Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1248 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #86242 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #79051 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C3×#1560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #71805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #70502 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #68485 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #68387 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | D3×#331 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #17770 | — | 3 | 1 | no | maximal, Sylow |
| 10 | C2×#1009 | C4 | 1 | 2 | yes | — |
| 11 | C3×#532 | C22 | 1 | 1 | yes | characteristic |
| 12 | #5830 | C4 | 1 | 2 | yes | — |
| 13 | #5725 | C22 | 1 | 2 | yes | — |
| 14 | D3×#127 | C22 | 1 | 2 | yes | — |
| 15 | #5674 | C4 | 1 | 4 | yes | — |
| 16 | #5609 | — | 2 | 4 | no | — |
| 17 | #5553 | — | 2 | 2 | no | — |
| 18 | D4×D12 | — | 2 | 2 | no | — |
| 19 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 20 | C4×#235 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×#423 | C22 | 1 | 2 | yes | complemented |
| 22 | #5127 | — | 2 | 4 | no | — |
| 23 | #4925 | C22 | 1 | 2 | yes | complemented |
| 24 | #4835 | C22 | 1 | 4 | yes | complemented |
| 25 | #4834 | — | 2 | 2 | no | — |
| 26 | D3×C4⋊C8 | C22 | 1 | 4 | yes | complemented |
| 27 | #4831 | — | 2 | 2 | no | — |
| 28 | C3×#333 | C22 | 1 | 2 | yes | complemented |
| 29 | C3×#331 | C22 | 1 | 2 | yes | complemented |
| 30 | #4546 | C22 | 1 | 2 | yes | complemented |
| 31 | #4544 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #4544 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #4485 | C22 | 1 | 4 | yes | complemented |
| 34 | #4485 | C22 | 1 | 4 | yes | complemented |
| 35 | #3498 | — | 3 | 1 | no | — |
| 36 | #2990 | — | 3 | 2 | no | — |
| 37 | #1560 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | #1555 | — | 3 | 2 | no | — |
| 39 | #1551 | — | 3 | 4 | no | — |
| 40 | #1545 | — | 3 | 2 | no | — |
| 41 | #1543 | — | 3 | 1 | no | — |
| 42 | C2×#331 | — | 3 | 2 | no | — |
| 43 | C2×C3×#41 | C2×C4 | 1 | 2 | yes | — |
| 44 | #1009 | — | 4 | 8 | no | — |
| 45 | C2×#239 | C2×C4 | 1 | 4 | yes | — |
| 46 | C2×D3×D4 | — | 2 | 4 | no | — |
| 47 | C2×D3×D4 | — | 2 | 4 | no | — |
| 48 | C2×D3×D4 | C2×C4 | 1 | 4 | yes | — |
| 49 | C2×#235 | — | 2 | 2 | no | — |
| 50 | C2×#235 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C22×D12 | — | 2 | 2 | no | — |
| 52 | C22×D12 | — | 2 | 2 | no | — |
| 53 | C22×D12 | C2×C4 | 1 | 2 | yes | — |
| 54 | C2×C3×M16 | — | 2 | 2 | no | — |
| 55 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 56 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 57 | C3×#124 | C2×C4 | 1 | 2 | yes | — |
| 58 | C3×#121 | — | 2 | 2 | no | — |
| 59 | C3×C4×D4 | — | 2 | 2 | no | — |
| 60 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 61 | #947 | C2×C4 | 1 | 4 | yes | — |
| 62 | #940 | — | 2 | 4 | no | — |
| 63 | #940 | C2×C4 | 1 | 4 | yes | — |
| 64 | #937 | — | 2 | 4 | no | — |
| 65 | #930 | — | 2 | 4 | no | — |
| 66 | C4×#67 | D4 | 1 | 4 | yes | — |
| 67 | #926 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C2×D3×C8 | — | 2 | 4 | no | — |
| 69 | #895 | — | 2 | 4 | no | — |
| 70 | #893 | — | 2 | 4 | no | — |
| 71 | #884 | — | 2 | 8 | no | — |
| 72 | #882 | — | 2 | 8 | no | — |
| 73 | #874 | — | 2 | 2 | no | — |
| 74 | #874 | C2×C4 | 1 | 2 | yes | — |
| 75 | #874 | C23 | 1 | 2 | yes | — |
| 76 | C4×D12 | D4 | 1 | 2 | yes | — |
| 77 | #872 | C2×C4 | 1 | 2 | yes | — |
| 78 | C42×D3 | C23 | 1 | 2 | yes | — |
| 79 | C4×Dic6 | D4 | 1 | 2 | yes | — |
| 80 | C3×C4⋊C8 | — | 2 | 2 | no | — |
| 81 | C3×C4⋊C8 | C23 | 1 | 4 | yes | — |
| 82 | #830 | — | 2 | 2 | no | — |
| 83 | (C2×D3)⋊C8 | — | 2 | 4 | no | — |
| 84 | #815 | — | 2 | 4 | no | — |
| 85 | Dic3⋊C8 | — | 2 | 4 | no | — |
| 86 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 87 | C4⋊(C3⋊C8) | C23 | 1 | 2 | yes | — |
| 88 | C4×C3⋊C8 | — | 2 | 2 | no | — |
| 89 | C2×H(5,𝔽2) | — | 3 | 2 | no | — |
| 90 | #550 | — | 6 | 2 | no | — |
| 91 | D42 | — | 6 | 2 | no | — |
| 92 | D42 | — | 6 | 4 | no | — |
| 93 | #535 | — | 3 | 2 | no | — |
| 94 | #535 | — | 3 | 4 | no | — |
| 95 | #532 | — | 3 | 2 | no | — |
| 96 | #532 | C2×D3 | 1 | 1 | yes | characteristic |
| 97 | C2×#127 | — | 3 | 2 | no | — |
| 98 | C2×#127 | — | 3 | 1 | no | — |
| 99 | C4×#41 | — | 3 | 1 | no | — |
| 100 | #446 | — | 6 | 2 | no | — |
| 101 | #435 | — | 6 | 4 | no | — |
| 102 | C8×D4 | — | 6 | 2 | no | — |
| 103 | #432 | — | 3 | 4 | no | — |
| 104 | #431 | — | 3 | 2 | no | — |
| 105 | #423 | C2×D3 | 1 | 2 | yes | complemented |
| 106 | C2×C4⋊C8 | — | 3 | 4 | no | — |
| 107 | #333 | — | 3 | 2 | no | — |
| 108 | #333 | C2×D3 | 1 | 2 | yes | complemented |
| 109 | #331 | — | 3 | 1 | no | — |
| 110 | #331 | — | 3 | 1 | no | — |
| 111 | #331 | — | 3 | 4 | no | — |
| 112 | #331 | — | 3 | 4 | no | — |
| 113 | #331 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | C23×D3 | — | 2 | 2 | no | — |
| 115 | C23×D3 | — | 2 | 4 | no | — |
| 116 | C3×#41 | — | 4 | 4 | no | — |
| 117 | C2×C3×Q8 | C22×C4 | 1 | 2 | yes | — |
| 118 | C2×C3×D4 | — | 2 | 2 | no | — |
| 119 | C2×C3×D4 | — | 2 | 2 | no | — |
| 120 | C2×C3×D4 | C22×C4 | 1 | 2 | yes | — |
| 121 | C22×C3×C4 | — | 2 | 2 | no | — |
| 122 | C22×C3×C4 | C22×C4 | 1 | 1 | yes | characteristic |
| 123 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 124 | C2×#67 | — | 2 | 4 | no | — |
| 125 | C2×#67 | — | 2 | 8 | no | — |
| 126 | C2×#67 | C22⋊C4 | 1 | 2 | yes | — |
| 127 | #239 | — | 4 | 8 | no | — |
| 128 | D3×D4 | — | 4 | 8 | no | — |
| 129 | D3×D4 | — | 4 | 16 | no | — |
| 130 | D3×D4 | — | 8 | 4 | no | — |
| 131 | D3×D4 | — | 8 | 4 | no | — |
| 132 | #235 | — | 2 | 4 | no | — |
| 133 | #235 | — | 4 | 8 | no | — |
| 134 | C2×D12 | — | 2 | 4 | no | — |
| 135 | C2×D12 | — | 2 | 2 | no | — |
| 136 | C2×D12 | — | 2 | 4 | no | — |
| 137 | C2×D12 | — | 2 | 4 | no | — |
| 138 | C2×D12 | — | 4 | 8 | no | — |
| 139 | C2×D12 | — | 4 | 4 | no | — |
| 140 | C2×D12 | — | 8 | 2 | no | — |
| 141 | C2×D12 | — | 8 | 2 | no | — |
| 142 | C2×D12 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 143 | C2×D12 | C22×C4 | 1 | 4 | yes | — |
| 144 | C2×C4×D3 | — | 2 | 4 | no | — |
| 145 | C2×C4×D3 | C22×C4 | 1 | 2 | yes | — |
| 146 | C2×C4×D3 | C2×D4 | 1 | 4 | yes | — |
| 147 | C2×Dic6 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 148 | C3×M16 | — | 8 | 2 | no | — |
| 149 | C2×C3×C8 | — | 2 | 4 | no | — |
| 150 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 151 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 152 | C3×C42 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 154 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 155 | #217 | C22⋊C4 | 1 | 2 | yes | — |
| 156 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 157 | (C2×D3)⋊C4 | C22⋊C4 | 1 | 4 | yes | — |
| 158 | C4⋊Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | Dic3⋊C4 | C22⋊C4 | 1 | 4 | yes | — |
| 160 | C4×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 161 | C4×Dic3 | C2×D4 | 1 | 4 | yes | — |
| 162 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 163 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 164 | D3×C8 | — | 8 | 4 | no | — |
| 165 | H(5,𝔽2) | — | 12 | 8 | no | — |
| 166 | C2×#41 | — | 3 | 1 | no | — |
| 167 | C2×#41 | — | 3 | 4 | no | — |
| 168 | C2×#41 | — | 6 | 2 | no | — |
| 169 | C2×#41 | C4×D3 | 1 | 2 | yes | — |
| 170 | C22×D4 | — | 3 | 4 | no | — |
| 171 | C22×D4 | — | 3 | 2 | no | — |
| 172 | C22×D4 | — | 6 | 2 | no | — |
| 173 | C22×D4 | — | 6 | 4 | no | — |
| 174 | C22×D4 | — | 6 | 4 | no | — |
| 175 | C22×D4 | — | 6 | 2 | no | — |
| 176 | C2×M16 | — | 2 | 2 | no | — |
| 177 | C22×C8 | — | 6 | 4 | no | — |
| 178 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 179 | #127 | — | 3 | 4 | no | — |
| 180 | #127 | — | 3 | 2 | no | — |
| 181 | #127 | — | 3 | 2 | no | — |
| 182 | #127 | — | 6 | 4 | no | — |
| 183 | #127 | — | 6 | 2 | no | — |
| 184 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | #124 | — | 3 | 4 | no | — |
| 186 | #124 | C4×D3 | 1 | 2 | yes | — |
| 187 | #121 | — | 2 | 2 | no | — |
| 188 | #121 | — | 6 | 8 | no | — |
| 189 | #121 | — | 6 | 4 | no | — |
| 190 | #121 | — | 6 | 4 | no | — |
| 191 | #120 | — | 6 | 8 | no | — |
| 192 | #120 | — | 6 | 4 | no | — |
| 193 | C4×Q8 | — | 3 | 2 | no | — |
| 194 | C4×D4 | — | 2 | 2 | no | — |
| 195 | C4×D4 | — | 3 | 4 | no | — |
| 196 | C4×D4 | — | 3 | 2 | no | — |
| 197 | C4×D4 | — | 6 | 4 | no | — |
| 198 | #117 | — | 3 | 1 | no | — |
| 199 | #117 | — | 3 | 2 | no | — |
| 200 | C2×C42 | — | 3 | 2 | no | — |
| 201 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 202 | C4⋊C8 | — | 2 | 2 | no | — |
| 203 | C4⋊C8 | — | 3 | 2 | no | — |
| 204 | C4⋊C8 | — | 3 | 2 | no | — |
| 205 | C4⋊C8 | — | 6 | 4 | no | — |
| 206 | C4⋊C8 | C22×D3 | 1 | 4 | yes | — |
| 207 | C22⋊C8 | — | 6 | 4 | no | — |
| 208 | C22⋊C8 | — | 6 | 2 | no | — |
| 209 | #97 | — | 6 | 4 | no | — |
| 210 | C4×C8 | — | 6 | 2 | no | — |
| 211 | C23×C3 | — | 2 | 2 | no | — |
| 212 | C23×C3 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C22×D3 | — | 2 | 4 | no | — |
| 214 | C22×D3 | — | 4 | 4 | no | — |
| 215 | C22×D3 | — | 4 | 8 | no | — |
| 216 | C22×D3 | — | 8 | 8 | no | — |
| 217 | C22×D3 | — | 8 | 4 | no | — |
| 218 | C22×D3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 219 | C3×Q8 | — | 4 | 2 | no | — |
| 220 | C3×D4 | — | 4 | 2 | no | — |
| 221 | C3×D4 | — | 4 | 4 | no | — |
| 222 | C3×D4 | — | 4 | 2 | no | — |
| 223 | C3×D4 | — | 4 | 2 | no | — |
| 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 | 2 | no | — |
| 228 | C2×C3×C4 | — | 4 | 4 | no | — |
| 229 | C2×C3×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 230 | C2×C3×C4 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 231 | C2×C3×C4 | C23×C4 | 1 | 1 | yes | characteristic |
| 232 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 233 | #67 | — | 2 | 4 | no | — |
| 234 | #67 | — | 4 | 8 | no | — |
| 235 | #67 | — | 8 | 8 | no | — |
| 236 | C2×Dic3 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 237 | C2×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 238 | D12 | — | 4 | 4 | no | — |
| 239 | D12 | — | 4 | 8 | no | — |
| 240 | D12 | — | 4 | 4 | no | — |
| 241 | D12 | — | 4 | 4 | no | — |
| 242 | D12 | — | 4 | 4 | no | — |
| 243 | D12 | — | 8 | 4 | no | — |
| 244 | D12 | #100 | 1 | 4 | yes | — |
| 245 | C4×D3 | — | 2 | 4 | no | — |
| 246 | C4×D3 | — | 2 | 4 | no | — |
| 247 | C4×D3 | — | 2 | 4 | no | — |
| 248 | C4×D3 | — | 4 | 8 | no | — |
| 249 | Dic6 | — | 2 | 2 | no | — |
| 250 | C3×C8 | — | 4 | 4 | no | — |
| 251 | C3⋊C8 | — | 4 | 2 | no | — |
| 252 | C3⋊C8 | — | 4 | 2 | no | — |
| 253 | C24 | — | 6 | 4 | no | — |
| 254 | C24 | — | 6 | 2 | no | — |
| 255 | #41 | — | 4 | 4 | no | — |
| 256 | #41 | — | 6 | 4 | no | — |
| 257 | #41 | — | 12 | 8 | no | — |
| 258 | #41 | — | 12 | 8 | no | — |
| 259 | C2×Q8 | — | 3 | 1 | no | — |
| 260 | C2×Q8 | C2×C4×D3 | 1 | 2 | yes | — |
| 261 | C2×D4 | — | 2 | 2 | no | — |
| 262 | C2×D4 | — | 2 | 2 | no | — |
| 263 | C2×D4 | — | 3 | 2 | no | — |
| 264 | C2×D4 | — | 3 | 1 | no | — |
| 265 | C2×D4 | — | 3 | 4 | no | — |
| 266 | C2×D4 | — | 6 | 4 | no | — |
| 267 | C2×D4 | — | 6 | 4 | no | — |
| 268 | C2×D4 | — | 6 | 8 | no | — |
| 269 | C2×D4 | — | 6 | 2 | no | — |
| 270 | C2×D4 | — | 6 | 4 | no | — |
| 271 | C2×D4 | — | 6 | 4 | no | — |
| 272 | C2×D4 | — | 12 | 4 | no | — |
| 273 | C2×D4 | — | 12 | 8 | no | — |
| 274 | C2×D4 | — | 12 | 8 | no | — |
| 275 | C2×D4 | — | 12 | 16 | no | — |
| 276 | C2×D4 | — | 24 | 2 | no | — |
| 277 | C2×D4 | — | 24 | 2 | no | — |
| 278 | C2×D4 | — | 24 | 4 | no | — |
| 279 | C2×D4 | — | 24 | 4 | no | — |
| 280 | C2×D4 | C2×C4×D3 | 1 | 2 | yes | — |
| 281 | C22×C4 | — | 2 | 2 | no | — |
| 282 | C22×C4 | — | 3 | 2 | no | — |
| 283 | C22×C4 | — | 3 | 4 | no | — |
| 284 | C22×C4 | — | 6 | 4 | no | — |
| 285 | C22×C4 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 286 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 287 | M16 | — | 8 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 4 | no | — |
| 289 | C2×C8 | — | 6 | 2 | no | — |
| 290 | C2×C8 | — | 6 | 2 | no | — |
| 291 | C2×C8 | — | 24 | 4 | no | — |
| 292 | C4⋊C4 | — | 2 | 2 | no | — |
| 293 | C4⋊C4 | — | 3 | 4 | no | — |
| 294 | C4⋊C4 | — | 3 | 2 | no | — |
| 295 | C22⋊C4 | — | 2 | 4 | no | — |
| 296 | C22⋊C4 | — | 3 | 2 | no | — |
| 297 | C22⋊C4 | — | 3 | 4 | no | — |
| 298 | C22⋊C4 | — | 6 | 8 | no | — |
| 299 | C42 | — | 3 | 2 | no | — |
| 300 | C42 | — | 3 | 4 | no | — |
| 301 | C42 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 302 | C42 | D3×D4 | 1 | 2 | yes | — |
| 303 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 304 | C22×C3 | — | 2 | 1 | no | — |
| 305 | C22×C3 | — | 2 | 2 | no | — |
| 306 | C22×C3 | — | 4 | 2 | no | — |
| 307 | C22×C3 | — | 4 | 4 | no | — |
| 308 | C22×C3 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 309 | C2×D3 | — | 2 | 4 | no | — |
| 310 | C2×D3 | — | 4 | 4 | no | — |
| 311 | C2×D3 | — | 4 | 8 | no | — |
| 312 | C2×D3 | — | 16 | 8 | no | — |
| 313 | C2×D3 | — | 16 | 4 | no | — |
| 314 | C2×D3 | C2×#100 | 1 | 4 | yes | — |
| 315 | C3×C4 | — | 2 | 1 | no | — |
| 316 | C3×C4 | — | 2 | 2 | no | — |
| 317 | C3×C4 | — | 4 | 2 | no | — |
| 318 | C3×C4 | C2×#100 | 1 | 2 | yes | — |
| 319 | C3×C4 | #576 | 1 | 2 | yes | — |
| 320 | C3×C4 | #577 | 1 | 2 | yes | — |
| 321 | Dic3 | — | 2 | 2 | no | — |
| 322 | Dic3 | — | 2 | 4 | no | — |
| 323 | C23 | — | 2 | 2 | no | — |
| 324 | C23 | — | 3 | 2 | no | — |
| 325 | C23 | — | 6 | 4 | no | — |
| 326 | C23 | — | 12 | 4 | no | — |
| 327 | C23 | — | 12 | 8 | no | — |
| 328 | C23 | — | 24 | 4 | no | — |
| 329 | C23 | — | 24 | 8 | no | — |
| 330 | C23 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 331 | Q8 | — | 4 | 2 | no | — |
| 332 | Q8 | — | 6 | 2 | no | — |
| 333 | D4 | — | 3 | 4 | no | — |
| 334 | D4 | — | 4 | 2 | no | — |
| 335 | D4 | — | 4 | 4 | no | — |
| 336 | D4 | — | 4 | 2 | no | — |
| 337 | D4 | — | 4 | 2 | no | — |
| 338 | D4 | — | 6 | 4 | no | — |
| 339 | D4 | — | 12 | 4 | no | — |
| 340 | D4 | — | 12 | 8 | no | — |
| 341 | D4 | — | 12 | 8 | no | — |
| 342 | D4 | — | 12 | 4 | no | — |
| 343 | D4 | — | 12 | 4 | no | — |
| 344 | D4 | — | 12 | 4 | no | — |
| 345 | D4 | — | 24 | 4 | no | — |
| 346 | D4 | — | 24 | 8 | no | — |
| 347 | C2×C4 | — | 2 | 2 | no | — |
| 348 | C2×C4 | — | 2 | 2 | no | — |
| 349 | C2×C4 | — | 2 | 2 | no | — |
| 350 | C2×C4 | — | 2 | 2 | no | — |
| 351 | C2×C4 | — | 3 | 4 | no | — |
| 352 | C2×C4 | — | 3 | 2 | no | — |
| 353 | C2×C4 | — | 4 | 4 | no | — |
| 354 | C2×C4 | — | 6 | 4 | no | — |
| 355 | C2×C4 | — | 6 | 4 | no | — |
| 356 | C2×C4 | — | 6 | 4 | no | — |
| 357 | C2×C4 | — | 12 | 8 | no | — |
| 358 | C2×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 359 | C2×C4 | D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 360 | C2×C4 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 362 | C8 | — | 4 | 4 | no | — |
| 363 | C8 | — | 12 | 2 | no | — |
| 364 | C8 | — | 12 | 2 | no | — |
| 365 | C2×C3 | — | 4 | 1 | no | — |
| 366 | C2×C3 | — | 8 | 2 | no | — |
| 367 | C2×C3 | C22×#100 | 1 | 1 | yes | characteristic |
| 368 | C2×C3 | #2897 | 1 | 2 | yes | — |
| 369 | D3 | — | 2 | 4 | no | — |
| 370 | D3 | — | 8 | 4 | no | — |
| 371 | C22 | — | 2 | 2 | no | — |
| 372 | C22 | — | 2 | 1 | no | — |
| 373 | C22 | — | 3 | 4 | no | — |
| 374 | C22 | — | 4 | 4 | no | — |
| 375 | C22 | — | 4 | 2 | no | — |
| 376 | C22 | — | 6 | 4 | no | — |
| 377 | C22 | — | 12 | 8 | no | — |
| 378 | C22 | — | 12 | 4 | no | — |
| 379 | C22 | — | 48 | 4 | no | — |
| 380 | C22 | — | 48 | 8 | no | — |
| 381 | C22 | C2×D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 382 | C4 | — | 2 | 2 | no | — |
| 383 | C4 | — | 2 | 1 | no | — |
| 384 | C4 | — | 4 | 2 | no | — |
| 385 | C4 | — | 6 | 4 | no | — |
| 386 | C4 | — | 6 | 2 | no | — |
| 387 | C4 | D3×#100 | 1 | 2 | yes | — |
| 388 | C4 | #5774 | 1 | 2 | yes | — |
| 389 | C4 | #5778 | 1 | 2 | yes | — |
| 390 | C3 | #17770 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 391 | C2 | — | 4 | 1 | no | — |
| 392 | C2 | — | 6 | 4 | no | — |
| 393 | C2 | — | 8 | 2 | no | — |
| 394 | C2 | — | 24 | 4 | no | — |
| 395 | C2 | C2×D3×#100 | 1 | 1 | yes | characteristic |
| 396 | C2 | #78882 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #79051 | C2 | semidirect |
| 3. C3×#1560 | C2 | semidirect |
| 4. #71805 | C2 | semidirect |
| 5. #70502 | C2 | semidirect |
| 6. #68485 | C2 | semidirect |
| 7. #68387 | C2 | semidirect |
| 8. D3×#331 | C2 | semidirect |
| 21. C3×#423 | C22 | semidirect |
| 23. #4925 | C22 | semidirect |
| 24. #4835 | C22 | semidirect |
| 26. D3×C4⋊C8 | C22 | semidirect |
| 28. C3×#333 | C22 | semidirect |
| 29. C3×#331 | C22 | semidirect |
| 30. #4546 | C22 | semidirect |
| 31. #4544 | C22 | semidirect |
| 32. #4544 | C22 | semidirect |
| 33. #4485 | C22 | semidirect |
| 34. #4485 | C22 | semidirect |
| 37. #1560 | D3 | semidirect |
| 105. #423 | C2×D3 | semidirect |
| 108. #333 | C2×D3 | semidirect |
| 113. #331 | C2×D3 | semidirect |
| 390. C3 | #17770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86242 | 2 |
| #79051 | 2 |
| C3×#1560 | 2 |
| #71805 | 2 |
| #70502 | 2 |
| #68485 | 2 |
| #68387 | 2 |
| D3×#331 | 2 |
| #17770 | 3 |