← C2×#14526925 #16954530
Subgroups — C2×#14526925 #16954530
Order 4352.
294 conjugacy classes of subgroups.
The subgroup lattice has 220 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11763225 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11762643 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14526925 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C22×C17×C32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#10587587 | C4 | 1 | 1 | yes | characteristic |
| 6 | #11763225 | — | 2 | 1 | no | — |
| 7 | #11763225 | — | 2 | 1 | no | — |
| 8 | #11763225 | C4 | 1 | 2 | yes | — |
| 9 | #11763225 | C22 | 1 | 2 | yes | — |
| 10 | C2×#10587483 | C4 | 1 | 1 | yes | characteristic |
| 11 | C2×#10587469 | — | 2 | 1 | no | — |
| 12 | C2×C16×D17 | — | 2 | 1 | no | — |
| 13 | #11762643 | — | 2 | 1 | no | — |
| 14 | #11762643 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×#10587465 | — | 2 | 1 | no | — |
| 16 | C22×C16×C17 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C17×C32 | — | 2 | 1 | no | — |
| 18 | C2×C17×C32 | — | 2 | 1 | no | — |
| 19 | C2×C17×C32 | C22 | 1 | 2 | yes | complemented |
| 20 | C2×#63252 | C8 | 1 | 1 | yes | characteristic |
| 21 | C22×C8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 22 | C2×#63223 | C8 | 1 | 1 | yes | characteristic |
| 23 | #10587587 | — | 2 | 1 | no | — |
| 24 | #10587587 | — | 2 | 1 | no | — |
| 25 | #10587587 | C8 | 1 | 2 | yes | — |
| 26 | #10587587 | C2×C4 | 1 | 2 | yes | — |
| 27 | C2×#63218 | — | 2 | 1 | no | — |
| 28 | C2×C8×D17 | — | 2 | 1 | no | — |
| 29 | C2×C16×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C2×C16×C17 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×C16×C17 | D4 | 1 | 1 | yes | characteristic |
| 32 | C2×C16×C17 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C16×C17 | D4 | 1 | 1 | yes | characteristic |
| 34 | C2×C16×C17 | C23 | 1 | 1 | yes | characteristic |
| 35 | #10587483 | — | 2 | 1 | no | — |
| 36 | #10587483 | C2×C4 | 1 | 2 | yes | — |
| 37 | C2×#63214 | — | 2 | 1 | no | — |
| 38 | #10587469 | — | 2 | 2 | no | — |
| 39 | #10587469 | — | 2 | 2 | no | — |
| 40 | C16×D17 | — | 2 | 2 | no | — |
| 41 | C16×D17 | — | 2 | 2 | no | — |
| 42 | C17×C32 | — | 2 | 2 | no | — |
| 43 | #10587465 | — | 2 | 2 | no | — |
| 44 | C22×C4×C17 | C2×C8 | 1 | 1 | yes | characteristic |
| 45 | C2×C22⋊D17 | — | 2 | 1 | no | — |
| 46 | #63252 | — | 2 | 1 | no | — |
| 47 | #63252 | — | 2 | 1 | no | — |
| 48 | #63252 | C16 | 1 | 2 | yes | — |
| 49 | #63252 | C2×C8 | 1 | 2 | yes | — |
| 50 | C2×D68 | C16 | 1 | 1 | yes | characteristic |
| 51 | C2×C4×D17 | — | 2 | 1 | no | — |
| 52 | C2×Dic34 | C16 | 1 | 1 | yes | characteristic |
| 53 | C2×C8×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 54 | C2×C8×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 55 | C2×C8×C17 | C2×C8 | 1 | 1 | yes | characteristic |
| 56 | C2×C8×C17 | M16 | 1 | 1 | yes | characteristic |
| 57 | C2×C8×C17 | M16 | 1 | 1 | yes | characteristic |
| 58 | C2×C8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 59 | #63223 | — | 2 | 1 | no | — |
| 60 | #63223 | C2×C8 | 1 | 2 | yes | — |
| 61 | C2×#3622 | — | 2 | 1 | no | — |
| 62 | #63218 | — | 2 | 2 | no | — |
| 63 | #63218 | — | 2 | 2 | no | — |
| 64 | C8×D17 | — | 2 | 2 | no | — |
| 65 | C8×D17 | — | 2 | 2 | no | — |
| 66 | C16×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 67 | C16×C17 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 68 | C16×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C16×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 70 | #63214 | — | 2 | 2 | no | — |
| 71 | C2×#1401 | — | 17 | 1 | no | maximal, Sylow |
| 72 | C23×C17 | M32 | 1 | 1 | yes | characteristic |
| 73 | C22×D17 | — | 2 | 1 | no | — |
| 74 | C2×C4×C17 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×C17 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 76 | C2×C4×C17 | C2×C16 | 1 | 1 | yes | characteristic |
| 77 | C2×C4×C17 | C2×C16 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×C17 | M32 | 1 | 1 | yes | characteristic |
| 79 | C2×C4×C17 | C22×C8 | 1 | 1 | yes | characteristic |
| 80 | C22⋊D17 | — | 2 | 2 | no | — |
| 81 | C22⋊D17 | — | 2 | 2 | no | — |
| 82 | C2×Dic17 | — | 2 | 1 | no | — |
| 83 | D68 | — | 2 | 1 | no | — |
| 84 | D68 | C2×C16 | 1 | 2 | yes | — |
| 85 | C4×D17 | — | 2 | 2 | no | — |
| 86 | C4×D17 | — | 2 | 2 | no | — |
| 87 | Dic34 | — | 2 | 1 | no | — |
| 88 | Dic34 | C2×C16 | 1 | 2 | yes | — |
| 89 | C8×C17 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 90 | C8×C17 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 91 | C8×C17 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 92 | C8×C17 | C2×M16 | 1 | 1 | yes | characteristic |
| 93 | #3622 | — | 2 | 2 | no | — |
| 94 | C2×#504 | — | 17 | 1 | no | — |
| 95 | C2×M64 | — | 17 | 1 | no | — |
| 96 | C22×C32 | D17 | 1 | 1 | yes | characteristic, complemented |
| 97 | #1401 | — | 17 | 4 | no | — |
| 98 | C22×C17 | — | 2 | 2 | no | — |
| 99 | C22×C17 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 100 | C22×C17 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 101 | C22×C17 | C2×M32 | 1 | 1 | yes | characteristic |
| 102 | C2×D17 | — | 2 | 2 | no | — |
| 103 | C2×D17 | — | 4 | 2 | no | — |
| 104 | C4×C17 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 105 | C4×C17 | C22⋊C16 | 1 | 1 | yes | characteristic |
| 106 | C4×C17 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 107 | C4×C17 | C22×C16 | 1 | 1 | yes | characteristic |
| 108 | Dic17 | — | 2 | 2 | no | — |
| 109 | C2×#131 | — | 17 | 1 | no | — |
| 110 | #504 | — | 17 | 2 | no | — |
| 111 | #504 | — | 17 | 2 | no | — |
| 112 | #504 | — | 34 | 1 | no | — |
| 113 | #504 | — | 34 | 1 | no | — |
| 114 | C2×M32 | — | 17 | 1 | no | — |
| 115 | C2×M32 | — | 34 | 1 | no | — |
| 116 | C22×C16 | — | 34 | 1 | no | — |
| 117 | C22×C16 | C2×D17 | 1 | 1 | yes | characteristic |
| 118 | M64 | — | 17 | 2 | no | — |
| 119 | M64 | — | 34 | 1 | no | — |
| 120 | C2×C32 | — | 2 | 1 | no | — |
| 121 | C2×C32 | — | 2 | 1 | no | — |
| 122 | C2×C32 | — | 34 | 1 | no | — |
| 123 | C2×C32 | C2×D17 | 1 | 2 | yes | complemented |
| 124 | C2×C17 | — | 2 | 1 | no | — |
| 125 | C2×C17 | — | 2 | 1 | no | — |
| 126 | C2×C17 | #1401 | 1 | 2 | yes | complemented |
| 127 | C2×C17 | C2×C22⋊C16 | 1 | 1 | yes | characteristic |
| 128 | D17 | — | 4 | 2 | no | — |
| 129 | C2×#41 | — | 17 | 1 | no | — |
| 130 | #131 | — | 17 | 2 | no | — |
| 131 | #131 | — | 17 | 2 | no | — |
| 132 | #131 | — | 34 | 1 | no | — |
| 133 | #131 | — | 34 | 1 | no | — |
| 134 | C2×M16 | — | 17 | 1 | no | — |
| 135 | C2×M16 | — | 34 | 1 | no | — |
| 136 | C22×C8 | — | 34 | 1 | no | — |
| 137 | C22×C8 | C4×D17 | 1 | 1 | yes | characteristic |
| 138 | M32 | — | 17 | 2 | no | — |
| 139 | M32 | — | 34 | 1 | no | — |
| 140 | M32 | — | 34 | 2 | no | — |
| 141 | M32 | — | 34 | 2 | no | — |
| 142 | C2×C16 | — | 34 | 1 | no | — |
| 143 | C2×C16 | — | 34 | 2 | no | — |
| 144 | C2×C16 | — | 34 | 2 | no | — |
| 145 | C2×C16 | C4×D17 | 1 | 1 | yes | characteristic |
| 146 | C2×C16 | D68 | 1 | 1 | yes | characteristic |
| 147 | C2×C16 | D68 | 1 | 1 | yes | characteristic |
| 148 | C2×C16 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 149 | C2×C16 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 150 | C2×C16 | C22×D17 | 1 | 1 | yes | characteristic |
| 151 | C32 | — | 2 | 2 | no | — |
| 152 | C32 | — | 34 | 2 | no | — |
| 153 | C17 | C2×#1401 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 154 | #41 | — | 17 | 2 | no | — |
| 155 | #41 | — | 17 | 2 | no | — |
| 156 | #41 | — | 34 | 1 | no | — |
| 157 | #41 | — | 34 | 1 | no | — |
| 158 | C2×Q8 | — | 17 | 1 | no | — |
| 159 | C2×D4 | — | 17 | 1 | no | — |
| 160 | C2×D4 | — | 34 | 1 | no | — |
| 161 | C22×C4 | — | 34 | 1 | no | — |
| 162 | C22×C4 | C8×D17 | 1 | 1 | yes | characteristic |
| 163 | M16 | — | 17 | 2 | no | — |
| 164 | M16 | — | 34 | 1 | no | — |
| 165 | M16 | — | 34 | 2 | no | — |
| 166 | M16 | — | 34 | 2 | no | — |
| 167 | C2×C8 | — | 34 | 1 | no | — |
| 168 | C2×C8 | — | 34 | 2 | no | — |
| 169 | C2×C8 | — | 34 | 2 | no | — |
| 170 | C2×C8 | C8×D17 | 1 | 1 | yes | characteristic |
| 171 | C2×C8 | #63218 | 1 | 1 | yes | characteristic |
| 172 | C2×C8 | #63218 | 1 | 1 | yes | characteristic |
| 173 | C2×C8 | #63227 | 1 | 1 | yes | characteristic |
| 174 | C2×C8 | #63227 | 1 | 1 | yes | characteristic |
| 175 | C2×C8 | C2×C4×D17 | 1 | 1 | yes | characteristic |
| 176 | C16 | — | 34 | 2 | no | — |
| 177 | C16 | #63227 | 1 | 1 | yes | characteristic |
| 178 | C16 | #63227 | 1 | 1 | yes | characteristic |
| 179 | C16 | C2×D68 | 1 | 1 | yes | characteristic |
| 180 | C16 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 181 | C23 | — | 34 | 1 | no | — |
| 182 | C23 | #10587469 | 1 | 1 | yes | characteristic |
| 183 | Q8 | — | 17 | 2 | no | — |
| 184 | Q8 | — | 34 | 1 | no | — |
| 185 | D4 | — | 17 | 2 | no | — |
| 186 | D4 | — | 34 | 2 | no | — |
| 187 | D4 | — | 34 | 2 | no | — |
| 188 | D4 | — | 34 | 1 | no | — |
| 189 | C2×C4 | — | 34 | 1 | no | — |
| 190 | C2×C4 | — | 34 | 2 | no | — |
| 191 | C2×C4 | — | 34 | 2 | no | — |
| 192 | C2×C4 | C16×D17 | 1 | 1 | yes | characteristic |
| 193 | C2×C4 | C16×D17 | 1 | 1 | yes | characteristic |
| 194 | C2×C4 | #10587469 | 1 | 1 | yes | characteristic |
| 195 | C2×C4 | #10587491 | 1 | 1 | yes | characteristic |
| 196 | C2×C4 | #10587491 | 1 | 1 | yes | characteristic |
| 197 | C2×C4 | C2×C8×D17 | 1 | 1 | yes | characteristic |
| 198 | C8 | — | 34 | 2 | no | — |
| 199 | C8 | #10587491 | 1 | 1 | yes | characteristic |
| 200 | C8 | #10587491 | 1 | 1 | yes | characteristic |
| 201 | C8 | C2×#63218 | 1 | 1 | yes | characteristic |
| 202 | C8 | C2×#63227 | 1 | 1 | yes | characteristic |
| 203 | C22 | — | 2 | 2 | no | — |
| 204 | C22 | — | 34 | 2 | no | — |
| 205 | C22 | — | 68 | 2 | no | — |
| 206 | C22 | #11762588 | 1 | 1 | yes | characteristic |
| 207 | C22 | #11762588 | 1 | 1 | yes | characteristic |
| 208 | C22 | C2×#10587469 | 1 | 1 | yes | characteristic |
| 209 | C4 | — | 34 | 2 | no | — |
| 210 | C4 | #11762588 | 1 | 1 | yes | characteristic |
| 211 | C4 | #11762588 | 1 | 1 | yes | characteristic |
| 212 | C4 | C2×#10587491 | 1 | 1 | yes | characteristic |
| 213 | C4 | C2×C16×D17 | 1 | 1 | yes | characteristic |
| 214 | C2 | — | 2 | 1 | no | — |
| 215 | C2 | — | 2 | 1 | no | — |
| 216 | C2 | — | 68 | 2 | no | — |
| 217 | C2 | #14526925 | 1 | 2 | yes | direct product factor |
| 218 | C2 | C2×#11762588 | 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