← #44535020
Subgroups — #44535020
Order 31347.
718 conjugacy classes of subgroups.
The subgroup lattice has 210 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×#16812525 | C3 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23782848 | C3 | 1 | 3 | yes | maximal, complemented |
| 3 | #23782842 | C3 | 1 | 6 | yes | maximal, complemented |
| 4 | #23782827 | C3 | 1 | 3 | yes | maximal, complemented |
| 5 | #23782826 | C3 | 1 | 6 | yes | maximal, complemented |
| 6 | #23782822 | C3 | 1 | 2 | yes | maximal, complemented |
| 7 | #23782815 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #23782815 | C3 | 1 | 2 | yes | maximal, complemented |
| 9 | #23782813 | C3 | 1 | 6 | yes | maximal, complemented |
| 10 | #23782803 | C3 | 1 | 1 | yes | maximal, characteristic |
| 11 | #23782803 | C3 | 1 | 2 | yes | maximal |
| 12 | C9×#11923958 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C9×#11923958 | C3 | 1 | 2 | yes | maximal, complemented |
| 14 | #11923956⋊C9 | C3 | 1 | 3 | yes | maximal, complemented |
| 15 | C3×C43×C9⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #16812525 | — | 3 | 9 | no | — |
| 17 | C3×#11923958 | C32 | 1 | 1 | yes | characteristic |
| 18 | C3×#11923958 | C32 | 1 | 1 | yes | characteristic |
| 19 | C3×#11923957 | C32 | 1 | 3 | yes | — |
| 20 | C3×#11923956 | C32 | 1 | 3 | yes | — |
| 21 | C3×#11923956 | C32 | 1 | 3 | yes | — |
| 22 | C3×#11923956 | C32 | 1 | 6 | yes | — |
| 23 | C3×C32⋊(C43⋊C3) | C32 | 1 | 1 | yes | characteristic |
| 24 | C3×C9×C43⋊C3 | C32 | 1 | 3 | yes | — |
| 25 | #16812499 | C32 | 1 | 3 | yes | — |
| 26 | #16812499 | C32 | 1 | 6 | yes | — |
| 27 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 28 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 29 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 30 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 31 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 32 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 33 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 34 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 35 | (C43⋊C9)⋊C9 | C32 | 1 | 6 | yes | — |
| 36 | C32⋊(C43⋊C9) | C32 | 1 | 2 | yes | — |
| 37 | C32⋊(C43⋊C9) | C32 | 1 | 2 | yes | — |
| 38 | C32⋊(C43⋊C9) | C32 | 1 | 2 | yes | — |
| 39 | (C3×C43⋊C3)⋊C9 | C32 | 1 | 6 | yes | — |
| 40 | (C3×C43⋊C3)⋊C9 | C32 | 1 | 6 | yes | — |
| 41 | (C3×C43⋊C3)⋊C9 | C32 | 1 | 6 | yes | — |
| 42 | C9×C43⋊C9 | C32 | 1 | 6 | yes | — |
| 43 | C9×C43⋊C9 | C32 | 1 | 3 | yes | — |
| 44 | C32×C9×C43 | C32 | 1 | 1 | yes | characteristic |
| 45 | C32×C9×C43 | C32 | 1 | 1 | yes | characteristic |
| 46 | C32×C9×C43 | C32 | 1 | 2 | yes | — |
| 47 | C43×C9⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 48 | C43×C9⋊C9 | C32 | 1 | 2 | yes | — |
| 49 | C43×C9⋊C9 | C32 | 1 | 2 | yes | — |
| 50 | C43×C9⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 51 | C43×C9⋊C9 | C32 | 1 | 2 | yes | — |
| 52 | C43×C9⋊C9 | C32 | 1 | 1 | yes | characteristic |
| 53 | C32×C43⋊C3 | C33 | 1 | 3 | yes | — |
| 54 | #11923958 | — | 3 | 3 | no | — |
| 55 | #11923958 | 3−1+2 | 1 | 9 | yes | complemented |
| 56 | #11923957 | — | 3 | 9 | no | — |
| 57 | #11923956 | — | 3 | 9 | no | — |
| 58 | #11923956 | — | 3 | 9 | no | — |
| 59 | #11923956 | — | 9 | 6 | no | — |
| 60 | C32⋊(C43⋊C3) | — | 3 | 3 | no | — |
| 61 | C3×C43⋊C9 | C33 | 1 | 6 | yes | — |
| 62 | C3×C43⋊C9 | C33 | 1 | 6 | yes | — |
| 63 | C3×C43⋊C9 | C33 | 1 | 6 | yes | — |
| 64 | C3×C43⋊C9 | C33 | 1 | 3 | yes | — |
| 65 | C3×C43⋊C9 | C33 | 1 | 3 | yes | — |
| 66 | C9×C43⋊C3 | — | 3 | 9 | no | — |
| 67 | C33×C43 | C33 | 1 | 1 | yes | characteristic |
| 68 | C3×C9×C43 | — | 3 | 3 | no | — |
| 69 | C3×C9×C43 | — | 3 | 3 | no | — |
| 70 | C3×C9×C43 | — | 9 | 2 | no | — |
| 71 | C3×C9×C43 | C33 | 1 | 2 | yes | — |
| 72 | C3×C9×C43 | C33 | 1 | 2 | yes | — |
| 73 | C3×C9×C43 | C33 | 1 | 2 | yes | — |
| 74 | C3×C9×C43 | C33 | 1 | 1 | yes | characteristic |
| 75 | C3×C9×C43 | C33 | 1 | 1 | yes | characteristic |
| 76 | C3×C9×C43 | C33 | 1 | 2 | yes | — |
| 77 | C3×C9×C43 | C33 | 1 | 1 | yes | characteristic |
| 78 | C3×C9×C43 | C33 | 1 | 1 | yes | characteristic |
| 79 | #10624901 | — | 43 | 1 | no | maximal, Sylow |
| 80 | C32×C43 | — | 3 | 1 | no | — |
| 81 | C32×C43 | — | 3 | 2 | no | — |
| 82 | C32×C43 | C3×3−1+2 | 1 | 3 | yes | — |
| 83 | C32×C43 | C34 | 1 | 1 | yes | characteristic |
| 84 | C3×C43⋊C3 | — | 3 | 3 | no | — |
| 85 | C3×C43⋊C3 | — | 3 | 3 | no | — |
| 86 | C3×C43⋊C3 | — | 3 | 6 | no | — |
| 87 | C9×C43 | — | 3 | 1 | no | — |
| 88 | C9×C43 | — | 3 | 1 | no | — |
| 89 | C9×C43 | — | 3 | 1 | no | — |
| 90 | C9×C43 | — | 3 | 2 | no | — |
| 91 | C9×C43 | — | 3 | 2 | no | — |
| 92 | C9×C43 | — | 3 | 2 | no | — |
| 93 | C9×C43 | — | 3 | 2 | no | — |
| 94 | C9×C43 | #737 | 1 | 3 | yes | complemented |
| 95 | C43⋊C9 | — | 3 | 3 | no | — |
| 96 | C43⋊C9 | — | 3 | 6 | no | — |
| 97 | C43⋊C9 | — | 3 | 6 | no | — |
| 98 | C43⋊C9 | — | 3 | 6 | no | — |
| 99 | C43⋊C9 | C3×3−1+2 | 1 | 9 | yes | — |
| 100 | C3×#737 | — | 43 | 1 | no | — |
| 101 | #6900 | — | 43 | 3 | no | — |
| 102 | #6899 | — | 43 | 6 | no | — |
| 103 | #6896 | — | 43 | 6 | no | — |
| 104 | #6896 | — | 43 | 3 | no | — |
| 105 | #6895 | — | 43 | 2 | no | — |
| 106 | #6894 | — | 43 | 2 | no | — |
| 107 | #6894 | — | 43 | 1 | no | — |
| 108 | #6894 | — | 43 | 6 | no | — |
| 109 | C9⋊H(3,𝔽3) | — | 43 | 2 | no | — |
| 110 | C9⋊H(3,𝔽3) | — | 43 | 1 | no | — |
| 111 | C9×3−1+2 | — | 43 | 2 | no | — |
| 112 | C9×3−1+2 | — | 43 | 1 | no | — |
| 113 | C9×3−1+2 | — | 43 | 3 | no | — |
| 114 | C3×C9⋊C9 | C43⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 115 | C3×C43 | — | 3 | 3 | no | — |
| 116 | C3×C43 | C32×3−1+2 | 1 | 1 | yes | characteristic |
| 117 | C3×C43 | C3×#737 | 1 | 1 | yes | characteristic |
| 118 | C3×C43 | 3−1+4 | 1 | 2 | yes | — |
| 119 | C43⋊C3 | — | 9 | 3 | no | — |
| 120 | #737 | — | 129 | 9 | no | — |
| 121 | C3×3−1+2 | — | 43 | 1 | no | — |
| 122 | C3×3−1+2 | — | 43 | 1 | no | — |
| 123 | C3×3−1+2 | — | 43 | 3 | no | — |
| 124 | C3×3−1+2 | — | 43 | 3 | no | — |
| 125 | C3×3−1+2 | — | 43 | 3 | no | — |
| 126 | C3×3−1+2 | — | 43 | 6 | no | — |
| 127 | C3×H(3,𝔽3) | — | 43 | 1 | no | — |
| 128 | C32×C9 | — | 43 | 3 | no | — |
| 129 | C32×C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 130 | C32×C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 131 | C32×C9 | C3×C43⋊C3 | 1 | 2 | yes | — |
| 132 | C9⋊C9 | — | 43 | 6 | no | — |
| 133 | C9⋊C9 | — | 43 | 6 | no | — |
| 134 | C9⋊C9 | — | 43 | 6 | no | — |
| 135 | C9⋊C9 | — | 43 | 6 | no | — |
| 136 | C9⋊C9 | — | 43 | 6 | no | — |
| 137 | C9⋊C9 | — | 43 | 6 | no | — |
| 138 | C9⋊C9 | — | 43 | 6 | no | — |
| 139 | C9⋊C9 | — | 43 | 6 | no | — |
| 140 | C9⋊C9 | — | 43 | 6 | no | — |
| 141 | C9⋊C9 | — | 43 | 3 | no | — |
| 142 | C9⋊C9 | — | 43 | 6 | no | — |
| 143 | C9⋊C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 144 | C9⋊C9 | C3×C43⋊C3 | 1 | 2 | yes | — |
| 145 | C9⋊C9 | C3×C43⋊C3 | 1 | 2 | yes | — |
| 146 | C9⋊C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 147 | C9⋊C9 | C3×C43⋊C3 | 1 | 2 | yes | — |
| 148 | C9⋊C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 149 | C32⋊C9 | — | 43 | 2 | no | — |
| 150 | C32⋊C9 | — | 43 | 2 | no | — |
| 151 | C32⋊C9 | — | 43 | 2 | no | — |
| 152 | C32⋊C9 | — | 43 | 6 | no | — |
| 153 | C32⋊C9 | — | 43 | 6 | no | — |
| 154 | C32⋊C9 | — | 43 | 6 | no | — |
| 155 | C92 | — | 43 | 6 | no | — |
| 156 | C92 | — | 43 | 3 | no | — |
| 157 | C43 | #10624901 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 158 | C33 | — | 43 | 3 | no | — |
| 159 | C33 | C32×C43⋊C3 | 1 | 1 | yes | characteristic |
| 160 | 3−1+2 | — | 43 | 9 | no | — |
| 161 | 3−1+2 | — | 129 | 9 | no | — |
| 162 | 3−1+2 | — | 129 | 9 | no | — |
| 163 | 3−1+2 | — | 129 | 3 | no | — |
| 164 | 3−1+2 | — | 129 | 9 | no | — |
| 165 | 3−1+2 | — | 387 | 6 | no | — |
| 166 | H(3,𝔽3) | — | 129 | 3 | no | — |
| 167 | C3×C9 | — | 3 | 3 | no | — |
| 168 | C3×C9 | — | 3 | 3 | no | — |
| 169 | C3×C9 | — | 9 | 2 | no | — |
| 170 | C3×C9 | — | 43 | 3 | no | — |
| 171 | C3×C9 | — | 43 | 6 | no | — |
| 172 | C3×C9 | — | 43 | 6 | no | — |
| 173 | C3×C9 | — | 43 | 6 | no | — |
| 174 | C3×C9 | — | 43 | 3 | no | — |
| 175 | C3×C9 | — | 129 | 9 | no | — |
| 176 | C3×C9 | C32×C43⋊C3 | 1 | 2 | yes | — |
| 177 | C3×C9 | C32×C43⋊C3 | 1 | 2 | yes | — |
| 178 | C3×C9 | C32×C43⋊C3 | 1 | 2 | yes | — |
| 179 | C3×C9 | C32×C43⋊C3 | 1 | 1 | yes | characteristic |
| 180 | C3×C9 | C32×C43⋊C3 | 1 | 1 | yes | characteristic |
| 181 | C3×C9 | C32×C43⋊C3 | 1 | 1 | yes | characteristic |
| 182 | C3×C9 | C32×C43⋊C3 | 1 | 2 | yes | — |
| 183 | C3×C9 | C32×C43⋊C3 | 1 | 1 | yes | characteristic |
| 184 | C32 | — | 3 | 1 | no | — |
| 185 | C32 | — | 3 | 2 | no | — |
| 186 | C32 | — | 129 | 3 | no | — |
| 187 | C32 | — | 129 | 3 | no | — |
| 188 | C32 | — | 129 | 6 | no | — |
| 189 | C32 | 3−1+2×C43⋊C3 | 1 | 3 | yes | — |
| 190 | C32 | C33×C43⋊C3 | 1 | 1 | yes | characteristic |
| 191 | C9 | — | 3 | 1 | no | — |
| 192 | C9 | — | 3 | 1 | no | — |
| 193 | C9 | — | 3 | 1 | no | — |
| 194 | C9 | — | 3 | 2 | no | — |
| 195 | C9 | — | 3 | 2 | no | — |
| 196 | C9 | — | 3 | 2 | no | — |
| 197 | C9 | — | 3 | 2 | no | — |
| 198 | C9 | — | 43 | 9 | no | — |
| 199 | C9 | — | 129 | 3 | no | — |
| 200 | C9 | — | 129 | 6 | no | — |
| 201 | C9 | — | 129 | 6 | no | — |
| 202 | C9 | — | 129 | 6 | no | — |
| 203 | C9 | #16812525 | 1 | 3 | yes | complemented |
| 204 | C3 | — | 3 | 3 | no | — |
| 205 | C3 | — | 387 | 3 | no | — |
| 206 | C3 | C3×3−1+2×C43⋊C3 | 1 | 1 | yes | characteristic |
| 207 | C3 | C3×#16812525 | 1 | 1 | yes | characteristic |
| 208 | C3 | #23782923 | 1 | 2 | yes | — |
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