | 1 | no | — |
| 189 | #41 | — | 61 | 3 | no | — |
| 190 | #41 | — | 61 | 3 | no | — |
| 191 | #41 | C4⋊#6923 | 1 | 1 | yes | characteristic |
| 192 | C2×Q8 | — | 61 | 1 | no | — |
| 193 | C2×D4 | — | 61 | 3 | no | — |
| 194 | C22×C4 | — | 61 | 3 | no | — |
| 195 | C22×C4 | — | 244 | 3 | no | — |
| 196 | M16 | — | 61 | 3 | no | — |
| 197 | M16 | — | 61 | 6 | no | — |
| 198 | M16 | — | 122 | 3 | no | — |
| 199 | M16 | — | 122 | 1 | no | — |
| 200 | M16 | — | 244 | 3 | no | — |
| 201 | M16 | — | 244 | 3 | no | — |
| 202 | M16 | C4⋊#6923 | 1 | 3 | yes | — |
| 203 | C2×C8 | — | 61 | 3 | no | — |
| 204 | C2×C8 | — | 61 | 3 | no | — |
| 205 | C2×C8 | — | 61 | 3 | no | — |
| 206 | C2×C8 | — | 61 | 1 | no | — |
| 207 | C2×C8 | — | 61 | 3 | no | — |
| 208 | C2×C8 | — | 244 | 3 | no | — |
| 209 | C2×C8 | — | 244 | 3 | no | — |
| 210 | C2×C8 | C22×#6923 | 1 | 3 | yes | — |
| 211 | C4⋊C4 | — | 122 | 3 | no | — |
| 212 | C4⋊C4 | — | 122 | 1 | no | — |
| 213 | C4⋊C4 | — | 244 | 3 | no | — |
| 214 | C22⋊C4 | — | 244 | 3 | no | — |
| 215 | C42 | — | 244 | 3 | no | — |
| 216 | C16 | — | 61 | 3 | no | — |
| 217 | C16 | — | 61 | 1 | no | — |
| 218 | C16 | C22×#6923 | 1 | 3 | yes | — |
| 219 | C16 | C22×#6923 | 1 | 1 | yes | characteristic |
| 220 | C23 | — | 61 | 3 | no | — |
| 221 | Q8 | — | 61 | 3 | no | — |
| 222 | Q8 | #14519845 | 1 | 1 | yes | characteristic |
| 223 | D4 | — | 61 | 6 | no | — |
| 224 | D4 | — | 61 | 3 | no | — |
| 225 | D4 | #14519845 | 1 | 3 | yes | — |
| 226 | C2×C4 | — | 61 | 3 | no | — |
| 227 | C2×C4 | — | 61 | 3 | no | — |
| 228 | C2×C4 | — | 61 | 3 | no | — |
| 229 | C2×C4 | — | 61 | 3 | no | — |
| 230 | C2×C4 | — | 61 | 1 | no | — |
| 231 | C2×C4 | — | 976 | 3 | no | — |
| 232 | C2×C4 | — | 244 | 1 | no | — |
| 233 | C2×C4 | — | 244 | 3 | no | — |
| 234 | C2×C4 | C2×C4⋊#6923 | 1 | 3 | yes | — |
| 235 | C8 | — | 61 | 3 | no | — |
| 236 | C8 | — | 61 | 1 | no | — |
| 237 | C8 | — | 244 | 1 | no | — |
| 238 | C8 | — | 244 | 3 | no | — |
| 239 | C8 | C2×C4⋊#6923 | 1 | 3 | yes | — |
| 240 | C8 | C23×#6923 | 1 | 1 | yes | characteristic |
| 241 | C22 | — | 61 | 1 | no | — |
| 242 | C22 | — | 61 | 3 | no | — |
| 243 | C22 | — | 244 | 3 | no | — |
| 244 | C22 | C2×#14519845 | 1 | 3 | yes | — |
| 245 | C4 | — | 61 | 1 | no | — |
| 246 | C4 | — | 61 | 3 | no | — |
| 247 | C4 | — | 488 | 3 | no | — |
| 248 | C4 | — | 488 | 1 | no | — |
| 249 | C4 | C2×#14519845 | 1 | 3 | yes | — |
| 250 | C4 | C22×C4⋊#6923 | 1 | 1 | yes | characteristic |
| 251 | C2 | — | 2 | 3 | no | — |
| 252 | C2 | — | 122 | 1 | no | — |
| 253 | C2 | — | 122 | 3 | no | — |
| 254 | C2 | C22×#14519845 | 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