← #10765321
Subgroups — #10765321
Order 768.
626 conjugacy classes of subgroups.
The subgroup lattice has 386 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #83315 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #83280 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #79263 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#1484 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #70747 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69857 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #69848 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #68159 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #68155 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #68150 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #68149 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #17923 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×#431 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 17 | #5234 | — | 2 | 2 | no | — |
| 18 | #5094 | C4 | 1 | 2 | yes | — |
| 19 | #5075 | C4 | 1 | 2 | yes | — |
| 20 | #5040 | C4 | 1 | 2 | yes | — |
| 21 | #5034 | C4 | 1 | 2 | yes | — |
| 22 | C4×#214 | C22 | 1 | 2 | yes | — |
| 23 | C4×#214 | C22 | 1 | 2 | yes | — |
| 24 | #5012 | C22 | 1 | 2 | yes | — |
| 25 | #5011 | — | 2 | 2 | no | — |
| 26 | D4×C3⋊C8 | C22 | 1 | 2 | yes | — |
| 27 | #4926 | C22 | 1 | 1 | yes | characteristic |
| 28 | #4925 | C22 | 1 | 1 | yes | characteristic |
| 29 | #4925 | C22 | 1 | 1 | yes | characteristic |
| 30 | #4830 | C22 | 1 | 2 | yes | — |
| 31 | #4830 | C22 | 1 | 2 | yes | — |
| 32 | #4718 | — | 2 | 2 | no | — |
| 33 | C8×Dic6 | — | 2 | 2 | no | — |
| 34 | C3×D4⋊C8 | C22 | 1 | 2 | yes | — |
| 35 | C3×D4⋊C8 | C22 | 1 | 2 | yes | — |
| 36 | #4480 | C22 | 1 | 2 | yes | — |
| 37 | #4479 | C22 | 1 | 2 | yes | — |
| 38 | #4456 | C22 | 1 | 2 | yes | — |
| 39 | #4456 | C22 | 1 | 2 | yes | — |
| 40 | #4455 | C22 | 1 | 1 | yes | characteristic |
| 41 | #4454 | C22 | 1 | 1 | yes | characteristic |
| 42 | #4454 | C22 | 1 | 1 | yes | characteristic |
| 43 | C8×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 44 | #3103 | — | 3 | 1 | no | — |
| 45 | #2982 | — | 3 | 1 | no | — |
| 46 | #2981 | — | 3 | 1 | no | — |
| 47 | #1588 | — | 3 | 2 | no | — |
| 48 | #1583 | — | 3 | 2 | no | — |
| 49 | SD16⋊C8 | — | 3 | 2 | no | — |
| 50 | C8×SD16 | — | 3 | 2 | no | — |
| 51 | #1572 | — | 3 | 1 | no | — |
| 52 | #1491 | — | 3 | 1 | no | — |
| 53 | #1484 | D3 | 1 | 1 | yes | characteristic |
| 54 | #1453 | — | 3 | 1 | no | — |
| 55 | C2×C3×#41 | — | 2 | 1 | no | — |
| 56 | C22×Dic6 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×M16 | — | 2 | 1 | no | — |
| 58 | C3×C4⋊Q8 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | C3×#127 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C3×#124 | — | 2 | 1 | no | — |
| 61 | C3×#121 | — | 2 | 1 | no | — |
| 62 | C3×#121 | C2×C4 | 1 | 2 | yes | — |
| 63 | C3×C4×D4 | — | 2 | 1 | no | — |
| 64 | C3×C4×D4 | C23 | 1 | 2 | yes | — |
| 65 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×#214 | C2×C4 | 1 | 2 | yes | — |
| 67 | C2×#214 | C2×C4 | 1 | 2 | yes | — |
| 68 | C2×C4⋊Dic3 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | C2×Dic3⋊C4 | — | 2 | 1 | no | — |
| 70 | C2×C4×Dic3 | — | 2 | 1 | no | — |
| 71 | C2×#208 | — | 2 | 2 | no | — |
| 72 | C22×C3⋊C8 | — | 2 | 2 | no | — |
| 73 | C4×Dic6 | — | 2 | 1 | no | — |
| 74 | C4×Dic6 | — | 2 | 1 | no | — |
| 75 | C4×Dic6 | C2×C4 | 1 | 2 | yes | — |
| 76 | C4×Dic6 | C23 | 1 | 2 | yes | — |
| 77 | C3×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 78 | C3×C22⋊C8 | — | 2 | 1 | no | — |
| 79 | C3×#97 | — | 2 | 1 | no | — |
| 80 | C3×C4×C8 | — | 2 | 1 | no | — |
| 81 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 83 | #832 | C2×C4 | 1 | 2 | yes | — |
| 84 | #832 | C2×C4 | 1 | 2 | yes | — |
| 85 | #830 | — | 2 | 1 | no | — |
| 86 | #830 | — | 2 | 2 | no | — |
| 87 | #830 | — | 2 | 2 | no | — |
| 88 | #830 | C2×C4 | 1 | 2 | yes | — |
| 89 | #830 | D4 | 1 | 2 | yes | — |
| 90 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 91 | Dic3⋊C8 | — | 2 | 2 | no | — |
| 92 | C8×Dic3 | — | 2 | 2 | no | — |
| 93 | C8×Dic3 | — | 2 | 2 | no | — |
| 94 | #810 | C2×C4 | 1 | 2 | yes | — |
| 95 | #810 | C2×C4 | 1 | 2 | yes | — |
| 96 | #808 | C2×C4 | 1 | 2 | yes | — |
| 97 | #808 | C2×C4 | 1 | 2 | yes | — |
| 98 | C4⋊(C3⋊C8) | C2×C4 | 1 | 2 | yes | — |
| 99 | C4⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 100 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 101 | #803 | — | 2 | 1 | no | — |
| 102 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 104 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 106 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×Q8 | — | 3 | 1 | no | — |
| 108 | #481 | — | 3 | 2 | no | — |
| 109 | #475 | — | 3 | 2 | no | — |
| 110 | #460 | — | 3 | 2 | no | — |
| 111 | #448 | — | 3 | 2 | no | — |
| 112 | C8×Q8 | — | 3 | 2 | no | — |
| 113 | C8×Q8 | — | 3 | 2 | no | — |
| 114 | C8×Q8 | — | 6 | 2 | no | — |
| 115 | C4×SD16 | — | 3 | 2 | no | — |
| 116 | C4×SD16 | — | 3 | 2 | no | — |
| 117 | #436 | — | 3 | 2 | no | — |
| 118 | #435 | — | 6 | 2 | no | — |
| 119 | C8×D4 | — | 3 | 2 | no | — |
| 120 | #432 | — | 3 | 1 | no | — |
| 121 | #431 | — | 3 | 1 | no | — |
| 122 | #431 | — | 3 | 1 | no | — |
| 123 | #431 | — | 6 | 2 | no | — |
| 124 | #431 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | #408 | — | 6 | 2 | no | — |
| 126 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 127 | #335 | — | 3 | 2 | no | — |
| 128 | #334 | — | 3 | 2 | no | — |
| 129 | Q8⋊C8 | — | 3 | 2 | no | — |
| 130 | Q8⋊C8 | — | 3 | 2 | no | — |
| 131 | D4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 132 | D4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 133 | #322 | — | 3 | 1 | no | — |
| 134 | #322 | — | 3 | 1 | no | — |
| 135 | #322 | — | 3 | 1 | no | — |
| 136 | C82 | — | 3 | 1 | no | — |
| 137 | C3×#41 | — | 8 | 2 | no | — |
| 138 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 139 | C2×C3×D4 | — | 2 | 2 | no | — |
| 140 | C2×C3×D4 | — | 2 | 1 | no | — |
| 141 | C2×C3×D4 | — | 2 | 1 | no | — |
| 142 | C2×C3×D4 | C22×C4 | 1 | 2 | yes | — |
| 143 | C22×C3×C4 | — | 2 | 2 | no | — |
| 144 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 145 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic |
| 147 | C22×Dic3 | — | 2 | 1 | no | — |
| 148 | C22×Dic3 | — | 2 | 1 | no | — |
| 149 | C2×Dic6 | — | 2 | 1 | no | — |
| 150 | C2×Dic6 | — | 2 | 4 | no | — |
| 151 | C2×Dic6 | C22×C4 | 1 | 2 | yes | — |
| 152 | C3×M16 | — | 4 | 2 | no | — |
| 153 | C2×C3×C8 | — | 2 | 1 | no | — |
| 154 | C2×C3×C8 | — | 2 | 2 | no | — |
| 155 | C2×C3×C8 | — | 2 | 1 | no | — |
| 156 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 157 | C3×C4⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 158 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 159 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 160 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 161 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 163 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 164 | #214 | — | 2 | 4 | no | — |
| 165 | #214 | — | 2 | 4 | no | — |
| 166 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 167 | C4⋊Dic3 | C22×C4 | 1 | 2 | yes | — |
| 168 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 169 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 170 | C4×Dic3 | — | 2 | 2 | no | — |
| 171 | C4×Dic3 | — | 2 | 2 | no | — |
| 172 | #208 | — | 8 | 2 | no | — |
| 173 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 174 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 175 | C2×C3⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 176 | C2×C3⋊C8 | C22×C4 | 1 | 2 | yes | — |
| 177 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 178 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 179 | C2×#41 | — | 2 | 1 | no | — |
| 180 | C22×Q8 | — | 3 | 1 | no | — |
| 181 | C2×SD16 | — | 3 | 2 | no | — |
| 182 | C2×SD16 | — | 3 | 2 | no | — |
| 183 | C2×M16 | — | 2 | 1 | no | — |
| 184 | C2×M16 | — | 6 | 2 | no | — |
| 185 | C22×C8 | — | 6 | 2 | no | — |
| 186 | C4⋊Q8 | C4×D3 | 1 | 1 | yes | characteristic |
| 187 | #127 | C4×D3 | 1 | 1 | yes | characteristic |
| 188 | #124 | — | 2 | 1 | no | — |
| 189 | #121 | — | 2 | 1 | no | — |
| 190 | #121 | C4×D3 | 1 | 2 | yes | — |
| 191 | C4×Q8 | — | 3 | 2 | no | — |
| 192 | C4×Q8 | — | 3 | 2 | no | — |
| 193 | C4×Q8 | — | 6 | 1 | no | — |
| 194 | C4×Q8 | — | 6 | 1 | no | — |
| 195 | C4×D4 | — | 2 | 1 | no | — |
| 196 | C4×D4 | C22×D3 | 1 | 2 | yes | — |
| 197 | C2×C4⋊C4 | — | 3 | 1 | no | — |
| 198 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 199 | C2×C42 | — | 6 | 1 | no | — |
| 200 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 201 | #106 | — | 3 | 2 | no | — |
| 202 | #106 | — | 3 | 2 | no | — |
| 203 | C4⋊C8 | — | 3 | 2 | no | — |
| 204 | C4⋊C8 | — | 3 | 2 | no | — |
| 205 | C4⋊C8 | — | 3 | 2 | no | — |
| 206 | C4⋊C8 | — | 6 | 2 | no | — |
| 207 | C4⋊C8 | — | 6 | 2 | no | — |
| 208 | C4⋊C8 | C22×D3 | 1 | 2 | yes | — |
| 209 | #103 | — | 3 | 2 | no | — |
| 210 | #103 | — | 3 | 2 | no | — |
| 211 | #102 | — | 3 | 2 | no | — |
| 212 | #102 | — | 3 | 2 | no | — |
| 213 | C22⋊C8 | — | 2 | 1 | no | — |
| 214 | C22⋊C8 | — | 3 | 2 | no | — |
| 215 | C22⋊C8 | — | 3 | 2 | no | — |
| 216 | C22⋊C8 | — | 6 | 2 | no | — |
| 217 | C22⋊C8 | — | 6 | 2 | no | — |
| 218 | C22⋊C8 | — | 6 | 1 | no | — |
| 219 | #97 | — | 2 | 1 | no | — |
| 220 | #97 | — | 6 | 1 | no | — |
| 221 | C4×C8 | — | 2 | 1 | no | — |
| 222 | C4×C8 | — | 3 | 1 | no | — |
| 223 | C4×C8 | — | 3 | 1 | no | — |
| 224 | C4×C8 | — | 3 | 1 | no | — |
| 225 | C4×C8 | — | 3 | 1 | no | — |
| 226 | C4×C8 | — | 6 | 2 | no | — |
| 227 | C4×C8 | — | 6 | 2 | no | — |
| 228 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 229 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 230 | C23×C3 | — | 2 | 2 | no | — |
| 231 | C23×C3 | C4×D4 | 1 | 1 | yes | characteristic |
| 232 | C3×Q8 | — | 8 | 1 | no | — |
| 233 | C3×D4 | — | 2 | 2 | no | — |
| 234 | C3×D4 | — | 2 | 2 | no | — |
| 235 | C3×D4 | — | 8 | 1 | no | — |
| 236 | C3×D4 | — | 8 | 1 | no | — |
| 237 | C3×D4 | — | 8 | 2 | no | — |
| 238 | C2×C3×C4 | — | 2 | 2 | no | — |
| 239 | C2×C3×C4 | — | 2 | 2 | no | — |
| 240 | C2×C3×C4 | — | 2 | 2 | no | — |
| 241 | C2×C3×C4 | — | 4 | 1 | no | — |
| 242 | C2×C3×C4 | — | 4 | 2 | no | — |
| 243 | C2×C3×C4 | — | 4 | 2 | no | — |
| 244 | C2×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 246 | C2×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 247 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 248 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 250 | C2×Dic3 | — | 2 | 4 | no | — |
| 251 | C2×Dic3 | — | 2 | 2 | no | — |
| 252 | C2×Dic3 | — | 2 | 2 | no | — |
| 253 | C2×Dic3 | — | 8 | 1 | no | — |
| 254 | Dic6 | — | 2 | 4 | no | — |
| 255 | Dic6 | — | 2 | 2 | no | — |
| 256 | Dic6 | #131 | 1 | 4 | yes | — |
| 257 | C3×C8 | — | 2 | 2 | no | — |
| 258 | C3×C8 | — | 4 | 1 | no | — |
| 259 | C3×C8 | — | 4 | 2 | no | — |
| 260 | C3⋊C8 | — | 2 | 2 | no | — |
| 261 | C3⋊C8 | — | 2 | 2 | no | — |
| 262 | C3⋊C8 | — | 2 | 2 | no | — |
| 263 | C3⋊C8 | — | 2 | 2 | no | — |
| 264 | C3⋊C8 | — | 4 | 2 | no | — |
| 265 | #41 | — | 8 | 2 | no | — |
| 266 | C2×Q8 | — | 2 | 1 | no | — |
| 267 | C2×Q8 | — | 3 | 2 | no | — |
| 268 | C2×Q8 | — | 6 | 4 | no | — |
| 269 | C2×Q8 | — | 6 | 1 | no | — |
| 270 | C2×D4 | — | 2 | 2 | no | — |
| 271 | C2×D4 | — | 2 | 1 | no | — |
| 272 | C2×D4 | — | 2 | 1 | no | — |
| 273 | C2×D4 | C2×C4×D3 | 1 | 2 | yes | — |
| 274 | C22×C4 | — | 2 | 2 | no | — |
| 275 | C22×C4 | — | 6 | 1 | no | — |
| 276 | C22×C4 | — | 6 | 1 | no | — |
| 277 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 278 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 279 | C22×C4 | #237 | 1 | 1 | yes | characteristic |
| 280 | SD16 | — | 6 | 4 | no | — |
| 281 | SD16 | — | 6 | 4 | no | — |
| 282 | M16 | — | 4 | 2 | no | — |
| 283 | M16 | — | 24 | 2 | no | — |
| 284 | C2×C8 | — | 2 | 1 | no | — |
| 285 | C2×C8 | — | 2 | 2 | no | — |
| 286 | C2×C8 | — | 2 | 1 | no | — |
| 287 | C2×C8 | — | 3 | 2 | no | — |
| 288 | C2×C8 | — | 3 | 2 | no | — |
| 289 | C2×C8 | — | 3 | 2 | no | — |
| 290 | C2×C8 | — | 3 | 2 | no | — |
| 291 | C2×C8 | — | 6 | 2 | no | — |
| 292 | C2×C8 | — | 24 | 2 | no | — |
| 293 | C4⋊C4 | — | 2 | 1 | no | — |
| 294 | C4⋊C4 | — | 3 | 2 | no | — |
| 295 | C4⋊C4 | — | 6 | 1 | no | — |
| 296 | C4⋊C4 | — | 6 | 2 | no | — |
| 297 | C4⋊C4 | — | 6 | 2 | no | — |
| 298 | C4⋊C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 299 | C22⋊C4 | — | 2 | 2 | no | — |
| 300 | C22⋊C4 | — | 2 | 2 | no | — |
| 301 | C42 | — | 6 | 2 | no | — |
| 302 | C42 | — | 6 | 2 | no | — |
| 303 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 304 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 305 | C42 | #237 | 1 | 1 | yes | characteristic |
| 306 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 307 | C22×C3 | — | 2 | 1 | no | — |
| 308 | C22×C3 | — | 2 | 1 | no | — |
| 309 | C22×C3 | — | 2 | 1 | no | — |
| 310 | C22×C3 | — | 4 | 2 | no | — |
| 311 | C22×C3 | — | 4 | 2 | no | — |
| 312 | C22×C3 | — | 4 | 2 | no | — |
| 313 | C22×C3 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 314 | C3×C4 | — | 2 | 1 | no | — |
| 315 | C3×C4 | — | 2 | 1 | no | — |
| 316 | C3×C4 | — | 2 | 1 | no | — |
| 317 | C3×C4 | — | 2 | 1 | no | — |
| 318 | C3×C4 | — | 4 | 2 | no | — |
| 319 | C3×C4 | C2×#131 | 1 | 2 | yes | — |
| 320 | C3×C4 | #577 | 1 | 2 | yes | — |
| 321 | Dic3 | — | 2 | 4 | no | — |
| 322 | Dic3 | — | 4 | 2 | no | — |
| 323 | C23 | — | 2 | 2 | no | — |
| 324 | C23 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 325 | Q8 | — | 3 | 4 | no | — |
| 326 | Q8 | — | 6 | 4 | no | — |
| 327 | Q8 | — | 6 | 2 | no | — |
| 328 | Q8 | — | 8 | 1 | no | — |
| 329 | D4 | — | 2 | 2 | no | — |
| 330 | D4 | — | 2 | 2 | no | — |
| 331 | D4 | — | 8 | 1 | no | — |
| 332 | D4 | — | 8 | 1 | no | — |
| 333 | D4 | — | 8 | 2 | no | — |
| 334 | C2×C4 | — | 2 | 2 | no | — |
| 335 | C2×C4 | — | 2 | 2 | no | — |
| 336 | C2×C4 | — | 2 | 2 | no | — |
| 337 | C2×C4 | — | 4 | 1 | no | — |
| 338 | C2×C4 | — | 4 | 2 | no | — |
| 339 | C2×C4 | — | 4 | 2 | no | — |
| 340 | C2×C4 | — | 6 | 4 | no | — |
| 341 | C2×C4 | — | 6 | 2 | no | — |
| 342 | C2×C4 | — | 6 | 2 | no | — |
| 343 | C2×C4 | — | 24 | 1 | no | — |
| 344 | C2×C4 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 346 | C2×C4 | #67⋊C4 | 1 | 1 | yes | characteristic |
| 347 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 348 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×C4 | C2×#237 | 1 | 1 | yes | characteristic |
| 350 | C8 | — | 2 | 2 | no | — |
| 351 | C8 | — | 4 | 1 | no | — |
| 352 | C8 | — | 4 | 2 | no | — |
| 353 | C8 | — | 6 | 2 | no | — |
| 354 | C8 | — | 6 | 2 | no | — |
| 355 | C8 | — | 6 | 2 | no | — |
| 356 | C8 | — | 6 | 2 | no | — |
| 357 | C8 | — | 12 | 2 | no | — |
| 358 | C2×C3 | — | 4 | 1 | no | — |
| 359 | C2×C3 | — | 8 | 2 | no | — |
| 360 | C2×C3 | #2929 | 1 | 1 | yes | characteristic |
| 361 | C2×C3 | #2949 | 1 | 1 | yes | characteristic |
| 362 | C2×C3 | #2956 | 1 | 1 | yes | characteristic |
| 363 | C22 | — | 2 | 1 | no | — |
| 364 | C22 | — | 2 | 1 | no | — |
| 365 | C22 | — | 2 | 1 | no | — |
| 366 | C22 | — | 4 | 2 | no | — |
| 367 | C22 | — | 4 | 2 | no | — |
| 368 | C22 | — | 4 | 2 | no | — |
| 369 | C22 | C2×#67⋊C4 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 2 | 1 | no | — |
| 371 | C4 | — | 2 | 1 | no | — |
| 372 | C4 | — | 2 | 1 | no | — |
| 373 | C4 | — | 2 | 1 | no | — |
| 374 | C4 | — | 4 | 2 | no | — |
| 375 | C4 | — | 6 | 4 | no | — |
| 376 | C4 | — | 12 | 2 | no | — |
| 377 | C4 | D3×#131 | 1 | 2 | yes | — |
| 378 | C4 | #5775 | 1 | 2 | yes | — |
| 379 | C3 | #17923 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 380 | C2 | — | 4 | 1 | no | — |
| 381 | C2 | — | 8 | 2 | no | — |
| 382 | C2 | #78655 | 1 | 1 | yes | characteristic |
| 383 | C2 | #78916 | 1 | 1 | yes | characteristic |
| 384 | C2 | #78980 | 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