← #14574161
Subgroups — #14574161
Order 2432.
340 conjugacy classes of subgroups.
The subgroup lattice has 226 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11927172 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11926954 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11926950 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #11926943 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11926940 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11926587 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11926584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11926580 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | C2×#10597265 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11926500 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C19×#544 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C19×C4⋊Q8 | — | 2 | 1 | no | — |
| 13 | C19×C4⋊Q8 | C22 | 1 | 2 | yes | — |
| 14 | C19×#125 | — | 2 | 1 | no | — |
| 15 | C19×#125 | C22 | 1 | 2 | yes | — |
| 16 | C19×C22⋊Q8 | — | 2 | 2 | no | — |
| 17 | C19×#117 | C22 | 1 | 1 | yes | characteristic |
| 18 | C19×#117 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4⋊C4×C19 | C22 | 1 | 1 | yes | characteristic |
| 20 | #10597372 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4⋊Dic19 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#64520 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×C19⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 24 | #10597336 | — | 2 | 1 | no | — |
| 25 | #10597334 | — | 2 | 1 | no | — |
| 26 | #10597324 | — | 2 | 2 | no | — |
| 27 | #10597316 | C22 | 1 | 2 | yes | — |
| 28 | #10597315 | C22 | 1 | 2 | yes | — |
| 29 | #10597265 | C22 | 1 | 2 | yes | — |
| 30 | #10597265 | C22 | 1 | 2 | yes | — |
| 31 | #10597265 | C22 | 1 | 1 | yes | characteristic |
| 32 | #10597265 | C22 | 1 | 1 | yes | characteristic |
| 33 | #10597265 | C22 | 1 | 2 | yes | — |
| 34 | #10597265 | C22 | 1 | 2 | yes | — |
| 35 | #10597264 | C22 | 1 | 1 | yes | characteristic |
| 36 | #10597264 | C22 | 1 | 1 | yes | characteristic |
| 37 | #10597264 | C22 | 1 | 2 | yes | — |
| 38 | #10597264 | C22 | 1 | 2 | yes | — |
| 39 | #10597260 | C22 | 1 | 2 | yes | — |
| 40 | C4×C19⋊C8 | C22 | 1 | 2 | yes | — |
| 41 | C2×Q8×C19 | — | 2 | 2 | no | — |
| 42 | C22×C4×C19 | — | 2 | 1 | no | — |
| 43 | C22×C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 44 | C22×Dic19 | — | 2 | 1 | no | — |
| 45 | C2×Dic38 | — | 2 | 2 | no | — |
| 46 | C4⋊C4×C19 | — | 2 | 1 | no | — |
| 47 | C4⋊C4×C19 | — | 2 | 2 | no | — |
| 48 | C4⋊C4×C19 | — | 2 | 2 | no | — |
| 49 | C4⋊C4×C19 | — | 2 | 2 | no | — |
| 50 | C4⋊C4×C19 | D4 | 1 | 1 | yes | characteristic |
| 51 | C4⋊C4×C19 | D4 | 1 | 1 | yes | characteristic |
| 52 | C4⋊C4×C19 | C23 | 1 | 2 | yes | — |
| 53 | C4⋊C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 54 | C4⋊C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22⋊C4×C19 | — | 2 | 1 | no | — |
| 56 | C22⋊C4×C19 | D4 | 1 | 2 | yes | — |
| 57 | C42×C19 | — | 2 | 1 | no | — |
| 58 | C42×C19 | C23 | 1 | 2 | yes | — |
| 59 | C22⋊Dic19 | — | 2 | 1 | no | — |
| 60 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 61 | C4⋊Dic19 | — | 2 | 1 | no | — |
| 62 | C4⋊Dic19 | C23 | 1 | 1 | yes | characteristic |
| 63 | C4⋊Dic19 | C23 | 1 | 1 | yes | characteristic |
| 64 | C4⋊Dic19 | C23 | 1 | 2 | yes | — |
| 65 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 66 | Dic19⋊C4 | — | 2 | 2 | no | — |
| 67 | C4×Dic19 | — | 2 | 1 | no | — |
| 68 | #64520 | Q8 | 1 | 4 | yes | complemented |
| 69 | C2×C19⋊C8 | Q8 | 1 | 4 | yes | complemented |
| 70 | C2×C19⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C19⋊C8 | C23 | 1 | 2 | yes | — |
| 72 | C2×C19⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 73 | C23×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | Q8×C19 | — | 8 | 2 | no | — |
| 75 | C2×C4×C19 | — | 2 | 1 | no | — |
| 76 | C2×C4×C19 | — | 2 | 1 | no | — |
| 77 | C2×C4×C19 | — | 2 | 2 | no | — |
| 78 | C2×C4×C19 | — | 8 | 1 | no | — |
| 79 | C2×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 80 | C2×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 81 | C2×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 82 | C2×C4×C19 | C2×Q8 | 1 | 2 | yes | — |
| 83 | C2×C4×C19 | C2×Q8 | 1 | 2 | yes | — |
| 84 | C2×C4×C19 | C24 | 1 | 1 | yes | characteristic |
| 85 | C2×Dic19 | — | 2 | 1 | no | — |
| 86 | C2×Dic19 | — | 2 | 1 | no | — |
| 87 | C2×Dic19 | — | 2 | 2 | no | — |
| 88 | C2×Dic19 | — | 8 | 1 | no | — |
| 89 | Dic38 | — | 8 | 2 | no | — |
| 90 | C19⋊C8 | C2×Q8 | 1 | 2 | yes | — |
| 91 | C19⋊C8 | C2×Q8 | 1 | 2 | yes | — |
| 92 | C19⋊C8 | C2×Q8 | 1 | 4 | yes | — |
| 93 | #3163 | — | 19 | 1 | no | maximal, Sylow |
| 94 | C22×C19 | — | 2 | 1 | no | — |
| 95 | C22×C19 | — | 2 | 1 | no | — |
| 96 | C22×C19 | C4⋊Q8 | 1 | 2 | yes | — |
| 97 | C22×C19 | C22×D4 | 1 | 1 | yes | characteristic |
| 98 | C4×C19 | — | 2 | 2 | no | — |
| 99 | C4×C19 | — | 2 | 2 | no | — |
| 100 | C4×C19 | — | 4 | 1 | no | — |
| 101 | C4×C19 | — | 4 | 2 | no | — |
| 102 | C4×C19 | — | 4 | 1 | no | — |
| 103 | C4×C19 | C4⋊Q8 | 1 | 2 | yes | — |
| 104 | C4×C19 | C22×Q8 | 1 | 1 | yes | characteristic |
| 105 | C4×C19 | C22×Q8 | 1 | 1 | yes | characteristic |
| 106 | Dic19 | — | 4 | 1 | no | — |
| 107 | Dic19 | — | 4 | 2 | no | — |
| 108 | Dic19 | — | 4 | 1 | no | — |
| 109 | #544 | — | 19 | 1 | no | — |
| 110 | #544 | D19 | 1 | 1 | yes | characteristic |
| 111 | #501 | — | 19 | 2 | no | — |
| 112 | #501 | — | 19 | 2 | no | — |
| 113 | #499 | — | 19 | 2 | no | — |
| 114 | #498 | — | 19 | 2 | no | — |
| 115 | #428 | — | 19 | 1 | no | — |
| 116 | #428 | — | 19 | 1 | no | — |
| 117 | #427 | — | 19 | 1 | no | — |
| 118 | C2×#106 | — | 19 | 1 | no | — |
| 119 | #405 | — | 19 | 1 | no | — |
| 120 | C2×C19 | — | 2 | 2 | no | — |
| 121 | C2×C19 | C2×C4⋊Q8 | 1 | 1 | yes | characteristic |
| 122 | C2×C19 | #577 | 1 | 1 | yes | characteristic |
| 123 | C2×C19 | #577 | 1 | 1 | yes | characteristic |
| 124 | C2×M16 | — | 19 | 1 | no | — |
| 125 | C22×C8 | — | 19 | 1 | no | — |
| 126 | C4⋊Q8 | — | 2 | 1 | no | — |
| 127 | C4⋊Q8 | — | 19 | 2 | no | — |
| 128 | C4⋊Q8 | — | 38 | 1 | no | — |
| 129 | C4⋊Q8 | C2×D19 | 1 | 2 | yes | — |
| 130 | #125 | — | 2 | 1 | no | — |
| 131 | #125 | — | 19 | 2 | no | — |
| 132 | #125 | — | 38 | 1 | no | — |
| 133 | #125 | C2×D19 | 1 | 2 | yes | — |
| 134 | C22⋊Q8 | — | 2 | 2 | no | — |
| 135 | C22⋊Q8 | — | 38 | 2 | no | — |
| 136 | #117 | — | 19 | 1 | no | — |
| 137 | #117 | C2×D19 | 1 | 1 | yes | characteristic |
| 138 | #117 | C2×D19 | 1 | 1 | yes | characteristic |
| 139 | C2×C4⋊C4 | — | 19 | 1 | no | — |
| 140 | C2×C4⋊C4 | C2×D19 | 1 | 1 | yes | characteristic |
| 141 | #107 | — | 19 | 1 | no | — |
| 142 | #107 | — | 19 | 1 | no | — |
| 143 | #107 | — | 19 | 2 | no | — |
| 144 | #107 | — | 19 | 2 | no | — |
| 145 | #106 | — | 19 | 2 | no | — |
| 146 | #106 | — | 19 | 2 | no | — |
| 147 | #106 | — | 19 | 1 | no | — |
| 148 | #106 | — | 19 | 1 | no | — |
| 149 | #106 | — | 19 | 2 | no | — |
| 150 | #106 | — | 19 | 2 | no | — |
| 151 | #97 | — | 19 | 2 | no | — |
| 152 | C4×C8 | — | 19 | 2 | no | — |
| 153 | C19 | #3163 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 154 | C2×Q8 | — | 2 | 2 | no | — |
| 155 | C2×Q8 | — | 38 | 2 | no | — |
| 156 | C22×C4 | — | 2 | 1 | no | — |
| 157 | C22×C4 | — | 38 | 1 | no | — |
| 158 | C22×C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 159 | M16 | — | 19 | 4 | no | — |
| 160 | C2×C8 | — | 19 | 4 | no | — |
| 161 | C2×C8 | — | 19 | 1 | no | — |
| 162 | C2×C8 | — | 19 | 2 | no | — |
| 163 | C2×C8 | — | 19 | 1 | no | — |
| 164 | C4⋊C4 | — | 2 | 1 | no | — |
| 165 | C4⋊C4 | — | 2 | 2 | no | — |
| 166 | C4⋊C4 | — | 2 | 2 | no | — |
| 167 | C4⋊C4 | — | 2 | 2 | no | — |
| 168 | C4⋊C4 | — | 19 | 2 | no | — |
| 169 | C4⋊C4 | — | 19 | 1 | no | — |
| 170 | C4⋊C4 | — | 19 | 1 | no | — |
| 171 | C4⋊C4 | — | 38 | 2 | no | — |
| 172 | C4⋊C4 | — | 38 | 2 | no | — |
| 173 | C4⋊C4 | — | 38 | 1 | no | — |
| 174 | C4⋊C4 | — | 38 | 2 | no | — |
| 175 | C4⋊C4 | C22⋊D19 | 1 | 1 | yes | characteristic |
| 176 | C4⋊C4 | C22⋊D19 | 1 | 1 | yes | characteristic |
| 177 | C4⋊C4 | C22×D19 | 1 | 2 | yes | — |
| 178 | C4⋊C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 179 | C4⋊C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 180 | C22⋊C4 | — | 2 | 1 | no | — |
| 181 | C22⋊C4 | — | 38 | 1 | no | — |
| 182 | C22⋊C4 | C22⋊D19 | 1 | 2 | yes | — |
| 183 | C42 | — | 2 | 1 | no | — |
| 184 | C42 | — | 38 | 1 | no | — |
| 185 | C42 | C22×D19 | 1 | 2 | yes | — |
| 186 | C23 | C2×C22⋊D19 | 1 | 1 | yes | characteristic |
| 187 | Q8 | — | 8 | 2 | no | — |
| 188 | Q8 | — | 152 | 2 | no | — |
| 189 | C2×C4 | — | 2 | 1 | no | — |
| 190 | C2×C4 | — | 2 | 1 | no | — |
| 191 | C2×C4 | — | 2 | 2 | no | — |
| 192 | C2×C4 | — | 8 | 1 | no | — |
| 193 | C2×C4 | — | 38 | 1 | no | — |
| 194 | C2×C4 | — | 38 | 1 | no | — |
| 195 | C2×C4 | — | 38 | 2 | no | — |
| 196 | C2×C4 | — | 152 | 1 | no | — |
| 197 | C2×C4 | Q8×D19 | 1 | 2 | yes | — |
| 198 | C2×C4 | Q8×D19 | 1 | 2 | yes | — |
| 199 | C2×C4 | C2×C22⋊D19 | 1 | 2 | yes | — |
| 200 | C2×C4 | C2×C22⋊D19 | 1 | 2 | yes | — |
| 201 | C2×C4 | C2×C22⋊D19 | 1 | 1 | yes | characteristic |
| 202 | C2×C4 | C23×D19 | 1 | 1 | yes | characteristic |
| 203 | C8 | — | 19 | 2 | no | — |
| 204 | C8 | — | 19 | 2 | no | — |
| 205 | C8 | — | 19 | 4 | no | — |
| 206 | C22 | — | 2 | 1 | no | — |
| 207 | C22 | — | 2 | 1 | no | — |
| 208 | C22 | #10597390 | 1 | 2 | yes | — |
| 209 | C22 | C22×C22⋊D19 | 1 | 1 | yes | characteristic |
| 210 | C4 | — | 2 | 2 | no | — |
| 211 | C4 | — | 2 | 2 | no | — |
| 212 | C4 | — | 4 | 1 | no | — |
| 213 | C4 | — | 4 | 2 | no | — |
| 214 | C4 | — | 4 | 1 | no | — |
| 215 | C4 | — | 76 | 2 | no | — |
| 216 | C4 | — | 76 | 1 | no | — |
| 217 | C4 | — | 76 | 1 | no | — |
| 218 | C4 | #10597390 | 1 | 2 | yes | — |
| 219 | C4 | C2×Q8×D19 | 1 | 1 | yes | characteristic |
| 220 | C4 | C2×Q8×D19 | 1 | 1 | yes | characteristic |
| 221 | C2 | — | 2 | 2 | no | — |
| 222 | C2 | C2×#10597390 | 1 | 1 | yes | characteristic |
| 223 | C2 | #11927352 | 1 | 1 | yes | characteristic |
| 224 | C2 | #11927355 | 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