Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1386 conjugacy classes of subgroups.
The subgroup lattice has 422 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5525 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#2921 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #82209 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #70523 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #70521 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #69989 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #69988 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #69878 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #69876 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #21801 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C22×#235 | C22 | 1 | 1 | yes | characteristic |
| 12 | C23×D12 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C3×#117 | C22 | 1 | 1 | yes | characteristic |
| 14 | #5525 | — | 2 | 4 | no | — |
| 15 | #5525 | — | 2 | 4 | no | — |
| 16 | C2×#895 | C4 | 1 | 4 | yes | — |
| 17 | C2×#882 | C4 | 1 | 4 | yes | — |
| 18 | C2×#875 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#875 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#433 | — | 2 | 4 | no | — |
| 23 | C3×#423 | C22 | 1 | 2 | yes | complemented |
| 24 | C3×#407 | C22 | 1 | 2 | yes | — |
| 25 | C3×C4×M16 | C22 | 1 | 2 | yes | complemented |
| 26 | #5207 | C22 | 1 | 2 | yes | — |
| 27 | C2×#824 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#823 | C22 | 1 | 4 | yes | — |
| 29 | C2×#823 | C22 | 1 | 4 | yes | — |
| 30 | C2×#823 | C22 | 1 | 4 | yes | complemented |
| 31 | #5000 | — | 2 | 4 | no | — |
| 32 | #4924 | C22 | 1 | 2 | yes | complemented |
| 33 | C4×#208 | C22 | 1 | 2 | yes | complemented |
| 34 | C2×#535 | — | 3 | 1 | no | — |
| 35 | #2921 | — | 3 | 1 | no | — |
| 36 | #2921 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #1967 | — | 3 | 2 | no | — |
| 38 | #1967 | — | 3 | 2 | no | — |
| 39 | #1965 | — | 3 | 2 | no | — |
| 40 | #1965 | — | 3 | 2 | no | — |
| 41 | #1785 | — | 3 | 2 | no | — |
| 42 | #1783 | — | 3 | 2 | no | — |
| 43 | C24×D3 | C2×C4 | 1 | 2 | yes | — |
| 44 | C23×C3×C4 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×#67 | C2×C4 | 1 | 2 | yes | — |
| 46 | C2×#235 | — | 2 | 2 | no | — |
| 47 | C2×#235 | — | 2 | 2 | no | — |
| 48 | C2×#235 | — | 4 | 4 | no | — |
| 49 | C22×D12 | — | 2 | 2 | no | — |
| 50 | C22×D12 | — | 2 | 2 | no | — |
| 51 | C22×D12 | — | 4 | 4 | no | — |
| 52 | C22×D12 | C2×C4 | 1 | 2 | yes | — |
| 53 | C22×D12 | C2×C4 | 1 | 4 | yes | — |
| 54 | C22×D12 | C2×C4 | 1 | 4 | yes | — |
| 55 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×D3 | C2×C4 | 1 | 2 | yes | — |
| 59 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×C3×M16 | C23 | 1 | 4 | yes | — |
| 61 | C3×#117 | D4 | 1 | 4 | yes | — |
| 62 | C3×#117 | D4 | 1 | 4 | yes | — |
| 63 | C2×C3×C4⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 64 | C2×C3×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 65 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×(C2×D3)⋊C4 | C2×C4 | 1 | 4 | yes | — |
| 68 | C2×(C2×D3)⋊C4 | C2×C4 | 1 | 4 | yes | — |
| 69 | C2×#208 | C23 | 1 | 4 | yes | — |
| 70 | #895 | — | 2 | 16 | no | — |
| 71 | #882 | — | 2 | 16 | no | — |
| 72 | #875 | — | 2 | 2 | no | — |
| 73 | #875 | — | 2 | 2 | no | — |
| 74 | #875 | — | 2 | 2 | no | — |
| 75 | #875 | — | 2 | 2 | no | — |
| 76 | #874 | — | 2 | 2 | no | — |
| 77 | #874 | — | 2 | 2 | no | — |
| 78 | #874 | — | 2 | 2 | no | — |
| 79 | #874 | — | 2 | 2 | no | — |
| 80 | C3×C4⋊C8 | — | 2 | 4 | no | — |
| 81 | C3×C22⋊C8 | — | 2 | 4 | no | — |
| 82 | C3×#97 | — | 2 | 2 | no | — |
| 83 | C3×C4×C8 | — | 2 | 2 | no | — |
| 84 | #830 | — | 2 | 4 | no | — |
| 85 | #824 | — | 4 | 4 | no | — |
| 86 | #823 | — | 4 | 4 | no | — |
| 87 | #823 | — | 4 | 4 | no | — |
| 88 | #823 | — | 4 | 4 | no | — |
| 89 | C4⋊(C3⋊C8) | — | 2 | 4 | no | — |
| 90 | #803 | — | 2 | 2 | no | — |
| 91 | C4×C3⋊C8 | — | 2 | 2 | no | — |
| 92 | C22×#41 | — | 3 | 1 | no | — |
| 93 | C23×D4 | — | 3 | 1 | no | — |
| 94 | #535 | — | 6 | 4 | no | — |
| 95 | #535 | — | 6 | 4 | no | — |
| 96 | C2×#127 | — | 3 | 1 | no | — |
| 97 | C2×#127 | — | 3 | 1 | no | — |
| 98 | C2×#124 | — | 3 | 1 | no | — |
| 99 | C2×#124 | — | 3 | 1 | no | — |
| 100 | C2×#121 | — | 3 | 4 | no | — |
| 101 | C2×#120 | — | 3 | 4 | no | — |
| 102 | C2×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | #433 | — | 2 | 4 | no | — |
| 104 | #433 | — | 6 | 4 | no | — |
| 105 | #423 | — | 3 | 2 | no | — |
| 106 | #423 | C2×D3 | 1 | 2 | yes | complemented |
| 107 | C2×#101 | — | 3 | 4 | no | — |
| 108 | C2×#100 | — | 3 | 4 | no | — |
| 109 | C2×#100 | — | 3 | 4 | no | — |
| 110 | C2×#100 | — | 3 | 4 | no | — |
| 111 | #407 | — | 3 | 2 | no | — |
| 112 | #407 | C2×D3 | 1 | 2 | yes | — |
| 113 | C4×M16 | — | 3 | 2 | no | — |
| 114 | C4×M16 | C2×D3 | 1 | 2 | yes | complemented |
| 115 | C24×C3 | C22×C4 | 1 | 1 | yes | characteristic |
| 116 | C23×D3 | — | 2 | 4 | no | — |
| 117 | C23×D3 | — | 4 | 4 | no | — |
| 118 | C23×D3 | — | 8 | 4 | no | — |
| 119 | C23×D3 | C22×C4 | 1 | 2 | yes | — |
| 120 | C23×D3 | C22×C4 | 1 | 2 | yes | — |
| 121 | C23×D3 | C22×C4 | 1 | 2 | yes | — |
| 122 | C22×C3×C4 | — | 2 | 4 | no | — |
| 123 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 124 | C22×C3×C4 | C22×C4 | 1 | 2 | yes | — |
| 125 | C22×C3×C4 | C22×C4 | 1 | 2 | yes | — |
| 126 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 127 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 128 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 129 | C2×#67 | — | 2 | 4 | no | — |
| 130 | C2×#67 | — | 4 | 4 | no | — |
| 131 | C22×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 132 | #235 | — | 4 | 8 | no | — |
| 133 | #235 | — | 4 | 8 | no | — |
| 134 | C2×D12 | — | 2 | 4 | no | — |
| 135 | C2×D12 | — | 2 | 1 | no | — |
| 136 | C2×D12 | — | 2 | 1 | no | — |
| 137 | C2×D12 | — | 2 | 1 | no | — |
| 138 | C2×D12 | — | 2 | 1 | no | — |
| 139 | C2×D12 | — | 2 | 1 | no | — |
| 140 | C2×D12 | — | 2 | 1 | no | — |
| 141 | C2×D12 | — | 2 | 4 | no | — |
| 142 | C2×D12 | — | 2 | 4 | no | — |
| 143 | C2×D12 | — | 2 | 4 | no | — |
| 144 | C2×D12 | — | 2 | 8 | no | — |
| 145 | C2×D12 | — | 2 | 8 | no | — |
| 146 | C2×D12 | — | 4 | 4 | no | — |
| 147 | C2×D12 | — | 4 | 8 | no | — |
| 148 | C2×D12 | — | 4 | 8 | no | — |
| 149 | C2×D12 | — | 8 | 4 | no | — |
| 150 | C2×D12 | — | 8 | 4 | no | — |
| 151 | C2×C4×D3 | — | 2 | 4 | no | — |
| 152 | C2×C4×D3 | — | 4 | 4 | no | — |
| 153 | C2×Dic6 | — | 2 | 1 | no | — |
| 154 | C2×Dic6 | — | 2 | 1 | no | — |
| 155 | C2×Dic6 | — | 2 | 4 | no | — |
| 156 | C3×M16 | — | 2 | 4 | no | — |
| 157 | C3×M16 | — | 2 | 4 | no | — |
| 158 | C2×C3×C8 | — | 2 | 4 | no | — |
| 159 | C3×C4⋊C4 | C22⋊C4 | 1 | 8 | yes | — |
| 160 | C3×C22⋊C4 | C22⋊C4 | 1 | 8 | yes | — |
| 161 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 162 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 163 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 164 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 165 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 166 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 167 | #208 | — | 2 | 4 | no | — |
| 168 | #208 | — | 2 | 4 | no | — |
| 169 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 170 | C25 | — | 3 | 2 | no | — |
| 171 | C2×#41 | — | 6 | 2 | no | — |
| 172 | C2×#41 | — | 6 | 2 | no | — |
| 173 | C2×#41 | — | 12 | 4 | no | — |
| 174 | C22×Q8 | — | 3 | 1 | no | — |
| 175 | C22×D4 | — | 3 | 2 | no | — |
| 176 | C22×D4 | — | 3 | 2 | no | — |
| 177 | C22×D4 | — | 3 | 4 | no | — |
| 178 | C22×D4 | — | 3 | 4 | no | — |
| 179 | C22×D4 | — | 3 | 1 | no | — |
| 180 | C22×D4 | — | 3 | 1 | no | — |
| 181 | C22×D4 | — | 3 | 1 | no | — |
| 182 | C22×D4 | — | 6 | 2 | no | — |
| 183 | C22×D4 | — | 6 | 2 | no | — |
| 184 | C22×D4 | — | 12 | 4 | no | — |
| 185 | C23×C4 | — | 3 | 2 | no | — |
| 186 | C23×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 187 | C2×M16 | — | 3 | 4 | no | — |
| 188 | C2×M16 | C22×D3 | 1 | 4 | yes | — |
| 189 | #127 | — | 6 | 2 | no | — |
| 190 | #127 | — | 6 | 2 | no | — |
| 191 | #127 | — | 6 | 2 | no | — |
| 192 | #127 | — | 6 | 2 | no | — |
| 193 | #124 | — | 6 | 2 | no | — |
| 194 | #124 | — | 6 | 2 | no | — |
| 195 | #124 | — | 6 | 2 | no | — |
| 196 | #124 | — | 6 | 2 | no | — |
| 197 | #121 | — | 6 | 16 | no | — |
| 198 | #120 | — | 6 | 16 | no | — |
| 199 | #117 | D12 | 1 | 4 | yes | — |
| 200 | #117 | #67 | 1 | 4 | yes | — |
| 201 | C2×C4⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 202 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 203 | C2×C22⋊C4 | — | 3 | 4 | no | — |
| 204 | C2×C22⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 205 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 207 | C4⋊C8 | — | 2 | 4 | no | — |
| 208 | C4⋊C8 | — | 6 | 4 | no | — |
| 209 | #101 | — | 12 | 4 | no | — |
| 210 | #100 | — | 12 | 4 | no | — |
| 211 | #100 | — | 12 | 4 | no | — |
| 212 | #100 | — | 12 | 4 | no | — |
| 213 | C22⋊C8 | — | 2 | 4 | no | — |
| 214 | C22⋊C8 | — | 6 | 4 | no | — |
| 215 | #97 | — | 2 | 2 | no | — |
| 216 | #97 | — | 6 | 2 | no | — |
| 217 | C4×C8 | — | 2 | 2 | no | — |
| 218 | C4×C8 | — | 6 | 2 | no | — |
| 219 | C23×C3 | — | 2 | 2 | no | — |
| 220 | C23×C3 | — | 4 | 2 | no | — |
| 221 | C23×C3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 222 | C23×C3 | C23×C4 | 1 | 1 | yes | characteristic |
| 223 | C22×D3 | — | 2 | 2 | no | — |
| 224 | C22×D3 | — | 2 | 2 | no | — |
| 225 | C22×D3 | — | 2 | 2 | no | — |
| 226 | C22×D3 | — | 2 | 4 | no | — |
| 227 | C22×D3 | — | 2 | 4 | no | — |
| 228 | C22×D3 | — | 2 | 4 | no | — |
| 229 | C22×D3 | — | 4 | 8 | no | — |
| 230 | C22×D3 | — | 4 | 4 | no | — |
| 231 | C22×D3 | — | 4 | 4 | no | — |
| 232 | C22×D3 | — | 4 | 4 | no | — |
| 233 | C22×D3 | — | 8 | 8 | no | — |
| 234 | C22×D3 | — | 8 | 16 | no | — |
| 235 | C2×C3×C4 | — | 2 | 2 | no | — |
| 236 | C2×C3×C4 | — | 2 | 4 | no | — |
| 237 | C2×C3×C4 | — | 2 | 4 | no | — |
| 238 | C2×C3×C4 | — | 4 | 2 | no | — |
| 239 | C2×C3×C4 | — | 4 | 2 | no | — |
| 240 | C2×C3×C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 241 | C2×C3×C4 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 242 | C2×C3×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 243 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 245 | C2×C3×C4 | H(5,𝔽2) | 1 | 4 | yes | — |
| 246 | #67 | — | 4 | 8 | no | — |
| 247 | C2×Dic3 | — | 2 | 2 | no | — |
| 248 | C2×Dic3 | — | 2 | 4 | no | — |
| 249 | D12 | — | 4 | 8 | no | — |
| 250 | D12 | — | 4 | 2 | no | — |
| 251 | D12 | — | 4 | 2 | no | — |
| 252 | D12 | — | 4 | 2 | no | — |
| 253 | D12 | — | 4 | 2 | no | — |
| 254 | D12 | — | 4 | 2 | no | — |
| 255 | D12 | — | 4 | 2 | no | — |
| 256 | D12 | — | 8 | 8 | no | — |
| 257 | D12 | — | 8 | 8 | no | — |
| 258 | C4×D3 | — | 4 | 8 | no | — |
| 259 | Dic6 | — | 4 | 2 | no | — |
| 260 | Dic6 | — | 4 | 2 | no | — |
| 261 | C3×C8 | — | 4 | 4 | no | — |
| 262 | C3⋊C8 | — | 4 | 4 | no | — |
| 263 | C24 | — | 3 | 2 | no | — |
| 264 | C24 | — | 3 | 2 | no | — |
| 265 | C24 | — | 3 | 2 | no | — |
| 266 | C24 | — | 6 | 4 | no | — |
| 267 | C24 | — | 12 | 4 | no | — |
| 268 | C24 | — | 24 | 4 | no | — |
| 269 | C24 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 270 | #41 | — | 12 | 8 | no | — |
| 271 | #41 | — | 12 | 8 | no | — |
| 272 | C2×Q8 | — | 6 | 1 | no | — |
| 273 | C2×Q8 | — | 6 | 4 | no | — |
| 274 | C2×Q8 | — | 6 | 1 | no | — |
| 275 | C2×D4 | — | 6 | 4 | no | — |
| 276 | C2×D4 | — | 6 | 4 | no | — |
| 277 | C2×D4 | — | 6 | 8 | no | — |
| 278 | C2×D4 | — | 6 | 8 | no | — |
| 279 | C2×D4 | — | 6 | 1 | no | — |
| 280 | C2×D4 | — | 6 | 1 | no | — |
| 281 | C2×D4 | — | 6 | 1 | no | — |
| 282 | C2×D4 | — | 6 | 4 | no | — |
| 283 | C2×D4 | — | 6 | 4 | no | — |
| 284 | C2×D4 | — | 6 | 4 | no | — |
| 285 | C2×D4 | — | 6 | 1 | no | — |
| 286 | C2×D4 | — | 6 | 1 | no | — |
| 287 | C2×D4 | — | 6 | 1 | no | — |
| 288 | C2×D4 | — | 12 | 4 | no | — |
| 289 | C2×D4 | — | 12 | 8 | no | — |
| 290 | C2×D4 | — | 12 | 8 | no | — |
| 291 | C2×D4 | — | 12 | 4 | no | — |
| 292 | C2×D4 | — | 24 | 4 | no | — |
| 293 | C2×D4 | — | 24 | 4 | no | — |
| 294 | C22×C4 | — | 2 | 4 | no | — |
| 295 | C22×C4 | — | 3 | 2 | no | — |
| 296 | C22×C4 | — | 6 | 4 | no | — |
| 297 | C22×C4 | — | 12 | 4 | no | — |
| 298 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 299 | C22×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 300 | C22×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 301 | C22×C4 | C2×D12 | 1 | 2 | yes | — |
| 302 | C22×C4 | C2×#67 | 1 | 2 | yes | — |
| 303 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 304 | M16 | — | 2 | 4 | no | — |
| 305 | M16 | — | 2 | 4 | no | — |
| 306 | M16 | — | 6 | 4 | no | — |
| 307 | M16 | — | 6 | 4 | no | — |
| 308 | C2×C8 | — | 2 | 4 | no | — |
| 309 | C2×C8 | — | 6 | 4 | no | — |
| 310 | C4⋊C4 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 311 | C22⋊C4 | — | 6 | 8 | no | — |
| 312 | C22⋊C4 | — | 6 | 8 | no | — |
| 313 | C22⋊C4 | (C2×D3)⋊C4 | 1 | 8 | yes | — |
| 314 | C42 | C2×D12 | 1 | 2 | yes | — |
| 315 | C42 | C2×D12 | 1 | 2 | yes | — |
| 316 | C42 | C2×#67 | 1 | 2 | yes | — |
| 317 | C42 | C2×#67 | 1 | 2 | yes | — |
| 318 | C22×C3 | — | 2 | 2 | no | — |
| 319 | C22×C3 | — | 2 | 2 | no | — |
| 320 | C22×C3 | — | 2 | 4 | no | — |
| 321 | C22×C3 | — | 4 | 4 | no | — |
| 322 | C22×C3 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 323 | C22×C3 | #518 | 1 | 2 | yes | — |
| 324 | C2×D3 | — | 4 | 2 | no | — |
| 325 | C2×D3 | — | 4 | 2 | no | — |
| 326 | C2×D3 | — | 4 | 2 | no | — |
| 327 | C2×D3 | — | 4 | 4 | no | — |
| 328 | C2×D3 | — | 4 | 4 | no | — |
| 329 | C2×D3 | — | 4 | 4 | no | — |
| 330 | C2×D3 | — | 8 | 16 | no | — |
| 331 | C2×D3 | — | 8 | 4 | no | — |
| 332 | C2×D3 | — | 8 | 4 | no | — |
| 333 | C2×D3 | — | 8 | 4 | no | — |
| 334 | C3×C4 | — | 2 | 2 | no | — |
| 335 | C3×C4 | — | 2 | 4 | no | — |
| 336 | C3×C4 | — | 2 | 4 | no | — |
| 337 | C3×C4 | #535 | 1 | 2 | yes | — |
| 338 | C3×C4 | #535 | 1 | 2 | yes | — |
| 339 | Dic3 | — | 4 | 2 | no | — |
| 340 | C23 | — | 2 | 2 | no | — |
| 341 | C23 | — | 4 | 2 | no | — |
| 342 | C23 | — | 6 | 2 | no | — |
| 343 | C23 | — | 6 | 2 | no | — |
| 344 | C23 | — | 6 | 2 | no | — |
| 345 | C23 | — | 6 | 4 | no | — |
| 346 | C23 | — | 6 | 4 | no | — |
| 347 | C23 | — | 6 | 4 | no | — |
| 348 | C23 | — | 12 | 8 | no | — |
| 349 | C23 | — | 12 | 4 | no | — |
| 350 | C23 | — | 12 | 4 | no | — |
| 351 | C23 | — | 12 | 4 | no | — |
| 352 | C23 | — | 24 | 8 | no | — |
| 353 | C23 | — | 24 | 16 | no | — |
| 354 | C23 | C2×(C2×D3)⋊C4 | 1 | 2 | yes | — |
| 355 | C23 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 356 | Q8 | — | 12 | 2 | no | — |
| 357 | Q8 | — | 12 | 2 | no | — |
| 358 | D4 | — | 12 | 8 | no | — |
| 359 | D4 | — | 12 | 8 | no | — |
| 360 | D4 | — | 12 | 2 | no | — |
| 361 | D4 | — | 12 | 2 | no | — |
| 362 | D4 | — | 12 | 2 | no | — |
| 363 | D4 | — | 12 | 2 | no | — |
| 364 | D4 | — | 12 | 2 | no | — |
| 365 | D4 | — | 12 | 2 | no | — |
| 366 | D4 | — | 24 | 8 | no | — |
| 367 | D4 | — | 24 | 8 | no | — |
| 368 | C2×C4 | — | 2 | 2 | no | — |
| 369 | C2×C4 | — | 2 | 4 | no | — |
| 370 | C2×C4 | — | 2 | 4 | no | — |
| 371 | C2×C4 | — | 4 | 2 | no | — |
| 372 | C2×C4 | — | 4 | 2 | no | — |
| 373 | C2×C4 | — | 6 | 4 | no | — |
| 374 | C2×C4 | — | 6 | 2 | no | — |
| 375 | C2×C4 | — | 12 | 8 | no | — |
| 376 | C2×C4 | C2×(C2×D3)⋊C4 | 1 | 4 | yes | — |
| 377 | C2×C4 | C2×(C2×D3)⋊C4 | 1 | 4 | yes | — |
| 378 | C2×C4 | C2×(C2×D3)⋊C4 | 1 | 2 | yes | — |
| 379 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | #1009 | 1 | 4 | yes | — |
| 381 | C2×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 382 | C8 | — | 4 | 4 | no | — |
| 383 | C8 | — | 12 | 4 | no | — |
| 384 | C2×C3 | — | 2 | 2 | no | — |
| 385 | C2×C3 | — | 4 | 2 | no | — |
| 386 | C2×C3 | #2309 | 1 | 1 | yes | characteristic |
| 387 | C2×C3 | #2888 | 1 | 2 | yes | — |
| 388 | D3 | — | 8 | 2 | no | — |
| 389 | D3 | — | 8 | 2 | no | — |
| 390 | D3 | — | 8 | 2 | no | — |
| 391 | C22 | — | 2 | 2 | no | — |
| 392 | C22 | — | 2 | 2 | no | — |
| 393 | C22 | — | 2 | 4 | no | — |
| 394 | C22 | — | 4 | 4 | no | — |
| 395 | C22 | — | 12 | 2 | no | — |
| 396 | C22 | — | 12 | 2 | no | — |
| 397 | C22 | — | 12 | 2 | no | — |
| 398 | C22 | — | 12 | 4 | no | — |
| 399 | C22 | — | 12 | 4 | no | — |
| 400 | C22 | — | 12 | 4 | no | — |
| 401 | C22 | — | 24 | 4 | no | — |
| 402 | C22 | — | 24 | 4 | no | — |
| 403 | C22 | — | 24 | 4 | no | — |
| 404 | C22 | — | 24 | 16 | no | — |
| 405 | C22 | #5521 | 1 | 2 | yes | — |
| 406 | C22 | C22×(C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
| 407 | C4 | — | 2 | 2 | no | — |
| 408 | C4 | — | 2 | 4 | no | — |
| 409 | C4 | — | 2 | 4 | no | — |
| 410 | C4 | — | 12 | 2 | no | — |
| 411 | C4 | #5525 | 1 | 2 | yes | — |
| 412 | C4 | #5830 | 1 | 2 | yes | — |
| 413 | C3 | #21801 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 414 | C2 | — | 2 | 2 | no | — |
| 415 | C2 | — | 4 | 2 | no | — |
| 416 | C2 | — | 24 | 2 | no | — |
| 417 | C2 | — | 24 | 2 | no | — |
| 418 | C2 | — | 24 | 2 | no | — |
| 419 | C2 | #82269 | 1 | 1 | yes | characteristic |
| 420 | C2 | #83813 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#2921 | C2 | semidirect |
| 3. #82209 | C2 | semidirect |
| 4. #70523 | C2 | semidirect |
| 5. #70521 | C2 | semidirect |
| 6. #69989 | C2 | semidirect |
| 7. #69988 | C2 | semidirect |
| 8. #69878 | C2 | semidirect |
| 9. #69876 | C2 | semidirect |
| 23. C3×#423 | C22 | semidirect |
| 25. C3×C4×M16 | C22 | semidirect |
| 27. C2×#824 | C22 | semidirect |
| 30. C2×#823 | C22 | semidirect |
| 32. #4924 | C22 | semidirect |
| 33. C4×#208 | C22 | semidirect |
| 36. #2921 | D3 | semidirect |
| 106. #423 | C2×D3 | semidirect |
| 114. C4×M16 | C2×D3 | semidirect |
| 413. C3 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5525 | 2 |
| C3×#2921 | 2 |
| #82209 | 2 |
| #70523 | 2 |
| #70521 | 2 |
| #69989 | 2 |
| #69988 | 2 |
| #69878 | 2 |
| #69876 | 2 |
| #21801 | 3 |