← #17026199
Subgroups — #17026199
Order 4352.
622 conjugacy classes of subgroups.
The subgroup lattice has 390 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #14541788 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14541709 | C2 | 1 | 2 | yes | maximal |
| 3 | D4×Dic68 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #14528400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14528301 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #14528155 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #14528032 | C2 | 1 | 2 | yes | maximal |
| 8 | #14528027 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #14527680 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C8×#63229 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C17×#1669 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C22×Dic68 | — | 2 | 1 | no | — |
| 13 | #11763534 | C22 | 1 | 2 | yes | — |
| 14 | D4×Dic34 | C22 | 1 | 2 | yes | — |
| 15 | #11763217 | — | 2 | 2 | no | — |
| 16 | #11763212 | C22 | 1 | 2 | yes | — |
| 17 | #11763212 | C22 | 1 | 2 | yes | — |
| 18 | #11763189 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11763187 | — | 2 | 1 | no | — |
| 20 | #11763111 | — | 2 | 2 | no | — |
| 21 | #11763103 | — | 2 | 2 | no | — |
| 22 | #11763095 | C22 | 1 | 2 | yes | — |
| 23 | #11763050 | — | 2 | 1 | no | — |
| 24 | #11763020 | C22 | 1 | 2 | yes | — |
| 25 | #11763017 | — | 2 | 2 | no | — |
| 26 | #11763016 | C22 | 1 | 2 | yes | — |
| 27 | #11762967 | — | 2 | 2 | no | — |
| 28 | #11762936 | C22 | 1 | 2 | yes | — |
| 29 | C8×Dic34 | C22 | 1 | 1 | yes | characteristic |
| 30 | #11762906 | — | 2 | 2 | no | — |
| 31 | C4×Dic68 | C22 | 1 | 1 | yes | characteristic |
| 32 | Q16×Dic17 | — | 2 | 1 | no | — |
| 33 | C4×#63229 | C22 | 1 | 1 | yes | characteristic |
| 34 | #11762559 | C22 | 1 | 1 | yes | characteristic |
| 35 | #11762554 | C22 | 1 | 2 | yes | — |
| 36 | #11762539 | C22 | 1 | 1 | yes | characteristic |
| 37 | #11762539 | C22 | 1 | 2 | yes | — |
| 38 | D4⋊#3622 | C22 | 1 | 1 | yes | characteristic |
| 39 | C8×#3622 | C22 | 1 | 1 | yes | characteristic |
| 40 | C17×#494 | C22 | 1 | 1 | yes | characteristic |
| 41 | C17×#474 | C22 | 1 | 2 | yes | — |
| 42 | C8×D4×C17 | C22 | 1 | 1 | yes | characteristic |
| 43 | C17×#335 | C22 | 1 | 1 | yes | characteristic |
| 44 | C17×#332 | C22 | 1 | 2 | yes | — |
| 45 | C22×Dic34 | — | 2 | 2 | no | — |
| 46 | C2×Q16×C17 | — | 2 | 1 | no | — |
| 47 | C2×Q16×C17 | — | 2 | 1 | no | — |
| 48 | C22×C8×C17 | — | 2 | 1 | no | — |
| 49 | C17×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 50 | C4×D4×C17 | C23 | 1 | 1 | yes | characteristic |
| 51 | Q8×Dic17 | — | 2 | 2 | no | — |
| 52 | #10587630 | — | 2 | 2 | no | — |
| 53 | C2×#63231 | — | 2 | 2 | no | — |
| 54 | D4×Dic17 | — | 2 | 2 | no | — |
| 55 | C2×#63229 | D4 | 1 | 1 | yes | characteristic |
| 56 | #10587610 | — | 2 | 2 | no | — |
| 57 | C2×Dic68 | — | 2 | 2 | no | — |
| 58 | C2×Dic68 | — | 2 | 1 | no | — |
| 59 | C2×Dic68 | — | 2 | 1 | no | — |
| 60 | C2×Dic68 | — | 4 | 4 | no | — |
| 61 | C2×Dic68 | D4 | 1 | 1 | yes | characteristic |
| 62 | #10587576 | — | 2 | 2 | no | — |
| 63 | #10587575 | — | 4 | 2 | no | — |
| 64 | #10587574 | — | 2 | 2 | no | — |
| 65 | #10587573 | — | 2 | 2 | no | — |
| 66 | #10587564 | — | 4 | 2 | no | — |
| 67 | #10587555 | C23 | 1 | 2 | yes | — |
| 68 | C4×Dic34 | C23 | 1 | 2 | yes | — |
| 69 | C4×Dic34 | C23 | 1 | 1 | yes | characteristic |
| 70 | C17×#107 | — | 2 | 2 | no | — |
| 71 | C17×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 72 | C17×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 73 | C17×#102 | — | 2 | 2 | no | — |
| 74 | C17×C22⋊C8 | — | 2 | 1 | no | — |
| 75 | C4×C8×C17 | C23 | 1 | 1 | yes | characteristic |
| 76 | #10587506 | — | 2 | 2 | no | — |
| 77 | #10587503 | D4 | 1 | 1 | yes | characteristic |
| 78 | #10587489 | D4 | 1 | 1 | yes | characteristic |
| 79 | #10587488 | — | 2 | 2 | no | — |
| 80 | #10587487 | — | 2 | 2 | no | — |
| 81 | #10587487 | — | 2 | 2 | no | — |
| 82 | #10587487 | D4 | 1 | 2 | yes | — |
| 83 | #10587486 | — | 2 | 2 | no | — |
| 84 | #10587485 | — | 2 | 2 | no | — |
| 85 | #10587485 | — | 2 | 1 | no | — |
| 86 | C8×Dic17 | — | 2 | 1 | no | — |
| 87 | #10587481 | D4 | 1 | 1 | yes | characteristic |
| 88 | #10587479 | D4 | 1 | 1 | yes | characteristic |
| 89 | #10587478 | — | 2 | 2 | no | — |
| 90 | #10587478 | — | 2 | 2 | no | — |
| 91 | #10587478 | — | 4 | 2 | no | — |
| 92 | C4⋊#3622 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4×#3622 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4×#3622 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×Q8×C17 | — | 2 | 2 | no | — |
| 96 | C2×D4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C22×C4×C17 | — | 2 | 1 | no | — |
| 98 | C22×Dic17 | — | 4 | 2 | no | — |
| 99 | C2×Dic34 | — | 2 | 2 | no | — |
| 100 | C2×Dic34 | — | 4 | 4 | no | — |
| 101 | C2×Dic34 | — | 4 | 2 | no | — |
| 102 | C2×Dic34 | — | 8 | 2 | no | — |
| 103 | C2×Dic34 | C2×D4 | 1 | 2 | yes | — |
| 104 | C2×Dic34 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | Q16×C17 | — | 4 | 2 | no | — |
| 106 | Q16×C17 | — | 8 | 1 | no | — |
| 107 | C2×C8×C17 | — | 2 | 1 | no | — |
| 108 | C2×C8×C17 | — | 2 | 2 | no | — |
| 109 | C2×C8×C17 | — | 4 | 2 | no | — |
| 110 | C2×C8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C2×C8×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 113 | C4⋊C4×C17 | — | 2 | 2 | no | — |
| 114 | C4⋊C4×C17 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | C22⋊C4×C17 | — | 2 | 1 | no | — |
| 116 | C42×C17 | C24 | 1 | 1 | yes | characteristic |
| 117 | C22⋊Dic17 | — | 4 | 2 | no | — |
| 118 | #63231 | — | 8 | 2 | no | — |
| 119 | #63229 | Q16 | 1 | 4 | yes | complemented |
| 120 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 121 | C4⋊Dic17 | — | 2 | 2 | no | — |
| 122 | C4⋊Dic17 | — | 4 | 2 | no | — |
| 123 | C4⋊Dic17 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C4⋊Dic17 | C2×D4 | 1 | 2 | yes | — |
| 125 | #63225 | — | 2 | 2 | no | — |
| 126 | #63225 | — | 2 | 1 | no | — |
| 127 | #63225 | — | 4 | 2 | no | — |
| 128 | #63225 | — | 4 | 2 | no | — |
| 129 | #63225 | — | 4 | 2 | no | — |
| 130 | C4×Dic17 | — | 2 | 1 | no | — |
| 131 | C4×Dic17 | — | 2 | 2 | no | — |
| 132 | C4×Dic17 | — | 4 | 2 | no | — |
| 133 | C2×#3622 | — | 2 | 1 | no | — |
| 134 | C2×#3622 | — | 2 | 1 | no | — |
| 135 | C2×#3622 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×#3622 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | Dic68 | — | 2 | 2 | no | — |
| 138 | Dic68 | — | 4 | 4 | no | — |
| 139 | Dic68 | — | 4 | 2 | no | — |
| 140 | Dic68 | — | 8 | 1 | no | — |
| 141 | #19928 | — | 17 | 1 | no | maximal, Sylow |
| 142 | C23×C17 | — | 2 | 1 | no | — |
| 143 | Q8×C17 | — | 4 | 2 | no | — |
| 144 | Q8×C17 | — | 4 | 2 | no | — |
| 145 | D4×C17 | — | 2 | 1 | no | — |
| 146 | D4×C17 | C2×Q16 | 1 | 2 | yes | — |
| 147 | C2×C4×C17 | — | 2 | 1 | no | — |
| 148 | C2×C4×C17 | — | 4 | 1 | no | — |
| 149 | C2×C4×C17 | — | 4 | 1 | no | — |
| 150 | C2×C4×C17 | — | 4 | 2 | no | — |
| 151 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C17 | C22×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×C4×C17 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 154 | C2×Dic17 | — | 2 | 1 | no | — |
| 155 | C2×Dic17 | — | 2 | 2 | no | — |
| 156 | C2×Dic17 | — | 2 | 2 | no | — |
| 157 | C2×Dic17 | — | 2 | 1 | no | — |
| 158 | C2×Dic17 | — | 4 | 2 | no | — |
| 159 | C2×Dic17 | — | 8 | 4 | no | — |
| 160 | Dic34 | — | 2 | 1 | no | — |
| 161 | Dic34 | — | 2 | 2 | no | — |
| 162 | Dic34 | — | 2 | 2 | no | — |
| 163 | Dic34 | — | 4 | 2 | no | — |
| 164 | Dic34 | — | 4 | 2 | no | — |
| 165 | Dic34 | — | 8 | 4 | no | — |
| 166 | Dic34 | C2×Q16 | 1 | 2 | yes | complemented |
| 167 | C8×C17 | — | 2 | 1 | no | — |
| 168 | C8×C17 | — | 4 | 1 | no | — |
| 169 | C8×C17 | — | 4 | 2 | no | — |
| 170 | C8×C17 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 171 | #3622 | — | 2 | 2 | no | — |
| 172 | #3622 | — | 2 | 1 | no | — |
| 173 | #3622 | — | 4 | 1 | no | — |
| 174 | #3622 | C2×Q16 | 1 | 2 | yes | complemented |
| 175 | #3395 | — | 17 | 1 | no | — |
| 176 | #3386 | — | 17 | 2 | no | — |
| 177 | D4×Q16 | — | 17 | 1 | no | — |
| 178 | #1713 | — | 17 | 1 | no | — |
| 179 | #1694 | — | 17 | 2 | no | — |
| 180 | #1670 | — | 17 | 1 | no | — |
| 181 | #1669 | D17 | 1 | 1 | yes | characteristic |
| 182 | #1649 | — | 17 | 2 | no | — |
| 183 | #1648 | — | 17 | 2 | no | — |
| 184 | #1591 | — | 17 | 1 | no | — |
| 185 | C8×SD16 | — | 17 | 1 | no | — |
| 186 | C22×C17 | — | 2 | 2 | no | — |
| 187 | C22×C17 | — | 4 | 1 | no | — |
| 188 | C22×C17 | — | 4 | 1 | no | — |
| 189 | C22×C17 | D42 | 1 | 1 | yes | characteristic |
| 190 | C4×C17 | — | 2 | 1 | no | — |
| 191 | C4×C17 | — | 4 | 1 | no | — |
| 192 | C4×C17 | — | 8 | 2 | no | — |
| 193 | C4×C17 | C22×Q16 | 1 | 1 | yes | characteristic |
| 194 | C4×C17 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 195 | C4×C17 | #576 | 1 | 1 | yes | characteristic |
| 196 | C4×C17 | #578 | 1 | 1 | yes | characteristic |
| 197 | Dic17 | — | 2 | 2 | no | — |
| 198 | Dic17 | — | 4 | 2 | no | — |
| 199 | Dic17 | — | 4 | 2 | no | — |
| 200 | Dic17 | — | 4 | 1 | no | — |
| 201 | Dic17 | — | 8 | 2 | no | — |
| 202 | C22×Q16 | — | 34 | 1 | no | — |
| 203 | #557 | — | 17 | 2 | no | — |
| 204 | D4×Q8 | — | 17 | 2 | no | — |
| 205 | #501 | — | 34 | 2 | no | — |
| 206 | #500 | — | 17 | 2 | no | — |
| 207 | #500 | — | 17 | 2 | no | — |
| 208 | #494 | — | 17 | 1 | no | — |
| 209 | #494 | — | 34 | 1 | no | — |
| 210 | #494 | C2×D17 | 1 | 1 | yes | characteristic |
| 211 | #478 | — | 34 | 2 | no | — |
| 212 | #477 | — | 34 | 2 | no | — |
| 213 | #475 | — | 17 | 2 | no | — |
| 214 | #474 | C2×D17 | 1 | 2 | yes | — |
| 215 | #467 | — | 34 | 1 | no | — |
| 216 | #462 | — | 17 | 2 | no | — |
| 217 | #462 | — | 17 | 2 | no | — |
| 218 | #462 | — | 34 | 2 | no | — |
| 219 | #451 | — | 34 | 2 | no | — |
| 220 | #446 | — | 17 | 2 | no | — |
| 221 | C8×Q8 | — | 17 | 1 | no | — |
| 222 | #440 | — | 34 | 2 | no | — |
| 223 | C4×Q16 | — | 17 | 1 | no | — |
| 224 | C4×Q16 | — | 34 | 1 | no | — |
| 225 | C4×SD16 | — | 17 | 1 | no | — |
| 226 | C8×D4 | C2×D17 | 1 | 1 | yes | characteristic |
| 227 | #335 | C2×D17 | 1 | 1 | yes | characteristic |
| 228 | #334 | — | 17 | 1 | no | — |
| 229 | #332 | — | 17 | 2 | no | — |
| 230 | #332 | C2×D17 | 1 | 2 | yes | — |
| 231 | Q8⋊C8 | — | 17 | 1 | no | — |
| 232 | Q8⋊C8 | — | 17 | 2 | no | — |
| 233 | D4⋊C8 | — | 17 | 1 | no | — |
| 234 | C82 | — | 17 | 1 | no | — |
| 235 | C2×C17 | — | 4 | 2 | no | — |
| 236 | C2×C17 | #3274 | 1 | 1 | yes | characteristic |
| 237 | C2×C17 | D4×Q16 | 1 | 1 | yes | characteristic |
| 238 | C2×C17 | #3293 | 1 | 1 | yes | characteristic |
| 239 | C22×Q8 | — | 34 | 2 | no | — |
| 240 | C2×Q16 | — | 2 | 1 | no | — |
| 241 | C2×Q16 | — | 2 | 1 | no | — |
| 242 | C2×Q16 | — | 17 | 1 | no | — |
| 243 | C2×Q16 | — | 34 | 2 | no | — |
| 244 | C2×Q16 | — | 34 | 2 | no | — |
| 245 | C2×Q16 | — | 34 | 1 | no | — |
| 246 | C2×Q16 | — | 34 | 1 | no | — |
| 247 | C2×Q16 | — | 68 | 4 | no | — |
| 248 | C2×SD16 | — | 17 | 1 | no | — |
| 249 | C22×C8 | — | 2 | 1 | no | — |
| 250 | C4⋊Q8 | — | 17 | 2 | no | — |
| 251 | C4⋊Q8 | — | 34 | 2 | no | — |
| 252 | C4⋊Q8 | — | 34 | 2 | no | — |
| 253 | C4⋊Q8 | C22×D17 | 1 | 2 | yes | — |
| 254 | #125 | — | 34 | 2 | no | — |
| 255 | #125 | — | 68 | 2 | no | — |
| 256 | C22⋊Q8 | — | 34 | 2 | no | — |
| 257 | C22⋊Q8 | — | 68 | 2 | no | — |
| 258 | C4×Q8 | — | 17 | 2 | no | — |
| 259 | C4×Q8 | — | 17 | 1 | no | — |
| 260 | C4×Q8 | — | 34 | 2 | no | — |
| 261 | C4×Q8 | — | 34 | 2 | no | — |
| 262 | C4×D4 | — | 34 | 2 | no | — |
| 263 | C4×D4 | C22×D17 | 1 | 1 | yes | characteristic |
| 264 | #107 | — | 2 | 2 | no | — |
| 265 | #107 | — | 17 | 1 | no | — |
| 266 | #107 | — | 34 | 2 | no | — |
| 267 | #107 | — | 34 | 2 | no | — |
| 268 | #107 | — | 68 | 2 | no | — |
| 269 | #106 | — | 17 | 1 | no | — |
| 270 | #106 | — | 34 | 2 | no | — |
| 271 | C4⋊C8 | — | 17 | 1 | no | — |
| 272 | C4⋊C8 | — | 34 | 2 | no | — |
| 273 | C4⋊C8 | — | 34 | 1 | no | — |
| 274 | C4⋊C8 | C22×D17 | 1 | 2 | yes | — |
| 275 | C4⋊C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 276 | #103 | — | 17 | 2 | no | — |
| 277 | #103 | — | 17 | 1 | no | — |
| 278 | #103 | — | 34 | 2 | no | — |
| 279 | #103 | — | 34 | 2 | no | — |
| 280 | #103 | — | 34 | 2 | no | — |
| 281 | #102 | — | 2 | 2 | no | — |
| 282 | #102 | — | 17 | 1 | no | — |
| 283 | C22⋊C8 | — | 2 | 1 | no | — |
| 284 | #97 | — | 34 | 2 | no | — |
| 285 | C4×C8 | — | 17 | 1 | no | — |
| 286 | C4×C8 | — | 17 | 1 | no | — |
| 287 | C4×C8 | — | 34 | 1 | no | — |
| 288 | C4×C8 | C22×D17 | 1 | 1 | yes | characteristic |
| 289 | C17 | #19928 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 290 | C2×Q8 | — | 2 | 2 | no | — |
| 291 | C2×Q8 | — | 17 | 1 | no | — |
| 292 | C2×Q8 | — | 17 | 2 | no | — |
| 293 | C2×Q8 | — | 34 | 2 | no | — |
| 294 | C2×Q8 | — | 68 | 2 | no | — |
| 295 | C2×Q8 | — | 68 | 4 | no | — |
| 296 | C2×Q8 | — | 136 | 2 | no | — |
| 297 | C2×D4 | D4×D17 | 1 | 1 | yes | characteristic |
| 298 | C22×C4 | — | 2 | 1 | no | — |
| 299 | C22×C4 | — | 68 | 2 | no | — |
| 300 | Q16 | — | 4 | 2 | no | — |
| 301 | Q16 | — | 8 | 1 | no | — |
| 302 | Q16 | — | 34 | 2 | no | — |
| 303 | Q16 | — | 68 | 4 | no | — |
| 304 | Q16 | — | 68 | 2 | no | — |
| 305 | Q16 | — | 136 | 1 | no | — |
| 306 | Q16 | — | 136 | 2 | no | — |
| 307 | SD16 | — | 17 | 4 | no | — |
| 308 | C2×C8 | — | 2 | 2 | no | — |
| 309 | C2×C8 | — | 2 | 1 | no | — |
| 310 | C2×C8 | — | 4 | 2 | no | — |
| 311 | C2×C8 | — | 17 | 1 | no | — |
| 312 | C2×C8 | — | 17 | 1 | no | — |
| 313 | C2×C8 | — | 34 | 1 | no | — |
| 314 | C2×C8 | — | 34 | 1 | no | — |
| 315 | C2×C8 | D4×D17 | 1 | 1 | yes | characteristic |
| 316 | C2×C8 | D4×D17 | 1 | 1 | yes | characteristic |
| 317 | C4⋊C4 | — | 2 | 2 | no | — |
| 318 | C4⋊C4 | — | 2 | 2 | no | — |
| 319 | C4⋊C4 | — | 17 | 1 | no | — |
| 320 | C4⋊C4 | — | 17 | 2 | no | — |
| 321 | C4⋊C4 | — | 34 | 2 | no | — |
| 322 | C4⋊C4 | — | 34 | 1 | no | — |
| 323 | C4⋊C4 | — | 34 | 2 | no | — |
| 324 | C4⋊C4 | — | 34 | 2 | no | — |
| 325 | C4⋊C4 | — | 68 | 2 | no | — |
| 326 | C4⋊C4 | — | 68 | 2 | no | — |
| 327 | C4⋊C4 | — | 68 | 2 | no | — |
| 328 | C4⋊C4 | — | 68 | 2 | no | — |
| 329 | C4⋊C4 | D4×D17 | 1 | 1 | yes | characteristic |
| 330 | C22⋊C4 | — | 2 | 1 | no | — |
| 331 | C22⋊C4 | — | 68 | 2 | no | — |
| 332 | C42 | — | 34 | 1 | no | — |
| 333 | C42 | — | 34 | 2 | no | — |
| 334 | C42 | — | 68 | 2 | no | — |
| 335 | C42 | C23×D17 | 1 | 1 | yes | characteristic |
| 336 | C23 | — | 2 | 1 | no | — |
| 337 | Q8 | — | 4 | 2 | no | — |
| 338 | Q8 | — | 4 | 2 | no | — |
| 339 | Q8 | — | 17 | 2 | no | — |
| 340 | Q8 | — | 34 | 1 | no | — |
| 341 | Q8 | — | 34 | 2 | no | — |
| 342 | Q8 | — | 34 | 2 | no | — |
| 343 | Q8 | — | 68 | 2 | no | — |
| 344 | Q8 | — | 68 | 2 | no | — |
| 345 | Q8 | — | 136 | 4 | no | — |
| 346 | D4 | — | 2 | 1 | no | — |
| 347 | D4 | Q16×D17 | 1 | 2 | yes | — |
| 348 | C2×C4 | — | 2 | 1 | no | — |
| 349 | C2×C4 | — | 4 | 1 | no | — |
| 350 | C2×C4 | — | 4 | 1 | no | — |
| 351 | C2×C4 | — | 4 | 2 | no | — |
| 352 | C2×C4 | — | 34 | 1 | no | — |
| 353 | C2×C4 | — | 34 | 2 | no | — |
| 354 | C2×C4 | — | 34 | 1 | no | — |
| 355 | C2×C4 | — | 34 | 2 | no | — |
| 356 | C2×C4 | — | 68 | 2 | no | — |
| 357 | C2×C4 | — | 136 | 4 | no | — |
| 358 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C2×D4×D17 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | #10587696 | 1 | 1 | yes | characteristic |
| 361 | C8 | — | 2 | 1 | no | — |
| 362 | C8 | — | 4 | 1 | no | — |
| 363 | C8 | — | 4 | 2 | no | — |
| 364 | C8 | — | 17 | 2 | no | — |
| 365 | C8 | — | 34 | 2 | no | — |
| 366 | C8 | — | 34 | 1 | no | — |
| 367 | C8 | — | 68 | 1 | no | — |
| 368 | C8 | #10587597 | 1 | 2 | yes | — |
| 369 | C22 | — | 2 | 2 | no | — |
| 370 | C22 | — | 4 | 1 | no | — |
| 371 | C22 | — | 4 | 1 | no | — |
| 372 | C22 | #11763443 | 1 | 1 | yes | characteristic |
| 373 | C4 | — | 2 | 1 | no | — |
| 374 | C4 | — | 4 | 1 | no | — |
| 375 | C4 | — | 8 | 2 | no | — |
| 376 | C4 | — | 34 | 2 | no | — |
| 377 | C4 | — | 68 | 2 | no | — |
| 378 | C4 | — | 68 | 1 | no | — |
| 379 | C4 | — | 68 | 2 | no | — |
| 380 | C4 | — | 136 | 2 | no | — |
| 381 | C4 | C2×Q16×D17 | 1 | 1 | yes | characteristic |
| 382 | C4 | C2×#10587597 | 1 | 1 | yes | characteristic |
| 383 | C4 | #11763613 | 1 | 1 | yes | characteristic |
| 384 | C4 | #11763623 | 1 | 1 | yes | characteristic |
| 385 | C2 | — | 4 | 2 | no | — |
| 386 | C2 | #14540407 | 1 | 1 | yes | characteristic |
| 387 | C2 | #14540533 | 1 | 1 | yes | characteristic |
| 388 | C2 | #14540587 | 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