← #34034517
Subgroups — #34034517
Order 18688.
734 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 | #22627175 | C2 | 1 | 2 | yes | maximal |
| 2 | #22627056 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #22627055 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#17989676 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #131×#64408 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | Q8×#10596842 | — | 2 | 2 | no | — |
| 7 | D4×#10596842 | — | 2 | 6 | no | — |
| 8 | #17989700 | C22 | 1 | 6 | yes | — |
| 9 | C2×C4⋊#10596842 | C22 | 1 | 6 | yes | — |
| 10 | #17989677 | C22 | 1 | 6 | yes | — |
| 11 | #17989676 | C22 | 1 | 3 | yes | — |
| 12 | #17989676 | C22 | 1 | 6 | yes | — |
| 13 | #17989676 | C22 | 1 | 1 | yes | characteristic |
| 14 | D73⋊#131 | C4 | 1 | 1 | yes | characteristic |
| 15 | #41×#64408 | C22 | 1 | 1 | yes | characteristic |
| 16 | #17989553 | C4 | 1 | 3 | yes | — |
| 17 | #17989550 | C4 | 1 | 3 | yes | — |
| 18 | M16×#64408 | C22 | 1 | 3 | yes | — |
| 19 | C2×C8×#64408 | C22 | 1 | 3 | yes | — |
| 20 | #131×D73 | C4 | 1 | 1 | yes | characteristic |
| 21 | C22×#10596842 | — | 2 | 6 | no | — |
| 22 | C4⋊#10596842 | — | 2 | 6 | no | — |
| 23 | C4⋊#10596842 | C23 | 1 | 6 | yes | — |
| 24 | C4⋊#10596842 | C23 | 1 | 2 | yes | — |
| 25 | C22⋊#10596842 | — | 2 | 6 | no | — |
| 26 | C4×#10596842 | — | 2 | 6 | no | — |
| 27 | #14556679 | — | 2 | 1 | no | — |
| 28 | #14556678 | — | 2 | 3 | no | — |
| 29 | D73⋊M16 | C2×C4 | 1 | 3 | yes | — |
| 30 | C2×#11924036 | C2×C4 | 1 | 3 | yes | — |
| 31 | Q8×#64408 | D4 | 1 | 1 | yes | characteristic |
| 32 | Q8×#64408 | Q8 | 1 | 1 | yes | characteristic |
| 33 | D4×#64408 | D4 | 1 | 3 | yes | — |
| 34 | D4×#64408 | Q8 | 1 | 3 | yes | — |
| 35 | #14556670 | C2×C4 | 1 | 3 | yes | — |
| 36 | C2×C4×#64408 | C23 | 1 | 3 | yes | — |
| 37 | #14556645 | C2×C4 | 1 | 6 | yes | — |
| 38 | C8×#64408 | C2×C4 | 1 | 3 | yes | — |
| 39 | C8×#64408 | C2×C4 | 1 | 3 | yes | — |
| 40 | C8×#64408 | C23 | 1 | 1 | yes | characteristic |
| 41 | C8×#64408 | C23 | 1 | 3 | yes | — |
| 42 | #41×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | #14556599 | C8 | 1 | 3 | yes | complemented |
| 44 | #14556598 | C8 | 1 | 1 | yes | characteristic, complemented |
| 45 | #14556597 | C8 | 1 | 3 | yes | complemented |
| 46 | M16×D73 | C2×C4 | 1 | 3 | yes | — |
| 47 | C2×C8×D73 | C2×C4 | 1 | 3 | yes | — |
| 48 | #131×C73 | C8 | 1 | 1 | yes | characteristic, complemented |
| 49 | C2×#10596842 | — | 2 | 2 | no | — |
| 50 | C2×#10596842 | — | 2 | 6 | no | — |
| 51 | C2×#10596842 | — | 8 | 6 | no | — |
| 52 | C22×#64408 | C2×D4 | 1 | 3 | yes | — |
| 53 | C22×#64408 | C2×Q8 | 1 | 3 | yes | — |
| 54 | #11924038 | — | 2 | 3 | no | — |
| 55 | #11924037 | — | 2 | 3 | no | — |
| 56 | #11924036 | — | 2 | 3 | no | — |
| 57 | #11924036 | C22×C4 | 1 | 1 | yes | characteristic |
| 58 | #11924036 | C22×C4 | 1 | 3 | yes | — |
| 59 | C2×#10596833 | — | 2 | 3 | no | — |
| 60 | C4⋊#64408 | C4⋊C4 | 1 | 3 | yes | — |
| 61 | C4⋊#64408 | C4⋊C4 | 1 | 3 | yes | — |
| 62 | C22⋊#64408 | C4⋊C4 | 1 | 6 | yes | — |
| 63 | C4×#64408 | C22×C4 | 1 | 3 | yes | — |
| 64 | C4×#64408 | C2×D4 | 1 | 3 | yes | — |
| 65 | C4×#64408 | C2×Q8 | 1 | 3 | yes | — |
| 66 | C4×#64408 | C24 | 1 | 1 | yes | characteristic |
| 67 | #11924029 | M16 | 1 | 1 | yes | characteristic |
| 68 | #11924028 | C2×C8 | 1 | 3 | yes | — |
| 69 | #11924027 | M16 | 1 | 3 | yes | — |
| 70 | Q8×D73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 71 | D4×D73 | C4⋊C4 | 1 | 3 | yes | — |
| 72 | C2×C4×D73 | C22×C4 | 1 | 3 | yes | — |
| 73 | #11924012 | C2×C8 | 1 | 3 | yes | complemented |
| 74 | #11924011 | C2×C8 | 1 | 6 | yes | complemented |
| 75 | C2×#10596831 | C2×C8 | 1 | 3 | yes | complemented |
| 76 | C8×D73 | C2×C8 | 1 | 3 | yes | complemented |
| 77 | C8×D73 | C2×C8 | 1 | 3 | yes | complemented |
| 78 | C8×D73 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 80 | #41×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 81 | M16×C73 | C2×C8 | 1 | 3 | yes | complemented |
| 82 | C2×C8×C73 | C2×C8 | 1 | 3 | yes | complemented |
| 83 | C22×D73 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 84 | C2×#64408 | — | 2 | 6 | no | — |
| 85 | C2×#64408 | — | 4 | 3 | no | — |
| 86 | C2×#64408 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 87 | C2×#64408 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 88 | C2×#64408 | C22×D4 | 1 | 1 | yes | characteristic |
| 89 | C2×#64408 | C22×Q8 | 1 | 1 | yes | characteristic |
| 90 | #10596842 | — | 4 | 2 | no | — |
| 91 | #10596842 | — | 4 | 6 | no | — |
| 92 | Q8×C73 | C4⋊C8 | 1 | 1 | yes | characteristic |
| 93 | D4×C73 | C4⋊C8 | 1 | 3 | yes | — |
| 94 | C2×C4×C73 | C22×C8 | 1 | 3 | yes | — |
| 95 | C22⋊D73 | C4⋊C8 | 1 | 6 | yes | — |
| 96 | C2×Dic73 | C2×M16 | 1 | 3 | yes | — |
| 97 | D292 | C4⋊C8 | 1 | 3 | yes | — |
| 98 | C4×D73 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 99 | C4×D73 | C22×C8 | 1 | 3 | yes | — |
| 100 | C4×D73 | C2×M16 | 1 | 3 | yes | — |
| 101 | C4×D73 | C23×C4 | 1 | 1 | yes | characteristic |
| 102 | Dic146 | C4⋊C8 | 1 | 3 | yes | — |
| 103 | #10596833 | — | 2 | 1 | no | — |
| 104 | #10596833 | — | 2 | 3 | no | — |
| 105 | C8×C73 | C22×C8 | 1 | 1 | yes | characteristic |
| 106 | C8×C73 | C22×C8 | 1 | 3 | yes | — |
| 107 | #10596831 | C22×C8 | 1 | 1 | yes | characteristic |
| 108 | #10596831 | C22×C8 | 1 | 3 | yes | — |
| 109 | C22×C73 | C2×C4⋊C8 | 1 | 3 | yes | — |
| 110 | C2×D73 | — | 2 | 3 | no | — |
| 111 | C2×D73 | — | 2 | 3 | no | — |
| 112 | C2×D73 | C2×C4⋊C8 | 1 | 3 | yes | — |
| 113 | C2×D73 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 114 | #64408 | — | 2 | 3 | no | — |
| 115 | #64408 | — | 2 | 1 | no | — |
| 116 | #64408 | — | 2 | 3 | no | — |
| 117 | #64408 | #577 | 1 | 2 | yes | — |
| 118 | C4×C73 | C2×C4⋊C8 | 1 | 3 | yes | — |
| 119 | C4×C73 | C23×C8 | 1 | 1 | yes | characteristic |
| 120 | Dic73 | C2×C4⋊C8 | 1 | 3 | yes | — |
| 121 | Dic73 | C22×M16 | 1 | 1 | yes | characteristic |
| 122 | #17788 | — | 73 | 1 | no | maximal, Sylow |
| 123 | C2×C73 | — | 2 | 3 | no | — |
| 124 | C2×C73 | C22×C4⋊C8 | 1 | 1 | yes | characteristic |
| 125 | D73 | — | 2 | 3 | no | — |
| 126 | D73 | #2912 | 1 | 1 | yes | characteristic |
| 127 | D73 | #2916 | 1 | 1 | yes | characteristic |
| 128 | #2988 | — | 73 | 2 | no | — |
| 129 | C4×#131 | — | 73 | 1 | no | — |
| 130 | #1565 | — | 73 | 6 | no | — |
| 131 | #1564 | — | 73 | 3 | no | — |
| 132 | C2×#334 | — | 73 | 3 | no | — |
| 133 | C73 | #17788 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 134 | C2×#131 | — | 73 | 1 | no | — |
| 135 | C2×#131 | — | 73 | 1 | no | — |
| 136 | C4×#41 | — | 73 | 1 | no | — |
| 137 | C8×Q8 | — | 146 | 2 | no | — |
| 138 | C8×D4 | — | 146 | 6 | no | — |
| 139 | #431 | — | 73 | 6 | no | — |
| 140 | C2×C4⋊C8 | — | 73 | 6 | no | — |
| 141 | #405 | — | 73 | 3 | no | — |
| 142 | #405 | — | 73 | 3 | no | — |
| 143 | C4×M16 | — | 73 | 3 | no | — |
| 144 | C2×C4×C8 | — | 73 | 3 | no | — |
| 145 | #335 | — | 73 | 6 | no | — |
| 146 | #334 | — | 73 | 3 | no | — |
| 147 | #334 | — | 73 | 6 | no | — |
| 148 | #334 | — | 73 | 1 | no | — |
| 149 | C2×#41 | — | 73 | 1 | no | — |
| 150 | #131 | — | 73 | 1 | no | — |
| 151 | #131 | — | 73 | 3 | no | — |
| 152 | #131 | — | 73 | 3 | no | — |
| 153 | #131 | — | 146 | 3 | no | — |
| 154 | #131 | — | 146 | 1 | no | — |
| 155 | #131 | #10596842 | 1 | 1 | yes | characteristic, complemented |
| 156 | C2×M16 | — | 73 | 3 | no | — |
| 157 | C2×M16 | — | 73 | 3 | no | — |
| 158 | C22×C8 | — | 73 | 3 | no | — |
| 159 | C22×C8 | — | 73 | 3 | no | — |
| 160 | C22×C8 | — | 146 | 6 | no | — |
| 161 | C4×Q8 | — | 73 | 1 | no | — |
| 162 | C4×Q8 | — | 73 | 1 | no | — |
| 163 | C4×D4 | — | 73 | 3 | no | — |
| 164 | C4×D4 | — | 73 | 3 | no | — |
| 165 | #117 | — | 73 | 3 | no | — |
| 166 | C2×C42 | — | 73 | 3 | no | — |
| 167 | C4⋊C8 | — | 73 | 6 | no | — |
| 168 | C4⋊C8 | — | 73 | 2 | no | — |
| 169 | C4⋊C8 | — | 146 | 6 | no | — |
| 170 | C22⋊C8 | — | 146 | 6 | no | — |
| 171 | #97 | — | 73 | 6 | no | — |
| 172 | C4×C8 | — | 73 | 1 | no | — |
| 173 | C4×C8 | — | 73 | 3 | no | — |
| 174 | C4×C8 | — | 73 | 3 | no | — |
| 175 | C4×C8 | — | 73 | 3 | no | — |
| 176 | C4×C8 | — | 146 | 6 | no | — |
| 177 | #41 | — | 73 | 1 | no | — |
| 178 | #41 | — | 73 | 3 | no | — |
| 179 | #41 | — | 73 | 3 | no | — |
| 180 | #41 | C2×#10596842 | 1 | 1 | yes | characteristic |
| 181 | C2×Q8 | — | 73 | 1 | no | — |
| 182 | C2×D4 | — | 73 | 3 | no | — |
| 183 | C22×C4 | — | 73 | 3 | no | — |
| 184 | C22×C4 | — | 73 | 3 | no | — |
| 185 | C22×C4 | — | 73 | 3 | no | — |
| 186 | M16 | — | 73 | 3 | no | — |
| 187 | M16 | — | 73 | 6 | no | — |
| 188 | M16 | — | 146 | 3 | no | — |
| 189 | M16 | — | 146 | 3 | no | — |
| 190 | M16 | C2×#10596842 | 1 | 3 | yes | complemented |
| 191 | C2×C8 | — | 584 | 6 | no | — |
| 192 | C2×C8 | — | 73 | 3 | no | — |
| 193 | C2×C8 | — | 73 | 3 | no | — |
| 194 | C2×C8 | — | 73 | 3 | no | — |
| 195 | C2×C8 | — | 73 | 1 | no | — |
| 196 | C2×C8 | — | 73 | 3 | no | — |
| 197 | C2×C8 | — | 73 | 1 | no | — |
| 198 | C2×C8 | — | 73 | 3 | no | — |
| 199 | C2×C8 | — | 146 | 2 | no | — |
| 200 | C2×C8 | — | 146 | 6 | no | — |
| 201 | C2×C8 | — | 146 | 3 | no | — |
| 202 | C2×C8 | — | 146 | 3 | no | — |
| 203 | C2×C8 | C2×#10596842 | 1 | 3 | yes | complemented |
| 204 | C4⋊C4 | — | 73 | 3 | no | — |
| 205 | C4⋊C4 | — | 73 | 3 | no | — |
| 206 | C22⋊C4 | — | 73 | 6 | no | — |
| 207 | C42 | — | 73 | 3 | no | — |
| 208 | C42 | — | 73 | 3 | no | — |
| 209 | C42 | — | 73 | 3 | no | — |
| 210 | C42 | — | 73 | 1 | no | — |
| 211 | C23 | — | 73 | 3 | no | — |
| 212 | Q8 | — | 73 | 3 | no | — |
| 213 | Q8 | C4⋊#10596842 | 1 | 1 | yes | characteristic |
| 214 | D4 | — | 73 | 6 | no | — |
| 215 | D4 | — | 73 | 3 | no | — |
| 216 | D4 | C4⋊#10596842 | 1 | 3 | yes | — |
| 217 | C2×C4 | — | 292 | 3 | no | — |
| 218 | C2×C4 | — | 73 | 1 | no | — |
| 219 | C2×C4 | — | 73 | 3 | no | — |
| 220 | C2×C4 | — | 73 | 3 | no | — |
| 221 | C2×C4 | — | 73 | 3 | no | — |
| 222 | C2×C4 | — | 73 | 1 | no | — |
| 223 | C2×C4 | — | 73 | 3 | no | — |
| 224 | C2×C4 | — | 73 | 1 | no | — |
| 225 | C2×C4 | — | 73 | 3 | no | — |
| 226 | C2×C4 | — | 73 | 3 | no | — |
| 227 | C2×C4 | — | 146 | 6 | no | — |
| 228 | C2×C4 | C22×#10596842 | 1 | 3 | yes | — |
| 229 | C8 | — | 292 | 6 | no | — |
| 230 | C8 | — | 292 | 2 | no | — |
| 231 | C8 | — | 73 | 1 | no | — |
| 232 | C8 | — | 73 | 3 | no | — |
| 233 | C8 | — | 146 | 1 | no | — |
| 234 | C8 | — | 146 | 3 | no | — |
| 235 | C8 | C22×#10596842 | 1 | 1 | yes | characteristic |
| 236 | C8 | C22×#10596842 | 1 | 3 | yes | — |
| 237 | C22 | — | 73 | 1 | no | — |
| 238 | C22 | — | 73 | 3 | no | — |
| 239 | C22 | — | 146 | 3 | no | — |
| 240 | C22 | — | 146 | 3 | no | — |
| 241 | C22 | C2×C4⋊#10596842 | 1 | 3 | yes | — |
| 242 | C4 | — | 73 | 2 | no | — |
| 243 | C4 | — | 73 | 1 | no | — |
| 244 | C4 | — | 73 | 3 | no | — |
| 245 | C4 | — | 146 | 1 | no | — |
| 246 | C4 | — | 146 | 3 | no | — |
| 247 | C4 | — | 146 | 3 | no | — |
| 248 | C4 | C2×C4⋊#10596842 | 1 | 3 | yes | — |
| 249 | C4 | C23×#10596842 | 1 | 1 | yes | characteristic |
| 250 | C2 | — | 2 | 3 | no | — |
| 251 | C2 | — | 73 | 1 | no | — |
| 252 | C2 | — | 73 | 1 | no | — |
| 253 | C2 | — | 146 | 3 | no | — |
| 254 | C2 | C22×C4⋊#10596842 | 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