← #36446673
Subgroups — #36446673
Order 22784.
682 conjugacy classes of subgroups.
The subgroup lattice has 440 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #26034138 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #26021241 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #26021240 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #26018989 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #26018846 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #26018691 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C89×#1489 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #19152326 | — | 2 | 1 | no | — |
| 9 | #19152326 | — | 2 | 1 | no | — |
| 10 | #19152318 | — | 2 | 1 | no | — |
| 11 | #19152318 | — | 2 | 1 | no | — |
| 12 | #19152288 | — | 2 | 2 | no | — |
| 13 | #19152288 | — | 2 | 2 | no | — |
| 14 | #19152210 | — | 2 | 2 | no | — |
| 15 | #19152169 | C4 | 1 | 2 | yes | — |
| 16 | #19152155 | — | 2 | 1 | no | — |
| 17 | #19152155 | — | 2 | 1 | no | — |
| 18 | #19152155 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#15668012 | C22 | 1 | 1 | yes | characteristic |
| 20 | #19152075 | C4 | 1 | 2 | yes | — |
| 21 | #19151622 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×#13083558 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19151366 | — | 2 | 2 | no | — |
| 24 | #19151366 | — | 2 | 2 | no | — |
| 25 | #19151345 | — | 2 | 1 | no | — |
| 26 | #19151343 | — | 2 | 1 | no | — |
| 27 | #19151339 | — | 2 | 2 | no | — |
| 28 | Q8⋊#10623494 | — | 2 | 1 | no | — |
| 29 | D4⋊#10623494 | — | 2 | 1 | no | — |
| 30 | C4×#41×C89 | C22 | 1 | 1 | yes | characteristic |
| 31 | #423×C89 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×M16×C89 | C22 | 1 | 1 | yes | characteristic |
| 33 | Q8⋊C8×C89 | — | 2 | 1 | no | — |
| 34 | D4⋊C8×C89 | — | 2 | 1 | no | — |
| 35 | C22×Dic178 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×#13083558 | — | 2 | 1 | no | — |
| 37 | C2×#13083558 | — | 2 | 1 | no | — |
| 38 | #15668012 | — | 2 | 1 | no | — |
| 39 | #15668012 | — | 2 | 1 | no | — |
| 40 | #15668012 | — | 2 | 1 | no | — |
| 41 | #15668012 | — | 2 | 1 | no | — |
| 42 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 43 | #15668012 | D4 | 1 | 1 | yes | characteristic |
| 44 | #15668010 | — | 2 | 2 | no | — |
| 45 | #15668005 | — | 2 | 4 | no | — |
| 46 | #15668005 | — | 2 | 4 | no | — |
| 47 | #15668004 | — | 2 | 2 | no | — |
| 48 | #15668004 | — | 2 | 2 | no | — |
| 49 | #15668004 | D4 | 1 | 2 | yes | — |
| 50 | #15668002 | — | 2 | 4 | no | — |
| 51 | #15668002 | — | 2 | 4 | no | — |
| 52 | #15667999 | — | 2 | 2 | no | — |
| 53 | #15667993 | — | 2 | 4 | no | — |
| 54 | #15667991 | — | 2 | 2 | no | — |
| 55 | #15667991 | — | 2 | 2 | no | — |
| 56 | #15667991 | — | 2 | 2 | no | — |
| 57 | #15667991 | — | 2 | 2 | no | — |
| 58 | #15667991 | — | 2 | 1 | no | — |
| 59 | #15667991 | — | 2 | 1 | no | — |
| 60 | C4×Dic178 | — | 2 | 2 | no | — |
| 61 | C4×Dic178 | — | 2 | 2 | no | — |
| 62 | C4×Dic178 | — | 2 | 2 | no | — |
| 63 | C4×Dic178 | — | 2 | 2 | no | — |
| 64 | C4×Dic178 | — | 2 | 1 | no | — |
| 65 | C4×Dic178 | — | 2 | 1 | no | — |
| 66 | #15667977 | — | 2 | 2 | no | — |
| 67 | #15667977 | — | 2 | 2 | no | — |
| 68 | #15667971 | — | 2 | 2 | no | — |
| 69 | #15667971 | — | 2 | 2 | no | — |
| 70 | #15667971 | C2×C4 | 1 | 2 | yes | — |
| 71 | #15667968 | — | 2 | 4 | no | — |
| 72 | C2×C4⋊Dic89 | D4 | 1 | 2 | yes | — |
| 73 | C2×C4⋊Dic89 | D4 | 1 | 2 | yes | — |
| 74 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 75 | C4⋊#10623494 | — | 2 | 1 | no | — |
| 76 | #15667923 | — | 2 | 1 | no | — |
| 77 | C4×#10623494 | — | 2 | 1 | no | — |
| 78 | C2×#41×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×M16×C89 | — | 2 | 1 | no | — |
| 80 | C2×M16×C89 | — | 2 | 1 | no | — |
| 81 | C4×Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 82 | C4×Q8×C89 | D4 | 1 | 1 | yes | characteristic |
| 83 | C4×D4×C89 | — | 2 | 1 | no | — |
| 84 | C4×D4×C89 | — | 2 | 1 | no | — |
| 85 | C4×D4×C89 | D4 | 1 | 1 | yes | characteristic |
| 86 | C4×D4×C89 | D4 | 1 | 1 | yes | characteristic |
| 87 | #117×C89 | — | 2 | 1 | no | — |
| 88 | #117×C89 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | C2×C42×C89 | — | 2 | 1 | no | — |
| 90 | C2×C42×C89 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 92 | C4⋊C8×C89 | — | 2 | 1 | no | — |
| 93 | #97×C89 | — | 2 | 1 | no | — |
| 94 | C4×C8×C89 | — | 2 | 1 | no | — |
| 95 | C2×Dic178 | — | 2 | 2 | no | — |
| 96 | C2×Dic178 | — | 2 | 2 | no | — |
| 97 | C2×Dic178 | — | 2 | 1 | no | — |
| 98 | C2×Dic178 | — | 2 | 1 | no | — |
| 99 | C2×Dic178 | — | 4 | 4 | no | — |
| 100 | C22×Dic89 | C22⋊C4 | 1 | 4 | yes | — |
| 101 | #13083558 | — | 2 | 2 | no | — |
| 102 | #13083558 | — | 4 | 1 | no | — |
| 103 | #13083558 | — | 4 | 2 | no | — |
| 104 | C2×#10623494 | — | 4 | 1 | no | — |
| 105 | C2×#10623494 | — | 4 | 1 | no | — |
| 106 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 107 | C4⋊Dic89 | — | 2 | 1 | no | — |
| 108 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 109 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 110 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 111 | C4⋊Dic89 | — | 2 | 2 | no | — |
| 112 | C4⋊Dic89 | C22⋊C4 | 1 | 2 | yes | — |
| 113 | C4⋊Dic89 | C22⋊C4 | 1 | 2 | yes | — |
| 114 | #13083553 | — | 2 | 4 | no | — |
| 115 | #13083553 | — | 2 | 4 | no | — |
| 116 | #13083553 | — | 2 | 4 | no | — |
| 117 | #13083553 | — | 2 | 4 | no | — |
| 118 | #13083553 | — | 2 | 2 | no | — |
| 119 | #13083553 | — | 2 | 2 | no | — |
| 120 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 121 | C22⋊Dic89 | — | 2 | 4 | no | — |
| 122 | C22⋊Dic89 | — | 2 | 2 | no | — |
| 123 | C4×Dic89 | — | 2 | 4 | no | — |
| 124 | C4×Dic89 | — | 2 | 4 | no | — |
| 125 | C4×Dic89 | — | 2 | 2 | no | — |
| 126 | #41×C89 | — | 4 | 2 | no | — |
| 127 | C2×Q8×C89 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 128 | C2×D4×C89 | — | 2 | 1 | no | — |
| 129 | C2×D4×C89 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C89 | — | 2 | 1 | no | — |
| 131 | C22×C4×C89 | — | 2 | 1 | no | — |
| 132 | C22×C4×C89 | — | 2 | 1 | no | — |
| 133 | C22×C4×C89 | C22×C4 | 1 | 1 | yes | characteristic |
| 134 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | M16×C89 | — | 2 | 2 | no | — |
| 137 | M16×C89 | — | 4 | 1 | no | — |
| 138 | M16×C89 | — | 4 | 2 | no | — |
| 139 | C2×C8×C89 | — | 4 | 1 | no | — |
| 140 | C2×C8×C89 | — | 4 | 1 | no | — |
| 141 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 142 | C4⋊C4×C89 | — | 2 | 1 | no | — |
| 143 | C4⋊C4×C89 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | C4⋊C4×C89 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 145 | C22⋊C4×C89 | — | 2 | 1 | no | — |
| 146 | C22⋊C4×C89 | — | 2 | 1 | no | — |
| 147 | C22⋊C4×C89 | — | 2 | 1 | no | — |
| 148 | C42×C89 | — | 2 | 1 | no | — |
| 149 | C42×C89 | — | 2 | 1 | no | — |
| 150 | C42×C89 | — | 2 | 1 | no | — |
| 151 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C42×C89 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C23×C89 | — | 2 | 1 | no | — |
| 156 | C23×C89 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 157 | Q8×C89 | — | 2 | 2 | no | — |
| 158 | D4×C89 | — | 2 | 2 | no | — |
| 159 | D4×C89 | — | 4 | 2 | no | — |
| 160 | C2×C4×C89 | — | 2 | 2 | no | — |
| 161 | C2×C4×C89 | — | 2 | 1 | no | — |
| 162 | C2×C4×C89 | — | 2 | 1 | no | — |
| 163 | C2×C4×C89 | — | 2 | 1 | no | — |
| 164 | C2×C4×C89 | — | 2 | 1 | no | — |
| 165 | C2×C4×C89 | — | 2 | 1 | no | — |
| 166 | C2×C4×C89 | — | 2 | 1 | no | — |
| 167 | C2×C4×C89 | — | 2 | 1 | no | — |
| 168 | C2×C4×C89 | — | 4 | 2 | no | — |
| 169 | C2×C4×C89 | — | 4 | 1 | no | — |
| 170 | C2×C4×C89 | — | 4 | 1 | no | — |
| 171 | C2×C4×C89 | — | 4 | 1 | no | — |
| 172 | C2×C4×C89 | — | 4 | 1 | no | — |
| 173 | C2×C4×C89 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C89 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 177 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 178 | C2×C4×C89 | #120 | 1 | 1 | yes | characteristic |
| 179 | C2×Dic89 | — | 2 | 2 | no | — |
| 180 | C2×Dic89 | — | 2 | 2 | no | — |
| 181 | C2×Dic89 | — | 2 | 4 | no | — |
| 182 | C2×Dic89 | — | 4 | 4 | no | — |
| 183 | Dic178 | — | 4 | 4 | no | — |
| 184 | Dic178 | — | 4 | 4 | no | — |
| 185 | Dic178 | — | 4 | 1 | no | — |
| 186 | Dic178 | — | 4 | 1 | no | — |
| 187 | Dic178 | — | 4 | 1 | no | — |
| 188 | Dic178 | — | 4 | 1 | no | — |
| 189 | C8×C89 | — | 4 | 2 | no | — |
| 190 | C8×C89 | — | 8 | 1 | no | — |
| 191 | #10623494 | — | 4 | 2 | no | — |
| 192 | #10623494 | — | 8 | 1 | no | — |
| 193 | C22×C89 | — | 2 | 1 | no | — |
| 194 | C22×C89 | — | 2 | 1 | no | — |
| 195 | C22×C89 | — | 2 | 1 | no | — |
| 196 | C22×C89 | — | 4 | 1 | no | — |
| 197 | C22×C89 | — | 4 | 1 | no | — |
| 198 | C22×C89 | — | 4 | 1 | no | — |
| 199 | C22×C89 | #379 | 1 | 1 | yes | characteristic |
| 200 | C4×C89 | — | 2 | 1 | no | — |
| 201 | C4×C89 | — | 2 | 1 | no | — |
| 202 | C4×C89 | — | 2 | 1 | no | — |
| 203 | C4×C89 | — | 4 | 1 | no | — |
| 204 | C4×C89 | — | 4 | 1 | no | — |
| 205 | C4×C89 | — | 4 | 1 | no | — |
| 206 | C4×C89 | #413 | 1 | 2 | yes | — |
| 207 | C4×C89 | #454 | 1 | 1 | yes | characteristic |
| 208 | C4×C89 | #454 | 1 | 1 | yes | characteristic |
| 209 | C4×C89 | #456 | 1 | 1 | yes | characteristic |
| 210 | C4×C89 | #456 | 1 | 1 | yes | characteristic |
| 211 | Dic89 | — | 4 | 2 | no | — |
| 212 | Dic89 | — | 4 | 2 | no | — |
| 213 | Dic89 | — | 4 | 4 | no | — |
| 214 | #8474 | — | 89 | 1 | no | maximal, Sylow |
| 215 | C2×C89 | — | 4 | 1 | no | — |
| 216 | C2×C89 | — | 8 | 1 | no | — |
| 217 | C2×C89 | #1785 | 1 | 1 | yes | characteristic |
| 218 | C2×C89 | #1793 | 1 | 1 | yes | characteristic |
| 219 | C2×C89 | #1793 | 1 | 1 | yes | characteristic |
| 220 | #3509 | — | 89 | 1 | no | — |
| 221 | #1997 | — | 89 | 1 | no | — |
| 222 | #1997 | — | 89 | 1 | no | — |
| 223 | #1561 | — | 89 | 1 | no | — |
| 224 | #1526 | — | 89 | 1 | no | — |
| 225 | #1489 | — | 89 | 1 | no | — |
| 226 | #1489 | D89 | 1 | 1 | yes | characteristic |
| 227 | C89 | #8474 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 228 | #557 | — | 178 | 1 | no | — |
| 229 | #557 | — | 178 | 1 | no | — |
| 230 | #556 | — | 178 | 1 | no | — |
| 231 | #556 | — | 178 | 1 | no | — |
| 232 | #552 | — | 178 | 2 | no | — |
| 233 | #552 | — | 178 | 2 | no | — |
| 234 | #541 | — | 178 | 2 | no | — |
| 235 | #536 | — | 89 | 2 | no | — |
| 236 | #533 | — | 89 | 1 | no | — |
| 237 | #533 | — | 178 | 1 | no | — |
| 238 | #533 | — | 178 | 1 | no | — |
| 239 | C2×C4⋊Q8 | — | 89 | 1 | no | — |
| 240 | #519 | — | 89 | 2 | no | — |
| 241 | C4×#41 | C2×D89 | 1 | 1 | yes | characteristic |
| 242 | #423 | — | 89 | 1 | no | — |
| 243 | #423 | C2×D89 | 1 | 1 | yes | characteristic |
| 244 | C4×M16 | — | 89 | 1 | no | — |
| 245 | C4×M16 | C2×D89 | 1 | 1 | yes | characteristic |
| 246 | #343 | — | 178 | 2 | no | — |
| 247 | #343 | — | 178 | 2 | no | — |
| 248 | #332 | — | 178 | 1 | no | — |
| 249 | #332 | — | 178 | 1 | no | — |
| 250 | #330 | — | 178 | 2 | no | — |
| 251 | Q8⋊C8 | — | 2 | 1 | no | — |
| 252 | Q8⋊C8 | — | 178 | 1 | no | — |
| 253 | D4⋊C8 | — | 2 | 1 | no | — |
| 254 | D4⋊C8 | — | 178 | 1 | no | — |
| 255 | C2×#41 | C4×D89 | 1 | 1 | yes | characteristic |
| 256 | C22×Q8 | — | 89 | 2 | no | — |
| 257 | C2×M16 | — | 2 | 1 | no | — |
| 258 | C2×M16 | — | 2 | 1 | no | — |
| 259 | C2×M16 | — | 178 | 1 | no | — |
| 260 | C2×M16 | — | 178 | 1 | no | — |
| 261 | C4⋊Q8 | — | 89 | 1 | no | — |
| 262 | C4⋊Q8 | — | 89 | 1 | no | — |
| 263 | C4⋊Q8 | — | 178 | 2 | no | — |
| 264 | C4⋊Q8 | — | 178 | 1 | no | — |
| 265 | C4⋊Q8 | — | 178 | 1 | no | — |
| 266 | C4⋊Q8 | — | 178 | 1 | no | — |
| 267 | C4⋊Q8 | — | 178 | 1 | no | — |
| 268 | #126 | — | 178 | 4 | no | — |
| 269 | #126 | — | 178 | 4 | no | — |
| 270 | #125 | — | 89 | 2 | no | — |
| 271 | #125 | — | 178 | 2 | no | — |
| 272 | #125 | — | 178 | 2 | no | — |
| 273 | #125 | — | 178 | 4 | no | — |
| 274 | #125 | — | 178 | 4 | no | — |
| 275 | #124 | — | 178 | 2 | no | — |
| 276 | #123 | — | 178 | 4 | no | — |
| 277 | C22⋊Q8 | — | 178 | 2 | no | — |
| 278 | C22⋊Q8 | — | 178 | 2 | no | — |
| 279 | C22⋊Q8 | — | 178 | 2 | no | — |
| 280 | C22⋊Q8 | — | 178 | 2 | no | — |
| 281 | C22⋊Q8 | — | 178 | 1 | no | — |
| 282 | C22⋊Q8 | — | 178 | 1 | no | — |
| 283 | C4×Q8 | — | 178 | 2 | no | — |
| 284 | C4×Q8 | — | 178 | 2 | no | — |
| 285 | C4×Q8 | — | 178 | 2 | no | — |
| 286 | C4×Q8 | — | 178 | 2 | no | — |
| 287 | C4×Q8 | — | 178 | 2 | no | — |
| 288 | C4×Q8 | — | 178 | 2 | no | — |
| 289 | C4×Q8 | — | 178 | 1 | no | — |
| 290 | C4×Q8 | — | 178 | 1 | no | — |
| 291 | C4×Q8 | D356 | 1 | 1 | yes | characteristic |
| 292 | C4×Q8 | C22⋊D89 | 1 | 1 | yes | characteristic |
| 293 | C4×D4 | — | 2 | 1 | no | — |
| 294 | C4×D4 | — | 2 | 1 | no | — |
| 295 | C4×D4 | D356 | 1 | 1 | yes | characteristic |
| 296 | C4×D4 | C22⋊D89 | 1 | 1 | yes | characteristic |
| 297 | #117 | — | 2 | 1 | no | — |
| 298 | #117 | — | 89 | 2 | no | — |
| 299 | #117 | — | 178 | 4 | no | — |
| 300 | #117 | — | 178 | 2 | no | — |
| 301 | #117 | — | 178 | 2 | no | — |
| 302 | #117 | C4×D89 | 1 | 1 | yes | characteristic |
| 303 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 304 | C2×C4⋊C4 | — | 89 | 2 | no | — |
| 305 | C2×C42 | — | 2 | 1 | no | — |
| 306 | C2×C42 | C22×D89 | 1 | 1 | yes | characteristic |
| 307 | C4⋊C8 | — | 2 | 1 | no | — |
| 308 | C4⋊C8 | — | 2 | 1 | no | — |
| 309 | C4⋊C8 | — | 178 | 1 | no | — |
| 310 | C4⋊C8 | — | 178 | 1 | no | — |
| 311 | #97 | — | 2 | 1 | no | — |
| 312 | #97 | — | 178 | 1 | no | — |
| 313 | C4×C8 | — | 2 | 1 | no | — |
| 314 | C4×C8 | — | 178 | 1 | no | — |
| 315 | #41 | — | 4 | 2 | no | — |
| 316 | C2×Q8 | — | 356 | 4 | no | — |
| 317 | C2×Q8 | — | 178 | 1 | no | — |
| 318 | C2×Q8 | — | 178 | 1 | no | — |
| 319 | C2×Q8 | — | 178 | 2 | no | — |
| 320 | C2×Q8 | — | 178 | 2 | no | — |
| 321 | C2×Q8 | #13083551 | 1 | 1 | yes | characteristic |
| 322 | C2×D4 | — | 2 | 1 | no | — |
| 323 | C2×D4 | #13083551 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | — | 2 | 1 | no | — |
| 325 | C22×C4 | — | 2 | 1 | no | — |
| 326 | C22×C4 | — | 2 | 1 | no | — |
| 327 | C22×C4 | — | 89 | 4 | no | — |
| 328 | C22×C4 | C2×C4×D89 | 1 | 1 | yes | characteristic |
| 329 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 330 | C22×C4 | D4×D89 | 1 | 1 | yes | characteristic |
| 331 | M16 | — | 2 | 2 | no | — |
| 332 | M16 | — | 4 | 1 | no | — |
| 333 | M16 | — | 4 | 2 | no | — |
| 334 | M16 | — | 356 | 1 | no | — |
| 335 | M16 | — | 356 | 2 | no | — |
| 336 | M16 | — | 178 | 2 | no | — |
| 337 | C2×C8 | — | 4 | 1 | no | — |
| 338 | C2×C8 | — | 4 | 1 | no | — |
| 339 | C2×C8 | — | 356 | 1 | no | — |
| 340 | C2×C8 | — | 356 | 1 | no | — |
| 341 | C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C4⋊C4 | — | 89 | 2 | no | — |
| 344 | C4⋊C4 | — | 89 | 2 | no | — |
| 345 | C4⋊C4 | — | 178 | 4 | no | — |
| 346 | C4⋊C4 | — | 178 | 4 | no | — |
| 347 | C4⋊C4 | — | 178 | 4 | no | — |
| 348 | C4⋊C4 | — | 178 | 4 | no | — |
| 349 | C4⋊C4 | — | 178 | 2 | no | — |
| 350 | C4⋊C4 | — | 178 | 2 | no | — |
| 351 | C4⋊C4 | — | 178 | 1 | no | — |
| 352 | C4⋊C4 | — | 178 | 2 | no | — |
| 353 | C4⋊C4 | — | 178 | 2 | no | — |
| 354 | C4⋊C4 | — | 178 | 2 | no | — |
| 355 | C4⋊C4 | — | 178 | 1 | no | — |
| 356 | C4⋊C4 | — | 178 | 2 | no | — |
| 357 | C4⋊C4 | #13083551 | 1 | 1 | yes | characteristic |
| 358 | C4⋊C4 | #13083551 | 1 | 1 | yes | characteristic |
| 359 | C22⋊C4 | — | 2 | 1 | no | — |
| 360 | C22⋊C4 | — | 2 | 1 | no | — |
| 361 | C22⋊C4 | — | 2 | 1 | no | — |
| 362 | C22⋊C4 | — | 178 | 4 | no | — |
| 363 | C22⋊C4 | — | 178 | 4 | no | — |
| 364 | C22⋊C4 | — | 178 | 2 | no | — |
| 365 | C42 | — | 2 | 1 | no | — |
| 366 | C42 | — | 2 | 1 | no | — |
| 367 | C42 | — | 2 | 1 | no | — |
| 368 | C42 | — | 178 | 4 | no | — |
| 369 | C42 | — | 178 | 4 | no | — |
| 370 | C42 | — | 178 | 2 | no | — |
| 371 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 372 | C42 | D4×D89 | 1 | 1 | yes | characteristic |
| 373 | C42 | C2×C22⋊D89 | 1 | 1 | yes | characteristic |
| 374 | C42 | C2×D356 | 1 | 1 | yes | characteristic |
| 375 | C23 | — | 2 | 1 | no | — |
| 376 | C23 | C22⋊C4×D89 | 1 | 1 | yes | characteristic |
| 377 | Q8 | — | 2 | 2 | no | — |
| 378 | Q8 | — | 356 | 4 | no | — |
| 379 | Q8 | — | 356 | 1 | no | — |
| 380 | Q8 | — | 356 | 1 | no | — |
| 381 | Q8 | — | 356 | 1 | no | — |
| 382 | Q8 | — | 356 | 1 | no | — |
| 383 | Q8 | — | 356 | 4 | no | — |
| 384 | D4 | — | 2 | 2 | no | — |
| 385 | D4 | — | 4 | 2 | no | — |
| 386 | C2×C4 | — | 2 | 1 | no | — |
| 387 | C2×C4 | — | 2 | 1 | no | — |
| 388 | C2×C4 | — | 2 | 1 | no | — |
| 389 | C2×C4 | — | 2 | 1 | no | — |
| 390 | C2×C4 | — | 2 | 2 | no | — |
| 391 | C2×C4 | — | 2 | 1 | no | — |
| 392 | C2×C4 | — | 2 | 1 | no | — |
| 393 | C2×C4 | — | 2 | 1 | no | — |
| 394 | C2×C4 | — | 4 | 2 | no | — |
| 395 | C2×C4 | — | 4 | 1 | no | — |
| 396 | C2×C4 | — | 4 | 1 | no | — |
| 397 | C2×C4 | — | 4 | 1 | no | — |
| 398 | C2×C4 | — | 4 | 1 | no | — |
| 399 | C2×C4 | — | 356 | 4 | no | — |
| 400 | C2×C4 | — | 178 | 2 | no | — |
| 401 | C2×C4 | — | 178 | 2 | no | — |
| 402 | C2×C4 | — | 178 | 4 | no | — |
| 403 | C2×C4 | C22⋊C4×D89 | 1 | 1 | yes | characteristic |
| 404 | C2×C4 | C2×#13083551 | 1 | 1 | yes | characteristic |
| 405 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 406 | C2×C4 | #15667980 | 1 | 1 | yes | characteristic |
| 407 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 408 | C2×C4 | #15667982 | 1 | 1 | yes | characteristic |
| 409 | C8 | — | 4 | 2 | no | — |
| 410 | C8 | — | 8 | 1 | no | — |
| 411 | C8 | — | 356 | 2 | no | — |
| 412 | C8 | — | 712 | 1 | no | — |
| 413 | C22 | — | 2 | 1 | no | — |
| 414 | C22 | — | 2 | 1 | no | — |
| 415 | C22 | — | 2 | 1 | no | — |
| 416 | C22 | — | 4 | 1 | no | — |
| 417 | C22 | — | 4 | 1 | no | — |
| 418 | C22 | — | 4 | 1 | no | — |
| 419 | C22 | #19151453 | 1 | 1 | yes | characteristic |
| 420 | C4 | — | 2 | 1 | no | — |
| 421 | C4 | — | 2 | 1 | no | — |
| 422 | C4 | — | 2 | 1 | no | — |
| 423 | C4 | — | 4 | 1 | no | — |
| 424 | C4 | — | 4 | 1 | no | — |
| 425 | C4 | — | 4 | 1 | no | — |
| 426 | C4 | — | 356 | 4 | no | — |
| 427 | C4 | — | 356 | 2 | no | — |
| 428 | C4 | — | 356 | 2 | no | — |
| 429 | C4 | #19151580 | 1 | 2 | yes | — |
| 430 | C4 | #19151769 | 1 | 1 | yes | characteristic |
| 431 | C4 | #19151772 | 1 | 1 | yes | characteristic |
| 432 | C4 | #19151779 | 1 | 1 | yes | characteristic |
| 433 | C4 | #19151782 | 1 | 1 | yes | characteristic |
| 434 | C2 | — | 4 | 1 | no | — |
| 435 | C2 | — | 8 | 1 | no | — |
| 436 | C2 | #26020178 | 1 | 1 | yes | characteristic |
| 437 | C2 | #26020209 | 1 | 1 | yes | characteristic |
| 438 | C2 | #26020212 | 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