← #17929918
Subgroups — #17929918
Order 4352.
1948 conjugacy classes of subgroups.
The subgroup lattice has 494 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #41×Dic34 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | Q8×#63229 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14541426 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #14541141 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | #14540643 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #14540100 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #14539928 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #14538811 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#11763091 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #14537895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C17×#3499 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | Q8×Dic34 | C22 | 1 | 1 | yes | characteristic |
| 13 | #11763538 | C22 | 1 | 1 | yes | characteristic |
| 14 | #11763535 | — | 2 | 1 | no | — |
| 15 | #11763518 | — | 2 | 3 | no | — |
| 16 | #11763516 | C22 | 1 | 3 | yes | — |
| 17 | D4×Dic34 | C22 | 1 | 3 | yes | — |
| 18 | #11763366 | C22 | 1 | 3 | yes | — |
| 19 | #11763362 | — | 2 | 3 | no | — |
| 20 | #41×Dic17 | — | 2 | 1 | no | — |
| 21 | C2×C4×Dic34 | C22 | 1 | 3 | yes | — |
| 22 | #11763205 | C22 | 1 | 6 | yes | — |
| 23 | #11763161 | C22 | 1 | 6 | yes | — |
| 24 | #11763139 | C22 | 1 | 12 | yes | — |
| 25 | #11763125 | C22 | 1 | 6 | yes | — |
| 26 | #11763099 | C22 | 1 | 6 | yes | — |
| 27 | #11763091 | C22 | 1 | 3 | yes | — |
| 28 | #11763091 | C22 | 1 | 6 | yes | — |
| 29 | #11763091 | C22 | 1 | 6 | yes | — |
| 30 | #11763091 | C22 | 1 | 6 | yes | — |
| 31 | #11763091 | C22 | 1 | 3 | yes | — |
| 32 | #11763036 | C22 | 1 | 12 | yes | — |
| 33 | #11763014 | C22 | 1 | 6 | yes | — |
| 34 | #11763006 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11763006 | C22 | 1 | 3 | yes | — |
| 36 | #11762947 | C22 | 1 | 6 | yes | — |
| 37 | Q8×#3622 | C22 | 1 | 2 | yes | — |
| 38 | C4×#63229 | C22 | 1 | 6 | yes | — |
| 39 | C4×#63229 | C22 | 1 | 6 | yes | — |
| 40 | D4×#3622 | C22 | 1 | 6 | yes | — |
| 41 | #11762862 | C22 | 1 | 3 | yes | — |
| 42 | C2×#10587479 | C22 | 1 | 6 | yes | — |
| 43 | C2×C4⋊#3622 | C22 | 1 | 3 | yes | — |
| 44 | C2×#10587481 | C22 | 1 | 6 | yes | — |
| 45 | C2×C17×2−1+4 | — | 2 | 1 | no | — |
| 46 | D4×Q8×C17 | — | 2 | 1 | no | — |
| 47 | D4×Q8×C17 | C22 | 1 | 2 | yes | — |
| 48 | C17×#547 | — | 2 | 3 | no | — |
| 49 | C17×#547 | C22 | 1 | 6 | yes | — |
| 50 | C17×#536 | — | 2 | 3 | no | — |
| 51 | C17×#532 | C22 | 1 | 3 | yes | — |
| 52 | C2×C17×C4⋊Q8 | C22 | 1 | 3 | yes | — |
| 53 | C4×#41×C17 | C22 | 1 | 1 | yes | characteristic |
| 54 | C17×2−1+4 | — | 4 | 8 | no | — |
| 55 | C2×#41×C17 | — | 2 | 6 | no | — |
| 56 | C2×#41×C17 | — | 2 | 3 | no | — |
| 57 | C2×#41×C17 | D4 | 1 | 1 | yes | characteristic |
| 58 | C22×Q8×C17 | — | 2 | 2 | no | — |
| 59 | C22×Q8×C17 | — | 2 | 3 | no | — |
| 60 | C22×Dic34 | C23 | 1 | 3 | yes | — |
| 61 | C17×C4⋊Q8 | — | 2 | 3 | no | — |
| 62 | C17×C4⋊Q8 | — | 2 | 3 | no | — |
| 63 | C17×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 64 | C17×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 65 | C17×#127 | C23 | 1 | 1 | yes | characteristic |
| 66 | C17×#124 | — | 2 | 3 | no | — |
| 67 | C17×#123 | — | 2 | 12 | no | — |
| 68 | C17×C22⋊Q8 | — | 2 | 6 | no | — |
| 69 | C17×C22⋊Q8 | — | 2 | 6 | no | — |
| 70 | C17×#121 | — | 2 | 3 | no | — |
| 71 | C17×#121 | C23 | 1 | 6 | yes | — |
| 72 | C4×Q8×C17 | D4 | 1 | 1 | yes | characteristic |
| 73 | C4×Q8×C17 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×D4×C17 | — | 2 | 3 | no | — |
| 75 | C4×D4×C17 | D4 | 1 | 3 | yes | — |
| 76 | C4×D4×C17 | C23 | 1 | 6 | yes | — |
| 77 | C4×D4×C17 | C23 | 1 | 3 | yes | — |
| 78 | C17×#117 | D4 | 1 | 3 | yes | — |
| 79 | C2×C4⋊C4×C17 | — | 2 | 3 | no | — |
| 80 | C2×C4⋊C4×C17 | C23 | 1 | 6 | yes | — |
| 81 | C2×C42×C17 | C23 | 1 | 3 | yes | — |
| 82 | Q8×Dic17 | — | 2 | 1 | no | — |
| 83 | Q8×Dic17 | — | 2 | 1 | no | — |
| 84 | D4×Dic17 | — | 2 | 3 | no | — |
| 85 | D4×Dic17 | — | 2 | 3 | no | — |
| 86 | C2×#63229 | C23 | 1 | 2 | yes | — |
| 87 | C2×#63229 | C23 | 1 | 6 | yes | — |
| 88 | #10587612 | — | 2 | 3 | no | — |
| 89 | C2×C4⋊Dic17 | C23 | 1 | 3 | yes | — |
| 90 | #10587610 | — | 2 | 3 | no | — |
| 91 | #10587610 | C23 | 1 | 6 | yes | — |
| 92 | C2×#63225 | — | 2 | 3 | no | — |
| 93 | C2×C4×Dic17 | — | 2 | 3 | no | — |
| 94 | C22×#3622 | C23 | 1 | 6 | yes | — |
| 95 | #10587576 | — | 2 | 3 | no | — |
| 96 | #10587576 | — | 2 | 3 | no | — |
| 97 | #10587574 | — | 2 | 3 | no | — |
| 98 | #10587574 | — | 2 | 3 | no | — |
| 99 | #10587564 | — | 2 | 6 | no | — |
| 100 | #10587564 | — | 2 | 6 | no | — |
| 101 | #10587556 | — | 2 | 3 | no | — |
| 102 | #10587555 | C23 | 1 | 3 | yes | — |
| 103 | #10587555 | C23 | 1 | 3 | yes | — |
| 104 | C4×Dic34 | — | 2 | 3 | no | — |
| 105 | C4×Dic34 | — | 2 | 3 | no | — |
| 106 | C4×Dic34 | — | 2 | 3 | no | — |
| 107 | C4×Dic34 | C23 | 1 | 3 | yes | — |
| 108 | C4×Dic34 | C23 | 1 | 3 | yes | — |
| 109 | C4×Dic34 | C23 | 1 | 1 | yes | characteristic |
| 110 | C4×Dic34 | C23 | 1 | 3 | yes | — |
| 111 | #10587503 | C23 | 1 | 6 | yes | — |
| 112 | #10587503 | C23 | 1 | 2 | yes | — |
| 113 | C22⋊#3622 | C23 | 1 | 6 | yes | — |
| 114 | #10587481 | C23 | 1 | 6 | yes | — |
| 115 | #10587481 | C23 | 1 | 6 | yes | — |
| 116 | #10587481 | C23 | 1 | 12 | yes | — |
| 117 | #10587479 | C23 | 1 | 6 | yes | — |
| 118 | #10587479 | C23 | 1 | 12 | yes | — |
| 119 | #10587479 | C23 | 1 | 6 | yes | — |
| 120 | C4⋊#3622 | C23 | 1 | 3 | yes | — |
| 121 | C4⋊#3622 | C23 | 1 | 1 | yes | characteristic |
| 122 | C4⋊#3622 | C23 | 1 | 6 | yes | — |
| 123 | C4×#3622 | C23 | 1 | 6 | yes | — |
| 124 | #41×C17 | — | 4 | 24 | no | — |
| 125 | #41×C17 | — | 4 | 12 | no | — |
| 126 | #41×C17 | SD16 | 1 | 8 | yes | complemented |
| 127 | C2×Q8×C17 | — | 2 | 6 | no | — |
| 128 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 129 | C2×Q8×C17 | — | 4 | 8 | no | — |
| 130 | C2×Q8×C17 | — | 4 | 12 | no | — |
| 131 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×D4×C17 | — | 2 | 6 | no | — |
| 133 | C2×D4×C17 | — | 2 | 1 | no | — |
| 134 | C2×D4×C17 | — | 2 | 1 | no | — |
| 135 | C2×D4×C17 | C2×D4 | 1 | 3 | yes | — |
| 136 | C2×D4×C17 | C24 | 1 | 2 | yes | — |
| 137 | C22×C4×C17 | — | 2 | 6 | no | — |
| 138 | C22×C4×C17 | — | 2 | 6 | no | — |
| 139 | C22×C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 140 | C22×C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 141 | C22×C4×C17 | C24 | 1 | 3 | yes | — |
| 142 | C22×Dic17 | — | 2 | 3 | no | — |
| 143 | C22×Dic17 | — | 2 | 3 | no | — |
| 144 | C2×Dic34 | — | 2 | 6 | no | — |
| 145 | C2×Dic34 | — | 2 | 3 | no | — |
| 146 | C2×Dic34 | — | 2 | 3 | no | — |
| 147 | C2×Dic34 | — | 4 | 3 | no | — |
| 148 | C2×Dic34 | C24 | 1 | 3 | yes | — |
| 149 | C2×Dic34 | C24 | 1 | 1 | yes | characteristic |
| 150 | C4⋊C4×C17 | — | 2 | 6 | no | — |
| 151 | C4⋊C4×C17 | — | 2 | 6 | no | — |
| 152 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 153 | C4⋊C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 154 | C4⋊C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 155 | C4⋊C4×C17 | C24 | 1 | 6 | yes | — |
| 156 | C22⋊C4×C17 | — | 2 | 6 | no | — |
| 157 | C22⋊C4×C17 | — | 2 | 6 | no | — |
| 158 | C22⋊C4×C17 | C2×D4 | 1 | 6 | yes | — |
| 159 | C42×C17 | C2×D4 | 1 | 3 | yes | — |
| 160 | C42×C17 | C2×D4 | 1 | 3 | yes | — |
| 161 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 162 | C42×C17 | C24 | 1 | 3 | yes | — |
| 163 | C22⋊Dic17 | — | 2 | 6 | no | — |
| 164 | #63229 | — | 2 | 4 | no | — |
| 165 | #63229 | — | 4 | 6 | no | — |
| 166 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 167 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 168 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 169 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 170 | C4⋊Dic17 | C24 | 1 | 1 | yes | characteristic |
| 171 | C4⋊Dic17 | C24 | 1 | 3 | yes | — |
| 172 | #63225 | — | 2 | 1 | no | — |
| 173 | #63225 | — | 2 | 3 | no | — |
| 174 | #63225 | — | 2 | 3 | no | — |
| 175 | #63225 | — | 2 | 3 | no | — |
| 176 | #63225 | — | 2 | 6 | no | — |
| 177 | C4×Dic17 | — | 2 | 1 | no | — |
| 178 | C4×Dic17 | — | 2 | 3 | no | — |
| 179 | C4×Dic17 | — | 2 | 3 | no | — |
| 180 | C4×Dic17 | — | 2 | 3 | no | — |
| 181 | C2×#3622 | — | 4 | 6 | no | — |
| 182 | C2×#3622 | C24 | 1 | 2 | yes | — |
| 183 | C2×#3622 | C24 | 1 | 6 | yes | — |
| 184 | #62099 | — | 17 | 1 | no | maximal, Sylow |
| 185 | C23×C17 | — | 2 | 2 | no | — |
| 186 | C23×C17 | C22×D4 | 1 | 3 | yes | — |
| 187 | Q8×C17 | — | 4 | 12 | no | — |
| 188 | Q8×C17 | — | 4 | 6 | no | — |
| 189 | Q8×C17 | C2×SD16 | 1 | 4 | yes | — |
| 190 | D4×C17 | — | 2 | 2 | no | — |
| 191 | D4×C17 | — | 2 | 2 | no | — |
| 192 | D4×C17 | — | 4 | 2 | no | — |
| 193 | D4×C17 | — | 4 | 12 | no | — |
| 194 | D4×C17 | — | 4 | 2 | no | — |
| 195 | D4×C17 | C2×SD16 | 1 | 12 | yes | — |
| 196 | C2×C4×C17 | — | 2 | 3 | no | — |
| 197 | C2×C4×C17 | — | 2 | 3 | no | — |
| 198 | C2×C4×C17 | — | 2 | 6 | no | — |
| 199 | C2×C4×C17 | — | 4 | 3 | no | — |
| 200 | C2×C4×C17 | — | 4 | 12 | no | — |
| 201 | C2×C4×C17 | — | 4 | 12 | no | — |
| 202 | C2×C4×C17 | C2×SD16 | 1 | 12 | yes | — |
| 203 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 204 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 205 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 206 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 208 | C2×C4×C17 | C25 | 1 | 1 | yes | characteristic |
| 209 | C2×Dic17 | — | 2 | 1 | no | — |
| 210 | C2×Dic17 | — | 2 | 3 | no | — |
| 211 | C2×Dic17 | — | 2 | 3 | no | — |
| 212 | C2×Dic17 | — | 2 | 1 | no | — |
| 213 | C2×Dic17 | — | 4 | 6 | no | — |
| 214 | C2×Dic17 | — | 8 | 3 | no | — |
| 215 | Dic34 | — | 2 | 1 | no | — |
| 216 | Dic34 | — | 2 | 3 | no | — |
| 217 | Dic34 | — | 2 | 3 | no | — |
| 218 | Dic34 | — | 4 | 6 | no | — |
| 219 | Dic34 | — | 8 | 3 | no | — |
| 220 | Dic34 | 2−1+4 | 1 | 2 | yes | complemented |
| 221 | #3622 | — | 2 | 2 | no | — |
| 222 | #3622 | — | 2 | 6 | no | — |
| 223 | #3499 | D17 | 1 | 1 | yes | characteristic |
| 224 | Q8×#41 | — | 17 | 1 | no | — |
| 225 | Q8×SD16 | — | 17 | 2 | no | — |
| 226 | #3359 | — | 17 | 2 | no | — |
| 227 | #3335 | — | 17 | 6 | no | — |
| 228 | #3298 | — | 17 | 6 | no | — |
| 229 | #3246 | — | 17 | 3 | no | — |
| 230 | #3229 | — | 17 | 3 | no | — |
| 231 | #3103 | — | 17 | 3 | no | — |
| 232 | C2×#475 | — | 17 | 3 | no | — |
| 233 | #2988 | — | 17 | 1 | no | — |
| 234 | C22×C17 | — | 2 | 3 | no | — |
| 235 | C22×C17 | — | 2 | 3 | no | — |
| 236 | C22×C17 | — | 4 | 2 | no | — |
| 237 | C22×C17 | — | 4 | 2 | no | — |
| 238 | C22×C17 | — | 4 | 2 | no | — |
| 239 | C22×C17 | C22×SD16 | 1 | 6 | yes | — |
| 240 | C22×C17 | C23×D4 | 1 | 1 | yes | characteristic |
| 241 | C4×C17 | — | 2 | 3 | no | — |
| 242 | C4×C17 | — | 2 | 1 | no | — |
| 243 | C4×C17 | — | 2 | 3 | no | — |
| 244 | C4×C17 | — | 4 | 6 | no | — |
| 245 | C4×C17 | C22×SD16 | 1 | 6 | yes | — |
| 246 | C4×C17 | C22×SD16 | 1 | 2 | yes | — |
| 247 | C4×C17 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 248 | C4×C17 | #585 | 1 | 1 | yes | characteristic |
| 249 | Dic17 | — | 2 | 2 | no | — |
| 250 | Dic17 | — | 4 | 3 | no | — |
| 251 | Dic17 | — | 4 | 1 | no | — |
| 252 | Dic17 | — | 4 | 3 | no | — |
| 253 | C2×2−1+4 | — | 2 | 1 | no | — |
| 254 | Q82 | — | 17 | 1 | no | — |
| 255 | #557 | — | 17 | 1 | no | — |
| 256 | #557 | — | 34 | 1 | no | — |
| 257 | #554 | — | 17 | 3 | no | — |
| 258 | #554 | — | 34 | 3 | no | — |
| 259 | D4×Q8 | — | 2 | 1 | no | — |
| 260 | D4×Q8 | — | 17 | 3 | no | — |
| 261 | D4×Q8 | C2×D17 | 1 | 2 | yes | — |
| 262 | #547 | — | 2 | 3 | no | — |
| 263 | #547 | C2×D17 | 1 | 6 | yes | — |
| 264 | #536 | — | 2 | 3 | no | — |
| 265 | #533 | — | 17 | 3 | no | — |
| 266 | #533 | — | 34 | 3 | no | — |
| 267 | #532 | C2×D17 | 1 | 3 | yes | — |
| 268 | C2×C4⋊Q8 | C2×D17 | 1 | 3 | yes | — |
| 269 | C4×#41 | — | 34 | 1 | no | — |
| 270 | C4×#41 | C2×D17 | 1 | 1 | yes | characteristic |
| 271 | C2×C4×Q8 | — | 17 | 3 | no | — |
| 272 | #498 | — | 17 | 6 | no | — |
| 273 | #487 | — | 17 | 6 | no | — |
| 274 | #483 | — | 17 | 12 | no | — |
| 275 | #481 | — | 17 | 6 | no | — |
| 276 | #476 | — | 17 | 6 | no | — |
| 277 | #475 | — | 17 | 3 | no | — |
| 278 | #475 | — | 17 | 6 | no | — |
| 279 | #475 | — | 17 | 6 | no | — |
| 280 | #475 | — | 17 | 6 | no | — |
| 281 | #475 | — | 17 | 3 | no | — |
| 282 | #465 | — | 17 | 12 | no | — |
| 283 | #461 | — | 17 | 6 | no | — |
| 284 | #460 | — | 17 | 1 | no | — |
| 285 | #460 | — | 17 | 3 | no | — |
| 286 | #448 | — | 17 | 6 | no | — |
| 287 | C8×Q8 | — | 17 | 2 | no | — |
| 288 | C4×SD16 | — | 17 | 6 | no | — |
| 289 | C4×SD16 | — | 17 | 6 | no | — |
| 290 | C8×D4 | — | 17 | 6 | no | — |
| 291 | #431 | — | 17 | 3 | no | — |
| 292 | C2×#106 | — | 17 | 6 | no | — |
| 293 | C2×C4⋊C8 | — | 17 | 3 | no | — |
| 294 | C2×#103 | — | 17 | 6 | no | — |
| 295 | C2×C17 | — | 2 | 6 | no | — |
| 296 | C2×C17 | — | 8 | 2 | no | — |
| 297 | C2×C17 | #3489 | 1 | 1 | yes | characteristic |
| 298 | C2×C17 | C23×SD16 | 1 | 1 | yes | characteristic |
| 299 | C2×C17 | #3586 | 1 | 1 | yes | characteristic |
| 300 | 2−1+4 | — | 4 | 8 | no | — |
| 301 | C2×#41 | — | 2 | 6 | no | — |
| 302 | C2×#41 | — | 2 | 3 | no | — |
| 303 | C2×#41 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 304 | C22×Q8 | — | 2 | 2 | no | — |
| 305 | C22×Q8 | — | 2 | 3 | no | — |
| 306 | C22×Q8 | — | 17 | 3 | no | — |
| 307 | C2×SD16 | — | 17 | 2 | no | — |
| 308 | C2×SD16 | — | 17 | 6 | no | — |
| 309 | C22×C8 | — | 17 | 6 | no | — |
| 310 | C4⋊Q8 | — | 2 | 3 | no | — |
| 311 | C4⋊Q8 | — | 2 | 3 | no | — |
| 312 | C4⋊Q8 | — | 17 | 3 | no | — |
| 313 | C4⋊Q8 | — | 17 | 3 | no | — |
| 314 | C4⋊Q8 | — | 34 | 3 | no | — |
| 315 | C4⋊Q8 | — | 34 | 3 | no | — |
| 316 | C4⋊Q8 | C22×D17 | 1 | 3 | yes | — |
| 317 | C4⋊Q8 | C22×D17 | 1 | 6 | yes | — |
| 318 | #127 | C22×D17 | 1 | 1 | yes | characteristic |
| 319 | #125 | — | 34 | 3 | no | — |
| 320 | #125 | — | 34 | 3 | no | — |
| 321 | #125 | — | 34 | 3 | no | — |
| 322 | #124 | — | 2 | 3 | no | — |
| 323 | #123 | — | 2 | 12 | no | — |
| 324 | C22⋊Q8 | — | 2 | 6 | no | — |
| 325 | C22⋊Q8 | — | 2 | 6 | no | — |
| 326 | C22⋊Q8 | — | 17 | 6 | no | — |
| 327 | C22⋊Q8 | — | 34 | 3 | no | — |
| 328 | C22⋊Q8 | — | 34 | 6 | no | — |
| 329 | C22⋊Q8 | — | 34 | 6 | no | — |
| 330 | #121 | — | 2 | 3 | no | — |
| 331 | #121 | C22×D17 | 1 | 6 | yes | — |
| 332 | C4×Q8 | — | 17 | 1 | no | — |
| 333 | C4×Q8 | — | 17 | 3 | no | — |
| 334 | C4×Q8 | — | 17 | 3 | no | — |
| 335 | C4×Q8 | — | 17 | 3 | no | — |
| 336 | C4×Q8 | — | 34 | 1 | no | — |
| 337 | C4×Q8 | — | 34 | 1 | no | — |
| 338 | C4×Q8 | — | 34 | 3 | no | — |
| 339 | C4×Q8 | — | 34 | 3 | no | — |
| 340 | C4×Q8 | — | 34 | 3 | no | — |
| 341 | C4×Q8 | C22⋊D17 | 1 | 1 | yes | characteristic |
| 342 | C4×Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 343 | C4×D4 | — | 2 | 3 | no | — |
| 344 | C4×D4 | — | 34 | 3 | no | — |
| 345 | C4×D4 | — | 34 | 3 | no | — |
| 346 | C4×D4 | C22⋊D17 | 1 | 3 | yes | — |
| 347 | C4×D4 | C22×D17 | 1 | 6 | yes | — |
| 348 | C4×D4 | C22×D17 | 1 | 3 | yes | — |
| 349 | #117 | — | 34 | 3 | no | — |
| 350 | #117 | C22⋊D17 | 1 | 3 | yes | — |
| 351 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 352 | C2×C4⋊C4 | — | 17 | 3 | no | — |
| 353 | C2×C4⋊C4 | — | 34 | 3 | no | — |
| 354 | C2×C4⋊C4 | C22×D17 | 1 | 6 | yes | — |
| 355 | C2×C42 | — | 34 | 3 | no | — |
| 356 | C2×C42 | C22×D17 | 1 | 3 | yes | — |
| 357 | #106 | — | 17 | 6 | no | — |
| 358 | #106 | — | 17 | 12 | no | — |
| 359 | #106 | — | 17 | 6 | no | — |
| 360 | C4⋊C8 | — | 17 | 3 | no | — |
| 361 | C4⋊C8 | — | 17 | 6 | no | — |
| 362 | C4⋊C8 | — | 17 | 1 | no | — |
| 363 | #103 | — | 17 | 6 | no | — |
| 364 | #103 | — | 17 | 12 | no | — |
| 365 | #103 | — | 17 | 6 | no | — |
| 366 | #102 | — | 17 | 2 | no | — |
| 367 | #102 | — | 17 | 6 | no | — |
| 368 | C22⋊C8 | — | 17 | 6 | no | — |
| 369 | C4×C8 | — | 17 | 6 | no | — |
| 370 | C17 | #62099 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 371 | #41 | — | 4 | 24 | no | — |
| 372 | #41 | — | 4 | 12 | no | — |
| 373 | #41 | #63229 | 1 | 8 | yes | complemented |
| 374 | C2×Q8 | — | 2 | 6 | no | — |
| 375 | C2×Q8 | — | 2 | 3 | no | — |
| 376 | C2×Q8 | — | 4 | 8 | no | — |
| 377 | C2×Q8 | — | 4 | 12 | no | — |
| 378 | C2×Q8 | — | 17 | 1 | no | — |
| 379 | C2×Q8 | — | 17 | 3 | no | — |
| 380 | C2×Q8 | — | 34 | 6 | no | — |
| 381 | C2×Q8 | — | 34 | 3 | no | — |
| 382 | C2×Q8 | — | 34 | 3 | no | — |
| 383 | C2×Q8 | — | 68 | 3 | no | — |
| 384 | C2×Q8 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 385 | C2×D4 | — | 2 | 6 | no | — |
| 386 | C2×D4 | — | 2 | 1 | no | — |
| 387 | C2×D4 | — | 2 | 1 | no | — |
| 388 | C2×D4 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 389 | C2×D4 | C23×D17 | 1 | 2 | yes | — |
| 390 | C22×C4 | — | 2 | 6 | no | — |
| 391 | C22×C4 | — | 2 | 6 | no | — |
| 392 | C22×C4 | — | 34 | 3 | no | — |
| 393 | C22×C4 | — | 34 | 3 | no | — |
| 394 | C22×C4 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 395 | C22×C4 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 396 | C22×C4 | C23×D17 | 1 | 3 | yes | — |
| 397 | SD16 | — | 34 | 4 | no | — |
| 398 | SD16 | — | 68 | 6 | no | — |
| 399 | C2×C8 | — | 17 | 2 | no | — |
| 400 | C2×C8 | — | 17 | 6 | no | — |
| 401 | C2×C8 | — | 68 | 6 | no | — |
| 402 | C4⋊C4 | — | 2 | 3 | no | — |
| 403 | C4⋊C4 | — | 2 | 6 | no | — |
| 404 | C4⋊C4 | — | 2 | 6 | no | — |
| 405 | C4⋊C4 | — | 17 | 1 | no | — |
| 406 | C4⋊C4 | — | 17 | 3 | no | — |
| 407 | C4⋊C4 | — | 34 | 3 | no | — |
| 408 | C4⋊C4 | — | 34 | 1 | no | — |
| 409 | C4⋊C4 | — | 34 | 3 | no | — |
| 410 | C4⋊C4 | — | 34 | 3 | no | — |
| 411 | C4⋊C4 | — | 34 | 3 | no | — |
| 412 | C4⋊C4 | — | 34 | 3 | no | — |
| 413 | C4⋊C4 | — | 34 | 3 | no | — |
| 414 | C4⋊C4 | — | 34 | 6 | no | — |
| 415 | C4⋊C4 | — | 34 | 3 | no | — |
| 416 | C4⋊C4 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 417 | C4⋊C4 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 418 | C4⋊C4 | C23×D17 | 1 | 6 | yes | — |
| 419 | C22⋊C4 | — | 2 | 6 | no | — |
| 420 | C22⋊C4 | — | 2 | 6 | no | — |
| 421 | C22⋊C4 | — | 34 | 6 | no | — |
| 422 | C22⋊C4 | C2×C22⋊D17 | 1 | 6 | yes | — |
| 423 | C42 | — | 34 | 1 | no | — |
| 424 | C42 | — | 34 | 3 | no | — |
| 425 | C42 | — | 34 | 3 | no | — |
| 426 | C42 | — | 34 | 3 | no | — |
| 427 | C42 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 428 | C42 | C2×C22⋊D17 | 1 | 3 | yes | — |
| 429 | C42 | C23×D17 | 1 | 3 | yes | — |
| 430 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 431 | C23 | — | 2 | 2 | no | — |
| 432 | C23 | C22×C22⋊D17 | 1 | 3 | yes | — |
| 433 | Q8 | — | 4 | 12 | no | — |
| 434 | Q8 | — | 4 | 6 | no | — |
| 435 | Q8 | — | 17 | 2 | no | — |
| 436 | Q8 | — | 34 | 1 | no | — |
| 437 | Q8 | — | 34 | 3 | no | — |
| 438 | Q8 | — | 34 | 3 | no | — |
| 439 | Q8 | — | 68 | 6 | no | — |
| 440 | Q8 | — | 136 | 3 | no | — |
| 441 | Q8 | C2×#63229 | 1 | 4 | yes | — |
| 442 | D4 | — | 2 | 2 | no | — |
| 443 | D4 | — | 2 | 2 | no | — |
| 444 | D4 | — | 4 | 2 | no | — |
| 445 | D4 | — | 4 | 12 | no | — |
| 446 | D4 | — | 4 | 2 | no | — |
| 447 | D4 | C2×#63229 | 1 | 12 | yes | — |
| 448 | C2×C4 | — | 2 | 3 | no | — |
| 449 | C2×C4 | — | 2 | 3 | no | — |
| 450 | C2×C4 | — | 2 | 6 | no | — |
| 451 | C2×C4 | — | 4 | 3 | no | — |
| 452 | C2×C4 | — | 4 | 12 | no | — |
| 453 | C2×C4 | — | 4 | 12 | no | — |
| 454 | C2×C4 | — | 34 | 1 | no | — |
| 455 | C2×C4 | — | 34 | 1 | no | — |
| 456 | C2×C4 | — | 34 | 3 | no | — |
| 457 | C2×C4 | — | 34 | 3 | no | — |
| 458 | C2×C4 | — | 68 | 6 | no | — |
| 459 | C2×C4 | — | 136 | 3 | no | — |
| 460 | C2×C4 | C2×#63229 | 1 | 12 | yes | — |
| 461 | C2×C4 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 462 | C2×C4 | C22×C22⋊D17 | 1 | 3 | yes | — |
| 463 | C2×C4 | C22×C22⋊D17 | 1 | 3 | yes | — |
| 464 | C2×C4 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 465 | C2×C4 | C22×C22⋊D17 | 1 | 3 | yes | — |
| 466 | C2×C4 | C24×D17 | 1 | 1 | yes | characteristic |
| 467 | C8 | — | 34 | 2 | no | — |
| 468 | C8 | — | 34 | 6 | no | — |
| 469 | C22 | — | 2 | 3 | no | — |
| 470 | C22 | — | 2 | 3 | no | — |
| 471 | C22 | — | 4 | 2 | no | — |
| 472 | C22 | — | 4 | 2 | no | — |
| 473 | C22 | — | 4 | 2 | no | — |
| 474 | C22 | C22×#63229 | 1 | 6 | yes | — |
| 475 | C22 | C23×C22⋊D17 | 1 | 1 | yes | characteristic |
| 476 | C4 | — | 2 | 3 | no | — |
| 477 | C4 | — | 2 | 1 | no | — |
| 478 | C4 | — | 2 | 3 | no | — |
| 479 | C4 | — | 4 | 6 | no | — |
| 480 | C4 | — | 34 | 2 | no | — |
| 481 | C4 | — | 68 | 3 | no | — |
| 482 | C4 | — | 68 | 1 | no | — |
| 483 | C4 | — | 68 | 3 | no | — |
| 484 | C4 | C22×#63229 | 1 | 6 | yes | — |
| 485 | C4 | C22×#63229 | 1 | 2 | yes | — |
| 486 | C4 | 2−1+4×D17 | 1 | 1 | yes | characteristic |
| 487 | C4 | #11763646 | 1 | 1 | yes | characteristic |
| 488 | C2 | — | 2 | 6 | no | — |
| 489 | C2 | — | 8 | 2 | no | — |
| 490 | C2 | #14542457 | 1 | 1 | yes | characteristic |
| 491 | C2 | C23×#63229 | 1 | 1 | yes | characteristic |
| 492 | C2 | #14543571 | 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