← #72225831
Subgroups — #72225831
Order 1536.
962 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #10948601 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #10948443 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10706949 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10706944 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10706783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#67441 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C3×C8×M32 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #483512 | — | 3 | 1 | no | maximal, Sylow |
| 9 | #82009 | C4 | 1 | 1 | yes | characteristic |
| 10 | #82007 | — | 2 | 2 | no | — |
| 11 | C2×#4700 | C22 | 1 | 2 | yes | — |
| 12 | C3×C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×C4×M32 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C3×C82 | C22 | 1 | 1 | yes | characteristic |
| 15 | #71448 | C4 | 1 | 2 | yes | — |
| 16 | #71437 | — | 2 | 2 | no | — |
| 17 | #71429 | C4 | 1 | 1 | yes | characteristic |
| 18 | C2×#4463 | C22 | 1 | 2 | yes | — |
| 19 | #69085 | C4 | 1 | 4 | yes | — |
| 20 | #69076 | — | 2 | 4 | no | — |
| 21 | #69067 | C22 | 1 | 4 | yes | — |
| 22 | #69056 | C22 | 1 | 8 | yes | complemented |
| 23 | C3×#1311 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×C8×C16 | C22 | 1 | 2 | yes | complemented |
| 25 | #67502 | C22 | 1 | 4 | yes | complemented |
| 26 | #67441 | C22 | 1 | 4 | yes | complemented |
| 27 | #67441 | C22 | 1 | 4 | yes | complemented |
| 28 | #33463 | — | 3 | 1 | no | — |
| 29 | #33443 | — | 3 | 2 | no | — |
| 30 | #12047 | — | 3 | 4 | no | — |
| 31 | #12046 | — | 3 | 4 | no | — |
| 32 | #12011 | — | 3 | 1 | no | — |
| 33 | C2×#1335 | — | 3 | 2 | no | — |
| 34 | C8×M32 | D3 | 1 | 1 | yes | characteristic, complemented |
| 35 | C2×#904 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×#901 | — | 2 | 2 | no | — |
| 37 | C2×C3×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | C2×C3×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 39 | C2×C3×M32 | D4 | 1 | 1 | yes | characteristic |
| 40 | C2×C3×M32 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C3×C4×C8 | — | 2 | 1 | no | — |
| 42 | C2×C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 43 | C2×#819 | C2×C4 | 1 | 2 | yes | — |
| 44 | C2×#812 | — | 2 | 2 | no | — |
| 45 | C2×#805 | — | 2 | 2 | no | — |
| 46 | #4909 | C8 | 1 | 4 | yes | complemented |
| 47 | #4908 | C8 | 1 | 4 | yes | complemented |
| 48 | #4907 | — | 4 | 4 | no | — |
| 49 | D3×M32 | — | 4 | 4 | no | — |
| 50 | #4904 | C2×C4 | 1 | 4 | yes | — |
| 51 | #4901 | — | 2 | 8 | no | — |
| 52 | #4700 | — | 2 | 2 | no | — |
| 53 | #4700 | — | 2 | 2 | no | — |
| 54 | #4700 | C2×C4 | 1 | 4 | yes | — |
| 55 | #4700 | C23 | 1 | 4 | yes | — |
| 56 | C3×#346 | C2×C4 | 1 | 2 | yes | — |
| 57 | C3×#346 | D4 | 1 | 2 | yes | — |
| 58 | C3×C4×C16 | C23 | 1 | 2 | yes | — |
| 59 | C3×C4×C16 | C23 | 1 | 2 | yes | — |
| 60 | C3×C82 | — | 2 | 1 | no | — |
| 61 | C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 62 | C3×C82 | C23 | 1 | 1 | yes | characteristic |
| 63 | #4510 | C2×C4 | 1 | 8 | yes | — |
| 64 | #4508 | — | 2 | 8 | no | — |
| 65 | #4506 | C2×C4 | 1 | 4 | yes | — |
| 66 | #4463 | — | 2 | 2 | no | — |
| 67 | #4463 | C23 | 1 | 4 | yes | — |
| 68 | #3414 | — | 3 | 1 | no | — |
| 69 | #3407 | — | 6 | 2 | no | — |
| 70 | C2×#443 | — | 3 | 2 | no | — |
| 71 | #2179 | — | 3 | 4 | no | — |
| 72 | #2178 | — | 3 | 4 | no | — |
| 73 | #2171 | — | 6 | 4 | no | — |
| 74 | #2170 | — | 3 | 8 | no | — |
| 75 | #2161 | — | 3 | 1 | no | — |
| 76 | C2×#364 | — | 3 | 2 | no | — |
| 77 | #2143 | — | 3 | 2 | no | — |
| 78 | #2117 | — | 6 | 2 | no | — |
| 79 | C4×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 80 | C4×M32 | C2×D3 | 1 | 1 | yes | characteristic |
| 81 | C2×C82 | C2×D3 | 1 | 1 | yes | characteristic |
| 82 | #1373 | — | 3 | 4 | no | — |
| 83 | #1335 | — | 3 | 4 | no | — |
| 84 | #1335 | — | 3 | 4 | no | — |
| 85 | #1311 | C2×D3 | 1 | 2 | yes | complemented |
| 86 | C8×C16 | C2×D3 | 1 | 2 | yes | complemented |
| 87 | C2×#235 | — | 2 | 2 | no | — |
| 88 | C22×C3×C8 | — | 2 | 2 | no | — |
| 89 | C22×C3×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 90 | C22×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 91 | C2×C3×C42 | #41 | 1 | 1 | yes | characteristic |
| 92 | C2×#208 | — | 2 | 2 | no | — |
| 93 | C2×Dic12 | C2×C8 | 1 | 2 | yes | — |
| 94 | #904 | — | 2 | 2 | no | — |
| 95 | #904 | — | 2 | 2 | no | — |
| 96 | #904 | C2×C8 | 1 | 4 | yes | — |
| 97 | #904 | C22×C4 | 1 | 4 | yes | — |
| 98 | C2×D24 | C2×C8 | 1 | 2 | yes | — |
| 99 | C2×#204 | — | 2 | 2 | no | — |
| 100 | #901 | — | 2 | 4 | no | — |
| 101 | #901 | — | 2 | 4 | no | — |
| 102 | #901 | — | 4 | 2 | no | — |
| 103 | #901 | — | 4 | 2 | no | — |
| 104 | C2×ΓL(1,𝔽25) | — | 4 | 2 | no | — |
| 105 | C2×D3×C8 | — | 4 | 2 | no | — |
| 106 | C3×M32 | — | 2 | 2 | no | — |
| 107 | C3×M32 | — | 2 | 2 | no | — |
| 108 | C3×M32 | C2×C8 | 1 | 4 | yes | — |
| 109 | C3×M32 | D8 | 1 | 4 | yes | — |
| 110 | C2×C3×C16 | C22×C4 | 1 | 2 | yes | — |
| 111 | C2×C3×C16 | C22×C4 | 1 | 2 | yes | — |
| 112 | C2×C3×C16 | C2×D4 | 1 | 2 | yes | — |
| 113 | C2×C3×C16 | C2×D4 | 1 | 2 | yes | — |
| 114 | C3×C4×C8 | — | 2 | 2 | no | — |
| 115 | C3×C4×C8 | — | 2 | 1 | no | — |
| 116 | C3×C4×C8 | — | 2 | 1 | no | — |
| 117 | C3×C4×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 118 | C3×C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C3×C4×C8 | #41 | 1 | 1 | yes | characteristic |
| 120 | C3×C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 121 | #819 | — | 2 | 2 | no | — |
| 122 | #819 | C22×C4 | 1 | 4 | yes | — |
| 123 | #812 | — | 2 | 4 | no | — |
| 124 | #812 | — | 4 | 2 | no | — |
| 125 | C2×C3⋊C16 | — | 4 | 2 | no | — |
| 126 | #805 | — | 2 | 4 | no | — |
| 127 | #805 | — | 2 | 4 | no | — |
| 128 | Dic24 | C2×C8 | 1 | 4 | yes | complemented |
| 129 | #800 | C2×C8 | 1 | 8 | yes | complemented |
| 130 | D48 | C2×C8 | 1 | 4 | yes | complemented |
| 131 | #798 | — | 4 | 8 | no | — |
| 132 | D3×C16 | — | 4 | 8 | no | — |
| 133 | C2×#135 | — | 3 | 2 | no | — |
| 134 | C2×#131 | — | 6 | 2 | no | — |
| 135 | #510 | — | 3 | 4 | no | — |
| 136 | #509 | — | 3 | 4 | no | — |
| 137 | #508 | — | 3 | 4 | no | — |
| 138 | #504 | — | 6 | 8 | no | — |
| 139 | #504 | — | 12 | 4 | no | — |
| 140 | C2×M32 | — | 6 | 2 | no | — |
| 141 | C2×M32 | — | 12 | 4 | no | — |
| 142 | C2×M32 | C4×D3 | 1 | 1 | yes | characteristic |
| 143 | C2×M32 | C4×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×M32 | D12 | 1 | 1 | yes | characteristic |
| 145 | C2×M32 | D12 | 1 | 1 | yes | characteristic |
| 146 | #443 | — | 3 | 4 | no | — |
| 147 | #443 | — | 3 | 4 | no | — |
| 148 | #443 | — | 6 | 2 | no | — |
| 149 | #443 | — | 6 | 2 | no | — |
| 150 | C2×#108 | — | 3 | 2 | no | — |
| 151 | C2×#104 | — | 6 | 2 | no | — |
| 152 | C2×C4×C8 | — | 2 | 1 | no | — |
| 153 | C2×C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 154 | #368 | — | 3 | 4 | no | — |
| 155 | #364 | — | 3 | 4 | no | — |
| 156 | #364 | — | 6 | 2 | no | — |
| 157 | #359 | — | 3 | 8 | no | — |
| 158 | #350 | — | 6 | 8 | no | — |
| 159 | #346 | C4×D3 | 1 | 2 | yes | — |
| 160 | #346 | D12 | 1 | 2 | yes | — |
| 161 | C4×C16 | C22×D3 | 1 | 2 | yes | — |
| 162 | C4×C16 | C22×D3 | 1 | 2 | yes | — |
| 163 | C82 | — | 2 | 1 | no | — |
| 164 | C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 165 | C82 | C22×D3 | 1 | 1 | yes | characteristic |
| 166 | C22×C3×C4 | — | 2 | 1 | no | — |
| 167 | C22×C3×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×#67 | — | 4 | 2 | no | — |
| 169 | #235 | — | 2 | 4 | no | — |
| 170 | #235 | — | 2 | 4 | no | — |
| 171 | #235 | — | 4 | 2 | no | — |
| 172 | #235 | — | 4 | 2 | no | — |
| 173 | C2×D12 | — | 2 | 2 | no | — |
| 174 | C2×C4×D3 | — | 4 | 2 | no | — |
| 175 | C2×Dic6 | — | 2 | 2 | no | — |
| 176 | C2×C3×C8 | — | 2 | 2 | no | — |
| 177 | C2×C3×C8 | — | 2 | 2 | no | — |
| 178 | C2×C3×C8 | — | 4 | 4 | no | — |
| 179 | C2×C3×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C3×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 181 | C2×C3×C8 | C22×C8 | 1 | 2 | yes | — |
| 182 | C2×C3×C8 | #131 | 1 | 2 | yes | — |
| 183 | C2×C3×C8 | C2×D8 | 1 | 2 | yes | — |
| 184 | C2×C3×C8 | #135 | 1 | 2 | yes | — |
| 185 | C2×C3×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 186 | C2×C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 187 | C3×C42 | — | 2 | 1 | no | — |
| 188 | C3×C42 | C4×D4 | 1 | 1 | yes | characteristic |
| 189 | C3×C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 190 | #208 | — | 2 | 4 | no | — |
| 191 | #208 | — | 4 | 2 | no | — |
| 192 | C2×C3⋊C8 | — | 4 | 2 | no | — |
| 193 | Dic12 | — | 2 | 2 | no | — |
| 194 | Dic12 | C22×C8 | 1 | 4 | yes | — |
| 195 | D24 | — | 2 | 2 | no | — |
| 196 | D24 | C22×C8 | 1 | 4 | yes | — |
| 197 | #204 | — | 2 | 4 | no | — |
| 198 | #204 | — | 2 | 4 | no | — |
| 199 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 200 | ΓL(1,𝔽25) | — | 4 | 4 | no | — |
| 201 | D3×C8 | — | 4 | 4 | no | — |
| 202 | D3×C8 | — | 4 | 4 | no | — |
| 203 | C3×C16 | — | 2 | 2 | no | — |
| 204 | C3×C16 | — | 2 | 2 | no | — |
| 205 | C3×C16 | C22×C8 | 1 | 4 | yes | — |
| 206 | C3×C16 | C2×D8 | 1 | 4 | yes | — |
| 207 | C3⋊C16 | — | 4 | 4 | no | — |
| 208 | C2×#41 | — | 6 | 2 | no | — |
| 209 | #135 | — | 3 | 4 | no | — |
| 210 | #135 | — | 3 | 4 | no | — |
| 211 | #135 | — | 6 | 2 | no | — |
| 212 | #135 | — | 6 | 2 | no | — |
| 213 | C2×Q16 | — | 3 | 2 | no | — |
| 214 | C2×SD16 | — | 6 | 2 | no | — |
| 215 | C2×D8 | — | 3 | 2 | no | — |
| 216 | #131 | — | 6 | 4 | no | — |
| 217 | #131 | — | 6 | 4 | no | — |
| 218 | #131 | — | 12 | 2 | no | — |
| 219 | #131 | — | 12 | 2 | no | — |
| 220 | C2×M16 | — | 6 | 2 | no | — |
| 221 | C2×M16 | — | 12 | 2 | no | — |
| 222 | C22×C8 | — | 2 | 2 | no | — |
| 223 | C22×C8 | — | 12 | 2 | no | — |
| 224 | C22×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 225 | C22×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 226 | C2×C42 | #235 | 1 | 1 | yes | characteristic |
| 227 | Q32 | — | 3 | 4 | no | — |
| 228 | SD32 | — | 3 | 8 | no | — |
| 229 | D16 | — | 3 | 4 | no | — |
| 230 | M32 | — | 2 | 2 | no | — |
| 231 | M32 | — | 2 | 2 | no | — |
| 232 | M32 | — | 6 | 4 | no | — |
| 233 | M32 | — | 12 | 2 | no | — |
| 234 | M32 | — | 12 | 8 | no | — |
| 235 | M32 | D3×C8 | 1 | 4 | yes | — |
| 236 | M32 | D24 | 1 | 4 | yes | — |
| 237 | C2×C16 | — | 12 | 2 | no | — |
| 238 | C2×C16 | — | 12 | 8 | no | — |
| 239 | C2×C16 | C2×C4×D3 | 1 | 2 | yes | — |
| 240 | C2×C16 | C2×C4×D3 | 1 | 2 | yes | — |
| 241 | C2×C16 | C2×D12 | 1 | 2 | yes | — |
| 242 | C2×C16 | C2×D12 | 1 | 2 | yes | — |
| 243 | #108 | — | 3 | 4 | no | — |
| 244 | #108 | — | 6 | 2 | no | — |
| 245 | #104 | — | 6 | 4 | no | — |
| 246 | #104 | — | 6 | 4 | no | — |
| 247 | C4×C8 | — | 2 | 2 | no | — |
| 248 | C4×C8 | — | 2 | 1 | no | — |
| 249 | C4×C8 | — | 2 | 1 | no | — |
| 250 | C4×C8 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 251 | C4×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 252 | C4×C8 | #235 | 1 | 1 | yes | characteristic |
| 253 | C4×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 254 | C23×C3 | #443 | 1 | 1 | yes | characteristic |
| 255 | C22×D3 | — | 4 | 2 | no | — |
| 256 | C2×C3×C4 | — | 2 | 1 | no | — |
| 257 | C2×C3×C4 | — | 2 | 1 | no | — |
| 258 | C2×C3×C4 | — | 4 | 2 | no | — |
| 259 | C2×C3×C4 | C8×D4 | 1 | 2 | yes | — |
| 260 | C2×C3×C4 | C4×D8 | 1 | 2 | yes | — |
| 261 | C2×C3×C4 | #443 | 1 | 1 | yes | characteristic |
| 262 | C2×C3×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 263 | #67 | — | 4 | 4 | no | — |
| 264 | #67 | — | 4 | 4 | no | — |
| 265 | C2×Dic3 | — | 4 | 2 | no | — |
| 266 | D12 | — | 2 | 4 | no | — |
| 267 | D12 | — | 4 | 2 | no | — |
| 268 | C4×D3 | — | 4 | 4 | no | — |
| 269 | C4×D3 | — | 4 | 4 | no | — |
| 270 | Dic6 | — | 2 | 4 | no | — |
| 271 | Dic6 | — | 4 | 2 | no | — |
| 272 | C3×C8 | — | 2 | 4 | no | — |
| 273 | C3×C8 | — | 4 | 2 | no | — |
| 274 | C3×C8 | C8×D4 | 1 | 2 | yes | — |
| 275 | C3×C8 | C4×D8 | 1 | 2 | yes | — |
| 276 | C3×C8 | C23×C8 | 1 | 1 | yes | characteristic |
| 277 | C3×C8 | C2×#131 | 1 | 1 | yes | characteristic |
| 278 | C3×C8 | C22×D8 | 1 | 1 | yes | characteristic |
| 279 | C3×C8 | C2×#135 | 1 | 1 | yes | characteristic |
| 280 | C3⋊C8 | — | 4 | 4 | no | — |
| 281 | #41 | — | 6 | 4 | no | — |
| 282 | #41 | — | 6 | 4 | no | — |
| 283 | #41 | — | 12 | 2 | no | — |
| 284 | #41 | — | 12 | 2 | no | — |
| 285 | C2×Q8 | — | 6 | 2 | no | — |
| 286 | C2×D4 | — | 6 | 2 | no | — |
| 287 | C2×D4 | — | 12 | 2 | no | — |
| 288 | C22×C4 | — | 2 | 1 | no | — |
| 289 | C22×C4 | — | 12 | 2 | no | — |
| 290 | C22×C4 | C4×D12 | 1 | 1 | yes | characteristic |
| 291 | Q16 | — | 3 | 4 | no | — |
| 292 | Q16 | — | 6 | 2 | no | — |
| 293 | SD16 | — | 6 | 4 | no | — |
| 294 | SD16 | — | 6 | 4 | no | — |
| 295 | D8 | — | 3 | 4 | no | — |
| 296 | D8 | — | 6 | 2 | no | — |
| 297 | M16 | — | 6 | 4 | no | — |
| 298 | M16 | — | 12 | 2 | no | — |
| 299 | M16 | — | 12 | 4 | no | — |
| 300 | M16 | — | 12 | 4 | no | — |
| 301 | C2×C8 | — | 2 | 2 | no | — |
| 302 | C2×C8 | — | 2 | 2 | no | — |
| 303 | C2×C8 | — | 4 | 4 | no | — |
| 304 | C2×C8 | — | 12 | 2 | no | — |
| 305 | C2×C8 | — | 12 | 4 | no | — |
| 306 | C2×C8 | — | 12 | 4 | no | — |
| 307 | C2×C8 | C4×D12 | 1 | 1 | yes | characteristic |
| 308 | C2×C8 | C4×D12 | 1 | 1 | yes | characteristic |
| 309 | C2×C8 | C2×D3×C8 | 1 | 2 | yes | — |
| 310 | C2×C8 | #901 | 1 | 2 | yes | — |
| 311 | C2×C8 | C2×D24 | 1 | 2 | yes | — |
| 312 | C2×C8 | #904 | 1 | 2 | yes | — |
| 313 | C2×C8 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 314 | C2×C8 | C22×D12 | 1 | 1 | yes | characteristic |
| 315 | C42 | — | 2 | 1 | no | — |
| 316 | C42 | C4×D12 | 1 | 1 | yes | characteristic |
| 317 | C42 | C2×#235 | 1 | 1 | yes | characteristic |
| 318 | C16 | — | 2 | 2 | no | — |
| 319 | C16 | — | 2 | 2 | no | — |
| 320 | C16 | — | 12 | 4 | no | — |
| 321 | C16 | C2×D3×C8 | 1 | 4 | yes | — |
| 322 | C16 | C2×D24 | 1 | 4 | yes | — |
| 323 | C22×C3 | — | 4 | 1 | no | — |
| 324 | C22×C3 | C8×D8 | 1 | 2 | yes | — |
| 325 | C22×C3 | C2×#443 | 1 | 1 | yes | characteristic |
| 326 | C2×D3 | — | 4 | 4 | no | — |
| 327 | C2×D3 | — | 16 | 2 | no | — |
| 328 | C3×C4 | — | 2 | 2 | no | — |
| 329 | C3×C4 | — | 4 | 1 | no | — |
| 330 | C3×C4 | C8×D8 | 1 | 2 | yes | — |
| 331 | C3×C4 | C2×C8×D4 | 1 | 1 | yes | characteristic |
| 332 | C3×C4 | C2×C4×D8 | 1 | 1 | yes | characteristic |
| 333 | Dic3 | — | 4 | 4 | no | — |
| 334 | C23 | — | 12 | 2 | no | — |
| 335 | C23 | #4700 | 1 | 1 | yes | characteristic |
| 336 | Q8 | — | 6 | 4 | no | — |
| 337 | Q8 | — | 12 | 2 | no | — |
| 338 | D4 | — | 6 | 4 | no | — |
| 339 | D4 | — | 12 | 4 | no | — |
| 340 | D4 | — | 12 | 4 | no | — |
| 341 | D4 | — | 12 | 2 | no | — |
| 342 | C2×C4 | — | 2 | 1 | no | — |
| 343 | C2×C4 | — | 2 | 1 | no | — |
| 344 | C2×C4 | — | 4 | 2 | no | — |
| 345 | C2×C4 | — | 12 | 2 | no | — |
| 346 | C2×C4 | — | 12 | 4 | no | — |
| 347 | C2×C4 | — | 12 | 4 | no | — |
| 348 | C2×C4 | C8×D12 | 1 | 2 | yes | — |
| 349 | C2×C4 | C4×D24 | 1 | 2 | yes | — |
| 350 | C2×C4 | #4700 | 1 | 1 | yes | characteristic |
| 351 | C2×C4 | C2×C4×D12 | 1 | 1 | yes | characteristic |
| 352 | C8 | — | 2 | 4 | no | — |
| 353 | C8 | — | 4 | 2 | no | — |
| 354 | C8 | — | 12 | 4 | no | — |
| 355 | C8 | C8×D12 | 1 | 2 | yes | — |
| 356 | C8 | C4×D24 | 1 | 2 | yes | — |
| 357 | C8 | C22×D3×C8 | 1 | 1 | yes | characteristic |
| 358 | C8 | C2×#901 | 1 | 1 | yes | characteristic |
| 359 | C8 | C22×D24 | 1 | 1 | yes | characteristic |
| 360 | C8 | C2×#904 | 1 | 1 | yes | characteristic |
| 361 | C2×C3 | — | 2 | 1 | no | — |
| 362 | C2×C3 | — | 2 | 2 | no | — |
| 363 | C2×C3 | C2×C8×D8 | 1 | 1 | yes | characteristic |
| 364 | D3 | — | 8 | 4 | no | — |
| 365 | C22 | — | 4 | 1 | no | — |
| 366 | C22 | — | 12 | 4 | no | — |
| 367 | C22 | — | 48 | 2 | no | — |
| 368 | C22 | C8×D24 | 1 | 2 | yes | — |
| 369 | C22 | C2×#4700 | 1 | 1 | yes | characteristic |
| 370 | C4 | — | 2 | 2 | no | — |
| 371 | C4 | — | 4 | 1 | no | — |
| 372 | C4 | — | 12 | 4 | no | — |
| 373 | C4 | C8×D24 | 1 | 2 | yes | — |
| 374 | C4 | C2×C8×D12 | 1 | 1 | yes | characteristic |
| 375 | C4 | C2×C4×D24 | 1 | 1 | yes | characteristic |
| 376 | C3 | #483512 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 377 | C2 | — | 2 | 1 | no | — |
| 378 | C2 | — | 2 | 2 | no | — |
| 379 | C2 | — | 24 | 4 | no | — |
| 380 | C2 | C2×C8×D24 | 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