← C67×#60308 #30739559
Subgroups — C67×#60308 #30739559
Order 17152.
1964 conjugacy classes of subgroups.
The subgroup lattice has 180 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C67×#3483 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C67×#2991 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | C67×#2979 | C2 | 1 | 9 | yes | maximal, complemented |
| 4 | C8×#41×C67 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C67×#2931 | C2 | 1 | 9 | yes | maximal, complemented |
| 6 | C2×#131×C67 | C22 | 1 | 6 | yes | — |
| 7 | Q82×C67 | C4 | 1 | 1 | yes | characteristic |
| 8 | #555×C67 | C4 | 1 | 9 | yes | — |
| 9 | #550×C67 | C4 | 1 | 6 | yes | — |
| 10 | #532×C67 | C22 | 1 | 9 | yes | — |
| 11 | C4×#41×C67 | C22 | 1 | 6 | yes | — |
| 12 | C8×Q8×C67 | C22 | 1 | 2 | yes | — |
| 13 | C8×Q8×C67 | C22 | 1 | 6 | yes | — |
| 14 | #436×C67 | C22 | 1 | 36 | yes | — |
| 15 | C8×D4×C67 | C22 | 1 | 18 | yes | — |
| 16 | C8×D4×C67 | C22 | 1 | 18 | yes | — |
| 17 | #431×C67 | C22 | 1 | 18 | yes | — |
| 18 | #423×C67 | C22 | 1 | 9 | yes | — |
| 19 | #408×C67 | C22 | 1 | 18 | yes | — |
| 20 | C2×C4×C8×C67 | C22 | 1 | 9 | yes | — |
| 21 | C2×#41×C67 | C2×C4 | 1 | 6 | yes | — |
| 22 | C2×#41×C67 | C23 | 1 | 6 | yes | — |
| 23 | #131×C67 | — | 4 | 12 | no | — |
| 24 | C2×M16×C67 | C23 | 1 | 18 | yes | — |
| 25 | C22×C8×C67 | C23 | 1 | 9 | yes | — |
| 26 | C22×C8×C67 | C23 | 1 | 9 | yes | — |
| 27 | C4⋊Q8×C67 | C2×C4 | 1 | 9 | yes | — |
| 28 | #127×C67 | C2×C4 | 1 | 9 | yes | — |
| 29 | #124×C67 | C2×C4 | 1 | 18 | yes | — |
| 30 | #121×C67 | C2×C4 | 1 | 36 | yes | — |
| 31 | C4×Q8×C67 | C2×C4 | 1 | 6 | yes | — |
| 32 | C4×Q8×C67 | C23 | 1 | 2 | yes | — |
| 33 | C4×D4×C67 | C2×C4 | 1 | 18 | yes | — |
| 34 | C4×D4×C67 | C23 | 1 | 18 | yes | — |
| 35 | #117×C67 | C2×C4 | 1 | 18 | yes | — |
| 36 | C2×C42×C67 | C23 | 1 | 9 | yes | — |
| 37 | C4⋊C8×C67 | C23 | 1 | 18 | yes | — |
| 38 | C4⋊C8×C67 | C23 | 1 | 6 | yes | — |
| 39 | C22⋊C8×C67 | C23 | 1 | 36 | yes | — |
| 40 | C4×C8×C67 | C23 | 1 | 18 | yes | — |
| 41 | C4×C8×C67 | C23 | 1 | 6 | yes | — |
| 42 | #41×C67 | — | 2 | 24 | no | — |
| 43 | #41×C67 | — | 4 | 6 | no | — |
| 44 | #41×C67 | — | 4 | 6 | no | — |
| 45 | C2×Q8×C67 | C22×C4 | 1 | 6 | yes | — |
| 46 | C2×Q8×C67 | C22×C4 | 1 | 2 | yes | — |
| 47 | C2×D4×C67 | C22×C4 | 1 | 18 | yes | — |
| 48 | C2×D4×C67 | C22×C4 | 1 | 18 | yes | — |
| 49 | C22×C4×C67 | C22×C4 | 1 | 18 | yes | — |
| 50 | C22×C4×C67 | C24 | 1 | 9 | yes | — |
| 51 | M16×C67 | — | 4 | 18 | no | — |
| 52 | C2×C8×C67 | — | 2 | 18 | no | — |
| 53 | C2×C8×C67 | — | 4 | 9 | no | — |
| 54 | C2×C8×C67 | C24 | 1 | 9 | yes | — |
| 55 | C2×C8×C67 | C24 | 1 | 6 | yes | — |
| 56 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 57 | C4⋊C4×C67 | C22×C4 | 1 | 6 | yes | — |
| 58 | C4⋊C4×C67 | C22×C4 | 1 | 18 | yes | — |
| 59 | C22⋊C4×C67 | C22×C4 | 1 | 36 | yes | — |
| 60 | C42×C67 | C22×C4 | 1 | 9 | yes | — |
| 61 | C42×C67 | C22×C4 | 1 | 9 | yes | — |
| 62 | C42×C67 | C24 | 1 | 6 | yes | — |
| 63 | C23×C67 | C23×C4 | 1 | 9 | yes | — |
| 64 | Q8×C67 | — | 4 | 6 | no | — |
| 65 | Q8×C67 | #131 | 1 | 8 | yes | complemented |
| 66 | D4×C67 | — | 2 | 36 | no | — |
| 67 | D4×C67 | — | 4 | 18 | no | — |
| 68 | C2×C4×C67 | — | 2 | 36 | no | — |
| 69 | C2×C4×C67 | — | 2 | 9 | no | — |
| 70 | C2×C4×C67 | — | 2 | 9 | no | — |
| 71 | C2×C4×C67 | C23×C4 | 1 | 6 | yes | — |
| 72 | C2×C4×C67 | C23×C4 | 1 | 9 | yes | — |
| 73 | C2×C4×C67 | C23×C4 | 1 | 6 | yes | — |
| 74 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 75 | C8×C67 | — | 2 | 9 | no | — |
| 76 | C8×C67 | — | 2 | 6 | no | — |
| 77 | C8×C67 | H(5,𝔽2) | 1 | 2 | yes | — |
| 78 | C22×C67 | — | 2 | 9 | no | — |
| 79 | C22×C67 | — | 2 | 18 | no | — |
| 80 | C22×C67 | C24×C4 | 1 | 1 | yes | characteristic |
| 81 | C4×C67 | — | 2 | 9 | no | — |
| 82 | C4×C67 | — | 2 | 6 | no | — |
| 83 | C4×C67 | C2×#131 | 1 | 12 | yes | — |
| 84 | C4×C67 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 85 | C4×C67 | #585 | 1 | 1 | yes | characteristic |
| 86 | #60308 | C67 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 87 | C2×C67 | — | 4 | 9 | no | — |
| 88 | C2×C67 | C4×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 89 | C2×C67 | C22×#131 | 1 | 2 | yes | — |
| 90 | #3483 | C2×C67 | 1 | 1 | yes | characteristic |
| 91 | #2991 | C2×C67 | 1 | 6 | yes | complemented |
| 92 | #2979 | C2×C67 | 1 | 9 | yes | complemented |
| 93 | C8×#41 | C2×C67 | 1 | 6 | yes | complemented |
| 94 | #2931 | C2×C67 | 1 | 9 | yes | complemented |
| 95 | C67 | #60308 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 96 | C2×#131 | C22×C67 | 1 | 6 | yes | — |
| 97 | Q82 | C4×C67 | 1 | 1 | yes | characteristic |
| 98 | #555 | C4×C67 | 1 | 9 | yes | — |
| 99 | #550 | C4×C67 | 1 | 6 | yes | — |
| 100 | #532 | C22×C67 | 1 | 9 | yes | — |
| 101 | C4×#41 | C22×C67 | 1 | 6 | yes | — |
| 102 | C8×Q8 | C22×C67 | 1 | 2 | yes | — |
| 103 | C8×Q8 | C22×C67 | 1 | 6 | yes | — |
| 104 | #436 | C22×C67 | 1 | 36 | yes | — |
| 105 | C8×D4 | C22×C67 | 1 | 18 | yes | — |
| 106 | C8×D4 | C22×C67 | 1 | 18 | yes | — |
| 107 | #431 | C22×C67 | 1 | 18 | yes | — |
| 108 | #423 | C22×C67 | 1 | 9 | yes | — |
| 109 | #408 | C22×C67 | 1 | 18 | yes | — |
| 110 | C2×C4×C8 | C22×C67 | 1 | 9 | yes | — |
| 111 | C2×#41 | C2×C4×C67 | 1 | 6 | yes | — |
| 112 | C2×#41 | C23×C67 | 1 | 6 | yes | — |
| 113 | #131 | — | 4 | 12 | no | — |
| 114 | C2×M16 | C23×C67 | 1 | 18 | yes | — |
| 115 | C22×C8 | C23×C67 | 1 | 9 | yes | — |
| 116 | C22×C8 | C23×C67 | 1 | 9 | yes | — |
| 117 | C4⋊Q8 | C2×C4×C67 | 1 | 9 | yes | — |
| 118 | #127 | C2×C4×C67 | 1 | 9 | yes | — |
| 119 | #124 | C2×C4×C67 | 1 | 18 | yes | — |
| 120 | #121 | C2×C4×C67 | 1 | 36 | yes | — |
| 121 | C4×Q8 | C2×C4×C67 | 1 | 6 | yes | — |
| 122 | C4×Q8 | C23×C67 | 1 | 2 | yes | — |
| 123 | C4×D4 | C2×C4×C67 | 1 | 18 | yes | — |
| 124 | C4×D4 | C23×C67 | 1 | 18 | yes | — |
| 125 | #117 | C2×C4×C67 | 1 | 18 | yes | — |
| 126 | C2×C42 | C23×C67 | 1 | 9 | yes | — |
| 127 | C4⋊C8 | C23×C67 | 1 | 18 | yes | — |
| 128 | C4⋊C8 | C23×C67 | 1 | 6 | yes | — |
| 129 | C22⋊C8 | C23×C67 | 1 | 36 | yes | — |
| 130 | C4×C8 | C23×C67 | 1 | 6 | yes | — |
| 131 | C4×C8 | C23×C67 | 1 | 18 | yes | — |
| 132 | #41 | — | 2 | 24 | no | — |
| 133 | #41 | — | 4 | 6 | no | — |
| 134 | #41 | — | 4 | 6 | no | — |
| 135 | C2×Q8 | C22×C4×C67 | 1 | 6 | yes | — |
| 136 | C2×Q8 | C22×C4×C67 | 1 | 2 | yes | — |
| 137 | C2×D4 | C22×C4×C67 | 1 | 18 | yes | — |
| 138 | C2×D4 | C22×C4×C67 | 1 | 18 | yes | — |
| 139 | C22×C4 | C22×C4×C67 | 1 | 18 | yes | — |
| 140 | C22×C4 | C24×C67 | 1 | 9 | yes | — |
| 141 | M16 | — | 4 | 18 | no | — |
| 142 | C2×C8 | — | 2 | 18 | no | — |
| 143 | C2×C8 | — | 4 | 9 | no | — |
| 144 | C2×C8 | C24×C67 | 1 | 6 | yes | — |
| 145 | C2×C8 | C24×C67 | 1 | 9 | yes | — |
| 146 | C2×C8 | C24×C67 | 1 | 1 | yes | characteristic |
| 147 | C4⋊C4 | C22×C4×C67 | 1 | 6 | yes | — |
| 148 | C4⋊C4 | C22×C4×C67 | 1 | 18 | yes | — |
| 149 | C22⋊C4 | C22×C4×C67 | 1 | 36 | yes | — |
| 150 | C42 | C22×C4×C67 | 1 | 9 | yes | — |
| 151 | C42 | C22×C4×C67 | 1 | 9 | yes | — |
| 152 | C42 | C24×C67 | 1 | 6 | yes | — |
| 153 | C23 | C23×C4×C67 | 1 | 9 | yes | — |
| 154 | Q8 | — | 4 | 6 | no | — |
| 155 | Q8 | #131×C67 | 1 | 8 | yes | complemented |
| 156 | D4 | — | 2 | 36 | no | — |
| 157 | D4 | — | 4 | 18 | no | — |
| 158 | C2×C4 | — | 2 | 36 | no | — |
| 159 | C2×C4 | — | 2 | 9 | no | — |
| 160 | C2×C4 | — | 2 | 9 | no | — |
| 161 | C2×C4 | C23×C4×C67 | 1 | 6 | yes | — |
| 162 | C2×C4 | C23×C4×C67 | 1 | 9 | yes | — |
| 163 | C2×C4 | C23×C4×C67 | 1 | 6 | yes | — |
| 164 | C2×C4 | C25×C67 | 1 | 1 | yes | characteristic |
| 165 | C8 | — | 2 | 9 | no | — |
| 166 | C8 | — | 2 | 6 | no | — |
| 167 | C8 | H(5,𝔽2)×C67 | 1 | 2 | yes | — |
| 168 | C22 | — | 2 | 18 | no | — |
| 169 | C22 | — | 2 | 9 | no | — |
| 170 | C22 | C24×C4×C67 | 1 | 1 | yes | characteristic |
| 171 | C4 | — | 2 | 6 | no | — |
| 172 | C4 | — | 2 | 9 | no | — |
| 173 | C4 | C2×#131×C67 | 1 | 12 | yes | — |
| 174 | C4 | C2×H(5,𝔽2)×C67 | 1 | 1 | yes | characteristic |
| 175 | C4 | #585×C67 | 1 | 1 | yes | characteristic |
| 176 | C2 | — | 4 | 9 | no | — |
| 177 | C2 | C4×H(5,𝔽2)×C67 | 1 | 1 | yes | characteristic |
| 178 | C2 | C22×#131×C67 | 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