Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1782 conjugacy classes of subgroups.
The subgroup lattice has 620 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14542802 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14542411 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q8×#63230 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14541455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14541420 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14541206 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #14541200 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #14540731 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #14540725 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #14540113 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #14539923 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #14538808 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #14538575 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #14537894 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | Q8×Q16×C17 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #11763533 | — | 2 | 3 | no | — |
| 17 | #11763532 | C22 | 1 | 3 | yes | — |
| 18 | #11763525 | — | 2 | 3 | no | — |
| 19 | #11763525 | C22 | 1 | 3 | yes | — |
| 20 | #11763525 | C22 | 1 | 3 | yes | — |
| 21 | #11763481 | — | 2 | 1 | no | — |
| 22 | #11763481 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11763481 | C22 | 1 | 3 | yes | — |
| 24 | Q8×D68 | C22 | 1 | 1 | yes | characteristic |
| 25 | #11763471 | — | 2 | 1 | no | — |
| 26 | #11763433 | — | 2 | 3 | no | — |
| 27 | #11763364 | C22 | 1 | 3 | yes | — |
| 28 | #11763360 | — | 2 | 3 | no | — |
| 29 | #11763360 | C22 | 1 | 3 | yes | — |
| 30 | #11763346 | C22 | 1 | 3 | yes | — |
| 31 | #11763285 | — | 2 | 1 | no | — |
| 32 | C4×#63256 | — | 2 | 1 | no | — |
| 33 | C4×#63256 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×#63256 | C22 | 1 | 3 | yes | — |
| 35 | #11763205 | C22 | 1 | 3 | yes | — |
| 36 | #11763157 | C22 | 1 | 3 | yes | — |
| 37 | #11763156 | C22 | 1 | 3 | yes | — |
| 38 | #11763149 | C22 | 1 | 3 | yes | — |
| 39 | #11763136 | C22 | 1 | 3 | yes | — |
| 40 | #11763136 | C22 | 1 | 6 | yes | — |
| 41 | #11763136 | C22 | 1 | 6 | yes | — |
| 42 | #11763118 | C22 | 1 | 3 | yes | — |
| 43 | #11763112 | C22 | 1 | 3 | yes | — |
| 44 | #11763112 | C22 | 1 | 6 | yes | — |
| 45 | #11763096 | C22 | 1 | 3 | yes | — |
| 46 | #11763096 | C22 | 1 | 3 | yes | — |
| 47 | #11763094 | C22 | 1 | 3 | yes | — |
| 48 | #11763090 | C22 | 1 | 3 | yes | — |
| 49 | #11763046 | C22 | 1 | 6 | yes | — |
| 50 | #11763041 | C22 | 1 | 6 | yes | — |
| 51 | #11763033 | C22 | 1 | 1 | yes | characteristic |
| 52 | #11763027 | C22 | 1 | 3 | yes | — |
| 53 | #11763009 | C22 | 1 | 3 | yes | — |
| 54 | #11763005 | C22 | 1 | 3 | yes | — |
| 55 | #11762970 | C22 | 1 | 3 | yes | — |
| 56 | #11762957 | C22 | 1 | 3 | yes | — |
| 57 | Q8×#3622 | C22 | 1 | 1 | yes | characteristic |
| 58 | C4×#63230 | C22 | 1 | 3 | yes | — |
| 59 | C4×#63230 | C22 | 1 | 3 | yes | — |
| 60 | C4×D136 | C22 | 1 | 3 | yes | — |
| 61 | C8×D68 | C22 | 1 | 3 | yes | — |
| 62 | #11762874 | C22 | 1 | 3 | yes | — |
| 63 | #11762860 | C22 | 1 | 3 | yes | — |
| 64 | #11762846 | C22 | 1 | 6 | yes | — |
| 65 | C4⋊C8×D17 | C22 | 1 | 3 | yes | — |
| 66 | #11762804 | C22 | 1 | 6 | yes | — |
| 67 | Q82×C17 | C22 | 1 | 1 | yes | characteristic |
| 68 | Q82×C17 | C22 | 1 | 1 | yes | characteristic |
| 69 | C17×#500 | C22 | 1 | 3 | yes | — |
| 70 | C17×#477 | C22 | 1 | 3 | yes | — |
| 71 | C17×#477 | C22 | 1 | 3 | yes | — |
| 72 | C8×Q8×C17 | C22 | 1 | 1 | yes | characteristic |
| 73 | C4×Q16×C17 | C22 | 1 | 3 | yes | — |
| 74 | C2×#63256 | — | 2 | 1 | no | — |
| 75 | C2×#63256 | — | 2 | 3 | no | — |
| 76 | C2×#63256 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#63256 | C23 | 1 | 3 | yes | — |
| 78 | C2×Q8×D17 | — | 2 | 1 | no | — |
| 79 | C2×Q16×C17 | C23 | 1 | 1 | yes | characteristic |
| 80 | C17×C4⋊Q8 | — | 2 | 3 | no | — |
| 81 | C17×C4⋊Q8 | — | 2 | 3 | no | — |
| 82 | C17×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 83 | C17×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 84 | C4×Q8×C17 | — | 2 | 1 | no | — |
| 85 | C4×Q8×C17 | — | 2 | 1 | no | — |
| 86 | C4×Q8×C17 | C23 | 1 | 3 | yes | — |
| 87 | C4×Q8×C17 | C23 | 1 | 3 | yes | — |
| 88 | C4×Q8×C17 | C23 | 1 | 1 | yes | characteristic |
| 89 | #10587633 | — | 2 | 6 | no | — |
| 90 | #10587633 | — | 2 | 6 | no | — |
| 91 | #10587633 | — | 2 | 3 | no | — |
| 92 | #10587633 | C23 | 1 | 1 | yes | characteristic |
| 93 | #10587632 | — | 2 | 3 | no | — |
| 94 | #10587632 | C23 | 1 | 3 | yes | — |
| 95 | Q8×Dic17 | — | 2 | 3 | no | — |
| 96 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 97 | Q8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 98 | C2×#63230 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#63230 | C23 | 1 | 3 | yes | — |
| 100 | C2×D136 | C23 | 1 | 3 | yes | — |
| 101 | C2×C8×D17 | C23 | 1 | 6 | yes | — |
| 102 | #10587584 | — | 2 | 6 | no | — |
| 103 | #10587584 | — | 2 | 3 | no | — |
| 104 | #10587583 | — | 2 | 3 | no | — |
| 105 | #10587583 | — | 2 | 3 | no | — |
| 106 | #10587581 | — | 2 | 6 | no | — |
| 107 | #10587581 | — | 2 | 3 | no | — |
| 108 | #10587581 | — | 2 | 3 | no | — |
| 109 | #10587581 | — | 2 | 3 | no | — |
| 110 | #10587581 | — | 2 | 3 | no | — |
| 111 | #10587581 | C23 | 1 | 3 | yes | — |
| 112 | #10587581 | C23 | 1 | 6 | yes | — |
| 113 | #10587580 | — | 2 | 3 | no | — |
| 114 | #10587579 | — | 2 | 3 | no | — |
| 115 | #10587579 | — | 2 | 3 | no | — |
| 116 | #10587579 | D4 | 1 | 3 | yes | — |
| 117 | #10587579 | C23 | 1 | 3 | yes | — |
| 118 | #10587578 | — | 2 | 3 | no | — |
| 119 | #10587578 | — | 2 | 3 | no | — |
| 120 | #10587578 | — | 2 | 3 | no | — |
| 121 | #10587578 | D4 | 1 | 3 | yes | — |
| 122 | #10587578 | C23 | 1 | 3 | yes | — |
| 123 | #10587578 | C23 | 1 | 6 | yes | — |
| 124 | #10587576 | C23 | 1 | 3 | yes | — |
| 125 | #10587573 | — | 2 | 3 | no | — |
| 126 | #10587561 | — | 2 | 3 | no | — |
| 127 | #10587560 | — | 2 | 3 | no | — |
| 128 | #10587560 | C23 | 1 | 3 | yes | — |
| 129 | C4×D68 | — | 2 | 3 | no | — |
| 130 | C4×D68 | — | 2 | 3 | no | — |
| 131 | C4×D68 | — | 2 | 3 | no | — |
| 132 | C4×D68 | C23 | 1 | 3 | yes | — |
| 133 | C4×D68 | C23 | 1 | 3 | yes | — |
| 134 | C4×D68 | C23 | 1 | 3 | yes | — |
| 135 | #10587558 | — | 2 | 3 | no | — |
| 136 | C42×D17 | — | 2 | 3 | no | — |
| 137 | C42×D17 | C23 | 1 | 3 | yes | — |
| 138 | #10587555 | C23 | 1 | 3 | yes | — |
| 139 | C4×Dic34 | — | 2 | 3 | no | — |
| 140 | C17×#107 | C23 | 1 | 3 | yes | — |
| 141 | C17×#107 | C23 | 1 | 6 | yes | — |
| 142 | C17×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 143 | C17×#103 | C23 | 1 | 3 | yes | — |
| 144 | C17×#103 | C23 | 1 | 3 | yes | — |
| 145 | C4×C8×C17 | C23 | 1 | 3 | yes | — |
| 146 | #10587506 | C23 | 1 | 3 | yes | — |
| 147 | #10587506 | C23 | 1 | 1 | yes | characteristic |
| 148 | #10587492 | C23 | 1 | 3 | yes | — |
| 149 | #10587492 | C23 | 1 | 6 | yes | — |
| 150 | #10587492 | C23 | 1 | 1 | yes | characteristic |
| 151 | #10587491 | C23 | 1 | 3 | yes | — |
| 152 | #10587491 | C23 | 1 | 3 | yes | — |
| 153 | #10587489 | C23 | 1 | 3 | yes | — |
| 154 | #10587485 | C23 | 1 | 3 | yes | — |
| 155 | #10587485 | C23 | 1 | 1 | yes | characteristic |
| 156 | #10587480 | C23 | 1 | 3 | yes | — |
| 157 | #10587480 | C23 | 1 | 6 | yes | — |
| 158 | #10587480 | C23 | 1 | 3 | yes | — |
| 159 | #10587479 | C23 | 1 | 3 | yes | — |
| 160 | #10587479 | C23 | 1 | 6 | yes | — |
| 161 | #10587479 | C23 | 1 | 3 | yes | — |
| 162 | C4⋊#3622 | C23 | 1 | 3 | yes | — |
| 163 | C4×#3622 | C23 | 1 | 3 | yes | — |
| 164 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 165 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 166 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×Q8×C17 | C24 | 1 | 1 | yes | characteristic |
| 168 | C2×Q8×C17 | C24 | 1 | 1 | yes | characteristic |
| 169 | #63256 | — | 2 | 4 | no | — |
| 170 | #63256 | — | 2 | 6 | no | — |
| 171 | #63256 | — | 4 | 3 | no | — |
| 172 | #63256 | — | 4 | 4 | no | — |
| 173 | #63256 | — | 8 | 6 | no | — |
| 174 | Q8×D17 | — | 4 | 4 | no | — |
| 175 | C2×D68 | — | 2 | 3 | no | — |
| 176 | C2×D68 | — | 2 | 3 | no | — |
| 177 | C2×D68 | — | 2 | 6 | no | — |
| 178 | C2×D68 | — | 2 | 3 | no | — |
| 179 | C2×D68 | — | 2 | 3 | no | — |
| 180 | C2×D68 | C2×D4 | 1 | 3 | yes | — |
| 181 | C2×D68 | C24 | 1 | 3 | yes | — |
| 182 | C2×D68 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×D17 | — | 2 | 3 | no | — |
| 184 | C2×C4×D17 | — | 2 | 3 | no | — |
| 185 | C2×C4×D17 | — | 2 | 3 | no | — |
| 186 | C2×C4×D17 | — | 2 | 3 | no | — |
| 187 | C2×C4×D17 | C2×D4 | 1 | 3 | yes | — |
| 188 | C2×C4×D17 | C2×D4 | 1 | 3 | yes | — |
| 189 | C2×C4×D17 | C24 | 1 | 3 | yes | — |
| 190 | C2×Dic34 | — | 2 | 3 | no | — |
| 191 | Q16×C17 | — | 2 | 2 | no | — |
| 192 | C2×C8×C17 | C24 | 1 | 1 | yes | characteristic |
| 193 | C2×C8×C17 | C24 | 1 | 3 | yes | — |
| 194 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 195 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 196 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 197 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 198 | C4⋊C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 199 | C4⋊C4×C17 | C24 | 1 | 3 | yes | — |
| 200 | C4⋊C4×C17 | C24 | 1 | 3 | yes | — |
| 201 | C42×C17 | — | 2 | 3 | no | — |
| 202 | C42×C17 | — | 2 | 3 | no | — |
| 203 | C42×C17 | C24 | 1 | 3 | yes | — |
| 204 | #63230 | — | 2 | 2 | no | — |
| 205 | #63230 | — | 4 | 3 | no | — |
| 206 | #63227 | — | 2 | 3 | no | — |
| 207 | #63227 | — | 2 | 3 | no | — |
| 208 | #63227 | — | 2 | 6 | no | — |
| 209 | #63227 | — | 2 | 3 | no | — |
| 210 | #63227 | — | 2 | 3 | no | — |
| 211 | #63227 | — | 2 | 1 | no | — |
| 212 | #63227 | — | 2 | 3 | no | — |
| 213 | #63227 | — | 2 | 1 | no | — |
| 214 | #63227 | — | 2 | 6 | no | — |
| 215 | #63227 | — | 2 | 3 | no | — |
| 216 | #63227 | C2×D4 | 1 | 6 | yes | — |
| 217 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 218 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 219 | C4⋊Dic17 | — | 2 | 3 | no | — |
| 220 | C4⋊Dic17 | C2×D4 | 1 | 3 | yes | — |
| 221 | C4⋊Dic17 | C24 | 1 | 1 | yes | characteristic |
| 222 | C4⋊Dic17 | C24 | 1 | 3 | yes | — |
| 223 | #63225 | — | 2 | 3 | no | — |
| 224 | #63225 | — | 2 | 3 | no | — |
| 225 | C4×Dic17 | — | 2 | 6 | no | — |
| 226 | C4×Dic17 | — | 2 | 1 | no | — |
| 227 | C4×Dic17 | — | 2 | 3 | no | — |
| 228 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 229 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 230 | C4×Dic17 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×#3622 | C24 | 1 | 1 | yes | characteristic |
| 232 | C2×#3622 | C24 | 1 | 3 | yes | — |
| 233 | D136 | — | 4 | 3 | no | — |
| 234 | C8×D17 | — | 4 | 6 | no | — |
| 235 | #62106 | — | 17 | 1 | no | maximal, Sylow |
| 236 | C22×D17 | — | 2 | 3 | no | — |
| 237 | C22×D17 | — | 2 | 1 | no | — |
| 238 | C22×D17 | C22×D4 | 1 | 3 | yes | — |
| 239 | Q8×C17 | — | 2 | 1 | no | — |
| 240 | Q8×C17 | — | 2 | 1 | no | — |
| 241 | Q8×C17 | — | 2 | 1 | no | — |
| 242 | Q8×C17 | — | 8 | 3 | no | — |
| 243 | Q8×C17 | — | 8 | 3 | no | — |
| 244 | Q8×C17 | #135 | 1 | 4 | yes | — |
| 245 | Q8×C17 | 2−1+4 | 1 | 2 | yes | — |
| 246 | C2×C4×C17 | — | 2 | 1 | no | — |
| 247 | C2×C4×C17 | — | 2 | 1 | no | — |
| 248 | C2×C4×C17 | — | 2 | 3 | no | — |
| 249 | C2×C4×C17 | — | 2 | 3 | no | — |
| 250 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 251 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 252 | C2×C4×C17 | C25 | 1 | 1 | yes | characteristic |
| 253 | C2×Dic17 | — | 2 | 3 | no | — |
| 254 | C2×Dic17 | — | 2 | 1 | no | — |
| 255 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×Dic17 | C22×D4 | 1 | 3 | yes | — |
| 257 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 258 | D68 | — | 2 | 6 | no | — |
| 259 | D68 | — | 2 | 3 | no | — |
| 260 | D68 | — | 2 | 1 | no | — |
| 261 | D68 | — | 2 | 3 | no | — |
| 262 | D68 | — | 2 | 1 | no | — |
| 263 | D68 | — | 4 | 6 | no | — |
| 264 | D68 | — | 4 | 6 | no | — |
| 265 | D68 | — | 8 | 3 | no | — |
| 266 | D68 | — | 8 | 3 | no | — |
| 267 | D68 | — | 8 | 6 | no | — |
| 268 | C4×D17 | — | 2 | 6 | no | — |
| 269 | C4×D17 | — | 2 | 3 | no | — |
| 270 | C4×D17 | — | 2 | 3 | no | — |
| 271 | C4×D17 | — | 4 | 3 | no | — |
| 272 | C4×D17 | — | 4 | 6 | no | — |
| 273 | C4×D17 | — | 4 | 6 | no | — |
| 274 | C4×D17 | — | 4 | 6 | no | — |
| 275 | C4×D17 | — | 4 | 6 | no | — |
| 276 | Dic34 | — | 4 | 6 | no | — |
| 277 | C8×C17 | — | 2 | 1 | no | — |
| 278 | C8×C17 | — | 2 | 3 | no | — |
| 279 | #3622 | — | 2 | 1 | no | — |
| 280 | #3622 | — | 2 | 3 | no | — |
| 281 | #3518 | — | 17 | 1 | no | — |
| 282 | #3483 | — | 17 | 1 | no | — |
| 283 | Q8×Q16 | D17 | 1 | 1 | yes | characteristic, complemented |
| 284 | Q8×SD16 | — | 17 | 1 | no | — |
| 285 | #3362 | — | 17 | 1 | no | — |
| 286 | #3358 | — | 17 | 1 | no | — |
| 287 | #3341 | — | 17 | 3 | no | — |
| 288 | #3340 | — | 17 | 3 | no | — |
| 289 | #3305 | — | 17 | 3 | no | — |
| 290 | #3304 | — | 17 | 3 | no | — |
| 291 | #3247 | — | 17 | 3 | no | — |
| 292 | #3228 | — | 17 | 3 | no | — |
| 293 | #3102 | — | 17 | 3 | no | — |
| 294 | #3076 | — | 17 | 3 | no | — |
| 295 | #2988 | — | 17 | 1 | no | — |
| 296 | C22×C17 | C23×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×D17 | — | 2 | 3 | no | — |
| 298 | C2×D17 | — | 2 | 3 | no | — |
| 299 | C2×D17 | — | 2 | 3 | no | — |
| 300 | C2×D17 | — | 4 | 3 | no | — |
| 301 | C2×D17 | — | 4 | 1 | no | — |
| 302 | C2×D17 | — | 4 | 3 | no | — |
| 303 | C2×D17 | — | 4 | 1 | no | — |
| 304 | C2×D17 | — | 4 | 1 | no | — |
| 305 | C2×D17 | — | 4 | 3 | no | — |
| 306 | C4×C17 | — | 2 | 3 | no | — |
| 307 | C4×C17 | — | 2 | 2 | no | — |
| 308 | C4×C17 | — | 4 | 3 | no | — |
| 309 | C4×C17 | — | 4 | 3 | no | — |
| 310 | C4×C17 | — | 4 | 1 | no | — |
| 311 | C4×C17 | C2×#135 | 1 | 6 | yes | — |
| 312 | C4×C17 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 313 | C4×C17 | #585 | 1 | 1 | yes | characteristic |
| 314 | Dic17 | — | 2 | 1 | no | — |
| 315 | Dic17 | — | 2 | 3 | no | — |
| 316 | Dic17 | — | 2 | 1 | no | — |
| 317 | Dic17 | — | 4 | 3 | no | — |
| 318 | Dic17 | — | 4 | 1 | no | — |
| 319 | Q82 | C2×D17 | 1 | 1 | yes | characteristic |
| 320 | Q82 | C2×D17 | 1 | 1 | yes | characteristic |
| 321 | #556 | — | 17 | 3 | no | — |
| 322 | #556 | — | 34 | 3 | no | — |
| 323 | #555 | — | 17 | 3 | no | — |
| 324 | #555 | — | 17 | 3 | no | — |
| 325 | #555 | — | 34 | 3 | no | — |
| 326 | #550 | — | 17 | 1 | no | — |
| 327 | #550 | — | 17 | 3 | no | — |
| 328 | #550 | — | 34 | 1 | no | — |
| 329 | D4×Q8 | — | 17 | 1 | no | — |
| 330 | #548 | — | 34 | 1 | no | — |
| 331 | #542 | — | 34 | 3 | no | — |
| 332 | #533 | — | 17 | 3 | no | — |
| 333 | #532 | — | 17 | 3 | no | — |
| 334 | #532 | — | 34 | 3 | no | — |
| 335 | #529 | — | 17 | 3 | no | — |
| 336 | #519 | — | 34 | 1 | no | — |
| 337 | C4×#41 | — | 17 | 1 | no | — |
| 338 | C4×#41 | — | 17 | 3 | no | — |
| 339 | C4×#41 | — | 34 | 1 | no | — |
| 340 | #500 | C2×D17 | 1 | 3 | yes | — |
| 341 | #498 | — | 17 | 3 | no | — |
| 342 | #486 | — | 17 | 3 | no | — |
| 343 | #486 | — | 17 | 3 | no | — |
| 344 | #485 | — | 17 | 3 | no | — |
| 345 | #482 | — | 17 | 6 | no | — |
| 346 | #482 | — | 17 | 3 | no | — |
| 347 | #482 | — | 17 | 6 | no | — |
| 348 | #479 | — | 17 | 3 | no | — |
| 349 | #478 | — | 17 | 6 | no | — |
| 350 | #478 | — | 17 | 3 | no | — |
| 351 | #477 | C2×D17 | 1 | 3 | yes | — |
| 352 | #477 | C2×D17 | 1 | 3 | yes | — |
| 353 | #476 | — | 17 | 3 | no | — |
| 354 | #476 | — | 17 | 3 | no | — |
| 355 | #475 | — | 17 | 3 | no | — |
| 356 | #474 | — | 17 | 3 | no | — |
| 357 | #466 | — | 17 | 6 | no | — |
| 358 | #465 | — | 17 | 6 | no | — |
| 359 | #464 | — | 17 | 1 | no | — |
| 360 | #463 | — | 17 | 3 | no | — |
| 361 | #460 | — | 17 | 3 | no | — |
| 362 | #459 | — | 17 | 3 | no | — |
| 363 | #452 | — | 17 | 3 | no | — |
| 364 | #449 | — | 17 | 3 | no | — |
| 365 | C8×Q8 | — | 17 | 1 | no | — |
| 366 | C8×Q8 | C2×D17 | 1 | 1 | yes | characteristic |
| 367 | C4×Q16 | C2×D17 | 1 | 3 | yes | — |
| 368 | C4×SD16 | — | 17 | 3 | no | — |
| 369 | C4×SD16 | — | 17 | 3 | no | — |
| 370 | C4×D8 | — | 17 | 3 | no | — |
| 371 | C8×D4 | — | 17 | 3 | no | — |
| 372 | C8×D4 | — | 17 | 3 | no | — |
| 373 | #431 | — | 17 | 3 | no | — |
| 374 | #427 | — | 17 | 6 | no | — |
| 375 | C2×C4⋊C8 | — | 17 | 3 | no | — |
| 376 | #416 | — | 17 | 6 | no | — |
| 377 | C2×C17 | #3489 | 1 | 1 | yes | characteristic |
| 378 | C2×C17 | C22×#135 | 1 | 1 | yes | characteristic |
| 379 | C2×C17 | #3585 | 1 | 1 | yes | characteristic |
| 380 | D17 | — | 4 | 3 | no | — |
| 381 | D17 | — | 8 | 3 | no | — |
| 382 | D17 | — | 8 | 1 | no | — |
| 383 | C2×#41 | — | 17 | 1 | no | — |
| 384 | C2×#41 | — | 17 | 3 | no | — |
| 385 | C2×#41 | — | 34 | 3 | no | — |
| 386 | C2×#41 | — | 34 | 1 | no | — |
| 387 | C22×Q8 | — | 34 | 1 | no | — |
| 388 | C2×Q16 | C22×D17 | 1 | 1 | yes | characteristic |
| 389 | C2×SD16 | — | 17 | 1 | no | — |
| 390 | C2×SD16 | — | 17 | 3 | no | — |
| 391 | C2×D8 | — | 17 | 3 | no | — |
| 392 | C22×C8 | — | 17 | 6 | no | — |
| 393 | C4⋊Q8 | — | 2 | 3 | no | — |
| 394 | C4⋊Q8 | — | 2 | 3 | no | — |
| 395 | C4⋊Q8 | — | 17 | 3 | no | — |
| 396 | C4⋊Q8 | C22×D17 | 1 | 3 | yes | — |
| 397 | C4⋊Q8 | C22×D17 | 1 | 3 | yes | — |
| 398 | #127 | — | 17 | 3 | no | — |
| 399 | #127 | — | 34 | 3 | no | — |
| 400 | #126 | — | 34 | 3 | no | — |
| 401 | #126 | — | 34 | 6 | no | — |
| 402 | #125 | — | 17 | 3 | no | — |
| 403 | #124 | — | 17 | 1 | no | — |
| 404 | #124 | — | 34 | 3 | no | — |
| 405 | #124 | — | 34 | 3 | no | — |
| 406 | #124 | — | 34 | 6 | no | — |
| 407 | #124 | — | 34 | 6 | no | — |
| 408 | #123 | — | 34 | 3 | no | — |
| 409 | C22⋊Q8 | — | 17 | 3 | no | — |
| 410 | C22⋊Q8 | — | 34 | 3 | no | — |
| 411 | C22⋊Q8 | — | 34 | 3 | no | — |
| 412 | C22⋊Q8 | — | 34 | 3 | no | — |
| 413 | #121 | — | 17 | 3 | no | — |
| 414 | #121 | — | 17 | 6 | no | — |
| 415 | #121 | — | 34 | 6 | no | — |
| 416 | #121 | — | 34 | 3 | no | — |
| 417 | #121 | — | 34 | 3 | no | — |
| 418 | #121 | — | 34 | 3 | no | — |
| 419 | #121 | — | 34 | 3 | no | — |
| 420 | C4×Q8 | — | 2 | 1 | no | — |
| 421 | C4×Q8 | — | 2 | 1 | no | — |
| 422 | C4×Q8 | — | 17 | 1 | no | — |
| 423 | C4×Q8 | — | 17 | 1 | no | — |
| 424 | C4×Q8 | — | 34 | 3 | no | — |
| 425 | C4×Q8 | — | 34 | 3 | no | — |
| 426 | C4×Q8 | — | 34 | 3 | no | — |
| 427 | C4×Q8 | C22×D17 | 1 | 3 | yes | — |
| 428 | C4×Q8 | C22×D17 | 1 | 3 | yes | — |
| 429 | C4×Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 430 | C4×D4 | — | 17 | 3 | no | — |
| 431 | C4×D4 | — | 17 | 3 | no | — |
| 432 | C4×D4 | — | 17 | 3 | no | — |
| 433 | C4×D4 | — | 17 | 3 | no | — |
| 434 | C4×D4 | — | 17 | 3 | no | — |
| 435 | C4×D4 | — | 34 | 3 | no | — |
| 436 | C4×D4 | — | 34 | 3 | no | — |
| 437 | C4×D4 | — | 34 | 3 | no | — |
| 438 | C4×D4 | — | 34 | 3 | no | — |
| 439 | C4×D4 | — | 34 | 3 | no | — |
| 440 | #117 | — | 17 | 3 | no | — |
| 441 | #117 | — | 17 | 3 | no | — |
| 442 | #117 | — | 17 | 6 | no | — |
| 443 | #117 | — | 34 | 3 | no | — |
| 444 | #117 | — | 34 | 3 | no | — |
| 445 | #117 | — | 34 | 3 | no | — |
| 446 | #117 | — | 34 | 3 | no | — |
| 447 | C2×C42 | — | 17 | 3 | no | — |
| 448 | C2×C42 | — | 34 | 3 | no | — |
| 449 | #107 | — | 17 | 3 | no | — |
| 450 | #107 | C22×D17 | 1 | 6 | yes | — |
| 451 | #107 | C22×D17 | 1 | 3 | yes | — |
| 452 | #106 | — | 17 | 3 | no | — |
| 453 | #106 | — | 17 | 6 | no | — |
| 454 | #106 | — | 17 | 3 | no | — |
| 455 | C4⋊C8 | — | 17 | 3 | no | — |
| 456 | C4⋊C8 | — | 17 | 1 | no | — |
| 457 | C4⋊C8 | — | 17 | 3 | no | — |
| 458 | C4⋊C8 | C22×D17 | 1 | 3 | yes | — |
| 459 | #103 | — | 17 | 3 | no | — |
| 460 | #103 | — | 17 | 1 | no | — |
| 461 | #103 | C22×D17 | 1 | 3 | yes | — |
| 462 | #103 | C22×D17 | 1 | 3 | yes | — |
| 463 | #102 | — | 17 | 6 | no | — |
| 464 | #102 | — | 17 | 1 | no | — |
| 465 | #102 | — | 17 | 3 | no | — |
| 466 | #102 | — | 17 | 6 | no | — |
| 467 | #102 | — | 17 | 3 | no | — |
| 468 | #102 | — | 17 | 3 | no | — |
| 469 | C22⋊C8 | — | 17 | 3 | no | — |
| 470 | C22⋊C8 | — | 17 | 3 | no | — |
| 471 | C4×C8 | — | 17 | 3 | no | — |
| 472 | C4×C8 | C22×D17 | 1 | 3 | yes | — |
| 473 | C17 | #62106 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 474 | #41 | — | 34 | 4 | no | — |
| 475 | #41 | — | 34 | 6 | no | — |
| 476 | #41 | — | 68 | 3 | no | — |
| 477 | #41 | — | 68 | 4 | no | — |
| 478 | #41 | — | 136 | 6 | no | — |
| 479 | C2×Q8 | — | 2 | 3 | no | — |
| 480 | C2×Q8 | — | 2 | 3 | no | — |
| 481 | C2×Q8 | — | 34 | 3 | no | — |
| 482 | C2×Q8 | — | 68 | 4 | no | — |
| 483 | C2×Q8 | D4×D17 | 1 | 1 | yes | characteristic |
| 484 | C2×Q8 | C23×D17 | 1 | 1 | yes | characteristic |
| 485 | C2×Q8 | C23×D17 | 1 | 1 | yes | characteristic |
| 486 | C2×D4 | — | 17 | 3 | no | — |
| 487 | C2×D4 | — | 17 | 3 | no | — |
| 488 | C2×D4 | — | 17 | 1 | no | — |
| 489 | C2×D4 | — | 34 | 3 | no | — |
| 490 | C2×D4 | — | 34 | 3 | no | — |
| 491 | C2×D4 | — | 34 | 6 | no | — |
| 492 | C2×D4 | — | 34 | 3 | no | — |
| 493 | C2×D4 | — | 34 | 3 | no | — |
| 494 | C22×C4 | — | 17 | 3 | no | — |
| 495 | C22×C4 | — | 17 | 3 | no | — |
| 496 | C22×C4 | — | 17 | 3 | no | — |
| 497 | C22×C4 | — | 34 | 3 | no | — |
| 498 | C22×C4 | — | 34 | 3 | no | — |
| 499 | C22×C4 | — | 34 | 3 | no | — |
| 500 | C22×C4 | — | 34 | 3 | no | — |
| 501 | Q16 | — | 2 | 2 | no | — |
| 502 | SD16 | — | 34 | 2 | no | — |
| 503 | SD16 | — | 68 | 3 | no | — |
| 504 | D8 | — | 68 | 3 | no | — |
| 505 | C2×C8 | — | 17 | 1 | no | — |
| 506 | C2×C8 | — | 17 | 3 | no | — |
| 507 | C2×C8 | — | 68 | 6 | no | — |
| 508 | C2×C8 | C23×D17 | 1 | 1 | yes | characteristic |
| 509 | C2×C8 | C23×D17 | 1 | 3 | yes | — |
| 510 | C4⋊C4 | — | 2 | 3 | no | — |
| 511 | C4⋊C4 | — | 2 | 3 | no | — |
| 512 | C4⋊C4 | — | 2 | 3 | no | — |
| 513 | C4⋊C4 | — | 2 | 3 | no | — |
| 514 | C4⋊C4 | — | 17 | 3 | no | — |
| 515 | C4⋊C4 | — | 17 | 3 | no | — |
| 516 | C4⋊C4 | — | 17 | 1 | no | — |
| 517 | C4⋊C4 | — | 34 | 1 | no | — |
| 518 | C4⋊C4 | — | 34 | 3 | no | — |
| 519 | C4⋊C4 | — | 34 | 3 | no | — |
| 520 | C4⋊C4 | — | 34 | 3 | no | — |
| 521 | C4⋊C4 | — | 34 | 3 | no | — |
| 522 | C4⋊C4 | D4×D17 | 1 | 3 | yes | — |
| 523 | C4⋊C4 | C23×D17 | 1 | 3 | yes | — |
| 524 | C4⋊C4 | C23×D17 | 1 | 3 | yes | — |
| 525 | C22⋊C4 | — | 17 | 6 | no | — |
| 526 | C22⋊C4 | — | 34 | 3 | no | — |
| 527 | C22⋊C4 | — | 34 | 1 | no | — |
| 528 | C22⋊C4 | — | 34 | 3 | no | — |
| 529 | C22⋊C4 | — | 34 | 6 | no | — |
| 530 | C22⋊C4 | — | 34 | 1 | no | — |
| 531 | C22⋊C4 | — | 34 | 3 | no | — |
| 532 | C22⋊C4 | — | 34 | 6 | no | — |
| 533 | C22⋊C4 | — | 34 | 3 | no | — |
| 534 | C22⋊C4 | — | 34 | 3 | no | — |
| 535 | C22⋊C4 | — | 34 | 3 | no | — |
| 536 | C42 | — | 2 | 3 | no | — |
| 537 | C42 | — | 2 | 3 | no | — |
| 538 | C42 | — | 17 | 3 | no | — |
| 539 | C42 | — | 17 | 3 | no | — |
| 540 | C42 | — | 17 | 1 | no | — |
| 541 | C42 | — | 34 | 1 | no | — |
| 542 | C42 | — | 34 | 3 | no | — |
| 543 | C42 | — | 34 | 6 | no | — |
| 544 | C42 | C23×D17 | 1 | 3 | yes | — |
| 545 | C23 | — | 17 | 3 | no | — |
| 546 | C23 | — | 34 | 1 | no | — |
| 547 | C23 | — | 34 | 3 | no | — |
| 548 | Q8 | — | 2 | 1 | no | — |
| 549 | Q8 | — | 2 | 1 | no | — |
| 550 | Q8 | — | 2 | 1 | no | — |
| 551 | Q8 | — | 8 | 3 | no | — |
| 552 | Q8 | — | 8 | 3 | no | — |
| 553 | Q8 | — | 68 | 6 | no | — |
| 554 | Q8 | #10587605 | 1 | 4 | yes | — |
| 555 | Q8 | #10587694 | 1 | 2 | yes | — |
| 556 | D4 | — | 34 | 6 | no | — |
| 557 | D4 | — | 34 | 1 | no | — |
| 558 | D4 | — | 34 | 3 | no | — |
| 559 | D4 | — | 34 | 1 | no | — |
| 560 | D4 | — | 34 | 3 | no | — |
| 561 | D4 | — | 68 | 6 | no | — |
| 562 | D4 | — | 68 | 6 | no | — |
| 563 | D4 | — | 136 | 3 | no | — |
| 564 | D4 | — | 136 | 6 | no | — |
| 565 | D4 | — | 136 | 3 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 1 | no | — |
| 568 | C2×C4 | — | 2 | 3 | no | — |
| 569 | C2×C4 | — | 2 | 3 | no | — |
| 570 | C2×C4 | — | 17 | 1 | no | — |
| 571 | C2×C4 | — | 17 | 1 | no | — |
| 572 | C2×C4 | — | 17 | 3 | no | — |
| 573 | C2×C4 | — | 34 | 6 | no | — |
| 574 | C2×C4 | — | 34 | 3 | no | — |
| 575 | C2×C4 | — | 34 | 3 | no | — |
| 576 | C2×C4 | — | 34 | 1 | no | — |
| 577 | C2×C4 | — | 34 | 3 | no | — |
| 578 | C2×C4 | — | 68 | 3 | no | — |
| 579 | C2×C4 | — | 68 | 6 | no | — |
| 580 | C2×C4 | — | 68 | 6 | no | — |
| 581 | C2×C4 | — | 68 | 6 | no | — |
| 582 | C2×C4 | — | 68 | 6 | no | — |
| 583 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 584 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 585 | C2×C4 | C24×D17 | 1 | 1 | yes | characteristic |
| 586 | C8 | — | 2 | 1 | no | — |
| 587 | C8 | — | 2 | 3 | no | — |
| 588 | C8 | — | 34 | 1 | no | — |
| 589 | C8 | — | 34 | 3 | no | — |
| 590 | C22 | — | 34 | 3 | no | — |
| 591 | C22 | — | 34 | 3 | no | — |
| 592 | C22 | — | 34 | 3 | no | — |
| 593 | C22 | — | 68 | 3 | no | — |
| 594 | C22 | — | 68 | 1 | no | — |
| 595 | C22 | — | 68 | 1 | no | — |
| 596 | C22 | — | 68 | 3 | no | — |
| 597 | C22 | — | 68 | 3 | no | — |
| 598 | C22 | — | 68 | 1 | no | — |
| 599 | C22 | C22×D4×D17 | 1 | 1 | yes | characteristic |
| 600 | C4 | — | 2 | 2 | no | — |
| 601 | C4 | — | 2 | 3 | no | — |
| 602 | C4 | — | 4 | 1 | no | — |
| 603 | C4 | — | 4 | 3 | no | — |
| 604 | C4 | — | 4 | 3 | no | — |
| 605 | C4 | — | 34 | 3 | no | — |
| 606 | C4 | — | 34 | 1 | no | — |
| 607 | C4 | — | 34 | 1 | no | — |
| 608 | C4 | — | 68 | 1 | no | — |
| 609 | C4 | — | 68 | 3 | no | — |
| 610 | C4 | C2×#10587605 | 1 | 6 | yes | — |
| 611 | C4 | C2×#10587694 | 1 | 1 | yes | characteristic |
| 612 | C4 | #11763646 | 1 | 1 | yes | characteristic |
| 613 | C2 | — | 68 | 3 | no | — |
| 614 | C2 | — | 136 | 3 | no | — |
| 615 | C2 | — | 136 | 1 | no | — |
| 616 | C2 | #14542461 | 1 | 1 | yes | characteristic |
| 617 | C2 | C22×#10587605 | 1 | 1 | yes | characteristic |
| 618 | C2 | #14543559 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14542802 | C2 | semidirect |
| 2. #14542411 | C2 | semidirect |
| 3. Q8×#63230 | C2 | semidirect |
| 4. #14541455 | C2 | semidirect |
| 5. #14541420 | C2 | semidirect |
| 6. #14541206 | C2 | semidirect |
| 7. #14541200 | C2 | semidirect |
| 8. #14540731 | C2 | semidirect |
| 9. #14540725 | C2 | semidirect |
| 10. #14540113 | C2 | semidirect |
| 11. #14539923 | C2 | semidirect |
| 12. #14538808 | C2 | semidirect |
| 13. #14538575 | C2 | semidirect |
| 14. #14537894 | C2 | semidirect |
| 15. Q8×Q16×C17 | C2 | semidirect |
| 283. Q8×Q16 | D17 | semidirect |
| 473. C17 | #62106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14542802 | 2 |
| #14542411 | 2 |
| Q8×#63230 | 2 |
| #14541455 | 2 |
| #14541420 | 2 |
| #14541206 | 2 |
| #14541200 | 2 |
| #14540731 | 2 |
| #14540725 | 2 |
| #14540113 | 2 |
| #14539923 | 2 |
| #14538808 | 2 |
| #14538575 | 2 |
| #14537894 | 2 |
| Q8×Q16×C17 | 2 |
| #62106 | 17 |