Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1922 conjugacy classes of subgroups.
The subgroup lattice has 634 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #14542791 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14542411 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14541761 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14541759 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14541455 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14540731 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #14540711 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #14540543 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #14540509 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #14540113 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #14539720 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #14538808 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #14538242 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | #14537894 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C17×#3363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#10587605 | C22 | 1 | 6 | yes | — |
| 17 | #11763525 | — | 2 | 3 | no | — |
| 18 | #11763525 | C22 | 1 | 3 | yes | — |
| 19 | #11763512 | — | 2 | 3 | no | — |
| 20 | #11763481 | — | 2 | 1 | no | — |
| 21 | #11763481 | — | 2 | 1 | no | — |
| 22 | #11763481 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11763481 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11763481 | C22 | 1 | 3 | yes | — |
| 25 | #11763481 | C22 | 1 | 3 | yes | — |
| 26 | #11763462 | C22 | 1 | 3 | yes | — |
| 27 | #11763415 | — | 2 | 3 | no | — |
| 28 | #11763360 | — | 2 | 3 | no | — |
| 29 | #11763360 | C22 | 1 | 3 | yes | — |
| 30 | #11763360 | C22 | 1 | 3 | yes | — |
| 31 | #11763346 | C22 | 1 | 3 | yes | — |
| 32 | #11763291 | — | 2 | 1 | no | — |
| 33 | C4×#63256 | — | 2 | 1 | no | — |
| 34 | C4×#63256 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×#63256 | C22 | 1 | 3 | yes | — |
| 36 | #11763186 | C22 | 1 | 3 | yes | — |
| 37 | #11763183 | C22 | 1 | 3 | yes | — |
| 38 | #11763157 | C22 | 1 | 3 | yes | — |
| 39 | #11763149 | C22 | 1 | 3 | yes | — |
| 40 | #11763136 | C22 | 1 | 3 | yes | — |
| 41 | #11763118 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11763112 | C22 | 1 | 3 | yes | — |
| 43 | #11763096 | C22 | 1 | 3 | yes | — |
| 44 | #11763046 | C22 | 1 | 6 | yes | — |
| 45 | #11763041 | C22 | 1 | 6 | yes | — |
| 46 | #11763033 | C22 | 1 | 3 | yes | — |
| 47 | #11763027 | C22 | 1 | 6 | yes | — |
| 48 | #11763027 | C22 | 1 | 3 | yes | — |
| 49 | #11763011 | C22 | 1 | 3 | yes | — |
| 50 | #11763009 | C22 | 1 | 3 | yes | — |
| 51 | #11763009 | C22 | 1 | 3 | yes | — |
| 52 | #11763005 | C22 | 1 | 3 | yes | — |
| 53 | #11763005 | C22 | 1 | 3 | yes | — |
| 54 | #11762970 | C22 | 1 | 3 | yes | — |
| 55 | #11762957 | C22 | 1 | 3 | yes | — |
| 56 | #11762957 | C22 | 1 | 6 | yes | — |
| 57 | #11762957 | C22 | 1 | 6 | yes | — |
| 58 | Q8×#3622 | C22 | 1 | 1 | yes | characteristic |
| 59 | C4×#63230 | C22 | 1 | 3 | yes | — |
| 60 | C4×#63230 | C22 | 1 | 3 | yes | — |
| 61 | C4×D136 | C22 | 1 | 3 | yes | — |
| 62 | C8×D68 | C22 | 1 | 3 | yes | — |
| 63 | #11762874 | C22 | 1 | 3 | yes | — |
| 64 | #11762860 | C22 | 1 | 3 | yes | — |
| 65 | C4⋊C8×D17 | C22 | 1 | 3 | yes | — |
| 66 | #11762804 | C22 | 1 | 6 | yes | — |
| 67 | Q82×C17 | C22 | 1 | 1 | yes | characteristic |
| 68 | C17×#557 | C22 | 1 | 1 | yes | characteristic |
| 69 | C17×#487 | C22 | 1 | 3 | yes | — |
| 70 | C17×#477 | C22 | 1 | 3 | yes | — |
| 71 | C17×#462 | 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 | 1 | no | — |
| 76 | C2×#63256 | — | 2 | 3 | no | — |
| 77 | C2×#63256 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×#63256 | C23 | 1 | 3 | yes | — |
| 79 | C2×#63256 | C23 | 1 | 6 | yes | — |
| 80 | C2×Q16×C17 | C23 | 1 | 3 | yes | — |
| 81 | C17×C4⋊Q8 | — | 2 | 3 | no | — |
| 82 | C17×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 83 | C17×C4⋊Q8 | C23 | 1 | 3 | yes | — |
| 84 | C17×#125 | — | 2 | 3 | no | — |
| 85 | C4×Q8×C17 | — | 2 | 1 | no | — |
| 86 | C4×Q8×C17 | — | 2 | 1 | no | — |
| 87 | C4×Q8×C17 | C23 | 1 | 3 | yes | — |
| 88 | C4×Q8×C17 | C23 | 1 | 3 | yes | — |
| 89 | C4×Q8×C17 | C23 | 1 | 1 | yes | characteristic |
| 90 | #10587633 | — | 2 | 6 | no | — |
| 91 | #10587633 | — | 2 | 3 | no | — |
| 92 | #10587633 | C23 | 1 | 3 | yes | — |
| 93 | #10587632 | C23 | 1 | 3 | yes | — |
| 94 | Q8×Dic17 | D4 | 1 | 1 | yes | characteristic |
| 95 | Q8×Dic17 | C23 | 1 | 1 | yes | characteristic |
| 96 | C2×#63230 | C23 | 1 | 3 | yes | — |
| 97 | C2×#63230 | C23 | 1 | 3 | yes | — |
| 98 | C2×#63230 | C23 | 1 | 6 | yes | — |
| 99 | #10587605 | — | 4 | 12 | no | — |
| 100 | C2×D136 | C23 | 1 | 3 | yes | — |
| 101 | C2×D136 | C23 | 1 | 6 | yes | — |
| 102 | C2×C8×D17 | C23 | 1 | 6 | yes | — |
| 103 | #10587584 | — | 2 | 3 | no | — |
| 104 | #10587581 | — | 2 | 6 | no | — |
| 105 | #10587581 | — | 2 | 6 | no | — |
| 106 | #10587581 | — | 2 | 3 | no | — |
| 107 | #10587581 | — | 2 | 3 | no | — |
| 108 | #10587581 | — | 2 | 3 | no | — |
| 109 | #10587581 | — | 2 | 3 | no | — |
| 110 | #10587581 | — | 2 | 3 | no | — |
| 111 | #10587581 | — | 2 | 3 | no | — |
| 112 | #10587581 | — | 2 | 3 | no | — |
| 113 | #10587581 | C23 | 1 | 6 | yes | — |
| 114 | #10587581 | C23 | 1 | 3 | yes | — |
| 115 | #10587580 | — | 2 | 6 | no | — |
| 116 | #10587580 | — | 2 | 3 | no | — |
| 117 | #10587579 | — | 2 | 3 | no | — |
| 118 | #10587579 | — | 2 | 3 | no | — |
| 119 | #10587579 | — | 2 | 3 | no | — |
| 120 | #10587579 | — | 2 | 3 | no | — |
| 121 | #10587579 | D4 | 1 | 3 | yes | — |
| 122 | #10587579 | C23 | 1 | 3 | yes | — |
| 123 | #10587578 | — | 2 | 3 | no | — |
| 124 | #10587578 | — | 2 | 3 | no | — |
| 125 | #10587578 | D4 | 1 | 3 | yes | — |
| 126 | #10587578 | C23 | 1 | 3 | yes | — |
| 127 | C4⋊C4×D17 | — | 2 | 3 | no | — |
| 128 | #10587576 | C23 | 1 | 1 | yes | characteristic |
| 129 | #10587560 | — | 2 | 3 | no | — |
| 130 | #10587560 | — | 2 | 3 | no | — |
| 131 | #10587560 | C23 | 1 | 3 | yes | — |
| 132 | #10587560 | C23 | 1 | 3 | yes | — |
| 133 | C4×D68 | — | 2 | 3 | no | — |
| 134 | C4×D68 | — | 2 | 3 | no | — |
| 135 | C4×D68 | — | 2 | 3 | no | — |
| 136 | C4×D68 | — | 2 | 3 | no | — |
| 137 | C4×D68 | C23 | 1 | 3 | yes | — |
| 138 | C4×D68 | C23 | 1 | 3 | yes | — |
| 139 | C4×D68 | C23 | 1 | 3 | yes | — |
| 140 | #10587558 | — | 2 | 3 | no | — |
| 141 | C42×D17 | — | 2 | 3 | no | — |
| 142 | C42×D17 | C23 | 1 | 3 | yes | — |
| 143 | C17×#107 | C23 | 1 | 3 | yes | — |
| 144 | C17×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 145 | C17×#103 | C23 | 1 | 1 | yes | characteristic |
| 146 | C17×#103 | C23 | 1 | 3 | yes | — |
| 147 | C17×#103 | C23 | 1 | 6 | yes | — |
| 148 | C4×C8×C17 | C23 | 1 | 3 | yes | — |
| 149 | #10587506 | C23 | 1 | 1 | yes | characteristic |
| 150 | #10587506 | C23 | 1 | 3 | yes | — |
| 151 | #10587492 | C23 | 1 | 3 | yes | — |
| 152 | #10587492 | C23 | 1 | 3 | yes | — |
| 153 | #10587491 | C23 | 1 | 3 | yes | — |
| 154 | #10587491 | C23 | 1 | 3 | yes | — |
| 155 | #10587489 | C23 | 1 | 1 | yes | characteristic |
| 156 | #10587485 | C23 | 1 | 1 | yes | characteristic |
| 157 | #10587485 | C23 | 1 | 3 | yes | — |
| 158 | #10587480 | C23 | 1 | 3 | yes | — |
| 159 | #10587480 | C23 | 1 | 3 | yes | — |
| 160 | #10587480 | C23 | 1 | 6 | yes | — |
| 161 | #10587479 | C23 | 1 | 3 | yes | — |
| 162 | #10587479 | C23 | 1 | 1 | yes | characteristic |
| 163 | C4⋊#3622 | C23 | 1 | 3 | yes | — |
| 164 | C4×#3622 | C23 | 1 | 3 | yes | — |
| 165 | C2×Q8×C17 | — | 2 | 3 | no | — |
| 166 | C2×Q8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×Q8×C17 | C24 | 1 | 3 | yes | — |
| 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 | 6 | no | — |
| 173 | #63256 | — | 4 | 6 | no | — |
| 174 | #63256 | — | 4 | 4 | no | — |
| 175 | #63256 | — | 4 | 4 | no | — |
| 176 | #63256 | — | 8 | 6 | no | — |
| 177 | C2×D68 | — | 2 | 3 | no | — |
| 178 | C2×D68 | — | 2 | 3 | no | — |
| 179 | C2×D68 | — | 2 | 3 | no | — |
| 180 | C2×D68 | — | 2 | 6 | no | — |
| 181 | C2×D68 | — | 2 | 6 | no | — |
| 182 | C2×D68 | — | 2 | 3 | no | — |
| 183 | C2×D68 | — | 2 | 3 | no | — |
| 184 | C2×D68 | — | 2 | 3 | no | — |
| 185 | C2×D68 | C2×D4 | 1 | 3 | yes | — |
| 186 | C2×D68 | C24 | 1 | 3 | yes | — |
| 187 | C2×D68 | C24 | 1 | 3 | yes | — |
| 188 | C2×C4×D17 | — | 2 | 3 | no | — |
| 189 | C2×C4×D17 | — | 2 | 3 | no | — |
| 190 | C2×C4×D17 | — | 2 | 3 | no | — |
| 191 | C2×C4×D17 | — | 2 | 3 | no | — |
| 192 | C2×C4×D17 | — | 2 | 6 | no | — |
| 193 | C2×C4×D17 | C2×D4 | 1 | 3 | yes | — |
| 194 | C2×C4×D17 | C2×D4 | 1 | 3 | yes | — |
| 195 | C2×C4×D17 | C24 | 1 | 3 | yes | — |
| 196 | Q16×C17 | — | 2 | 6 | no | — |
| 197 | C2×C8×C17 | C24 | 1 | 3 | yes | — |
| 198 | C2×C8×C17 | C24 | 1 | 1 | yes | characteristic |
| 199 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 200 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 201 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 202 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 203 | C4⋊C4×C17 | — | 2 | 3 | no | — |
| 204 | C4⋊C4×C17 | C2×D4 | 1 | 3 | yes | — |
| 205 | C4⋊C4×C17 | C24 | 1 | 3 | yes | — |
| 206 | C4⋊C4×C17 | C24 | 1 | 1 | yes | characteristic |
| 207 | C42×C17 | — | 2 | 3 | no | — |
| 208 | C42×C17 | — | 2 | 3 | no | — |
| 209 | C42×C17 | C24 | 1 | 3 | yes | — |
| 210 | #63230 | — | 2 | 6 | no | — |
| 211 | #63230 | — | 4 | 6 | no | — |
| 212 | #63230 | — | 4 | 3 | no | — |
| 213 | #63227 | — | 2 | 3 | no | — |
| 214 | #63227 | — | 2 | 3 | no | — |
| 215 | #63227 | — | 2 | 3 | no | — |
| 216 | #63227 | — | 2 | 3 | no | — |
| 217 | #63227 | — | 2 | 3 | no | — |
| 218 | #63227 | — | 2 | 3 | no | — |
| 219 | #63227 | — | 2 | 6 | no | — |
| 220 | #63227 | — | 2 | 3 | no | — |
| 221 | #63227 | — | 2 | 3 | no | — |
| 222 | #63227 | C2×D4 | 1 | 6 | yes | — |
| 223 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 224 | C4⋊Dic17 | — | 2 | 1 | no | — |
| 225 | C4⋊Dic17 | C2×D4 | 1 | 3 | yes | — |
| 226 | C4⋊Dic17 | C24 | 1 | 1 | yes | characteristic |
| 227 | C4⋊Dic17 | C24 | 1 | 1 | yes | characteristic |
| 228 | #63225 | — | 2 | 1 | no | — |
| 229 | #63225 | — | 2 | 3 | no | — |
| 230 | C4×Dic17 | — | 2 | 1 | no | — |
| 231 | C4×Dic17 | — | 2 | 3 | no | — |
| 232 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 233 | C4×Dic17 | C2×D4 | 1 | 3 | yes | — |
| 234 | C4×Dic17 | C24 | 1 | 1 | yes | characteristic |
| 235 | C2×#3622 | C24 | 1 | 1 | yes | characteristic |
| 236 | C2×#3622 | C24 | 1 | 3 | yes | — |
| 237 | D136 | — | 4 | 3 | no | — |
| 238 | D136 | — | 4 | 6 | no | — |
| 239 | C8×D17 | — | 4 | 6 | no | — |
| 240 | #61958 | — | 17 | 1 | no | maximal, Sylow |
| 241 | C22×D17 | — | 2 | 3 | no | — |
| 242 | C22×D17 | — | 2 | 3 | no | — |
| 243 | C22×D17 | C22×D4 | 1 | 3 | yes | — |
| 244 | Q8×C17 | — | 2 | 1 | no | — |
| 245 | Q8×C17 | — | 2 | 3 | no | — |
| 246 | Q8×C17 | — | 2 | 3 | no | — |
| 247 | Q8×C17 | — | 8 | 3 | no | — |
| 248 | Q8×C17 | #135 | 1 | 4 | yes | complemented |
| 249 | Q8×C17 | H(5,𝔽2) | 1 | 2 | yes | — |
| 250 | C2×C4×C17 | — | 2 | 1 | no | — |
| 251 | C2×C4×C17 | — | 2 | 1 | no | — |
| 252 | C2×C4×C17 | — | 2 | 3 | no | — |
| 253 | C2×C4×C17 | — | 2 | 3 | no | — |
| 254 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 255 | C2×C4×C17 | C22×D4 | 1 | 3 | yes | — |
| 256 | C2×C4×C17 | C25 | 1 | 1 | yes | characteristic |
| 257 | C2×Dic17 | — | 2 | 1 | no | — |
| 258 | C2×Dic17 | — | 2 | 1 | no | — |
| 259 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×Dic17 | C22×D4 | 1 | 3 | yes | — |
| 261 | C2×Dic17 | C22×D4 | 1 | 1 | yes | characteristic |
| 262 | D68 | — | 2 | 6 | no | — |
| 263 | D68 | — | 2 | 3 | no | — |
| 264 | D68 | — | 2 | 3 | no | — |
| 265 | D68 | — | 2 | 3 | no | — |
| 266 | D68 | — | 2 | 3 | no | — |
| 267 | D68 | — | 4 | 6 | no | — |
| 268 | D68 | — | 4 | 6 | no | — |
| 269 | D68 | — | 4 | 6 | no | — |
| 270 | D68 | — | 8 | 3 | no | — |
| 271 | D68 | — | 8 | 3 | no | — |
| 272 | D68 | — | 8 | 3 | no | — |
| 273 | D68 | — | 8 | 6 | no | — |
| 274 | D68 | — | 8 | 6 | no | — |
| 275 | C4×D17 | — | 2 | 6 | no | — |
| 276 | C4×D17 | — | 2 | 3 | no | — |
| 277 | C4×D17 | — | 2 | 3 | no | — |
| 278 | C4×D17 | — | 4 | 3 | no | — |
| 279 | C4×D17 | — | 4 | 6 | no | — |
| 280 | C4×D17 | — | 4 | 6 | no | — |
| 281 | C4×D17 | — | 4 | 6 | no | — |
| 282 | C4×D17 | — | 4 | 6 | no | — |
| 283 | C4×D17 | — | 8 | 6 | no | — |
| 284 | C8×C17 | — | 2 | 3 | no | — |
| 285 | C8×C17 | — | 2 | 1 | no | — |
| 286 | #3622 | — | 2 | 3 | no | — |
| 287 | #3622 | — | 2 | 1 | no | — |
| 288 | #3517 | — | 17 | 1 | no | — |
| 289 | #3483 | — | 17 | 1 | no | — |
| 290 | #3392 | — | 17 | 1 | no | — |
| 291 | #3391 | — | 17 | 1 | no | — |
| 292 | #3363 | D17 | 1 | 1 | yes | characteristic, complemented |
| 293 | #3362 | — | 17 | 1 | no | — |
| 294 | #3305 | — | 17 | 3 | no | — |
| 295 | #3303 | — | 17 | 3 | no | — |
| 296 | #3287 | — | 17 | 3 | no | — |
| 297 | #3284 | — | 17 | 3 | no | — |
| 298 | #3247 | — | 17 | 3 | no | — |
| 299 | #3207 | — | 17 | 3 | no | — |
| 300 | #3102 | — | 17 | 3 | no | — |
| 301 | #3035 | — | 17 | 3 | no | — |
| 302 | #2988 | — | 17 | 1 | no | — |
| 303 | C22×C17 | C23×D4 | 1 | 1 | yes | characteristic |
| 304 | C2×D17 | — | 2 | 3 | no | — |
| 305 | C2×D17 | — | 2 | 3 | no | — |
| 306 | C2×D17 | — | 2 | 3 | no | — |
| 307 | C2×D17 | — | 4 | 3 | no | — |
| 308 | C2×D17 | — | 4 | 3 | no | — |
| 309 | C2×D17 | — | 4 | 3 | no | — |
| 310 | C2×D17 | — | 4 | 3 | no | — |
| 311 | C2×D17 | — | 4 | 3 | no | — |
| 312 | C2×D17 | — | 4 | 3 | no | — |
| 313 | C4×C17 | — | 2 | 3 | no | — |
| 314 | C4×C17 | — | 2 | 2 | no | — |
| 315 | C4×C17 | — | 4 | 3 | no | — |
| 316 | C4×C17 | — | 4 | 1 | no | — |
| 317 | C4×C17 | — | 4 | 3 | no | — |
| 318 | C4×C17 | C2×#135 | 1 | 6 | yes | — |
| 319 | C4×C17 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 320 | C4×C17 | #585 | 1 | 1 | yes | characteristic |
| 321 | Dic17 | — | 2 | 1 | no | — |
| 322 | Dic17 | — | 2 | 3 | no | — |
| 323 | Dic17 | — | 2 | 1 | no | — |
| 324 | Dic17 | — | 4 | 1 | no | — |
| 325 | Dic17 | — | 4 | 1 | no | — |
| 326 | C2×#135 | — | 17 | 6 | no | — |
| 327 | Q82 | C2×D17 | 1 | 1 | yes | characteristic |
| 328 | #557 | C2×D17 | 1 | 1 | yes | characteristic |
| 329 | #555 | — | 17 | 3 | no | — |
| 330 | #555 | — | 34 | 3 | no | — |
| 331 | #553 | — | 34 | 3 | no | — |
| 332 | #550 | — | 17 | 1 | no | — |
| 333 | #550 | — | 17 | 1 | no | — |
| 334 | #550 | — | 17 | 3 | no | — |
| 335 | #550 | — | 17 | 3 | no | — |
| 336 | #550 | — | 34 | 1 | no | — |
| 337 | #550 | — | 34 | 1 | no | — |
| 338 | #547 | — | 17 | 3 | no | — |
| 339 | #540 | — | 34 | 3 | no | — |
| 340 | #532 | — | 17 | 3 | no | — |
| 341 | #532 | — | 17 | 3 | no | — |
| 342 | #532 | — | 34 | 3 | no | — |
| 343 | #529 | — | 17 | 3 | no | — |
| 344 | #520 | — | 34 | 1 | no | — |
| 345 | C4×#41 | — | 17 | 1 | no | — |
| 346 | C4×#41 | — | 17 | 3 | no | — |
| 347 | C4×#41 | — | 34 | 1 | no | — |
| 348 | #493 | — | 17 | 3 | no | — |
| 349 | #492 | — | 17 | 3 | no | — |
| 350 | #487 | C2×D17 | 1 | 3 | yes | — |
| 351 | #486 | — | 17 | 3 | no | — |
| 352 | #485 | — | 17 | 3 | no | — |
| 353 | #482 | — | 17 | 3 | no | — |
| 354 | #479 | — | 17 | 1 | no | — |
| 355 | #478 | — | 17 | 3 | no | — |
| 356 | #477 | C2×D17 | 1 | 3 | yes | — |
| 357 | #476 | — | 17 | 3 | no | — |
| 358 | #466 | — | 17 | 6 | no | — |
| 359 | #465 | — | 17 | 6 | no | — |
| 360 | #464 | — | 17 | 3 | no | — |
| 361 | #463 | — | 17 | 3 | no | — |
| 362 | #463 | — | 17 | 6 | no | — |
| 363 | #462 | C2×D17 | 1 | 3 | yes | — |
| 364 | #461 | — | 17 | 3 | no | — |
| 365 | #460 | — | 17 | 3 | no | — |
| 366 | #460 | — | 17 | 3 | no | — |
| 367 | #459 | — | 17 | 3 | no | — |
| 368 | #459 | — | 17 | 3 | no | — |
| 369 | #452 | — | 17 | 3 | no | — |
| 370 | #449 | — | 17 | 3 | no | — |
| 371 | #449 | — | 17 | 6 | no | — |
| 372 | #449 | — | 17 | 6 | no | — |
| 373 | C8×Q8 | — | 17 | 1 | no | — |
| 374 | C8×Q8 | C2×D17 | 1 | 1 | yes | characteristic |
| 375 | C4×Q16 | C2×D17 | 1 | 3 | yes | — |
| 376 | C4×SD16 | — | 17 | 3 | no | — |
| 377 | C4×SD16 | — | 17 | 3 | no | — |
| 378 | C4×D8 | — | 17 | 3 | no | — |
| 379 | C8×D4 | — | 17 | 3 | no | — |
| 380 | C8×D4 | — | 17 | 3 | no | — |
| 381 | #431 | — | 17 | 3 | no | — |
| 382 | C2×C4⋊C8 | — | 17 | 3 | no | — |
| 383 | #416 | — | 17 | 6 | no | — |
| 384 | C2×C17 | #3488 | 1 | 1 | yes | characteristic |
| 385 | C2×C17 | C22×#135 | 1 | 1 | yes | characteristic |
| 386 | C2×C17 | #3585 | 1 | 1 | yes | characteristic |
| 387 | D17 | — | 4 | 3 | no | — |
| 388 | D17 | — | 8 | 3 | no | — |
| 389 | D17 | — | 8 | 3 | no | — |
| 390 | C2×#41 | — | 17 | 1 | no | — |
| 391 | C2×#41 | — | 17 | 3 | no | — |
| 392 | C2×#41 | — | 17 | 6 | no | — |
| 393 | C2×#41 | — | 34 | 3 | no | — |
| 394 | C2×#41 | — | 34 | 1 | no | — |
| 395 | C2×#41 | — | 34 | 1 | no | — |
| 396 | #135 | — | 68 | 12 | no | — |
| 397 | C2×Q16 | C22×D17 | 1 | 3 | yes | — |
| 398 | C2×SD16 | — | 17 | 3 | no | — |
| 399 | C2×SD16 | — | 17 | 6 | no | — |
| 400 | C2×SD16 | — | 17 | 3 | no | — |
| 401 | C2×D8 | — | 17 | 6 | no | — |
| 402 | C2×D8 | — | 17 | 3 | no | — |
| 403 | C22×C8 | — | 17 | 6 | no | — |
| 404 | C4⋊Q8 | — | 2 | 3 | no | — |
| 405 | C4⋊Q8 | C22×D17 | 1 | 3 | yes | — |
| 406 | C4⋊Q8 | C22×D17 | 1 | 3 | yes | — |
| 407 | #127 | — | 17 | 3 | no | — |
| 408 | #127 | — | 17 | 3 | no | — |
| 409 | #127 | — | 34 | 3 | no | — |
| 410 | #127 | — | 34 | 3 | no | — |
| 411 | #126 | — | 34 | 3 | no | — |
| 412 | #125 | — | 2 | 3 | no | — |
| 413 | #125 | — | 17 | 1 | no | — |
| 414 | #124 | — | 17 | 3 | no | — |
| 415 | #124 | — | 34 | 3 | no | — |
| 416 | #124 | — | 34 | 6 | no | — |
| 417 | #123 | — | 34 | 6 | no | — |
| 418 | #123 | — | 34 | 3 | no | — |
| 419 | C22⋊Q8 | — | 17 | 3 | no | — |
| 420 | #121 | — | 17 | 3 | no | — |
| 421 | #121 | — | 17 | 6 | no | — |
| 422 | #121 | — | 34 | 6 | no | — |
| 423 | #121 | — | 34 | 6 | no | — |
| 424 | #121 | — | 34 | 3 | no | — |
| 425 | #121 | — | 34 | 3 | no | — |
| 426 | #121 | — | 34 | 3 | no | — |
| 427 | #121 | — | 34 | 3 | no | — |
| 428 | #121 | — | 34 | 3 | no | — |
| 429 | #121 | — | 34 | 3 | no | — |
| 430 | #121 | — | 34 | 3 | no | — |
| 431 | C4×Q8 | — | 2 | 1 | no | — |
| 432 | C4×Q8 | — | 2 | 1 | no | — |
| 433 | C4×Q8 | — | 17 | 1 | no | — |
| 434 | C4×Q8 | — | 17 | 1 | no | — |
| 435 | C4×Q8 | C22×D17 | 1 | 3 | yes | — |
| 436 | C4×Q8 | C22×D17 | 1 | 3 | yes | — |
| 437 | C4×Q8 | C22×D17 | 1 | 1 | yes | characteristic |
| 438 | C4×D4 | — | 17 | 3 | no | — |
| 439 | C4×D4 | — | 17 | 3 | no | — |
| 440 | C4×D4 | — | 17 | 3 | no | — |
| 441 | C4×D4 | — | 17 | 3 | no | — |
| 442 | C4×D4 | — | 17 | 3 | no | — |
| 443 | C4×D4 | — | 34 | 3 | no | — |
| 444 | C4×D4 | — | 34 | 3 | no | — |
| 445 | C4×D4 | — | 34 | 3 | no | — |
| 446 | C4×D4 | — | 34 | 3 | no | — |
| 447 | C4×D4 | — | 34 | 3 | no | — |
| 448 | C4×D4 | — | 34 | 3 | no | — |
| 449 | C4×D4 | — | 34 | 3 | no | — |
| 450 | C4×D4 | — | 34 | 3 | no | — |
| 451 | #117 | — | 17 | 3 | no | — |
| 452 | #117 | — | 17 | 3 | no | — |
| 453 | #117 | — | 34 | 3 | no | — |
| 454 | #117 | — | 34 | 3 | no | — |
| 455 | #117 | — | 34 | 3 | no | — |
| 456 | C2×C4⋊C4 | — | 34 | 3 | no | — |
| 457 | C2×C42 | — | 17 | 3 | no | — |
| 458 | C2×C42 | — | 34 | 3 | no | — |
| 459 | #107 | — | 17 | 1 | no | — |
| 460 | #107 | C22×D17 | 1 | 3 | yes | — |
| 461 | #106 | — | 17 | 1 | no | — |
| 462 | #106 | — | 17 | 3 | no | — |
| 463 | C4⋊C8 | — | 17 | 3 | no | — |
| 464 | C4⋊C8 | — | 17 | 1 | no | — |
| 465 | C4⋊C8 | — | 17 | 3 | no | — |
| 466 | C4⋊C8 | C22×D17 | 1 | 3 | yes | — |
| 467 | #103 | — | 17 | 3 | no | — |
| 468 | #103 | — | 17 | 1 | no | — |
| 469 | #103 | C22×D17 | 1 | 6 | yes | — |
| 470 | #103 | C22×D17 | 1 | 1 | yes | characteristic |
| 471 | #103 | C22×D17 | 1 | 3 | yes | — |
| 472 | #102 | — | 17 | 3 | no | — |
| 473 | #102 | — | 17 | 3 | no | — |
| 474 | #102 | — | 17 | 6 | no | — |
| 475 | #102 | — | 17 | 3 | no | — |
| 476 | #102 | — | 17 | 3 | no | — |
| 477 | C22⋊C8 | — | 17 | 3 | no | — |
| 478 | C22⋊C8 | — | 17 | 3 | no | — |
| 479 | C4×C8 | — | 17 | 3 | no | — |
| 480 | C4×C8 | C22×D17 | 1 | 3 | yes | — |
| 481 | C17 | #61958 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 482 | #41 | — | 34 | 4 | no | — |
| 483 | #41 | — | 34 | 6 | no | — |
| 484 | #41 | — | 68 | 3 | no | — |
| 485 | #41 | — | 68 | 6 | no | — |
| 486 | #41 | — | 68 | 6 | no | — |
| 487 | #41 | — | 68 | 4 | no | — |
| 488 | #41 | — | 68 | 4 | no | — |
| 489 | #41 | — | 136 | 6 | no | — |
| 490 | C2×Q8 | — | 2 | 3 | no | — |
| 491 | C2×Q8 | D4×D17 | 1 | 1 | yes | characteristic |
| 492 | C2×Q8 | C23×D17 | 1 | 3 | yes | — |
| 493 | C2×Q8 | C23×D17 | 1 | 1 | yes | characteristic |
| 494 | C2×D4 | — | 17 | 3 | no | — |
| 495 | C2×D4 | — | 17 | 3 | no | — |
| 496 | C2×D4 | — | 17 | 3 | no | — |
| 497 | C2×D4 | — | 34 | 3 | no | — |
| 498 | C2×D4 | — | 34 | 3 | no | — |
| 499 | C2×D4 | — | 34 | 6 | no | — |
| 500 | C2×D4 | — | 34 | 6 | no | — |
| 501 | C2×D4 | — | 34 | 3 | no | — |
| 502 | C2×D4 | — | 34 | 3 | no | — |
| 503 | C2×D4 | — | 34 | 3 | no | — |
| 504 | C2×D4 | — | 34 | 3 | no | — |
| 505 | C22×C4 | — | 17 | 3 | no | — |
| 506 | C22×C4 | — | 17 | 3 | no | — |
| 507 | C22×C4 | — | 17 | 3 | no | — |
| 508 | C22×C4 | — | 34 | 3 | no | — |
| 509 | C22×C4 | — | 34 | 3 | no | — |
| 510 | C22×C4 | — | 34 | 6 | no | — |
| 511 | C22×C4 | — | 34 | 3 | no | — |
| 512 | C22×C4 | — | 34 | 3 | no | — |
| 513 | Q16 | — | 2 | 6 | no | — |
| 514 | SD16 | — | 34 | 6 | no | — |
| 515 | SD16 | — | 68 | 6 | no | — |
| 516 | SD16 | — | 68 | 3 | no | — |
| 517 | D8 | — | 68 | 6 | no | — |
| 518 | D8 | — | 68 | 3 | no | — |
| 519 | C2×C8 | — | 17 | 1 | no | — |
| 520 | C2×C8 | — | 17 | 3 | no | — |
| 521 | C2×C8 | — | 68 | 6 | no | — |
| 522 | C2×C8 | C23×D17 | 1 | 1 | yes | characteristic |
| 523 | C2×C8 | C23×D17 | 1 | 3 | yes | — |
| 524 | C4⋊C4 | — | 2 | 3 | no | — |
| 525 | C4⋊C4 | — | 2 | 3 | no | — |
| 526 | C4⋊C4 | — | 2 | 3 | no | — |
| 527 | C4⋊C4 | — | 2 | 3 | no | — |
| 528 | C4⋊C4 | — | 2 | 3 | no | — |
| 529 | C4⋊C4 | — | 17 | 3 | no | — |
| 530 | C4⋊C4 | — | 17 | 1 | no | — |
| 531 | C4⋊C4 | — | 17 | 1 | no | — |
| 532 | C4⋊C4 | — | 34 | 3 | no | — |
| 533 | C4⋊C4 | — | 34 | 1 | no | — |
| 534 | C4⋊C4 | — | 34 | 1 | no | — |
| 535 | C4⋊C4 | — | 34 | 1 | no | — |
| 536 | C4⋊C4 | D4×D17 | 1 | 3 | yes | — |
| 537 | C4⋊C4 | C23×D17 | 1 | 3 | yes | — |
| 538 | C4⋊C4 | C23×D17 | 1 | 1 | yes | characteristic |
| 539 | C22⋊C4 | — | 17 | 6 | no | — |
| 540 | C22⋊C4 | — | 34 | 3 | no | — |
| 541 | C22⋊C4 | — | 34 | 3 | no | — |
| 542 | C22⋊C4 | — | 34 | 6 | no | — |
| 543 | C22⋊C4 | — | 34 | 3 | no | — |
| 544 | C22⋊C4 | — | 34 | 3 | no | — |
| 545 | C22⋊C4 | — | 34 | 3 | no | — |
| 546 | C22⋊C4 | — | 34 | 3 | no | — |
| 547 | C22⋊C4 | — | 34 | 3 | no | — |
| 548 | C22⋊C4 | — | 34 | 3 | no | — |
| 549 | C42 | — | 2 | 3 | no | — |
| 550 | C42 | — | 2 | 3 | no | — |
| 551 | C42 | — | 17 | 3 | no | — |
| 552 | C42 | — | 17 | 3 | no | — |
| 553 | C42 | — | 17 | 1 | no | — |
| 554 | C42 | — | 34 | 1 | no | — |
| 555 | C42 | — | 34 | 3 | no | — |
| 556 | C42 | C23×D17 | 1 | 3 | yes | — |
| 557 | C23 | — | 17 | 3 | no | — |
| 558 | C23 | — | 34 | 3 | no | — |
| 559 | C23 | — | 34 | 3 | no | — |
| 560 | Q8 | — | 2 | 1 | no | — |
| 561 | Q8 | — | 2 | 3 | no | — |
| 562 | Q8 | — | 2 | 3 | no | — |
| 563 | Q8 | — | 8 | 3 | no | — |
| 564 | Q8 | #10587605 | 1 | 4 | yes | complemented |
| 565 | Q8 | #10587696 | 1 | 2 | yes | — |
| 566 | D4 | — | 34 | 6 | no | — |
| 567 | D4 | — | 34 | 3 | no | — |
| 568 | D4 | — | 34 | 3 | no | — |
| 569 | D4 | — | 34 | 3 | no | — |
| 570 | D4 | — | 34 | 3 | no | — |
| 571 | D4 | — | 68 | 6 | no | — |
| 572 | D4 | — | 68 | 6 | no | — |
| 573 | D4 | — | 68 | 6 | no | — |
| 574 | D4 | — | 136 | 3 | no | — |
| 575 | D4 | — | 136 | 3 | no | — |
| 576 | D4 | — | 136 | 6 | no | — |
| 577 | D4 | — | 136 | 6 | no | — |
| 578 | D4 | — | 136 | 3 | no | — |
| 579 | C2×C4 | — | 2 | 1 | no | — |
| 580 | C2×C4 | — | 2 | 1 | no | — |
| 581 | C2×C4 | — | 2 | 3 | no | — |
| 582 | C2×C4 | — | 2 | 3 | no | — |
| 583 | C2×C4 | — | 17 | 1 | no | — |
| 584 | C2×C4 | — | 17 | 1 | no | — |
| 585 | C2×C4 | — | 17 | 3 | no | — |
| 586 | C2×C4 | — | 34 | 6 | no | — |
| 587 | C2×C4 | — | 34 | 3 | no | — |
| 588 | C2×C4 | — | 34 | 3 | no | — |
| 589 | C2×C4 | — | 34 | 1 | no | — |
| 590 | C2×C4 | — | 34 | 1 | no | — |
| 591 | C2×C4 | — | 68 | 3 | no | — |
| 592 | C2×C4 | — | 68 | 6 | no | — |
| 593 | C2×C4 | — | 68 | 6 | no | — |
| 594 | C2×C4 | — | 68 | 6 | no | — |
| 595 | C2×C4 | — | 68 | 6 | no | — |
| 596 | C2×C4 | — | 136 | 6 | no | — |
| 597 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 598 | C2×C4 | C2×D4×D17 | 1 | 3 | yes | — |
| 599 | C2×C4 | C24×D17 | 1 | 1 | yes | characteristic |
| 600 | C8 | — | 2 | 3 | no | — |
| 601 | C8 | — | 2 | 1 | no | — |
| 602 | C8 | — | 34 | 3 | no | — |
| 603 | C8 | — | 34 | 1 | no | — |
| 604 | C22 | — | 34 | 3 | no | — |
| 605 | C22 | — | 34 | 3 | no | — |
| 606 | C22 | — | 34 | 3 | no | — |
| 607 | C22 | — | 68 | 3 | no | — |
| 608 | C22 | — | 68 | 3 | no | — |
| 609 | C22 | — | 68 | 3 | no | — |
| 610 | C22 | — | 68 | 3 | no | — |
| 611 | C22 | — | 68 | 3 | no | — |
| 612 | C22 | — | 68 | 3 | no | — |
| 613 | C22 | C22×D4×D17 | 1 | 1 | yes | characteristic |
| 614 | C4 | — | 2 | 2 | no | — |
| 615 | C4 | — | 2 | 3 | no | — |
| 616 | C4 | — | 4 | 3 | no | — |
| 617 | C4 | — | 4 | 3 | no | — |
| 618 | C4 | — | 4 | 1 | no | — |
| 619 | C4 | — | 34 | 3 | no | — |
| 620 | C4 | — | 34 | 1 | no | — |
| 621 | C4 | — | 34 | 1 | no | — |
| 622 | C4 | — | 68 | 1 | no | — |
| 623 | C4 | — | 68 | 1 | no | — |
| 624 | C4 | C2×#10587605 | 1 | 6 | yes | — |
| 625 | C4 | C2×#10587696 | 1 | 1 | yes | characteristic |
| 626 | C4 | #11763646 | 1 | 1 | yes | characteristic |
| 627 | C2 | — | 68 | 3 | no | — |
| 628 | C2 | — | 136 | 3 | no | — |
| 629 | C2 | — | 136 | 3 | no | — |
| 630 | C2 | #14542450 | 1 | 1 | yes | characteristic |
| 631 | C2 | C22×#10587605 | 1 | 1 | yes | characteristic |
| 632 | C2 | #14543562 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14542791 | C2 | semidirect |
| 2. #14542411 | C2 | semidirect |
| 3. #14541761 | C2 | semidirect |
| 4. #14541759 | C2 | semidirect |
| 5. #14541455 | C2 | semidirect |
| 6. #14540731 | C2 | semidirect |
| 7. #14540711 | C2 | semidirect |
| 8. #14540543 | C2 | semidirect |
| 9. #14540509 | C2 | semidirect |
| 10. #14540113 | C2 | semidirect |
| 11. #14539720 | C2 | semidirect |
| 12. #14538808 | C2 | semidirect |
| 13. #14538242 | C2 | semidirect |
| 14. #14537894 | C2 | semidirect |
| 15. C17×#3363 | C2 | semidirect |
| 248. Q8×C17 | #135 | semidirect |
| 292. #3363 | D17 | semidirect |
| 481. C17 | #61958 | semidirect |
| 564. Q8 | #10587605 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14542791 | 2 |
| #14542411 | 2 |
| #14541761 | 2 |
| #14541759 | 2 |
| #14541455 | 2 |
| #14540731 | 2 |
| #14540711 | 2 |
| #14540543 | 2 |
| #14540509 | 2 |
| #14540113 | 2 |
| #14539720 | 2 |
| #14538808 | 2 |
| #14538242 | 2 |
| #14537894 | 2 |
| C17×#3363 | 2 |
| #61958 | 17 |