Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1280 conjugacy classes of subgroups.
The subgroup lattice has 416 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5697 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#4695 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #74244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #69753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #69553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #68897 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #68886 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #25608 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×C3×#125 | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×D24 | C22 | 1 | 4 | yes | — |
| 13 | #5697 | — | 2 | 4 | no | — |
| 14 | #5697 | — | 2 | 4 | no | — |
| 15 | C2×#895 | — | 2 | 2 | no | — |
| 16 | C2×#895 | C22 | 1 | 2 | yes | — |
| 17 | C2×#895 | C22 | 1 | 2 | yes | — |
| 18 | C2×#894 | — | 2 | 2 | no | — |
| 19 | C2×#893 | C22 | 1 | 2 | yes | — |
| 20 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#872 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×C4×C8 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#382 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×(C2×D3)⋊C8 | C22 | 1 | 2 | yes | — |
| 26 | #5067 | — | 2 | 4 | no | — |
| 27 | #4988 | C22 | 1 | 2 | yes | — |
| 28 | C2×#809 | C22 | 1 | 4 | yes | — |
| 29 | C2×#809 | C22 | 1 | 4 | yes | — |
| 30 | C2×#803 | C22 | 1 | 1 | yes | characteristic |
| 31 | #4695 | — | 2 | 4 | no | — |
| 32 | #4672 | — | 2 | 2 | no | — |
| 33 | #4671 | — | 2 | 2 | no | — |
| 34 | C3×#340 | C22 | 1 | 4 | yes | — |
| 35 | #4550 | C22 | 1 | 2 | yes | — |
| 36 | C2×#540 | — | 3 | 1 | no | — |
| 37 | C2×#493 | — | 3 | 1 | no | — |
| 38 | C2×#490 | — | 3 | 1 | no | — |
| 39 | #2619 | — | 3 | 1 | no | — |
| 40 | #1999 | — | 3 | 4 | no | — |
| 41 | #1991 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #1961 | — | 3 | 1 | no | — |
| 43 | #1879 | — | 3 | 4 | no | — |
| 44 | #1750 | — | 3 | 1 | no | — |
| 45 | C22×D12 | — | 2 | 2 | no | — |
| 46 | C22×D12 | — | 2 | 2 | no | — |
| 47 | C22×D12 | — | 2 | 2 | no | — |
| 48 | C22×D12 | — | 2 | 2 | no | — |
| 49 | C22×D12 | C23 | 1 | 2 | yes | — |
| 50 | C22×D12 | C23 | 1 | 2 | yes | — |
| 51 | C22×C4×D3 | — | 2 | 2 | no | — |
| 52 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 53 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 54 | C3×#125 | — | 2 | 2 | no | — |
| 55 | C3×#125 | D4 | 1 | 4 | yes | complemented |
| 56 | C2×C3×C4⋊C4 | — | 2 | 2 | no | — |
| 57 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 58 | C2×C3×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 59 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 61 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 62 | C2×(C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 63 | C2×(C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 64 | C2×(C2×D3)⋊C4 | D4 | 1 | 2 | yes | — |
| 65 | C2×Dic3⋊C4 | D4 | 1 | 2 | yes | — |
| 66 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C3⋊C8 | C23 | 1 | 2 | yes | — |
| 68 | C2×D24 | — | 2 | 8 | no | — |
| 69 | C2×D24 | — | 2 | 8 | no | — |
| 70 | C2×D24 | — | 4 | 4 | no | — |
| 71 | #895 | — | 2 | 16 | no | — |
| 72 | #895 | — | 2 | 4 | no | — |
| 73 | #895 | — | 2 | 4 | no | — |
| 74 | #895 | — | 4 | 4 | no | — |
| 75 | #894 | — | 2 | 16 | no | — |
| 76 | #893 | — | 2 | 4 | no | — |
| 77 | #893 | — | 2 | 4 | no | — |
| 78 | #874 | — | 2 | 2 | no | — |
| 79 | #874 | — | 2 | 2 | no | — |
| 80 | #874 | — | 2 | 2 | no | — |
| 81 | #874 | D4 | 1 | 4 | yes | complemented |
| 82 | #872 | — | 2 | 2 | no | — |
| 83 | #872 | — | 2 | 2 | no | — |
| 84 | C3×C4×C8 | — | 2 | 2 | no | — |
| 85 | C3×#95 | — | 2 | 2 | no | — |
| 86 | (C2×D3)⋊C8 | — | 2 | 4 | no | — |
| 87 | #809 | — | 2 | 8 | no | — |
| 88 | #809 | — | 4 | 4 | no | — |
| 89 | #803 | — | 2 | 2 | no | — |
| 90 | C22×D8 | — | 3 | 4 | no | — |
| 91 | #540 | — | 6 | 4 | no | — |
| 92 | #540 | — | 6 | 4 | no | — |
| 93 | C2×#127 | — | 3 | 1 | no | — |
| 94 | C2×#127 | — | 3 | 1 | no | — |
| 95 | C2×#125 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | C2×#123 | — | 6 | 2 | no | — |
| 97 | C2×#121 | — | 3 | 2 | no | — |
| 98 | C2×#121 | — | 3 | 2 | no | — |
| 99 | C2×#121 | — | 6 | 2 | no | — |
| 100 | C2×C4×D4 | — | 3 | 2 | no | — |
| 101 | C2×#117 | — | 3 | 1 | no | — |
| 102 | #493 | — | 6 | 4 | no | — |
| 103 | #490 | — | 6 | 4 | no | — |
| 104 | C2×#102 | — | 3 | 4 | no | — |
| 105 | C2×#102 | — | 3 | 4 | no | — |
| 106 | C2×C22⋊C8 | — | 3 | 2 | no | — |
| 107 | C2×#97 | — | 3 | 1 | no | — |
| 108 | C2×C4×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | #394 | — | 6 | 2 | no | — |
| 110 | #392 | — | 6 | 2 | no | — |
| 111 | #390 | — | 3 | 2 | no | — |
| 112 | #382 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | #340 | C2×D3 | 1 | 4 | yes | — |
| 114 | #336 | — | 3 | 2 | no | — |
| 115 | C23×D3 | — | 2 | 2 | no | — |
| 116 | C23×D3 | — | 2 | 2 | no | — |
| 117 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 118 | C22×C3×C4 | — | 2 | 2 | no | — |
| 119 | C22×C3×C4 | — | 2 | 2 | no | — |
| 120 | C22×C3×C4 | C2×D4 | 1 | 2 | yes | — |
| 121 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 122 | C22×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 123 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×D12 | — | 2 | 4 | no | — |
| 125 | C2×D12 | — | 2 | 4 | no | — |
| 126 | C2×D12 | — | 2 | 2 | no | — |
| 127 | C2×D12 | — | 2 | 2 | no | — |
| 128 | C2×D12 | — | 2 | 2 | no | — |
| 129 | C2×D12 | — | 2 | 4 | no | — |
| 130 | C2×D12 | — | 2 | 4 | no | — |
| 131 | C2×D12 | — | 2 | 8 | no | — |
| 132 | C2×D12 | — | 2 | 8 | no | — |
| 133 | C2×D12 | — | 4 | 4 | no | — |
| 134 | C2×D12 | — | 4 | 4 | no | — |
| 135 | C2×D12 | — | 8 | 4 | no | — |
| 136 | C2×D12 | — | 8 | 4 | no | — |
| 137 | C2×D12 | — | 8 | 4 | no | — |
| 138 | C2×D12 | — | 8 | 4 | no | — |
| 139 | C2×D12 | C2×D4 | 1 | 4 | yes | — |
| 140 | C2×C4×D3 | — | 2 | 1 | no | — |
| 141 | C2×C4×D3 | — | 2 | 1 | no | — |
| 142 | C2×C4×D3 | — | 2 | 2 | no | — |
| 143 | C2×C4×D3 | — | 2 | 2 | no | — |
| 144 | C2×C4×D3 | — | 2 | 8 | no | — |
| 145 | C2×C4×D3 | — | 8 | 4 | no | — |
| 146 | C2×C3×C8 | — | 2 | 2 | no | — |
| 147 | C2×C3×C8 | — | 2 | 2 | no | — |
| 148 | C2×C3×C8 | #41 | 1 | 4 | yes | — |
| 149 | C3×C4⋊C4 | — | 2 | 8 | no | — |
| 150 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 151 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 152 | C3×C4⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 153 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 154 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 155 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 156 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 157 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 158 | (C2×D3)⋊C4 | — | 4 | 4 | no | — |
| 159 | (C2×D3)⋊C4 | — | 8 | 4 | no | — |
| 160 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 161 | C4×Dic3 | — | 2 | 1 | no | — |
| 162 | C4×Dic3 | — | 2 | 1 | no | — |
| 163 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 164 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 165 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 166 | D24 | — | 4 | 16 | no | — |
| 167 | C22×D4 | — | 3 | 2 | no | — |
| 168 | C22×D4 | — | 3 | 2 | no | — |
| 169 | C22×D4 | — | 6 | 2 | no | — |
| 170 | C22×D4 | — | 6 | 2 | no | — |
| 171 | C22×D4 | — | 6 | 2 | no | — |
| 172 | C22×D4 | — | 6 | 2 | no | — |
| 173 | C23×C4 | — | 3 | 1 | no | — |
| 174 | C23×C4 | — | 6 | 2 | no | — |
| 175 | C2×D8 | — | 6 | 8 | no | — |
| 176 | C2×D8 | — | 6 | 8 | no | — |
| 177 | C2×D8 | — | 12 | 4 | no | — |
| 178 | C22×C8 | — | 3 | 2 | no | — |
| 179 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 180 | #127 | — | 3 | 4 | no | — |
| 181 | #127 | — | 6 | 2 | no | — |
| 182 | #127 | — | 6 | 2 | no | — |
| 183 | #127 | — | 6 | 2 | no | — |
| 184 | #125 | — | 2 | 2 | no | — |
| 185 | #125 | D12 | 1 | 4 | yes | complemented |
| 186 | #123 | — | 6 | 16 | no | — |
| 187 | #121 | — | 6 | 4 | no | — |
| 188 | #121 | — | 6 | 16 | no | — |
| 189 | #121 | — | 6 | 4 | no | — |
| 190 | #121 | — | 12 | 4 | no | — |
| 191 | C4×D4 | — | 6 | 4 | no | — |
| 192 | C4×D4 | — | 6 | 4 | no | — |
| 193 | #117 | — | 6 | 2 | no | — |
| 194 | #117 | — | 6 | 2 | no | — |
| 195 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 196 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 197 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 198 | C2×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 199 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 200 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 201 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 202 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 203 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 204 | C2×C42 | — | 3 | 1 | no | — |
| 205 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | #102 | — | 6 | 8 | no | — |
| 207 | #102 | — | 12 | 4 | no | — |
| 208 | C22⋊C8 | — | 6 | 4 | no | — |
| 209 | #97 | — | 6 | 2 | no | — |
| 210 | C4×C8 | — | 2 | 2 | no | — |
| 211 | #95 | — | 2 | 2 | no | — |
| 212 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 213 | C22×D3 | — | 2 | 1 | no | — |
| 214 | C22×D3 | — | 2 | 4 | no | — |
| 215 | C22×D3 | — | 2 | 1 | no | — |
| 216 | C22×D3 | — | 2 | 1 | no | — |
| 217 | C22×D3 | — | 2 | 4 | no | — |
| 218 | C22×D3 | — | 4 | 2 | no | — |
| 219 | C22×D3 | — | 4 | 2 | no | — |
| 220 | C22×D3 | — | 4 | 4 | no | — |
| 221 | C22×D3 | — | 4 | 4 | no | — |
| 222 | C22×D3 | — | 4 | 2 | no | — |
| 223 | C22×D3 | — | 4 | 2 | no | — |
| 224 | C22×D3 | — | 4 | 2 | no | — |
| 225 | C22×D3 | — | 4 | 4 | no | — |
| 226 | C22×D3 | — | 4 | 4 | no | — |
| 227 | C2×C3×C4 | — | 2 | 4 | no | — |
| 228 | C2×C3×C4 | — | 2 | 4 | no | — |
| 229 | C2×C3×C4 | — | 4 | 4 | no | — |
| 230 | C2×C3×C4 | — | 4 | 2 | no | — |
| 231 | C2×C3×C4 | — | 4 | 4 | no | — |
| 232 | C2×C3×C4 | #120 | 1 | 4 | yes | — |
| 233 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×C3×C4 | C2×#41 | 1 | 2 | yes | — |
| 236 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 237 | C2×Dic3 | — | 2 | 2 | no | — |
| 238 | C2×Dic3 | — | 2 | 1 | no | — |
| 239 | C2×Dic3 | — | 2 | 1 | no | — |
| 240 | C2×Dic3 | — | 2 | 1 | no | — |
| 241 | C2×Dic3 | — | 2 | 4 | no | — |
| 242 | D12 | — | 2 | 8 | no | — |
| 243 | D12 | — | 4 | 4 | no | — |
| 244 | D12 | — | 4 | 4 | no | — |
| 245 | D12 | — | 4 | 4 | no | — |
| 246 | D12 | — | 8 | 8 | no | — |
| 247 | D12 | — | 8 | 8 | no | — |
| 248 | D12 | — | 8 | 8 | no | — |
| 249 | D12 | — | 8 | 8 | no | — |
| 250 | C4×D3 | — | 4 | 2 | no | — |
| 251 | C4×D3 | — | 4 | 2 | no | — |
| 252 | C4×D3 | — | 8 | 8 | no | — |
| 253 | C3×C8 | — | 2 | 4 | no | — |
| 254 | C3⋊C8 | — | 4 | 2 | no | — |
| 255 | C24 | — | 3 | 1 | no | — |
| 256 | C24 | — | 6 | 2 | no | — |
| 257 | C24 | — | 6 | 2 | no | — |
| 258 | C2×D4 | — | 3 | 4 | no | — |
| 259 | C2×D4 | — | 6 | 8 | no | — |
| 260 | C2×D4 | — | 6 | 8 | no | — |
| 261 | C2×D4 | — | 6 | 2 | no | — |
| 262 | C2×D4 | — | 6 | 2 | no | — |
| 263 | C2×D4 | — | 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 | — | 12 | 4 | no | — |
| 269 | C2×D4 | — | 12 | 4 | no | — |
| 270 | C2×D4 | — | 24 | 4 | no | — |
| 271 | C2×D4 | — | 24 | 4 | no | — |
| 272 | C2×D4 | — | 24 | 4 | no | — |
| 273 | C2×D4 | — | 24 | 4 | no | — |
| 274 | C22×C4 | — | 2 | 2 | no | — |
| 275 | C22×C4 | — | 2 | 2 | no | — |
| 276 | C22×C4 | — | 3 | 2 | no | — |
| 277 | C22×C4 | — | 3 | 1 | no | — |
| 278 | C22×C4 | — | 6 | 8 | no | — |
| 279 | C22×C4 | — | 6 | 1 | no | — |
| 280 | C22×C4 | — | 6 | 1 | no | — |
| 281 | C22×C4 | — | 6 | 2 | no | — |
| 282 | C22×C4 | — | 6 | 2 | no | — |
| 283 | C22×C4 | — | 24 | 4 | no | — |
| 284 | C22×C4 | D3×D4 | 1 | 2 | yes | — |
| 285 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 286 | D8 | — | 12 | 16 | no | — |
| 287 | C2×C8 | — | 2 | 2 | no | — |
| 288 | C2×C8 | — | 2 | 2 | no | — |
| 289 | C2×C8 | — | 6 | 2 | no | — |
| 290 | C2×C8 | — | 6 | 2 | no | — |
| 291 | C2×C8 | — | 6 | 2 | no | — |
| 292 | C2×C8 | #239 | 1 | 4 | yes | — |
| 293 | C4⋊C4 | — | 2 | 8 | no | — |
| 294 | C4⋊C4 | — | 2 | 2 | no | — |
| 295 | C4⋊C4 | — | 2 | 4 | no | — |
| 296 | C4⋊C4 | — | 6 | 4 | no | — |
| 297 | C4⋊C4 | C2×D12 | 1 | 4 | yes | — |
| 298 | C22⋊C4 | — | 6 | 8 | no | — |
| 299 | C22⋊C4 | — | 6 | 8 | no | — |
| 300 | C22⋊C4 | — | 6 | 4 | no | — |
| 301 | C22⋊C4 | — | 12 | 4 | no | — |
| 302 | C22⋊C4 | — | 24 | 4 | no | — |
| 303 | C42 | — | 6 | 1 | no | — |
| 304 | C42 | — | 6 | 1 | no | — |
| 305 | C42 | C2×D12 | 1 | 2 | yes | — |
| 306 | C42 | D3×D4 | 1 | 2 | yes | — |
| 307 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 308 | C22×C3 | #532 | 1 | 1 | yes | characteristic |
| 309 | C22×C3 | #535 | 1 | 1 | yes | characteristic |
| 310 | C22×C3 | #576 | 1 | 4 | yes | — |
| 311 | C2×D3 | — | 4 | 2 | no | — |
| 312 | C2×D3 | — | 4 | 1 | no | — |
| 313 | C2×D3 | — | 4 | 4 | no | — |
| 314 | C2×D3 | — | 4 | 2 | no | — |
| 315 | C2×D3 | — | 4 | 4 | no | — |
| 316 | C2×D3 | — | 4 | 2 | no | — |
| 317 | C2×D3 | — | 4 | 4 | no | — |
| 318 | C2×D3 | — | 8 | 4 | no | — |
| 319 | C2×D3 | — | 8 | 4 | no | — |
| 320 | C2×D3 | — | 8 | 4 | no | — |
| 321 | C2×D3 | — | 8 | 2 | no | — |
| 322 | C2×D3 | — | 8 | 2 | no | — |
| 323 | C2×D3 | — | 8 | 2 | no | — |
| 324 | C2×D3 | — | 8 | 4 | no | — |
| 325 | C3×C4 | — | 2 | 4 | no | — |
| 326 | C3×C4 | — | 4 | 4 | no | — |
| 327 | C3×C4 | — | 8 | 2 | no | — |
| 328 | C3×C4 | #546 | 1 | 2 | yes | — |
| 329 | C3×C4 | #550 | 1 | 2 | yes | — |
| 330 | Dic3 | — | 4 | 1 | no | — |
| 331 | Dic3 | — | 4 | 2 | no | — |
| 332 | C23 | — | 6 | 1 | no | — |
| 333 | C23 | — | 6 | 1 | no | — |
| 334 | C23 | — | 6 | 4 | no | — |
| 335 | C23 | — | 6 | 1 | no | — |
| 336 | C23 | — | 6 | 4 | no | — |
| 337 | C23 | — | 12 | 2 | no | — |
| 338 | C23 | — | 12 | 2 | no | — |
| 339 | C23 | — | 12 | 4 | no | — |
| 340 | C23 | — | 12 | 4 | no | — |
| 341 | C23 | — | 12 | 2 | no | — |
| 342 | C23 | — | 12 | 2 | no | — |
| 343 | C23 | — | 12 | 2 | no | — |
| 344 | C23 | — | 12 | 4 | no | — |
| 345 | C23 | — | 12 | 4 | no | — |
| 346 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 347 | D4 | — | 6 | 8 | no | — |
| 348 | D4 | — | 12 | 4 | no | — |
| 349 | D4 | — | 12 | 4 | no | — |
| 350 | D4 | — | 12 | 4 | no | — |
| 351 | D4 | — | 24 | 8 | no | — |
| 352 | D4 | — | 24 | 8 | no | — |
| 353 | D4 | — | 24 | 8 | no | — |
| 354 | D4 | — | 24 | 8 | no | — |
| 355 | C2×C4 | — | 2 | 4 | no | — |
| 356 | C2×C4 | — | 2 | 4 | no | — |
| 357 | C2×C4 | — | 4 | 4 | no | — |
| 358 | C2×C4 | — | 4 | 2 | no | — |
| 359 | C2×C4 | — | 4 | 4 | no | — |
| 360 | C2×C4 | — | 6 | 1 | no | — |
| 361 | C2×C4 | — | 6 | 1 | no | — |
| 362 | C2×C4 | — | 6 | 2 | no | — |
| 363 | C2×C4 | — | 6 | 1 | no | — |
| 364 | C2×C4 | — | 6 | 4 | no | — |
| 365 | C2×C4 | — | 12 | 2 | no | — |
| 366 | C2×C4 | — | 12 | 2 | no | — |
| 367 | C2×C4 | — | 24 | 8 | no | — |
| 368 | C2×C4 | #882 | 1 | 4 | yes | — |
| 369 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 370 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 371 | C2×C4 | C2×#239 | 1 | 2 | yes | — |
| 372 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 373 | C8 | — | 2 | 4 | no | — |
| 374 | C8 | — | 12 | 2 | no | — |
| 375 | C2×C3 | #2431 | 1 | 1 | yes | characteristic |
| 376 | C2×C3 | #3008 | 1 | 2 | yes | — |
| 377 | C2×C3 | #3176 | 1 | 2 | yes | — |
| 378 | C2×C3 | #3220 | 1 | 2 | yes | — |
| 379 | D3 | — | 8 | 1 | no | — |
| 380 | D3 | — | 8 | 4 | no | — |
| 381 | D3 | — | 16 | 2 | no | — |
| 382 | C22 | — | 12 | 1 | no | — |
| 383 | C22 | — | 12 | 4 | no | — |
| 384 | C22 | — | 12 | 2 | no | — |
| 385 | C22 | — | 12 | 4 | no | — |
| 386 | C22 | — | 12 | 2 | no | — |
| 387 | C22 | — | 12 | 4 | no | — |
| 388 | C22 | — | 12 | 2 | no | — |
| 389 | C22 | — | 24 | 4 | no | — |
| 390 | C22 | — | 24 | 4 | no | — |
| 391 | C22 | — | 24 | 2 | no | — |
| 392 | C22 | — | 24 | 2 | no | — |
| 393 | C22 | — | 24 | 2 | no | — |
| 394 | C22 | — | 24 | 4 | no | — |
| 395 | C22 | — | 24 | 4 | no | — |
| 396 | C22 | C2×#882 | 1 | 1 | yes | characteristic |
| 397 | C22 | #5674 | 1 | 1 | yes | characteristic |
| 398 | C22 | #5725 | 1 | 1 | yes | characteristic |
| 399 | C22 | #5769 | 1 | 4 | yes | — |
| 400 | C4 | — | 2 | 4 | no | — |
| 401 | C4 | — | 4 | 4 | no | — |
| 402 | C4 | — | 8 | 2 | no | — |
| 403 | C4 | — | 12 | 1 | no | — |
| 404 | C4 | — | 12 | 2 | no | — |
| 405 | C4 | #5577 | 1 | 2 | yes | — |
| 406 | C4 | #5630 | 1 | 2 | yes | — |
| 407 | C3 | #25608 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 408 | C2 | — | 24 | 1 | no | — |
| 409 | C2 | — | 24 | 4 | no | — |
| 410 | C2 | — | 48 | 2 | no | — |
| 411 | C2 | #76626 | 1 | 1 | yes | characteristic |
| 412 | C2 | #78834 | 1 | 2 | yes | — |
| 413 | C2 | #81644 | 1 | 2 | yes | — |
| 414 | C2 | #81909 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5697 | C2 | semidirect |
| 2. C2×#5067 | C2 | semidirect |
| 3. C2×#4695 | C2 | semidirect |
| 4. #74244 | C2 | semidirect |
| 5. C3×#1991 | C2 | semidirect |
| 6. #69753 | C2 | semidirect |
| 7. #69553 | C2 | semidirect |
| 8. #68897 | C2 | semidirect |
| 9. #68886 | C2 | semidirect |
| 41. #1991 | D3 | semidirect |
| 55. C3×#125 | D4 | semidirect |
| 81. #874 | D4 | semidirect |
| 185. #125 | D12 | semidirect |
| 407. C3 | #25608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5697 | 2 |
| C2×#5067 | 2 |
| C2×#4695 | 2 |
| #74244 | 2 |
| C3×#1991 | 2 |
| #69753 | 2 |
| #69553 | 2 |
| #68897 | 2 |
| #68886 | 2 |
| #25608 | 3 |