Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1494 conjugacy classes of subgroups.
The subgroup lattice has 426 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#901 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5115 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4865 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #74030 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C3×#1807 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70578 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #69517 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #68883 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #32939 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 11 | C23×C3×C8 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#930 | C22 | 1 | 2 | yes | — |
| 13 | C22×#208 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×D24 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#901 | — | 2 | 4 | no | — |
| 16 | C2×#901 | — | 2 | 8 | no | — |
| 17 | C22×ΓL(1,𝔽25) | C22 | 1 | 2 | yes | — |
| 18 | C22×D3×C8 | C22 | 1 | 2 | yes | — |
| 19 | C2×#895 | C22 | 1 | 4 | yes | — |
| 20 | C2×C3×#106 | C22 | 1 | 2 | yes | — |
| 21 | C3×#380 | C22 | 1 | 2 | yes | — |
| 22 | #5115 | — | 2 | 4 | no | — |
| 23 | C2×#821 | C22 | 1 | 2 | yes | — |
| 24 | C2×#818 | C22 | 1 | 1 | yes | characteristic |
| 25 | #4987 | C22 | 1 | 4 | yes | — |
| 26 | C2×#809 | C22 | 1 | 4 | yes | — |
| 27 | #4960 | — | 2 | 4 | no | — |
| 28 | #4865 | — | 2 | 8 | no | — |
| 29 | #4673 | — | 2 | 2 | no | — |
| 30 | #4671 | — | 2 | 2 | no | — |
| 31 | C3×#340 | C22 | 1 | 2 | yes | — |
| 32 | #4529 | C22 | 1 | 4 | yes | — |
| 33 | C22×#131 | — | 3 | 1 | no | — |
| 34 | C2×#469 | — | 3 | 2 | no | — |
| 35 | C2×#466 | — | 3 | 1 | no | — |
| 36 | #2615 | — | 3 | 2 | no | — |
| 37 | #1895 | — | 3 | 2 | no | — |
| 38 | #1893 | — | 3 | 4 | no | — |
| 39 | #1809 | — | 3 | 2 | no | — |
| 40 | #1807 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 42 | C22×#67 | — | 2 | 2 | no | — |
| 43 | C22×#67 | D4 | 1 | 2 | yes | — |
| 44 | C2×#235 | — | 2 | 2 | no | — |
| 45 | C2×#235 | — | 2 | 2 | no | — |
| 46 | C2×#235 | — | 2 | 4 | no | — |
| 47 | C2×#235 | — | 2 | 4 | no | — |
| 48 | C22×D12 | — | 2 | 4 | no | — |
| 49 | C22×D12 | D4 | 1 | 1 | yes | characteristic |
| 50 | C22×D12 | C23 | 1 | 2 | yes | — |
| 51 | C22×C4×D3 | C23 | 1 | 2 | yes | — |
| 52 | C22×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×C3×C8 | — | 2 | 4 | no | — |
| 54 | C22×C3×C8 | D4 | 1 | 4 | yes | complemented |
| 55 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 57 | C2×C3×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 58 | C2×C3×C22⋊C4 | — | 2 | 2 | no | — |
| 59 | #930 | — | 2 | 4 | no | — |
| 60 | #930 | — | 2 | 4 | no | — |
| 61 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 62 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 63 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 64 | C2×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 65 | C2×#208 | — | 2 | 2 | no | — |
| 66 | C2×#208 | — | 2 | 4 | no | — |
| 67 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 68 | C2×D24 | — | 2 | 4 | no | — |
| 69 | C2×D24 | — | 2 | 2 | no | — |
| 70 | #901 | — | 2 | 32 | no | — |
| 71 | C2×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 72 | C2×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 73 | C2×ΓL(1,𝔽25) | D4 | 1 | 8 | yes | complemented |
| 74 | C2×D3×C8 | — | 2 | 4 | no | — |
| 75 | C2×D3×C8 | — | 2 | 4 | no | — |
| 76 | C2×D3×C8 | — | 2 | 4 | no | — |
| 77 | #895 | — | 2 | 8 | no | — |
| 78 | #895 | — | 2 | 8 | no | — |
| 79 | C3×#106 | — | 2 | 4 | no | — |
| 80 | C3×#95 | — | 2 | 2 | no | — |
| 81 | C3⋊#95 | — | 2 | 4 | no | — |
| 82 | #821 | — | 2 | 4 | no | — |
| 83 | #818 | — | 2 | 2 | no | — |
| 84 | #809 | — | 2 | 8 | no | — |
| 85 | C22×#41 | — | 3 | 1 | no | — |
| 86 | C22×D8 | — | 3 | 1 | no | — |
| 87 | C2×#131 | — | 6 | 8 | no | — |
| 88 | C2×#131 | — | 6 | 4 | no | — |
| 89 | C22×M16 | — | 3 | 1 | no | — |
| 90 | C22×M16 | — | 3 | 2 | no | — |
| 91 | C23×C8 | — | 3 | 2 | no | — |
| 92 | C23×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | C2×#121 | — | 3 | 2 | no | — |
| 94 | C2×#121 | — | 3 | 4 | no | — |
| 95 | #469 | — | 6 | 8 | no | — |
| 96 | #466 | — | 6 | 4 | no | — |
| 97 | C2×#107 | — | 3 | 1 | no | — |
| 98 | C2×#106 | C2×D3 | 1 | 2 | yes | — |
| 99 | C2×#102 | — | 3 | 2 | no | — |
| 100 | C2×#102 | — | 3 | 4 | no | — |
| 101 | #393 | — | 6 | 2 | no | — |
| 102 | #392 | — | 6 | 2 | no | — |
| 103 | #392 | — | 6 | 4 | no | — |
| 104 | #380 | — | 3 | 4 | no | — |
| 105 | #380 | C2×D3 | 1 | 2 | yes | — |
| 106 | #340 | — | 3 | 4 | no | — |
| 107 | #340 | C2×D3 | 1 | 2 | yes | — |
| 108 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C23×D3 | — | 2 | 2 | no | — |
| 110 | C23×D3 | C2×D4 | 1 | 2 | yes | — |
| 111 | C22×C3×C4 | — | 2 | 2 | no | — |
| 112 | C22×C3×C4 | — | 2 | 2 | no | — |
| 113 | C22×C3×C4 | — | 2 | 4 | no | — |
| 114 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 115 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×C3×C4 | #41 | 1 | 2 | yes | — |
| 117 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 118 | C2×#67 | — | 2 | 4 | no | — |
| 119 | C2×#67 | — | 2 | 4 | no | — |
| 120 | C2×#67 | — | 2 | 4 | no | — |
| 121 | C2×#67 | — | 4 | 4 | no | — |
| 122 | C2×#67 | — | 8 | 4 | no | — |
| 123 | C22×Dic3 | — | 2 | 2 | no | — |
| 124 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 125 | #235 | — | 2 | 8 | no | — |
| 126 | #235 | — | 2 | 16 | no | — |
| 127 | #235 | — | 2 | 8 | no | — |
| 128 | C2×D12 | — | 2 | 4 | no | — |
| 129 | C2×D12 | — | 2 | 2 | no | — |
| 130 | C2×D12 | — | 2 | 4 | no | — |
| 131 | C2×D12 | — | 2 | 2 | no | — |
| 132 | C2×D12 | — | 2 | 4 | no | — |
| 133 | C2×D12 | — | 2 | 2 | no | — |
| 134 | C2×D12 | — | 4 | 8 | no | — |
| 135 | C2×D12 | — | 8 | 4 | no | — |
| 136 | C2×D12 | — | 8 | 4 | no | — |
| 137 | C2×C4×D3 | — | 2 | 2 | no | — |
| 138 | C2×C4×D3 | — | 2 | 2 | no | — |
| 139 | C2×C4×D3 | — | 2 | 2 | no | — |
| 140 | C2×C4×D3 | — | 2 | 2 | no | — |
| 141 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 142 | C2×C4×D3 | #41 | 1 | 4 | yes | — |
| 143 | C2×Dic6 | — | 2 | 2 | no | — |
| 144 | C2×Dic6 | — | 2 | 4 | no | — |
| 145 | C2×C3×C8 | — | 2 | 2 | no | — |
| 146 | C2×C3×C8 | — | 2 | 8 | no | — |
| 147 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 148 | C2×C3×C8 | C2×D4 | 1 | 2 | yes | — |
| 149 | C2×C3×C8 | C2×D4 | 1 | 4 | yes | — |
| 150 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 151 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 152 | C3×C22⋊C4 | — | 8 | 2 | no | — |
| 153 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 154 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 155 | (C2×D3)⋊C4 | — | 8 | 4 | no | — |
| 156 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 157 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 158 | #208 | — | 2 | 8 | no | — |
| 159 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 160 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 161 | C2×C3⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 162 | D24 | — | 4 | 4 | no | — |
| 163 | ΓL(1,𝔽25) | — | 2 | 16 | no | — |
| 164 | D3×C8 | — | 2 | 16 | no | — |
| 165 | C2×#41 | — | 6 | 4 | no | — |
| 166 | C2×#41 | — | 6 | 4 | no | — |
| 167 | C2×#41 | — | 6 | 2 | no | — |
| 168 | C2×#41 | — | 6 | 2 | no | — |
| 169 | C22×Q8 | — | 3 | 1 | no | — |
| 170 | C22×D4 | — | 3 | 2 | no | — |
| 171 | C22×D4 | — | 3 | 1 | no | — |
| 172 | C22×D4 | — | 3 | 2 | no | — |
| 173 | C22×D4 | — | 6 | 4 | no | — |
| 174 | C22×D4 | — | 6 | 2 | no | — |
| 175 | C23×C4 | — | 3 | 2 | no | — |
| 176 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 177 | C2×D8 | — | 6 | 2 | no | — |
| 178 | C2×D8 | — | 6 | 4 | no | — |
| 179 | #131 | — | 6 | 32 | no | — |
| 180 | C2×M16 | — | 3 | 8 | no | — |
| 181 | C2×M16 | — | 6 | 4 | no | — |
| 182 | C2×M16 | — | 6 | 2 | no | — |
| 183 | C2×M16 | — | 6 | 4 | no | — |
| 184 | C2×M16 | — | 6 | 4 | no | — |
| 185 | C22×C8 | — | 2 | 4 | no | — |
| 186 | C22×C8 | — | 3 | 2 | no | — |
| 187 | C22×C8 | — | 6 | 4 | no | — |
| 188 | C22×C8 | — | 6 | 4 | no | — |
| 189 | C22×C8 | — | 6 | 4 | no | — |
| 190 | C22×C8 | D12 | 1 | 4 | yes | complemented |
| 191 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 192 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 193 | #121 | — | 6 | 8 | no | — |
| 194 | #121 | — | 6 | 8 | no | — |
| 195 | #121 | — | 6 | 4 | no | — |
| 196 | #121 | — | 6 | 4 | no | — |
| 197 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 198 | C2×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 199 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 200 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 201 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 202 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 203 | #107 | — | 6 | 2 | no | — |
| 204 | #106 | — | 2 | 4 | no | — |
| 205 | #102 | — | 6 | 8 | no | — |
| 206 | #102 | — | 6 | 4 | no | — |
| 207 | #95 | — | 2 | 2 | no | — |
| 208 | #95 | — | 6 | 4 | no | — |
| 209 | C23×C3 | — | 2 | 2 | no | — |
| 210 | C23×C3 | — | 2 | 2 | no | — |
| 211 | C23×C3 | — | 2 | 2 | no | — |
| 212 | C23×C3 | #121 | 1 | 2 | yes | — |
| 213 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | C22×D3 | — | 2 | 2 | no | — |
| 215 | C22×D3 | — | 2 | 2 | no | — |
| 216 | C22×D3 | — | 2 | 4 | no | — |
| 217 | C22×D3 | — | 2 | 4 | no | — |
| 218 | C22×D3 | — | 4 | 4 | no | — |
| 219 | C22×D3 | — | 4 | 2 | no | — |
| 220 | C22×D3 | — | 4 | 4 | no | — |
| 221 | C22×D3 | — | 4 | 2 | no | — |
| 222 | C22×D3 | — | 4 | 2 | no | — |
| 223 | C22×D3 | #121 | 1 | 4 | yes | — |
| 224 | C2×C3×C4 | — | 2 | 2 | no | — |
| 225 | C2×C3×C4 | — | 2 | 2 | no | — |
| 226 | C2×C3×C4 | — | 2 | 2 | no | — |
| 227 | C2×C3×C4 | — | 2 | 4 | no | — |
| 228 | C2×C3×C4 | — | 4 | 4 | no | — |
| 229 | C2×C3×C4 | — | 4 | 4 | no | — |
| 230 | C2×C3×C4 | — | 4 | 4 | no | — |
| 231 | C2×C3×C4 | #121 | 1 | 2 | yes | — |
| 232 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 233 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 234 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 235 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 236 | #67 | — | 2 | 16 | no | — |
| 237 | #67 | — | 8 | 8 | no | — |
| 238 | C2×Dic3 | — | 2 | 2 | no | — |
| 239 | C2×Dic3 | — | 2 | 2 | no | — |
| 240 | C2×Dic3 | — | 4 | 2 | no | — |
| 241 | C2×Dic3 | — | 4 | 4 | no | — |
| 242 | C2×Dic3 | #121 | 1 | 4 | yes | — |
| 243 | D12 | — | 2 | 8 | no | — |
| 244 | D12 | — | 4 | 2 | no | — |
| 245 | D12 | — | 4 | 2 | no | — |
| 246 | D12 | — | 4 | 4 | no | — |
| 247 | D12 | — | 8 | 16 | no | — |
| 248 | C4×D3 | — | 2 | 4 | no | — |
| 249 | C4×D3 | — | 2 | 4 | no | — |
| 250 | C4×D3 | — | 2 | 4 | no | — |
| 251 | C4×D3 | — | 2 | 4 | no | — |
| 252 | Dic6 | — | 2 | 8 | no | — |
| 253 | C3×C8 | — | 2 | 2 | no | — |
| 254 | C3×C8 | #120 | 1 | 4 | yes | — |
| 255 | C3⋊C8 | — | 2 | 4 | no | — |
| 256 | C24 | — | 3 | 2 | no | — |
| 257 | C24 | — | 6 | 2 | no | — |
| 258 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 259 | #41 | — | 6 | 8 | no | — |
| 260 | #41 | — | 6 | 8 | no | — |
| 261 | #41 | — | 6 | 16 | no | — |
| 262 | C2×Q8 | — | 6 | 4 | no | — |
| 263 | C2×Q8 | — | 6 | 2 | no | — |
| 264 | C2×D4 | — | 6 | 4 | no | — |
| 265 | C2×D4 | — | 6 | 4 | no | — |
| 266 | C2×D4 | — | 6 | 4 | no | — |
| 267 | C2×D4 | — | 6 | 4 | no | — |
| 268 | C2×D4 | — | 6 | 2 | no | — |
| 269 | C2×D4 | — | 6 | 2 | no | — |
| 270 | C2×D4 | — | 6 | 4 | no | — |
| 271 | C2×D4 | — | 6 | 2 | no | — |
| 272 | C2×D4 | — | 6 | 4 | no | — |
| 273 | C2×D4 | — | 12 | 8 | no | — |
| 274 | C2×D4 | — | 12 | 4 | no | — |
| 275 | C2×D4 | — | 24 | 4 | no | — |
| 276 | C2×D4 | — | 24 | 4 | no | — |
| 277 | C2×D4 | — | 24 | 4 | no | — |
| 278 | C22×C4 | — | 2 | 2 | no | — |
| 279 | C22×C4 | — | 2 | 2 | no | — |
| 280 | C22×C4 | — | 2 | 4 | no | — |
| 281 | C22×C4 | — | 3 | 2 | no | — |
| 282 | C22×C4 | — | 3 | 4 | no | — |
| 283 | C22×C4 | — | 3 | 4 | no | — |
| 284 | C22×C4 | — | 6 | 2 | no | — |
| 285 | C22×C4 | — | 6 | 2 | no | — |
| 286 | C22×C4 | — | 6 | 2 | no | — |
| 287 | C22×C4 | — | 6 | 2 | no | — |
| 288 | C22×C4 | — | 6 | 2 | no | — |
| 289 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 290 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | #239 | 1 | 2 | yes | — |
| 292 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 293 | D8 | — | 12 | 4 | no | — |
| 294 | M16 | — | 6 | 8 | no | — |
| 295 | M16 | — | 6 | 16 | no | — |
| 296 | C2×C8 | — | 2 | 2 | no | — |
| 297 | C2×C8 | — | 2 | 8 | no | — |
| 298 | C2×C8 | — | 3 | 4 | no | — |
| 299 | C2×C8 | — | 6 | 16 | no | — |
| 300 | C2×C8 | — | 6 | 2 | no | — |
| 301 | C2×C8 | — | 6 | 2 | no | — |
| 302 | C2×C8 | C2×D12 | 1 | 2 | yes | — |
| 303 | C2×C8 | C2×D12 | 1 | 2 | yes | — |
| 304 | C2×C8 | D3×D4 | 1 | 4 | yes | — |
| 305 | C4⋊C4 | — | 2 | 4 | no | — |
| 306 | C4⋊C4 | — | 2 | 4 | no | — |
| 307 | C4⋊C4 | — | 6 | 2 | no | — |
| 308 | C4⋊C4 | — | 6 | 2 | no | — |
| 309 | C22⋊C4 | — | 8 | 2 | no | — |
| 310 | C22⋊C4 | — | 12 | 8 | no | — |
| 311 | C22⋊C4 | — | 12 | 4 | no | — |
| 312 | C22⋊C4 | — | 24 | 4 | no | — |
| 313 | C22×C3 | — | 2 | 2 | no | — |
| 314 | C22×C3 | — | 2 | 2 | no | — |
| 315 | C22×C3 | — | 2 | 2 | no | — |
| 316 | C22×C3 | — | 4 | 4 | no | — |
| 317 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 318 | C22×C3 | C2×#121 | 1 | 2 | yes | — |
| 319 | C22×C3 | #576 | 1 | 2 | yes | — |
| 320 | C22×C3 | #577 | 1 | 2 | yes | — |
| 321 | C2×D3 | — | 2 | 4 | no | — |
| 322 | C2×D3 | — | 2 | 8 | no | — |
| 323 | C2×D3 | — | 4 | 2 | no | — |
| 324 | C2×D3 | — | 4 | 2 | no | — |
| 325 | C2×D3 | — | 4 | 4 | no | — |
| 326 | C2×D3 | — | 8 | 2 | no | — |
| 327 | C2×D3 | — | 8 | 2 | no | — |
| 328 | C2×D3 | — | 8 | 2 | no | — |
| 329 | C2×D3 | — | 8 | 4 | no | — |
| 330 | C2×D3 | — | 8 | 4 | no | — |
| 331 | C3×C4 | — | 2 | 2 | no | — |
| 332 | C3×C4 | — | 8 | 4 | no | — |
| 333 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 334 | C3×C4 | #525 | 1 | 1 | yes | characteristic |
| 335 | C3×C4 | #525 | 1 | 2 | yes | — |
| 336 | Dic3 | — | 2 | 4 | no | — |
| 337 | Dic3 | — | 8 | 2 | no | — |
| 338 | C23 | — | 2 | 2 | no | — |
| 339 | C23 | — | 2 | 2 | no | — |
| 340 | C23 | — | 2 | 2 | no | — |
| 341 | C23 | — | 3 | 4 | no | — |
| 342 | C23 | — | 6 | 2 | no | — |
| 343 | C23 | — | 6 | 4 | no | — |
| 344 | C23 | — | 6 | 4 | no | — |
| 345 | C23 | — | 6 | 2 | no | — |
| 346 | C23 | — | 12 | 2 | no | — |
| 347 | C23 | — | 12 | 2 | no | — |
| 348 | C23 | — | 12 | 2 | no | — |
| 349 | C23 | — | 12 | 4 | no | — |
| 350 | C23 | — | 12 | 4 | no | — |
| 351 | C23 | #895 | 1 | 2 | yes | — |
| 352 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 353 | Q8 | — | 6 | 8 | no | — |
| 354 | D4 | — | 6 | 8 | no | — |
| 355 | D4 | — | 6 | 16 | no | — |
| 356 | D4 | — | 12 | 2 | no | — |
| 357 | D4 | — | 12 | 2 | no | — |
| 358 | D4 | — | 12 | 4 | no | — |
| 359 | D4 | — | 24 | 16 | no | — |
| 360 | D4 | — | 24 | 8 | no | — |
| 361 | C2×C4 | — | 2 | 2 | no | — |
| 362 | C2×C4 | — | 2 | 2 | no | — |
| 363 | C2×C4 | — | 2 | 2 | no | — |
| 364 | C2×C4 | — | 2 | 4 | no | — |
| 365 | C2×C4 | — | 3 | 4 | no | — |
| 366 | C2×C4 | — | 4 | 4 | no | — |
| 367 | C2×C4 | — | 4 | 4 | no | — |
| 368 | C2×C4 | — | 4 | 4 | no | — |
| 369 | C2×C4 | — | 6 | 2 | no | — |
| 370 | C2×C4 | — | 6 | 2 | no | — |
| 371 | C2×C4 | — | 6 | 4 | no | — |
| 372 | C2×C4 | — | 6 | 4 | no | — |
| 373 | C2×C4 | — | 6 | 4 | no | — |
| 374 | C2×C4 | — | 6 | 4 | no | — |
| 375 | C2×C4 | — | 12 | 2 | no | — |
| 376 | C2×C4 | — | 12 | 4 | no | — |
| 377 | C2×C4 | #895 | 1 | 2 | yes | — |
| 378 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 380 | C2×C4 | C2×#239 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | D3×#41 | 1 | 2 | yes | — |
| 382 | C8 | — | 2 | 2 | no | — |
| 383 | C8 | — | 6 | 4 | no | — |
| 384 | C8 | #882 | 1 | 4 | yes | — |
| 385 | C2×C3 | — | 4 | 2 | no | — |
| 386 | C2×C3 | #2847 | 1 | 1 | yes | characteristic |
| 387 | C2×C3 | #3058 | 1 | 1 | yes | characteristic |
| 388 | C2×C3 | #3060 | 1 | 1 | yes | characteristic |
| 389 | C2×C3 | #3062 | 1 | 4 | yes | — |
| 390 | D3 | — | 4 | 4 | no | — |
| 391 | D3 | — | 16 | 2 | no | — |
| 392 | C22 | — | 2 | 2 | no | — |
| 393 | C22 | — | 2 | 2 | no | — |
| 394 | C22 | — | 2 | 2 | no | — |
| 395 | C22 | — | 4 | 4 | no | — |
| 396 | C22 | — | 6 | 8 | no | — |
| 397 | C22 | — | 6 | 4 | no | — |
| 398 | C22 | — | 12 | 2 | no | — |
| 399 | C22 | — | 12 | 4 | no | — |
| 400 | C22 | — | 12 | 2 | no | — |
| 401 | C22 | — | 24 | 2 | no | — |
| 402 | C22 | — | 24 | 4 | no | — |
| 403 | C22 | — | 24 | 4 | no | — |
| 404 | C22 | — | 24 | 2 | no | — |
| 405 | C22 | — | 24 | 2 | no | — |
| 406 | C22 | C2×#895 | 1 | 1 | yes | characteristic |
| 407 | C22 | D3×#121 | 1 | 2 | yes | — |
| 408 | C22 | #5762 | 1 | 2 | yes | — |
| 409 | C22 | #5769 | 1 | 2 | yes | — |
| 410 | C4 | — | 2 | 2 | no | — |
| 411 | C4 | — | 6 | 4 | no | — |
| 412 | C4 | — | 8 | 4 | no | — |
| 413 | C4 | — | 24 | 2 | no | — |
| 414 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 415 | C4 | #5524 | 1 | 1 | yes | characteristic |
| 416 | C4 | #5627 | 1 | 2 | yes | — |
| 417 | C3 | #32939 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 418 | C2 | — | 4 | 2 | no | — |
| 419 | C2 | — | 12 | 4 | no | — |
| 420 | C2 | — | 48 | 2 | no | — |
| 421 | C2 | #74048 | 1 | 1 | yes | characteristic |
| 422 | C2 | #79120 | 1 | 1 | yes | characteristic |
| 423 | C2 | #79183 | 1 | 1 | yes | characteristic |
| 424 | C2 | #80661 | 1 | 4 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#901 | C2 | semidirect |
| 2. C2×#5115 | C2 | semidirect |
| 3. C2×#4865 | C2 | semidirect |
| 4. #74030 | C2 | semidirect |
| 5. C3×#1807 | C2 | semidirect |
| 6. #70578 | C2 | semidirect |
| 7. #69517 | C2 | semidirect |
| 8. #68883 | C2 | semidirect |
| 40. #1807 | D3 | semidirect |
| 54. C22×C3×C8 | D4 | semidirect |
| 73. C2×ΓL(1,𝔽25) | D4 | semidirect |
| 190. C22×C8 | D12 | semidirect |
| 417. C3 | #32939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#901 | 2 |
| C2×#5115 | 2 |
| C2×#4865 | 2 |
| #74030 | 2 |
| C3×#1807 | 2 |
| #70578 | 2 |
| #69517 | 2 |
| #68883 | 2 |
| #32939 | 3 |