← #34032722
Subgroups — #34032722
Order 18688.
10796 conjugacy classes of subgroups.
The subgroup lattice has 238 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22626927 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | #22626926 | C2 | 1 | 20 | yes | maximal, complemented |
| 3 | C2×#17989666 | C2 | 1 | 15 | yes | maximal, complemented |
| 4 | D73⋊#568 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | #585×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #17989667 | C22 | 1 | 30 | yes | complemented |
| 7 | #17989666 | C22 | 1 | 20 | yes | complemented |
| 8 | #17989666 | C22 | 1 | 60 | yes | complemented |
| 9 | #17989666 | C22 | 1 | 120 | yes | complemented |
| 10 | #17989665 | C22 | 1 | 90 | yes | complemented |
| 11 | C2×#14556679 | C22 | 1 | 30 | yes | complemented |
| 12 | D73⋊#131 | C22 | 1 | 120 | yes | complemented |
| 13 | C2×#14556678 | C22 | 1 | 90 | yes | complemented |
| 14 | C22×#11924038 | C22 | 1 | 15 | yes | complemented |
| 15 | C2×D73⋊M16 | C22 | 1 | 45 | yes | complemented |
| 16 | #17989424 | C22 | 1 | 6 | yes | — |
| 17 | #17989423 | C4 | 1 | 15 | yes | — |
| 18 | #17989422 | C22 | 1 | 10 | yes | — |
| 19 | 2−1+4×D73 | C4 | 1 | 6 | yes | — |
| 20 | H(5,𝔽2)×D73 | C4 | 1 | 10 | yes | — |
| 21 | C2×#41×D73 | C22 | 1 | 15 | yes | — |
| 22 | #585×C73 | C4 | 1 | 1 | yes | characteristic |
| 23 | #14556679 | C23 | 1 | 40 | yes | complemented |
| 24 | #14556679 | C23 | 1 | 120 | yes | complemented |
| 25 | #14556678 | C23 | 1 | 360 | yes | complemented |
| 26 | #14556678 | C23 | 1 | 120 | yes | complemented |
| 27 | C2×#11924038 | C23 | 1 | 15 | yes | — |
| 28 | C2×#11924038 | C23 | 1 | 45 | yes | — |
| 29 | C2×#11924038 | C23 | 1 | 90 | yes | complemented |
| 30 | D73⋊M16 | C23 | 1 | 60 | yes | — |
| 31 | D73⋊M16 | C23 | 1 | 180 | yes | complemented |
| 32 | C2×#11924037 | C23 | 1 | 90 | yes | complemented |
| 33 | C2×#11924036 | C23 | 1 | 90 | yes | complemented |
| 34 | C22×#10596833 | C23 | 1 | 30 | yes | complemented |
| 35 | #14556639 | C2×C4 | 1 | 30 | yes | — |
| 36 | #14556638 | C2×C4 | 1 | 60 | yes | — |
| 37 | #14556637 | C2×C4 | 1 | 60 | yes | — |
| 38 | #14556636 | C2×C4 | 1 | 90 | yes | — |
| 39 | C2×#11924029 | C23 | 1 | 15 | yes | — |
| 40 | C2×#11924028 | C2×C4 | 1 | 45 | yes | — |
| 41 | C2×#11924027 | C23 | 1 | 45 | yes | — |
| 42 | #41×D73 | C2×C4 | 1 | 60 | yes | — |
| 43 | #41×D73 | C2×C4 | 1 | 60 | yes | — |
| 44 | #41×D73 | C23 | 1 | 60 | yes | — |
| 45 | #41×D73 | C23 | 1 | 20 | yes | — |
| 46 | C2×Q8×D73 | C2×C4 | 1 | 15 | yes | — |
| 47 | C2×D4×D73 | C2×C4 | 1 | 45 | yes | — |
| 48 | C22×C4×D73 | C23 | 1 | 15 | yes | — |
| 49 | 2−1+4×C73 | C2×C4 | 1 | 6 | yes | — |
| 50 | H(5,𝔽2)×C73 | C2×C4 | 1 | 10 | yes | — |
| 51 | C2×#41×C73 | C2×C4 | 1 | 15 | yes | — |
| 52 | #11924038 | C24 | 1 | 6 | yes | — |
| 53 | #11924038 | C24 | 1 | 10 | yes | — |
| 54 | #11924038 | C24 | 1 | 30 | yes | — |
| 55 | #11924038 | C24 | 1 | 90 | yes | — |
| 56 | #11924037 | C24 | 1 | 120 | yes | — |
| 57 | #11924036 | C24 | 1 | 120 | yes | — |
| 58 | C2×#10596833 | C24 | 1 | 90 | yes | — |
| 59 | C2×#10596833 | C24 | 1 | 30 | yes | — |
| 60 | C23×D73 | C22×C4 | 1 | 15 | yes | — |
| 61 | #11924029 | C22×C4 | 1 | 60 | yes | — |
| 62 | #11924029 | C24 | 1 | 20 | yes | — |
| 63 | #11924028 | C22×C4 | 1 | 60 | yes | — |
| 64 | #11924028 | C22×C4 | 1 | 180 | yes | — |
| 65 | #11924027 | C22×C4 | 1 | 180 | yes | — |
| 66 | #11924027 | C24 | 1 | 60 | yes | — |
| 67 | C2×Dic146 | C22×C4 | 1 | 45 | yes | — |
| 68 | Q8×D73 | C22×C4 | 1 | 20 | yes | — |
| 69 | Q8×D73 | C22×C4 | 1 | 60 | yes | — |
| 70 | C2×D292 | C22×C4 | 1 | 45 | yes | — |
| 71 | C2×C22⋊D73 | C22×C4 | 1 | 90 | yes | — |
| 72 | D4×D73 | C22×C4 | 1 | 60 | yes | — |
| 73 | D4×D73 | C22×C4 | 1 | 180 | yes | — |
| 74 | C22×Dic73 | C24 | 1 | 15 | yes | — |
| 75 | C2×C4×D73 | C22×C4 | 1 | 45 | yes | — |
| 76 | C2×C4×D73 | C22×C4 | 1 | 45 | yes | — |
| 77 | C2×C4×D73 | C24 | 1 | 45 | yes | — |
| 78 | C2×C4×D73 | C24 | 1 | 15 | yes | — |
| 79 | #41×C73 | C22×C4 | 1 | 20 | yes | — |
| 80 | #41×C73 | C22×C4 | 1 | 60 | yes | — |
| 81 | C2×Q8×C73 | C22×C4 | 1 | 15 | yes | — |
| 82 | C2×D4×C73 | C22×C4 | 1 | 45 | yes | — |
| 83 | C22×C4×C73 | C22×C4 | 1 | 15 | yes | — |
| 84 | C23×C73 | C23×C4 | 1 | 15 | yes | — |
| 85 | C22×D73 | — | 8 | 15 | no | — |
| 86 | C22×D73 | C23×C4 | 1 | 15 | yes | — |
| 87 | C22×D73 | C23×C4 | 1 | 45 | yes | — |
| 88 | Q8×C73 | C23×C4 | 1 | 20 | yes | — |
| 89 | D4×C73 | C23×C4 | 1 | 60 | yes | — |
| 90 | C2×C4×C73 | C23×C4 | 1 | 15 | yes | — |
| 91 | C2×C4×C73 | C23×C4 | 1 | 45 | yes | — |
| 92 | C22⋊D73 | C23×C4 | 1 | 120 | yes | — |
| 93 | C2×Dic73 | C23×C4 | 1 | 45 | yes | — |
| 94 | C2×Dic73 | C25 | 1 | 15 | yes | — |
| 95 | D292 | C23×C4 | 1 | 60 | yes | — |
| 96 | C4×D73 | C23×C4 | 1 | 15 | yes | — |
| 97 | C4×D73 | C23×C4 | 1 | 15 | yes | — |
| 98 | C4×D73 | C23×C4 | 1 | 90 | yes | — |
| 99 | C4×D73 | C25 | 1 | 1 | yes | characteristic |
| 100 | C4×D73 | C25 | 1 | 15 | yes | — |
| 101 | Dic146 | C23×C4 | 1 | 60 | yes | — |
| 102 | #10596833 | C25 | 1 | 20 | yes | — |
| 103 | #10596833 | C25 | 1 | 12 | yes | — |
| 104 | C22×C73 | — | 4 | 15 | no | — |
| 105 | C22×C73 | C24×C4 | 1 | 15 | yes | — |
| 106 | C2×D73 | — | 4 | 15 | no | — |
| 107 | C2×D73 | — | 4 | 45 | no | — |
| 108 | C2×D73 | C24×C4 | 1 | 1 | yes | characteristic |
| 109 | C2×D73 | C24×C4 | 1 | 15 | yes | — |
| 110 | C4×C73 | C24×C4 | 1 | 15 | yes | — |
| 111 | C4×C73 | C24×C4 | 1 | 1 | yes | characteristic |
| 112 | Dic73 | C24×C4 | 1 | 15 | yes | — |
| 113 | Dic73 | C26 | 1 | 1 | yes | characteristic |
| 114 | #63076 | — | 73 | 1 | no | maximal, Sylow |
| 115 | C2×C73 | — | 2 | 15 | no | — |
| 116 | C2×C73 | C25×C4 | 1 | 1 | yes | characteristic |
| 117 | D73 | — | 2 | 1 | no | — |
| 118 | D73 | — | 2 | 15 | no | — |
| 119 | C2×#585 | — | 73 | 1 | no | — |
| 120 | #3573 | — | 73 | 20 | no | — |
| 121 | #3573 | — | 73 | 12 | no | — |
| 122 | C2×#568 | — | 73 | 15 | no | — |
| 123 | C2×#568 | — | 73 | 15 | no | — |
| 124 | C73 | #63076 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 125 | #585 | — | 73 | 6 | no | — |
| 126 | #585 | — | 73 | 10 | no | — |
| 127 | #585 | — | 73 | 15 | no | — |
| 128 | #585 | #64408 | 1 | 1 | yes | characteristic |
| 129 | C2×2−1+4 | — | 73 | 6 | no | — |
| 130 | C2×H(5,𝔽2) | — | 73 | 10 | no | — |
| 131 | C22×#41 | — | 73 | 15 | no | — |
| 132 | #568 | — | 73 | 90 | no | — |
| 133 | #568 | — | 73 | 20 | no | — |
| 134 | #568 | — | 73 | 60 | no | — |
| 135 | #568 | — | 73 | 120 | no | — |
| 136 | #568 | — | 73 | 30 | no | — |
| 137 | C2×#131 | — | 73 | 90 | no | — |
| 138 | C2×#131 | — | 73 | 120 | no | — |
| 139 | C2×#131 | — | 73 | 30 | no | — |
| 140 | C22×M16 | — | 73 | 45 | no | — |
| 141 | C22×M16 | — | 73 | 15 | no | — |
| 142 | 2−1+4 | — | 73 | 60 | no | — |
| 143 | 2−1+4 | — | 73 | 30 | no | — |
| 144 | 2−1+4 | C2×#64408 | 1 | 6 | yes | — |
| 145 | H(5,𝔽2) | — | 73 | 60 | no | — |
| 146 | H(5,𝔽2) | — | 73 | 90 | no | — |
| 147 | H(5,𝔽2) | C2×#64408 | 1 | 10 | yes | — |
| 148 | C2×#41 | — | 73 | 60 | no | — |
| 149 | C2×#41 | — | 73 | 20 | no | — |
| 150 | C2×#41 | — | 73 | 60 | no | — |
| 151 | C2×#41 | — | 73 | 60 | no | — |
| 152 | C2×#41 | — | 73 | 15 | no | — |
| 153 | C2×#41 | — | 73 | 45 | no | — |
| 154 | C2×#41 | — | 73 | 45 | no | — |
| 155 | C2×#41 | C2×#64408 | 1 | 15 | yes | — |
| 156 | C22×Q8 | — | 73 | 15 | no | — |
| 157 | C22×D4 | — | 73 | 45 | no | — |
| 158 | C23×C4 | — | 73 | 15 | no | — |
| 159 | #131 | — | 73 | 360 | no | — |
| 160 | #131 | — | 73 | 120 | no | — |
| 161 | #131 | — | 73 | 40 | no | — |
| 162 | #131 | — | 73 | 120 | no | — |
| 163 | C2×M16 | — | 73 | 90 | no | — |
| 164 | C2×M16 | — | 73 | 60 | no | — |
| 165 | C2×M16 | — | 73 | 180 | no | — |
| 166 | C2×M16 | — | 73 | 15 | no | — |
| 167 | C2×M16 | — | 73 | 45 | no | — |
| 168 | C2×M16 | — | 73 | 90 | no | — |
| 169 | C22×C8 | — | 73 | 30 | no | — |
| 170 | C22×C8 | — | 73 | 90 | no | — |
| 171 | C24 | — | 73 | 15 | no | — |
| 172 | #41 | — | 73 | 60 | no | — |
| 173 | #41 | — | 73 | 20 | no | — |
| 174 | #41 | — | 73 | 180 | no | — |
| 175 | #41 | — | 73 | 60 | no | — |
| 176 | #41 | — | 73 | 60 | no | — |
| 177 | #41 | — | 73 | 180 | no | — |
| 178 | #41 | C22×#64408 | 1 | 20 | yes | — |
| 179 | #41 | C22×#64408 | 1 | 60 | yes | — |
| 180 | C2×Q8 | — | 73 | 20 | no | — |
| 181 | C2×Q8 | — | 73 | 60 | no | — |
| 182 | C2×Q8 | — | 73 | 45 | no | — |
| 183 | C2×Q8 | C22×#64408 | 1 | 15 | yes | — |
| 184 | C2×D4 | — | 73 | 90 | no | — |
| 185 | C2×D4 | — | 73 | 60 | no | — |
| 186 | C2×D4 | — | 73 | 180 | no | — |
| 187 | C2×D4 | — | 73 | 45 | no | — |
| 188 | C2×D4 | C22×#64408 | 1 | 45 | yes | — |
| 189 | C22×C4 | — | 73 | 15 | no | — |
| 190 | C22×C4 | — | 73 | 45 | no | — |
| 191 | C22×C4 | — | 73 | 45 | no | — |
| 192 | C22×C4 | — | 73 | 45 | no | — |
| 193 | C22×C4 | — | 73 | 15 | no | — |
| 194 | C22×C4 | C22×#64408 | 1 | 15 | yes | — |
| 195 | M16 | — | 73 | 120 | no | — |
| 196 | M16 | — | 73 | 6 | no | — |
| 197 | M16 | — | 73 | 10 | no | — |
| 198 | M16 | — | 73 | 30 | no | — |
| 199 | M16 | — | 73 | 90 | no | — |
| 200 | C2×C8 | — | 73 | 90 | no | — |
| 201 | C2×C8 | — | 73 | 30 | no | — |
| 202 | C2×C8 | — | 73 | 120 | no | — |
| 203 | C23 | — | 584 | 15 | no | — |
| 204 | C23 | — | 73 | 15 | no | — |
| 205 | C23 | — | 73 | 45 | no | — |
| 206 | C23 | C23×#64408 | 1 | 15 | yes | — |
| 207 | Q8 | — | 73 | 60 | no | — |
| 208 | Q8 | C23×#64408 | 1 | 20 | yes | — |
| 209 | D4 | — | 73 | 120 | no | — |
| 210 | D4 | — | 73 | 60 | no | — |
| 211 | D4 | C23×#64408 | 1 | 60 | yes | — |
| 212 | C2×C4 | — | 73 | 15 | no | — |
| 213 | C2×C4 | — | 73 | 45 | no | — |
| 214 | C2×C4 | — | 73 | 15 | no | — |
| 215 | C2×C4 | — | 73 | 1 | no | — |
| 216 | C2×C4 | — | 73 | 15 | no | — |
| 217 | C2×C4 | — | 73 | 15 | no | — |
| 218 | C2×C4 | — | 73 | 90 | no | — |
| 219 | C2×C4 | C23×#64408 | 1 | 15 | yes | — |
| 220 | C2×C4 | C23×#64408 | 1 | 45 | yes | — |
| 221 | C8 | — | 73 | 20 | no | — |
| 222 | C8 | — | 73 | 12 | no | — |
| 223 | C22 | — | 4 | 15 | no | — |
| 224 | C22 | — | 292 | 15 | no | — |
| 225 | C22 | — | 292 | 45 | no | — |
| 226 | C22 | — | 73 | 1 | no | — |
| 227 | C22 | — | 73 | 15 | no | — |
| 228 | C22 | C24×#64408 | 1 | 15 | yes | — |
| 229 | C4 | — | 73 | 1 | no | — |
| 230 | C4 | — | 73 | 15 | no | — |
| 231 | C4 | C24×#64408 | 1 | 1 | yes | characteristic |
| 232 | C4 | C24×#64408 | 1 | 15 | yes | — |
| 233 | C2 | — | 2 | 15 | no | — |
| 234 | C2 | — | 146 | 1 | no | — |
| 235 | C2 | — | 146 | 15 | no | — |
| 236 | C2 | C25×#64408 | 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