← #34030097
Subgroups — #34030097
Order 18688.
658 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 | #22626586 | C2 | 1 | 2 | yes | maximal |
| 2 | #22626283 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #22626282 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C2×#17989514 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #504×D73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #17989656 | — | 2 | 2 | no | — |
| 7 | #17989598 | — | 2 | 6 | no | — |
| 8 | #17989597 | C22 | 1 | 6 | yes | — |
| 9 | C2×#14556660 | C22 | 1 | 6 | yes | — |
| 10 | #17989514 | C22 | 1 | 3 | yes | — |
| 11 | #17989514 | C22 | 1 | 6 | yes | — |
| 12 | #17989514 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17989513 | C22 | 1 | 6 | yes | — |
| 14 | #131×D73 | C22 | 1 | 1 | yes | characteristic |
| 15 | #17989005 | C4 | 1 | 3 | yes | complemented |
| 16 | #17989004 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #17989003 | C4 | 1 | 3 | yes | complemented |
| 18 | M32×D73 | C22 | 1 | 3 | yes | — |
| 19 | C2×C16×D73 | C22 | 1 | 3 | yes | — |
| 20 | #504×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | Q8×#64408 | — | 4 | 2 | no | — |
| 22 | D4×#64408 | — | 4 | 6 | no | — |
| 23 | #14556670 | — | 2 | 6 | no | — |
| 24 | C2×C4⋊#64408 | — | 2 | 6 | no | — |
| 25 | #14556660 | — | 2 | 6 | no | — |
| 26 | #14556660 | C23 | 1 | 2 | yes | — |
| 27 | #14556660 | C23 | 1 | 6 | yes | — |
| 28 | #14556659 | — | 2 | 6 | no | — |
| 29 | #41×D73 | D4 | 1 | 1 | yes | characteristic |
| 30 | #14556599 | Q8 | 1 | 3 | yes | — |
| 31 | #14556598 | Q8 | 1 | 1 | yes | characteristic |
| 32 | #14556597 | C2×C4 | 1 | 3 | yes | — |
| 33 | M16×D73 | D4 | 1 | 3 | yes | — |
| 34 | C2×C8×D73 | C23 | 1 | 3 | yes | — |
| 35 | #14556531 | C2×C4 | 1 | 3 | yes | complemented |
| 36 | #14556530 | C2×C4 | 1 | 6 | yes | complemented |
| 37 | C2×#11924003 | C2×C4 | 1 | 3 | yes | complemented |
| 38 | C16×D73 | C2×C4 | 1 | 3 | yes | complemented |
| 39 | C16×D73 | C2×C4 | 1 | 3 | yes | complemented |
| 40 | C16×D73 | C23 | 1 | 1 | yes | characteristic |
| 41 | C16×D73 | C23 | 1 | 3 | yes | — |
| 42 | #131×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 43 | M32×C73 | C2×C4 | 1 | 3 | yes | complemented |
| 44 | C2×C16×C73 | C2×C4 | 1 | 3 | yes | complemented |
| 45 | C22×#64408 | — | 4 | 6 | no | — |
| 46 | C4⋊#64408 | — | 2 | 2 | no | — |
| 47 | C4⋊#64408 | — | 2 | 6 | no | — |
| 48 | C4⋊#64408 | — | 4 | 6 | no | — |
| 49 | C22⋊#64408 | — | 4 | 6 | no | — |
| 50 | C4×#64408 | — | 4 | 6 | no | — |
| 51 | #11924029 | Q16 | 1 | 1 | yes | characteristic |
| 52 | #11924028 | C4⋊C4 | 1 | 3 | yes | — |
| 53 | #11924027 | Q16 | 1 | 3 | yes | — |
| 54 | Q8×D73 | D8 | 1 | 1 | yes | characteristic |
| 55 | D4×D73 | D8 | 1 | 3 | yes | — |
| 56 | C2×C4×D73 | C2×D4 | 1 | 3 | yes | — |
| 57 | #11924012 | C4⋊C4 | 1 | 3 | yes | — |
| 58 | #11924011 | C4⋊C4 | 1 | 6 | yes | — |
| 59 | C2×#10596831 | C2×Q8 | 1 | 3 | yes | — |
| 60 | C8×D73 | C22×C4 | 1 | 3 | yes | — |
| 61 | C8×D73 | C2×D4 | 1 | 3 | yes | — |
| 62 | C8×D73 | C2×Q8 | 1 | 3 | yes | — |
| 63 | C8×D73 | C24 | 1 | 1 | yes | characteristic |
| 64 | #11924003 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | #11924003 | C22×C4 | 1 | 3 | yes | — |
| 66 | #41×C73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 67 | M16×C73 | C4⋊C4 | 1 | 3 | yes | — |
| 68 | C2×C8×C73 | C22×C4 | 1 | 3 | yes | — |
| 69 | C16×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | C16×C73 | C22×C4 | 1 | 3 | yes | — |
| 71 | C22×D73 | C2×D8 | 1 | 3 | yes | — |
| 72 | C2×#64408 | — | 4 | 2 | no | — |
| 73 | C2×#64408 | — | 4 | 6 | no | — |
| 74 | C2×#64408 | — | 16 | 6 | no | — |
| 75 | Q8×C73 | #107 | 1 | 1 | yes | characteristic |
| 76 | D4×C73 | #107 | 1 | 3 | yes | — |
| 77 | C2×C4×C73 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 78 | C22⋊D73 | #107 | 1 | 6 | yes | — |
| 79 | C2×Dic73 | C2×Q16 | 1 | 3 | yes | — |
| 80 | D292 | #107 | 1 | 3 | yes | — |
| 81 | C4×D73 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 82 | C4×D73 | C2×D8 | 1 | 3 | yes | — |
| 83 | C4×D73 | C2×Q16 | 1 | 3 | yes | — |
| 84 | C4×D73 | C22×D4 | 1 | 1 | yes | characteristic |
| 85 | Dic146 | #107 | 1 | 3 | yes | — |
| 86 | C8×C73 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 87 | C8×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 88 | #10596831 | C2×C4⋊C4 | 1 | 3 | yes | — |
| 89 | #10596831 | C22×Q8 | 1 | 1 | yes | characteristic |
| 90 | C22×C73 | C2×#107 | 1 | 3 | yes | — |
| 91 | C2×D73 | — | 2 | 6 | no | — |
| 92 | C2×D73 | C2×#107 | 1 | 3 | yes | — |
| 93 | C2×D73 | C22×D8 | 1 | 1 | yes | characteristic |
| 94 | #64408 | — | 8 | 2 | no | — |
| 95 | #64408 | — | 8 | 6 | no | — |
| 96 | C4×C73 | C2×#107 | 1 | 3 | yes | — |
| 97 | C4×C73 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 98 | Dic73 | C2×#107 | 1 | 3 | yes | — |
| 99 | Dic73 | C22×Q16 | 1 | 1 | yes | characteristic |
| 100 | #33411 | — | 73 | 1 | no | maximal, Sylow |
| 101 | C2×C73 | — | 2 | 3 | no | — |
| 102 | C2×C73 | C22×#107 | 1 | 1 | yes | characteristic |
| 103 | D73 | — | 2 | 3 | no | — |
| 104 | D73 | #3416 | 1 | 2 | yes | — |
| 105 | C2×#504 | — | 73 | 1 | no | — |
| 106 | #2913 | — | 73 | 2 | no | — |
| 107 | #2159 | — | 73 | 6 | no | — |
| 108 | #2158 | — | 73 | 3 | no | — |
| 109 | C2×#367 | — | 73 | 3 | no | — |
| 110 | C73 | #33411 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 111 | C2×#131 | — | 73 | 1 | no | — |
| 112 | #520 | — | 146 | 2 | no | — |
| 113 | #504 | — | 73 | 1 | no | — |
| 114 | #504 | — | 73 | 3 | no | — |
| 115 | #504 | — | 73 | 3 | no | — |
| 116 | #504 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 117 | C2×M32 | — | 73 | 3 | no | — |
| 118 | C22×C16 | — | 73 | 3 | no | — |
| 119 | #428 | — | 146 | 6 | no | — |
| 120 | #427 | — | 73 | 6 | no | — |
| 121 | C2×#107 | — | 73 | 6 | no | — |
| 122 | #367 | — | 73 | 3 | no | — |
| 123 | #367 | — | 73 | 6 | no | — |
| 124 | #367 | — | 73 | 1 | no | — |
| 125 | #366 | — | 73 | 6 | no | — |
| 126 | C2×#41 | — | 73 | 1 | no | — |
| 127 | #131 | — | 73 | 1 | no | — |
| 128 | #131 | — | 73 | 3 | no | — |
| 129 | #131 | — | 73 | 3 | no | — |
| 130 | #131 | C2×#64408 | 1 | 1 | yes | characteristic |
| 131 | C2×M16 | — | 73 | 3 | no | — |
| 132 | C22×C8 | — | 73 | 3 | no | — |
| 133 | C4×Q8 | — | 292 | 2 | no | — |
| 134 | C4×D4 | — | 292 | 6 | no | — |
| 135 | #117 | — | 146 | 6 | no | — |
| 136 | C2×C4⋊C4 | — | 146 | 6 | no | — |
| 137 | M32 | — | 73 | 3 | no | — |
| 138 | M32 | — | 73 | 6 | no | — |
| 139 | M32 | C2×#64408 | 1 | 3 | yes | complemented |
| 140 | C2×C16 | — | 73 | 3 | no | — |
| 141 | C2×C16 | — | 73 | 3 | no | — |
| 142 | C2×C16 | — | 73 | 1 | no | — |
| 143 | C2×C16 | — | 73 | 3 | no | — |
| 144 | C2×C16 | — | 73 | 3 | no | — |
| 145 | C2×C16 | C2×#64408 | 1 | 3 | yes | complemented |
| 146 | #107 | — | 73 | 2 | no | — |
| 147 | #107 | — | 73 | 6 | no | — |
| 148 | #107 | — | 146 | 6 | no | — |
| 149 | #106 | — | 146 | 6 | no | — |
| 150 | #41 | — | 73 | 1 | no | — |
| 151 | #41 | — | 73 | 3 | no | — |
| 152 | #41 | — | 73 | 3 | no | — |
| 153 | #41 | C4⋊#64408 | 1 | 1 | yes | characteristic |
| 154 | C2×Q8 | — | 73 | 1 | no | — |
| 155 | C2×D4 | — | 73 | 3 | no | — |
| 156 | C22×C4 | — | 292 | 6 | no | — |
| 157 | C22×C4 | — | 73 | 3 | no | — |
| 158 | M16 | — | 73 | 3 | no | — |
| 159 | M16 | — | 73 | 6 | no | — |
| 160 | M16 | C4⋊#64408 | 1 | 3 | yes | — |
| 161 | C2×C8 | — | 73 | 3 | no | — |
| 162 | C2×C8 | — | 73 | 3 | no | — |
| 163 | C2×C8 | — | 73 | 1 | no | — |
| 164 | C2×C8 | — | 73 | 3 | no | — |
| 165 | C2×C8 | — | 73 | 3 | no | — |
| 166 | C2×C8 | C22×#64408 | 1 | 3 | yes | — |
| 167 | C4⋊C4 | — | 292 | 6 | no | — |
| 168 | C4⋊C4 | — | 146 | 2 | no | — |
| 169 | C4⋊C4 | — | 146 | 6 | no | — |
| 170 | C22⋊C4 | — | 292 | 6 | no | — |
| 171 | C42 | — | 292 | 6 | no | — |
| 172 | C16 | — | 73 | 1 | no | — |
| 173 | C16 | — | 73 | 3 | no | — |
| 174 | C16 | C22×#64408 | 1 | 1 | yes | characteristic |
| 175 | C16 | C22×#64408 | 1 | 3 | yes | — |
| 176 | C23 | — | 73 | 3 | no | — |
| 177 | Q8 | — | 73 | 3 | no | — |
| 178 | Q8 | #14556660 | 1 | 1 | yes | characteristic |
| 179 | D4 | — | 73 | 6 | no | — |
| 180 | D4 | — | 73 | 3 | no | — |
| 181 | D4 | #14556660 | 1 | 3 | yes | — |
| 182 | C2×C4 | — | 292 | 2 | no | — |
| 183 | C2×C4 | — | 292 | 6 | no | — |
| 184 | C2×C4 | — | 73 | 3 | no | — |
| 185 | C2×C4 | — | 73 | 1 | no | — |
| 186 | C2×C4 | — | 73 | 3 | no | — |
| 187 | C2×C4 | — | 73 | 3 | no | — |
| 188 | C2×C4 | — | 73 | 3 | no | — |
| 189 | C2×C4 | — | 1168 | 6 | no | — |
| 190 | C2×C4 | C2×C4⋊#64408 | 1 | 3 | yes | — |
| 191 | C8 | — | 73 | 1 | no | — |
| 192 | C8 | — | 73 | 3 | no | — |
| 193 | C8 | C2×C4⋊#64408 | 1 | 3 | yes | — |
| 194 | C8 | C23×#64408 | 1 | 1 | yes | characteristic |
| 195 | C22 | — | 73 | 1 | no | — |
| 196 | C22 | — | 73 | 3 | no | — |
| 197 | C22 | — | 146 | 6 | no | — |
| 198 | C22 | C2×#14556660 | 1 | 3 | yes | — |
| 199 | C4 | — | 584 | 6 | no | — |
| 200 | C4 | — | 584 | 2 | no | — |
| 201 | C4 | — | 73 | 1 | no | — |
| 202 | C4 | — | 73 | 3 | no | — |
| 203 | C4 | C2×#14556660 | 1 | 3 | yes | — |
| 204 | C4 | C22×C4⋊#64408 | 1 | 1 | yes | characteristic |
| 205 | C2 | — | 2 | 3 | no | — |
| 206 | C2 | — | 73 | 2 | no | — |
| 207 | C2 | — | 146 | 3 | no | — |
| 208 | C2 | C22×#14556660 | 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