← C67×#22283 #30701534
Subgroups — C67×#22283 #30701534
Order 17152.
826 conjugacy classes of subgroups.
The subgroup lattice has 214 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C67×#3150 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C67×#2932 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C67×#1962 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C67×#1876 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | C67×#1838 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C67×#1745 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#135×C67 | C22 | 1 | 4 | yes | — |
| 8 | C2×#131×C67 | C22 | 1 | 4 | yes | — |
| 9 | #532×C67 | C22 | 1 | 2 | yes | — |
| 10 | #497×C67 | C4 | 1 | 4 | yes | complemented |
| 11 | #496×C67 | C4 | 1 | 4 | yes | complemented |
| 12 | #435×C67 | — | 2 | 8 | no | — |
| 13 | #423×C67 | C22 | 1 | 2 | yes | — |
| 14 | C2×#104×C67 | C22 | 1 | 8 | yes | — |
| 15 | #408×C67 | C22 | 1 | 4 | yes | — |
| 16 | C2×#97×C67 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#97×C67 | C22 | 1 | 1 | yes | characteristic |
| 18 | C43×C67 | C22 | 1 | 1 | yes | characteristic |
| 19 | #341×C67 | C22 | 1 | 4 | yes | — |
| 20 | #336×C67 | C22 | 1 | 4 | yes | — |
| 21 | C2×#41×C67 | C23 | 1 | 4 | yes | — |
| 22 | #135×C67 | — | 4 | 8 | no | — |
| 23 | C2×Q16×C67 | C2×C4 | 1 | 4 | yes | — |
| 24 | C2×SD16×C67 | C2×C4 | 1 | 8 | yes | — |
| 25 | C2×D8×C67 | C2×C4 | 1 | 4 | yes | — |
| 26 | #131×C67 | — | 4 | 8 | no | — |
| 27 | C2×M16×C67 | — | 2 | 4 | no | — |
| 28 | C2×M16×C67 | C23 | 1 | 4 | yes | — |
| 29 | C22×C8×C67 | — | 2 | 4 | no | — |
| 30 | C22×C8×C67 | C23 | 1 | 2 | yes | — |
| 31 | C22×C8×C67 | C23 | 1 | 2 | yes | — |
| 32 | C4⋊Q8×C67 | C2×C4 | 1 | 2 | yes | — |
| 33 | #127×C67 | C2×C4 | 1 | 2 | yes | — |
| 34 | #124×C67 | C2×C4 | 1 | 4 | yes | — |
| 35 | #121×C67 | — | 2 | 4 | no | — |
| 36 | C4×D4×C67 | — | 2 | 4 | no | — |
| 37 | C2×C42×C67 | — | 2 | 2 | no | — |
| 38 | C2×C42×C67 | C23 | 1 | 2 | yes | — |
| 39 | C2×C42×C67 | C23 | 1 | 1 | yes | characteristic |
| 40 | C4⋊C8×C67 | — | 2 | 4 | no | — |
| 41 | #104×C67 | — | 4 | 8 | no | — |
| 42 | C22⋊C8×C67 | — | 2 | 8 | no | — |
| 43 | #97×C67 | C2×C4 | 1 | 4 | yes | — |
| 44 | #97×C67 | D4 | 1 | 4 | yes | — |
| 45 | #41×C67 | — | 2 | 8 | no | — |
| 46 | #41×C67 | — | 2 | 8 | no | — |
| 47 | C2×Q8×C67 | C22×C4 | 1 | 4 | yes | — |
| 48 | C2×D4×C67 | — | 2 | 4 | no | — |
| 49 | C2×D4×C67 | — | 2 | 4 | no | — |
| 50 | C2×D4×C67 | C22×C4 | 1 | 4 | yes | — |
| 51 | C22×C4×C67 | — | 2 | 2 | no | — |
| 52 | C22×C4×C67 | — | 2 | 4 | no | — |
| 53 | C22×C4×C67 | #41 | 1 | 2 | yes | — |
| 54 | C22×C4×C67 | C24 | 1 | 1 | yes | characteristic |
| 55 | Q16×C67 | — | 4 | 4 | no | — |
| 56 | SD16×C67 | — | 4 | 8 | no | — |
| 57 | D8×C67 | — | 4 | 4 | no | — |
| 58 | M16×C67 | — | 2 | 8 | no | — |
| 59 | M16×C67 | — | 4 | 8 | no | — |
| 60 | C2×C8×C67 | — | 2 | 4 | no | — |
| 61 | C2×C8×C67 | — | 2 | 4 | no | — |
| 62 | C2×C8×C67 | — | 2 | 4 | no | — |
| 63 | C2×C8×C67 | — | 4 | 8 | no | — |
| 64 | C2×C8×C67 | C22×C4 | 1 | 4 | yes | — |
| 65 | C2×C8×C67 | C2×D4 | 1 | 4 | yes | — |
| 66 | C4⋊C4×C67 | — | 2 | 4 | no | — |
| 67 | C22⋊C4×C67 | — | 2 | 8 | no | — |
| 68 | C42×C67 | — | 2 | 4 | no | — |
| 69 | C42×C67 | — | 4 | 4 | no | — |
| 70 | C42×C67 | C22×C4 | 1 | 2 | yes | — |
| 71 | C42×C67 | C2×D4 | 1 | 2 | yes | — |
| 72 | C23×C67 | — | 2 | 4 | no | — |
| 73 | C23×C67 | C2×#41 | 1 | 1 | yes | characteristic |
| 74 | Q8×C67 | — | 2 | 8 | no | — |
| 75 | D4×C67 | — | 2 | 8 | no | — |
| 76 | D4×C67 | — | 4 | 8 | no | — |
| 77 | D4×C67 | — | 8 | 4 | no | — |
| 78 | C2×C4×C67 | — | 2 | 4 | no | — |
| 79 | C2×C4×C67 | — | 2 | 4 | no | — |
| 80 | C2×C4×C67 | — | 4 | 2 | no | — |
| 81 | C2×C4×C67 | — | 4 | 2 | no | — |
| 82 | C2×C4×C67 | — | 4 | 2 | no | — |
| 83 | C2×C4×C67 | — | 4 | 4 | no | — |
| 84 | C2×C4×C67 | — | 4 | 4 | no | — |
| 85 | C2×C4×C67 | C4×D4 | 1 | 4 | yes | — |
| 86 | C2×C4×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×C4×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×C67 | H(5,𝔽2) | 1 | 4 | yes | — |
| 89 | C8×C67 | — | 2 | 4 | no | — |
| 90 | C8×C67 | — | 2 | 4 | no | — |
| 91 | C8×C67 | — | 4 | 4 | no | — |
| 92 | C22×C67 | — | 2 | 2 | no | — |
| 93 | C22×C67 | — | 4 | 4 | no | — |
| 94 | C22×C67 | — | 4 | 8 | no | — |
| 95 | C22×C67 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 96 | C22×C67 | #540 | 1 | 2 | yes | — |
| 97 | C4×C67 | — | 2 | 4 | no | — |
| 98 | C4×C67 | — | 4 | 4 | no | — |
| 99 | C4×C67 | — | 4 | 4 | no | — |
| 100 | C4×C67 | #518 | 1 | 2 | yes | — |
| 101 | C4×C67 | #535 | 1 | 2 | yes | — |
| 102 | #22283 | C67 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 103 | C2×C67 | — | 2 | 2 | no | — |
| 104 | C2×C67 | — | 8 | 4 | no | — |
| 105 | C2×C67 | #2328 | 1 | 1 | yes | characteristic |
| 106 | C2×C67 | #2956 | 1 | 2 | yes | — |
| 107 | #3150 | C2×C67 | 1 | 1 | yes | characteristic |
| 108 | #2932 | C2×C67 | 1 | 2 | yes | complemented |
| 109 | #1962 | C2×C67 | 1 | 2 | yes | complemented |
| 110 | #1876 | C2×C67 | 1 | 8 | yes | complemented |
| 111 | #1838 | C2×C67 | 1 | 1 | yes | characteristic, complemented |
| 112 | #1745 | C2×C67 | 1 | 1 | yes | characteristic, complemented |
| 113 | C67 | #22283 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 114 | C2×#135 | C22×C67 | 1 | 4 | yes | — |
| 115 | C2×#131 | C22×C67 | 1 | 4 | yes | — |
| 116 | #532 | C22×C67 | 1 | 2 | yes | — |
| 117 | #497 | C4×C67 | 1 | 4 | yes | complemented |
| 118 | #496 | C4×C67 | 1 | 4 | yes | complemented |
| 119 | #435 | — | 2 | 8 | no | — |
| 120 | #423 | C22×C67 | 1 | 2 | yes | — |
| 121 | C2×#104 | C22×C67 | 1 | 8 | yes | — |
| 122 | #408 | C22×C67 | 1 | 4 | yes | — |
| 123 | C2×#97 | C22×C67 | 1 | 1 | yes | characteristic |
| 124 | C2×#97 | C22×C67 | 1 | 1 | yes | characteristic |
| 125 | C43 | C22×C67 | 1 | 1 | yes | characteristic |
| 126 | #341 | C22×C67 | 1 | 4 | yes | — |
| 127 | #336 | C22×C67 | 1 | 4 | yes | — |
| 128 | C2×#41 | C23×C67 | 1 | 4 | yes | — |
| 129 | #135 | — | 4 | 8 | no | — |
| 130 | C2×Q16 | C2×C4×C67 | 1 | 4 | yes | — |
| 131 | C2×SD16 | C2×C4×C67 | 1 | 8 | yes | — |
| 132 | C2×D8 | C2×C4×C67 | 1 | 4 | yes | — |
| 133 | #131 | — | 4 | 8 | no | — |
| 134 | C2×M16 | — | 2 | 4 | no | — |
| 135 | C2×M16 | C23×C67 | 1 | 4 | yes | — |
| 136 | C22×C8 | — | 2 | 4 | no | — |
| 137 | C22×C8 | C23×C67 | 1 | 2 | yes | — |
| 138 | C22×C8 | C23×C67 | 1 | 2 | yes | — |
| 139 | C4⋊Q8 | C2×C4×C67 | 1 | 2 | yes | — |
| 140 | #127 | C2×C4×C67 | 1 | 2 | yes | — |
| 141 | #124 | C2×C4×C67 | 1 | 4 | yes | — |
| 142 | #121 | — | 2 | 4 | no | — |
| 143 | C4×D4 | — | 2 | 4 | no | — |
| 144 | C2×C42 | — | 2 | 2 | no | — |
| 145 | C2×C42 | C23×C67 | 1 | 2 | yes | — |
| 146 | C2×C42 | C23×C67 | 1 | 1 | yes | characteristic |
| 147 | C4⋊C8 | — | 2 | 4 | no | — |
| 148 | #104 | — | 4 | 8 | no | — |
| 149 | C22⋊C8 | — | 2 | 8 | no | — |
| 150 | #97 | C2×C4×C67 | 1 | 4 | yes | — |
| 151 | #97 | D4×C67 | 1 | 4 | yes | — |
| 152 | #41 | — | 2 | 8 | no | — |
| 153 | #41 | — | 2 | 8 | no | — |
| 154 | C2×Q8 | C22×C4×C67 | 1 | 4 | yes | — |
| 155 | C2×D4 | — | 2 | 4 | no | — |
| 156 | C2×D4 | — | 2 | 4 | no | — |
| 157 | C2×D4 | C22×C4×C67 | 1 | 4 | yes | — |
| 158 | C22×C4 | — | 2 | 2 | no | — |
| 159 | C22×C4 | — | 2 | 4 | no | — |
| 160 | C22×C4 | #41×C67 | 1 | 2 | yes | — |
| 161 | C22×C4 | C24×C67 | 1 | 1 | yes | characteristic |
| 162 | Q16 | — | 4 | 4 | no | — |
| 163 | SD16 | — | 4 | 8 | no | — |
| 164 | D8 | — | 4 | 4 | no | — |
| 165 | M16 | — | 2 | 8 | no | — |
| 166 | M16 | — | 4 | 8 | no | — |
| 167 | C2×C8 | — | 2 | 4 | no | — |
| 168 | C2×C8 | — | 2 | 4 | no | — |
| 169 | C2×C8 | — | 2 | 4 | no | — |
| 170 | C2×C8 | — | 4 | 8 | no | — |
| 171 | C2×C8 | C22×C4×C67 | 1 | 4 | yes | — |
| 172 | C2×C8 | C2×D4×C67 | 1 | 4 | yes | — |
| 173 | C4⋊C4 | — | 2 | 4 | no | — |
| 174 | C22⋊C4 | — | 2 | 8 | no | — |
| 175 | C42 | — | 2 | 4 | no | — |
| 176 | C42 | — | 4 | 4 | no | — |
| 177 | C42 | C22×C4×C67 | 1 | 2 | yes | — |
| 178 | C42 | C2×D4×C67 | 1 | 2 | yes | — |
| 179 | C23 | — | 2 | 4 | no | — |
| 180 | C23 | C2×#41×C67 | 1 | 1 | yes | characteristic |
| 181 | Q8 | — | 2 | 8 | no | — |
| 182 | D4 | — | 2 | 8 | no | — |
| 183 | D4 | — | 4 | 8 | no | — |
| 184 | D4 | — | 8 | 4 | no | — |
| 185 | C2×C4 | — | 2 | 4 | no | — |
| 186 | C2×C4 | — | 2 | 4 | no | — |
| 187 | C2×C4 | — | 4 | 2 | no | — |
| 188 | C2×C4 | — | 4 | 2 | no | — |
| 189 | C2×C4 | — | 4 | 2 | no | — |
| 190 | C2×C4 | — | 4 | 4 | no | — |
| 191 | C2×C4 | — | 4 | 4 | no | — |
| 192 | C2×C4 | C4×D4×C67 | 1 | 4 | yes | — |
| 193 | C2×C4 | C23×C4×C67 | 1 | 1 | yes | characteristic |
| 194 | C2×C4 | C22×D4×C67 | 1 | 1 | yes | characteristic |
| 195 | C2×C4 | H(5,𝔽2)×C67 | 1 | 4 | yes | — |
| 196 | C8 | — | 2 | 4 | no | — |
| 197 | C8 | — | 2 | 4 | no | — |
| 198 | C8 | — | 4 | 4 | no | — |
| 199 | C22 | — | 2 | 2 | no | — |
| 200 | C22 | — | 4 | 4 | no | — |
| 201 | C22 | — | 4 | 8 | no | — |
| 202 | C22 | C2×C4×D4×C67 | 1 | 1 | yes | characteristic |
| 203 | C22 | #540×C67 | 1 | 2 | yes | — |
| 204 | C4 | — | 2 | 4 | no | — |
| 205 | C4 | — | 4 | 4 | no | — |
| 206 | C4 | — | 4 | 4 | no | — |
| 207 | C4 | #518×C67 | 1 | 2 | yes | — |
| 208 | C4 | #535×C67 | 1 | 2 | yes | — |
| 209 | C2 | — | 2 | 2 | no | — |
| 210 | C2 | — | 8 | 4 | no | — |
| 211 | C2 | C67×#2328 | 1 | 1 | yes | characteristic |
| 212 | C2 | C67×#2956 | 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