← D9×#504 #11899374
Subgroups — D9×#504 #11899374
Order 1152.
552 conjugacy classes of subgroups.
The subgroup lattice has 219 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | D9×#131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C9×#504 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10588820 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10588587 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | D9×M32 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10588581 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×C16×D9 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | D3×#504 | — | 3 | 1 | no | maximal |
| 9 | #41×D9 | C4 | 1 | 1 | yes | characteristic |
| 10 | C9×#131 | C22 | 1 | 1 | yes | characteristic |
| 11 | #63510 | C4 | 1 | 1 | yes | characteristic |
| 12 | #63469 | C4 | 1 | 3 | yes | — |
| 13 | M16×D9 | C4 | 1 | 3 | yes | — |
| 14 | #63464 | C22 | 1 | 3 | yes | — |
| 15 | C2×C8×D9 | C22 | 1 | 3 | yes | — |
| 16 | C9×M32 | C22 | 1 | 3 | yes | complemented |
| 17 | C2×C9×C16 | C22 | 1 | 3 | yes | complemented |
| 18 | #63371 | C22 | 1 | 3 | yes | complemented |
| 19 | C2×C9⋊C16 | C22 | 1 | 3 | yes | complemented |
| 20 | #63357 | C22 | 1 | 6 | yes | complemented |
| 21 | C16×D9 | C22 | 1 | 1 | yes | characteristic |
| 22 | C16×D9 | C22 | 1 | 3 | yes | — |
| 23 | C16×D9 | C22 | 1 | 3 | yes | complemented |
| 24 | C16×D9 | C22 | 1 | 3 | yes | complemented |
| 25 | D3×#131 | — | 3 | 1 | no | — |
| 26 | C3×#504 | D3 | 1 | 1 | yes | characteristic |
| 27 | #5140 | — | 3 | 1 | no | — |
| 28 | #4907 | — | 3 | 3 | no | — |
| 29 | D3×M32 | — | 3 | 3 | no | — |
| 30 | #4901 | — | 3 | 3 | no | — |
| 31 | C2×D3×C16 | — | 3 | 3 | no | — |
| 32 | C9×#41 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | #3701 | C8 | 1 | 1 | yes | characteristic |
| 34 | Q8×D9 | C8 | 1 | 1 | yes | characteristic |
| 35 | #3699 | C8 | 1 | 3 | yes | — |
| 36 | D4×D9 | C8 | 1 | 3 | yes | — |
| 37 | #3697 | C2×C4 | 1 | 3 | yes | — |
| 38 | C2×C4×D9 | C2×C4 | 1 | 3 | yes | — |
| 39 | C9×M16 | C2×C4 | 1 | 3 | yes | — |
| 40 | C2×C8×C9 | C23 | 1 | 3 | yes | — |
| 41 | #3667 | C2×C4 | 1 | 3 | yes | — |
| 42 | C2×C9⋊C8 | C2×C4 | 1 | 3 | yes | — |
| 43 | #3663 | C2×C4 | 1 | 6 | yes | — |
| 44 | C8×D9 | C2×C4 | 1 | 3 | yes | — |
| 45 | C8×D9 | C2×C4 | 1 | 3 | yes | — |
| 46 | C8×D9 | C23 | 1 | 1 | yes | characteristic |
| 47 | C8×D9 | C23 | 1 | 3 | yes | — |
| 48 | C9×C16 | C23 | 1 | 1 | yes | characteristic |
| 49 | C9×C16 | C23 | 1 | 3 | yes | — |
| 50 | C9⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 51 | C9⋊C16 | C23 | 1 | 3 | yes | — |
| 52 | C2×#504 | — | 9 | 1 | no | Sylow |
| 53 | D3×#41 | — | 3 | 1 | no | — |
| 54 | C3×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 55 | #948 | — | 3 | 1 | no | — |
| 56 | #907 | — | 3 | 3 | no | — |
| 57 | D3×M16 | — | 3 | 3 | no | — |
| 58 | #901 | — | 3 | 3 | no | — |
| 59 | C2×D3×C8 | — | 3 | 3 | no | — |
| 60 | C3×M32 | C2×D3 | 1 | 3 | yes | — |
| 61 | C2×C3×C16 | C2×D3 | 1 | 3 | yes | — |
| 62 | #812 | — | 3 | 3 | no | — |
| 63 | C2×C3⋊C16 | — | 3 | 3 | no | — |
| 64 | #798 | — | 3 | 6 | no | — |
| 65 | D3×C16 | — | 3 | 1 | no | — |
| 66 | D3×C16 | — | 3 | 3 | no | — |
| 67 | D3×C16 | — | 3 | 3 | no | — |
| 68 | D3×C16 | — | 3 | 3 | no | — |
| 69 | C22×D9 | C2×C8 | 1 | 3 | yes | — |
| 70 | Q8×C9 | C2×C8 | 1 | 1 | yes | characteristic |
| 71 | D4×C9 | C2×C8 | 1 | 3 | yes | — |
| 72 | C2×C4×C9 | C22×C4 | 1 | 3 | yes | — |
| 73 | #611 | C2×C8 | 1 | 6 | yes | — |
| 74 | C2×Dic9 | C2×C8 | 1 | 3 | yes | — |
| 75 | D36 | C2×C8 | 1 | 3 | yes | — |
| 76 | C4×D9 | C2×C8 | 1 | 3 | yes | — |
| 77 | C4×D9 | C2×C8 | 1 | 3 | yes | — |
| 78 | C4×D9 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C4×D9 | C22×C4 | 1 | 3 | yes | — |
| 80 | Dic18 | C2×C8 | 1 | 3 | yes | — |
| 81 | C8×C9 | C22×C4 | 1 | 3 | yes | — |
| 82 | C8×C9 | C24 | 1 | 1 | yes | characteristic |
| 83 | C9⋊C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 84 | C9⋊C8 | C22×C4 | 1 | 3 | yes | — |
| 85 | C2×#131 | — | 9 | 1 | no | — |
| 86 | #504 | — | 9 | 1 | no | — |
| 87 | #504 | — | 9 | 3 | no | — |
| 88 | #504 | — | 9 | 3 | no | — |
| 89 | #504 | D9 | 1 | 1 | yes | characteristic, direct product factor |
| 90 | C2×M32 | — | 9 | 3 | no | — |
| 91 | C22×C16 | — | 9 | 3 | no | — |
| 92 | C3×#41 | C4×D3 | 1 | 1 | yes | characteristic |
| 93 | #239 | — | 3 | 1 | no | — |
| 94 | D3×Q8 | — | 3 | 1 | no | — |
| 95 | #237 | — | 3 | 3 | no | — |
| 96 | D3×D4 | — | 3 | 3 | no | — |
| 97 | #235 | — | 3 | 3 | no | — |
| 98 | C2×C4×D3 | — | 3 | 3 | no | — |
| 99 | C3×M16 | C4×D3 | 1 | 3 | yes | — |
| 100 | C2×C3×C8 | C22×D3 | 1 | 3 | yes | — |
| 101 | #208 | — | 3 | 3 | no | — |
| 102 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 103 | ΓL(1,𝔽25) | — | 3 | 6 | no | — |
| 104 | D3×C8 | — | 3 | 3 | no | — |
| 105 | D3×C8 | — | 3 | 3 | no | — |
| 106 | D3×C8 | — | 3 | 1 | no | — |
| 107 | D3×C8 | — | 3 | 3 | no | — |
| 108 | C3×C16 | C22×D3 | 1 | 3 | yes | — |
| 109 | C3×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 110 | C3⋊C16 | — | 3 | 1 | no | — |
| 111 | C3⋊C16 | — | 3 | 3 | no | — |
| 112 | C22×C9 | C22×C8 | 1 | 3 | yes | — |
| 113 | C2×D9 | — | 2 | 6 | no | — |
| 114 | C2×D9 | C22×C8 | 1 | 3 | yes | — |
| 115 | C2×D9 | C22×C8 | 1 | 1 | yes | characteristic |
| 116 | C4×C9 | C22×C8 | 1 | 3 | yes | — |
| 117 | C4×C9 | C23×C4 | 1 | 1 | yes | characteristic |
| 118 | Dic9 | C22×C8 | 1 | 3 | yes | — |
| 119 | Dic9 | C22×C8 | 1 | 1 | yes | characteristic |
| 120 | C2×#41 | — | 9 | 1 | no | — |
| 121 | #131 | — | 9 | 1 | no | — |
| 122 | #131 | — | 9 | 3 | no | — |
| 123 | #131 | — | 9 | 3 | no | — |
| 124 | #131 | C2×D9 | 1 | 1 | yes | characteristic |
| 125 | C2×M16 | — | 9 | 3 | no | — |
| 126 | C22×C8 | — | 9 | 3 | no | — |
| 127 | M32 | — | 9 | 3 | no | — |
| 128 | M32 | — | 9 | 6 | no | — |
| 129 | M32 | C2×D9 | 1 | 3 | yes | complemented |
| 130 | C2×C16 | — | 9 | 3 | no | — |
| 131 | C2×C16 | — | 9 | 3 | no | — |
| 132 | C2×C16 | — | 9 | 3 | no | — |
| 133 | C2×C16 | — | 9 | 1 | no | — |
| 134 | C2×C16 | — | 9 | 3 | no | — |
| 135 | C2×C16 | C2×D9 | 1 | 3 | yes | complemented |
| 136 | C22×D3 | — | 3 | 3 | no | — |
| 137 | C3×Q8 | D3×C8 | 1 | 1 | yes | characteristic |
| 138 | C3×D4 | D3×C8 | 1 | 3 | yes | — |
| 139 | C2×C3×C4 | C2×C4×D3 | 1 | 3 | yes | — |
| 140 | #67 | — | 3 | 6 | no | — |
| 141 | C2×Dic3 | — | 3 | 3 | no | — |
| 142 | D12 | — | 3 | 3 | no | — |
| 143 | C4×D3 | — | 3 | 3 | no | — |
| 144 | C4×D3 | — | 3 | 3 | no | — |
| 145 | C4×D3 | — | 3 | 1 | no | — |
| 146 | C4×D3 | — | 3 | 3 | no | — |
| 147 | Dic6 | — | 3 | 3 | no | — |
| 148 | C3×C8 | C2×C4×D3 | 1 | 3 | yes | — |
| 149 | C3×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 150 | C3⋊C8 | — | 3 | 1 | no | — |
| 151 | C3⋊C8 | — | 3 | 3 | no | — |
| 152 | C2×C9 | — | 2 | 3 | no | — |
| 153 | C2×C9 | C23×C8 | 1 | 1 | yes | characteristic |
| 154 | D9 | — | 2 | 3 | no | — |
| 155 | D9 | #504 | 1 | 2 | yes | direct product factor |
| 156 | #41 | — | 9 | 1 | no | — |
| 157 | #41 | — | 9 | 3 | no | — |
| 158 | #41 | — | 9 | 3 | no | — |
| 159 | #41 | C4×D9 | 1 | 1 | yes | characteristic |
| 160 | C2×Q8 | — | 9 | 1 | no | — |
| 161 | C2×D4 | — | 9 | 3 | no | — |
| 162 | C22×C4 | — | 9 | 3 | no | — |
| 163 | M16 | — | 9 | 3 | no | — |
| 164 | M16 | — | 9 | 6 | no | — |
| 165 | M16 | C4×D9 | 1 | 3 | yes | — |
| 166 | C2×C8 | — | 9 | 3 | no | — |
| 167 | C2×C8 | — | 9 | 3 | no | — |
| 168 | C2×C8 | — | 9 | 3 | no | — |
| 169 | C2×C8 | — | 9 | 1 | no | — |
| 170 | C2×C8 | — | 9 | 3 | no | — |
| 171 | C2×C8 | C22×D9 | 1 | 3 | yes | — |
| 172 | C16 | — | 9 | 1 | no | — |
| 173 | C16 | — | 9 | 3 | no | — |
| 174 | C16 | C22×D9 | 1 | 3 | yes | — |
| 175 | C16 | C22×D9 | 1 | 1 | yes | characteristic |
| 176 | C22×C3 | C2×D3×C8 | 1 | 3 | yes | — |
| 177 | C2×D3 | — | 3 | 1 | no | — |
| 178 | C2×D3 | — | 3 | 3 | no | — |
| 179 | C2×D3 | — | 6 | 6 | no | — |
| 180 | C3×C4 | C2×D3×C8 | 1 | 3 | yes | — |
| 181 | C3×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 182 | Dic3 | — | 3 | 3 | no | — |
| 183 | Dic3 | — | 3 | 1 | no | — |
| 184 | C9 | C2×#504 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 185 | C23 | — | 9 | 3 | no | — |
| 186 | Q8 | — | 9 | 3 | no | — |
| 187 | Q8 | C8×D9 | 1 | 1 | yes | characteristic |
| 188 | D4 | — | 9 | 6 | no | — |
| 189 | D4 | — | 9 | 3 | no | — |
| 190 | D4 | C8×D9 | 1 | 3 | yes | — |
| 191 | C2×C4 | — | 9 | 3 | no | — |
| 192 | C2×C4 | — | 9 | 1 | no | — |
| 193 | C2×C4 | — | 9 | 3 | no | — |
| 194 | C2×C4 | — | 9 | 3 | no | — |
| 195 | C2×C4 | — | 9 | 3 | no | — |
| 196 | C2×C4 | C2×C4×D9 | 1 | 3 | yes | — |
| 197 | C8 | — | 9 | 1 | no | — |
| 198 | C8 | — | 9 | 3 | no | — |
| 199 | C8 | C2×C4×D9 | 1 | 3 | yes | — |
| 200 | C8 | C23×D9 | 1 | 1 | yes | characteristic |
| 201 | C2×C3 | — | 2 | 3 | no | — |
| 202 | C2×C3 | C22×D3×C8 | 1 | 1 | yes | characteristic |
| 203 | D3 | — | 3 | 2 | no | — |
| 204 | D3 | — | 6 | 3 | no | — |
| 205 | C22 | — | 9 | 1 | no | — |
| 206 | C22 | — | 9 | 3 | no | — |
| 207 | C22 | — | 18 | 6 | no | — |
| 208 | C22 | C2×C8×D9 | 1 | 3 | yes | — |
| 209 | C4 | — | 9 | 1 | no | — |
| 210 | C4 | — | 9 | 3 | no | — |
| 211 | C4 | C2×C8×D9 | 1 | 3 | yes | — |
| 212 | C4 | C22×C4×D9 | 1 | 1 | yes | characteristic |
| 213 | C3 | D3×#504 | 1 | 1 | yes | characteristic |
| 214 | C2 | — | 2 | 3 | no | — |
| 215 | C2 | — | 9 | 2 | no | — |
| 216 | C2 | — | 18 | 3 | no | — |
| 217 | C2 | C22×C8×D9 | 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