← #17907378
Subgroups — #17907378
Order 4352.
1886 conjugacy classes of subgroups.
The subgroup lattice has 540 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#11763414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14540225 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #14540219 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #14540195 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #14538606 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14538577 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #14538405 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #14538264 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #14538244 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #14537348 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C17×#3455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#10587635 | C22 | 1 | 4 | yes | — |
| 13 | C22×#63223 | C22 | 1 | 2 | yes | — |
| 14 | #11763414 | — | 2 | 4 | no | — |
| 15 | #11763414 | C22 | 1 | 4 | yes | — |
| 16 | #11763414 | C22 | 1 | 4 | yes | — |
| 17 | C2×#10587560 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#10587556 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#10587580 | — | 2 | 2 | no | — |
| 20 | C2×#10587616 | C22 | 1 | 2 | yes | — |
| 21 | C2×#10587570 | — | 2 | 2 | no | — |
| 22 | C2×C4×D68 | C22 | 1 | 2 | yes | — |
| 23 | #11763116 | C22 | 1 | 8 | yes | complemented |
| 24 | #11763109 | C22 | 1 | 8 | yes | complemented |
| 25 | #11763106 | C22 | 1 | 8 | yes | complemented |
| 26 | #11763096 | C22 | 1 | 4 | yes | complemented |
| 27 | #11763086 | C22 | 1 | 4 | yes | complemented |
| 28 | #11763060 | C22 | 1 | 8 | yes | complemented |
| 29 | #11763057 | C22 | 1 | 8 | yes | complemented |
| 30 | #11763043 | C22 | 1 | 8 | yes | complemented |
| 31 | #11763040 | C22 | 1 | 8 | yes | complemented |
| 32 | #11763021 | C22 | 1 | 8 | yes | complemented |
| 33 | #11763011 | C22 | 1 | 4 | yes | complemented |
| 34 | #11763009 | C22 | 1 | 8 | yes | complemented |
| 35 | #11763004 | C22 | 1 | 8 | yes | complemented |
| 36 | #11763001 | C22 | 1 | 4 | yes | complemented |
| 37 | #11762852 | C22 | 1 | 4 | yes | — |
| 38 | #11762836 | C22 | 1 | 4 | yes | complemented |
| 39 | #11762836 | C22 | 1 | 4 | yes | complemented |
| 40 | #11762833 | C22 | 1 | 2 | yes | — |
| 41 | #11762833 | C22 | 1 | 2 | yes | — |
| 42 | #11762813 | C22 | 1 | 4 | yes | — |
| 43 | #11762810 | C22 | 1 | 4 | yes | — |
| 44 | C17×#542 | C22 | 1 | 4 | yes | complemented |
| 45 | C17×#541 | C22 | 1 | 2 | yes | complemented |
| 46 | C17×#540 | C22 | 1 | 2 | yes | complemented |
| 47 | C17×#539 | — | 2 | 2 | no | — |
| 48 | C17×#538 | — | 2 | 2 | no | — |
| 49 | C17×#533 | C22 | 1 | 1 | yes | characteristic |
| 50 | C17×#532 | C22 | 1 | 1 | yes | characteristic |
| 51 | C17×#529 | — | 2 | 4 | no | — |
| 52 | C17×#525 | C22 | 1 | 2 | yes | — |
| 53 | C4×#41×C17 | C22 | 1 | 2 | yes | — |
| 54 | C2×C17×#117 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#41×C17 | C23 | 1 | 2 | yes | — |
| 56 | C23×C4×C17 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×C22⋊D17 | — | 2 | 2 | no | — |
| 58 | C22×D68 | — | 2 | 2 | no | — |
| 59 | C22×D68 | C23 | 1 | 2 | yes | — |
| 60 | C22×C4×D17 | — | 2 | 2 | no | — |
| 61 | C17×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C17×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 63 | C17×#127 | C23 | 1 | 1 | yes | characteristic |
| 64 | C17×#126 | — | 2 | 4 | no | — |
| 65 | C17×#126 | — | 2 | 4 | no | — |
| 66 | C17×#125 | — | 2 | 4 | no | — |
| 67 | C17×#125 | C23 | 1 | 2 | yes | — |
| 68 | C17×#124 | — | 2 | 4 | no | — |
| 69 | C17×#124 | C23 | 1 | 2 | yes | — |
| 70 | C17×#123 | — | 2 | 2 | no | — |
| 71 | C17×#123 | — | 2 | 4 | no | — |
| 72 | C17×#123 | — | 2 | 4 | no | — |
| 73 | C17×C22⋊Q8 | — | 2 | 2 | no | — |
| 74 | C17×C22⋊Q8 | — | 2 | 4 | no | — |
| 75 | C17×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 76 | C17×#121 | — | 2 | 2 | no | — |
| 77 | C17×#121 | — | 2 | 4 | no | — |
| 78 | C17×#121 | C23 | 1 | 4 | yes | — |
| 79 | C17×#120 | — | 2 | 2 | no | — |
| 80 | C4×Q8×C17 | — | 2 | 2 | no | — |
| 81 | C4×Q8×C17 | C23 | 1 | 4 | yes | — |
| 82 | C4×D4×C17 | — | 2 | 4 | no | — |
| 83 | C4×D4×C17 | — | 2 | 4 | no | — |
| 84 | C4×D4×C17 | — | 2 | 2 | no | — |
| 85 | C4×D4×C17 | C23 | 1 | 4 | yes | — |
| 86 | C17×#117 | — | 2 | 2 | no | — |
| 87 | C17×#117 | D4 | 1 | 4 | yes | — |
| 88 | C17×#117 | C23 | 1 | 2 | yes | — |
| 89 | C17×#117 | C23 | 1 | 2 | yes | — |
| 90 | C17×#117 | C23 | 1 | 2 | yes | — |
| 91 | C2×C4⋊C4×C17 | D4 | 1 | 2 | yes | — |
| 92 | C2×C22⋊C4×C17 | D4 | 1 | 2 | yes | — |
| 93 | C2×C42×C17 | — | 2 | 2 | no | — |
| 94 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C42×C17 | C23 | 1 | 1 | yes | characteristic |
| 96 | #10587635 | — | 4 | 8 | no | — |
| 97 | C2×#63230 | C23 | 1 | 8 | yes | — |
| 98 | C2×#63228 | C23 | 1 | 8 | yes | — |
| 99 | #10587616 | — | 2 | 4 | no | — |
| 100 | #10587616 | C23 | 1 | 8 | yes | — |
| 101 | C2×#63227 | — | 2 | 2 | no | — |
| 102 | C2×#63227 | — | 2 | 2 | no | — |
| 103 | C2×C4⋊Dic17 | C23 | 1 | 2 | yes | — |
| 104 | C2×#63225 | — | 2 | 2 | no | — |
| 105 | C2×#63223 | — | 4 | 4 | no | — |
| 106 | C2×#63223 | C23 | 1 | 4 | yes | — |
| 107 | C2×#63223 | C23 | 1 | 4 | yes | — |
| 108 | C22×#3622 | C23 | 1 | 4 | yes | — |
| 109 | #10587580 | — | 2 | 8 | no | — |
| 110 | #10587580 | — | 2 | 8 | no | — |
| 111 | #10587570 | — | 2 | 8 | no | — |
| 112 | #10587570 | — | 2 | 8 | no | — |
| 113 | #10587560 | — | 2 | 2 | no | — |
| 114 | #10587560 | C23 | 1 | 4 | yes | — |
| 115 | C4×D68 | — | 2 | 2 | no | — |
| 116 | C4×D68 | — | 2 | 2 | no | — |
| 117 | C4×D68 | C23 | 1 | 4 | yes | — |
| 118 | C4×D68 | C23 | 1 | 4 | yes | — |
| 119 | #10587556 | — | 2 | 2 | no | — |
| 120 | #10587556 | C23 | 1 | 4 | yes | — |
| 121 | #10587506 | C23 | 1 | 8 | yes | — |
| 122 | #10587503 | C23 | 1 | 8 | yes | — |
| 123 | #10587480 | C23 | 1 | 8 | yes | — |
| 124 | #10587480 | C23 | 1 | 8 | yes | — |
| 125 | #10587479 | C23 | 1 | 8 | yes | — |
| 126 | #10587478 | C23 | 1 | 8 | yes | — |
| 127 | C4⋊#3622 | C23 | 1 | 4 | yes | — |
| 128 | C4⋊#3622 | C23 | 1 | 8 | yes | — |
| 129 | C4⋊#3622 | C23 | 1 | 4 | yes | — |
| 130 | C24×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C23×D17 | — | 2 | 2 | no | — |
| 132 | #41×C17 | — | 2 | 4 | no | — |
| 133 | #41×C17 | — | 2 | 4 | no | — |
| 134 | C2×Q8×C17 | — | 2 | 2 | no | — |
| 135 | C2×Q8×C17 | C24 | 1 | 2 | yes | — |
| 136 | C2×D4×C17 | — | 2 | 2 | no | — |
| 137 | C2×D4×C17 | — | 2 | 4 | no | — |
| 138 | C2×D4×C17 | — | 2 | 2 | no | — |
| 139 | C2×D4×C17 | C24 | 1 | 2 | yes | — |
| 140 | C22×C4×C17 | — | 2 | 2 | no | — |
| 141 | C22×C4×C17 | — | 2 | 2 | no | — |
| 142 | C22×C4×C17 | — | 2 | 2 | no | — |
| 143 | C22×C4×C17 | — | 2 | 4 | no | — |
| 144 | C22×C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C22×C4×C17 | C2×D4 | 1 | 2 | yes | — |
| 146 | C22×C4×C17 | C2×D4 | 1 | 2 | yes | — |
| 147 | C22×C4×C17 | C2×D4 | 1 | 2 | yes | — |
| 148 | C22×C4×C17 | C24 | 1 | 2 | yes | — |
| 149 | C22×C4×C17 | C24 | 1 | 1 | yes | characteristic |
| 150 | C2×C22⋊D17 | — | 2 | 8 | no | — |
| 151 | C2×C22⋊D17 | — | 8 | 4 | no | — |
| 152 | C22×Dic17 | — | 2 | 2 | no | — |
| 153 | C2×D68 | — | 2 | 4 | no | — |
| 154 | C2×D68 | — | 2 | 4 | no | — |
| 155 | C2×D68 | — | 2 | 2 | no | — |
| 156 | C2×D68 | — | 2 | 8 | no | — |
| 157 | C2×D68 | — | 8 | 4 | no | — |
| 158 | C2×D68 | C24 | 1 | 4 | yes | — |
| 159 | C2×C4×D17 | — | 2 | 4 | no | — |
| 160 | C2×C4×D17 | — | 2 | 4 | no | — |
| 161 | C2×C4×D17 | — | 8 | 4 | no | — |
| 162 | C4⋊C4×C17 | — | 2 | 4 | no | — |
| 163 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 164 | C4⋊C4×C17 | — | 2 | 4 | no | — |
| 165 | C4⋊C4×C17 | — | 2 | 4 | no | — |
| 166 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 167 | C4⋊C4×C17 | C2×D4 | 1 | 4 | yes | — |
| 168 | C4⋊C4×C17 | C2×D4 | 1 | 4 | yes | — |
| 169 | C4⋊C4×C17 | C24 | 1 | 4 | yes | — |
| 170 | C22⋊C4×C17 | — | 2 | 2 | no | — |
| 171 | C22⋊C4×C17 | — | 2 | 4 | no | — |
| 172 | C22⋊C4×C17 | — | 2 | 4 | no | — |
| 173 | C22⋊C4×C17 | — | 2 | 4 | no | — |
| 174 | C22⋊C4×C17 | — | 2 | 4 | no | — |
| 175 | C22⋊C4×C17 | C2×D4 | 1 | 4 | yes | — |
| 176 | C22⋊C4×C17 | C2×D4 | 1 | 4 | yes | — |
| 177 | C42×C17 | — | 2 | 4 | no | — |
| 178 | C42×C17 | — | 2 | 2 | no | — |
| 179 | C42×C17 | C2×D4 | 1 | 2 | yes | — |
| 180 | C42×C17 | C2×D4 | 1 | 2 | yes | — |
| 181 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 182 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 183 | C42×C17 | C24 | 1 | 2 | yes | — |
| 184 | #63230 | — | 4 | 8 | no | — |
| 185 | #63228 | — | 4 | 8 | no | — |
| 186 | #63227 | — | 2 | 4 | no | — |
| 187 | #63227 | — | 2 | 4 | no | — |
| 188 | #63227 | — | 2 | 8 | no | — |
| 189 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 190 | C4⋊Dic17 | C24 | 1 | 4 | yes | — |
| 191 | #63225 | — | 2 | 8 | no | — |
| 192 | #63223 | — | 2 | 8 | no | — |
| 193 | #63223 | — | 4 | 4 | no | — |
| 194 | C2×#3622 | — | 4 | 4 | no | — |
| 195 | C2×#3622 | C24 | 1 | 8 | yes | — |
| 196 | #60920 | — | 17 | 1 | no | maximal, Sylow |
| 197 | C23×C17 | — | 2 | 2 | no | — |
| 198 | C23×C17 | — | 2 | 2 | no | — |
| 199 | C23×C17 | — | 4 | 2 | no | — |
| 200 | C23×C17 | C22×D4 | 1 | 2 | yes | — |
| 201 | C23×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×D17 | — | 2 | 4 | no | — |
| 203 | C22×D17 | — | 4 | 4 | no | — |
| 204 | C22×D17 | — | 4 | 4 | no | — |
| 205 | C22×D17 | — | 4 | 4 | no | — |
| 206 | Q8×C17 | — | 2 | 2 | no | — |
| 207 | Q8×C17 | — | 2 | 2 | no | — |
| 208 | Q8×C17 | — | 8 | 2 | no | — |
| 209 | D4×C17 | — | 2 | 2 | no | — |
| 210 | D4×C17 | — | 2 | 2 | no | — |
| 211 | D4×C17 | — | 4 | 4 | no | — |
| 212 | D4×C17 | — | 8 | 2 | no | — |
| 213 | D4×C17 | — | 8 | 4 | no | — |
| 214 | C2×C4×C17 | — | 2 | 2 | no | — |
| 215 | C2×C4×C17 | — | 2 | 4 | no | — |
| 216 | C2×C4×C17 | — | 2 | 2 | no | — |
| 217 | C2×C4×C17 | — | 2 | 2 | no | — |
| 218 | C2×C4×C17 | — | 2 | 2 | no | — |
| 219 | C2×C4×C17 | — | 2 | 4 | no | — |
| 220 | C2×C4×C17 | — | 4 | 2 | no | — |
| 221 | C2×C4×C17 | — | 4 | 2 | no | — |
| 222 | C2×C4×C17 | — | 4 | 4 | no | — |
| 223 | C2×C4×C17 | — | 8 | 4 | no | — |
| 224 | C2×C4×C17 | C22×D4 | 1 | 4 | yes | — |
| 225 | C2×C4×C17 | C22×D4 | 1 | 2 | yes | — |
| 226 | C2×C4×C17 | C22×D4 | 1 | 2 | yes | — |
| 227 | C2×C4×C17 | C22×D4 | 1 | 2 | yes | — |
| 228 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×C4×C17 | H(5,𝔽2) | 1 | 2 | yes | — |
| 230 | C2×C4×C17 | 2−1+4 | 1 | 2 | yes | — |
| 231 | C2×C4×C17 | C25 | 1 | 1 | yes | characteristic |
| 232 | C22⋊D17 | — | 8 | 8 | no | — |
| 233 | C2×Dic17 | — | 2 | 4 | no | — |
| 234 | C2×Dic17 | — | 4 | 4 | no | — |
| 235 | D68 | — | 2 | 4 | no | — |
| 236 | D68 | — | 2 | 4 | no | — |
| 237 | D68 | — | 4 | 4 | no | — |
| 238 | D68 | — | 8 | 8 | no | — |
| 239 | C4×D17 | — | 8 | 4 | no | — |
| 240 | C4×D17 | — | 8 | 4 | no | — |
| 241 | #3622 | — | 2 | 8 | no | — |
| 242 | #3455 | D17 | 1 | 1 | yes | characteristic, complemented |
| 243 | C2×#540 | — | 17 | 1 | no | — |
| 244 | #3260 | — | 17 | 4 | no | — |
| 245 | #3259 | — | 17 | 4 | no | — |
| 246 | #3257 | — | 17 | 8 | no | — |
| 247 | #3080 | — | 17 | 2 | no | — |
| 248 | #3077 | — | 17 | 2 | no | — |
| 249 | #3055 | — | 17 | 4 | no | — |
| 250 | #3038 | — | 17 | 2 | no | — |
| 251 | #3036 | — | 17 | 2 | no | — |
| 252 | #2905 | — | 17 | 1 | no | — |
| 253 | C22×C17 | — | 2 | 2 | no | — |
| 254 | C22×C17 | — | 2 | 4 | no | — |
| 255 | C22×C17 | — | 2 | 2 | no | — |
| 256 | C22×C17 | — | 4 | 4 | no | — |
| 257 | C22×C17 | — | 4 | 2 | no | — |
| 258 | C22×C17 | — | 8 | 2 | no | — |
| 259 | C22×C17 | #537 | 1 | 2 | yes | — |
| 260 | C22×C17 | C23×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×D17 | — | 4 | 4 | no | — |
| 262 | C2×D17 | — | 4 | 4 | no | — |
| 263 | C2×D17 | — | 4 | 4 | no | — |
| 264 | C2×D17 | — | 8 | 8 | no | — |
| 265 | C4×C17 | — | 2 | 2 | no | — |
| 266 | C4×C17 | — | 2 | 2 | no | — |
| 267 | C4×C17 | — | 2 | 4 | no | — |
| 268 | C4×C17 | — | 2 | 2 | no | — |
| 269 | C4×C17 | — | 4 | 4 | no | — |
| 270 | C4×C17 | — | 4 | 2 | no | — |
| 271 | C4×C17 | #537 | 1 | 2 | yes | — |
| 272 | C4×C17 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 273 | C4×C17 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 274 | Dic17 | — | 4 | 4 | no | — |
| 275 | C2×AGL(1,ℤ/8) | — | 17 | 4 | no | — |
| 276 | C22×M16 | — | 17 | 2 | no | — |
| 277 | #542 | C2×D17 | 1 | 4 | yes | complemented |
| 278 | #541 | C2×D17 | 1 | 2 | yes | complemented |
| 279 | #540 | — | 17 | 4 | no | — |
| 280 | #540 | — | 17 | 4 | no | — |
| 281 | #540 | — | 34 | 4 | no | — |
| 282 | #540 | C2×D17 | 1 | 2 | yes | complemented |
| 283 | #539 | — | 2 | 2 | no | — |
| 284 | #538 | — | 2 | 2 | no | — |
| 285 | #533 | C2×D17 | 1 | 1 | yes | characteristic |
| 286 | #532 | C2×D17 | 1 | 1 | yes | characteristic |
| 287 | C2×#127 | — | 17 | 1 | no | — |
| 288 | #529 | — | 2 | 4 | no | — |
| 289 | C2×#125 | — | 17 | 1 | no | — |
| 290 | #525 | C2×D17 | 1 | 2 | yes | — |
| 291 | C2×#123 | — | 34 | 2 | no | — |
| 292 | C2×#121 | — | 17 | 2 | no | — |
| 293 | C2×#121 | — | 34 | 2 | no | — |
| 294 | C4×#41 | C2×D17 | 1 | 2 | yes | — |
| 295 | C2×C4×D4 | — | 17 | 2 | no | — |
| 296 | C2×#117 | C2×D17 | 1 | 1 | yes | characteristic |
| 297 | #479 | — | 17 | 8 | no | — |
| 298 | #478 | — | 17 | 8 | no | — |
| 299 | #478 | — | 17 | 8 | no | — |
| 300 | #476 | — | 17 | 4 | no | — |
| 301 | #474 | — | 17 | 4 | no | — |
| 302 | #469 | — | 17 | 8 | no | — |
| 303 | #468 | — | 17 | 8 | no | — |
| 304 | #466 | — | 17 | 8 | no | — |
| 305 | #465 | — | 17 | 8 | no | — |
| 306 | #463 | — | 17 | 8 | no | — |
| 307 | #461 | — | 17 | 4 | no | — |
| 308 | #460 | — | 17 | 8 | no | — |
| 309 | #459 | — | 17 | 4 | no | — |
| 310 | #459 | — | 17 | 8 | no | — |
| 311 | #428 | — | 17 | 4 | no | — |
| 312 | #424 | — | 17 | 4 | no | — |
| 313 | #424 | — | 17 | 4 | no | — |
| 314 | #423 | — | 17 | 2 | no | — |
| 315 | #423 | — | 17 | 2 | no | — |
| 316 | #418 | — | 17 | 4 | no | — |
| 317 | #417 | — | 17 | 4 | no | — |
| 318 | C2×C17 | — | 2 | 2 | no | — |
| 319 | C2×C17 | — | 4 | 2 | no | — |
| 320 | C2×C17 | — | 8 | 2 | no | — |
| 321 | C2×C17 | C2×#537 | 1 | 1 | yes | characteristic |
| 322 | C2×C17 | #3585 | 1 | 2 | yes | — |
| 323 | D17 | — | 8 | 4 | no | — |
| 324 | C2×#41 | C22×D17 | 1 | 2 | yes | — |
| 325 | C22×D4 | — | 17 | 2 | no | — |
| 326 | C22×D4 | — | 34 | 2 | no | — |
| 327 | C22×D4 | — | 34 | 2 | no | — |
| 328 | C23×C4 | — | 34 | 2 | no | — |
| 329 | C23×C4 | C22×D17 | 1 | 1 | yes | characteristic |
| 330 | AGL(1,ℤ/8) | — | 68 | 8 | no | — |
| 331 | C2×SD16 | — | 17 | 8 | no | — |
| 332 | C2×D8 | — | 17 | 8 | no | — |
| 333 | C2×M16 | — | 17 | 4 | no | — |
| 334 | C2×M16 | — | 17 | 4 | no | — |
| 335 | C2×M16 | — | 68 | 4 | no | — |
| 336 | C22×C8 | — | 17 | 4 | no | — |
| 337 | C4⋊Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 338 | C4⋊Q8 | C22×D17 | 1 | 2 | yes | — |
| 339 | #127 | — | 17 | 4 | no | — |
| 340 | #127 | — | 34 | 2 | no | — |
| 341 | #127 | C22×D17 | 1 | 1 | yes | characteristic |
| 342 | #126 | — | 2 | 4 | no | — |
| 343 | #126 | — | 2 | 4 | no | — |
| 344 | #125 | — | 2 | 4 | no | — |
| 345 | #125 | — | 17 | 4 | no | — |
| 346 | #125 | — | 34 | 2 | no | — |
| 347 | #125 | C22×D17 | 1 | 2 | yes | — |
| 348 | #124 | — | 2 | 4 | no | — |
| 349 | #124 | C22×D17 | 1 | 2 | yes | — |
| 350 | #123 | — | 2 | 2 | no | — |
| 351 | #123 | — | 2 | 4 | no | — |
| 352 | #123 | — | 2 | 4 | no | — |
| 353 | #123 | — | 34 | 8 | no | — |
| 354 | #123 | — | 34 | 8 | no | — |
| 355 | C22⋊Q8 | — | 2 | 2 | no | — |
| 356 | C22⋊Q8 | — | 2 | 4 | no | — |
| 357 | C22⋊Q8 | C22×D17 | 1 | 4 | yes | — |
| 358 | #121 | — | 2 | 2 | no | — |
| 359 | #121 | — | 2 | 4 | no | — |
| 360 | #121 | — | 17 | 8 | no | — |
| 361 | #121 | — | 34 | 4 | no | — |
| 362 | #121 | — | 34 | 8 | no | — |
| 363 | #121 | — | 34 | 8 | no | — |
| 364 | #121 | C22×D17 | 1 | 4 | yes | — |
| 365 | #120 | — | 2 | 2 | no | — |
| 366 | C4×Q8 | — | 2 | 2 | no | — |
| 367 | C4×Q8 | C22×D17 | 1 | 4 | yes | — |
| 368 | C4×D4 | — | 2 | 4 | no | — |
| 369 | C4×D4 | — | 2 | 4 | no | — |
| 370 | C4×D4 | — | 2 | 2 | no | — |
| 371 | C4×D4 | — | 17 | 4 | no | — |
| 372 | C4×D4 | — | 17 | 4 | no | — |
| 373 | C4×D4 | — | 34 | 2 | no | — |
| 374 | C4×D4 | — | 34 | 2 | no | — |
| 375 | C4×D4 | C22×D17 | 1 | 4 | yes | — |
| 376 | #117 | — | 2 | 2 | no | — |
| 377 | #117 | C22⋊D17 | 1 | 4 | yes | — |
| 378 | #117 | C22×D17 | 1 | 2 | yes | — |
| 379 | #117 | C22×D17 | 1 | 2 | yes | — |
| 380 | #117 | C22×D17 | 1 | 2 | yes | — |
| 381 | C2×C4⋊C4 | — | 17 | 2 | no | — |
| 382 | C2×C4⋊C4 | — | 34 | 2 | no | — |
| 383 | C2×C4⋊C4 | C22⋊D17 | 1 | 2 | yes | — |
| 384 | C2×C22⋊C4 | — | 34 | 2 | no | — |
| 385 | C2×C22⋊C4 | — | 34 | 2 | no | — |
| 386 | C2×C22⋊C4 | C22⋊D17 | 1 | 2 | yes | — |
| 387 | C2×C42 | — | 2 | 2 | no | — |
| 388 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 389 | C2×C42 | C22×D17 | 1 | 1 | yes | characteristic |
| 390 | #107 | — | 17 | 8 | no | — |
| 391 | #106 | — | 17 | 8 | no | — |
| 392 | C4⋊C8 | — | 17 | 8 | no | — |
| 393 | C4⋊C8 | — | 17 | 4 | no | — |
| 394 | C4⋊C8 | — | 17 | 4 | no | — |
| 395 | #103 | — | 17 | 8 | no | — |
| 396 | #102 | — | 17 | 8 | no | — |
| 397 | #102 | — | 17 | 8 | no | — |
| 398 | #102 | — | 17 | 8 | no | — |
| 399 | C17 | #60920 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 400 | C24 | — | 34 | 2 | no | — |
| 401 | C24 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 402 | #41 | — | 2 | 4 | no | — |
| 403 | #41 | — | 2 | 4 | no | — |
| 404 | C2×Q8 | — | 2 | 2 | no | — |
| 405 | C2×Q8 | C23×D17 | 1 | 2 | yes | — |
| 406 | C2×D4 | — | 2 | 2 | no | — |
| 407 | C2×D4 | — | 2 | 4 | no | — |
| 408 | C2×D4 | — | 2 | 2 | no | — |
| 409 | C2×D4 | — | 17 | 4 | no | — |
| 410 | C2×D4 | — | 34 | 8 | no | — |
| 411 | C2×D4 | — | 34 | 4 | no | — |
| 412 | C2×D4 | — | 34 | 4 | no | — |
| 413 | C2×D4 | — | 34 | 2 | no | — |
| 414 | C2×D4 | — | 34 | 8 | no | — |
| 415 | C2×D4 | — | 136 | 4 | no | — |
| 416 | C2×D4 | — | 136 | 4 | no | — |
| 417 | C2×D4 | C23×D17 | 1 | 2 | yes | — |
| 418 | C22×C4 | — | 2 | 2 | no | — |
| 419 | C22×C4 | — | 2 | 2 | no | — |
| 420 | C22×C4 | — | 2 | 2 | no | — |
| 421 | C22×C4 | — | 2 | 4 | no | — |
| 422 | C22×C4 | — | 34 | 2 | no | — |
| 423 | C22×C4 | — | 34 | 4 | no | — |
| 424 | C22×C4 | — | 34 | 4 | no | — |
| 425 | C22×C4 | — | 136 | 4 | no | — |
| 426 | C22×C4 | C2×C22⋊D17 | 1 | 1 | yes | characteristic |
| 427 | C22×C4 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 428 | C22×C4 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 429 | C22×C4 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 430 | C22×C4 | C23×D17 | 1 | 2 | yes | — |
| 431 | C22×C4 | C23×D17 | 1 | 1 | yes | characteristic |
| 432 | SD16 | — | 68 | 8 | no | — |
| 433 | D8 | — | 68 | 8 | no | — |
| 434 | M16 | — | 34 | 8 | no | — |
| 435 | M16 | — | 68 | 4 | no | — |
| 436 | C2×C8 | — | 17 | 8 | no | — |
| 437 | C2×C8 | — | 68 | 4 | no | — |
| 438 | C4⋊C4 | — | 2 | 4 | no | — |
| 439 | C4⋊C4 | — | 2 | 2 | no | — |
| 440 | C4⋊C4 | — | 2 | 4 | no | — |
| 441 | C4⋊C4 | — | 2 | 4 | no | — |
| 442 | C4⋊C4 | — | 2 | 2 | no | — |
| 443 | C4⋊C4 | — | 17 | 4 | no | — |
| 444 | C4⋊C4 | — | 34 | 2 | no | — |
| 445 | C4⋊C4 | — | 34 | 8 | no | — |
| 446 | C4⋊C4 | C2×C22⋊D17 | 1 | 4 | yes | — |
| 447 | C4⋊C4 | C2×C22⋊D17 | 1 | 4 | yes | — |
| 448 | C4⋊C4 | C23×D17 | 1 | 4 | yes | — |
| 449 | C22⋊C4 | — | 2 | 2 | no | — |
| 450 | C22⋊C4 | — | 2 | 4 | no | — |
| 451 | C22⋊C4 | — | 2 | 4 | no | — |
| 452 | C22⋊C4 | — | 2 | 4 | no | — |
| 453 | C22⋊C4 | — | 2 | 4 | no | — |
| 454 | C22⋊C4 | — | 34 | 4 | no | — |
| 455 | C22⋊C4 | — | 34 | 4 | no | — |
| 456 | C22⋊C4 | — | 34 | 8 | no | — |
| 457 | C22⋊C4 | C2×C22⋊D17 | 1 | 4 | yes | — |
| 458 | C22⋊C4 | C2×C22⋊D17 | 1 | 4 | yes | — |
| 459 | C42 | — | 2 | 2 | no | — |
| 460 | C42 | — | 2 | 4 | no | — |
| 461 | C42 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 462 | C42 | C2×C22⋊D17 | 1 | 2 | yes | — |
| 463 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 464 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 465 | C42 | C23×D17 | 1 | 2 | yes | — |
| 466 | C23 | — | 2 | 2 | no | — |
| 467 | C23 | — | 2 | 2 | no | — |
| 468 | C23 | — | 4 | 2 | no | — |
| 469 | C23 | — | 34 | 4 | no | — |
| 470 | C23 | — | 68 | 4 | no | — |
| 471 | C23 | — | 68 | 4 | no | — |
| 472 | C23 | — | 68 | 4 | no | — |
| 473 | C23 | C22×C22⋊D17 | 1 | 2 | yes | — |
| 474 | C23 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 475 | Q8 | — | 2 | 2 | no | — |
| 476 | Q8 | — | 2 | 2 | no | — |
| 477 | Q8 | — | 8 | 2 | no | — |
| 478 | D4 | — | 2 | 2 | no | — |
| 479 | D4 | — | 2 | 2 | no | — |
| 480 | D4 | — | 4 | 4 | no | — |
| 481 | D4 | — | 8 | 2 | no | — |
| 482 | D4 | — | 8 | 4 | no | — |
| 483 | D4 | — | 34 | 4 | no | — |
| 484 | D4 | — | 34 | 4 | no | — |
| 485 | D4 | — | 68 | 4 | no | — |
| 486 | D4 | — | 136 | 8 | no | — |
| 487 | D4 | — | 136 | 8 | no | — |
| 488 | C2×C4 | — | 2 | 2 | no | — |
| 489 | C2×C4 | — | 2 | 2 | no | — |
| 490 | C2×C4 | — | 2 | 2 | no | — |
| 491 | C2×C4 | — | 2 | 4 | no | — |
| 492 | C2×C4 | — | 2 | 2 | no | — |
| 493 | C2×C4 | — | 2 | 4 | no | — |
| 494 | C2×C4 | — | 4 | 2 | no | — |
| 495 | C2×C4 | — | 4 | 2 | no | — |
| 496 | C2×C4 | — | 4 | 4 | no | — |
| 497 | C2×C4 | — | 8 | 4 | no | — |
| 498 | C2×C4 | — | 34 | 4 | no | — |
| 499 | C2×C4 | — | 68 | 4 | no | — |
| 500 | C2×C4 | — | 136 | 4 | no | — |
| 501 | C2×C4 | — | 136 | 4 | no | — |
| 502 | C2×C4 | #10587696 | 1 | 2 | yes | — |
| 503 | C2×C4 | #10587697 | 1 | 2 | yes | — |
| 504 | C2×C4 | C22×C22⋊D17 | 1 | 4 | yes | — |
| 505 | C2×C4 | C22×C22⋊D17 | 1 | 2 | yes | — |
| 506 | C2×C4 | C22×C22⋊D17 | 1 | 2 | yes | — |
| 507 | C2×C4 | C22×C22⋊D17 | 1 | 2 | yes | — |
| 508 | C2×C4 | C22×C22⋊D17 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | C24×D17 | 1 | 1 | yes | characteristic |
| 510 | C8 | — | 34 | 8 | no | — |
| 511 | C22 | — | 2 | 2 | no | — |
| 512 | C22 | — | 2 | 2 | no | — |
| 513 | C22 | — | 2 | 4 | no | — |
| 514 | C22 | — | 4 | 2 | no | — |
| 515 | C22 | — | 4 | 4 | no | — |
| 516 | C22 | — | 8 | 2 | no | — |
| 517 | C22 | — | 68 | 4 | no | — |
| 518 | C22 | — | 68 | 4 | no | — |
| 519 | C22 | — | 68 | 4 | no | — |
| 520 | C22 | — | 136 | 8 | no | — |
| 521 | C22 | #11763387 | 1 | 2 | yes | — |
| 522 | C22 | C23×C22⋊D17 | 1 | 1 | yes | characteristic |
| 523 | C4 | — | 2 | 2 | no | — |
| 524 | C4 | — | 2 | 4 | no | — |
| 525 | C4 | — | 2 | 2 | no | — |
| 526 | C4 | — | 2 | 2 | no | — |
| 527 | C4 | — | 4 | 2 | no | — |
| 528 | C4 | — | 4 | 4 | no | — |
| 529 | C4 | — | 68 | 4 | no | — |
| 530 | C4 | #11763387 | 1 | 2 | yes | — |
| 531 | C4 | C2×#10587696 | 1 | 1 | yes | characteristic |
| 532 | C4 | C2×#10587697 | 1 | 1 | yes | characteristic |
| 533 | C2 | — | 2 | 2 | no | — |
| 534 | C2 | — | 4 | 2 | no | — |
| 535 | C2 | — | 8 | 2 | no | — |
| 536 | C2 | — | 136 | 4 | no | — |
| 537 | C2 | C2×#11763387 | 1 | 1 | yes | characteristic |
| 538 | C2 | #14543563 | 1 | 2 | yes | — |
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