← #72226300
Subgroups — #72226300
Order 1536.
934 conjugacy classes of subgroups.
The subgroup lattice has 362 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10948442 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10707077 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #10706752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#67767 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10704187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#33463 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #483600 | — | 3 | 1 | no | maximal, Sylow |
| 8 | C3×#3414 | C4 | 1 | 1 | yes | characteristic |
| 9 | C2×C3×#443 | C22 | 1 | 2 | yes | — |
| 10 | #83780 | — | 2 | 2 | no | — |
| 11 | C3×#2179 | C22 | 1 | 4 | yes | — |
| 12 | C3×#2178 | C4 | 1 | 4 | yes | — |
| 13 | C3×#2161 | C4 | 1 | 1 | yes | characteristic |
| 14 | C3×#2143 | C4 | 1 | 2 | yes | — |
| 15 | C3×C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 16 | #72006 | — | 2 | 2 | no | — |
| 17 | #70924 | C22 | 1 | 8 | yes | complemented |
| 18 | #70923 | — | 2 | 4 | no | — |
| 19 | C2×#4463 | C22 | 1 | 2 | yes | — |
| 20 | C4×#812 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#4455 | C22 | 1 | 1 | yes | characteristic |
| 22 | #67767 | C22 | 1 | 8 | yes | complemented |
| 23 | #67514 | C22 | 1 | 4 | yes | complemented |
| 24 | #67511 | C22 | 1 | 4 | yes | complemented |
| 25 | #33463 | D3 | 1 | 1 | yes | characteristic |
| 26 | #33443 | — | 3 | 2 | no | — |
| 27 | #12068 | — | 3 | 8 | no | — |
| 28 | #12002 | — | 3 | 1 | no | — |
| 29 | C2×#1336 | — | 3 | 2 | no | — |
| 30 | #11404 | — | 3 | 1 | no | — |
| 31 | C2×C3×#135 | C2×C4 | 1 | 2 | yes | — |
| 32 | C2×C3×#131 | — | 2 | 2 | no | — |
| 33 | C3×#510 | C8 | 1 | 4 | yes | complemented |
| 34 | C3×#509 | C8 | 1 | 4 | yes | complemented |
| 35 | C3×#508 | C2×C4 | 1 | 4 | yes | — |
| 36 | C2×C3×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C2×C3×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C3×#443 | — | 2 | 2 | no | — |
| 39 | C3×#443 | — | 2 | 2 | no | — |
| 40 | C3×#443 | C2×C4 | 1 | 4 | yes | — |
| 41 | C3×#443 | C23 | 1 | 4 | yes | — |
| 42 | C2×C3×#108 | C2×C4 | 1 | 2 | yes | — |
| 43 | C2×C3×#104 | — | 2 | 2 | no | — |
| 44 | C2×C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 45 | #5140 | — | 2 | 8 | no | — |
| 46 | #5140 | — | 4 | 4 | no | — |
| 47 | C2×#812 | — | 2 | 2 | no | — |
| 48 | C2×#812 | — | 4 | 4 | no | — |
| 49 | C2×#812 | D4 | 1 | 2 | yes | — |
| 50 | C2×C4×C3⋊C8 | — | 2 | 1 | no | — |
| 51 | C3×#368 | C2×C4 | 1 | 4 | yes | — |
| 52 | C3×#359 | C2×C4 | 1 | 8 | yes | — |
| 53 | C3×#346 | C23 | 1 | 2 | yes | — |
| 54 | C3×C4×C16 | C2×C4 | 1 | 2 | yes | — |
| 55 | #4561 | — | 2 | 8 | no | — |
| 56 | #4463 | — | 2 | 2 | no | — |
| 57 | #4463 | C23 | 1 | 4 | yes | — |
| 58 | #4461 | C23 | 1 | 2 | yes | — |
| 59 | C4×C3⋊C16 | D4 | 1 | 2 | yes | — |
| 60 | #4455 | — | 2 | 1 | no | — |
| 61 | #4455 | C23 | 1 | 2 | yes | — |
| 62 | #3414 | Dic3 | 1 | 1 | yes | characteristic |
| 63 | #3407 | — | 6 | 2 | no | — |
| 64 | C2×#443 | C2×D3 | 1 | 2 | yes | — |
| 65 | #2179 | C2×D3 | 1 | 4 | yes | — |
| 66 | #2178 | Dic3 | 1 | 4 | yes | — |
| 67 | #2171 | — | 3 | 8 | no | — |
| 68 | #2170 | — | 6 | 4 | no | — |
| 69 | #2161 | Dic3 | 1 | 1 | yes | characteristic |
| 70 | C2×#364 | — | 3 | 2 | no | — |
| 71 | #2143 | Dic3 | 1 | 2 | yes | — |
| 72 | #2117 | — | 6 | 2 | no | — |
| 73 | C4×M32 | — | 3 | 1 | no | — |
| 74 | C4×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 75 | C2×#322 | — | 3 | 1 | no | — |
| 76 | #1369 | — | 3 | 4 | no | — |
| 77 | #1336 | — | 3 | 8 | no | — |
| 78 | #1313 | — | 3 | 4 | no | — |
| 79 | C2×C3×#41 | — | 2 | 2 | no | — |
| 80 | C3×#135 | — | 2 | 2 | no | — |
| 81 | C3×#135 | — | 2 | 2 | no | — |
| 82 | C3×#135 | C2×C8 | 1 | 4 | yes | — |
| 83 | C3×#135 | C22×C4 | 1 | 4 | yes | — |
| 84 | C2×C3×Q16 | C2×C8 | 1 | 2 | yes | — |
| 85 | C2×C3×SD16 | — | 2 | 2 | no | — |
| 86 | C2×C3×D8 | C2×C8 | 1 | 2 | yes | — |
| 87 | C3×#131 | — | 2 | 4 | no | — |
| 88 | C3×#131 | — | 2 | 4 | no | — |
| 89 | C3×#131 | — | 4 | 2 | no | — |
| 90 | C3×#131 | — | 4 | 2 | no | — |
| 91 | C2×C3×M16 | — | 2 | 2 | no | — |
| 92 | C2×C3×M16 | — | 4 | 2 | no | — |
| 93 | C22×C3×C8 | — | 4 | 2 | no | — |
| 94 | C22×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 95 | C22×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 96 | C2×C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 97 | C22×C3⋊C8 | — | 4 | 1 | no | — |
| 98 | C3×Q32 | C2×C8 | 1 | 4 | yes | complemented |
| 99 | C3×SD32 | C2×C8 | 1 | 8 | yes | complemented |
| 100 | C3×D16 | C2×C8 | 1 | 4 | yes | complemented |
| 101 | C3×M32 | — | 2 | 2 | no | — |
| 102 | C3×M32 | C2×C8 | 1 | 4 | yes | — |
| 103 | C2×C3×C16 | C22×C4 | 1 | 2 | yes | — |
| 104 | C2×C3×C16 | C22×C4 | 1 | 2 | yes | — |
| 105 | C3×#108 | — | 2 | 2 | no | — |
| 106 | C3×#108 | C22×C4 | 1 | 4 | yes | — |
| 107 | C3×#104 | — | 2 | 4 | no | — |
| 108 | C3×#104 | — | 2 | 4 | no | — |
| 109 | C3×C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 110 | C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 111 | C3×C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 112 | C3×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 113 | #812 | — | 2 | 2 | no | — |
| 114 | #812 | — | 2 | 2 | no | — |
| 115 | #812 | — | 2 | 4 | no | — |
| 116 | #812 | — | 4 | 8 | no | — |
| 117 | #812 | — | 4 | 2 | no | — |
| 118 | C2×C3⋊C16 | — | 4 | 8 | no | — |
| 119 | C2×C3⋊C16 | — | 4 | 2 | no | — |
| 120 | C2×C3⋊C16 | C2×D4 | 1 | 4 | yes | — |
| 121 | C4×C3⋊C8 | — | 2 | 2 | no | — |
| 122 | C4×C3⋊C8 | — | 4 | 1 | no | — |
| 123 | C2×#135 | C2×Dic3 | 1 | 2 | yes | — |
| 124 | C2×#131 | — | 2 | 2 | no | — |
| 125 | #510 | C3⋊C8 | 1 | 4 | yes | complemented |
| 126 | #509 | C3⋊C8 | 1 | 4 | yes | complemented |
| 127 | #508 | C2×Dic3 | 1 | 4 | yes | — |
| 128 | #504 | — | 6 | 8 | no | — |
| 129 | #504 | — | 12 | 4 | no | — |
| 130 | C2×M32 | — | 3 | 2 | no | — |
| 131 | C2×M32 | — | 6 | 2 | no | — |
| 132 | C2×M32 | — | 12 | 4 | no | — |
| 133 | C2×M32 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 134 | C2×M32 | C2×Dic3 | 1 | 1 | yes | characteristic |
| 135 | #443 | — | 2 | 2 | no | — |
| 136 | #443 | — | 2 | 2 | no | — |
| 137 | #443 | C2×Dic3 | 1 | 4 | yes | — |
| 138 | #443 | C22×D3 | 1 | 4 | yes | — |
| 139 | C2×#108 | C2×Dic3 | 1 | 2 | yes | — |
| 140 | C2×#104 | — | 2 | 2 | no | — |
| 141 | C2×C4×C8 | — | 6 | 1 | no | — |
| 142 | C2×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 143 | #368 | C2×Dic3 | 1 | 4 | yes | — |
| 144 | #364 | — | 3 | 4 | no | — |
| 145 | #364 | — | 6 | 2 | no | — |
| 146 | #359 | C2×Dic3 | 1 | 8 | yes | — |
| 147 | #350 | — | 6 | 8 | no | — |
| 148 | #346 | — | 3 | 2 | no | — |
| 149 | #346 | C22×D3 | 1 | 2 | yes | — |
| 150 | C4×C16 | — | 3 | 2 | no | — |
| 151 | C4×C16 | C2×Dic3 | 1 | 2 | yes | — |
| 152 | #322 | — | 3 | 2 | no | — |
| 153 | #322 | — | 6 | 1 | no | — |
| 154 | C3×#41 | — | 2 | 4 | no | — |
| 155 | C3×#41 | — | 2 | 4 | no | — |
| 156 | C3×#41 | — | 4 | 2 | no | — |
| 157 | C3×#41 | — | 4 | 2 | no | — |
| 158 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 159 | C2×C3×D4 | — | 2 | 2 | no | — |
| 160 | C2×C3×D4 | — | 4 | 2 | no | — |
| 161 | C22×C3×C4 | — | 2 | 1 | no | — |
| 162 | C22×C3×C4 | — | 4 | 2 | no | — |
| 163 | C22×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 164 | C3×Q16 | — | 2 | 2 | no | — |
| 165 | C3×Q16 | C22×C8 | 1 | 4 | yes | — |
| 166 | C3×SD16 | — | 2 | 4 | no | — |
| 167 | C3×SD16 | — | 2 | 4 | no | — |
| 168 | C3×D8 | — | 2 | 2 | no | — |
| 169 | C3×D8 | C22×C8 | 1 | 4 | yes | — |
| 170 | C3×M16 | — | 2 | 4 | no | — |
| 171 | C3×M16 | — | 4 | 2 | no | — |
| 172 | C3×M16 | — | 4 | 4 | no | — |
| 173 | C3×M16 | — | 4 | 4 | no | — |
| 174 | C2×C3×C8 | — | 4 | 2 | no | — |
| 175 | C2×C3×C8 | — | 4 | 4 | no | — |
| 176 | C2×C3×C8 | — | 4 | 4 | no | — |
| 177 | C2×C3×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C3×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C3×C8 | C22×C8 | 1 | 2 | yes | — |
| 180 | C2×C3×C8 | #131 | 1 | 2 | yes | — |
| 181 | C2×C3×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 182 | C2×C3×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 183 | C2×C3×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 185 | C3×C42 | — | 2 | 1 | no | — |
| 186 | C3×C42 | C4×D4 | 1 | 1 | yes | characteristic |
| 187 | C3×C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 188 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 189 | C2×C3⋊C8 | — | 8 | 2 | no | — |
| 190 | C3×C16 | — | 2 | 2 | no | — |
| 191 | C3×C16 | C22×C8 | 1 | 4 | yes | — |
| 192 | C3⋊C16 | — | 2 | 4 | no | — |
| 193 | C3⋊C16 | — | 4 | 4 | no | — |
| 194 | C2×#41 | — | 2 | 2 | no | — |
| 195 | #135 | — | 2 | 2 | no | — |
| 196 | #135 | — | 2 | 2 | no | — |
| 197 | #135 | C2×C3⋊C8 | 1 | 4 | yes | — |
| 198 | #135 | C22×Dic3 | 1 | 4 | yes | — |
| 199 | C2×Q16 | C2×C3⋊C8 | 1 | 2 | yes | — |
| 200 | C2×SD16 | — | 2 | 2 | no | — |
| 201 | C2×D8 | C2×C3⋊C8 | 1 | 2 | yes | — |
| 202 | #131 | — | 2 | 4 | no | — |
| 203 | #131 | — | 2 | 4 | no | — |
| 204 | #131 | — | 4 | 2 | no | — |
| 205 | #131 | — | 4 | 2 | no | — |
| 206 | C2×M16 | — | 2 | 2 | no | — |
| 207 | C2×M16 | — | 4 | 2 | no | — |
| 208 | C22×C8 | — | 4 | 2 | no | — |
| 209 | C22×C8 | — | 12 | 1 | no | — |
| 210 | C22×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 211 | C22×C8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 212 | C2×C42 | #237 | 1 | 1 | yes | characteristic |
| 213 | Q32 | C2×C3⋊C8 | 1 | 4 | yes | complemented |
| 214 | SD32 | C2×C3⋊C8 | 1 | 8 | yes | complemented |
| 215 | D16 | C2×C3⋊C8 | 1 | 4 | yes | complemented |
| 216 | M32 | — | 2 | 2 | no | — |
| 217 | M32 | — | 6 | 2 | no | — |
| 218 | M32 | — | 6 | 2 | no | — |
| 219 | M32 | — | 6 | 4 | no | — |
| 220 | M32 | — | 12 | 8 | no | — |
| 221 | M32 | — | 12 | 2 | no | — |
| 222 | M32 | C2×C3⋊C8 | 1 | 4 | yes | — |
| 223 | C2×C16 | — | 3 | 4 | no | — |
| 224 | C2×C16 | — | 12 | 8 | no | — |
| 225 | C2×C16 | — | 12 | 2 | no | — |
| 226 | C2×C16 | C22×Dic3 | 1 | 2 | yes | — |
| 227 | C2×C16 | C22×Dic3 | 1 | 2 | yes | — |
| 228 | #108 | — | 2 | 2 | no | — |
| 229 | #108 | C22×Dic3 | 1 | 4 | yes | — |
| 230 | #104 | — | 2 | 4 | no | — |
| 231 | #104 | — | 2 | 4 | no | — |
| 232 | C4×C8 | — | 6 | 2 | no | — |
| 233 | C4×C8 | — | 12 | 1 | no | — |
| 234 | C4×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 235 | C4×C8 | #237 | 1 | 1 | yes | characteristic |
| 236 | C4×C8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 237 | C4×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 238 | C23×C3 | — | 4 | 2 | no | — |
| 239 | C23×C3 | #444 | 1 | 1 | yes | characteristic |
| 240 | C3×Q8 | — | 2 | 4 | no | — |
| 241 | C3×Q8 | — | 4 | 2 | no | — |
| 242 | C3×D4 | — | 2 | 4 | no | — |
| 243 | C3×D4 | — | 4 | 4 | no | — |
| 244 | C3×D4 | — | 4 | 4 | no | — |
| 245 | C3×D4 | — | 4 | 2 | no | — |
| 246 | C2×C3×C4 | — | 2 | 1 | no | — |
| 247 | C2×C3×C4 | — | 2 | 1 | no | — |
| 248 | C2×C3×C4 | — | 4 | 2 | no | — |
| 249 | C2×C3×C4 | — | 4 | 2 | no | — |
| 250 | C2×C3×C4 | — | 4 | 4 | no | — |
| 251 | C2×C3×C4 | — | 4 | 4 | no | — |
| 252 | C2×C3×C4 | C8×D4 | 1 | 2 | yes | — |
| 253 | C2×C3×C4 | #442 | 1 | 2 | yes | — |
| 254 | C2×C3×C4 | #444 | 1 | 1 | yes | characteristic |
| 255 | C2×C3×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 256 | C3×C8 | — | 4 | 4 | no | — |
| 257 | C3×C8 | C8×D4 | 1 | 2 | yes | — |
| 258 | C3×C8 | #442 | 1 | 1 | yes | characteristic |
| 259 | C3×C8 | #442 | 1 | 1 | yes | characteristic |
| 260 | C3×C8 | C23×C8 | 1 | 1 | yes | characteristic |
| 261 | C3×C8 | C2×#131 | 1 | 1 | yes | characteristic |
| 262 | C3×C8 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 263 | C3⋊C8 | — | 8 | 2 | no | — |
| 264 | #41 | — | 2 | 4 | no | — |
| 265 | #41 | — | 2 | 4 | no | — |
| 266 | #41 | — | 4 | 2 | no | — |
| 267 | #41 | — | 4 | 2 | no | — |
| 268 | C2×Q8 | — | 2 | 2 | no | — |
| 269 | C2×D4 | — | 2 | 2 | no | — |
| 270 | C2×D4 | — | 4 | 2 | no | — |
| 271 | C22×C4 | — | 2 | 1 | no | — |
| 272 | C22×C4 | — | 4 | 2 | no | — |
| 273 | C22×C4 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 274 | Q16 | — | 2 | 2 | no | — |
| 275 | Q16 | C22×C3⋊C8 | 1 | 4 | yes | — |
| 276 | SD16 | — | 2 | 4 | no | — |
| 277 | SD16 | — | 2 | 4 | no | — |
| 278 | D8 | — | 2 | 2 | no | — |
| 279 | D8 | C22×C3⋊C8 | 1 | 4 | yes | — |
| 280 | M16 | — | 2 | 4 | no | — |
| 281 | M16 | — | 4 | 2 | no | — |
| 282 | M16 | — | 4 | 4 | no | — |
| 283 | M16 | — | 4 | 4 | no | — |
| 284 | C2×C8 | — | 4 | 2 | no | — |
| 285 | C2×C8 | — | 4 | 4 | no | — |
| 286 | C2×C8 | — | 4 | 4 | no | — |
| 287 | C2×C8 | — | 12 | 2 | no | — |
| 288 | C2×C8 | — | 24 | 2 | no | — |
| 289 | C2×C8 | #911 | 1 | 2 | yes | — |
| 290 | C2×C8 | #911 | 1 | 2 | yes | — |
| 291 | C2×C8 | C22×C3⋊C8 | 1 | 2 | yes | — |
| 292 | C2×C8 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 294 | C2×C8 | #948 | 1 | 2 | yes | — |
| 295 | C2×C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 296 | C2×C8 | C23×Dic3 | 1 | 1 | yes | characteristic |
| 297 | C42 | — | 2 | 1 | no | — |
| 298 | C42 | D4×Dic3 | 1 | 1 | yes | characteristic |
| 299 | C42 | C2×#237 | 1 | 1 | yes | characteristic |
| 300 | C16 | — | 2 | 2 | no | — |
| 301 | C16 | — | 6 | 4 | no | — |
| 302 | C16 | — | 12 | 4 | no | — |
| 303 | C16 | C22×C3⋊C8 | 1 | 4 | yes | — |
| 304 | C22×C3 | — | 4 | 1 | no | — |
| 305 | C22×C3 | — | 4 | 4 | no | — |
| 306 | C22×C3 | — | 16 | 2 | no | — |
| 307 | C22×C3 | #1580 | 1 | 2 | yes | — |
| 308 | C22×C3 | C2×#444 | 1 | 1 | yes | characteristic |
| 309 | C3×C4 | — | 2 | 2 | no | — |
| 310 | C3×C4 | — | 4 | 1 | no | — |
| 311 | C3×C4 | — | 4 | 4 | no | — |
| 312 | C3×C4 | #1580 | 1 | 2 | yes | — |
| 313 | C3×C4 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 314 | C3×C4 | C2×#442 | 1 | 1 | yes | characteristic |
| 315 | C23 | — | 4 | 2 | no | — |
| 316 | C23 | #5197 | 1 | 1 | yes | characteristic |
| 317 | Q8 | — | 2 | 4 | no | — |
| 318 | Q8 | — | 4 | 2 | no | — |
| 319 | D4 | — | 2 | 4 | no | — |
| 320 | D4 | — | 4 | 4 | no | — |
| 321 | D4 | — | 4 | 4 | no | — |
| 322 | D4 | — | 4 | 2 | no | — |
| 323 | C2×C4 | — | 2 | 1 | no | — |
| 324 | C2×C4 | — | 2 | 1 | no | — |
| 325 | C2×C4 | — | 4 | 2 | no | — |
| 326 | C2×C4 | — | 4 | 2 | no | — |
| 327 | C2×C4 | — | 4 | 4 | no | — |
| 328 | C2×C4 | — | 4 | 4 | no | — |
| 329 | C2×C4 | D4×C3⋊C8 | 1 | 2 | yes | — |
| 330 | C2×C4 | #5152 | 1 | 2 | yes | — |
| 331 | C2×C4 | #5197 | 1 | 1 | yes | characteristic |
| 332 | C2×C4 | C2×D4×Dic3 | 1 | 1 | yes | characteristic |
| 333 | C8 | — | 4 | 4 | no | — |
| 334 | C8 | — | 24 | 2 | no | — |
| 335 | C8 | D4×C3⋊C8 | 1 | 2 | yes | — |
| 336 | C8 | #5152 | 1 | 1 | yes | characteristic |
| 337 | C8 | #5152 | 1 | 1 | yes | characteristic |
| 338 | C8 | C2×#911 | 1 | 2 | yes | — |
| 339 | C8 | C23×C3⋊C8 | 1 | 1 | yes | characteristic |
| 340 | C8 | C2×#948 | 1 | 1 | yes | characteristic |
| 341 | C2×C3 | — | 2 | 1 | no | — |
| 342 | C2×C3 | — | 2 | 2 | no | — |
| 343 | C2×C3 | — | 8 | 4 | no | — |
| 344 | C2×C3 | C2×#1580 | 1 | 1 | yes | characteristic |
| 345 | C22 | — | 4 | 1 | no | — |
| 346 | C22 | — | 4 | 4 | no | — |
| 347 | C22 | — | 16 | 2 | no | — |
| 348 | C22 | #70878 | 1 | 2 | yes | — |
| 349 | C22 | C2×#5197 | 1 | 1 | yes | characteristic |
| 350 | C4 | — | 2 | 2 | no | — |
| 351 | C4 | — | 4 | 1 | no | — |
| 352 | C4 | — | 4 | 4 | no | — |
| 353 | C4 | #70878 | 1 | 2 | yes | — |
| 354 | C4 | C2×D4×C3⋊C8 | 1 | 1 | yes | characteristic |
| 355 | C4 | C2×#5152 | 1 | 1 | yes | characteristic |
| 356 | C3 | #483600 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 357 | C2 | — | 2 | 1 | no | — |
| 358 | C2 | — | 2 | 2 | no | — |
| 359 | C2 | — | 8 | 4 | no | — |
| 360 | C2 | C2×#70878 | 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