Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1792 conjugacy classes of subgroups.
The subgroup lattice has 382 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C3×#2844 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #78356 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #78310 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #78292 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #78146 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #77252 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #77215 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #74192 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #74153 | C2 | 1 | 3 | yes | maximal |
| 10 | #47818 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C2×#946 | C22 | 1 | 6 | yes | — |
| 12 | C2×#897 | C22 | 1 | 3 | yes | — |
| 13 | C2×#893 | C22 | 1 | 3 | yes | — |
| 14 | C2×#893 | C22 | 1 | 3 | yes | — |
| 15 | C2×D3×C4⋊C4 | C22 | 1 | 3 | yes | — |
| 16 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 17 | C3×#400 | C22 | 1 | 3 | yes | — |
| 18 | C3×#400 | C22 | 1 | 3 | yes | — |
| 19 | C3×#395 | C22 | 1 | 6 | yes | — |
| 20 | C3×#382 | C22 | 1 | 3 | yes | — |
| 21 | #5231 | C22 | 1 | 2 | yes | — |
| 22 | #4994 | C22 | 1 | 6 | yes | — |
| 23 | #4993 | C22 | 1 | 3 | yes | — |
| 24 | #4993 | C22 | 1 | 3 | yes | — |
| 25 | #4989 | C22 | 1 | 6 | yes | — |
| 26 | #4988 | C22 | 1 | 3 | yes | — |
| 27 | #4988 | C22 | 1 | 3 | yes | — |
| 28 | #4986 | C22 | 1 | 3 | yes | — |
| 29 | #4982 | C22 | 1 | 6 | yes | — |
| 30 | #4979 | C22 | 1 | 3 | yes | — |
| 31 | #4932 | C22 | 1 | 3 | yes | — |
| 32 | #4677 | C22 | 1 | 1 | yes | characteristic |
| 33 | #4673 | C22 | 1 | 3 | yes | — |
| 34 | #4673 | C22 | 1 | 6 | yes | — |
| 35 | #4668 | C22 | 1 | 6 | yes | — |
| 36 | #4668 | C22 | 1 | 6 | yes | — |
| 37 | #4667 | C22 | 1 | 6 | yes | — |
| 38 | #4667 | C22 | 1 | 3 | yes | — |
| 39 | #4665 | C22 | 1 | 6 | yes | — |
| 40 | #4665 | C22 | 1 | 6 | yes | — |
| 41 | #4665 | C22 | 1 | 6 | yes | — |
| 42 | #4665 | C22 | 1 | 6 | yes | — |
| 43 | D3×#95 | C22 | 1 | 1 | yes | characteristic |
| 44 | #4655 | C22 | 1 | 6 | yes | — |
| 45 | #4654 | C22 | 1 | 6 | yes | — |
| 46 | #4647 | C22 | 1 | 6 | yes | — |
| 47 | #4646 | C22 | 1 | 6 | yes | — |
| 48 | #2844 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #2804 | — | 3 | 3 | no | — |
| 50 | #2784 | — | 3 | 3 | no | — |
| 51 | #2692 | — | 3 | 6 | no | — |
| 52 | #2612 | — | 3 | 3 | no | — |
| 53 | #2564 | — | 3 | 3 | no | — |
| 54 | #2487 | — | 3 | 3 | no | — |
| 55 | #2449 | — | 3 | 6 | no | — |
| 56 | #2328 | — | 3 | 3 | no | — |
| 57 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 58 | C22×D12 | C23 | 1 | 3 | yes | — |
| 59 | C22×D12 | C23 | 1 | 3 | yes | — |
| 60 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 61 | C22×C4×D3 | C23 | 1 | 3 | yes | — |
| 62 | C22×C4×D3 | C23 | 1 | 6 | yes | — |
| 63 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 64 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 65 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 66 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 67 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 68 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 69 | #946 | — | 4 | 12 | no | — |
| 70 | C2×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 71 | C2×(C2×D3)⋊C4 | C23 | 1 | 3 | yes | — |
| 72 | C2×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 73 | C2×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 74 | C2×(C2×D3)⋊C4 | C23 | 1 | 3 | yes | — |
| 75 | C2×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 76 | C2×(C2×D3)⋊C4 | C23 | 1 | 6 | yes | — |
| 77 | C2×C4⋊Dic3 | C23 | 1 | 6 | yes | — |
| 78 | C2×C4⋊Dic3 | C23 | 1 | 3 | yes | — |
| 79 | C2×Dic3⋊C4 | C23 | 1 | 6 | yes | — |
| 80 | C2×Dic3⋊C4 | C23 | 1 | 6 | yes | — |
| 81 | C2×Dic3⋊C4 | C23 | 1 | 6 | yes | — |
| 82 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 83 | C2×C4×Dic3 | C23 | 1 | 3 | yes | — |
| 84 | #897 | — | 4 | 6 | no | — |
| 85 | #893 | — | 4 | 6 | no | — |
| 86 | #893 | — | 4 | 6 | no | — |
| 87 | D3×C4⋊C4 | — | 4 | 6 | no | — |
| 88 | #874 | Q8 | 1 | 8 | yes | complemented |
| 89 | C3×#95 | C23 | 1 | 6 | yes | — |
| 90 | C3×#95 | C23 | 1 | 6 | yes | — |
| 91 | C3×#95 | C23 | 1 | 1 | yes | characteristic |
| 92 | C3×#95 | C23 | 1 | 1 | yes | characteristic |
| 93 | C3×#95 | C23 | 1 | 6 | yes | — |
| 94 | C3⋊#95 | C23 | 1 | 6 | yes | — |
| 95 | C3⋊#95 | C23 | 1 | 6 | yes | — |
| 96 | C3⋊#95 | C23 | 1 | 6 | yes | — |
| 97 | C3⋊#95 | C23 | 1 | 3 | yes | — |
| 98 | C3⋊#95 | C23 | 1 | 6 | yes | — |
| 99 | C3⋊#95 | C23 | 1 | 3 | yes | — |
| 100 | C2×#127 | — | 3 | 1 | no | — |
| 101 | C2×C22⋊Q8 | — | 3 | 6 | no | — |
| 102 | C2×C22⋊Q8 | — | 3 | 3 | no | — |
| 103 | C2×C4×D4 | — | 3 | 3 | no | — |
| 104 | C2×C4×D4 | — | 3 | 3 | no | — |
| 105 | C22×C4⋊C4 | — | 3 | 3 | no | — |
| 106 | #400 | — | 3 | 3 | no | — |
| 107 | #400 | C2×D3 | 1 | 3 | yes | — |
| 108 | #400 | C2×D3 | 1 | 3 | yes | — |
| 109 | #399 | — | 3 | 3 | no | — |
| 110 | #399 | — | 3 | 3 | no | — |
| 111 | #399 | — | 3 | 1 | no | — |
| 112 | #398 | — | 3 | 6 | no | — |
| 113 | #396 | — | 3 | 6 | no | — |
| 114 | #395 | — | 3 | 3 | no | — |
| 115 | #395 | C2×D3 | 1 | 6 | yes | — |
| 116 | #393 | — | 3 | 2 | no | — |
| 117 | #393 | — | 3 | 3 | no | — |
| 118 | #393 | — | 3 | 6 | no | — |
| 119 | #391 | — | 3 | 6 | no | — |
| 120 | #390 | — | 3 | 3 | no | — |
| 121 | #390 | — | 3 | 3 | no | — |
| 122 | #389 | — | 3 | 6 | no | — |
| 123 | #387 | — | 3 | 6 | no | — |
| 124 | #387 | — | 3 | 6 | no | — |
| 125 | #386 | — | 3 | 6 | no | — |
| 126 | #386 | — | 3 | 6 | no | — |
| 127 | #386 | — | 3 | 6 | no | — |
| 128 | #386 | — | 3 | 6 | no | — |
| 129 | #385 | — | 3 | 6 | no | — |
| 130 | #385 | — | 3 | 6 | no | — |
| 131 | #385 | — | 3 | 6 | no | — |
| 132 | #382 | C2×D3 | 1 | 3 | yes | — |
| 133 | #380 | — | 3 | 6 | no | — |
| 134 | #380 | — | 3 | 3 | no | — |
| 135 | #376 | — | 3 | 3 | no | — |
| 136 | C2×#95 | — | 3 | 1 | no | — |
| 137 | C23×D3 | C24 | 1 | 3 | yes | — |
| 138 | C23×D3 | C24 | 1 | 1 | yes | characteristic |
| 139 | C2×C3×Q8 | — | 4 | 6 | no | — |
| 140 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 141 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 142 | C22×C3×C4 | C24 | 1 | 6 | yes | — |
| 143 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 144 | C22×Dic3 | C24 | 1 | 6 | yes | — |
| 145 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 146 | C22×Dic3 | C24 | 1 | 3 | yes | — |
| 147 | C2×D12 | — | 4 | 3 | no | — |
| 148 | C2×D12 | — | 4 | 3 | no | — |
| 149 | C2×D12 | — | 4 | 3 | no | — |
| 150 | C2×D12 | — | 4 | 3 | no | — |
| 151 | C2×D12 | C2×Q8 | 1 | 12 | yes | — |
| 152 | C2×D12 | C2×Q8 | 1 | 12 | yes | — |
| 153 | C2×C4×D3 | — | 2 | 6 | no | — |
| 154 | C2×C4×D3 | — | 2 | 6 | no | — |
| 155 | C2×C4×D3 | — | 4 | 6 | no | — |
| 156 | C2×C4×D3 | — | 4 | 6 | no | — |
| 157 | C2×C4×D3 | — | 4 | 6 | no | — |
| 158 | C2×C4×D3 | — | 4 | 6 | no | — |
| 159 | C2×C4×D3 | — | 4 | 6 | no | — |
| 160 | C2×Dic6 | — | 4 | 3 | no | — |
| 161 | C2×Dic6 | — | 4 | 6 | no | — |
| 162 | C3×C4⋊C4 | — | 4 | 3 | no | — |
| 163 | C3×C4⋊C4 | — | 4 | 3 | no | — |
| 164 | C3×C4⋊C4 | — | 4 | 3 | no | — |
| 165 | C3×C4⋊C4 | — | 4 | 3 | no | — |
| 166 | C3×C42 | C2×Q8 | 1 | 4 | yes | — |
| 167 | (C2×D3)⋊C4 | — | 2 | 12 | no | — |
| 168 | (C2×D3)⋊C4 | — | 4 | 3 | no | — |
| 169 | (C2×D3)⋊C4 | — | 4 | 3 | no | — |
| 170 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 171 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 172 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 173 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 174 | C4⋊Dic3 | — | 2 | 12 | no | — |
| 175 | C4⋊Dic3 | — | 4 | 3 | no | — |
| 176 | Dic3⋊C4 | — | 2 | 12 | no | — |
| 177 | Dic3⋊C4 | — | 4 | 6 | no | — |
| 178 | Dic3⋊C4 | — | 4 | 6 | no | — |
| 179 | C4×Dic3 | — | 2 | 6 | no | — |
| 180 | C4×Dic3 | — | 4 | 3 | no | — |
| 181 | C22×Q8 | — | 3 | 3 | no | — |
| 182 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 183 | C22×D4 | — | 3 | 3 | no | — |
| 184 | C22×D4 | — | 3 | 3 | no | — |
| 185 | C23×C4 | — | 3 | 3 | no | — |
| 186 | C23×C4 | — | 3 | 3 | no | — |
| 187 | C23×C4 | — | 3 | 6 | no | — |
| 188 | #127 | — | 3 | 8 | no | — |
| 189 | C22⋊Q8 | — | 12 | 12 | no | — |
| 190 | C22⋊Q8 | — | 12 | 6 | no | — |
| 191 | C4×D4 | — | 12 | 6 | no | — |
| 192 | C4×D4 | — | 12 | 6 | no | — |
| 193 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 194 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 195 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 196 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 197 | C2×C4⋊C4 | — | 3 | 6 | no | — |
| 198 | C2×C4⋊C4 | — | 12 | 6 | no | — |
| 199 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 200 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 201 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 202 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 203 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 204 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 205 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 206 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 207 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 208 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 209 | C2×C22⋊C4 | — | 3 | 6 | no | — |
| 210 | C2×C42 | — | 3 | 3 | no | — |
| 211 | C2×C42 | — | 3 | 3 | no | — |
| 212 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 213 | #95 | — | 3 | 3 | no | — |
| 214 | #95 | — | 3 | 6 | no | — |
| 215 | #95 | — | 3 | 6 | no | — |
| 216 | #95 | — | 3 | 6 | no | — |
| 217 | #95 | — | 3 | 3 | no | — |
| 218 | #95 | — | 3 | 6 | no | — |
| 219 | #95 | C22×D3 | 1 | 1 | yes | characteristic |
| 220 | #95 | C22×D3 | 1 | 1 | yes | characteristic |
| 221 | #95 | C22×D3 | 1 | 6 | yes | — |
| 222 | #95 | C22×D3 | 1 | 6 | yes | — |
| 223 | #95 | C22×D3 | 1 | 6 | yes | — |
| 224 | C23×C3 | C25 | 1 | 1 | yes | characteristic |
| 225 | C22×D3 | — | 2 | 6 | no | — |
| 226 | C22×D3 | — | 2 | 3 | no | — |
| 227 | C22×D3 | — | 2 | 3 | no | — |
| 228 | C22×D3 | — | 2 | 3 | no | — |
| 229 | C22×D3 | — | 2 | 6 | no | — |
| 230 | C22×D3 | — | 2 | 3 | no | — |
| 231 | C22×D3 | C22×Q8 | 1 | 6 | yes | — |
| 232 | C22×D3 | C22×Q8 | 1 | 2 | yes | — |
| 233 | C3×Q8 | — | 8 | 4 | no | — |
| 234 | C2×C3×C4 | — | 2 | 3 | no | — |
| 235 | C2×C3×C4 | — | 2 | 3 | no | — |
| 236 | C2×C3×C4 | — | 2 | 6 | no | — |
| 237 | C2×C3×C4 | — | 2 | 6 | no | — |
| 238 | C2×C3×C4 | — | 2 | 6 | no | — |
| 239 | C2×C3×C4 | — | 2 | 3 | no | — |
| 240 | C2×C3×C4 | — | 2 | 3 | no | — |
| 241 | C2×C3×C4 | — | 2 | 6 | no | — |
| 242 | C2×C3×C4 | — | 2 | 6 | no | — |
| 243 | C2×C3×C4 | C22×Q8 | 1 | 6 | yes | — |
| 244 | C2×Dic3 | — | 2 | 6 | no | — |
| 245 | C2×Dic3 | — | 2 | 3 | no | — |
| 246 | C2×Dic3 | — | 2 | 6 | no | — |
| 247 | C2×Dic3 | — | 2 | 6 | no | — |
| 248 | C2×Dic3 | — | 2 | 6 | no | — |
| 249 | C2×Dic3 | — | 2 | 6 | no | — |
| 250 | C2×Dic3 | H(5,𝔽2) | 1 | 6 | yes | — |
| 251 | D12 | — | 4 | 12 | no | — |
| 252 | D12 | — | 4 | 12 | no | — |
| 253 | C4×D3 | — | 4 | 12 | no | — |
| 254 | C4×D3 | — | 8 | 6 | no | — |
| 255 | C4×D3 | — | 8 | 12 | no | — |
| 256 | Dic6 | — | 8 | 6 | no | — |
| 257 | C24 | — | 3 | 3 | no | — |
| 258 | C24 | — | 3 | 1 | no | — |
| 259 | C2×Q8 | — | 4 | 6 | no | — |
| 260 | C2×Q8 | — | 12 | 3 | no | — |
| 261 | C2×Q8 | — | 12 | 6 | no | — |
| 262 | C2×D4 | — | 3 | 12 | no | — |
| 263 | C2×D4 | — | 3 | 12 | no | — |
| 264 | C2×D4 | — | 12 | 3 | no | — |
| 265 | C2×D4 | — | 12 | 3 | no | — |
| 266 | C2×D4 | — | 12 | 3 | no | — |
| 267 | C2×D4 | — | 12 | 3 | no | — |
| 268 | C22×C4 | — | 3 | 3 | no | — |
| 269 | C22×C4 | — | 3 | 6 | no | — |
| 270 | C22×C4 | — | 3 | 3 | no | — |
| 271 | C22×C4 | — | 6 | 6 | no | — |
| 272 | C22×C4 | — | 6 | 6 | no | — |
| 273 | C22×C4 | — | 12 | 6 | no | — |
| 274 | C22×C4 | — | 12 | 6 | no | — |
| 275 | C22×C4 | — | 12 | 6 | no | — |
| 276 | C22×C4 | — | 12 | 6 | no | — |
| 277 | C22×C4 | — | 12 | 6 | no | — |
| 278 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 279 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 280 | C22×C4 | C23×D3 | 1 | 6 | yes | — |
| 281 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 282 | C4⋊C4 | — | 4 | 3 | no | — |
| 283 | C4⋊C4 | — | 4 | 3 | no | — |
| 284 | C4⋊C4 | — | 4 | 3 | no | — |
| 285 | C4⋊C4 | — | 4 | 3 | no | — |
| 286 | C4⋊C4 | — | 6 | 12 | no | — |
| 287 | C4⋊C4 | — | 6 | 12 | no | — |
| 288 | C4⋊C4 | — | 12 | 3 | no | — |
| 289 | C4⋊C4 | — | 12 | 6 | no | — |
| 290 | C4⋊C4 | — | 12 | 6 | no | — |
| 291 | C22⋊C4 | — | 6 | 12 | no | — |
| 292 | C22⋊C4 | — | 12 | 3 | no | — |
| 293 | C22⋊C4 | — | 12 | 3 | no | — |
| 294 | C22⋊C4 | — | 12 | 6 | no | — |
| 295 | C22⋊C4 | — | 12 | 6 | no | — |
| 296 | C22⋊C4 | — | 12 | 6 | no | — |
| 297 | C22⋊C4 | — | 12 | 6 | no | — |
| 298 | C42 | — | 6 | 6 | no | — |
| 299 | C42 | — | 12 | 3 | no | — |
| 300 | C42 | D3×Q8 | 1 | 4 | yes | — |
| 301 | C22×C3 | C23×Q8 | 1 | 1 | yes | characteristic |
| 302 | C22×C3 | C2×H(5,𝔽2) | 1 | 3 | yes | — |
| 303 | C22×C3 | #585 | 1 | 3 | yes | — |
| 304 | C2×D3 | — | 2 | 12 | no | — |
| 305 | C2×D3 | — | 2 | 6 | no | — |
| 306 | C2×D3 | — | 2 | 6 | no | — |
| 307 | C2×D3 | — | 4 | 3 | no | — |
| 308 | C2×D3 | — | 4 | 3 | no | — |
| 309 | C2×D3 | — | 4 | 6 | no | — |
| 310 | C2×D3 | — | 4 | 3 | no | — |
| 311 | C2×D3 | — | 4 | 1 | no | — |
| 312 | C3×C4 | — | 2 | 6 | no | — |
| 313 | C3×C4 | — | 4 | 3 | no | — |
| 314 | C3×C4 | — | 4 | 3 | no | — |
| 315 | C3×C4 | — | 4 | 6 | no | — |
| 316 | Dic3 | — | 2 | 6 | no | — |
| 317 | Dic3 | — | 4 | 6 | no | — |
| 318 | Dic3 | — | 4 | 3 | no | — |
| 319 | C23 | — | 3 | 6 | no | — |
| 320 | C23 | — | 3 | 2 | no | — |
| 321 | C23 | — | 6 | 6 | no | — |
| 322 | C23 | — | 6 | 3 | no | — |
| 323 | C23 | — | 6 | 3 | no | — |
| 324 | C23 | — | 6 | 3 | no | — |
| 325 | C23 | — | 6 | 6 | no | — |
| 326 | C23 | — | 6 | 3 | no | — |
| 327 | C23 | C24×D3 | 1 | 1 | yes | characteristic |
| 328 | Q8 | — | 8 | 4 | no | — |
| 329 | Q8 | — | 24 | 6 | no | — |
| 330 | D4 | — | 12 | 12 | no | — |
| 331 | D4 | — | 12 | 12 | no | — |
| 332 | C2×C4 | — | 2 | 3 | no | — |
| 333 | C2×C4 | — | 2 | 3 | no | — |
| 334 | C2×C4 | — | 2 | 6 | no | — |
| 335 | C2×C4 | — | 2 | 3 | no | — |
| 336 | C2×C4 | — | 2 | 3 | no | — |
| 337 | C2×C4 | — | 2 | 6 | no | — |
| 338 | C2×C4 | — | 2 | 6 | no | — |
| 339 | C2×C4 | — | 2 | 6 | no | — |
| 340 | C2×C4 | — | 2 | 6 | no | — |
| 341 | C2×C4 | — | 3 | 6 | no | — |
| 342 | C2×C4 | — | 6 | 6 | no | — |
| 343 | C2×C4 | — | 6 | 3 | no | — |
| 344 | C2×C4 | — | 6 | 6 | no | — |
| 345 | C2×C4 | — | 6 | 6 | no | — |
| 346 | C2×C4 | — | 6 | 6 | no | — |
| 347 | C2×C4 | — | 6 | 6 | no | — |
| 348 | C2×C4 | — | 12 | 12 | no | — |
| 349 | C2×C4 | — | 24 | 6 | no | — |
| 350 | C2×C4 | — | 24 | 12 | no | — |
| 351 | C2×C4 | C2×D3×Q8 | 1 | 6 | yes | — |
| 352 | C2×C3 | #3501 | 1 | 3 | yes | — |
| 353 | C2×C3 | #3533 | 1 | 3 | yes | — |
| 354 | C2×C3 | #3549 | 1 | 1 | yes | characteristic |
| 355 | D3 | — | 4 | 6 | no | — |
| 356 | D3 | — | 4 | 2 | no | — |
| 357 | C22 | — | 6 | 12 | no | — |
| 358 | C22 | — | 6 | 6 | no | — |
| 359 | C22 | — | 6 | 6 | no | — |
| 360 | C22 | — | 12 | 3 | no | — |
| 361 | C22 | — | 12 | 1 | no | — |
| 362 | C22 | — | 12 | 3 | no | — |
| 363 | C22 | — | 12 | 3 | no | — |
| 364 | C22 | — | 12 | 6 | no | — |
| 365 | C22 | C22×D3×Q8 | 1 | 1 | yes | characteristic |
| 366 | C22 | D3×H(5,𝔽2) | 1 | 3 | yes | — |
| 367 | C22 | #5968 | 1 | 3 | yes | — |
| 368 | C4 | — | 2 | 6 | no | — |
| 369 | C4 | — | 4 | 6 | no | — |
| 370 | C4 | — | 4 | 3 | no | — |
| 371 | C4 | — | 4 | 3 | no | — |
| 372 | C4 | — | 6 | 6 | no | — |
| 373 | C4 | — | 12 | 3 | no | — |
| 374 | C4 | — | 12 | 6 | no | — |
| 375 | C3 | #47818 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 376 | C2 | — | 12 | 6 | no | — |
| 377 | C2 | — | 12 | 2 | no | — |
| 378 | C2 | #86599 | 1 | 3 | yes | — |
| 379 | C2 | #87087 | 1 | 1 | yes | characteristic |
| 380 | C2 | #87128 | 1 | 3 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D3 |
| commutator, socle, cosocle | C23×C3 | C25 |
| Fitting | C3×#2844 | C2 |
| prime radical | C2×#874 | C22 |
| hypercenter | #2844 | D3 |
| hypocenter | C3 | #47818 |
| LCS | G ▷ C23×C3 ▷ C3 | |
| UCS | C1 ◁ C23 ◁ #2844 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#2844 | C2 | semidirect |
| 2. #78356 | C2 | semidirect |
| 3. #78310 | C2 | semidirect |
| 4. #78292 | C2 | semidirect |
| 5. #78146 | C2 | semidirect |
| 6. #77252 | C2 | semidirect |
| 7. #77215 | C2 | semidirect |
| 8. #74192 | C2 | semidirect |
| 48. #2844 | D3 | semidirect |
| 88. #874 | Q8 | semidirect |
| 375. C3 | #47818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2844 | 2 |
| #78356 | 2 |
| #78310 | 2 |
| #78292 | 2 |
| #78146 | 2 |
| #77252 | 2 |
| #77215 | 2 |
| #74192 | 2 |
| #74153 | 2 |
| #47818 | 3 |