← C23×#6554 #14267685
Subgroups — C23×#6554 #14267685
Order 1792.
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 | C23×C7×#41 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#6554 | C2 | 1 | 112 | yes | maximal, direct product factor |
| 3 | C23×Q8×D7 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C23×#1159 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C23×#1157 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C24×Dic14 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C22×C7×#41 | C22 | 1 | 56 | yes | complemented |
| 8 | C23×C7×Q8 | C22 | 1 | 1 | yes | characteristic |
| 9 | C23×C7×D4 | C22 | 1 | 3 | yes | — |
| 10 | C24×C4×C7 | C22 | 1 | 3 | yes | — |
| 11 | C23×C22⋊D7 | C22 | 1 | 6 | yes | — |
| 12 | C24×Dic7 | C22 | 1 | 6 | yes | — |
| 13 | C2×#6554 | C22 | 1 | 1792 | yes | direct product factor |
| 14 | C22×Q8×D7 | C22 | 1 | 112 | yes | complemented |
| 15 | C22×#1159 | C22 | 1 | 336 | yes | complemented |
| 16 | C22×#1157 | C22 | 1 | 168 | yes | complemented |
| 17 | C23×D28 | C22 | 1 | 1 | yes | characteristic |
| 18 | C23×C4×D7 | C22 | 1 | 6 | yes | — |
| 19 | C23×Dic14 | C22 | 1 | 3 | yes | — |
| 20 | C23×Dic14 | C22 | 1 | 6 | yes | — |
| 21 | C23×Dic14 | C22 | 1 | 168 | yes | complemented |
| 22 | C23×2−1+4 | — | 7 | 1 | no | maximal, Sylow |
| 23 | C25×C7 | C23 | 1 | 3 | yes | — |
| 24 | C24×D7 | C23 | 1 | 2 | yes | — |
| 25 | C2×C7×#41 | C23 | 1 | 448 | yes | complemented |
| 26 | C22×C7×Q8 | C23 | 1 | 28 | yes | — |
| 27 | C22×C7×D4 | C23 | 1 | 84 | yes | — |
| 28 | C23×C4×C7 | C23 | 1 | 3 | yes | — |
| 29 | C23×C4×C7 | C23 | 1 | 84 | yes | — |
| 30 | C23×C4×C7 | C23 | 1 | 1 | yes | characteristic |
| 31 | C22×C22⋊D7 | C23 | 1 | 168 | yes | — |
| 32 | C23×Dic7 | C23 | 1 | 6 | yes | — |
| 33 | C23×Dic7 | C23 | 1 | 168 | yes | — |
| 34 | #6554 | C23 | 1 | 4096 | yes | direct product factor |
| 35 | C2×Q8×D7 | C23 | 1 | 896 | yes | complemented |
| 36 | C2×#1159 | C23 | 1 | 2688 | yes | complemented |
| 37 | C2×#1157 | C23 | 1 | 1344 | yes | complemented |
| 38 | C22×D28 | C23 | 1 | 28 | yes | — |
| 39 | C22×C4×D7 | C23 | 1 | 168 | yes | — |
| 40 | C22×Dic14 | C23 | 1 | 84 | yes | — |
| 41 | C22×Dic14 | C23 | 1 | 168 | yes | — |
| 42 | C22×Dic14 | C23 | 1 | 1344 | yes | complemented |
| 43 | C22×2−1+4 | — | 7 | 112 | no | — |
| 44 | C23×#41 | — | 7 | 6 | no | — |
| 45 | C23×#41 | — | 7 | 3 | no | — |
| 46 | C23×#41 | D7 | 1 | 1 | yes | characteristic, complemented |
| 47 | C24×Q8 | — | 7 | 2 | no | — |
| 48 | C24×Q8 | — | 7 | 3 | no | — |
| 49 | C24×C7 | — | 2 | 24 | no | — |
| 50 | C24×C7 | C24 | 1 | 42 | yes | — |
| 51 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 52 | C23×D7 | — | 2 | 16 | no | — |
| 53 | C23×D7 | C24 | 1 | 28 | yes | — |
| 54 | C7×#41 | C24 | 1 | 512 | yes | complemented |
| 55 | C2×C7×Q8 | C24 | 1 | 112 | yes | — |
| 56 | C2×C7×D4 | C24 | 1 | 336 | yes | — |
| 57 | C22×C4×C7 | C24 | 1 | 14 | yes | — |
| 58 | C22×C4×C7 | C24 | 1 | 42 | yes | — |
| 59 | C22×C4×C7 | C24 | 1 | 336 | yes | — |
| 60 | C2×C22⋊D7 | C24 | 1 | 672 | yes | — |
| 61 | C22×Dic7 | C24 | 1 | 84 | yes | — |
| 62 | C22×Dic7 | C24 | 1 | 672 | yes | — |
| 63 | Q8×D7 | C24 | 1 | 1024 | yes | complemented |
| 64 | #1159 | C24 | 1 | 3072 | yes | complemented |
| 65 | #1157 | C24 | 1 | 1536 | yes | complemented |
| 66 | C2×D28 | C24 | 1 | 112 | yes | — |
| 67 | C2×C4×D7 | C24 | 1 | 672 | yes | — |
| 68 | C2×Dic14 | C24 | 1 | 336 | yes | — |
| 69 | C2×Dic14 | C24 | 1 | 672 | yes | — |
| 70 | C2×Dic14 | C24 | 1 | 1536 | yes | complemented |
| 71 | C2×2−1+4 | — | 7 | 1792 | no | — |
| 72 | C22×#41 | — | 7 | 336 | no | — |
| 73 | C22×#41 | — | 7 | 168 | no | — |
| 74 | C22×#41 | C2×D7 | 1 | 56 | yes | complemented |
| 75 | C23×Q8 | — | 7 | 112 | no | — |
| 76 | C23×Q8 | — | 7 | 6 | no | — |
| 77 | C23×Q8 | — | 7 | 3 | no | — |
| 78 | C23×Q8 | — | 7 | 168 | no | — |
| 79 | C23×Q8 | C2×D7 | 1 | 1 | yes | characteristic |
| 80 | C23×D4 | — | 7 | 6 | no | — |
| 81 | C23×D4 | — | 7 | 1 | no | — |
| 82 | C23×D4 | C2×D7 | 1 | 3 | yes | — |
| 83 | C24×C4 | — | 7 | 6 | no | — |
| 84 | C24×C4 | — | 7 | 6 | no | — |
| 85 | C24×C4 | C2×D7 | 1 | 3 | yes | — |
| 86 | C23×C7 | — | 2 | 168 | no | — |
| 87 | C23×C7 | 2−1+4 | 1 | 8 | yes | complemented |
| 88 | C23×C7 | C25 | 1 | 84 | yes | — |
| 89 | C23×C7 | C25 | 1 | 7 | yes | — |
| 90 | C22×D7 | — | 2 | 112 | no | — |
| 91 | C22×D7 | C25 | 1 | 56 | yes | — |
| 92 | C7×Q8 | C25 | 1 | 64 | yes | — |
| 93 | C7×D4 | C25 | 1 | 192 | yes | — |
| 94 | C2×C4×C7 | C25 | 1 | 28 | yes | — |
| 95 | C2×C4×C7 | C25 | 1 | 84 | yes | — |
| 96 | C2×C4×C7 | C25 | 1 | 192 | yes | — |
| 97 | C22⋊D7 | C25 | 1 | 384 | yes | — |
| 98 | C2×Dic7 | C25 | 1 | 168 | yes | — |
| 99 | C2×Dic7 | C25 | 1 | 384 | yes | — |
| 100 | D28 | C25 | 1 | 64 | yes | — |
| 101 | C4×D7 | C25 | 1 | 384 | yes | — |
| 102 | Dic14 | C25 | 1 | 192 | yes | — |
| 103 | Dic14 | C25 | 1 | 384 | yes | — |
| 104 | C25 | — | 7 | 2 | no | — |
| 105 | C25 | C22×D7 | 1 | 3 | yes | — |
| 106 | 2−1+4 | — | 7 | 4096 | no | — |
| 107 | C2×#41 | — | 7 | 2688 | no | — |
| 108 | C2×#41 | — | 7 | 1344 | no | — |
| 109 | C2×#41 | C22×D7 | 1 | 448 | yes | complemented |
| 110 | C22×Q8 | — | 7 | 896 | no | — |
| 111 | C22×Q8 | — | 7 | 168 | no | — |
| 112 | C22×Q8 | — | 7 | 84 | no | — |
| 113 | C22×Q8 | — | 7 | 1344 | no | — |
| 114 | C22×Q8 | C22×D7 | 1 | 28 | yes | — |
| 115 | C22×D4 | — | 7 | 168 | no | — |
| 116 | C22×D4 | — | 7 | 28 | no | — |
| 117 | C22×D4 | C22×D7 | 1 | 84 | yes | — |
| 118 | C23×C4 | — | 7 | 168 | no | — |
| 119 | C23×C4 | — | 7 | 6 | no | — |
| 120 | C23×C4 | — | 7 | 168 | no | — |
| 121 | C23×C4 | C22×D7 | 1 | 84 | yes | — |
| 122 | C23×C4 | C22×D7 | 1 | 3 | yes | — |
| 123 | C23×C4 | C22×D7 | 1 | 1 | yes | characteristic |
| 124 | C22×C7 | — | 2 | 168 | no | — |
| 125 | C22×C7 | C2×2−1+4 | 1 | 28 | yes | complemented |
| 126 | C22×C7 | C26 | 1 | 24 | yes | — |
| 127 | C22×C7 | C26 | 1 | 7 | yes | — |
| 128 | C2×D7 | — | 2 | 112 | no | — |
| 129 | C2×D7 | C26 | 1 | 16 | yes | — |
| 130 | C4×C7 | C26 | 1 | 8 | yes | — |
| 131 | C4×C7 | C26 | 1 | 24 | yes | — |
| 132 | Dic7 | C26 | 1 | 48 | yes | — |
| 133 | C24 | — | 2 | 24 | no | — |
| 134 | C24 | — | 7 | 28 | no | — |
| 135 | C24 | — | 14 | 16 | no | — |
| 136 | C24 | C23×D7 | 1 | 42 | yes | — |
| 137 | C24 | C23×D7 | 1 | 1 | yes | characteristic |
| 138 | #41 | — | 7 | 3072 | no | — |
| 139 | #41 | — | 7 | 1536 | no | — |
| 140 | #41 | C23×D7 | 1 | 512 | yes | complemented |
| 141 | C2×Q8 | — | 7 | 1024 | no | — |
| 142 | C2×Q8 | — | 7 | 672 | no | — |
| 143 | C2×Q8 | — | 7 | 336 | no | — |
| 144 | C2×Q8 | — | 7 | 1536 | no | — |
| 145 | C2×Q8 | C23×D7 | 1 | 112 | yes | — |
| 146 | C2×D4 | — | 7 | 672 | no | — |
| 147 | C2×D4 | — | 7 | 112 | no | — |
| 148 | C2×D4 | C23×D7 | 1 | 336 | yes | — |
| 149 | C22×C4 | — | 7 | 84 | no | — |
| 150 | C22×C4 | — | 7 | 672 | no | — |
| 151 | C22×C4 | — | 7 | 672 | no | — |
| 152 | C22×C4 | C23×D7 | 1 | 42 | yes | — |
| 153 | C22×C4 | C23×D7 | 1 | 14 | yes | — |
| 154 | C22×C4 | C23×D7 | 1 | 336 | yes | — |
| 155 | C2×C7 | — | 2 | 24 | no | — |
| 156 | C2×C7 | C22×2−1+4 | 1 | 14 | yes | complemented |
| 157 | C2×C7 | C27 | 1 | 1 | yes | characteristic |
| 158 | D7 | — | 2 | 16 | no | — |
| 159 | C23 | — | 2 | 168 | no | — |
| 160 | C23 | — | 7 | 56 | no | — |
| 161 | C23 | — | 14 | 112 | no | — |
| 162 | C23 | #6554 | 1 | 8 | yes | direct product factor |
| 163 | C23 | C24×D7 | 1 | 84 | yes | — |
| 164 | C23 | C24×D7 | 1 | 7 | yes | — |
| 165 | Q8 | — | 7 | 384 | no | — |
| 166 | Q8 | — | 7 | 192 | no | — |
| 167 | Q8 | C24×D7 | 1 | 64 | yes | — |
| 168 | D4 | — | 7 | 384 | no | — |
| 169 | D4 | — | 7 | 64 | no | — |
| 170 | D4 | C24×D7 | 1 | 192 | yes | — |
| 171 | C2×C4 | — | 7 | 168 | no | — |
| 172 | C2×C4 | — | 7 | 384 | no | — |
| 173 | C2×C4 | — | 7 | 384 | no | — |
| 174 | C2×C4 | C24×D7 | 1 | 84 | yes | — |
| 175 | C2×C4 | C24×D7 | 1 | 28 | yes | — |
| 176 | C2×C4 | C24×D7 | 1 | 192 | yes | — |
| 177 | C7 | C23×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 178 | C22 | — | 2 | 168 | no | — |
| 179 | C22 | — | 7 | 16 | no | — |
| 180 | C22 | — | 14 | 112 | no | — |
| 181 | C22 | C2×#6554 | 1 | 28 | yes | direct product factor |
| 182 | C22 | C25×D7 | 1 | 24 | yes | — |
| 183 | C22 | C25×D7 | 1 | 7 | yes | — |
| 184 | C4 | — | 7 | 48 | no | — |
| 185 | C4 | C25×D7 | 1 | 24 | yes | — |
| 186 | C4 | C25×D7 | 1 | 8 | yes | — |
| 187 | C2 | — | 2 | 24 | no | — |
| 188 | C2 | — | 14 | 16 | no | — |
| 189 | C2 | C22×#6554 | 1 | 14 | yes | direct product factor |
| 190 | C2 | C26×D7 | 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