← #17009561
Subgroups — #17009561
Order 4352.
848 conjugacy classes of subgroups.
The subgroup lattice has 534 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14543387 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14540002 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14539930 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14534903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14527793 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #14527782 | C2 | 1 | 4 | yes | maximal |
| 7 | #14527295 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #14527139 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C17×#1500 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C17⋊#564 | — | 2 | 1 | no | — |
| 11 | #11763559 | — | 2 | 1 | no | — |
| 12 | #11763537 | — | 2 | 1 | no | — |
| 13 | #11763516 | — | 2 | 1 | no | — |
| 14 | #11763499 | — | 2 | 1 | no | — |
| 15 | #11763499 | — | 2 | 1 | no | — |
| 16 | #11763496 | — | 2 | 2 | no | — |
| 17 | #11763438 | C22 | 1 | 2 | yes | — |
| 18 | #11763437 | — | 2 | 1 | no | — |
| 19 | #11763421 | — | 2 | 1 | no | — |
| 20 | #11763416 | — | 2 | 2 | no | — |
| 21 | #11763404 | C22 | 1 | 2 | yes | — |
| 22 | #11763366 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#10587555 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#10587556 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11763219 | — | 2 | 1 | no | — |
| 26 | #11763207 | — | 2 | 1 | no | — |
| 27 | #11763168 | — | 2 | 1 | no | — |
| 28 | #11763160 | — | 2 | 1 | no | — |
| 29 | #11763140 | C22 | 1 | 4 | yes | — |
| 30 | #11763137 | C22 | 1 | 2 | yes | — |
| 31 | #11763120 | C22 | 1 | 2 | yes | — |
| 32 | #11763104 | — | 2 | 1 | no | — |
| 33 | #11763099 | — | 2 | 1 | no | — |
| 34 | #11763095 | — | 2 | 2 | no | — |
| 35 | #11762866 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11762741 | C22 | 1 | 4 | yes | — |
| 37 | #11762730 | — | 2 | 2 | no | — |
| 38 | #11762679 | — | 2 | 1 | no | — |
| 39 | #11762675 | — | 2 | 1 | no | — |
| 40 | #11762545 | C22 | 1 | 4 | yes | — |
| 41 | #11762534 | C22 | 1 | 4 | yes | — |
| 42 | C17×#529 | C22 | 1 | 1 | yes | characteristic |
| 43 | C17×#431 | C22 | 1 | 1 | yes | characteristic |
| 44 | C17×#376 | C22 | 1 | 1 | yes | characteristic |
| 45 | C17×#328 | C22 | 1 | 2 | yes | — |
| 46 | C17×#327 | C22 | 1 | 2 | yes | — |
| 47 | C22×Dic34 | — | 2 | 1 | no | — |
| 48 | C17×#126 | — | 2 | 1 | no | — |
| 49 | C17×#125 | D4 | 1 | 1 | yes | characteristic |
| 50 | C17×#124 | D4 | 1 | 1 | yes | characteristic |
| 51 | C17×#123 | — | 2 | 1 | no | — |
| 52 | C17×C22⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 53 | C17×#121 | C23 | 1 | 1 | yes | characteristic |
| 54 | C4×Q8×C17 | D4 | 1 | 1 | yes | characteristic |
| 55 | C4×D4×C17 | — | 2 | 1 | no | — |
| 56 | C4×D4×C17 | D4 | 1 | 1 | yes | characteristic |
| 57 | C17×#117 | — | 2 | 1 | no | — |
| 58 | C2×C42×C17 | — | 2 | 1 | no | — |
| 59 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 60 | #10587630 | — | 2 | 2 | no | — |
| 61 | #10587621 | — | 2 | 2 | no | — |
| 62 | #10587621 | — | 2 | 2 | no | — |
| 63 | D4×Dic17 | — | 2 | 2 | no | — |
| 64 | #10587612 | — | 2 | 1 | no | — |
| 65 | #10587612 | — | 2 | 1 | no | — |
| 66 | C2×C4⋊Dic17 | — | 2 | 1 | no | — |
| 67 | C2×C4⋊Dic17 | — | 2 | 1 | no | — |
| 68 | C2×C4⋊Dic17 | — | 2 | 4 | no | — |
| 69 | C2×C4⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 70 | C2×C4⋊Dic17 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×C4⋊Dic17 | C23 | 1 | 2 | yes | — |
| 72 | #10587610 | — | 2 | 1 | no | — |
| 73 | #10587610 | — | 2 | 1 | no | — |
| 74 | #10587610 | — | 2 | 1 | no | — |
| 75 | #10587610 | C23 | 1 | 2 | yes | — |
| 76 | C2×#63225 | D4 | 1 | 2 | yes | — |
| 77 | C2×#63225 | C23 | 1 | 2 | yes | — |
| 78 | #10587576 | — | 2 | 2 | no | — |
| 79 | #10587576 | — | 2 | 2 | no | — |
| 80 | #10587575 | — | 2 | 2 | no | — |
| 81 | #10587575 | — | 2 | 2 | no | — |
| 82 | #10587575 | — | 2 | 2 | no | — |
| 83 | #10587575 | — | 2 | 2 | no | — |
| 84 | #10587575 | — | 2 | 2 | no | — |
| 85 | #10587575 | — | 2 | 2 | no | — |
| 86 | #10587574 | — | 2 | 2 | no | — |
| 87 | #10587573 | — | 2 | 2 | no | — |
| 88 | #10587565 | — | 2 | 2 | no | — |
| 89 | #10587565 | — | 2 | 2 | no | — |
| 90 | #10587565 | — | 2 | 2 | no | — |
| 91 | #10587565 | — | 2 | 2 | no | — |
| 92 | #10587564 | — | 2 | 2 | no | — |
| 93 | #10587564 | — | 2 | 2 | no | — |
| 94 | #10587564 | — | 2 | 2 | no | — |
| 95 | #10587564 | — | 2 | 2 | no | — |
| 96 | #10587563 | — | 2 | 2 | no | — |
| 97 | #10587563 | — | 2 | 2 | no | — |
| 98 | #10587556 | — | 2 | 1 | no | — |
| 99 | #10587556 | — | 2 | 1 | no | — |
| 100 | #10587556 | — | 2 | 1 | no | — |
| 101 | #10587556 | — | 2 | 1 | no | — |
| 102 | #10587556 | — | 2 | 1 | no | — |
| 103 | #10587556 | — | 2 | 1 | no | — |
| 104 | #10587555 | — | 2 | 1 | no | — |
| 105 | #10587555 | — | 2 | 1 | no | — |
| 106 | #10587555 | — | 2 | 1 | no | — |
| 107 | #10587555 | — | 2 | 1 | no | — |
| 108 | #10587555 | — | 2 | 1 | no | — |
| 109 | #10587555 | D4 | 1 | 1 | yes | characteristic |
| 110 | #10587555 | D4 | 1 | 1 | yes | characteristic |
| 111 | C4×Dic34 | — | 2 | 1 | no | — |
| 112 | C4×Dic34 | — | 2 | 1 | no | — |
| 113 | C4×Dic34 | — | 2 | 1 | no | — |
| 114 | C4×Dic34 | D4 | 1 | 2 | yes | — |
| 115 | C17×C4⋊C8 | — | 2 | 1 | no | — |
| 116 | C17×C22⋊C8 | C23 | 1 | 2 | yes | — |
| 117 | C4×C8×C17 | — | 2 | 1 | no | — |
| 118 | C17×#95 | — | 2 | 1 | no | — |
| 119 | C17×#95 | C23 | 1 | 2 | yes | — |
| 120 | #10587506 | — | 2 | 2 | no | — |
| 121 | #10587503 | — | 2 | 2 | no | — |
| 122 | #10587502 | — | 2 | 4 | no | — |
| 123 | C22⋊#3622 | C23 | 1 | 2 | yes | — |
| 124 | #10587488 | — | 2 | 4 | no | — |
| 125 | #10587487 | — | 2 | 4 | no | — |
| 126 | #10587479 | — | 2 | 2 | no | — |
| 127 | #10587478 | — | 2 | 2 | no | — |
| 128 | C4⋊#3622 | — | 2 | 1 | no | — |
| 129 | #10587474 | — | 2 | 1 | no | — |
| 130 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×D4×C17 | — | 2 | 1 | no | — |
| 132 | C2×D4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C22×C4×C17 | — | 2 | 2 | no | — |
| 134 | C22×C4×C17 | — | 2 | 1 | no | — |
| 135 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×C17 | C24 | 1 | 1 | yes | characteristic |
| 138 | C22×Dic17 | — | 2 | 2 | no | — |
| 139 | C22×Dic17 | — | 2 | 2 | no | — |
| 140 | C22×Dic17 | C2×D4 | 1 | 2 | yes | — |
| 141 | C22×Dic17 | C2×D4 | 1 | 2 | yes | — |
| 142 | C2×Dic34 | — | 2 | 1 | no | — |
| 143 | C2×Dic34 | — | 2 | 2 | no | — |
| 144 | C2×Dic34 | — | 4 | 1 | no | — |
| 145 | C2×Dic34 | — | 4 | 1 | no | — |
| 146 | C2×Dic34 | — | 8 | 2 | no | — |
| 147 | C2×Dic34 | C2×D4 | 1 | 2 | yes | — |
| 148 | C2×C8×C17 | — | 2 | 2 | no | — |
| 149 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 150 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 151 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 152 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 153 | C4⋊C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C4⋊C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 156 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 157 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 158 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 159 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 160 | C42×C17 | — | 2 | 4 | no | — |
| 161 | C42×C17 | — | 2 | 1 | no | — |
| 162 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | C42×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 166 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 167 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 168 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 169 | C22⋊Dic17 | — | 2 | 2 | no | — |
| 170 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 171 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 172 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 173 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 174 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 175 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 176 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 177 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 178 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 179 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 180 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 181 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 182 | C4⋊Dic17 | — | 4 | 1 | no | — |
| 183 | C4⋊Dic17 | — | 8 | 4 | no | — |
| 184 | C4⋊Dic17 | C2×D4 | 1 | 2 | yes | — |
| 185 | #63225 | — | 2 | 2 | no | — |
| 186 | #63225 | — | 2 | 2 | no | — |
| 187 | #63225 | — | 2 | 2 | no | — |
| 188 | #63225 | — | 2 | 2 | no | — |
| 189 | #63225 | — | 2 | 2 | no | — |
| 190 | #63225 | — | 2 | 2 | no | — |
| 191 | #63225 | — | 2 | 2 | no | — |
| 192 | #63225 | — | 2 | 2 | no | — |
| 193 | #63225 | — | 2 | 2 | no | — |
| 194 | #63225 | — | 2 | 2 | no | — |
| 195 | #63225 | — | 2 | 2 | no | — |
| 196 | #63225 | — | 2 | 2 | no | — |
| 197 | C4×Dic17 | — | 2 | 2 | no | — |
| 198 | C4×Dic17 | — | 2 | 2 | no | — |
| 199 | C4×Dic17 | — | 2 | 2 | no | — |
| 200 | C4×Dic17 | — | 2 | 2 | no | — |
| 201 | C2×#3622 | — | 2 | 2 | no | — |
| 202 | #18442 | — | 17 | 1 | no | maximal, Sylow |
| 203 | C23×C17 | — | 2 | 1 | no | — |
| 204 | C23×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 205 | Q8×C17 | — | 4 | 1 | no | — |
| 206 | D4×C17 | — | 4 | 1 | no | — |
| 207 | D4×C17 | — | 4 | 2 | no | — |
| 208 | C2×C4×C17 | — | 2 | 2 | no | — |
| 209 | C2×C4×C17 | — | 2 | 2 | no | — |
| 210 | C2×C4×C17 | — | 2 | 4 | no | — |
| 211 | C2×C4×C17 | — | 2 | 1 | no | — |
| 212 | C2×C4×C17 | — | 2 | 1 | no | — |
| 213 | C2×C4×C17 | — | 2 | 1 | no | — |
| 214 | C2×C4×C17 | — | 4 | 1 | no | — |
| 215 | C2×C4×C17 | — | 4 | 2 | no | — |
| 216 | C2×C4×C17 | — | 4 | 2 | no | — |
| 217 | C2×C4×C17 | — | 4 | 2 | no | — |
| 218 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 220 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 221 | C2×C4×C17 | #120 | 1 | 1 | yes | characteristic |
| 222 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×Dic17 | — | 2 | 2 | no | — |
| 225 | C2×Dic17 | — | 2 | 2 | no | — |
| 226 | C2×Dic17 | — | 2 | 2 | no | — |
| 227 | C2×Dic17 | — | 2 | 2 | no | — |
| 228 | C2×Dic17 | — | 2 | 4 | no | — |
| 229 | C2×Dic17 | — | 4 | 2 | no | — |
| 230 | C2×Dic17 | — | 4 | 2 | no | — |
| 231 | C2×Dic17 | — | 4 | 4 | no | — |
| 232 | C2×Dic17 | — | 8 | 2 | no | — |
| 233 | Dic34 | — | 4 | 2 | no | — |
| 234 | Dic34 | — | 4 | 2 | no | — |
| 235 | Dic34 | — | 8 | 2 | no | — |
| 236 | Dic34 | — | 8 | 2 | no | — |
| 237 | Dic34 | — | 8 | 2 | no | — |
| 238 | C8×C17 | — | 4 | 2 | no | — |
| 239 | #3622 | — | 4 | 2 | no | — |
| 240 | #3563 | — | 17 | 1 | no | — |
| 241 | #3238 | — | 17 | 1 | no | — |
| 242 | #3229 | — | 17 | 1 | no | — |
| 243 | #2660 | — | 17 | 1 | no | — |
| 244 | #1611 | — | 17 | 4 | no | — |
| 245 | #1609 | — | 17 | 4 | no | — |
| 246 | #1506 | — | 17 | 1 | no | — |
| 247 | #1500 | D17 | 1 | 1 | yes | characteristic |
| 248 | #1470 | — | 17 | 1 | no | — |
| 249 | C22×C17 | — | 2 | 1 | no | — |
| 250 | C22×C17 | — | 2 | 1 | no | — |
| 251 | C22×C17 | — | 4 | 1 | no | — |
| 252 | C22×C17 | — | 4 | 1 | no | — |
| 253 | C22×C17 | — | 4 | 1 | no | — |
| 254 | C22×C17 | C2×#120 | 1 | 1 | yes | characteristic |
| 255 | C22×C17 | #577 | 1 | 2 | yes | — |
| 256 | C4×C17 | — | 2 | 1 | no | — |
| 257 | C4×C17 | — | 2 | 1 | no | — |
| 258 | C4×C17 | — | 2 | 1 | no | — |
| 259 | C4×C17 | — | 2 | 1 | no | — |
| 260 | C4×C17 | — | 2 | 1 | no | — |
| 261 | C4×C17 | — | 4 | 4 | no | — |
| 262 | C4×C17 | — | 4 | 1 | no | — |
| 263 | C4×C17 | — | 4 | 1 | no | — |
| 264 | C4×C17 | — | 4 | 1 | no | — |
| 265 | C4×C17 | #456 | 1 | 2 | yes | — |
| 266 | Dic17 | — | 4 | 2 | no | — |
| 267 | Dic17 | — | 4 | 2 | no | — |
| 268 | Dic17 | — | 4 | 2 | no | — |
| 269 | Dic17 | — | 4 | 2 | no | — |
| 270 | Dic17 | — | 8 | 2 | no | — |
| 271 | #564 | — | 34 | 1 | no | — |
| 272 | #563 | — | 34 | 1 | no | — |
| 273 | #557 | — | 34 | 1 | no | — |
| 274 | #554 | — | 34 | 1 | no | — |
| 275 | #552 | — | 34 | 1 | no | — |
| 276 | #552 | — | 34 | 2 | no | — |
| 277 | #552 | — | 34 | 1 | no | — |
| 278 | #544 | — | 17 | 2 | no | — |
| 279 | #544 | — | 34 | 1 | no | — |
| 280 | #541 | — | 34 | 1 | no | — |
| 281 | #541 | — | 34 | 2 | no | — |
| 282 | #539 | — | 17 | 2 | no | — |
| 283 | #533 | — | 17 | 1 | no | — |
| 284 | C2×C4⋊Q8 | — | 17 | 1 | no | — |
| 285 | #529 | C2×D17 | 1 | 1 | yes | characteristic |
| 286 | C2×#125 | — | 17 | 1 | no | — |
| 287 | #501 | — | 34 | 1 | no | — |
| 288 | #498 | — | 34 | 1 | no | — |
| 289 | #489 | — | 34 | 1 | no | — |
| 290 | #487 | — | 34 | 1 | no | — |
| 291 | #483 | — | 17 | 2 | no | — |
| 292 | #483 | — | 17 | 4 | no | — |
| 293 | #480 | — | 17 | 2 | no | — |
| 294 | #477 | — | 34 | 1 | no | — |
| 295 | #476 | — | 34 | 1 | no | — |
| 296 | #475 | — | 34 | 2 | no | — |
| 297 | #432 | — | 17 | 1 | no | — |
| 298 | #431 | C2×D17 | 1 | 1 | yes | characteristic |
| 299 | #398 | — | 17 | 4 | no | — |
| 300 | #395 | — | 34 | 2 | no | — |
| 301 | #384 | — | 34 | 1 | no | — |
| 302 | #382 | — | 34 | 1 | no | — |
| 303 | #376 | C2×D17 | 1 | 1 | yes | characteristic |
| 304 | #328 | — | 17 | 4 | no | — |
| 305 | #328 | C2×D17 | 1 | 2 | yes | — |
| 306 | #327 | C2×D17 | 1 | 2 | yes | — |
| 307 | #324 | — | 17 | 4 | no | — |
| 308 | C2×C17 | — | 2 | 2 | no | — |
| 309 | C2×C17 | — | 8 | 1 | no | — |
| 310 | C2×C17 | #3010 | 1 | 1 | yes | characteristic |
| 311 | C2×C17 | C2×#456 | 1 | 1 | yes | characteristic |
| 312 | C2×C17 | #3028 | 1 | 1 | yes | characteristic |
| 313 | C22×Q8 | — | 34 | 1 | no | — |
| 314 | C4⋊Q8 | — | 17 | 1 | no | — |
| 315 | C4⋊Q8 | — | 17 | 1 | no | — |
| 316 | C4⋊Q8 | — | 34 | 1 | no | — |
| 317 | C4⋊Q8 | — | 34 | 2 | no | — |
| 318 | C4⋊Q8 | — | 34 | 2 | no | — |
| 319 | C4⋊Q8 | — | 34 | 1 | no | — |
| 320 | C4⋊Q8 | — | 34 | 1 | no | — |
| 321 | C4⋊Q8 | — | 34 | 1 | no | — |
| 322 | C4⋊Q8 | — | 34 | 1 | no | — |
| 323 | #126 | — | 2 | 1 | no | — |
| 324 | #126 | — | 34 | 2 | no | — |
| 325 | #126 | — | 34 | 2 | no | — |
| 326 | #126 | — | 34 | 2 | no | — |
| 327 | #126 | — | 34 | 2 | no | — |
| 328 | #125 | — | 34 | 1 | no | — |
| 329 | #125 | — | 34 | 2 | no | — |
| 330 | #125 | — | 34 | 2 | no | — |
| 331 | #125 | — | 34 | 2 | no | — |
| 332 | #125 | — | 34 | 2 | no | — |
| 333 | #125 | — | 34 | 2 | no | — |
| 334 | #125 | — | 34 | 2 | no | — |
| 335 | #125 | — | 34 | 2 | no | — |
| 336 | #125 | — | 34 | 2 | no | — |
| 337 | #125 | — | 34 | 1 | no | — |
| 338 | #125 | — | 34 | 1 | no | — |
| 339 | #125 | — | 34 | 1 | no | — |
| 340 | #125 | — | 34 | 1 | no | — |
| 341 | #125 | — | 34 | 1 | no | — |
| 342 | #125 | D68 | 1 | 1 | yes | characteristic |
| 343 | #124 | D68 | 1 | 1 | yes | characteristic |
| 344 | #123 | — | 2 | 1 | no | — |
| 345 | #123 | — | 34 | 2 | no | — |
| 346 | #123 | — | 34 | 2 | no | — |
| 347 | C22⋊Q8 | — | 17 | 2 | no | — |
| 348 | C22⋊Q8 | — | 34 | 2 | no | — |
| 349 | C22⋊Q8 | — | 34 | 2 | no | — |
| 350 | C22⋊Q8 | — | 34 | 2 | no | — |
| 351 | C22⋊Q8 | — | 34 | 2 | no | — |
| 352 | C22⋊Q8 | — | 34 | 1 | no | — |
| 353 | C22⋊Q8 | — | 34 | 1 | no | — |
| 354 | C22⋊Q8 | — | 34 | 1 | no | — |
| 355 | C22⋊Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 356 | #121 | C22×D17 | 1 | 1 | yes | characteristic |
| 357 | C4×Q8 | — | 17 | 2 | no | — |
| 358 | C4×Q8 | — | 34 | 1 | no | — |
| 359 | C4×Q8 | — | 34 | 1 | no | — |
| 360 | C4×Q8 | — | 34 | 2 | no | — |
| 361 | C4×Q8 | — | 34 | 1 | no | — |
| 362 | C4×Q8 | D68 | 1 | 1 | yes | characteristic |
| 363 | C4×D4 | — | 2 | 1 | no | — |
| 364 | C4×D4 | — | 34 | 2 | no | — |
| 365 | C4×D4 | D68 | 1 | 1 | yes | characteristic |
| 366 | #117 | — | 2 | 1 | no | — |
| 367 | #117 | — | 34 | 2 | no | — |
| 368 | #117 | — | 34 | 2 | no | — |
| 369 | #117 | — | 34 | 1 | no | — |
| 370 | #117 | — | 34 | 1 | no | — |
| 371 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 372 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 373 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 374 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 375 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 376 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 377 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 378 | C2×C4⋊C4 | — | 34 | 4 | no | — |
| 379 | C2×C42 | — | 2 | 1 | no | — |
| 380 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 381 | #107 | — | 34 | 2 | no | — |
| 382 | #106 | — | 34 | 4 | no | — |
| 383 | #106 | — | 34 | 2 | no | — |
| 384 | C4⋊C8 | — | 2 | 1 | no | — |
| 385 | C4⋊C8 | — | 34 | 1 | no | — |
| 386 | #103 | — | 34 | 4 | no | — |
| 387 | #103 | — | 34 | 2 | no | — |
| 388 | #102 | — | 34 | 2 | no | — |
| 389 | C22⋊C8 | — | 17 | 2 | no | — |
| 390 | C22⋊C8 | C22×D17 | 1 | 2 | yes | — |
| 391 | #97 | — | 34 | 1 | no | — |
| 392 | C4×C8 | — | 2 | 1 | no | — |
| 393 | #95 | — | 2 | 1 | no | — |
| 394 | #95 | — | 34 | 4 | no | — |
| 395 | #95 | C22×D17 | 1 | 2 | yes | — |
| 396 | C17 | #18442 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 397 | C2×Q8 | — | 17 | 2 | no | — |
| 398 | C2×Q8 | — | 34 | 2 | no | — |
| 399 | C2×Q8 | — | 34 | 1 | no | — |
| 400 | C2×Q8 | — | 68 | 1 | no | — |
| 401 | C2×Q8 | — | 68 | 1 | no | — |
| 402 | C2×Q8 | — | 136 | 2 | no | — |
| 403 | C2×Q8 | C2×D68 | 1 | 1 | yes | characteristic |
| 404 | C2×D4 | — | 2 | 1 | no | — |
| 405 | C2×D4 | C2×D68 | 1 | 1 | yes | characteristic |
| 406 | C22×C4 | — | 2 | 2 | no | — |
| 407 | C22×C4 | — | 2 | 1 | no | — |
| 408 | C22×C4 | — | 17 | 2 | no | — |
| 409 | C22×C4 | — | 17 | 2 | no | — |
| 410 | C22×C4 | — | 34 | 2 | no | — |
| 411 | C22×C4 | — | 34 | 2 | no | — |
| 412 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 413 | C22×C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 414 | C22×C4 | C23×D17 | 1 | 1 | yes | characteristic |
| 415 | C2×C8 | — | 2 | 2 | no | — |
| 416 | C2×C8 | — | 34 | 2 | no | — |
| 417 | C4⋊C4 | — | 2 | 1 | no | — |
| 418 | C4⋊C4 | — | 2 | 1 | no | — |
| 419 | C4⋊C4 | — | 2 | 1 | no | — |
| 420 | C4⋊C4 | — | 2 | 1 | no | — |
| 421 | C4⋊C4 | — | 17 | 2 | no | — |
| 422 | C4⋊C4 | — | 34 | 2 | no | — |
| 423 | C4⋊C4 | — | 34 | 2 | no | — |
| 424 | C4⋊C4 | — | 34 | 2 | no | — |
| 425 | C4⋊C4 | — | 34 | 2 | no | — |
| 426 | C4⋊C4 | — | 34 | 2 | no | — |
| 427 | C4⋊C4 | — | 34 | 2 | no | — |
| 428 | C4⋊C4 | — | 34 | 2 | no | — |
| 429 | C4⋊C4 | — | 34 | 2 | no | — |
| 430 | C4⋊C4 | — | 34 | 2 | no | — |
| 431 | C4⋊C4 | — | 34 | 2 | no | — |
| 432 | C4⋊C4 | — | 34 | 2 | no | — |
| 433 | C4⋊C4 | — | 34 | 1 | no | — |
| 434 | C4⋊C4 | — | 34 | 1 | no | — |
| 435 | C4⋊C4 | — | 34 | 2 | no | — |
| 436 | C4⋊C4 | — | 34 | 1 | no | — |
| 437 | C4⋊C4 | — | 34 | 2 | no | — |
| 438 | C4⋊C4 | — | 34 | 1 | no | — |
| 439 | C4⋊C4 | — | 34 | 1 | no | — |
| 440 | C4⋊C4 | — | 34 | 1 | no | — |
| 441 | C4⋊C4 | — | 34 | 1 | no | — |
| 442 | C4⋊C4 | — | 34 | 2 | no | — |
| 443 | C4⋊C4 | — | 34 | 2 | no | — |
| 444 | C4⋊C4 | — | 34 | 2 | no | — |
| 445 | C4⋊C4 | — | 68 | 1 | no | — |
| 446 | C4⋊C4 | — | 68 | 1 | no | — |
| 447 | C4⋊C4 | — | 136 | 4 | no | — |
| 448 | C4⋊C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 449 | C4⋊C4 | C2×D68 | 1 | 1 | yes | characteristic |
| 450 | C22⋊C4 | — | 2 | 1 | no | — |
| 451 | C22⋊C4 | — | 2 | 1 | no | — |
| 452 | C22⋊C4 | — | 2 | 1 | no | — |
| 453 | C22⋊C4 | — | 2 | 1 | no | — |
| 454 | C22⋊C4 | — | 2 | 1 | no | — |
| 455 | C22⋊C4 | — | 34 | 2 | no | — |
| 456 | C22⋊C4 | — | 34 | 2 | no | — |
| 457 | C22⋊C4 | — | 34 | 2 | no | — |
| 458 | C22⋊C4 | — | 34 | 2 | no | — |
| 459 | C42 | — | 2 | 4 | no | — |
| 460 | C42 | — | 2 | 1 | no | — |
| 461 | C42 | — | 34 | 2 | no | — |
| 462 | C42 | — | 34 | 2 | no | — |
| 463 | C42 | — | 34 | 2 | no | — |
| 464 | C42 | — | 34 | 2 | no | — |
| 465 | C42 | C2×D68 | 1 | 1 | yes | characteristic |
| 466 | C42 | C2×D68 | 1 | 1 | yes | characteristic |
| 467 | C42 | D4×D17 | 1 | 1 | yes | characteristic |
| 468 | C42 | D4×D17 | 1 | 1 | yes | characteristic |
| 469 | C23 | — | 2 | 1 | no | — |
| 470 | C23 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 471 | Q8 | — | 4 | 1 | no | — |
| 472 | Q8 | — | 68 | 2 | no | — |
| 473 | Q8 | — | 68 | 2 | no | — |
| 474 | Q8 | — | 136 | 2 | no | — |
| 475 | Q8 | — | 136 | 2 | no | — |
| 476 | Q8 | — | 136 | 2 | no | — |
| 477 | D4 | — | 4 | 1 | no | — |
| 478 | D4 | — | 4 | 2 | no | — |
| 479 | C2×C4 | — | 2 | 2 | no | — |
| 480 | C2×C4 | — | 2 | 2 | no | — |
| 481 | C2×C4 | — | 2 | 4 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 4 | 1 | no | — |
| 486 | C2×C4 | — | 4 | 2 | no | — |
| 487 | C2×C4 | — | 4 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 2 | no | — |
| 489 | C2×C4 | — | 34 | 2 | no | — |
| 490 | C2×C4 | — | 34 | 2 | no | — |
| 491 | C2×C4 | — | 34 | 2 | no | — |
| 492 | C2×C4 | — | 34 | 2 | no | — |
| 493 | C2×C4 | — | 34 | 4 | no | — |
| 494 | C2×C4 | — | 68 | 2 | no | — |
| 495 | C2×C4 | — | 68 | 2 | no | — |
| 496 | C2×C4 | — | 68 | 4 | no | — |
| 497 | C2×C4 | — | 136 | 2 | no | — |
| 498 | C2×C4 | #10587568 | 1 | 1 | yes | characteristic |
| 499 | C2×C4 | #10587568 | 1 | 1 | yes | characteristic |
| 500 | C2×C4 | #10587568 | 1 | 1 | yes | characteristic |
| 501 | C2×C4 | #10587568 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | C22×D68 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 504 | C8 | — | 4 | 2 | no | — |
| 505 | C8 | — | 68 | 2 | no | — |
| 506 | C22 | — | 2 | 1 | no | — |
| 507 | C22 | — | 2 | 1 | no | — |
| 508 | C22 | — | 4 | 1 | no | — |
| 509 | C22 | — | 4 | 1 | no | — |
| 510 | C22 | — | 4 | 1 | no | — |
| 511 | C22 | C2×#10587568 | 1 | 1 | yes | characteristic |
| 512 | C22 | #11763616 | 1 | 2 | yes | — |
| 513 | C4 | — | 2 | 1 | no | — |
| 514 | C4 | — | 2 | 1 | no | — |
| 515 | C4 | — | 2 | 1 | no | — |
| 516 | C4 | — | 2 | 1 | no | — |
| 517 | C4 | — | 2 | 1 | no | — |
| 518 | C4 | — | 4 | 4 | no | — |
| 519 | C4 | — | 4 | 1 | no | — |
| 520 | C4 | — | 4 | 1 | no | — |
| 521 | C4 | — | 4 | 1 | no | — |
| 522 | C4 | — | 68 | 2 | no | — |
| 523 | C4 | — | 68 | 2 | no | — |
| 524 | C4 | — | 68 | 2 | no | — |
| 525 | C4 | — | 68 | 2 | no | — |
| 526 | C4 | — | 136 | 2 | no | — |
| 527 | C4 | #11762993 | 1 | 2 | yes | — |
| 528 | C2 | — | 2 | 2 | no | — |
| 529 | C2 | — | 8 | 1 | no | — |
| 530 | C2 | #14538073 | 1 | 1 | yes | characteristic |
| 531 | C2 | C2×#11762993 | 1 | 1 | yes | characteristic |
| 532 | C2 | #14538191 | 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