← #34441664
Subgroups — #34441664
Order 20224.
674 conjugacy classes of subgroups.
The subgroup lattice has 254 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#19098995 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23772277 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #23765277 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #23765272 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C4×#14579106 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | C2×#19098391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #23765113 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C79×#2108 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#14579183 | C22 | 1 | 2 | yes | — |
| 10 | #19099043 | — | 2 | 2 | no | — |
| 11 | #19098995 | C4 | 1 | 8 | yes | complemented |
| 12 | C2×Dic632 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#14579106 | C22 | 1 | 2 | yes | — |
| 14 | C2×D1264 | C22 | 1 | 1 | yes | characteristic |
| 15 | #19098665 | — | 2 | 4 | no | — |
| 16 | C4×Dic316 | C22 | 1 | 4 | yes | — |
| 17 | C4×D632 | C22 | 1 | 4 | yes | — |
| 18 | C2×#14579095 | C22 | 1 | 2 | yes | — |
| 19 | #19098565 | — | 2 | 2 | no | — |
| 20 | #19098391 | C22 | 1 | 2 | yes | — |
| 21 | #19098391 | C22 | 1 | 2 | yes | — |
| 22 | #19098368 | C22 | 1 | 4 | yes | — |
| 23 | #19098365 | C22 | 1 | 4 | yes | — |
| 24 | C2×M32×C79 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×C16×C79 | C22 | 1 | 1 | yes | characteristic |
| 26 | #405×C79 | C22 | 1 | 1 | yes | characteristic |
| 27 | #346×C79 | C22 | 1 | 2 | yes | — |
| 28 | C4×C16×C79 | C22 | 1 | 2 | yes | — |
| 29 | C2×#11929624 | — | 2 | 2 | no | — |
| 30 | #14579183 | — | 2 | 4 | no | — |
| 31 | #14579183 | C2×C4 | 1 | 8 | yes | complemented |
| 32 | C2×Dic316 | C23 | 1 | 2 | yes | — |
| 33 | C2×#11929613 | — | 2 | 2 | no | — |
| 34 | C2×D632 | C23 | 1 | 2 | yes | — |
| 35 | C4×Dic158 | — | 2 | 4 | no | — |
| 36 | C4×D316 | — | 2 | 4 | no | — |
| 37 | (C22⋊D79)⋊C4 | — | 4 | 4 | no | — |
| 38 | #14579119 | — | 4 | 2 | no | — |
| 39 | C2×C4⋊Dic79 | — | 2 | 2 | no | — |
| 40 | C4⋊C4×D79 | — | 4 | 2 | no | — |
| 41 | Dic632 | C2×C4 | 1 | 4 | yes | complemented |
| 42 | #14579106 | C2×C4 | 1 | 8 | yes | complemented |
| 43 | D1264 | C2×C4 | 1 | 4 | yes | complemented |
| 44 | #14579095 | — | 2 | 2 | no | — |
| 45 | #14579095 | C23 | 1 | 4 | yes | — |
| 46 | #14579086 | — | 2 | 4 | no | — |
| 47 | #14579083 | — | 2 | 4 | no | — |
| 48 | C2×M16×C79 | D4 | 1 | 1 | yes | characteristic |
| 49 | C22×C8×C79 | C23 | 1 | 1 | yes | characteristic |
| 50 | #117×C79 | D4 | 1 | 1 | yes | characteristic |
| 51 | M32×C79 | — | 2 | 2 | no | — |
| 52 | C2×C16×C79 | C2×C4 | 1 | 4 | yes | complemented |
| 53 | C2×C16×C79 | C23 | 1 | 2 | yes | — |
| 54 | C2×C16×C79 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×C16×C79 | C23 | 1 | 1 | yes | characteristic |
| 56 | #97×C79 | D4 | 1 | 2 | yes | — |
| 57 | C4×C8×C79 | C23 | 1 | 2 | yes | — |
| 58 | #11929624 | — | 2 | 8 | no | — |
| 59 | #11929624 | — | 4 | 4 | no | — |
| 60 | C2×Dic158 | — | 2 | 2 | no | — |
| 61 | C2×D316 | — | 2 | 2 | no | — |
| 62 | C2×C22⋊D79 | — | 4 | 2 | no | — |
| 63 | C22×Dic79 | — | 4 | 2 | no | — |
| 64 | C2×C4×D79 | — | 4 | 2 | no | — |
| 65 | C2×C4×D79 | — | 4 | 4 | no | — |
| 66 | Dic316 | — | 2 | 2 | no | — |
| 67 | Dic316 | C22×C4 | 1 | 4 | yes | — |
| 68 | #11929613 | — | 2 | 8 | no | — |
| 69 | D632 | — | 2 | 2 | no | — |
| 70 | D632 | C22×C4 | 1 | 4 | yes | — |
| 71 | C4⋊Dic79 | — | 2 | 4 | no | — |
| 72 | C4⋊Dic79 | — | 4 | 2 | no | — |
| 73 | Dic79⋊C4 | — | 4 | 4 | no | — |
| 74 | (C2×D79)⋊C4 | — | 4 | 4 | no | — |
| 75 | C4×Dic79 | — | 4 | 4 | no | — |
| 76 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | M16×C79 | — | 2 | 2 | no | — |
| 78 | C2×C8×C79 | C22×C4 | 1 | 2 | yes | — |
| 79 | C2×C8×C79 | C2×D4 | 1 | 2 | yes | — |
| 80 | C2×C8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C79 | #41 | 1 | 2 | yes | — |
| 82 | C2×C8×C79 | C24 | 1 | 1 | yes | characteristic |
| 83 | C4⋊C4×C79 | D8 | 1 | 2 | yes | — |
| 84 | C22⋊C4×C79 | D8 | 1 | 2 | yes | — |
| 85 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 86 | C16×C79 | — | 2 | 2 | no | — |
| 87 | C16×C79 | C22×C4 | 1 | 2 | yes | — |
| 88 | C16×C79 | C22×C4 | 1 | 2 | yes | — |
| 89 | C23×C79 | C2×D8 | 1 | 1 | yes | characteristic |
| 90 | C22×D79 | — | 4 | 2 | no | — |
| 91 | C2×C4×C79 | C4×D4 | 1 | 2 | yes | — |
| 92 | C2×C4×C79 | C2×D8 | 1 | 4 | yes | — |
| 93 | C2×C4×C79 | C2×D8 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×C79 | #135 | 1 | 2 | yes | — |
| 95 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 96 | C22⋊D79 | — | 4 | 8 | no | — |
| 97 | C2×Dic79 | — | 4 | 2 | no | — |
| 98 | C2×Dic79 | — | 4 | 4 | no | — |
| 99 | C2×Dic79 | — | 16 | 2 | no | — |
| 100 | D316 | — | 2 | 4 | no | — |
| 101 | D316 | — | 4 | 2 | no | — |
| 102 | C4×D79 | — | 4 | 8 | no | — |
| 103 | C4×D79 | — | 16 | 4 | no | — |
| 104 | Dic158 | — | 2 | 4 | no | — |
| 105 | Dic158 | — | 4 | 2 | no | — |
| 106 | C8×C79 | — | 2 | 2 | no | — |
| 107 | C8×C79 | C4×D4 | 1 | 2 | yes | — |
| 108 | C8×C79 | C23×C4 | 1 | 1 | yes | characteristic |
| 109 | C8×C79 | C2×#41 | 1 | 1 | yes | characteristic |
| 110 | C22×C79 | — | 2 | 2 | no | — |
| 111 | C22×C79 | C4×D8 | 1 | 2 | yes | — |
| 112 | C22×C79 | C22×D8 | 1 | 1 | yes | characteristic |
| 113 | C2×D79 | — | 4 | 4 | no | — |
| 114 | C2×D79 | — | 8 | 2 | no | — |
| 115 | C2×D79 | — | 8 | 2 | no | — |
| 116 | C4×C79 | — | 2 | 4 | no | — |
| 117 | C4×C79 | C4×D8 | 1 | 2 | yes | — |
| 118 | C4×C79 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 119 | C4×C79 | C2×#135 | 1 | 1 | yes | characteristic |
| 120 | Dic79 | — | 4 | 4 | no | — |
| 121 | Dic79 | — | 8 | 4 | no | — |
| 122 | #33460 | — | 79 | 1 | no | maximal, Sylow |
| 123 | C2×C79 | — | 2 | 2 | no | — |
| 124 | C2×C79 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 125 | C2×C79 | #3416 | 1 | 2 | yes | — |
| 126 | D79 | — | 8 | 4 | no | — |
| 127 | C2×#508 | — | 79 | 1 | no | — |
| 128 | #2951 | — | 79 | 2 | no | — |
| 129 | #2177 | — | 79 | 2 | no | — |
| 130 | #2176 | — | 79 | 2 | no | — |
| 131 | C4×SD32 | — | 79 | 4 | no | — |
| 132 | C2×#367 | — | 79 | 1 | no | — |
| 133 | #2139 | — | 79 | 2 | no | — |
| 134 | #2108 | D79 | 1 | 1 | yes | characteristic, complemented |
| 135 | C79 | #33460 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 136 | C2×#135 | — | 79 | 2 | no | — |
| 137 | #520 | — | 158 | 2 | no | — |
| 138 | #508 | — | 79 | 8 | no | — |
| 139 | C2×Q32 | — | 79 | 1 | no | — |
| 140 | C2×SD32 | — | 79 | 2 | no | — |
| 141 | C2×D16 | — | 79 | 1 | no | — |
| 142 | C2×M32 | C2×D79 | 1 | 1 | yes | characteristic |
| 143 | C22×C16 | C2×D79 | 1 | 1 | yes | characteristic |
| 144 | #440 | — | 158 | 4 | no | — |
| 145 | C4×Q16 | — | 79 | 4 | no | — |
| 146 | C4×D8 | — | 79 | 4 | no | — |
| 147 | C2×#107 | — | 79 | 2 | no | — |
| 148 | #417 | — | 158 | 2 | no | — |
| 149 | #405 | C2×D79 | 1 | 1 | yes | characteristic |
| 150 | #367 | — | 79 | 2 | no | — |
| 151 | #367 | — | 79 | 2 | no | — |
| 152 | #358 | — | 79 | 4 | no | — |
| 153 | #357 | — | 79 | 4 | no | — |
| 154 | #346 | C2×D79 | 1 | 2 | yes | — |
| 155 | C4×C16 | C2×D79 | 1 | 2 | yes | — |
| 156 | C2×#41 | — | 158 | 2 | no | — |
| 157 | #135 | — | 79 | 8 | no | — |
| 158 | #135 | — | 158 | 4 | no | — |
| 159 | C2×Q16 | — | 79 | 2 | no | — |
| 160 | C2×SD16 | — | 158 | 2 | no | — |
| 161 | C2×D8 | — | 79 | 2 | no | — |
| 162 | C2×M16 | D316 | 1 | 1 | yes | characteristic |
| 163 | C22×C8 | C22×D79 | 1 | 1 | yes | characteristic |
| 164 | C4×Q8 | — | 158 | 4 | no | — |
| 165 | C4×D4 | — | 316 | 4 | no | — |
| 166 | C4×D4 | — | 158 | 4 | no | — |
| 167 | #117 | — | 316 | 2 | no | — |
| 168 | #117 | D316 | 1 | 1 | yes | characteristic |
| 169 | C2×C4⋊C4 | — | 316 | 2 | no | — |
| 170 | C2×C4⋊C4 | — | 158 | 2 | no | — |
| 171 | Q32 | — | 79 | 4 | no | — |
| 172 | SD32 | — | 79 | 8 | no | — |
| 173 | D16 | — | 79 | 4 | no | — |
| 174 | M32 | — | 2 | 2 | no | — |
| 175 | C2×C16 | C4×D79 | 1 | 4 | yes | complemented |
| 176 | C2×C16 | C22×D79 | 1 | 2 | yes | — |
| 177 | C2×C16 | C22×D79 | 1 | 1 | yes | characteristic |
| 178 | C2×C16 | C22×D79 | 1 | 1 | yes | characteristic |
| 179 | #107 | — | 79 | 4 | no | — |
| 180 | #107 | — | 158 | 2 | no | — |
| 181 | #103 | — | 158 | 4 | no | — |
| 182 | #102 | — | 158 | 4 | no | — |
| 183 | #97 | D316 | 1 | 2 | yes | — |
| 184 | C4×C8 | C22×D79 | 1 | 2 | yes | — |
| 185 | #41 | — | 316 | 4 | no | — |
| 186 | #41 | — | 158 | 8 | no | — |
| 187 | C2×Q8 | — | 158 | 2 | no | — |
| 188 | C2×D4 | — | 316 | 2 | no | — |
| 189 | C2×D4 | — | 158 | 2 | no | — |
| 190 | C22×C4 | — | 316 | 2 | no | — |
| 191 | C22×C4 | — | 316 | 2 | no | — |
| 192 | C22×C4 | — | 316 | 4 | no | — |
| 193 | C22×C4 | C2×D316 | 1 | 1 | yes | characteristic |
| 194 | Q16 | — | 79 | 4 | no | — |
| 195 | Q16 | — | 158 | 2 | no | — |
| 196 | SD16 | — | 158 | 8 | no | — |
| 197 | D8 | — | 79 | 4 | no | — |
| 198 | D8 | — | 158 | 2 | no | — |
| 199 | M16 | — | 2 | 2 | no | — |
| 200 | C2×C8 | C2×C4×D79 | 1 | 2 | yes | — |
| 201 | C2×C8 | C2×D316 | 1 | 2 | yes | — |
| 202 | C2×C8 | C2×D316 | 1 | 1 | yes | characteristic |
| 203 | C2×C8 | #11929624 | 1 | 2 | yes | — |
| 204 | C2×C8 | C23×D79 | 1 | 1 | yes | characteristic |
| 205 | C4⋊C4 | — | 316 | 4 | no | — |
| 206 | C4⋊C4 | — | 316 | 2 | no | — |
| 207 | C4⋊C4 | — | 158 | 4 | no | — |
| 208 | C4⋊C4 | D632 | 1 | 2 | yes | — |
| 209 | C22⋊C4 | — | 316 | 4 | no | — |
| 210 | C22⋊C4 | D632 | 1 | 2 | yes | — |
| 211 | C42 | — | 316 | 4 | no | — |
| 212 | C42 | C2×D316 | 1 | 2 | yes | — |
| 213 | C16 | — | 2 | 2 | no | — |
| 214 | C16 | C2×C4×D79 | 1 | 2 | yes | — |
| 215 | C16 | C2×C4×D79 | 1 | 2 | yes | — |
| 216 | C23 | — | 316 | 2 | no | — |
| 217 | C23 | C2×D632 | 1 | 1 | yes | characteristic |
| 218 | Q8 | — | 316 | 2 | no | — |
| 219 | Q8 | — | 158 | 4 | no | — |
| 220 | D4 | — | 316 | 8 | no | — |
| 221 | D4 | — | 316 | 2 | no | — |
| 222 | D4 | — | 158 | 4 | no | — |
| 223 | C2×C4 | — | 316 | 2 | no | — |
| 224 | C2×C4 | — | 316 | 8 | no | — |
| 225 | C2×C4 | — | 316 | 4 | no | — |
| 226 | C2×C4 | — | 1264 | 4 | no | — |
| 227 | C2×C4 | — | 1264 | 2 | no | — |
| 228 | C2×C4 | C4×D316 | 1 | 2 | yes | — |
| 229 | C2×C4 | C2×D632 | 1 | 4 | yes | — |
| 230 | C2×C4 | C2×D632 | 1 | 1 | yes | characteristic |
| 231 | C2×C4 | #14579183 | 1 | 2 | yes | — |
| 232 | C2×C4 | C22×D316 | 1 | 1 | yes | characteristic |
| 233 | C8 | — | 2 | 2 | no | — |
| 234 | C8 | C4×D316 | 1 | 2 | yes | — |
| 235 | C8 | C22×C4×D79 | 1 | 1 | yes | characteristic |
| 236 | C8 | C2×#11929624 | 1 | 1 | yes | characteristic |
| 237 | C22 | — | 2 | 2 | no | — |
| 238 | C22 | — | 316 | 4 | no | — |
| 239 | C22 | — | 632 | 2 | no | — |
| 240 | C22 | — | 632 | 2 | no | — |
| 241 | C22 | C4×D632 | 1 | 2 | yes | — |
| 242 | C22 | C22×D632 | 1 | 1 | yes | characteristic |
| 243 | C4 | — | 2 | 4 | no | — |
| 244 | C4 | — | 316 | 4 | no | — |
| 245 | C4 | — | 632 | 4 | no | — |
| 246 | C4 | C4×D632 | 1 | 2 | yes | — |
| 247 | C4 | C2×C4×D316 | 1 | 1 | yes | characteristic |
| 248 | C4 | C2×#14579183 | 1 | 1 | yes | characteristic |
| 249 | C2 | — | 2 | 2 | no | — |
| 250 | C2 | — | 632 | 4 | no | — |
| 251 | C2 | C2×C4×D632 | 1 | 1 | yes | characteristic |
| 252 | C2 | #23776548 | 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