← #33238974
Subgroups — #33238974
Order 18688.
706 conjugacy classes of subgroups.
The subgroup lattice has 228 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#17989004 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #131×Dic73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22611691 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #22611689 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #22611686 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | C2×#17988405 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#504×C73 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#14556598 | C4 | 1 | 1 | yes | characteristic |
| 9 | #41×Dic73 | C4 | 1 | 1 | yes | characteristic |
| 10 | #17989004 | — | 2 | 4 | no | — |
| 11 | C2×#14556531 | C22 | 1 | 3 | yes | — |
| 12 | C22×#11924003 | C22 | 1 | 3 | yes | — |
| 13 | #17988545 | C4 | 1 | 3 | yes | — |
| 14 | #17988542 | C22 | 1 | 3 | yes | — |
| 15 | M16×Dic73 | C4 | 1 | 3 | yes | — |
| 16 | C2×C8×Dic73 | C22 | 1 | 3 | yes | — |
| 17 | #17988405 | C22 | 1 | 1 | yes | characteristic |
| 18 | #17988405 | C22 | 1 | 3 | yes | — |
| 19 | #17988405 | C22 | 1 | 3 | yes | — |
| 20 | #17988405 | C22 | 1 | 3 | yes | — |
| 21 | #17988405 | C22 | 1 | 6 | yes | — |
| 22 | C2×#131×C73 | C22 | 1 | 1 | yes | characteristic |
| 23 | #504×C73 | — | 2 | 4 | no | — |
| 24 | C2×M32×C73 | C22 | 1 | 3 | yes | — |
| 25 | C22×C16×C73 | C22 | 1 | 3 | yes | — |
| 26 | #14556598 | — | 2 | 4 | no | — |
| 27 | C2×#11924012 | C2×C4 | 1 | 3 | yes | — |
| 28 | C22×#10596831 | C2×C4 | 1 | 3 | yes | — |
| 29 | Q8×Dic73 | C8 | 1 | 1 | yes | characteristic |
| 30 | Q8×Dic73 | C8 | 1 | 1 | yes | characteristic |
| 31 | D4×Dic73 | C8 | 1 | 3 | yes | — |
| 32 | D4×Dic73 | C8 | 1 | 3 | yes | — |
| 33 | #14556550 | C2×C4 | 1 | 3 | yes | — |
| 34 | C2×C4×Dic73 | C2×C4 | 1 | 3 | yes | — |
| 35 | #14556531 | — | 2 | 6 | no | — |
| 36 | C2×#11924003 | — | 2 | 6 | no | — |
| 37 | C2×#11924003 | C23 | 1 | 1 | yes | characteristic |
| 38 | C2×#11924003 | C23 | 1 | 3 | yes | — |
| 39 | #14556501 | C2×C4 | 1 | 6 | yes | — |
| 40 | C8×Dic73 | C2×C4 | 1 | 3 | yes | — |
| 41 | C8×Dic73 | C2×C4 | 1 | 3 | yes | — |
| 42 | C8×Dic73 | C23 | 1 | 1 | yes | characteristic |
| 43 | C8×Dic73 | C23 | 1 | 3 | yes | — |
| 44 | C2×#41×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #131×C73 | D4 | 1 | 4 | yes | — |
| 46 | #131×C73 | Q8 | 1 | 4 | yes | — |
| 47 | C2×M16×C73 | C2×C4 | 1 | 3 | yes | — |
| 48 | C22×C8×C73 | C23 | 1 | 3 | yes | — |
| 49 | M32×C73 | — | 2 | 6 | no | — |
| 50 | C2×C16×C73 | — | 2 | 6 | no | — |
| 51 | C2×C16×C73 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×C16×C73 | C23 | 1 | 3 | yes | — |
| 53 | C22×Dic73 | C2×C8 | 1 | 3 | yes | — |
| 54 | C22×Dic73 | C2×C8 | 1 | 3 | yes | — |
| 55 | #11924012 | — | 2 | 6 | no | — |
| 56 | C2×#10596831 | — | 2 | 6 | no | — |
| 57 | C2×#10596831 | C22×C4 | 1 | 1 | yes | characteristic |
| 58 | C2×#10596831 | C22×C4 | 1 | 3 | yes | — |
| 59 | C4⋊Dic73 | C2×C8 | 1 | 3 | yes | — |
| 60 | C4⋊Dic73 | C2×C8 | 1 | 3 | yes | — |
| 61 | C22⋊Dic73 | C2×C8 | 1 | 6 | yes | — |
| 62 | C4×Dic73 | C2×C8 | 1 | 3 | yes | — |
| 63 | C4×Dic73 | C2×C8 | 1 | 3 | yes | — |
| 64 | C4×Dic73 | C22×C4 | 1 | 1 | yes | characteristic |
| 65 | C4×Dic73 | C22×C4 | 1 | 3 | yes | — |
| 66 | #11924003 | — | 2 | 1 | no | — |
| 67 | #11924003 | — | 2 | 3 | no | — |
| 68 | #41×C73 | C4⋊C4 | 1 | 4 | yes | — |
| 69 | #41×C73 | M16 | 1 | 4 | yes | — |
| 70 | C2×Q8×C73 | C2×C8 | 1 | 1 | yes | characteristic |
| 71 | C2×D4×C73 | C2×C8 | 1 | 3 | yes | — |
| 72 | C22×C4×C73 | C22×C4 | 1 | 3 | yes | — |
| 73 | M16×C73 | C4⋊C4 | 1 | 12 | yes | — |
| 74 | C2×C8×C73 | C22×C4 | 1 | 3 | yes | — |
| 75 | C2×C8×C73 | C2×D4 | 1 | 6 | yes | — |
| 76 | C2×C8×C73 | C2×Q8 | 1 | 6 | yes | — |
| 77 | C2×C8×C73 | C24 | 1 | 1 | yes | characteristic |
| 78 | C16×C73 | — | 2 | 1 | no | — |
| 79 | C16×C73 | — | 2 | 3 | no | — |
| 80 | C23×C73 | C22×C8 | 1 | 3 | yes | — |
| 81 | Q8×C73 | C4⋊C8 | 1 | 4 | yes | — |
| 82 | D4×C73 | C4⋊C8 | 1 | 12 | yes | — |
| 83 | C2×C4×C73 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 84 | C2×C4×C73 | C22×C8 | 1 | 3 | yes | — |
| 85 | C2×C4×C73 | C2×M16 | 1 | 6 | yes | — |
| 86 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 87 | C2×Dic73 | — | 2 | 6 | no | — |
| 88 | C2×Dic73 | — | 4 | 3 | no | — |
| 89 | C2×Dic73 | C22×C8 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic73 | C22×C8 | 1 | 3 | yes | — |
| 91 | C2×Dic73 | C22×C8 | 1 | 3 | yes | — |
| 92 | C2×Dic73 | C22×C8 | 1 | 1 | yes | characteristic |
| 93 | C8×C73 | C2×C4⋊C4 | 1 | 6 | yes | — |
| 94 | C8×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 95 | C8×C73 | C22×Q8 | 1 | 1 | yes | characteristic |
| 96 | #10596831 | — | 2 | 1 | no | — |
| 97 | #10596831 | — | 2 | 3 | no | — |
| 98 | C22×C73 | — | 2 | 3 | no | — |
| 99 | C22×C73 | — | 2 | 3 | no | — |
| 100 | C22×C73 | C2×C4⋊C8 | 1 | 6 | yes | — |
| 101 | C22×C73 | C23×C8 | 1 | 1 | yes | characteristic |
| 102 | C4×C73 | C2×C4⋊C8 | 1 | 6 | yes | — |
| 103 | C4×C73 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 104 | C4×C73 | C22×M16 | 1 | 1 | yes | characteristic |
| 105 | Dic73 | — | 2 | 3 | no | — |
| 106 | Dic73 | — | 2 | 1 | no | — |
| 107 | Dic73 | — | 2 | 3 | no | — |
| 108 | Dic73 | #504 | 1 | 2 | yes | complemented |
| 109 | #33398 | — | 73 | 1 | no | maximal, Sylow |
| 110 | C2×C73 | — | 2 | 6 | no | — |
| 111 | C2×C73 | C22×C4⋊C8 | 1 | 1 | yes | characteristic |
| 112 | C2×C73 | C2×#504 | 1 | 1 | yes | characteristic |
| 113 | C2×C73 | #3407 | 1 | 1 | yes | characteristic |
| 114 | C2×#504 | — | 73 | 1 | no | — |
| 115 | C2×#504 | D73 | 1 | 1 | yes | characteristic |
| 116 | C4×#131 | — | 73 | 1 | no | — |
| 117 | #2151 | — | 73 | 3 | no | — |
| 118 | #2151 | — | 73 | 3 | no | — |
| 119 | #2150 | — | 73 | 3 | no | — |
| 120 | C2×C4⋊C16 | — | 73 | 3 | no | — |
| 121 | C73 | #33398 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 122 | C2×#131 | — | 73 | 1 | no | — |
| 123 | C2×#131 | C2×D73 | 1 | 1 | yes | characteristic |
| 124 | C4×#41 | — | 73 | 1 | no | — |
| 125 | #504 | — | 2 | 4 | no | — |
| 126 | #504 | — | 146 | 4 | no | — |
| 127 | C2×M32 | — | 73 | 3 | no | — |
| 128 | C2×M32 | C2×D73 | 1 | 3 | yes | — |
| 129 | C22×C16 | — | 73 | 3 | no | — |
| 130 | C22×C16 | C2×D73 | 1 | 3 | yes | — |
| 131 | #405 | — | 73 | 3 | no | — |
| 132 | #405 | — | 73 | 3 | no | — |
| 133 | C4×M16 | — | 73 | 3 | no | — |
| 134 | C2×C4×C8 | — | 73 | 3 | no | — |
| 135 | C4⋊C16 | — | 73 | 1 | no | — |
| 136 | C4⋊C16 | — | 73 | 3 | no | — |
| 137 | C4⋊C16 | — | 73 | 3 | no | — |
| 138 | C4⋊C16 | — | 73 | 3 | no | — |
| 139 | C4⋊C16 | — | 73 | 6 | no | — |
| 140 | C2×#41 | C4×D73 | 1 | 1 | yes | characteristic |
| 141 | #131 | — | 146 | 4 | no | — |
| 142 | #131 | Dic146 | 1 | 4 | yes | — |
| 143 | #131 | C22⋊D73 | 1 | 4 | yes | — |
| 144 | C2×M16 | — | 73 | 3 | no | — |
| 145 | C2×M16 | C4×D73 | 1 | 3 | yes | — |
| 146 | C22×C8 | — | 73 | 3 | no | — |
| 147 | C22×C8 | C22×D73 | 1 | 3 | yes | — |
| 148 | C4×Q8 | — | 73 | 1 | no | — |
| 149 | C4×Q8 | — | 73 | 1 | no | — |
| 150 | C4×D4 | — | 73 | 3 | no | — |
| 151 | C4×D4 | — | 73 | 3 | no | — |
| 152 | #117 | — | 73 | 3 | no | — |
| 153 | C2×C42 | — | 73 | 3 | no | — |
| 154 | M32 | — | 2 | 6 | no | — |
| 155 | M32 | — | 146 | 6 | no | — |
| 156 | C2×C16 | — | 2 | 6 | no | — |
| 157 | C2×C16 | — | 73 | 1 | no | — |
| 158 | C2×C16 | — | 73 | 3 | no | — |
| 159 | C2×C16 | — | 146 | 6 | no | — |
| 160 | C2×C16 | C22×D73 | 1 | 1 | yes | characteristic |
| 161 | C2×C16 | C22×D73 | 1 | 3 | yes | — |
| 162 | #97 | — | 73 | 6 | no | — |
| 163 | C4×C8 | — | 73 | 3 | no | — |
| 164 | C4×C8 | — | 73 | 3 | no | — |
| 165 | C4×C8 | — | 73 | 1 | no | — |
| 166 | C4×C8 | — | 73 | 3 | no | — |
| 167 | #41 | #11924007 | 1 | 4 | yes | — |
| 168 | #41 | #11924011 | 1 | 4 | yes | — |
| 169 | C2×Q8 | C8×D73 | 1 | 1 | yes | characteristic |
| 170 | C2×D4 | C8×D73 | 1 | 3 | yes | — |
| 171 | C22×C4 | — | 73 | 3 | no | — |
| 172 | C22×C4 | — | 73 | 3 | no | — |
| 173 | C22×C4 | C2×C4×D73 | 1 | 3 | yes | — |
| 174 | M16 | — | 146 | 6 | no | — |
| 175 | M16 | #11924007 | 1 | 12 | yes | — |
| 176 | C2×C8 | — | 73 | 1 | no | — |
| 177 | C2×C8 | — | 73 | 3 | no | — |
| 178 | C2×C8 | — | 146 | 6 | no | — |
| 179 | C2×C8 | C2×C4×D73 | 1 | 3 | yes | — |
| 180 | C2×C8 | C2×C22⋊D73 | 1 | 6 | yes | — |
| 181 | C2×C8 | C2×Dic146 | 1 | 6 | yes | — |
| 182 | C2×C8 | C23×D73 | 1 | 1 | yes | characteristic |
| 183 | C4⋊C4 | — | 73 | 3 | no | — |
| 184 | C4⋊C4 | — | 73 | 3 | no | — |
| 185 | C22⋊C4 | — | 73 | 6 | no | — |
| 186 | C42 | — | 73 | 3 | no | — |
| 187 | C42 | — | 73 | 3 | no | — |
| 188 | C42 | — | 73 | 1 | no | — |
| 189 | C42 | — | 73 | 3 | no | — |
| 190 | C16 | — | 2 | 1 | no | — |
| 191 | C16 | — | 2 | 3 | no | — |
| 192 | C16 | — | 146 | 1 | no | — |
| 193 | C16 | — | 146 | 3 | no | — |
| 194 | C23 | C2×C8×D73 | 1 | 3 | yes | — |
| 195 | Q8 | #14556520 | 1 | 4 | yes | — |
| 196 | D4 | #14556520 | 1 | 12 | yes | — |
| 197 | C2×C4 | — | 292 | 3 | no | — |
| 198 | C2×C4 | — | 73 | 1 | no | — |
| 199 | C2×C4 | — | 73 | 1 | no | — |
| 200 | C2×C4 | — | 73 | 3 | no | — |
| 201 | C2×C4 | — | 73 | 3 | no | — |
| 202 | C2×C4 | — | 146 | 6 | no | — |
| 203 | C2×C4 | C2×#11924007 | 1 | 6 | yes | — |
| 204 | C2×C4 | C2×C8×D73 | 1 | 3 | yes | — |
| 205 | C2×C4 | C2×#11924011 | 1 | 6 | yes | — |
| 206 | C2×C4 | C22×C4×D73 | 1 | 1 | yes | characteristic |
| 207 | C8 | — | 146 | 1 | no | — |
| 208 | C8 | — | 146 | 3 | no | — |
| 209 | C8 | C2×#11924007 | 1 | 6 | yes | — |
| 210 | C8 | C22×C22⋊D73 | 1 | 1 | yes | characteristic |
| 211 | C8 | C22×Dic146 | 1 | 1 | yes | characteristic |
| 212 | C22 | — | 2 | 3 | no | — |
| 213 | C22 | — | 2 | 3 | no | — |
| 214 | C22 | C2×#14556520 | 1 | 6 | yes | — |
| 215 | C22 | C22×C8×D73 | 1 | 1 | yes | characteristic |
| 216 | C4 | — | 73 | 2 | no | — |
| 217 | C4 | — | 146 | 3 | no | — |
| 218 | C4 | — | 146 | 1 | no | — |
| 219 | C4 | — | 146 | 3 | no | — |
| 220 | C4 | C2×#14556520 | 1 | 6 | yes | — |
| 221 | C4 | C22×#11924007 | 1 | 1 | yes | characteristic |
| 222 | C4 | C22×#11924011 | 1 | 1 | yes | characteristic |
| 223 | C2 | — | 2 | 6 | no | — |
| 224 | C2 | C22×#14556520 | 1 | 1 | yes | characteristic |
| 225 | C2 | #504×D73 | 1 | 1 | yes | characteristic |
| 226 | C2 | #22623032 | 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