← #33076260
Subgroups — #33076260
Order 18688.
554 conjugacy classes of subgroups.
The subgroup lattice has 528 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #22622868 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22622814 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #22622814 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #22622606 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #22609456 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #22609386 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #22609332 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #22609310 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #22609149 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #22609086 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #22609069 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #22609069 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #22608783 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #22608751 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C73×#1723 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #17989317 | C22 | 1 | 1 | yes | characteristic |
| 17 | #17989317 | C22 | 1 | 1 | yes | characteristic |
| 18 | #17989317 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17989312 | C22 | 1 | 1 | yes | characteristic |
| 20 | #17988994 | — | 2 | 1 | no | — |
| 21 | #17988991 | — | 2 | 1 | no | — |
| 22 | #17988991 | — | 2 | 1 | no | — |
| 23 | #17988936 | — | 2 | 1 | no | — |
| 24 | #17988897 | — | 2 | 1 | no | — |
| 25 | #17988881 | — | 2 | 1 | no | — |
| 26 | #17988881 | — | 2 | 1 | no | — |
| 27 | #17988881 | — | 2 | 1 | no | — |
| 28 | #17988881 | — | 2 | 1 | no | — |
| 29 | #17988880 | — | 2 | 1 | no | — |
| 30 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 31 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 32 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 33 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 34 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17988879 | C22 | 1 | 1 | yes | characteristic |
| 36 | #17988871 | — | 2 | 1 | no | — |
| 37 | #17988869 | C22 | 1 | 1 | yes | characteristic |
| 38 | #17988796 | — | 2 | 1 | no | — |
| 39 | #17988794 | C22 | 1 | 1 | yes | characteristic |
| 40 | #17988717 | C22 | 1 | 1 | yes | characteristic |
| 41 | C8×Dic146 | C22 | 1 | 1 | yes | characteristic |
| 42 | C8×Dic146 | C22 | 1 | 1 | yes | characteristic |
| 43 | C8×Dic146 | C22 | 1 | 1 | yes | characteristic |
| 44 | #17988693 | — | 2 | 1 | no | — |
| 45 | C4×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 46 | C4×Dic292 | C22 | 1 | 1 | yes | characteristic |
| 47 | #17988681 | — | 2 | 1 | no | — |
| 48 | #17988681 | — | 2 | 1 | no | — |
| 49 | #17988679 | — | 2 | 1 | no | — |
| 50 | #17988340 | C22 | 1 | 1 | yes | characteristic |
| 51 | #17988338 | C22 | 1 | 1 | yes | characteristic |
| 52 | #17988336 | C22 | 1 | 1 | yes | characteristic |
| 53 | #17988336 | C22 | 1 | 1 | yes | characteristic |
| 54 | #17988336 | C22 | 1 | 1 | yes | characteristic |
| 55 | #17988333 | C22 | 1 | 1 | yes | characteristic |
| 56 | #17988319 | C22 | 1 | 1 | yes | characteristic |
| 57 | #17988319 | C22 | 1 | 1 | yes | characteristic |
| 58 | #17988319 | C22 | 1 | 1 | yes | characteristic |
| 59 | #17988319 | C22 | 1 | 1 | yes | characteristic |
| 60 | #500×C73 | C22 | 1 | 1 | yes | characteristic |
| 61 | #500×C73 | C22 | 1 | 1 | yes | characteristic |
| 62 | #498×C73 | C22 | 1 | 1 | yes | characteristic |
| 63 | #494×C73 | C22 | 1 | 1 | yes | characteristic |
| 64 | #487×C73 | C22 | 1 | 1 | yes | characteristic |
| 65 | #487×C73 | C22 | 1 | 1 | yes | characteristic |
| 66 | #322×C73 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×Dic292 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×Dic292 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×#11924018 | — | 2 | 1 | no | — |
| 70 | #14556590 | — | 2 | 1 | no | — |
| 71 | #14556590 | — | 2 | 1 | no | — |
| 72 | #14556590 | — | 2 | 1 | no | — |
| 73 | #14556590 | — | 2 | 1 | no | — |
| 74 | #14556590 | — | 2 | 1 | no | — |
| 75 | #14556590 | — | 2 | 1 | no | — |
| 76 | #14556589 | — | 2 | 1 | no | — |
| 77 | #14556589 | — | 4 | 1 | no | — |
| 78 | #14556589 | — | 4 | 1 | no | — |
| 79 | #14556589 | — | 4 | 1 | no | — |
| 80 | #14556582 | — | 2 | 1 | no | — |
| 81 | #14556581 | — | 4 | 1 | no | — |
| 82 | Q8×Dic73 | — | 2 | 1 | no | — |
| 83 | C4×Dic146 | C23 | 1 | 1 | yes | characteristic |
| 84 | C4×Dic146 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×Dic146 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×Dic146 | C23 | 1 | 1 | yes | characteristic |
| 87 | #14556556 | — | 2 | 1 | no | — |
| 88 | #14556556 | — | 2 | 1 | no | — |
| 89 | #14556556 | — | 2 | 1 | no | — |
| 90 | #14556556 | — | 2 | 1 | no | — |
| 91 | #14556556 | — | 2 | 1 | no | — |
| 92 | #14556556 | — | 2 | 1 | no | — |
| 93 | #14556556 | — | 2 | 1 | no | — |
| 94 | #14556525 | D4 | 1 | 1 | yes | characteristic |
| 95 | #14556525 | D4 | 1 | 1 | yes | characteristic |
| 96 | #14556524 | — | 2 | 1 | no | — |
| 97 | #14556524 | — | 2 | 1 | no | — |
| 98 | #14556524 | — | 2 | 1 | no | — |
| 99 | #14556524 | — | 2 | 1 | no | — |
| 100 | #14556524 | — | 2 | 1 | no | — |
| 101 | #14556524 | — | 2 | 1 | no | — |
| 102 | #14556522 | — | 2 | 1 | no | — |
| 103 | C4⋊#10596831 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4⋊#10596831 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4⋊#10596831 | C23 | 1 | 1 | yes | characteristic |
| 106 | C4⋊#10596831 | C23 | 1 | 1 | yes | characteristic |
| 107 | #14556520 | — | 2 | 1 | no | — |
| 108 | #14556520 | — | 2 | 1 | no | — |
| 109 | #14556520 | — | 2 | 1 | no | — |
| 110 | #14556520 | — | 2 | 1 | no | — |
| 111 | #14556516 | D4 | 1 | 1 | yes | characteristic |
| 112 | #14556516 | D4 | 1 | 1 | yes | characteristic |
| 113 | #14556516 | D4 | 1 | 1 | yes | characteristic |
| 114 | #14556516 | D4 | 1 | 1 | yes | characteristic |
| 115 | #14556515 | — | 2 | 1 | no | — |
| 116 | #14556514 | — | 2 | 1 | no | — |
| 117 | #14556514 | — | 2 | 1 | no | — |
| 118 | #14556514 | — | 2 | 1 | no | — |
| 119 | #14556514 | — | 2 | 1 | no | — |
| 120 | #14556514 | — | 2 | 1 | no | — |
| 121 | #14556514 | — | 2 | 1 | no | — |
| 122 | #14556514 | — | 2 | 1 | no | — |
| 123 | #14556501 | — | 2 | 1 | no | — |
| 124 | C8×Dic73 | — | 2 | 1 | no | — |
| 125 | C8×Dic73 | — | 2 | 1 | no | — |
| 126 | C8×Dic73 | — | 2 | 1 | no | — |
| 127 | C2×Q16×C73 | — | 4 | 1 | no | — |
| 128 | C4⋊Q8×C73 | C23 | 1 | 1 | yes | characteristic |
| 129 | C4⋊Q8×C73 | C23 | 1 | 1 | yes | characteristic |
| 130 | C4⋊Q8×C73 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4⋊Q8×C73 | C23 | 1 | 1 | yes | characteristic |
| 132 | #107×C73 | — | 2 | 1 | no | — |
| 133 | #107×C73 | — | 2 | 1 | no | — |
| 134 | #107×C73 | — | 2 | 1 | no | — |
| 135 | #107×C73 | — | 2 | 1 | no | — |
| 136 | #106×C73 | — | 2 | 1 | no | — |
| 137 | #106×C73 | — | 2 | 1 | no | — |
| 138 | #103×C73 | — | 2 | 1 | no | — |
| 139 | #103×C73 | — | 2 | 1 | no | — |
| 140 | #103×C73 | — | 4 | 1 | no | — |
| 141 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 142 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4×C8×C73 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×Dic146 | — | 4 | 1 | no | — |
| 145 | C2×Dic146 | — | 4 | 1 | no | — |
| 146 | C2×Dic146 | — | 4 | 1 | no | — |
| 147 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×Dic146 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | Dic292 | — | 2 | 2 | no | — |
| 152 | Dic292 | Q16 | 1 | 4 | yes | complemented |
| 153 | #11924018 | — | 4 | 2 | no | — |
| 154 | C2×#10596831 | — | 2 | 1 | no | — |
| 155 | C2×#10596831 | — | 2 | 1 | no | — |
| 156 | C2×#10596831 | — | 2 | 1 | no | — |
| 157 | C2×#10596831 | — | 2 | 1 | no | — |
| 158 | C4⋊Dic73 | — | 4 | 1 | no | — |
| 159 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C4⋊Dic73 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | #11924007 | — | 2 | 1 | no | — |
| 164 | #11924007 | — | 2 | 1 | no | — |
| 165 | #11924007 | — | 2 | 1 | no | — |
| 166 | #11924007 | — | 2 | 1 | no | — |
| 167 | #11924007 | — | 4 | 1 | no | — |
| 168 | #11924007 | — | 4 | 1 | no | — |
| 169 | #11924007 | — | 4 | 1 | no | — |
| 170 | #11924007 | — | 4 | 1 | no | — |
| 171 | #11924007 | — | 4 | 1 | no | — |
| 172 | #11924007 | — | 4 | 1 | no | — |
| 173 | #11924007 | — | 4 | 1 | no | — |
| 174 | #11924007 | — | 4 | 1 | no | — |
| 175 | C4×Dic73 | — | 2 | 1 | no | — |
| 176 | C4×Dic73 | — | 2 | 1 | no | — |
| 177 | C4×Dic73 | — | 2 | 1 | no | — |
| 178 | C4×Dic73 | — | 2 | 1 | no | — |
| 179 | C4×Dic73 | — | 4 | 1 | no | — |
| 180 | C4×Dic73 | — | 4 | 1 | no | — |
| 181 | C4×Dic73 | — | 4 | 1 | no | — |
| 182 | C4×Dic73 | — | 4 | 1 | no | — |
| 183 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 184 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 185 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 186 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 187 | Q16×C73 | — | 8 | 2 | no | — |
| 188 | C2×C8×C73 | — | 2 | 1 | no | — |
| 189 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C8×C73 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 194 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 195 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 196 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 197 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 198 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 199 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 200 | C4⋊C4×C73 | — | 2 | 1 | no | — |
| 201 | C42×C73 | C24 | 1 | 1 | yes | characteristic |
| 202 | Q8×C73 | — | 4 | 1 | no | — |
| 203 | Q8×C73 | — | 4 | 1 | no | — |
| 204 | Q8×C73 | — | 8 | 1 | no | — |
| 205 | Q8×C73 | — | 8 | 1 | no | — |
| 206 | Q8×C73 | — | 8 | 1 | no | — |
| 207 | C2×C4×C73 | — | 4 | 1 | no | — |
| 208 | C2×C4×C73 | — | 4 | 1 | no | — |
| 209 | C2×C4×C73 | — | 4 | 1 | no | — |
| 210 | C2×C4×C73 | — | 4 | 1 | no | — |
| 211 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C73 | C22×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C73 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 214 | C2×Dic73 | — | 2 | 1 | no | — |
| 215 | C2×Dic73 | — | 2 | 1 | no | — |
| 216 | C2×Dic73 | — | 2 | 1 | no | — |
| 217 | C2×Dic73 | — | 2 | 1 | no | — |
| 218 | C2×Dic73 | — | 2 | 1 | no | — |
| 219 | C2×Dic73 | — | 2 | 1 | no | — |
| 220 | C2×Dic73 | — | 2 | 1 | no | — |
| 221 | C2×Dic73 | — | 2 | 1 | no | — |
| 222 | Dic146 | — | 2 | 1 | no | — |
| 223 | Dic146 | — | 2 | 1 | no | — |
| 224 | Dic146 | — | 2 | 1 | no | — |
| 225 | Dic146 | — | 2 | 1 | no | — |
| 226 | Dic146 | — | 2 | 1 | no | — |
| 227 | Dic146 | — | 16 | 1 | no | — |
| 228 | Dic146 | — | 16 | 1 | no | — |
| 229 | Dic146 | — | 16 | 1 | no | — |
| 230 | Dic146 | C2×Q16 | 1 | 2 | yes | — |
| 231 | Dic146 | C2×Q16 | 1 | 2 | yes | — |
| 232 | Dic146 | #137 | 1 | 2 | yes | — |
| 233 | C8×C73 | — | 2 | 1 | no | — |
| 234 | C8×C73 | — | 2 | 1 | no | — |
| 235 | C8×C73 | — | 2 | 1 | no | — |
| 236 | C8×C73 | — | 4 | 1 | no | — |
| 237 | C8×C73 | C2×Q16 | 1 | 2 | yes | — |
| 238 | #10596831 | — | 4 | 1 | no | — |
| 239 | #10596831 | — | 4 | 1 | no | — |
| 240 | #10596831 | — | 4 | 1 | no | — |
| 241 | #10596831 | — | 4 | 1 | no | — |
| 242 | C22×C73 | D42 | 1 | 1 | yes | characteristic |
| 243 | C4×C73 | — | 2 | 1 | no | — |
| 244 | C4×C73 | — | 8 | 1 | no | — |
| 245 | C4×C73 | — | 8 | 1 | no | — |
| 246 | C4×C73 | — | 8 | 1 | no | — |
| 247 | C4×C73 | — | 8 | 1 | no | — |
| 248 | C4×C73 | C22×Q16 | 1 | 1 | yes | characteristic |
| 249 | C4×C73 | C2×#137 | 1 | 1 | yes | characteristic |
| 250 | C4×C73 | #578 | 1 | 1 | yes | characteristic |
| 251 | C4×C73 | #578 | 1 | 1 | yes | characteristic |
| 252 | Dic73 | — | 2 | 2 | no | — |
| 253 | Dic73 | — | 2 | 2 | no | — |
| 254 | Dic73 | — | 2 | 2 | no | — |
| 255 | Dic73 | — | 4 | 1 | no | — |
| 256 | Dic73 | — | 4 | 1 | no | — |
| 257 | Dic73 | — | 4 | 1 | no | — |
| 258 | Dic73 | — | 4 | 1 | no | — |
| 259 | Dic73 | — | 4 | 1 | no | — |
| 260 | #19817 | — | 73 | 1 | no | maximal, Sylow |
| 261 | C2×C73 | #3270 | 1 | 1 | yes | characteristic |
| 262 | C2×C73 | D4×Q16 | 1 | 1 | yes | characteristic |
| 263 | C2×C73 | #3288 | 1 | 1 | yes | characteristic |
| 264 | #3387 | — | 73 | 1 | no | — |
| 265 | Q8×Q16 | — | 73 | 1 | no | — |
| 266 | Q8×Q16 | — | 73 | 1 | no | — |
| 267 | #3363 | — | 73 | 1 | no | — |
| 268 | #1723 | D73 | 1 | 1 | yes | characteristic |
| 269 | #1696 | — | 73 | 1 | no | — |
| 270 | #1684 | — | 73 | 1 | no | — |
| 271 | #1676 | — | 73 | 1 | no | — |
| 272 | #1672 | — | 73 | 1 | no | — |
| 273 | #1645 | — | 73 | 1 | no | — |
| 274 | #1636 | — | 73 | 1 | no | — |
| 275 | #1633 | — | 73 | 1 | no | — |
| 276 | #1633 | — | 73 | 1 | no | — |
| 277 | #1584 | — | 73 | 1 | no | — |
| 278 | #1579 | — | 73 | 1 | no | — |
| 279 | C73 | #19817 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 280 | Q82 | — | 73 | 1 | no | — |
| 281 | Q82 | — | 73 | 1 | no | — |
| 282 | Q82 | — | 73 | 1 | no | — |
| 283 | #557 | — | 73 | 1 | no | — |
| 284 | #501 | — | 146 | 1 | no | — |
| 285 | #500 | — | 146 | 1 | no | — |
| 286 | #500 | — | 146 | 1 | no | — |
| 287 | #500 | C2×D73 | 1 | 1 | yes | characteristic |
| 288 | #500 | C2×D73 | 1 | 1 | yes | characteristic |
| 289 | #498 | C2×D73 | 1 | 1 | yes | characteristic |
| 290 | #494 | C2×D73 | 1 | 1 | yes | characteristic |
| 291 | #487 | — | 146 | 1 | no | — |
| 292 | #487 | C2×D73 | 1 | 1 | yes | characteristic |
| 293 | #487 | C2×D73 | 1 | 1 | yes | characteristic |
| 294 | #479 | — | 146 | 1 | no | — |
| 295 | #477 | — | 73 | 1 | no | — |
| 296 | #477 | — | 73 | 1 | no | — |
| 297 | #477 | — | 73 | 1 | no | — |
| 298 | #477 | — | 73 | 1 | no | — |
| 299 | #477 | — | 73 | 1 | no | — |
| 300 | #477 | — | 73 | 1 | no | — |
| 301 | #477 | — | 146 | 1 | no | — |
| 302 | #477 | — | 146 | 1 | no | — |
| 303 | #477 | — | 146 | 1 | no | — |
| 304 | #477 | — | 146 | 1 | no | — |
| 305 | #477 | — | 146 | 1 | no | — |
| 306 | #475 | — | 73 | 1 | no | — |
| 307 | #475 | — | 146 | 1 | no | — |
| 308 | #462 | — | 73 | 1 | no | — |
| 309 | #462 | — | 146 | 1 | no | — |
| 310 | #446 | — | 73 | 1 | no | — |
| 311 | C8×Q8 | — | 73 | 1 | no | — |
| 312 | C8×Q8 | — | 73 | 1 | no | — |
| 313 | C8×Q8 | — | 73 | 1 | no | — |
| 314 | #441 | — | 146 | 1 | no | — |
| 315 | C4×Q16 | — | 73 | 1 | no | — |
| 316 | C4×Q16 | — | 73 | 1 | no | — |
| 317 | C4×Q16 | — | 146 | 1 | no | — |
| 318 | C4×Q16 | — | 146 | 1 | no | — |
| 319 | C4×Q16 | — | 146 | 1 | no | — |
| 320 | #335 | — | 73 | 1 | no | — |
| 321 | #334 | — | 73 | 1 | no | — |
| 322 | #333 | — | 73 | 1 | no | — |
| 323 | #333 | — | 73 | 1 | no | — |
| 324 | #333 | — | 73 | 1 | no | — |
| 325 | #332 | — | 73 | 1 | no | — |
| 326 | Q8⋊C8 | — | 73 | 1 | no | — |
| 327 | Q8⋊C8 | — | 73 | 1 | no | — |
| 328 | Q8⋊C8 | — | 73 | 1 | no | — |
| 329 | Q8⋊C8 | — | 73 | 1 | no | — |
| 330 | #322 | C2×D73 | 1 | 1 | yes | characteristic |
| 331 | C2×Q16 | — | 4 | 1 | no | — |
| 332 | C2×Q16 | — | 73 | 1 | no | — |
| 333 | C2×Q16 | — | 73 | 1 | no | — |
| 334 | C2×Q16 | — | 146 | 1 | no | — |
| 335 | C4⋊Q8 | — | 292 | 1 | no | — |
| 336 | C4⋊Q8 | — | 292 | 1 | no | — |
| 337 | C4⋊Q8 | — | 292 | 1 | no | — |
| 338 | C4⋊Q8 | — | 146 | 1 | no | — |
| 339 | C4⋊Q8 | — | 146 | 1 | no | — |
| 340 | C4⋊Q8 | — | 146 | 1 | no | — |
| 341 | C4⋊Q8 | — | 146 | 1 | no | — |
| 342 | C4⋊Q8 | — | 146 | 1 | no | — |
| 343 | C4⋊Q8 | — | 146 | 1 | no | — |
| 344 | C4⋊Q8 | — | 146 | 1 | no | — |
| 345 | C4⋊Q8 | C22×D73 | 1 | 1 | yes | characteristic |
| 346 | C4⋊Q8 | C22×D73 | 1 | 1 | yes | characteristic |
| 347 | C4⋊Q8 | C22×D73 | 1 | 1 | yes | characteristic |
| 348 | C4⋊Q8 | C22×D73 | 1 | 1 | yes | characteristic |
| 349 | #125 | — | 292 | 1 | no | — |
| 350 | #125 | — | 146 | 1 | no | — |
| 351 | C4×Q8 | — | 73 | 1 | no | — |
| 352 | C4×Q8 | — | 73 | 1 | no | — |
| 353 | C4×Q8 | — | 73 | 1 | no | — |
| 354 | C4×Q8 | — | 73 | 1 | no | — |
| 355 | C4×Q8 | — | 146 | 1 | no | — |
| 356 | C4×Q8 | — | 146 | 1 | no | — |
| 357 | C4×Q8 | — | 146 | 1 | no | — |
| 358 | C4×Q8 | — | 146 | 1 | no | — |
| 359 | C4×Q8 | — | 146 | 1 | no | — |
| 360 | C4×Q8 | — | 146 | 1 | no | — |
| 361 | C4×Q8 | — | 146 | 1 | no | — |
| 362 | C4×Q8 | — | 146 | 1 | no | — |
| 363 | #107 | — | 2 | 1 | no | — |
| 364 | #107 | — | 2 | 1 | no | — |
| 365 | #107 | — | 2 | 1 | no | — |
| 366 | #107 | — | 2 | 1 | no | — |
| 367 | #107 | — | 73 | 1 | no | — |
| 368 | #107 | — | 73 | 1 | no | — |
| 369 | #107 | — | 146 | 1 | no | — |
| 370 | #107 | — | 146 | 1 | no | — |
| 371 | #107 | — | 146 | 1 | no | — |
| 372 | #107 | — | 146 | 1 | no | — |
| 373 | #107 | — | 146 | 1 | no | — |
| 374 | #107 | — | 146 | 1 | no | — |
| 375 | #106 | — | 2 | 1 | no | — |
| 376 | #106 | — | 2 | 1 | no | — |
| 377 | #106 | — | 146 | 1 | no | — |
| 378 | C4⋊C8 | — | 73 | 1 | no | — |
| 379 | C4⋊C8 | — | 73 | 1 | no | — |
| 380 | C4⋊C8 | — | 73 | 1 | no | — |
| 381 | C4⋊C8 | — | 73 | 1 | no | — |
| 382 | C4⋊C8 | — | 146 | 1 | no | — |
| 383 | C4⋊C8 | — | 146 | 1 | no | — |
| 384 | C4⋊C8 | — | 146 | 1 | no | — |
| 385 | C4⋊C8 | — | 146 | 1 | no | — |
| 386 | #103 | — | 2 | 1 | no | — |
| 387 | #103 | — | 2 | 1 | no | — |
| 388 | #103 | — | 4 | 1 | no | — |
| 389 | #103 | — | 73 | 1 | no | — |
| 390 | #103 | — | 73 | 1 | no | — |
| 391 | #103 | — | 73 | 1 | no | — |
| 392 | #103 | — | 73 | 1 | no | — |
| 393 | #103 | — | 146 | 1 | no | — |
| 394 | #103 | — | 146 | 1 | no | — |
| 395 | #103 | — | 146 | 1 | no | — |
| 396 | #103 | — | 146 | 1 | no | — |
| 397 | #103 | — | 146 | 1 | no | — |
| 398 | #103 | — | 146 | 1 | no | — |
| 399 | #103 | — | 146 | 1 | no | — |
| 400 | #103 | — | 146 | 1 | no | — |
| 401 | #97 | — | 146 | 1 | no | — |
| 402 | C4×C8 | — | 146 | 1 | no | — |
| 403 | C4×C8 | — | 146 | 1 | no | — |
| 404 | C4×C8 | — | 146 | 1 | no | — |
| 405 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 406 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 407 | C4×C8 | C22×D73 | 1 | 1 | yes | characteristic |
| 408 | C2×Q8 | — | 2 | 1 | no | — |
| 409 | C2×Q8 | — | 2 | 1 | no | — |
| 410 | C2×Q8 | — | 2 | 1 | no | — |
| 411 | C2×Q8 | — | 2 | 1 | no | — |
| 412 | C2×Q8 | — | 292 | 1 | no | — |
| 413 | C2×Q8 | — | 292 | 1 | no | — |
| 414 | C2×Q8 | — | 292 | 1 | no | — |
| 415 | C2×Q8 | — | 73 | 1 | no | — |
| 416 | C2×Q8 | — | 73 | 1 | no | — |
| 417 | C2×Q8 | — | 73 | 1 | no | — |
| 418 | C2×Q8 | — | 73 | 1 | no | — |
| 419 | Q16 | — | 8 | 2 | no | — |
| 420 | Q16 | — | 292 | 2 | no | — |
| 421 | Q16 | — | 73 | 4 | no | — |
| 422 | Q16 | — | 146 | 2 | no | — |
| 423 | C2×C8 | — | 2 | 1 | no | — |
| 424 | C2×C8 | — | 146 | 1 | no | — |
| 425 | C2×C8 | — | 146 | 1 | no | — |
| 426 | C2×C8 | — | 146 | 1 | no | — |
| 427 | C2×C8 | — | 146 | 1 | no | — |
| 428 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 431 | C2×C8 | D4×D73 | 1 | 1 | yes | characteristic |
| 432 | C4⋊C4 | — | 2 | 1 | no | — |
| 433 | C4⋊C4 | — | 2 | 1 | no | — |
| 434 | C4⋊C4 | — | 2 | 1 | no | — |
| 435 | C4⋊C4 | — | 2 | 1 | no | — |
| 436 | C4⋊C4 | — | 2 | 1 | no | — |
| 437 | C4⋊C4 | — | 2 | 1 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 2 | 1 | no | — |
| 440 | C4⋊C4 | — | 292 | 1 | no | — |
| 441 | C4⋊C4 | — | 292 | 1 | no | — |
| 442 | C4⋊C4 | — | 292 | 1 | no | — |
| 443 | C4⋊C4 | — | 292 | 1 | no | — |
| 444 | C4⋊C4 | — | 292 | 1 | no | — |
| 445 | C4⋊C4 | — | 292 | 1 | no | — |
| 446 | C4⋊C4 | — | 292 | 1 | no | — |
| 447 | C4⋊C4 | — | 292 | 1 | no | — |
| 448 | C4⋊C4 | — | 292 | 1 | no | — |
| 449 | C4⋊C4 | — | 73 | 1 | no | — |
| 450 | C4⋊C4 | — | 73 | 1 | no | — |
| 451 | C4⋊C4 | — | 73 | 1 | no | — |
| 452 | C4⋊C4 | — | 73 | 1 | no | — |
| 453 | C4⋊C4 | — | 146 | 1 | no | — |
| 454 | C4⋊C4 | — | 146 | 1 | no | — |
| 455 | C4⋊C4 | — | 146 | 1 | no | — |
| 456 | C4⋊C4 | — | 146 | 1 | no | — |
| 457 | C42 | — | 292 | 1 | no | — |
| 458 | C42 | — | 292 | 1 | no | — |
| 459 | C42 | — | 292 | 1 | no | — |
| 460 | C42 | — | 292 | 1 | no | — |
| 461 | C42 | — | 146 | 1 | no | — |
| 462 | C42 | — | 146 | 1 | no | — |
| 463 | C42 | — | 146 | 1 | no | — |
| 464 | C42 | — | 146 | 1 | no | — |
| 465 | C42 | C23×D73 | 1 | 1 | yes | characteristic |
| 466 | Q8 | — | 4 | 1 | no | — |
| 467 | Q8 | — | 4 | 1 | no | — |
| 468 | Q8 | — | 8 | 1 | no | — |
| 469 | Q8 | — | 8 | 1 | no | — |
| 470 | Q8 | — | 8 | 1 | no | — |
| 471 | Q8 | — | 73 | 2 | no | — |
| 472 | Q8 | — | 73 | 2 | no | — |
| 473 | Q8 | — | 73 | 2 | no | — |
| 474 | Q8 | — | 1168 | 1 | no | — |
| 475 | Q8 | — | 1168 | 1 | no | — |
| 476 | Q8 | — | 1168 | 1 | no | — |
| 477 | Q8 | — | 146 | 1 | no | — |
| 478 | Q8 | — | 146 | 1 | no | — |
| 479 | Q8 | — | 146 | 1 | no | — |
| 480 | Q8 | — | 146 | 1 | no | — |
| 481 | Q8 | — | 146 | 1 | no | — |
| 482 | C2×C4 | — | 4 | 1 | no | — |
| 483 | C2×C4 | — | 4 | 1 | no | — |
| 484 | C2×C4 | — | 4 | 1 | no | — |
| 485 | C2×C4 | — | 4 | 1 | no | — |
| 486 | C2×C4 | — | 146 | 1 | no | — |
| 487 | C2×C4 | — | 146 | 1 | no | — |
| 488 | C2×C4 | — | 146 | 1 | no | — |
| 489 | C2×C4 | — | 146 | 1 | no | — |
| 490 | C2×C4 | — | 146 | 1 | no | — |
| 491 | C2×C4 | — | 146 | 1 | no | — |
| 492 | C2×C4 | — | 146 | 1 | no | — |
| 493 | C2×C4 | — | 146 | 1 | no | — |
| 494 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 495 | C2×C4 | C2×D4×D73 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | #14556636 | 1 | 1 | yes | characteristic |
| 497 | C8 | — | 2 | 1 | no | — |
| 498 | C8 | — | 2 | 1 | no | — |
| 499 | C8 | — | 2 | 1 | no | — |
| 500 | C8 | — | 4 | 1 | no | — |
| 501 | C8 | — | 292 | 1 | no | — |
| 502 | C8 | — | 292 | 1 | no | — |
| 503 | C8 | — | 292 | 1 | no | — |
| 504 | C8 | — | 292 | 1 | no | — |
| 505 | C8 | Q16×D73 | 1 | 2 | yes | — |
| 506 | C22 | #17989222 | 1 | 1 | yes | characteristic |
| 507 | C4 | — | 2 | 1 | no | — |
| 508 | C4 | — | 8 | 1 | no | — |
| 509 | C4 | — | 8 | 1 | no | — |
| 510 | C4 | — | 8 | 1 | no | — |
| 511 | C4 | — | 8 | 1 | no | — |
| 512 | C4 | — | 292 | 1 | no | — |
| 513 | C4 | — | 292 | 1 | no | — |
| 514 | C4 | — | 292 | 1 | no | — |
| 515 | C4 | — | 292 | 1 | no | — |
| 516 | C4 | — | 292 | 1 | no | — |
| 517 | C4 | — | 146 | 2 | no | — |
| 518 | C4 | — | 146 | 2 | no | — |
| 519 | C4 | — | 146 | 2 | no | — |
| 520 | C4 | C2×Q16×D73 | 1 | 1 | yes | characteristic |
| 521 | C4 | #137×D73 | 1 | 1 | yes | characteristic |
| 522 | C4 | #17989400 | 1 | 1 | yes | characteristic |
| 523 | C4 | #17989403 | 1 | 1 | yes | characteristic |
| 524 | C2 | #22621500 | 1 | 1 | yes | characteristic |
| 525 | C2 | #22621681 | 1 | 1 | yes | characteristic |
| 526 | C2 | #22621697 | 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