← C2×#10682657 #72255393
Subgroups — C2×#10682657 #72255393
Order 1536.
556 conjugacy classes of subgroups.
The subgroup lattice has 372 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×#69078 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#67519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10682657 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C2×C3×#1369 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#7390 | — | 3 | 1 | no | maximal, Sylow |
| 6 | C22×D48 | C4 | 1 | 1 | yes | characteristic |
| 7 | C2×C4×D24 | — | 2 | 1 | no | — |
| 8 | C2×C3×#364 | — | 2 | 1 | no | — |
| 9 | C2×C3×#346 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#4509 | — | 2 | 1 | no | — |
| 11 | C2×#4505 | C4 | 1 | 1 | yes | characteristic |
| 12 | C2×#4499 | — | 2 | 1 | no | — |
| 13 | #69078 | — | 2 | 1 | no | — |
| 14 | #69078 | — | 2 | 1 | no | — |
| 15 | #69078 | C4 | 1 | 2 | yes | — |
| 16 | #69078 | C22 | 1 | 2 | yes | — |
| 17 | C3×#1369 | — | 2 | 1 | no | — |
| 18 | C3×#1369 | C22 | 1 | 2 | yes | complemented |
| 19 | #67519 | — | 2 | 1 | no | — |
| 20 | #67519 | C22 | 1 | 2 | yes | complemented |
| 21 | C2×#2177 | — | 3 | 1 | no | — |
| 22 | C2×#1398 | — | 3 | 1 | no | — |
| 23 | C2×#1369 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #7390 | — | 3 | 4 | no | — |
| 25 | C22×D24 | — | 2 | 1 | no | — |
| 26 | C2×C4×D12 | — | 4 | 1 | no | — |
| 27 | C2×C3×M32 | — | 4 | 1 | no | — |
| 28 | C22×C3×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 29 | C22×C3×C16 | D4 | 1 | 1 | yes | characteristic |
| 30 | C2×C3×C4×C8 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×#821 | — | 4 | 1 | no | — |
| 32 | C2×#818 | — | 2 | 1 | no | — |
| 33 | C2×D48 | — | 2 | 1 | no | — |
| 34 | C2×D48 | — | 2 | 1 | no | — |
| 35 | C2×D48 | — | 2 | 1 | no | — |
| 36 | C2×D48 | C8 | 1 | 2 | yes | — |
| 37 | C2×D48 | C8 | 1 | 2 | yes | — |
| 38 | C2×D48 | C2×C4 | 1 | 2 | yes | — |
| 39 | C4×D24 | — | 2 | 2 | no | — |
| 40 | C4×D24 | — | 2 | 2 | no | — |
| 41 | C4×D24 | — | 4 | 1 | no | — |
| 42 | C4×D24 | — | 4 | 1 | no | — |
| 43 | C3×#364 | — | 2 | 2 | no | — |
| 44 | C3×#364 | — | 4 | 1 | no | — |
| 45 | C3×#346 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C3×#346 | D4 | 1 | 1 | yes | characteristic |
| 47 | C3×#346 | D4 | 1 | 1 | yes | characteristic |
| 48 | C3×#346 | C23 | 1 | 1 | yes | characteristic |
| 49 | #4509 | — | 2 | 2 | no | — |
| 50 | #4509 | — | 2 | 2 | no | — |
| 51 | #4505 | — | 2 | 1 | no | — |
| 52 | #4505 | C2×C4 | 1 | 2 | yes | — |
| 53 | #4499 | — | 2 | 2 | no | — |
| 54 | #4499 | — | 2 | 2 | no | — |
| 55 | C2×C3⋊C32 | — | 2 | 2 | no | — |
| 56 | C22×D16 | — | 3 | 1 | no | — |
| 57 | C2×C4×D8 | — | 6 | 1 | no | — |
| 58 | C2×M64 | — | 6 | 1 | no | — |
| 59 | #2177 | — | 3 | 2 | no | — |
| 60 | #2177 | — | 3 | 2 | no | — |
| 61 | #2177 | — | 6 | 1 | no | — |
| 62 | #2177 | — | 6 | 1 | no | — |
| 63 | C2×#367 | — | 3 | 1 | no | — |
| 64 | C2×#364 | — | 2 | 1 | no | — |
| 65 | C2×#357 | — | 6 | 1 | no | — |
| 66 | C2×#346 | C2×D3 | 1 | 1 | yes | characteristic |
| 67 | #1398 | — | 3 | 2 | no | — |
| 68 | #1398 | — | 6 | 1 | no | — |
| 69 | #1369 | — | 2 | 1 | no | — |
| 70 | #1369 | C2×D3 | 1 | 2 | yes | complemented |
| 71 | C22×D12 | — | 4 | 1 | no | — |
| 72 | C22×C4×D3 | — | 8 | 1 | no | — |
| 73 | C22×C3×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 74 | C22×C3×C8 | D8 | 1 | 1 | yes | characteristic |
| 75 | C2×C3×C42 | SD16 | 1 | 1 | yes | characteristic |
| 76 | C2×(C2×D3)⋊C4 | — | 8 | 1 | no | — |
| 77 | C2×C4⋊Dic3 | — | 4 | 1 | no | — |
| 78 | C2×D24 | — | 2 | 2 | no | — |
| 79 | C2×D24 | — | 2 | 2 | no | — |
| 80 | C2×D24 | — | 2 | 2 | no | — |
| 81 | C2×D24 | — | 4 | 1 | no | — |
| 82 | C2×D24 | — | 4 | 1 | no | — |
| 83 | C2×D24 | — | 4 | 1 | no | — |
| 84 | C4×D12 | — | 4 | 2 | no | — |
| 85 | C4×D12 | — | 4 | 2 | no | — |
| 86 | C4×D12 | — | 8 | 1 | no | — |
| 87 | C4×D12 | — | 8 | 1 | no | — |
| 88 | C3×M32 | — | 4 | 2 | no | — |
| 89 | C3×M32 | — | 8 | 1 | no | — |
| 90 | C2×C3×C16 | — | 2 | 1 | no | — |
| 91 | C2×C3×C16 | — | 2 | 1 | no | — |
| 92 | C2×C3×C16 | — | 8 | 1 | no | — |
| 93 | C2×C3×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 95 | C2×C3×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×C16 | C2×C8 | 1 | 1 | yes | characteristic |
| 97 | C2×C3×C16 | M16 | 1 | 1 | yes | characteristic |
| 98 | C2×C3×C16 | M16 | 1 | 1 | yes | characteristic |
| 99 | C2×C3×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 100 | C2×C3×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C3×C4×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 102 | C3×C4×C8 | D8 | 1 | 1 | yes | characteristic |
| 103 | C3×C4×C8 | SD16 | 1 | 1 | yes | characteristic |
| 104 | C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | #821 | — | 4 | 2 | no | — |
| 106 | #821 | — | 4 | 2 | no | — |
| 107 | #818 | — | 2 | 2 | no | — |
| 108 | #818 | — | 4 | 1 | no | — |
| 109 | D48 | — | 2 | 2 | no | — |
| 110 | D48 | — | 2 | 2 | no | — |
| 111 | D48 | — | 2 | 2 | no | — |
| 112 | D48 | C2×C8 | 1 | 4 | yes | — |
| 113 | C3⋊C32 | — | 2 | 4 | no | — |
| 114 | C22×D8 | — | 6 | 1 | no | — |
| 115 | C2×C4×D4 | — | 12 | 1 | no | — |
| 116 | C2×D16 | — | 3 | 2 | no | — |
| 117 | C2×D16 | — | 3 | 2 | no | — |
| 118 | C2×D16 | — | 3 | 2 | no | — |
| 119 | C2×D16 | — | 6 | 1 | no | — |
| 120 | C2×D16 | — | 6 | 1 | no | — |
| 121 | C2×D16 | — | 6 | 1 | no | — |
| 122 | C2×M32 | — | 4 | 1 | no | — |
| 123 | C22×C16 | C4×D3 | 1 | 1 | yes | characteristic |
| 124 | C22×C16 | D12 | 1 | 1 | yes | characteristic |
| 125 | C4×D8 | — | 6 | 2 | no | — |
| 126 | C4×D8 | — | 6 | 2 | no | — |
| 127 | C4×D8 | — | 12 | 1 | no | — |
| 128 | C4×D8 | — | 12 | 1 | no | — |
| 129 | C2×#107 | — | 6 | 1 | no | — |
| 130 | C2×#102 | — | 12 | 1 | no | — |
| 131 | C2×C4×C8 | #67 | 1 | 1 | yes | characteristic |
| 132 | M64 | — | 6 | 2 | no | — |
| 133 | M64 | — | 6 | 2 | no | — |
| 134 | C2×C32 | — | 6 | 2 | no | — |
| 135 | #367 | — | 3 | 2 | no | — |
| 136 | #367 | — | 6 | 1 | no | — |
| 137 | #364 | — | 2 | 2 | no | — |
| 138 | #364 | — | 4 | 1 | no | — |
| 139 | #357 | — | 6 | 2 | no | — |
| 140 | #357 | — | 6 | 2 | no | — |
| 141 | #346 | C4×D3 | 1 | 1 | yes | characteristic |
| 142 | #346 | D12 | 1 | 1 | yes | characteristic |
| 143 | #346 | #67 | 1 | 1 | yes | characteristic |
| 144 | #346 | C22×D3 | 1 | 1 | yes | characteristic |
| 145 | C23×D3 | — | 8 | 1 | no | — |
| 146 | C22×C3×C4 | — | 2 | 1 | no | — |
| 147 | C22×C3×C4 | #102 | 1 | 1 | yes | characteristic |
| 148 | C22×Dic3 | — | 8 | 1 | no | — |
| 149 | C2×D12 | — | 4 | 2 | no | — |
| 150 | C2×D12 | — | 4 | 2 | no | — |
| 151 | C2×D12 | — | 4 | 2 | no | — |
| 152 | C2×D12 | — | 8 | 1 | no | — |
| 153 | C2×D12 | — | 8 | 1 | no | — |
| 154 | C2×D12 | — | 8 | 1 | no | — |
| 155 | C2×C4×D3 | — | 8 | 2 | no | — |
| 156 | C2×C4×D3 | — | 8 | 2 | no | — |
| 157 | C2×C4×D3 | — | 16 | 4 | no | — |
| 158 | C2×C3×C8 | — | 2 | 1 | no | — |
| 159 | C2×C3×C8 | — | 2 | 1 | no | — |
| 160 | C2×C3×C8 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 161 | C2×C3×C8 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 162 | C2×C3×C8 | #102 | 1 | 1 | yes | characteristic |
| 163 | C2×C3×C8 | #102 | 1 | 1 | yes | characteristic |
| 164 | C2×C3×C8 | #104 | 1 | 1 | yes | characteristic |
| 165 | C2×C3×C8 | #104 | 1 | 1 | yes | characteristic |
| 166 | C2×C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | C2×C3×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 168 | C3×C42 | — | 2 | 1 | no | — |
| 169 | C3×C42 | #102 | 1 | 1 | yes | characteristic |
| 170 | C3×C42 | C2×SD16 | 1 | 1 | yes | characteristic |
| 171 | (C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 172 | (C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 173 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 174 | C4⋊Dic3 | — | 8 | 1 | no | — |
| 175 | D24 | — | 2 | 4 | no | — |
| 176 | D24 | — | 4 | 2 | no | — |
| 177 | D24 | — | 4 | 2 | no | — |
| 178 | D24 | — | 4 | 2 | no | — |
| 179 | C3×C16 | — | 2 | 1 | no | — |
| 180 | C3×C16 | — | 2 | 1 | no | — |
| 181 | C3×C16 | — | 8 | 2 | no | — |
| 182 | C3×C16 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 183 | C3×C16 | C22⋊C8 | 1 | 1 | yes | characteristic |
| 184 | C3×C16 | C22×C8 | 1 | 1 | yes | characteristic |
| 185 | C3×C16 | C2×M16 | 1 | 1 | yes | characteristic |
| 186 | C22×D4 | — | 12 | 1 | no | — |
| 187 | C23×C4 | — | 24 | 1 | no | — |
| 188 | C2×D8 | — | 6 | 2 | no | — |
| 189 | C2×D8 | — | 6 | 2 | no | — |
| 190 | C2×D8 | — | 6 | 2 | no | — |
| 191 | C2×D8 | — | 12 | 1 | no | — |
| 192 | C2×D8 | — | 12 | 1 | no | — |
| 193 | C2×D8 | — | 12 | 1 | no | — |
| 194 | C22×C8 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 195 | C22×C8 | #213 | 1 | 1 | yes | characteristic |
| 196 | C4×D4 | — | 12 | 2 | no | — |
| 197 | C4×D4 | — | 12 | 2 | no | — |
| 198 | C4×D4 | — | 24 | 1 | no | — |
| 199 | C4×D4 | — | 24 | 1 | no | — |
| 200 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 201 | C2×C22⋊C4 | — | 24 | 1 | no | — |
| 202 | C2×C42 | #215 | 1 | 1 | yes | characteristic |
| 203 | D16 | — | 3 | 4 | no | — |
| 204 | D16 | — | 6 | 2 | no | — |
| 205 | D16 | — | 6 | 2 | no | — |
| 206 | D16 | — | 6 | 2 | no | — |
| 207 | M32 | — | 4 | 2 | no | — |
| 208 | M32 | — | 8 | 1 | no | — |
| 209 | C2×C16 | — | 2 | 1 | no | — |
| 210 | C2×C16 | — | 2 | 1 | no | — |
| 211 | C2×C16 | — | 8 | 1 | no | — |
| 212 | C2×C16 | D3×C8 | 1 | 1 | yes | characteristic |
| 213 | C2×C16 | D3×C8 | 1 | 1 | yes | characteristic |
| 214 | C2×C16 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 215 | C2×C16 | ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 216 | C2×C16 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C2×C16 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 218 | C2×C16 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 219 | C2×C16 | C2×D12 | 1 | 1 | yes | characteristic |
| 220 | #107 | — | 6 | 2 | no | — |
| 221 | #107 | — | 12 | 1 | no | — |
| 222 | #102 | — | 12 | 2 | no | — |
| 223 | #102 | — | 12 | 2 | no | — |
| 224 | C4×C8 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 225 | C4×C8 | #213 | 1 | 1 | yes | characteristic |
| 226 | C4×C8 | #215 | 1 | 1 | yes | characteristic |
| 227 | C4×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 228 | C32 | — | 6 | 4 | no | — |
| 229 | C23×C3 | #361 | 1 | 1 | yes | characteristic |
| 230 | C22×D3 | — | 8 | 2 | no | — |
| 231 | C22×D3 | — | 8 | 2 | no | — |
| 232 | C22×D3 | — | 8 | 2 | no | — |
| 233 | C22×D3 | — | 16 | 2 | no | — |
| 234 | C22×D3 | — | 16 | 2 | no | — |
| 235 | C2×C3×C4 | — | 2 | 1 | no | — |
| 236 | C2×C3×C4 | — | 2 | 1 | no | — |
| 237 | C2×C3×C4 | — | 4 | 2 | no | — |
| 238 | C2×C3×C4 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 239 | C2×C3×C4 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 240 | C2×C3×C4 | #360 | 1 | 1 | yes | characteristic |
| 241 | C2×C3×C4 | #360 | 1 | 1 | yes | characteristic |
| 242 | C2×C3×C4 | #361 | 1 | 1 | yes | characteristic |
| 243 | C2×C3×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 244 | C2×Dic3 | — | 8 | 2 | no | — |
| 245 | C2×Dic3 | — | 16 | 2 | no | — |
| 246 | D12 | — | 4 | 4 | no | — |
| 247 | D12 | — | 8 | 2 | no | — |
| 248 | D12 | — | 8 | 2 | no | — |
| 249 | D12 | — | 8 | 2 | no | — |
| 250 | C4×D3 | — | 16 | 4 | no | — |
| 251 | C4×D3 | — | 16 | 4 | no | — |
| 252 | C3×C8 | — | 2 | 1 | no | — |
| 253 | C3×C8 | — | 2 | 1 | no | — |
| 254 | C3×C8 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 255 | C3×C8 | D4⋊C8 | 1 | 1 | yes | characteristic |
| 256 | C3×C8 | C2×C22⋊C8 | 1 | 1 | yes | characteristic |
| 257 | C3×C8 | C2×#104 | 1 | 1 | yes | characteristic |
| 258 | C24 | — | 24 | 1 | no | — |
| 259 | C2×D4 | — | 12 | 2 | no | — |
| 260 | C2×D4 | — | 12 | 2 | no | — |
| 261 | C2×D4 | — | 12 | 2 | no | — |
| 262 | C2×D4 | — | 24 | 1 | no | — |
| 263 | C2×D4 | — | 24 | 1 | no | — |
| 264 | C2×D4 | — | 24 | 1 | no | — |
| 265 | C22×C4 | — | 2 | 1 | no | — |
| 266 | C22×C4 | — | 24 | 2 | no | — |
| 267 | C22×C4 | — | 24 | 2 | no | — |
| 268 | C22×C4 | — | 24 | 1 | no | — |
| 269 | C22×C4 | — | 48 | 4 | no | — |
| 270 | C22×C4 | #809 | 1 | 1 | yes | characteristic |
| 271 | D8 | — | 6 | 4 | no | — |
| 272 | D8 | — | 12 | 2 | no | — |
| 273 | D8 | — | 12 | 2 | no | — |
| 274 | D8 | — | 12 | 2 | no | — |
| 275 | C2×C8 | — | 2 | 1 | no | — |
| 276 | C2×C8 | — | 2 | 1 | no | — |
| 277 | C2×C8 | #809 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | #809 | 1 | 1 | yes | characteristic |
| 279 | C2×C8 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 280 | C2×C8 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 281 | C2×C8 | #825 | 1 | 1 | yes | characteristic |
| 282 | C2×C8 | #825 | 1 | 1 | yes | characteristic |
| 283 | C2×C8 | C2×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 284 | C2×C8 | C2×#213 | 1 | 1 | yes | characteristic |
| 285 | C4⋊C4 | — | 12 | 2 | no | — |
| 286 | C4⋊C4 | — | 24 | 1 | no | — |
| 287 | C22⋊C4 | — | 24 | 2 | no | — |
| 288 | C22⋊C4 | — | 24 | 2 | no | — |
| 289 | C42 | — | 2 | 1 | no | — |
| 290 | C42 | #809 | 1 | 1 | yes | characteristic |
| 291 | C42 | C2×#215 | 1 | 1 | yes | characteristic |
| 292 | C16 | — | 2 | 1 | no | — |
| 293 | C16 | — | 2 | 1 | no | — |
| 294 | C16 | — | 8 | 2 | no | — |
| 295 | C16 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 296 | C16 | (C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 297 | C16 | C2×D3×C8 | 1 | 1 | yes | characteristic |
| 298 | C16 | C2×ΓL(1,𝔽25) | 1 | 1 | yes | characteristic |
| 299 | C22×C3 | — | 2 | 2 | no | — |
| 300 | C22×C3 | #1333 | 1 | 1 | yes | characteristic |
| 301 | C22×C3 | #1333 | 1 | 1 | yes | characteristic |
| 302 | C22×C3 | C2×#361 | 1 | 1 | yes | characteristic |
| 303 | C2×D3 | — | 8 | 4 | no | — |
| 304 | C2×D3 | — | 16 | 2 | no | — |
| 305 | C2×D3 | — | 16 | 2 | no | — |
| 306 | C2×D3 | — | 16 | 4 | no | — |
| 307 | C2×D3 | — | 16 | 4 | no | — |
| 308 | C3×C4 | — | 4 | 1 | no | — |
| 309 | C3×C4 | — | 4 | 1 | no | — |
| 310 | C3×C4 | #1333 | 1 | 1 | yes | characteristic |
| 311 | C3×C4 | #1333 | 1 | 1 | yes | characteristic |
| 312 | C3×C4 | C2×D4⋊C8 | 1 | 1 | yes | characteristic |
| 313 | C3×C4 | C2×#360 | 1 | 1 | yes | characteristic |
| 314 | Dic3 | — | 16 | 2 | no | — |
| 315 | C23 | — | 24 | 2 | no | — |
| 316 | C23 | — | 24 | 2 | no | — |
| 317 | C23 | — | 24 | 2 | no | — |
| 318 | C23 | — | 48 | 2 | no | — |
| 319 | C23 | — | 48 | 2 | no | — |
| 320 | C23 | #4495 | 1 | 1 | yes | characteristic |
| 321 | D4 | — | 12 | 4 | no | — |
| 322 | D4 | — | 24 | 2 | no | — |
| 323 | D4 | — | 24 | 2 | no | — |
| 324 | D4 | — | 24 | 2 | no | — |
| 325 | C2×C4 | — | 2 | 1 | no | — |
| 326 | C2×C4 | — | 2 | 1 | no | — |
| 327 | C2×C4 | — | 4 | 2 | no | — |
| 328 | C2×C4 | — | 24 | 2 | no | — |
| 329 | C2×C4 | — | 48 | 4 | no | — |
| 330 | C2×C4 | — | 48 | 4 | no | — |
| 331 | C2×C4 | — | 48 | 2 | no | — |
| 332 | C2×C4 | #4483 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | #4483 | 1 | 1 | yes | characteristic |
| 334 | C2×C4 | #4488 | 1 | 1 | yes | characteristic |
| 335 | C2×C4 | #4488 | 1 | 1 | yes | characteristic |
| 336 | C2×C4 | #4495 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | C2×#809 | 1 | 1 | yes | characteristic |
| 338 | C8 | — | 2 | 1 | no | — |
| 339 | C8 | — | 2 | 1 | no | — |
| 340 | C8 | #4483 | 1 | 1 | yes | characteristic |
| 341 | C8 | #4483 | 1 | 1 | yes | characteristic |
| 342 | C8 | C2×(C2×D3)⋊C8 | 1 | 1 | yes | characteristic |
| 343 | C8 | C2×#825 | 1 | 1 | yes | characteristic |
| 344 | C2×C3 | — | 2 | 1 | no | — |
| 345 | C2×C3 | — | 2 | 1 | no | — |
| 346 | C2×C3 | #7390 | 1 | 2 | yes | complemented |
| 347 | C2×C3 | C2×#1333 | 1 | 1 | yes | characteristic |
| 348 | D3 | — | 16 | 4 | no | — |
| 349 | C22 | — | 2 | 2 | no | — |
| 350 | C22 | — | 24 | 4 | no | — |
| 351 | C22 | — | 48 | 2 | no | — |
| 352 | C22 | — | 48 | 2 | no | — |
| 353 | C22 | — | 48 | 4 | no | — |
| 354 | C22 | — | 48 | 4 | no | — |
| 355 | C22 | #67465 | 1 | 1 | yes | characteristic |
| 356 | C22 | #67465 | 1 | 1 | yes | characteristic |
| 357 | C22 | C2×#4495 | 1 | 1 | yes | characteristic |
| 358 | C4 | — | 4 | 1 | no | — |
| 359 | C4 | — | 4 | 1 | no | — |
| 360 | C4 | — | 48 | 2 | no | — |
| 361 | C4 | #67465 | 1 | 1 | yes | characteristic |
| 362 | C4 | #67465 | 1 | 1 | yes | characteristic |
| 363 | C4 | C2×#4483 | 1 | 1 | yes | characteristic |
| 364 | C4 | C2×#4488 | 1 | 1 | yes | characteristic |
| 365 | C3 | C2×#7390 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 366 | C2 | — | 2 | 1 | no | — |
| 367 | C2 | — | 2 | 1 | no | — |
| 368 | C2 | — | 48 | 4 | no | — |
| 369 | C2 | #10682657 | 1 | 2 | yes | direct product factor |
| 370 | C2 | C2×#67465 | 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