← #72228272
Subgroups — #72228272
Order 1536.
578 conjugacy classes of subgroups.
The subgroup lattice has 440 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10711613 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10711298 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #10711288 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #10706752 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10682363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10682359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C3×#33443 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #134947 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C3×#3407 | — | 2 | 1 | no | — |
| 10 | C2×C3×#443 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#2171 | — | 2 | 2 | no | — |
| 12 | C3×#2170 | C4 | 1 | 4 | yes | complemented |
| 13 | C2×C3×#364 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#2117 | — | 2 | 1 | no | — |
| 15 | C3×C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 16 | #72081 | — | 2 | 1 | no | — |
| 17 | C2×#4566 | — | 2 | 1 | no | — |
| 18 | C2×#4513 | — | 2 | 1 | no | — |
| 19 | C2×#4513 | — | 2 | 1 | no | — |
| 20 | #69792 | C22 | 1 | 1 | yes | characteristic |
| 21 | #69764 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#4463 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#4463 | C22 | 1 | 1 | yes | characteristic |
| 24 | #67731 | — | 2 | 1 | no | — |
| 25 | #67730 | — | 2 | 1 | no | — |
| 26 | #67514 | — | 2 | 2 | no | — |
| 27 | #33443 | D3 | 1 | 1 | yes | characteristic |
| 28 | #12903 | — | 3 | 1 | no | — |
| 29 | #12825 | — | 3 | 1 | no | — |
| 30 | #12823 | — | 3 | 1 | no | — |
| 31 | #12002 | — | 3 | 1 | no | — |
| 32 | #7270 | — | 3 | 1 | no | — |
| 33 | #7268 | — | 3 | 1 | no | — |
| 34 | C2×C3×#135 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×C3×#131 | — | 2 | 1 | no | — |
| 36 | C3×#504 | — | 2 | 4 | no | — |
| 37 | C3×#504 | — | 4 | 2 | no | — |
| 38 | C2×C3×M32 | — | 2 | 1 | no | — |
| 39 | C2×C3×M32 | — | 4 | 2 | no | — |
| 40 | C2×C3×M32 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C3×M32 | D4 | 1 | 1 | yes | characteristic |
| 42 | C3×#443 | — | 2 | 1 | no | — |
| 43 | C3×#443 | — | 2 | 1 | no | — |
| 44 | C3×#443 | C2×C4 | 1 | 2 | yes | — |
| 45 | C3×#443 | Q8 | 1 | 2 | yes | — |
| 46 | C2×C3×#108 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×C3×#104 | — | 2 | 1 | no | — |
| 48 | C2×C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×#819 | — | 2 | 1 | no | — |
| 50 | C2×#819 | — | 2 | 1 | no | — |
| 51 | C2×#817 | — | 2 | 1 | no | — |
| 52 | C2×#817 | — | 2 | 1 | no | — |
| 53 | C2×#812 | — | 2 | 1 | no | — |
| 54 | C2×#812 | — | 2 | 1 | no | — |
| 55 | #4935 | — | 2 | 1 | no | — |
| 56 | #4924 | — | 2 | 1 | no | — |
| 57 | C3×#364 | — | 2 | 1 | no | — |
| 58 | C3×#364 | C2×C4 | 1 | 2 | yes | — |
| 59 | C3×#350 | — | 2 | 4 | no | — |
| 60 | C3×#346 | D4 | 1 | 2 | yes | — |
| 61 | C3×C4×C16 | C2×C4 | 1 | 2 | yes | — |
| 62 | #4566 | — | 4 | 2 | no | — |
| 63 | #4565 | — | 4 | 1 | no | — |
| 64 | #4563 | — | 4 | 1 | no | — |
| 65 | #4513 | — | 4 | 2 | no | — |
| 66 | #4513 | — | 4 | 2 | no | — |
| 67 | #4463 | — | 2 | 1 | no | — |
| 68 | #4463 | — | 2 | 1 | no | — |
| 69 | #4463 | — | 2 | 1 | no | — |
| 70 | #4463 | — | 2 | 1 | no | — |
| 71 | #3407 | — | 2 | 1 | no | — |
| 72 | C2×#443 | C2×D3 | 1 | 1 | yes | characteristic |
| 73 | #2171 | — | 2 | 2 | no | — |
| 74 | #2170 | Dic3 | 1 | 4 | yes | complemented |
| 75 | C2×#365 | — | 6 | 1 | no | — |
| 76 | C2×#365 | — | 6 | 1 | no | — |
| 77 | C2×#364 | — | 3 | 1 | no | — |
| 78 | C2×#364 | — | 3 | 1 | no | — |
| 79 | C2×#364 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | #2148 | — | 6 | 1 | no | — |
| 81 | C2×#360 | — | 6 | 1 | no | — |
| 82 | #2117 | — | 2 | 1 | no | — |
| 83 | C4×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #1848 | — | 3 | 1 | no | — |
| 85 | #1844 | — | 3 | 1 | no | — |
| 86 | #1385 | — | 6 | 1 | no | — |
| 87 | #1383 | — | 6 | 1 | no | — |
| 88 | #1369 | — | 6 | 2 | no | — |
| 89 | C2×C3×#41 | — | 2 | 1 | no | — |
| 90 | C3×#135 | — | 2 | 1 | no | — |
| 91 | C3×#135 | — | 2 | 1 | no | — |
| 92 | C3×#135 | C4⋊C4 | 1 | 2 | yes | — |
| 93 | C3×#135 | SD16 | 1 | 2 | yes | — |
| 94 | C2×C3×Q16 | SD16 | 1 | 1 | yes | characteristic |
| 95 | C2×C3×SD16 | — | 2 | 1 | no | — |
| 96 | C2×C3×D8 | SD16 | 1 | 1 | yes | characteristic |
| 97 | C3×#131 | — | 2 | 2 | no | — |
| 98 | C3×#131 | — | 2 | 2 | no | — |
| 99 | C3×#131 | — | 4 | 1 | no | — |
| 100 | C3×#131 | — | 4 | 1 | no | — |
| 101 | C2×C3×M16 | — | 2 | 1 | no | — |
| 102 | C2×C3×M16 | — | 4 | 1 | no | — |
| 103 | C22×C3×C8 | — | 4 | 1 | no | — |
| 104 | C22×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 105 | C22×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 107 | C2×C4⋊Dic3 | — | 4 | 1 | no | — |
| 108 | C2×C4⋊Dic3 | — | 8 | 1 | no | — |
| 109 | C2×#208 | — | 4 | 1 | no | — |
| 110 | C3×M32 | — | 2 | 1 | no | — |
| 111 | C3×M32 | — | 2 | 1 | no | — |
| 112 | C3×M32 | — | 2 | 2 | no | — |
| 113 | C3×M32 | — | 4 | 1 | no | — |
| 114 | C3×M32 | — | 4 | 4 | no | — |
| 115 | C3×M32 | D8 | 1 | 2 | yes | — |
| 116 | C3×M32 | SD16 | 1 | 2 | yes | — |
| 117 | C2×C3×C16 | — | 4 | 1 | no | — |
| 118 | C2×C3×C16 | — | 4 | 4 | no | — |
| 119 | C2×C3×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 120 | C2×C3×C16 | C22⋊C4 | 1 | 2 | yes | — |
| 121 | C3×#108 | — | 2 | 1 | no | — |
| 122 | C3×#108 | C4⋊C4 | 1 | 2 | yes | — |
| 123 | C3×#104 | — | 2 | 2 | no | — |
| 124 | C3×#104 | — | 2 | 2 | no | — |
| 125 | C3×C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 126 | C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C3×C4×C8 | C2×Q8 | 1 | 1 | yes | characteristic |
| 128 | C3×C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 129 | #819 | — | 4 | 1 | no | — |
| 130 | #819 | — | 4 | 1 | no | — |
| 131 | #819 | — | 4 | 1 | no | — |
| 132 | #819 | — | 4 | 1 | no | — |
| 133 | #817 | — | 4 | 1 | no | — |
| 134 | #817 | — | 4 | 1 | no | — |
| 135 | #817 | — | 4 | 1 | no | — |
| 136 | #817 | — | 4 | 1 | no | — |
| 137 | #812 | — | 4 | 1 | no | — |
| 138 | #812 | — | 4 | 1 | no | — |
| 139 | #812 | — | 4 | 1 | no | — |
| 140 | #812 | — | 4 | 1 | no | — |
| 141 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 142 | C2×C3⋊C16 | — | 4 | 1 | no | — |
| 143 | C4⋊(C3⋊C8) | — | 8 | 1 | no | — |
| 144 | C2×#135 | D12 | 1 | 1 | yes | characteristic |
| 145 | C2×#131 | — | 2 | 1 | no | — |
| 146 | #504 | — | 2 | 4 | no | — |
| 147 | #504 | — | 4 | 2 | no | — |
| 148 | C2×M32 | — | 2 | 1 | no | — |
| 149 | C2×M32 | — | 4 | 2 | no | — |
| 150 | C2×M32 | — | 6 | 1 | no | — |
| 151 | C2×M32 | — | 6 | 1 | no | — |
| 152 | C2×M32 | #67 | 1 | 1 | yes | characteristic |
| 153 | C2×M32 | #67 | 1 | 1 | yes | characteristic |
| 154 | #443 | — | 2 | 1 | no | — |
| 155 | #443 | — | 2 | 1 | no | — |
| 156 | #443 | Dic6 | 1 | 2 | yes | — |
| 157 | #443 | C2×Dic3 | 1 | 2 | yes | — |
| 158 | C2×#108 | — | 6 | 1 | no | — |
| 159 | C2×#108 | — | 6 | 1 | no | — |
| 160 | C2×#108 | D12 | 1 | 1 | yes | characteristic |
| 161 | C2×#106 | — | 6 | 1 | no | — |
| 162 | C2×#106 | — | 6 | 1 | no | — |
| 163 | #423 | — | 6 | 1 | no | — |
| 164 | C2×#104 | — | 2 | 1 | no | — |
| 165 | C2×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 166 | #384 | — | 6 | 1 | no | — |
| 167 | #365 | — | 12 | 2 | no | — |
| 168 | #365 | — | 12 | 2 | no | — |
| 169 | #364 | — | 2 | 1 | no | — |
| 170 | #364 | — | 6 | 1 | no | — |
| 171 | #364 | — | 6 | 1 | no | — |
| 172 | #364 | — | 6 | 1 | no | — |
| 173 | #364 | — | 6 | 1 | no | — |
| 174 | #364 | C2×Dic3 | 1 | 2 | yes | — |
| 175 | #362 | — | 12 | 1 | no | — |
| 176 | #361 | — | 12 | 1 | no | — |
| 177 | #360 | — | 12 | 2 | no | — |
| 178 | #350 | — | 2 | 4 | no | — |
| 179 | #346 | #67 | 1 | 2 | yes | — |
| 180 | C4×C16 | C2×Dic3 | 1 | 2 | yes | — |
| 181 | C3×#41 | — | 2 | 2 | no | — |
| 182 | C3×#41 | — | 2 | 2 | no | — |
| 183 | C3×#41 | — | 4 | 1 | no | — |
| 184 | C3×#41 | — | 4 | 1 | no | — |
| 185 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 186 | C2×C3×D4 | — | 2 | 1 | no | — |
| 187 | C2×C3×D4 | — | 4 | 1 | no | — |
| 188 | C22×C3×C4 | — | 2 | 1 | no | — |
| 189 | C22×C3×C4 | — | 4 | 1 | no | — |
| 190 | C22×C3×C4 | #121 | 1 | 1 | yes | characteristic |
| 191 | C22×Dic3 | — | 8 | 1 | no | — |
| 192 | C3×Q16 | — | 2 | 1 | no | — |
| 193 | C3×Q16 | #106 | 1 | 2 | yes | — |
| 194 | C3×SD16 | — | 2 | 2 | no | — |
| 195 | C3×SD16 | — | 2 | 2 | no | — |
| 196 | C3×D8 | — | 2 | 1 | no | — |
| 197 | C3×D8 | #106 | 1 | 2 | yes | — |
| 198 | C3×M16 | — | 2 | 2 | no | — |
| 199 | C3×M16 | — | 4 | 1 | no | — |
| 200 | C3×M16 | — | 4 | 2 | no | — |
| 201 | C3×M16 | — | 4 | 2 | no | — |
| 202 | C2×C3×C8 | — | 4 | 1 | no | — |
| 203 | C2×C3×C8 | — | 4 | 2 | no | — |
| 204 | C2×C3×C8 | — | 4 | 2 | no | — |
| 205 | C2×C3×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | C2×C3×C8 | C2×C4⋊C4 | 1 | 1 | yes | characteristic |
| 207 | C2×C3×C8 | #121 | 1 | 1 | yes | characteristic |
| 208 | C2×C3×C8 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 209 | C2×C3×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 211 | C2×C3×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 212 | C2×C3×C8 | C2×SD16 | 1 | 1 | yes | characteristic |
| 213 | C2×C3×C8 | #135 | 1 | 1 | yes | characteristic |
| 214 | C2×C3×C8 | #135 | 1 | 1 | yes | characteristic |
| 215 | C2×C3×C8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 216 | C2×C3×C8 | #137 | 1 | 1 | yes | characteristic |
| 217 | C3×C42 | — | 2 | 1 | no | — |
| 218 | C3×C42 | #117 | 1 | 1 | yes | characteristic |
| 219 | C3×C42 | C22⋊Q8 | 1 | 1 | yes | characteristic |
| 220 | C4⋊Dic3 | — | 8 | 1 | no | — |
| 221 | C4⋊Dic3 | — | 8 | 1 | no | — |
| 222 | C4⋊Dic3 | — | 16 | 2 | no | — |
| 223 | #208 | — | 8 | 1 | no | — |
| 224 | #208 | — | 8 | 1 | no | — |
| 225 | C2×C3⋊C8 | — | 8 | 1 | no | — |
| 226 | C3×C16 | — | 2 | 2 | no | — |
| 227 | C3×C16 | — | 4 | 2 | no | — |
| 228 | C3×C16 | #102 | 1 | 4 | yes | — |
| 229 | C3⋊C16 | — | 8 | 1 | no | — |
| 230 | C3⋊C16 | — | 8 | 1 | no | — |
| 231 | C2×#41 | — | 2 | 1 | no | — |
| 232 | #135 | — | 2 | 1 | no | — |
| 233 | #135 | — | 2 | 1 | no | — |
| 234 | #135 | #204 | 1 | 2 | yes | — |
| 235 | #135 | C4⋊Dic3 | 1 | 2 | yes | — |
| 236 | C2×Q16 | #204 | 1 | 1 | yes | characteristic |
| 237 | C2×SD16 | — | 2 | 1 | no | — |
| 238 | C2×D8 | #204 | 1 | 1 | yes | characteristic |
| 239 | #131 | — | 2 | 2 | no | — |
| 240 | #131 | — | 2 | 2 | no | — |
| 241 | #131 | — | 4 | 1 | no | — |
| 242 | #131 | — | 4 | 1 | no | — |
| 243 | C2×M16 | — | 2 | 1 | no | — |
| 244 | C2×M16 | — | 4 | 1 | no | — |
| 245 | C2×M16 | — | 12 | 1 | no | — |
| 246 | C22×C8 | — | 4 | 1 | no | — |
| 247 | C22×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 248 | C22×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 249 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 250 | C2×C4⋊C4 | — | 24 | 1 | no | — |
| 251 | C2×C42 | #235 | 1 | 1 | yes | characteristic |
| 252 | M32 | — | 2 | 1 | no | — |
| 253 | M32 | — | 2 | 1 | no | — |
| 254 | M32 | — | 2 | 2 | no | — |
| 255 | M32 | — | 4 | 1 | no | — |
| 256 | M32 | — | 4 | 4 | no | — |
| 257 | M32 | — | 12 | 1 | no | — |
| 258 | M32 | — | 12 | 1 | no | — |
| 259 | M32 | — | 12 | 1 | no | — |
| 260 | M32 | — | 12 | 1 | no | — |
| 261 | M32 | #213 | 1 | 2 | yes | — |
| 262 | M32 | #214 | 1 | 2 | yes | — |
| 263 | C2×C16 | — | 4 | 1 | no | — |
| 264 | C2×C16 | — | 4 | 4 | no | — |
| 265 | C2×C16 | — | 12 | 1 | no | — |
| 266 | C2×C16 | — | 12 | 1 | no | — |
| 267 | C2×C16 | #217 | 1 | 2 | yes | — |
| 268 | C2×C16 | #217 | 1 | 2 | yes | — |
| 269 | #108 | — | 2 | 1 | no | — |
| 270 | #108 | — | 12 | 1 | no | — |
| 271 | #108 | — | 12 | 1 | no | — |
| 272 | #108 | — | 12 | 1 | no | — |
| 273 | #108 | — | 12 | 1 | no | — |
| 274 | #108 | C4⋊Dic3 | 1 | 2 | yes | — |
| 275 | #106 | — | 12 | 1 | no | — |
| 276 | #106 | — | 12 | 1 | no | — |
| 277 | #106 | — | 12 | 1 | no | — |
| 278 | #106 | — | 12 | 1 | no | — |
| 279 | C4⋊C8 | — | 24 | 1 | no | — |
| 280 | #104 | — | 2 | 2 | no | — |
| 281 | #104 | — | 2 | 2 | no | — |
| 282 | C4×C8 | C2×Dic6 | 1 | 1 | yes | characteristic |
| 283 | C4×C8 | #235 | 1 | 1 | yes | characteristic |
| 284 | C4×C8 | C22×Dic3 | 1 | 1 | yes | characteristic |
| 285 | C4×C8 | C2×#67 | 1 | 1 | yes | characteristic |
| 286 | C23×C3 | — | 4 | 1 | no | — |
| 287 | C23×C3 | #471 | 1 | 1 | yes | characteristic |
| 288 | C3×Q8 | — | 2 | 2 | no | — |
| 289 | C3×Q8 | — | 4 | 1 | no | — |
| 290 | C3×D4 | — | 2 | 2 | no | — |
| 291 | C3×D4 | — | 4 | 2 | no | — |
| 292 | C3×D4 | — | 4 | 2 | no | — |
| 293 | C3×D4 | — | 4 | 1 | no | — |
| 294 | C2×C3×C4 | — | 2 | 1 | no | — |
| 295 | C2×C3×C4 | — | 2 | 1 | no | — |
| 296 | C2×C3×C4 | — | 4 | 2 | no | — |
| 297 | C2×C3×C4 | — | 4 | 1 | no | — |
| 298 | C2×C3×C4 | — | 4 | 2 | no | — |
| 299 | C2×C3×C4 | — | 4 | 2 | no | — |
| 300 | C2×C3×C4 | #380 | 1 | 1 | yes | characteristic |
| 301 | C2×C3×C4 | #459 | 1 | 1 | yes | characteristic |
| 302 | C2×C3×C4 | #461 | 1 | 1 | yes | characteristic |
| 303 | C2×C3×C4 | #465 | 1 | 1 | yes | characteristic |
| 304 | C2×C3×C4 | #465 | 1 | 1 | yes | characteristic |
| 305 | C2×C3×C4 | #471 | 1 | 1 | yes | characteristic |
| 306 | C2×Dic3 | — | 16 | 2 | no | — |
| 307 | C2×Dic3 | — | 16 | 1 | no | — |
| 308 | C3×C8 | — | 4 | 2 | no | — |
| 309 | C3×C8 | C2×#102 | 1 | 1 | yes | characteristic |
| 310 | C3×C8 | #417 | 1 | 1 | yes | characteristic |
| 311 | C3×C8 | C2×#106 | 1 | 1 | yes | characteristic |
| 312 | C3×C8 | #427 | 1 | 1 | yes | characteristic |
| 313 | C3×C8 | #465 | 1 | 1 | yes | characteristic |
| 314 | C3×C8 | #465 | 1 | 1 | yes | characteristic |
| 315 | C3×C8 | #474 | 1 | 1 | yes | characteristic |
| 316 | C3×C8 | #476 | 1 | 1 | yes | characteristic |
| 317 | C3⋊C8 | — | 16 | 1 | no | — |
| 318 | #41 | — | 2 | 2 | no | — |
| 319 | #41 | — | 2 | 2 | no | — |
| 320 | #41 | — | 4 | 1 | no | — |
| 321 | #41 | — | 4 | 1 | no | — |
| 322 | C2×Q8 | — | 2 | 1 | no | — |
| 323 | C2×D4 | — | 2 | 1 | no | — |
| 324 | C2×D4 | — | 4 | 1 | no | — |
| 325 | C22×C4 | — | 2 | 1 | no | — |
| 326 | C22×C4 | — | 4 | 1 | no | — |
| 327 | C22×C4 | — | 24 | 1 | no | — |
| 328 | C22×C4 | #930 | 1 | 1 | yes | characteristic |
| 329 | Q16 | — | 2 | 1 | no | — |
| 330 | Q16 | #817 | 1 | 2 | yes | — |
| 331 | SD16 | — | 2 | 2 | no | — |
| 332 | SD16 | — | 2 | 2 | no | — |
| 333 | D8 | — | 2 | 1 | no | — |
| 334 | D8 | #817 | 1 | 2 | yes | — |
| 335 | M16 | — | 2 | 2 | no | — |
| 336 | M16 | — | 4 | 1 | no | — |
| 337 | M16 | — | 4 | 2 | no | — |
| 338 | M16 | — | 4 | 2 | no | — |
| 339 | M16 | — | 24 | 1 | no | — |
| 340 | M16 | — | 24 | 1 | no | — |
| 341 | C2×C8 | — | 4 | 1 | no | — |
| 342 | C2×C8 | — | 4 | 2 | no | — |
| 343 | C2×C8 | — | 4 | 2 | no | — |
| 344 | C2×C8 | — | 24 | 1 | no | — |
| 345 | C2×C8 | C2×#204 | 1 | 1 | yes | characteristic |
| 346 | C2×C8 | C2×#204 | 1 | 1 | yes | characteristic |
| 347 | C2×C8 | #904 | 1 | 1 | yes | characteristic |
| 348 | C2×C8 | #904 | 1 | 1 | yes | characteristic |
| 349 | C2×C8 | #924 | 1 | 1 | yes | characteristic |
| 350 | C2×C8 | C2×C4⋊Dic3 | 1 | 1 | yes | characteristic |
| 351 | C2×C8 | #930 | 1 | 1 | yes | characteristic |
| 352 | C2×C8 | C2×#213 | 1 | 1 | yes | characteristic |
| 353 | C2×C8 | C2×#214 | 1 | 1 | yes | characteristic |
| 354 | C2×C8 | #949 | 1 | 1 | yes | characteristic |
| 355 | C2×C8 | #951 | 1 | 1 | yes | characteristic |
| 356 | C2×C8 | C2×#217 | 1 | 1 | yes | characteristic |
| 357 | C4⋊C4 | — | 24 | 1 | no | — |
| 358 | C4⋊C4 | — | 24 | 1 | no | — |
| 359 | C4⋊C4 | — | 48 | 2 | no | — |
| 360 | C42 | — | 2 | 1 | no | — |
| 361 | C42 | #924 | 1 | 1 | yes | characteristic |
| 362 | C42 | #926 | 1 | 1 | yes | characteristic |
| 363 | C16 | — | 2 | 2 | no | — |
| 364 | C16 | — | 4 | 2 | no | — |
| 365 | C16 | — | 24 | 1 | no | — |
| 366 | C16 | — | 24 | 1 | no | — |
| 367 | C16 | #832 | 1 | 4 | yes | — |
| 368 | C22×C3 | — | 4 | 1 | no | — |
| 369 | C22×C3 | — | 4 | 2 | no | — |
| 370 | C22×C3 | — | 16 | 1 | no | — |
| 371 | C22×C3 | #1665 | 1 | 1 | yes | characteristic |
| 372 | C22×C3 | #1671 | 1 | 1 | yes | characteristic |
| 373 | C22×C3 | #1815 | 1 | 1 | yes | characteristic |
| 374 | C3×C4 | — | 2 | 2 | no | — |
| 375 | C3×C4 | — | 4 | 1 | no | — |
| 376 | C3×C4 | — | 4 | 2 | no | — |
| 377 | C3×C4 | #1665 | 1 | 1 | yes | characteristic |
| 378 | C3×C4 | #1671 | 1 | 1 | yes | characteristic |
| 379 | C3×C4 | #1802 | 1 | 1 | yes | characteristic |
| 380 | C3×C4 | #1807 | 1 | 1 | yes | characteristic |
| 381 | Dic3 | — | 32 | 1 | no | — |
| 382 | C23 | — | 4 | 1 | no | — |
| 383 | C23 | #5141 | 1 | 1 | yes | characteristic |
| 384 | Q8 | — | 2 | 2 | no | — |
| 385 | Q8 | — | 4 | 1 | no | — |
| 386 | D4 | — | 2 | 2 | no | — |
| 387 | D4 | — | 4 | 2 | no | — |
| 388 | D4 | — | 4 | 2 | no | — |
| 389 | D4 | — | 4 | 1 | no | — |
| 390 | C2×C4 | — | 2 | 1 | no | — |
| 391 | C2×C4 | — | 2 | 1 | no | — |
| 392 | C2×C4 | — | 4 | 2 | no | — |
| 393 | C2×C4 | — | 4 | 1 | no | — |
| 394 | C2×C4 | — | 4 | 2 | no | — |
| 395 | C2×C4 | — | 4 | 2 | no | — |
| 396 | C2×C4 | — | 48 | 2 | no | — |
| 397 | C2×C4 | — | 48 | 1 | no | — |
| 398 | C2×C4 | #5015 | 1 | 1 | yes | characteristic |
| 399 | C2×C4 | #5019 | 1 | 1 | yes | characteristic |
| 400 | C2×C4 | #5114 | 1 | 1 | yes | characteristic |
| 401 | C2×C4 | #5114 | 1 | 1 | yes | characteristic |
| 402 | C2×C4 | #5141 | 1 | 1 | yes | characteristic |
| 403 | C2×C4 | #5212 | 1 | 1 | yes | characteristic |
| 404 | C8 | — | 4 | 2 | no | — |
| 405 | C8 | — | 48 | 1 | no | — |
| 406 | C8 | #5007 | 1 | 1 | yes | characteristic |
| 407 | C8 | #5008 | 1 | 1 | yes | characteristic |
| 408 | C8 | C2×#817 | 1 | 1 | yes | characteristic |
| 409 | C8 | #5106 | 1 | 1 | yes | characteristic |
| 410 | C8 | #5114 | 1 | 1 | yes | characteristic |
| 411 | C8 | #5114 | 1 | 1 | yes | characteristic |
| 412 | C8 | C2×#832 | 1 | 1 | yes | characteristic |
| 413 | C8 | #5232 | 1 | 1 | yes | characteristic |
| 414 | C2×C3 | — | 2 | 1 | no | — |
| 415 | C2×C3 | — | 2 | 1 | no | — |
| 416 | C2×C3 | — | 2 | 1 | no | — |
| 417 | C2×C3 | — | 8 | 2 | no | — |
| 418 | C2×C3 | #8642 | 1 | 1 | yes | characteristic |
| 419 | C22 | — | 4 | 1 | no | — |
| 420 | C22 | — | 4 | 2 | no | — |
| 421 | C22 | — | 16 | 1 | no | — |
| 422 | C22 | #70846 | 1 | 1 | yes | characteristic |
| 423 | C22 | #70851 | 1 | 1 | yes | characteristic |
| 424 | C22 | #72015 | 1 | 1 | yes | characteristic |
| 425 | C4 | — | 2 | 2 | no | — |
| 426 | C4 | — | 4 | 1 | no | — |
| 427 | C4 | — | 4 | 2 | no | — |
| 428 | C4 | — | 96 | 1 | no | — |
| 429 | C4 | #70846 | 1 | 1 | yes | characteristic |
| 430 | C4 | #70851 | 1 | 1 | yes | characteristic |
| 431 | C4 | #71604 | 1 | 1 | yes | characteristic |
| 432 | C4 | #71970 | 1 | 1 | yes | characteristic |
| 433 | C3 | #134947 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 434 | C2 | — | 2 | 1 | no | — |
| 435 | C2 | — | 2 | 1 | no | — |
| 436 | C2 | — | 2 | 1 | no | — |
| 437 | C2 | — | 8 | 2 | no | — |
| 438 | C2 | #10688231 | 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