← D17⋊#3573 #17981059
Subgroups — D17⋊#3573 #17981059
Order 4352.
10858 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 | #14545780 | C2 | 1 | 12 | yes | maximal, complemented |
| 2 | #14545779 | C2 | 1 | 20 | yes | maximal, complemented |
| 3 | D17⋊#568 | C2 | 1 | 15 | yes | maximal, complemented |
| 4 | C2×D17⋊#131 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | D17×#585 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11763889 | C22 | 1 | 30 | yes | complemented |
| 7 | #11763888 | C22 | 1 | 120 | yes | complemented |
| 8 | #11763887 | C22 | 1 | 90 | yes | complemented |
| 9 | C2×#10587680 | C22 | 1 | 30 | yes | complemented |
| 10 | D17⋊#131 | C22 | 1 | 20 | yes | complemented |
| 11 | D17⋊#131 | C22 | 1 | 60 | yes | complemented |
| 12 | D17⋊#131 | C22 | 1 | 120 | yes | complemented |
| 13 | C2×#10587678 | C22 | 1 | 90 | yes | complemented |
| 14 | C2×D17⋊M16 | C22 | 1 | 45 | yes | complemented |
| 15 | C22×#63242 | C22 | 1 | 15 | yes | complemented |
| 16 | #11763646 | C22 | 1 | 6 | yes | — |
| 17 | #11763645 | C4 | 1 | 15 | yes | — |
| 18 | #11763644 | C22 | 1 | 10 | yes | — |
| 19 | 2−1+4×D17 | C4 | 1 | 6 | yes | — |
| 20 | H(5,𝔽2)×D17 | C4 | 1 | 10 | yes | — |
| 21 | C2×#41×D17 | C22 | 1 | 15 | yes | — |
| 22 | C17×#585 | C4 | 1 | 1 | yes | characteristic |
| 23 | C17×2−1+4 | C2×C4 | 1 | 6 | yes | — |
| 24 | C17×H(5,𝔽2) | C2×C4 | 1 | 10 | yes | — |
| 25 | C2×#41×C17 | C2×C4 | 1 | 15 | yes | — |
| 26 | #10587697 | C2×C4 | 1 | 60 | yes | — |
| 27 | #10587696 | C2×C4 | 1 | 60 | yes | — |
| 28 | #41×D17 | C2×C4 | 1 | 60 | yes | — |
| 29 | #41×D17 | C2×C4 | 1 | 60 | yes | — |
| 30 | #41×D17 | C23 | 1 | 20 | yes | — |
| 31 | #41×D17 | C23 | 1 | 60 | yes | — |
| 32 | #10587694 | C2×C4 | 1 | 30 | yes | — |
| 33 | C2×#63256 | C23 | 1 | 15 | yes | — |
| 34 | C2×Q8×D17 | C2×C4 | 1 | 15 | yes | — |
| 35 | #10587691 | C2×C4 | 1 | 90 | yes | — |
| 36 | C2×#63254 | C23 | 1 | 45 | yes | — |
| 37 | C2×D4×D17 | C2×C4 | 1 | 45 | yes | — |
| 38 | C2×#63252 | C2×C4 | 1 | 45 | yes | — |
| 39 | C22×C4×D17 | C23 | 1 | 15 | yes | — |
| 40 | C2×#63247 | C23 | 1 | 90 | yes | complemented |
| 41 | C22×#3624 | C23 | 1 | 30 | yes | complemented |
| 42 | #10587680 | C23 | 1 | 40 | yes | complemented |
| 43 | #10587680 | C23 | 1 | 120 | yes | complemented |
| 44 | #10587678 | C23 | 1 | 120 | yes | complemented |
| 45 | #10587678 | C23 | 1 | 360 | yes | complemented |
| 46 | D17⋊M16 | C23 | 1 | 60 | yes | — |
| 47 | D17⋊M16 | C23 | 1 | 180 | yes | complemented |
| 48 | C2×#63243 | C23 | 1 | 90 | yes | complemented |
| 49 | C2×#63242 | C23 | 1 | 15 | yes | — |
| 50 | C2×#63242 | C23 | 1 | 45 | yes | — |
| 51 | C2×#63242 | C23 | 1 | 90 | yes | complemented |
| 52 | C23×D17 | C22×C4 | 1 | 15 | yes | — |
| 53 | #41×C17 | C22×C4 | 1 | 20 | yes | — |
| 54 | #41×C17 | C22×C4 | 1 | 60 | yes | — |
| 55 | C2×Q8×C17 | C22×C4 | 1 | 15 | yes | — |
| 56 | C2×D4×C17 | C22×C4 | 1 | 45 | yes | — |
| 57 | C22×C4×C17 | C22×C4 | 1 | 15 | yes | — |
| 58 | C2×C22⋊D17 | C22×C4 | 1 | 90 | yes | — |
| 59 | C22×Dic17 | C24 | 1 | 15 | yes | — |
| 60 | #63256 | C22×C4 | 1 | 60 | yes | — |
| 61 | #63256 | C24 | 1 | 20 | yes | — |
| 62 | Q8×D17 | C22×C4 | 1 | 20 | yes | — |
| 63 | Q8×D17 | C22×C4 | 1 | 60 | yes | — |
| 64 | #63254 | C22×C4 | 1 | 180 | yes | — |
| 65 | #63254 | C24 | 1 | 60 | yes | — |
| 66 | D4×D17 | C22×C4 | 1 | 60 | yes | — |
| 67 | D4×D17 | C22×C4 | 1 | 180 | yes | — |
| 68 | #63252 | C22×C4 | 1 | 60 | yes | — |
| 69 | #63252 | C22×C4 | 1 | 180 | yes | — |
| 70 | C2×D68 | C22×C4 | 1 | 45 | yes | — |
| 71 | C2×C4×D17 | C22×C4 | 1 | 45 | yes | — |
| 72 | C2×C4×D17 | C22×C4 | 1 | 45 | yes | — |
| 73 | C2×C4×D17 | C24 | 1 | 15 | yes | — |
| 74 | C2×C4×D17 | C24 | 1 | 45 | yes | — |
| 75 | C2×Dic34 | C22×C4 | 1 | 45 | yes | — |
| 76 | #63247 | C24 | 1 | 120 | yes | — |
| 77 | C2×#3624 | C24 | 1 | 30 | yes | — |
| 78 | C2×#3624 | C24 | 1 | 90 | yes | — |
| 79 | #63243 | C24 | 1 | 120 | yes | — |
| 80 | #63242 | C24 | 1 | 1 | yes | characteristic |
| 81 | #63242 | C24 | 1 | 15 | yes | — |
| 82 | #63242 | C24 | 1 | 30 | yes | — |
| 83 | #63242 | C24 | 1 | 90 | yes | — |
| 84 | C2×#3573 | — | 17 | 1 | no | maximal, Sylow |
| 85 | C23×C17 | C23×C4 | 1 | 15 | yes | — |
| 86 | C22×D17 | — | 4 | 30 | no | — |
| 87 | C22×D17 | C23×C4 | 1 | 15 | yes | — |
| 88 | C22×D17 | C23×C4 | 1 | 45 | yes | — |
| 89 | Q8×C17 | C23×C4 | 1 | 20 | yes | — |
| 90 | D4×C17 | C23×C4 | 1 | 60 | yes | — |
| 91 | C2×C4×C17 | C23×C4 | 1 | 45 | yes | — |
| 92 | C2×C4×C17 | C23×C4 | 1 | 15 | yes | — |
| 93 | C22⋊D17 | C23×C4 | 1 | 120 | yes | — |
| 94 | C2×Dic17 | C23×C4 | 1 | 45 | yes | — |
| 95 | C2×Dic17 | C25 | 1 | 15 | yes | — |
| 96 | D68 | C23×C4 | 1 | 60 | yes | — |
| 97 | C4×D17 | C23×C4 | 1 | 15 | yes | — |
| 98 | C4×D17 | C23×C4 | 1 | 15 | yes | — |
| 99 | C4×D17 | C23×C4 | 1 | 90 | yes | — |
| 100 | C4×D17 | C25 | 1 | 1 | yes | characteristic |
| 101 | C4×D17 | C25 | 1 | 15 | yes | — |
| 102 | Dic34 | C23×C4 | 1 | 60 | yes | — |
| 103 | #3624 | C25 | 1 | 2 | yes | — |
| 104 | #3624 | C25 | 1 | 30 | yes | — |
| 105 | C2×#585 | — | 17 | 1 | no | — |
| 106 | #3573 | — | 17 | 20 | no | — |
| 107 | #3573 | — | 17 | 12 | no | — |
| 108 | C2×#568 | — | 17 | 15 | no | — |
| 109 | C22×#131 | — | 17 | 15 | no | — |
| 110 | C22×C17 | — | 4 | 15 | no | — |
| 111 | C22×C17 | C24×C4 | 1 | 15 | yes | — |
| 112 | C2×D17 | — | 2 | 30 | no | — |
| 113 | C2×D17 | — | 4 | 45 | no | — |
| 114 | C2×D17 | C24×C4 | 1 | 15 | yes | — |
| 115 | C2×D17 | C24×C4 | 1 | 1 | yes | characteristic |
| 116 | C4×C17 | C24×C4 | 1 | 15 | yes | — |
| 117 | C4×C17 | C24×C4 | 1 | 1 | yes | characteristic |
| 118 | Dic17 | C24×C4 | 1 | 15 | yes | — |
| 119 | Dic17 | C26 | 1 | 1 | yes | characteristic |
| 120 | #585 | — | 17 | 6 | no | — |
| 121 | #585 | — | 17 | 10 | no | — |
| 122 | #585 | — | 17 | 15 | no | — |
| 123 | #585 | #595 | 1 | 1 | yes | characteristic |
| 124 | C2×2−1+4 | — | 17 | 6 | no | — |
| 125 | C2×H(5,𝔽2) | — | 17 | 10 | no | — |
| 126 | C22×#41 | — | 17 | 15 | no | — |
| 127 | #568 | — | 17 | 90 | no | — |
| 128 | #568 | — | 17 | 120 | no | — |
| 129 | #568 | — | 17 | 30 | no | — |
| 130 | C2×#131 | — | 17 | 90 | no | — |
| 131 | C2×#131 | — | 17 | 20 | no | — |
| 132 | C2×#131 | — | 17 | 60 | no | — |
| 133 | C2×#131 | — | 17 | 120 | no | — |
| 134 | C2×#131 | — | 17 | 30 | no | — |
| 135 | C22×M16 | — | 17 | 45 | no | — |
| 136 | C23×C8 | — | 17 | 15 | no | — |
| 137 | C2×C17 | — | 2 | 15 | no | — |
| 138 | C2×C17 | C25×C4 | 1 | 1 | yes | characteristic |
| 139 | D17 | — | 2 | 15 | no | — |
| 140 | D17 | #3573 | 1 | 2 | yes | complemented |
| 141 | 2−1+4 | — | 17 | 60 | no | — |
| 142 | 2−1+4 | — | 17 | 30 | no | — |
| 143 | 2−1+4 | C2×#595 | 1 | 6 | yes | — |
| 144 | H(5,𝔽2) | — | 17 | 60 | no | — |
| 145 | H(5,𝔽2) | — | 17 | 90 | no | — |
| 146 | H(5,𝔽2) | C2×#595 | 1 | 10 | yes | — |
| 147 | C2×#41 | — | 17 | 60 | no | — |
| 148 | C2×#41 | — | 17 | 60 | no | — |
| 149 | C2×#41 | — | 17 | 20 | no | — |
| 150 | C2×#41 | — | 17 | 60 | no | — |
| 151 | C2×#41 | — | 17 | 15 | no | — |
| 152 | C2×#41 | — | 17 | 45 | no | — |
| 153 | C2×#41 | — | 17 | 45 | no | — |
| 154 | C2×#41 | C2×#595 | 1 | 15 | yes | — |
| 155 | C22×Q8 | — | 17 | 15 | no | — |
| 156 | C22×D4 | — | 17 | 45 | no | — |
| 157 | C23×C4 | — | 17 | 15 | no | — |
| 158 | #131 | — | 17 | 120 | no | — |
| 159 | #131 | — | 17 | 360 | no | — |
| 160 | #131 | — | 17 | 40 | no | — |
| 161 | #131 | — | 17 | 120 | no | — |
| 162 | C2×M16 | — | 17 | 90 | no | — |
| 163 | C2×M16 | — | 17 | 60 | no | — |
| 164 | C2×M16 | — | 17 | 180 | no | — |
| 165 | C2×M16 | — | 17 | 90 | no | — |
| 166 | C22×C8 | — | 17 | 15 | no | — |
| 167 | C22×C8 | — | 17 | 45 | no | — |
| 168 | C22×C8 | — | 17 | 90 | no | — |
| 169 | C22×C8 | — | 17 | 30 | no | — |
| 170 | C17 | C2×#3573 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 171 | C24 | — | 17 | 15 | no | — |
| 172 | #41 | — | 17 | 60 | no | — |
| 173 | #41 | — | 17 | 20 | no | — |
| 174 | #41 | — | 17 | 180 | no | — |
| 175 | #41 | — | 17 | 60 | no | — |
| 176 | #41 | — | 17 | 60 | no | — |
| 177 | #41 | — | 17 | 180 | no | — |
| 178 | #41 | C22×#595 | 1 | 20 | yes | — |
| 179 | #41 | C22×#595 | 1 | 60 | yes | — |
| 180 | C2×Q8 | — | 17 | 20 | no | — |
| 181 | C2×Q8 | — | 17 | 60 | no | — |
| 182 | C2×Q8 | — | 17 | 45 | no | — |
| 183 | C2×Q8 | C22×#595 | 1 | 15 | yes | — |
| 184 | C2×D4 | — | 17 | 90 | no | — |
| 185 | C2×D4 | — | 17 | 60 | no | — |
| 186 | C2×D4 | — | 17 | 180 | no | — |
| 187 | C2×D4 | — | 17 | 45 | no | — |
| 188 | C2×D4 | C22×#595 | 1 | 45 | yes | — |
| 189 | C22×C4 | — | 17 | 15 | no | — |
| 190 | C22×C4 | — | 17 | 45 | no | — |
| 191 | C22×C4 | — | 17 | 45 | no | — |
| 192 | C22×C4 | — | 17 | 15 | no | — |
| 193 | C22×C4 | — | 17 | 45 | no | — |
| 194 | C22×C4 | C22×#595 | 1 | 15 | yes | — |
| 195 | M16 | — | 17 | 120 | no | — |
| 196 | M16 | — | 17 | 120 | no | — |
| 197 | C2×C8 | — | 17 | 1 | no | — |
| 198 | C2×C8 | — | 17 | 15 | no | — |
| 199 | C2×C8 | — | 17 | 30 | no | — |
| 200 | C2×C8 | — | 17 | 90 | no | — |
| 201 | C2×C8 | — | 17 | 30 | no | — |
| 202 | C2×C8 | — | 17 | 90 | no | — |
| 203 | C23 | — | 17 | 15 | no | — |
| 204 | C23 | — | 17 | 45 | no | — |
| 205 | C23 | — | 68 | 30 | no | — |
| 206 | C23 | C23×#595 | 1 | 15 | yes | — |
| 207 | Q8 | — | 17 | 60 | no | — |
| 208 | Q8 | C23×#595 | 1 | 20 | yes | — |
| 209 | D4 | — | 17 | 120 | no | — |
| 210 | D4 | — | 17 | 60 | no | — |
| 211 | D4 | C23×#595 | 1 | 60 | yes | — |
| 212 | C2×C4 | — | 17 | 15 | no | — |
| 213 | C2×C4 | — | 17 | 45 | no | — |
| 214 | C2×C4 | — | 17 | 15 | no | — |
| 215 | C2×C4 | — | 17 | 15 | no | — |
| 216 | C2×C4 | — | 17 | 90 | no | — |
| 217 | C2×C4 | — | 17 | 1 | no | — |
| 218 | C2×C4 | — | 17 | 15 | no | — |
| 219 | C2×C4 | C23×#595 | 1 | 45 | yes | — |
| 220 | C2×C4 | C23×#595 | 1 | 15 | yes | — |
| 221 | C8 | — | 17 | 2 | no | — |
| 222 | C8 | — | 17 | 30 | no | — |
| 223 | C22 | — | 4 | 15 | no | — |
| 224 | C22 | — | 17 | 1 | no | — |
| 225 | C22 | — | 17 | 15 | no | — |
| 226 | C22 | — | 34 | 30 | no | — |
| 227 | C22 | — | 68 | 45 | no | — |
| 228 | C22 | C24×#595 | 1 | 15 | yes | — |
| 229 | C4 | — | 17 | 1 | no | — |
| 230 | C4 | — | 17 | 15 | no | — |
| 231 | C4 | C24×#595 | 1 | 15 | yes | — |
| 232 | C4 | C24×#595 | 1 | 1 | yes | characteristic |
| 233 | C2 | — | 2 | 15 | no | — |
| 234 | C2 | — | 17 | 2 | no | — |
| 235 | C2 | — | 34 | 15 | no | — |
| 236 | C2 | C25×#595 | 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