← #17967751
Subgroups — #17967751
Order 4352.
638 conjugacy classes of subgroups.
The subgroup lattice has 488 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14545586 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×#63243 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14544422 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #14544397 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #14544396 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14544371 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #14544343 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #14544113 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #14544113 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | C8×#63243 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C4×Q16×D17 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #11763861 | — | 2 | 2 | no | — |
| 13 | #11763860 | C22 | 1 | 2 | yes | — |
| 14 | #11763859 | — | 2 | 2 | no | — |
| 15 | #11763859 | C22 | 1 | 2 | yes | — |
| 16 | #11763858 | C22 | 1 | 2 | yes | — |
| 17 | Q8×#3624 | C22 | 1 | 2 | yes | — |
| 18 | #11763828 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11763814 | — | 2 | 1 | no | — |
| 20 | #11763813 | — | 2 | 1 | no | — |
| 21 | #11763813 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11763813 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4×#63243 | — | 2 | 1 | no | — |
| 24 | C4×#63243 | — | 2 | 1 | no | — |
| 25 | C4×#63243 | C22 | 1 | 1 | yes | characteristic |
| 26 | #11763673 | C22 | 1 | 2 | yes | — |
| 27 | #11763673 | C22 | 1 | 2 | yes | — |
| 28 | #11763659 | C22 | 1 | 2 | yes | — |
| 29 | #11763659 | C22 | 1 | 2 | yes | — |
| 30 | Q8⋊#3624 | C22 | 1 | 2 | yes | — |
| 31 | Q8⋊#3624 | C22 | 1 | 2 | yes | — |
| 32 | #11763651 | C22 | 1 | 2 | yes | — |
| 33 | C8×#3624 | C22 | 1 | 2 | yes | — |
| 34 | C2×Q16×D17 | C4 | 1 | 1 | yes | characteristic |
| 35 | C4×Q8×D17 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×Q8×D17 | C22 | 1 | 1 | yes | characteristic |
| 37 | C4×Dic68 | C4 | 1 | 1 | yes | characteristic |
| 38 | Q16×Dic17 | C22 | 1 | 1 | yes | characteristic |
| 39 | #11762903 | C22 | 1 | 1 | yes | characteristic |
| 40 | C4×#63231 | C4 | 1 | 1 | yes | characteristic |
| 41 | C4×#63231 | C4 | 1 | 1 | yes | characteristic |
| 42 | #11762901 | C22 | 1 | 1 | yes | characteristic |
| 43 | #11762901 | C22 | 1 | 1 | yes | characteristic |
| 44 | #107×D17 | C4 | 1 | 1 | yes | characteristic |
| 45 | #103×D17 | C4 | 1 | 1 | yes | characteristic |
| 46 | #103×D17 | C4 | 1 | 1 | yes | characteristic |
| 47 | C4×C8×D17 | C22 | 1 | 1 | yes | characteristic |
| 48 | C4×Q16×C17 | C4 | 1 | 1 | yes | characteristic |
| 49 | C2×Q8×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | C2×Q8×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C2×#63243 | — | 2 | 1 | no | — |
| 52 | C2×#63243 | — | 2 | 1 | no | — |
| 53 | C2×#63243 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×#63243 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×Q16×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C4×Q8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C4×Q8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | Q8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 59 | Q8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#63231 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×#63231 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | Q16×D17 | — | 2 | 4 | no | — |
| 63 | C2×Dic68 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | C2×C8×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C2×C8×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C4⋊C4×D17 | — | 2 | 1 | no | — |
| 67 | C4⋊C4×D17 | — | 2 | 1 | no | — |
| 68 | C4⋊C4×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C4⋊C4×D17 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | #10587573 | — | 2 | 1 | no | — |
| 71 | #10587573 | — | 2 | 1 | no | — |
| 72 | #10587573 | C23 | 1 | 1 | yes | characteristic |
| 73 | #10587573 | C23 | 1 | 1 | yes | characteristic |
| 74 | C42×D17 | — | 2 | 1 | no | — |
| 75 | C42×D17 | — | 2 | 1 | no | — |
| 76 | C42×D17 | C23 | 1 | 1 | yes | characteristic |
| 77 | C4×Dic34 | — | 2 | 1 | no | — |
| 78 | C4×Dic34 | — | 2 | 1 | no | — |
| 79 | C4×Dic34 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic34 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #10587544 | — | 2 | 2 | no | — |
| 82 | #10587544 | — | 2 | 2 | no | — |
| 83 | #10587543 | — | 2 | 1 | no | — |
| 84 | #10587542 | — | 2 | 2 | no | — |
| 85 | #10587542 | — | 2 | 2 | no | — |
| 86 | #10587542 | D4 | 1 | 2 | yes | — |
| 87 | C4⋊#3624 | — | 2 | 1 | no | — |
| 88 | C4⋊#3624 | — | 2 | 1 | no | — |
| 89 | C4⋊#3624 | — | 2 | 1 | no | — |
| 90 | C4⋊#3624 | — | 2 | 2 | no | — |
| 91 | C4⋊#3624 | — | 2 | 2 | no | — |
| 92 | C4⋊#3624 | C23 | 1 | 2 | yes | — |
| 93 | C4⋊#3624 | C23 | 1 | 2 | yes | — |
| 94 | C4×#3624 | — | 2 | 2 | no | — |
| 95 | C4×#3624 | — | 2 | 2 | no | — |
| 96 | C4×#3624 | C23 | 1 | 2 | yes | — |
| 97 | C4×#3624 | C23 | 1 | 2 | yes | — |
| 98 | C17×#107 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | C17×#103 | C2×C4 | 1 | 1 | yes | characteristic |
| 100 | C17×#103 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | C4×C8×C17 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #10587506 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #10587506 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | #10587489 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | #10587487 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | #10587487 | C2×C4 | 1 | 1 | yes | characteristic |
| 107 | C8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 108 | C8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 109 | #10587481 | C2×C4 | 1 | 1 | yes | characteristic |
| 110 | #10587481 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | #10587478 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | #10587478 | C2×C4 | 1 | 1 | yes | characteristic |
| 113 | C4×#3622 | C2×C4 | 1 | 1 | yes | characteristic |
| 114 | C2×Q8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 115 | C2×Q8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | Q8×D17 | — | 2 | 2 | no | — |
| 117 | Q8×D17 | — | 2 | 2 | no | — |
| 118 | Q8×D17 | — | 4 | 1 | no | — |
| 119 | Q8×D17 | — | 4 | 1 | no | — |
| 120 | C2×C4×D17 | — | 2 | 1 | no | — |
| 121 | C2×C4×D17 | — | 2 | 1 | no | — |
| 122 | C2×C4×D17 | — | 2 | 1 | no | — |
| 123 | C2×C4×D17 | — | 2 | 1 | no | — |
| 124 | C2×C4×D17 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×D17 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×D17 | #41 | 1 | 1 | yes | characteristic |
| 127 | C2×Dic34 | — | 2 | 1 | no | — |
| 128 | C2×Dic34 | — | 2 | 1 | no | — |
| 129 | C2×Dic34 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | C2×Dic34 | C22×C4 | 1 | 1 | yes | characteristic |
| 131 | C2×#3624 | — | 2 | 2 | no | — |
| 132 | C2×#3624 | — | 2 | 2 | no | — |
| 133 | C2×#3624 | — | 2 | 2 | no | — |
| 134 | C2×#3624 | C2×D4 | 1 | 2 | yes | — |
| 135 | C2×#3624 | C2×D4 | 1 | 2 | yes | — |
| 136 | #63243 | — | 2 | 2 | no | — |
| 137 | #63243 | — | 4 | 2 | no | — |
| 138 | #63243 | — | 4 | 2 | no | — |
| 139 | #63243 | Q16 | 1 | 4 | yes | complemented |
| 140 | Q16×C17 | — | 2 | 2 | no | — |
| 141 | C2×C8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 142 | C2×C8×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 144 | C4⋊C4×C17 | — | 2 | 1 | no | — |
| 145 | C4⋊C4×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 146 | C4⋊C4×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | C42×C17 | — | 2 | 1 | no | — |
| 148 | C42×C17 | — | 2 | 1 | no | — |
| 149 | C42×C17 | C22×C4 | 1 | 1 | yes | characteristic |
| 150 | #63231 | — | 2 | 2 | no | — |
| 151 | #63231 | M16 | 1 | 4 | yes | complemented |
| 152 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 153 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 154 | C4⋊Dic17 | C22×C4 | 1 | 1 | yes | characteristic |
| 155 | C4⋊Dic17 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | #63225 | — | 2 | 1 | no | — |
| 157 | #63225 | — | 2 | 1 | no | — |
| 158 | #63225 | — | 2 | 1 | no | — |
| 159 | #63225 | — | 2 | 1 | no | — |
| 160 | #63225 | — | 2 | 1 | no | — |
| 161 | #63225 | — | 2 | 1 | no | — |
| 162 | C4×Dic17 | — | 2 | 1 | no | — |
| 163 | C4×Dic17 | — | 2 | 1 | no | — |
| 164 | C4×Dic17 | — | 2 | 1 | no | — |
| 165 | C4×Dic17 | — | 2 | 1 | no | — |
| 166 | C4×Dic17 | — | 2 | 1 | no | — |
| 167 | C4×Dic17 | — | 2 | 1 | no | — |
| 168 | C4×Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C4×Dic17 | #41 | 1 | 1 | yes | characteristic |
| 170 | C4×Dic17 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×#3622 | C22×C4 | 1 | 1 | yes | characteristic |
| 172 | C2×#3622 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | Dic68 | — | 2 | 2 | no | — |
| 174 | C8×D17 | — | 2 | 2 | no | — |
| 175 | C8×D17 | — | 4 | 1 | no | — |
| 176 | M16×Q16 | — | 17 | 1 | no | maximal, Sylow |
| 177 | C22×D17 | C4×D4 | 1 | 1 | yes | characteristic |
| 178 | Q8×C17 | — | 2 | 1 | no | — |
| 179 | Q8×C17 | — | 2 | 1 | no | — |
| 180 | Q8×C17 | — | 2 | 1 | no | — |
| 181 | Q8×C17 | C2×M16 | 1 | 2 | yes | — |
| 182 | C2×C4×C17 | — | 2 | 1 | no | — |
| 183 | C2×C4×C17 | — | 2 | 1 | no | — |
| 184 | C2×C4×C17 | — | 2 | 1 | no | — |
| 185 | C2×C4×C17 | — | 2 | 1 | no | — |
| 186 | C2×C4×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C4×C17 | C4×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×C4×C17 | C23×C4 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic17 | — | 2 | 1 | no | — |
| 190 | C2×Dic17 | — | 2 | 1 | no | — |
| 191 | C2×Dic17 | — | 2 | 1 | no | — |
| 192 | C2×Dic17 | — | 2 | 1 | no | — |
| 193 | C2×Dic17 | C4×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×Dic17 | C2×#41 | 1 | 1 | yes | characteristic |
| 196 | C4×D17 | — | 2 | 1 | no | — |
| 197 | C4×D17 | — | 2 | 1 | no | — |
| 198 | C4×D17 | — | 4 | 1 | no | — |
| 199 | C4×D17 | — | 4 | 2 | no | — |
| 200 | C4×D17 | — | 4 | 2 | no | — |
| 201 | C4×D17 | — | 8 | 1 | no | — |
| 202 | C4×D17 | — | 8 | 1 | no | — |
| 203 | C4×D17 | C2×Q16 | 1 | 2 | yes | — |
| 204 | C4×D17 | #135 | 1 | 2 | yes | — |
| 205 | Dic34 | — | 2 | 1 | no | — |
| 206 | Dic34 | — | 2 | 1 | no | — |
| 207 | Dic34 | — | 2 | 1 | no | — |
| 208 | Dic34 | — | 4 | 2 | no | — |
| 209 | Dic34 | — | 4 | 2 | no | — |
| 210 | Dic34 | C2×M16 | 1 | 2 | yes | — |
| 211 | #3624 | — | 2 | 2 | no | — |
| 212 | #3624 | — | 4 | 2 | no | — |
| 213 | #3624 | — | 4 | 2 | no | — |
| 214 | #3624 | — | 4 | 2 | no | — |
| 215 | #3624 | C2×Q16 | 1 | 4 | yes | complemented |
| 216 | C8×C17 | — | 2 | 1 | no | — |
| 217 | C8×C17 | — | 2 | 1 | no | — |
| 218 | #3622 | — | 2 | 1 | no | — |
| 219 | #3622 | C2×M16 | 1 | 2 | yes | — |
| 220 | Q8×M16 | — | 17 | 1 | no | — |
| 221 | Q8×M16 | — | 17 | 1 | no | — |
| 222 | C2×C4×Q16 | — | 17 | 1 | no | — |
| 223 | #1591 | — | 17 | 2 | no | — |
| 224 | #1584 | — | 17 | 2 | no | — |
| 225 | #1584 | — | 17 | 2 | no | — |
| 226 | C8×Q16 | — | 17 | 2 | no | — |
| 227 | #1567 | — | 17 | 1 | no | — |
| 228 | #1487 | — | 17 | 1 | no | — |
| 229 | #1487 | — | 17 | 1 | no | — |
| 230 | C8×M16 | — | 17 | 1 | no | — |
| 231 | C22×C17 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×D17 | — | 2 | 1 | no | — |
| 233 | C2×D17 | — | 2 | 1 | no | — |
| 234 | C2×D17 | C4×Q16 | 1 | 2 | yes | — |
| 235 | C4×C17 | — | 2 | 2 | no | — |
| 236 | C4×C17 | — | 2 | 1 | no | — |
| 237 | C4×C17 | — | 4 | 1 | no | — |
| 238 | C4×C17 | — | 4 | 1 | no | — |
| 239 | C4×C17 | — | 4 | 1 | no | — |
| 240 | C4×C17 | C4×Q16 | 1 | 2 | yes | — |
| 241 | C4×C17 | C22×M16 | 1 | 1 | yes | characteristic |
| 242 | C4×C17 | #568 | 1 | 1 | yes | characteristic |
| 243 | Dic17 | — | 2 | 2 | no | — |
| 244 | Dic17 | — | 2 | 1 | no | — |
| 245 | Dic17 | — | 2 | 1 | no | — |
| 246 | Dic17 | — | 4 | 1 | no | — |
| 247 | Dic17 | — | 4 | 1 | no | — |
| 248 | Dic17 | — | 4 | 1 | no | — |
| 249 | Dic17 | C22×Q16 | 1 | 1 | yes | characteristic |
| 250 | Dic17 | C2×#135 | 1 | 1 | yes | characteristic |
| 251 | C22×Q16 | — | 17 | 1 | no | — |
| 252 | C2×C4×Q8 | — | 17 | 1 | no | — |
| 253 | C2×C4×Q8 | — | 17 | 1 | no | — |
| 254 | #446 | — | 17 | 2 | no | — |
| 255 | #446 | — | 17 | 2 | no | — |
| 256 | #446 | — | 34 | 2 | no | — |
| 257 | #446 | — | 34 | 2 | no | — |
| 258 | C8×Q8 | — | 17 | 2 | no | — |
| 259 | C8×Q8 | — | 17 | 2 | no | — |
| 260 | C4×Q16 | — | 17 | 1 | no | — |
| 261 | C4×Q16 | — | 17 | 1 | no | — |
| 262 | C4×Q16 | — | 17 | 1 | no | — |
| 263 | C4×Q16 | — | 17 | 1 | no | — |
| 264 | C4×Q16 | — | 17 | 1 | no | — |
| 265 | C4×Q16 | — | 17 | 1 | no | — |
| 266 | C4×Q16 | — | 17 | 1 | no | — |
| 267 | C4×Q16 | #595 | 1 | 1 | yes | characteristic |
| 268 | #431 | — | 17 | 1 | no | — |
| 269 | C2×#107 | — | 17 | 1 | no | — |
| 270 | #423 | — | 17 | 1 | no | — |
| 271 | #423 | — | 17 | 1 | no | — |
| 272 | #423 | — | 34 | 1 | no | — |
| 273 | #423 | — | 34 | 1 | no | — |
| 274 | C2×#103 | — | 17 | 1 | no | — |
| 275 | C2×#103 | — | 17 | 1 | no | — |
| 276 | C4×M16 | — | 17 | 1 | no | — |
| 277 | C4×M16 | — | 34 | 1 | no | — |
| 278 | C4×M16 | — | 34 | 1 | no | — |
| 279 | C2×C4×C8 | — | 17 | 1 | no | — |
| 280 | #335 | — | 17 | 2 | no | — |
| 281 | #335 | — | 17 | 2 | no | — |
| 282 | Q8⋊C8 | — | 17 | 2 | no | — |
| 283 | Q8⋊C8 | — | 17 | 2 | no | — |
| 284 | Q8⋊C8 | — | 17 | 2 | no | — |
| 285 | Q8⋊C8 | — | 17 | 2 | no | — |
| 286 | #322 | — | 17 | 2 | no | — |
| 287 | C82 | — | 17 | 2 | no | — |
| 288 | C2×C17 | D4×M16 | 1 | 1 | yes | characteristic |
| 289 | C2×C17 | C2×C4×Q16 | 1 | 1 | yes | characteristic |
| 290 | C2×C17 | #2957 | 1 | 1 | yes | characteristic |
| 291 | D17 | — | 2 | 2 | no | — |
| 292 | C22×Q8 | — | 17 | 1 | no | — |
| 293 | C22×Q8 | — | 17 | 1 | no | — |
| 294 | C2×Q16 | — | 17 | 1 | no | — |
| 295 | C2×Q16 | — | 17 | 1 | no | — |
| 296 | C2×Q16 | — | 17 | 1 | no | — |
| 297 | C2×Q16 | — | 34 | 4 | no | — |
| 298 | C2×Q16 | C2×#595 | 1 | 1 | yes | characteristic |
| 299 | C2×M16 | — | 17 | 1 | no | — |
| 300 | C2×M16 | — | 17 | 1 | no | — |
| 301 | C2×M16 | — | 34 | 1 | no | — |
| 302 | C2×M16 | — | 34 | 1 | no | — |
| 303 | C22×C8 | — | 17 | 1 | no | — |
| 304 | C22×C8 | — | 17 | 1 | no | — |
| 305 | C4×Q8 | — | 17 | 1 | no | — |
| 306 | C4×Q8 | — | 17 | 1 | no | — |
| 307 | C4×Q8 | — | 17 | 1 | no | — |
| 308 | C4×Q8 | — | 17 | 1 | no | — |
| 309 | C4×Q8 | — | 17 | 1 | no | — |
| 310 | C4×Q8 | — | 17 | 1 | no | — |
| 311 | C4×Q8 | — | 34 | 1 | no | — |
| 312 | C4×Q8 | — | 34 | 1 | no | — |
| 313 | C4×Q8 | — | 34 | 1 | no | — |
| 314 | C4×Q8 | — | 34 | 1 | no | — |
| 315 | C4×Q8 | C2×#595 | 1 | 1 | yes | characteristic |
| 316 | C4×Q8 | C2×#595 | 1 | 1 | yes | characteristic |
| 317 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 318 | C2×C4⋊C4 | — | 17 | 1 | no | — |
| 319 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 320 | C2×C4⋊C4 | — | 34 | 1 | no | — |
| 321 | C2×C42 | — | 17 | 1 | no | — |
| 322 | C2×C42 | — | 34 | 1 | no | — |
| 323 | C2×C42 | — | 34 | 1 | no | — |
| 324 | #107 | — | 17 | 1 | no | — |
| 325 | #107 | — | 17 | 1 | no | — |
| 326 | #107 | — | 17 | 1 | no | — |
| 327 | #107 | C2×#595 | 1 | 1 | yes | characteristic |
| 328 | C4⋊C8 | — | 17 | 2 | no | — |
| 329 | C4⋊C8 | — | 17 | 2 | no | — |
| 330 | C4⋊C8 | — | 34 | 1 | no | — |
| 331 | C4⋊C8 | — | 34 | 1 | no | — |
| 332 | C4⋊C8 | — | 34 | 1 | no | — |
| 333 | C4⋊C8 | — | 34 | 2 | no | — |
| 334 | C4⋊C8 | — | 34 | 2 | no | — |
| 335 | C4⋊C8 | — | 34 | 2 | no | — |
| 336 | C4⋊C8 | — | 34 | 2 | no | — |
| 337 | #103 | — | 17 | 1 | no | — |
| 338 | #103 | — | 17 | 1 | no | — |
| 339 | #103 | — | 17 | 1 | no | — |
| 340 | #103 | — | 17 | 1 | no | — |
| 341 | #103 | — | 17 | 1 | no | — |
| 342 | #103 | — | 17 | 1 | no | — |
| 343 | #103 | C2×#595 | 1 | 1 | yes | characteristic |
| 344 | #103 | C2×#595 | 1 | 1 | yes | characteristic |
| 345 | C22⋊C8 | — | 34 | 1 | no | — |
| 346 | #97 | — | 17 | 2 | no | — |
| 347 | #97 | — | 34 | 2 | no | — |
| 348 | #97 | — | 34 | 2 | no | — |
| 349 | C4×C8 | — | 17 | 2 | no | — |
| 350 | C4×C8 | — | 17 | 1 | no | — |
| 351 | C4×C8 | — | 17 | 1 | no | — |
| 352 | C4×C8 | — | 17 | 2 | no | — |
| 353 | C4×C8 | — | 17 | 1 | no | — |
| 354 | C4×C8 | — | 34 | 2 | no | — |
| 355 | C4×C8 | — | 34 | 2 | no | — |
| 356 | C4×C8 | C2×#595 | 1 | 1 | yes | characteristic |
| 357 | C17 | M16×Q16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 358 | C2×Q8 | — | 17 | 1 | no | — |
| 359 | C2×Q8 | — | 17 | 1 | no | — |
| 360 | C2×Q8 | — | 34 | 1 | no | — |
| 361 | C2×Q8 | — | 34 | 1 | no | — |
| 362 | C2×Q8 | — | 34 | 2 | no | — |
| 363 | C2×Q8 | — | 34 | 2 | no | — |
| 364 | C2×Q8 | — | 68 | 1 | no | — |
| 365 | C2×Q8 | — | 68 | 1 | no | — |
| 366 | C2×Q8 | C22×#595 | 1 | 1 | yes | characteristic |
| 367 | C2×Q8 | C22×#595 | 1 | 1 | yes | characteristic |
| 368 | C22×C4 | — | 17 | 1 | no | — |
| 369 | C22×C4 | — | 17 | 1 | no | — |
| 370 | C22×C4 | — | 17 | 1 | no | — |
| 371 | C22×C4 | — | 34 | 1 | no | — |
| 372 | C22×C4 | — | 34 | 1 | no | — |
| 373 | C22×C4 | — | 34 | 1 | no | — |
| 374 | C22×C4 | — | 34 | 1 | no | — |
| 375 | Q16 | — | 2 | 2 | no | — |
| 376 | Q16 | — | 17 | 4 | no | — |
| 377 | Q16 | — | 34 | 2 | no | — |
| 378 | Q16 | — | 34 | 2 | no | — |
| 379 | M16 | — | 17 | 4 | no | — |
| 380 | M16 | — | 34 | 2 | no | — |
| 381 | M16 | — | 68 | 2 | no | — |
| 382 | M16 | — | 68 | 2 | no | — |
| 383 | C2×C8 | — | 17 | 2 | no | — |
| 384 | C2×C8 | — | 17 | 1 | no | — |
| 385 | C2×C8 | — | 17 | 2 | no | — |
| 386 | C2×C8 | — | 17 | 1 | no | — |
| 387 | C2×C8 | — | 34 | 2 | no | — |
| 388 | C2×C8 | — | 34 | 2 | no | — |
| 389 | C2×C8 | — | 34 | 2 | no | — |
| 390 | C2×C8 | — | 34 | 2 | no | — |
| 391 | C2×C8 | — | 68 | 1 | no | — |
| 392 | C2×C8 | C22×#595 | 1 | 1 | yes | characteristic |
| 393 | C2×C8 | C22×#595 | 1 | 1 | yes | characteristic |
| 394 | C4⋊C4 | — | 2 | 1 | no | — |
| 395 | C4⋊C4 | — | 2 | 1 | no | — |
| 396 | C4⋊C4 | — | 17 | 1 | no | — |
| 397 | C4⋊C4 | — | 17 | 1 | no | — |
| 398 | C4⋊C4 | — | 34 | 1 | no | — |
| 399 | C4⋊C4 | — | 34 | 1 | no | — |
| 400 | C4⋊C4 | — | 34 | 1 | no | — |
| 401 | C4⋊C4 | — | 34 | 1 | no | — |
| 402 | C4⋊C4 | — | 34 | 1 | no | — |
| 403 | C4⋊C4 | — | 34 | 1 | no | — |
| 404 | C4⋊C4 | — | 34 | 1 | no | — |
| 405 | C4⋊C4 | — | 34 | 1 | no | — |
| 406 | C4⋊C4 | C22×#595 | 1 | 1 | yes | characteristic |
| 407 | C4⋊C4 | C22×#595 | 1 | 1 | yes | characteristic |
| 408 | C42 | — | 2 | 1 | no | — |
| 409 | C42 | — | 2 | 1 | no | — |
| 410 | C42 | — | 17 | 1 | no | — |
| 411 | C42 | — | 17 | 1 | no | — |
| 412 | C42 | — | 17 | 1 | no | — |
| 413 | C42 | — | 34 | 1 | no | — |
| 414 | C42 | — | 34 | 1 | no | — |
| 415 | C42 | — | 34 | 1 | no | — |
| 416 | C42 | — | 34 | 1 | no | — |
| 417 | C42 | — | 34 | 1 | no | — |
| 418 | C42 | — | 34 | 1 | no | — |
| 419 | C42 | C22×#595 | 1 | 1 | yes | characteristic |
| 420 | C23 | — | 17 | 1 | no | — |
| 421 | Q8 | — | 2 | 1 | no | — |
| 422 | Q8 | — | 2 | 1 | no | — |
| 423 | Q8 | — | 2 | 1 | no | — |
| 424 | Q8 | — | 17 | 2 | no | — |
| 425 | Q8 | — | 34 | 1 | no | — |
| 426 | Q8 | — | 34 | 1 | no | — |
| 427 | Q8 | — | 34 | 1 | no | — |
| 428 | Q8 | — | 68 | 2 | no | — |
| 429 | Q8 | — | 68 | 2 | no | — |
| 430 | Q8 | D17⋊M16 | 1 | 2 | yes | — |
| 431 | C2×C4 | — | 2 | 1 | no | — |
| 432 | C2×C4 | — | 2 | 1 | no | — |
| 433 | C2×C4 | — | 2 | 1 | no | — |
| 434 | C2×C4 | — | 2 | 1 | no | — |
| 435 | C2×C4 | — | 17 | 1 | no | — |
| 436 | C2×C4 | — | 17 | 2 | no | — |
| 437 | C2×C4 | — | 17 | 2 | no | — |
| 438 | C2×C4 | — | 17 | 1 | no | — |
| 439 | C2×C4 | — | 17 | 1 | no | — |
| 440 | C2×C4 | — | 34 | 1 | no | — |
| 441 | C2×C4 | — | 34 | 1 | no | — |
| 442 | C2×C4 | — | 34 | 1 | no | — |
| 443 | C2×C4 | — | 34 | 1 | no | — |
| 444 | C2×C4 | — | 34 | 1 | no | — |
| 445 | C2×C4 | — | 34 | 1 | no | — |
| 446 | C2×C4 | — | 68 | 1 | no | — |
| 447 | C2×C4 | — | 68 | 2 | no | — |
| 448 | C2×C4 | — | 68 | 2 | no | — |
| 449 | C2×C4 | — | 136 | 1 | no | — |
| 450 | C2×C4 | — | 136 | 1 | no | — |
| 451 | C2×C4 | D4×#595 | 1 | 1 | yes | characteristic |
| 452 | C2×C4 | D4×#595 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | C23×#595 | 1 | 1 | yes | characteristic |
| 454 | C8 | — | 2 | 1 | no | — |
| 455 | C8 | — | 2 | 1 | no | — |
| 456 | C8 | — | 17 | 4 | no | — |
| 457 | C8 | — | 17 | 2 | no | — |
| 458 | C8 | — | 34 | 2 | no | — |
| 459 | C8 | — | 34 | 1 | no | — |
| 460 | C8 | — | 68 | 2 | no | — |
| 461 | C8 | — | 68 | 2 | no | — |
| 462 | C8 | — | 68 | 2 | no | — |
| 463 | C22 | — | 17 | 2 | no | — |
| 464 | C22 | — | 34 | 1 | no | — |
| 465 | C22 | — | 34 | 1 | no | — |
| 466 | C22 | C2×D4×#595 | 1 | 1 | yes | characteristic |
| 467 | C4 | — | 2 | 2 | no | — |
| 468 | C4 | — | 2 | 1 | no | — |
| 469 | C4 | — | 4 | 1 | no | — |
| 470 | C4 | — | 4 | 1 | no | — |
| 471 | C4 | — | 4 | 1 | no | — |
| 472 | C4 | — | 17 | 1 | no | — |
| 473 | C4 | — | 17 | 1 | no | — |
| 474 | C4 | — | 34 | 1 | no | — |
| 475 | C4 | — | 34 | 2 | no | — |
| 476 | C4 | — | 34 | 1 | no | — |
| 477 | C4 | — | 68 | 1 | no | — |
| 478 | C4 | — | 68 | 1 | no | — |
| 479 | C4 | — | 68 | 1 | no | — |
| 480 | C4 | Q16×#595 | 1 | 2 | yes | — |
| 481 | C4 | C2×D17⋊M16 | 1 | 1 | yes | characteristic |
| 482 | C4 | #11763888 | 1 | 1 | yes | characteristic |
| 483 | C2 | — | 34 | 2 | no | — |
| 484 | C2 | #14545523 | 1 | 1 | yes | characteristic |
| 485 | C2 | C2×Q16×#595 | 1 | 1 | yes | characteristic |
| 486 | C2 | #14545563 | 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