← C23×#14579208 #35202158
Subgroups — C23×#14579208 #35202158
Order 20224.
59806 conjugacy classes of subgroups.
The subgroup lattice has 192 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×#14579208 | C2 | 1 | 112 | yes | maximal, direct product factor |
| 2 | C23×#11929624 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C23×#11929623 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C24×Dic158 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C23×Q8×D79 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C23×#41×C79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#14579208 | C22 | 1 | 1792 | yes | direct product factor |
| 8 | C22×#11929624 | C22 | 1 | 168 | yes | complemented |
| 9 | C22×#11929623 | C22 | 1 | 336 | yes | complemented |
| 10 | C23×Dic158 | C22 | 1 | 6 | yes | — |
| 11 | C23×Dic158 | C22 | 1 | 3 | yes | — |
| 12 | C23×Dic158 | C22 | 1 | 168 | yes | complemented |
| 13 | C22×Q8×D79 | C22 | 1 | 112 | yes | complemented |
| 14 | C23×D316 | C22 | 1 | 1 | yes | characteristic |
| 15 | C23×C22⋊D79 | C22 | 1 | 6 | yes | — |
| 16 | C24×Dic79 | C22 | 1 | 6 | yes | — |
| 17 | C23×C4×D79 | C22 | 1 | 6 | yes | — |
| 18 | C22×#41×C79 | C22 | 1 | 56 | yes | complemented |
| 19 | C23×Q8×C79 | C22 | 1 | 1 | yes | characteristic |
| 20 | C23×D4×C79 | C22 | 1 | 3 | yes | — |
| 21 | C24×C4×C79 | C22 | 1 | 3 | yes | — |
| 22 | C24×D79 | C23 | 1 | 2 | yes | — |
| 23 | #14579208 | C23 | 1 | 4096 | yes | direct product factor |
| 24 | C2×#11929624 | C23 | 1 | 1344 | yes | complemented |
| 25 | C2×#11929623 | C23 | 1 | 2688 | yes | complemented |
| 26 | C22×Dic158 | C23 | 1 | 168 | yes | — |
| 27 | C22×Dic158 | C23 | 1 | 84 | yes | — |
| 28 | C22×Dic158 | C23 | 1 | 1344 | yes | complemented |
| 29 | C2×Q8×D79 | C23 | 1 | 896 | yes | complemented |
| 30 | C22×D316 | C23 | 1 | 28 | yes | — |
| 31 | C22×C22⋊D79 | C23 | 1 | 168 | yes | — |
| 32 | C23×Dic79 | C23 | 1 | 6 | yes | — |
| 33 | C23×Dic79 | C23 | 1 | 168 | yes | — |
| 34 | C22×C4×D79 | C23 | 1 | 168 | yes | — |
| 35 | C25×C79 | C23 | 1 | 3 | yes | — |
| 36 | C2×#41×C79 | C23 | 1 | 448 | yes | complemented |
| 37 | C22×Q8×C79 | C23 | 1 | 28 | yes | — |
| 38 | C22×D4×C79 | C23 | 1 | 84 | yes | — |
| 39 | C23×C4×C79 | C23 | 1 | 1 | yes | characteristic |
| 40 | C23×C4×C79 | C23 | 1 | 3 | yes | — |
| 41 | C23×C4×C79 | C23 | 1 | 84 | yes | — |
| 42 | C23×D79 | — | 2 | 16 | no | — |
| 43 | C23×D79 | C24 | 1 | 28 | yes | — |
| 44 | #11929624 | C24 | 1 | 1536 | yes | complemented |
| 45 | #11929623 | C24 | 1 | 3072 | yes | complemented |
| 46 | C2×Dic158 | C24 | 1 | 672 | yes | — |
| 47 | C2×Dic158 | C24 | 1 | 336 | yes | — |
| 48 | C2×Dic158 | C24 | 1 | 1536 | yes | complemented |
| 49 | Q8×D79 | C24 | 1 | 1024 | yes | complemented |
| 50 | C2×D316 | C24 | 1 | 112 | yes | — |
| 51 | C2×C22⋊D79 | C24 | 1 | 672 | yes | — |
| 52 | C22×Dic79 | C24 | 1 | 84 | yes | — |
| 53 | C22×Dic79 | C24 | 1 | 672 | yes | — |
| 54 | C2×C4×D79 | C24 | 1 | 672 | yes | — |
| 55 | C24×C79 | — | 2 | 24 | no | — |
| 56 | C24×C79 | C24 | 1 | 42 | yes | — |
| 57 | C24×C79 | C24 | 1 | 1 | yes | characteristic |
| 58 | #41×C79 | C24 | 1 | 512 | yes | complemented |
| 59 | C2×Q8×C79 | C24 | 1 | 112 | yes | — |
| 60 | C2×D4×C79 | C24 | 1 | 336 | yes | — |
| 61 | C22×C4×C79 | C24 | 1 | 14 | yes | — |
| 62 | C22×C4×C79 | C24 | 1 | 42 | yes | — |
| 63 | C22×C4×C79 | C24 | 1 | 336 | yes | — |
| 64 | C23×C79 | — | 2 | 168 | no | — |
| 65 | C23×C79 | 2−1+4 | 1 | 8 | yes | complemented |
| 66 | C23×C79 | C25 | 1 | 84 | yes | — |
| 67 | C23×C79 | C25 | 1 | 7 | yes | — |
| 68 | C22×D79 | — | 2 | 112 | no | — |
| 69 | C22×D79 | C25 | 1 | 56 | yes | — |
| 70 | Q8×C79 | C25 | 1 | 64 | yes | — |
| 71 | D4×C79 | C25 | 1 | 192 | yes | — |
| 72 | C2×C4×C79 | C25 | 1 | 84 | yes | — |
| 73 | C2×C4×C79 | C25 | 1 | 28 | yes | — |
| 74 | C2×C4×C79 | C25 | 1 | 192 | yes | — |
| 75 | C22⋊D79 | C25 | 1 | 384 | yes | — |
| 76 | C2×Dic79 | C25 | 1 | 168 | yes | — |
| 77 | C2×Dic79 | C25 | 1 | 384 | yes | — |
| 78 | D316 | C25 | 1 | 64 | yes | — |
| 79 | C4×D79 | C25 | 1 | 384 | yes | — |
| 80 | Dic158 | C25 | 1 | 384 | yes | — |
| 81 | Dic158 | C25 | 1 | 192 | yes | — |
| 82 | C22×C79 | — | 2 | 168 | no | — |
| 83 | C22×C79 | C2×2−1+4 | 1 | 28 | yes | complemented |
| 84 | C22×C79 | C26 | 1 | 24 | yes | — |
| 85 | C22×C79 | C26 | 1 | 7 | yes | — |
| 86 | C2×D79 | — | 2 | 112 | no | — |
| 87 | C2×D79 | C26 | 1 | 16 | yes | — |
| 88 | C4×C79 | C26 | 1 | 8 | yes | — |
| 89 | C4×C79 | C26 | 1 | 24 | yes | — |
| 90 | Dic79 | C26 | 1 | 48 | yes | — |
| 91 | C23×2−1+4 | — | 79 | 1 | no | maximal, Sylow |
| 92 | C2×C79 | — | 2 | 24 | no | — |
| 93 | C2×C79 | C22×2−1+4 | 1 | 14 | yes | complemented |
| 94 | C2×C79 | C27 | 1 | 1 | yes | characteristic |
| 95 | D79 | — | 2 | 16 | no | — |
| 96 | C22×2−1+4 | — | 79 | 112 | no | — |
| 97 | C23×#41 | — | 79 | 6 | no | — |
| 98 | C23×#41 | — | 79 | 3 | no | — |
| 99 | C23×#41 | D79 | 1 | 1 | yes | characteristic, complemented |
| 100 | C24×Q8 | — | 79 | 2 | no | — |
| 101 | C24×Q8 | — | 79 | 3 | no | — |
| 102 | C79 | C23×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 103 | C2×2−1+4 | — | 79 | 1792 | no | — |
| 104 | C22×#41 | — | 79 | 336 | no | — |
| 105 | C22×#41 | — | 79 | 168 | no | — |
| 106 | C22×#41 | C2×D79 | 1 | 56 | yes | complemented |
| 107 | C23×Q8 | — | 79 | 112 | no | — |
| 108 | C23×Q8 | — | 79 | 6 | no | — |
| 109 | C23×Q8 | — | 79 | 3 | no | — |
| 110 | C23×Q8 | — | 79 | 168 | no | — |
| 111 | C23×Q8 | C2×D79 | 1 | 1 | yes | characteristic |
| 112 | C23×D4 | — | 79 | 6 | no | — |
| 113 | C23×D4 | — | 79 | 1 | no | — |
| 114 | C23×D4 | C2×D79 | 1 | 3 | yes | — |
| 115 | C24×C4 | — | 79 | 6 | no | — |
| 116 | C24×C4 | — | 79 | 6 | no | — |
| 117 | C24×C4 | C2×D79 | 1 | 3 | yes | — |
| 118 | C25 | — | 79 | 2 | no | — |
| 119 | C25 | C22×D79 | 1 | 3 | yes | — |
| 120 | 2−1+4 | — | 79 | 4096 | no | — |
| 121 | C2×#41 | — | 79 | 2688 | no | — |
| 122 | C2×#41 | — | 79 | 1344 | no | — |
| 123 | C2×#41 | C22×D79 | 1 | 448 | yes | complemented |
| 124 | C22×Q8 | — | 79 | 896 | no | — |
| 125 | C22×Q8 | — | 79 | 168 | no | — |
| 126 | C22×Q8 | — | 79 | 84 | no | — |
| 127 | C22×Q8 | — | 79 | 1344 | no | — |
| 128 | C22×Q8 | C22×D79 | 1 | 28 | yes | — |
| 129 | C22×D4 | — | 79 | 168 | no | — |
| 130 | C22×D4 | — | 79 | 28 | no | — |
| 131 | C22×D4 | C22×D79 | 1 | 84 | yes | — |
| 132 | C23×C4 | — | 79 | 168 | no | — |
| 133 | C23×C4 | — | 79 | 6 | no | — |
| 134 | C23×C4 | — | 79 | 168 | no | — |
| 135 | C23×C4 | C22×D79 | 1 | 84 | yes | — |
| 136 | C23×C4 | C22×D79 | 1 | 3 | yes | — |
| 137 | C23×C4 | C22×D79 | 1 | 1 | yes | characteristic |
| 138 | C24 | — | 2 | 24 | no | — |
| 139 | C24 | — | 79 | 28 | no | — |
| 140 | C24 | — | 158 | 16 | no | — |
| 141 | C24 | C23×D79 | 1 | 42 | yes | — |
| 142 | C24 | C23×D79 | 1 | 1 | yes | characteristic |
| 143 | #41 | — | 79 | 3072 | no | — |
| 144 | #41 | — | 79 | 1536 | no | — |
| 145 | #41 | C23×D79 | 1 | 512 | yes | complemented |
| 146 | C2×Q8 | — | 79 | 1024 | no | — |
| 147 | C2×Q8 | — | 79 | 672 | no | — |
| 148 | C2×Q8 | — | 79 | 336 | no | — |
| 149 | C2×Q8 | — | 79 | 1536 | no | — |
| 150 | C2×Q8 | C23×D79 | 1 | 112 | yes | — |
| 151 | C2×D4 | — | 79 | 672 | no | — |
| 152 | C2×D4 | — | 79 | 112 | no | — |
| 153 | C2×D4 | C23×D79 | 1 | 336 | yes | — |
| 154 | C22×C4 | — | 79 | 84 | no | — |
| 155 | C22×C4 | — | 79 | 672 | no | — |
| 156 | C22×C4 | — | 79 | 672 | no | — |
| 157 | C22×C4 | C23×D79 | 1 | 42 | yes | — |
| 158 | C22×C4 | C23×D79 | 1 | 14 | yes | — |
| 159 | C22×C4 | C23×D79 | 1 | 336 | yes | — |
| 160 | C23 | — | 2 | 168 | no | — |
| 161 | C23 | — | 79 | 56 | no | — |
| 162 | C23 | — | 158 | 112 | no | — |
| 163 | C23 | #14579208 | 1 | 8 | yes | direct product factor |
| 164 | C23 | C24×D79 | 1 | 84 | yes | — |
| 165 | C23 | C24×D79 | 1 | 7 | yes | — |
| 166 | Q8 | — | 79 | 384 | no | — |
| 167 | Q8 | — | 79 | 192 | no | — |
| 168 | Q8 | C24×D79 | 1 | 64 | yes | — |
| 169 | D4 | — | 79 | 384 | no | — |
| 170 | D4 | — | 79 | 64 | no | — |
| 171 | D4 | C24×D79 | 1 | 192 | yes | — |
| 172 | C2×C4 | — | 79 | 168 | no | — |
| 173 | C2×C4 | — | 79 | 384 | no | — |
| 174 | C2×C4 | — | 79 | 384 | no | — |
| 175 | C2×C4 | C24×D79 | 1 | 84 | yes | — |
| 176 | C2×C4 | C24×D79 | 1 | 28 | yes | — |
| 177 | C2×C4 | C24×D79 | 1 | 192 | yes | — |
| 178 | C22 | — | 2 | 168 | no | — |
| 179 | C22 | — | 79 | 16 | no | — |
| 180 | C22 | — | 158 | 112 | no | — |
| 181 | C22 | C2×#14579208 | 1 | 28 | yes | direct product factor |
| 182 | C22 | C25×D79 | 1 | 24 | yes | — |
| 183 | C22 | C25×D79 | 1 | 7 | yes | — |
| 184 | C4 | — | 79 | 48 | no | — |
| 185 | C4 | C25×D79 | 1 | 24 | yes | — |
| 186 | C4 | C25×D79 | 1 | 8 | yes | — |
| 187 | C2 | — | 2 | 24 | no | — |
| 188 | C2 | — | 158 | 16 | no | — |
| 189 | C2 | C22×#14579208 | 1 | 14 | yes | direct product factor |
| 190 | C2 | C26×D79 | 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