← #33104875
Subgroups — #33104875
Order 18688.
658 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | M16×Dic146 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22618882 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#17988711 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22610707 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22610705 | C2 | 1 | 2 | yes | maximal |
| 6 | #22610703 | C2 | 1 | 2 | yes | maximal |
| 7 | #22610102 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #22610101 | C2 | 1 | 2 | yes | maximal |
| 9 | C4×#14556526 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #22609832 | C2 | 1 | 2 | yes | maximal |
| 11 | C73×#1950 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C2×C4×Dic146 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17988717 | — | 2 | 1 | no | — |
| 14 | #17988716 | — | 2 | 2 | no | — |
| 15 | #17988715 | — | 2 | 2 | no | — |
| 16 | #17988714 | — | 2 | 1 | no | — |
| 17 | C8×Dic146 | — | 2 | 1 | no | — |
| 18 | #17988711 | — | 2 | 1 | no | — |
| 19 | #17988711 | C4 | 1 | 4 | yes | — |
| 20 | #17988711 | C4 | 1 | 2 | yes | — |
| 21 | #17988711 | C4 | 1 | 2 | yes | — |
| 22 | C2×#14556527 | C22 | 1 | 2 | yes | — |
| 23 | C2×#14556526 | C22 | 1 | 2 | yes | — |
| 24 | C2×#14556526 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#14556526 | C22 | 1 | 2 | yes | — |
| 26 | C2×#14556526 | C22 | 1 | 1 | yes | characteristic |
| 27 | #17988611 | C22 | 1 | 1 | yes | characteristic |
| 28 | #17988610 | C22 | 1 | 2 | yes | — |
| 29 | #17988610 | C22 | 1 | 2 | yes | — |
| 30 | C2×#14556520 | C22 | 1 | 2 | yes | — |
| 31 | C4×#11924012 | C22 | 1 | 1 | yes | characteristic |
| 32 | M16×Dic73 | C22 | 1 | 2 | yes | — |
| 33 | M16×Dic73 | C22 | 1 | 2 | yes | — |
| 34 | C2×C4×#10596831 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×C8×Dic73 | C22 | 1 | 2 | yes | — |
| 36 | #17988352 | C22 | 1 | 2 | yes | — |
| 37 | #17988351 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17988351 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#108×C73 | C22 | 1 | 2 | yes | — |
| 40 | #423×C73 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×C4⋊C8×C73 | C22 | 1 | 1 | yes | characteristic |
| 42 | C4×M16×C73 | C22 | 1 | 1 | yes | characteristic |
| 43 | #341×C73 | C22 | 1 | 2 | yes | — |
| 44 | C22×Dic146 | Q8 | 1 | 1 | yes | characteristic |
| 45 | C2×#11924012 | C23 | 1 | 2 | yes | — |
| 46 | C2×#11924012 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#11924012 | C23 | 1 | 1 | yes | characteristic |
| 48 | C22×#10596831 | C23 | 1 | 1 | yes | characteristic |
| 49 | C22×#10596831 | C23 | 1 | 1 | yes | characteristic |
| 50 | C4×Dic146 | C2×C4 | 1 | 2 | yes | — |
| 51 | C4×Dic146 | C2×C4 | 1 | 1 | yes | characteristic |
| 52 | C4×Dic146 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C4×Dic146 | D4 | 1 | 1 | yes | characteristic |
| 54 | C4×Dic146 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×Dic146 | D4 | 1 | 2 | yes | — |
| 56 | C2×C4⋊Dic73 | Q8 | 1 | 1 | yes | characteristic |
| 57 | C2×#11924007 | Q8 | 1 | 2 | yes | — |
| 58 | C2×C4×Dic73 | C23 | 1 | 2 | yes | — |
| 59 | #14556527 | — | 4 | 2 | no | — |
| 60 | #14556526 | — | 2 | 4 | no | — |
| 61 | #14556526 | — | 2 | 2 | no | — |
| 62 | #14556526 | — | 4 | 2 | no | — |
| 63 | #14556526 | Q8 | 1 | 4 | yes | complemented |
| 64 | C4⋊#10596831 | — | 2 | 1 | no | — |
| 65 | C4⋊#10596831 | — | 2 | 1 | no | — |
| 66 | #14556520 | — | 2 | 2 | no | — |
| 67 | #14556520 | — | 2 | 2 | no | — |
| 68 | #14556520 | — | 2 | 2 | no | — |
| 69 | #14556520 | — | 2 | 2 | no | — |
| 70 | #14556520 | C2×C4 | 1 | 4 | yes | — |
| 71 | #14556520 | C2×C4 | 1 | 4 | yes | — |
| 72 | #14556502 | — | 2 | 1 | no | — |
| 73 | #14556501 | — | 2 | 2 | no | — |
| 74 | #14556501 | — | 2 | 2 | no | — |
| 75 | C4×#10596831 | — | 2 | 1 | no | — |
| 76 | C4×#10596831 | C2×C4 | 1 | 2 | yes | — |
| 77 | C4×#10596831 | C2×C4 | 1 | 2 | yes | — |
| 78 | C8×Dic73 | — | 2 | 2 | no | — |
| 79 | C8×Dic73 | — | 2 | 2 | no | — |
| 80 | C8×Dic73 | C2×C4 | 1 | 4 | yes | — |
| 81 | C8×Dic73 | C2×C4 | 1 | 4 | yes | — |
| 82 | C2×M16×C73 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×M16×C73 | C23 | 1 | 2 | yes | — |
| 84 | C2×M16×C73 | C23 | 1 | 1 | yes | characteristic |
| 85 | C22×C8×C73 | C23 | 1 | 2 | yes | — |
| 86 | C2×C42×C73 | C23 | 1 | 1 | yes | characteristic |
| 87 | #108×C73 | — | 4 | 2 | no | — |
| 88 | C4⋊C8×C73 | — | 2 | 1 | no | — |
| 89 | C4⋊C8×C73 | — | 2 | 1 | no | — |
| 90 | C4⋊C8×C73 | C2×C4 | 1 | 2 | yes | — |
| 91 | C4⋊C8×C73 | C2×C4 | 1 | 2 | yes | — |
| 92 | #97×C73 | — | 2 | 1 | no | — |
| 93 | C4×C8×C73 | — | 2 | 1 | no | — |
| 94 | C2×Dic146 | — | 2 | 4 | no | — |
| 95 | C2×Dic146 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 96 | C2×Dic146 | C4⋊C4 | 1 | 2 | yes | — |
| 97 | C2×Dic146 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 98 | C22×Dic73 | C2×Q8 | 1 | 2 | yes | — |
| 99 | C22×Dic73 | C2×Q8 | 1 | 2 | yes | — |
| 100 | #11924012 | — | 2 | 1 | no | — |
| 101 | #11924012 | — | 2 | 2 | no | — |
| 102 | #11924012 | — | 2 | 1 | no | — |
| 103 | #11924012 | — | 2 | 2 | no | — |
| 104 | #11924012 | — | 2 | 1 | no | — |
| 105 | #11924012 | C2×Q8 | 1 | 2 | yes | — |
| 106 | C2×#10596831 | — | 2 | 1 | no | — |
| 107 | C2×#10596831 | — | 2 | 1 | no | — |
| 108 | C2×#10596831 | — | 2 | 1 | no | — |
| 109 | C2×#10596831 | — | 2 | 2 | no | — |
| 110 | C2×#10596831 | — | 2 | 1 | no | — |
| 111 | C2×#10596831 | C22×C4 | 1 | 2 | yes | — |
| 112 | C2×#10596831 | C22×C4 | 1 | 2 | yes | — |
| 113 | C2×#10596831 | C2×Q8 | 1 | 2 | yes | — |
| 114 | C2×#10596831 | #41 | 1 | 2 | yes | — |
| 115 | C4⋊Dic73 | C4⋊C4 | 1 | 2 | yes | — |
| 116 | C4⋊Dic73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 117 | C4⋊Dic73 | C4⋊C4 | 1 | 1 | yes | characteristic |
| 118 | #11924007 | C4⋊C4 | 1 | 2 | yes | — |
| 119 | #11924007 | C4⋊C4 | 1 | 2 | yes | — |
| 120 | #11924007 | C4⋊C4 | 1 | 2 | yes | — |
| 121 | #11924007 | C4⋊C4 | 1 | 2 | yes | — |
| 122 | C4×Dic73 | C22×C4 | 1 | 2 | yes | — |
| 123 | C4×Dic73 | C22×C4 | 1 | 2 | yes | — |
| 124 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 125 | C4×Dic73 | C2×D4 | 1 | 2 | yes | — |
| 126 | C22×C4×C73 | C2×Q8 | 1 | 1 | yes | characteristic |
| 127 | C22×C4×C73 | C2×Q8 | 1 | 1 | yes | characteristic |
| 128 | C22×C4×C73 | C24 | 1 | 1 | yes | characteristic |
| 129 | M16×C73 | — | 2 | 1 | no | — |
| 130 | M16×C73 | — | 2 | 1 | no | — |
| 131 | M16×C73 | — | 2 | 2 | no | — |
| 132 | M16×C73 | — | 2 | 1 | no | — |
| 133 | M16×C73 | — | 2 | 2 | no | — |
| 134 | M16×C73 | C2×Q8 | 1 | 2 | yes | — |
| 135 | C2×C8×C73 | — | 2 | 1 | no | — |
| 136 | C2×C8×C73 | — | 2 | 2 | no | — |
| 137 | C2×C8×C73 | — | 2 | 2 | no | — |
| 138 | C2×C8×C73 | — | 2 | 1 | no | — |
| 139 | C2×C8×C73 | — | 2 | 2 | no | — |
| 140 | C2×C8×C73 | C22×C4 | 1 | 4 | yes | — |
| 141 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 142 | C42×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C42×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C23×C73 | C22×Q8 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C73 | — | 2 | 2 | no | — |
| 147 | C2×C4×C73 | — | 4 | 1 | no | — |
| 148 | C2×C4×C73 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C73 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C73 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 151 | C2×C4×C73 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C73 | C23×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C4×C73 | C22×Q8 | 1 | 1 | yes | characteristic |
| 155 | C2×C4×C73 | C2×#41 | 1 | 1 | yes | characteristic |
| 156 | C2×C4×C73 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C73 | 2−1+4 | 1 | 1 | yes | characteristic |
| 158 | C2×Dic73 | — | 2 | 4 | no | — |
| 159 | C2×Dic73 | — | 4 | 2 | no | — |
| 160 | C2×Dic73 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 161 | C2×Dic73 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 162 | C2×Dic73 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 163 | C2×Dic73 | C2×C4⋊C4 | 1 | 2 | yes | — |
| 164 | Dic146 | — | 2 | 2 | no | — |
| 165 | Dic146 | — | 2 | 4 | no | — |
| 166 | Dic146 | #108 | 1 | 4 | yes | complemented |
| 167 | C8×C73 | — | 2 | 4 | no | — |
| 168 | C8×C73 | — | 2 | 2 | no | — |
| 169 | C8×C73 | — | 4 | 1 | no | — |
| 170 | C8×C73 | — | 4 | 2 | no | — |
| 171 | #10596831 | — | 2 | 2 | no | — |
| 172 | #10596831 | — | 2 | 2 | no | — |
| 173 | #10596831 | — | 4 | 2 | no | — |
| 174 | #10596831 | — | 4 | 1 | no | — |
| 175 | #10596831 | C4×Q8 | 1 | 4 | yes | — |
| 176 | C22×C73 | — | 2 | 1 | no | — |
| 177 | C22×C73 | — | 2 | 1 | no | — |
| 178 | C22×C73 | C22×C4⋊C4 | 1 | 1 | yes | characteristic |
| 179 | C22×C73 | #557 | 1 | 1 | yes | characteristic |
| 180 | C22×C73 | Q82 | 1 | 1 | yes | characteristic |
| 181 | C4×C73 | — | 2 | 1 | no | — |
| 182 | C4×C73 | — | 2 | 1 | no | — |
| 183 | C4×C73 | — | 2 | 1 | no | — |
| 184 | C4×C73 | C2×#108 | 1 | 2 | yes | — |
| 185 | C4×C73 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 186 | C4×C73 | #520 | 1 | 1 | yes | characteristic |
| 187 | C4×C73 | D4×Q8 | 1 | 1 | yes | characteristic |
| 188 | C4×C73 | #550 | 1 | 1 | yes | characteristic |
| 189 | Dic73 | — | 2 | 2 | no | — |
| 190 | Dic73 | — | 2 | 2 | no | — |
| 191 | Dic73 | — | 2 | 2 | no | — |
| 192 | Dic73 | C2×#108 | 1 | 4 | yes | — |
| 193 | Q8×#108 | — | 73 | 1 | no | maximal, Sylow |
| 194 | C2×C73 | — | 2 | 1 | no | — |
| 195 | C2×C73 | — | 2 | 1 | no | — |
| 196 | C2×C73 | Q8×C4⋊C4 | 1 | 1 | yes | characteristic |
| 197 | C2×C73 | C22×#108 | 1 | 1 | yes | characteristic |
| 198 | C2×C73 | #2916 | 1 | 1 | yes | characteristic |
| 199 | Q8×M16 | — | 73 | 1 | no | — |
| 200 | Q8×M16 | — | 73 | 1 | no | — |
| 201 | C2×C8×Q8 | — | 73 | 1 | no | — |
| 202 | #1950 | — | 73 | 2 | no | — |
| 203 | #1950 | — | 73 | 1 | no | — |
| 204 | #1950 | — | 73 | 2 | no | — |
| 205 | #1950 | D73 | 1 | 1 | yes | characteristic |
| 206 | #1848 | — | 73 | 2 | no | — |
| 207 | #1848 | — | 73 | 1 | no | — |
| 208 | C4×#108 | — | 73 | 1 | no | — |
| 209 | C4×#108 | — | 73 | 2 | no | — |
| 210 | C73 | Q8×#108 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 211 | C2×C4×Q8 | — | 73 | 1 | no | — |
| 212 | #446 | — | 146 | 1 | no | — |
| 213 | #446 | — | 146 | 2 | no | — |
| 214 | #446 | — | 146 | 1 | no | — |
| 215 | #446 | — | 146 | 2 | no | — |
| 216 | C8×Q8 | — | 73 | 2 | no | — |
| 217 | C8×Q8 | — | 73 | 4 | no | — |
| 218 | C8×Q8 | — | 73 | 2 | no | — |
| 219 | C8×Q8 | — | 146 | 1 | no | — |
| 220 | C8×Q8 | — | 146 | 1 | no | — |
| 221 | C2×#108 | — | 73 | 2 | no | — |
| 222 | C2×#108 | — | 73 | 2 | no | — |
| 223 | C2×#108 | — | 73 | 1 | no | — |
| 224 | C2×#108 | — | 73 | 1 | no | — |
| 225 | C2×#108 | — | 73 | 2 | no | — |
| 226 | C2×#108 | C2×D73 | 1 | 2 | yes | — |
| 227 | #423 | — | 73 | 2 | no | — |
| 228 | #423 | — | 73 | 2 | no | — |
| 229 | #423 | — | 73 | 1 | no | — |
| 230 | #423 | C2×D73 | 1 | 1 | yes | characteristic |
| 231 | C2×C4⋊C8 | — | 73 | 2 | no | — |
| 232 | C2×C4⋊C8 | C2×D73 | 1 | 1 | yes | characteristic |
| 233 | C4×M16 | — | 73 | 2 | no | — |
| 234 | C4×M16 | — | 73 | 2 | no | — |
| 235 | C4×M16 | — | 73 | 1 | no | — |
| 236 | C4×M16 | C2×D73 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C8 | — | 73 | 2 | no | — |
| 238 | C2×C4×C8 | — | 73 | 1 | no | — |
| 239 | #341 | — | 73 | 1 | no | — |
| 240 | #341 | — | 73 | 1 | no | — |
| 241 | #341 | — | 73 | 2 | no | — |
| 242 | #341 | C2×D73 | 1 | 2 | yes | — |
| 243 | C22×Q8 | — | 73 | 1 | no | — |
| 244 | C2×M16 | — | 73 | 1 | no | — |
| 245 | C2×M16 | — | 73 | 1 | no | — |
| 246 | C2×M16 | — | 73 | 2 | no | — |
| 247 | C2×M16 | C22×D73 | 1 | 1 | yes | characteristic |
| 248 | C2×M16 | C22×D73 | 1 | 2 | yes | — |
| 249 | C2×M16 | C22×D73 | 1 | 1 | yes | characteristic |
| 250 | C22×C8 | — | 73 | 1 | no | — |
| 251 | C22×C8 | — | 73 | 1 | no | — |
| 252 | C22×C8 | C22×D73 | 1 | 2 | yes | — |
| 253 | C4×Q8 | — | 73 | 1 | no | — |
| 254 | C4×Q8 | — | 73 | 2 | no | — |
| 255 | C4×Q8 | — | 73 | 1 | no | — |
| 256 | C4×Q8 | — | 73 | 1 | no | — |
| 257 | C4×Q8 | — | 73 | 2 | no | — |
| 258 | C4×Q8 | — | 73 | 1 | no | — |
| 259 | C2×C4⋊C4 | — | 73 | 2 | no | — |
| 260 | C2×C4⋊C4 | — | 73 | 1 | no | — |
| 261 | C2×C42 | — | 73 | 2 | no | — |
| 262 | C2×C42 | C22×D73 | 1 | 1 | yes | characteristic |
| 263 | #108 | — | 4 | 2 | no | — |
| 264 | #108 | — | 292 | 2 | no | — |
| 265 | #108 | — | 292 | 2 | no | — |
| 266 | #108 | — | 73 | 4 | no | — |
| 267 | #108 | — | 146 | 2 | no | — |
| 268 | #108 | — | 146 | 4 | no | — |
| 269 | C4⋊C8 | — | 2 | 1 | no | — |
| 270 | C4⋊C8 | — | 2 | 1 | no | — |
| 271 | C4⋊C8 | — | 73 | 4 | no | — |
| 272 | C4⋊C8 | — | 73 | 4 | no | — |
| 273 | C4⋊C8 | — | 146 | 2 | no | — |
| 274 | C4⋊C8 | — | 146 | 2 | no | — |
| 275 | C4⋊C8 | — | 146 | 2 | no | — |
| 276 | C4⋊C8 | — | 146 | 2 | no | — |
| 277 | C4⋊C8 | — | 146 | 1 | no | — |
| 278 | C4⋊C8 | — | 146 | 1 | no | — |
| 279 | C4⋊C8 | C4×D73 | 1 | 2 | yes | — |
| 280 | C4⋊C8 | C4×D73 | 1 | 2 | yes | — |
| 281 | #97 | — | 2 | 1 | no | — |
| 282 | #97 | — | 146 | 2 | no | — |
| 283 | #97 | — | 146 | 2 | no | — |
| 284 | #97 | — | 146 | 1 | no | — |
| 285 | C4×C8 | — | 2 | 1 | no | — |
| 286 | C4×C8 | — | 73 | 4 | no | — |
| 287 | C4×C8 | — | 73 | 4 | no | — |
| 288 | C4×C8 | — | 73 | 2 | no | — |
| 289 | C4×C8 | — | 73 | 2 | no | — |
| 290 | C4×C8 | — | 146 | 2 | no | — |
| 291 | C4×C8 | — | 146 | 2 | no | — |
| 292 | C4×C8 | — | 146 | 1 | no | — |
| 293 | C2×Q8 | — | 73 | 1 | no | — |
| 294 | C2×Q8 | — | 73 | 2 | no | — |
| 295 | C2×Q8 | — | 73 | 1 | no | — |
| 296 | C2×Q8 | — | 146 | 4 | no | — |
| 297 | C22×C4 | — | 73 | 2 | no | — |
| 298 | C22×C4 | — | 73 | 2 | no | — |
| 299 | C22×C4 | Q8×D73 | 1 | 1 | yes | characteristic |
| 300 | C22×C4 | Q8×D73 | 1 | 1 | yes | characteristic |
| 301 | C22×C4 | C23×D73 | 1 | 1 | yes | characteristic |
| 302 | M16 | — | 2 | 1 | no | — |
| 303 | M16 | — | 2 | 1 | no | — |
| 304 | M16 | — | 2 | 2 | no | — |
| 305 | M16 | — | 2 | 1 | no | — |
| 306 | M16 | — | 2 | 2 | no | — |
| 307 | M16 | — | 73 | 2 | no | — |
| 308 | M16 | — | 146 | 2 | no | — |
| 309 | M16 | — | 146 | 1 | no | — |
| 310 | M16 | — | 146 | 2 | no | — |
| 311 | M16 | — | 146 | 1 | no | — |
| 312 | M16 | — | 146 | 1 | no | — |
| 313 | M16 | Q8×D73 | 1 | 2 | yes | — |
| 314 | C2×C8 | — | 2 | 1 | no | — |
| 315 | C2×C8 | — | 2 | 2 | no | — |
| 316 | C2×C8 | — | 2 | 2 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 2 | no | — |
| 319 | C2×C8 | — | 73 | 2 | no | — |
| 320 | C2×C8 | — | 73 | 2 | no | — |
| 321 | C2×C8 | — | 73 | 2 | no | — |
| 322 | C2×C8 | — | 73 | 2 | no | — |
| 323 | C2×C8 | — | 146 | 2 | no | — |
| 324 | C2×C8 | — | 146 | 1 | no | — |
| 325 | C2×C8 | — | 146 | 1 | no | — |
| 326 | C2×C8 | — | 146 | 1 | no | — |
| 327 | C2×C8 | — | 146 | 1 | no | — |
| 328 | C2×C8 | C2×C4×D73 | 1 | 4 | yes | — |
| 329 | C4⋊C4 | — | 73 | 2 | no | — |
| 330 | C4⋊C4 | — | 73 | 2 | no | — |
| 331 | C4⋊C4 | — | 73 | 2 | no | — |
| 332 | C4⋊C4 | — | 73 | 2 | no | — |
| 333 | C4⋊C4 | — | 73 | 2 | no | — |
| 334 | C4⋊C4 | — | 73 | 1 | no | — |
| 335 | C4⋊C4 | — | 73 | 1 | no | — |
| 336 | C42 | — | 73 | 2 | no | — |
| 337 | C42 | — | 73 | 2 | no | — |
| 338 | C42 | — | 73 | 2 | no | — |
| 339 | C42 | — | 73 | 2 | no | — |
| 340 | C42 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 341 | C42 | C2×C4×D73 | 1 | 1 | yes | characteristic |
| 342 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 343 | C42 | D4×D73 | 1 | 1 | yes | characteristic |
| 344 | C23 | C2×Q8×D73 | 1 | 1 | yes | characteristic |
| 345 | Q8 | — | 73 | 4 | no | — |
| 346 | Q8 | — | 146 | 4 | no | — |
| 347 | Q8 | — | 146 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 292 | 2 | no | — |
| 351 | C2×C4 | — | 73 | 2 | no | — |
| 352 | C2×C4 | — | 73 | 2 | no | — |
| 353 | C2×C4 | — | 73 | 2 | no | — |
| 354 | C2×C4 | — | 73 | 2 | no | — |
| 355 | C2×C4 | — | 146 | 4 | no | — |
| 356 | C2×C4 | C4⋊C4×D73 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C4⋊C4×D73 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C4⋊C4×D73 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C4⋊C4×D73 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C22×C4×D73 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 362 | C2×C4 | C2×Q8×D73 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #41×D73 | 1 | 1 | yes | characteristic |
| 364 | C2×C4 | #14556636 | 1 | 1 | yes | characteristic |
| 365 | C2×C4 | #14556638 | 1 | 1 | yes | characteristic |
| 366 | C8 | — | 2 | 2 | no | — |
| 367 | C8 | — | 2 | 4 | no | — |
| 368 | C8 | — | 4 | 1 | no | — |
| 369 | C8 | — | 4 | 2 | no | — |
| 370 | C8 | — | 292 | 2 | no | — |
| 371 | C8 | — | 292 | 1 | no | — |
| 372 | C8 | — | 73 | 4 | no | — |
| 373 | C8 | — | 146 | 2 | no | — |
| 374 | C8 | — | 146 | 2 | no | — |
| 375 | C22 | — | 2 | 1 | no | — |
| 376 | C22 | — | 2 | 1 | no | — |
| 377 | C22 | C2×C4⋊C4×D73 | 1 | 1 | yes | characteristic |
| 378 | C22 | #17989314 | 1 | 1 | yes | characteristic |
| 379 | C22 | #17989317 | 1 | 1 | yes | characteristic |
| 380 | C4 | — | 2 | 1 | no | — |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 2 | 1 | no | — |
| 383 | C4 | — | 73 | 4 | no | — |
| 384 | C4 | — | 146 | 2 | no | — |
| 385 | C4 | — | 146 | 2 | no | — |
| 386 | C4 | — | 146 | 2 | no | — |
| 387 | C4 | #108×D73 | 1 | 2 | yes | — |
| 388 | C4 | C4×Q8×D73 | 1 | 1 | yes | characteristic |
| 389 | C4 | #17989066 | 1 | 1 | yes | characteristic |
| 390 | C4 | #17989250 | 1 | 1 | yes | characteristic |
| 391 | C4 | #17989255 | 1 | 1 | yes | characteristic |
| 392 | C2 | — | 2 | 1 | no | — |
| 393 | C2 | — | 2 | 1 | no | — |
| 394 | C2 | #22612845 | 1 | 1 | yes | characteristic |
| 395 | C2 | C2×#108×D73 | 1 | 1 | yes | characteristic |
| 396 | C2 | #22618541 | 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