Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1310 conjugacy classes of subgroups.
The subgroup lattice has 436 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#5725 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #79038 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #78517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#1966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #71789 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #70521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70114 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #70099 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #69876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #21800 | — | 3 | 1 | no | maximal, Sylow |
| 11 | C22×#239 | C22 | 1 | 2 | yes | — |
| 12 | C2×C3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#947 | C22 | 1 | 2 | yes | — |
| 14 | #5725 | — | 2 | 2 | no | — |
| 15 | #5725 | — | 2 | 2 | no | — |
| 16 | #5725 | — | 2 | 2 | no | — |
| 17 | #5725 | — | 2 | 2 | no | — |
| 18 | C2×#895 | C4 | 1 | 4 | yes | — |
| 19 | C2×#893 | C4 | 1 | 4 | yes | — |
| 20 | C2×#874 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C42×D3 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#423 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×C3×#101 | C22 | 1 | 4 | yes | — |
| 24 | C3×C4×M16 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#836 | C22 | 1 | 4 | yes | — |
| 26 | C2×#823 | C22 | 1 | 4 | yes | — |
| 27 | C2×#823 | C22 | 1 | 4 | yes | — |
| 28 | #5126 | C22 | 1 | 2 | yes | — |
| 29 | #5126 | C22 | 1 | 2 | yes | — |
| 30 | #5118 | C22 | 1 | 2 | yes | — |
| 31 | Dic3×M16 | C22 | 1 | 2 | yes | — |
| 32 | #4924 | C22 | 1 | 1 | yes | characteristic |
| 33 | C4×#208 | C22 | 1 | 1 | yes | characteristic |
| 34 | #4835 | — | 2 | 2 | no | — |
| 35 | #4833 | — | 2 | 2 | no | — |
| 36 | #4705 | — | 2 | 2 | no | — |
| 37 | #4685 | — | 2 | 2 | no | — |
| 38 | C2×#532 | — | 3 | 1 | no | — |
| 39 | #2920 | — | 3 | 1 | no | — |
| 40 | #2920 | — | 3 | 1 | no | — |
| 41 | #1967 | — | 3 | 4 | no | — |
| 42 | #1966 | — | 3 | 1 | no | — |
| 43 | #1966 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | #1965 | — | 3 | 1 | no | — |
| 45 | #1965 | — | 3 | 1 | no | — |
| 46 | #1785 | — | 3 | 4 | no | — |
| 47 | C22×C3×Q8 | C23 | 1 | 2 | yes | — |
| 48 | C2×#239 | — | 2 | 4 | no | — |
| 49 | C2×#239 | — | 2 | 4 | no | — |
| 50 | C2×#239 | — | 4 | 4 | no | — |
| 51 | C2×#239 | — | 4 | 4 | no | — |
| 52 | C22×D12 | C2×C4 | 1 | 4 | yes | — |
| 53 | C22×D12 | C2×C4 | 1 | 4 | yes | — |
| 54 | C22×D12 | C23 | 1 | 2 | yes | — |
| 55 | C22×C4×D3 | C2×C4 | 1 | 4 | yes | — |
| 56 | C22×C4×D3 | C2×C4 | 1 | 2 | yes | — |
| 57 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 58 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 59 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 60 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 61 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 62 | C3×C4⋊Q8 | — | 2 | 2 | no | — |
| 63 | C2×C3×C4⋊C4 | C2×C4 | 1 | 4 | yes | — |
| 64 | C2×C3×C42 | C23 | 1 | 1 | yes | characteristic |
| 65 | #947 | — | 2 | 2 | no | — |
| 66 | #947 | — | 2 | 4 | no | — |
| 67 | #947 | — | 2 | 2 | no | — |
| 68 | C2×(C2×D3)⋊C4 | C2×C4 | 1 | 8 | yes | — |
| 69 | C2×C4×Dic3 | C2×C4 | 1 | 2 | yes | — |
| 70 | C2×C4×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×#208 | C23 | 1 | 2 | yes | — |
| 72 | C2×#208 | C23 | 1 | 2 | yes | — |
| 73 | #895 | — | 2 | 4 | no | — |
| 74 | #895 | — | 2 | 4 | no | — |
| 75 | #895 | — | 2 | 4 | no | — |
| 76 | #895 | — | 2 | 4 | no | — |
| 77 | #893 | — | 2 | 4 | no | — |
| 78 | #893 | — | 2 | 4 | no | — |
| 79 | #893 | — | 2 | 4 | no | — |
| 80 | #893 | — | 2 | 4 | no | — |
| 81 | #874 | — | 2 | 1 | no | — |
| 82 | #874 | — | 2 | 1 | no | — |
| 83 | #874 | — | 2 | 2 | no | — |
| 84 | C42×D3 | D4 | 1 | 2 | yes | — |
| 85 | C42×D3 | D4 | 1 | 2 | yes | — |
| 86 | C42×D3 | D4 | 1 | 2 | yes | — |
| 87 | C42×D3 | D4 | 1 | 2 | yes | — |
| 88 | C3×C4⋊C8 | — | 2 | 2 | no | — |
| 89 | C3×#101 | — | 4 | 4 | no | — |
| 90 | C3×#97 | — | 2 | 1 | no | — |
| 91 | C3×C4×C8 | — | 2 | 1 | no | — |
| 92 | #836 | — | 4 | 4 | no | — |
| 93 | #823 | — | 4 | 4 | no | — |
| 94 | #823 | — | 4 | 4 | no | — |
| 95 | (C2×D3)⋊C8 | — | 2 | 4 | no | — |
| 96 | (C2×D3)⋊C8 | — | 2 | 4 | no | — |
| 97 | #815 | — | 2 | 2 | no | — |
| 98 | Dic3⋊C8 | — | 2 | 4 | no | — |
| 99 | C8×Dic3 | — | 2 | 2 | no | — |
| 100 | C4⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 101 | #803 | — | 2 | 1 | no | — |
| 102 | C4×C3⋊C8 | — | 2 | 1 | no | — |
| 103 | C22×#41 | — | 3 | 2 | no | — |
| 104 | #532 | — | 6 | 2 | no | — |
| 105 | #532 | — | 6 | 2 | no | — |
| 106 | #532 | — | 6 | 2 | no | — |
| 107 | #532 | — | 6 | 2 | no | — |
| 108 | C2×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | C2×#127 | — | 3 | 1 | no | — |
| 110 | C2×#124 | — | 3 | 2 | no | — |
| 111 | C2×#121 | — | 3 | 4 | no | — |
| 112 | C2×C4×D4 | — | 3 | 4 | no | — |
| 113 | C22×C42 | — | 3 | 1 | no | — |
| 114 | #432 | — | 6 | 2 | no | — |
| 115 | #432 | — | 6 | 2 | no | — |
| 116 | #431 | — | 6 | 2 | no | — |
| 117 | #431 | — | 6 | 2 | no | — |
| 118 | #423 | — | 3 | 2 | no | — |
| 119 | #423 | — | 3 | 1 | no | — |
| 120 | #423 | C2×D3 | 1 | 1 | yes | characteristic |
| 121 | C2×#101 | — | 3 | 4 | no | — |
| 122 | C2×#101 | C2×D3 | 1 | 4 | yes | — |
| 123 | C2×#100 | — | 3 | 4 | no | — |
| 124 | C2×#100 | — | 3 | 4 | no | — |
| 125 | #407 | — | 3 | 2 | no | — |
| 126 | #407 | — | 3 | 2 | no | — |
| 127 | C4×M16 | — | 3 | 2 | no | — |
| 128 | C4×M16 | — | 3 | 1 | no | — |
| 129 | C4×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 130 | C23×D3 | C22×C4 | 1 | 4 | yes | — |
| 131 | C23×D3 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 133 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 134 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 135 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 136 | C22×C3×C4 | C22×C4 | 1 | 4 | yes | — |
| 137 | C22×C3×C4 | C22×C4 | 1 | 2 | yes | — |
| 138 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 139 | C22×Dic3 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | C22×Dic3 | C22×C4 | 1 | 2 | yes | — |
| 141 | #239 | — | 4 | 8 | no | — |
| 142 | #239 | — | 4 | 8 | no | — |
| 143 | #239 | — | 4 | 16 | no | — |
| 144 | C2×D12 | — | 2 | 8 | no | — |
| 145 | C2×D12 | — | 2 | 4 | no | — |
| 146 | C2×D12 | — | 2 | 4 | no | — |
| 147 | C2×D12 | — | 2 | 2 | no | — |
| 148 | C2×D12 | — | 2 | 2 | no | — |
| 149 | C2×D12 | — | 2 | 4 | no | — |
| 150 | C2×D12 | — | 2 | 4 | no | — |
| 151 | C2×D12 | — | 4 | 8 | no | — |
| 152 | C2×D12 | — | 4 | 8 | no | — |
| 153 | C2×C4×D3 | — | 2 | 2 | no | — |
| 154 | C2×C4×D3 | — | 2 | 2 | no | — |
| 155 | C2×C4×D3 | — | 2 | 8 | no | — |
| 156 | C2×C4×D3 | — | 4 | 4 | no | — |
| 157 | C2×C4×D3 | — | 4 | 8 | no | — |
| 158 | C2×C4×D3 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | C2×C4×D3 | C22⋊C4 | 1 | 2 | yes | — |
| 160 | C2×C4×D3 | C22⋊C4 | 1 | 2 | yes | — |
| 161 | C2×C4×D3 | C22⋊C4 | 1 | 2 | yes | — |
| 162 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 163 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 164 | C3×M16 | — | 2 | 2 | no | — |
| 165 | C3×M16 | — | 2 | 4 | no | — |
| 166 | C3×M16 | — | 2 | 2 | no | — |
| 167 | C2×C3×C8 | — | 2 | 2 | no | — |
| 168 | C2×C3×C8 | — | 2 | 2 | no | — |
| 169 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 170 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 171 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C3×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C3×C42 | C2×D4 | 1 | 2 | yes | — |
| 174 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 175 | (C2×D3)⋊C4 | — | 2 | 8 | no | — |
| 176 | C4×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 177 | C4×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 178 | C4×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 179 | C4×Dic3 | C22⋊C4 | 1 | 2 | yes | — |
| 180 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C4×Dic3 | C2×D4 | 1 | 2 | yes | — |
| 182 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | #208 | — | 2 | 2 | no | — |
| 184 | #208 | — | 2 | 4 | no | — |
| 185 | #208 | — | 2 | 2 | no | — |
| 186 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 187 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 188 | C2×#41 | — | 6 | 4 | no | — |
| 189 | C2×#41 | — | 6 | 4 | no | — |
| 190 | C2×#41 | — | 12 | 4 | no | — |
| 191 | C2×#41 | — | 12 | 4 | no | — |
| 192 | C22×Q8 | C22×D3 | 1 | 2 | yes | — |
| 193 | C22×D4 | — | 3 | 4 | no | — |
| 194 | C22×D4 | — | 3 | 4 | no | — |
| 195 | C22×D4 | — | 3 | 2 | no | — |
| 196 | C23×C4 | — | 3 | 1 | no | — |
| 197 | C23×C4 | — | 3 | 2 | no | — |
| 198 | C23×C4 | — | 3 | 4 | no | — |
| 199 | C2×M16 | — | 3 | 2 | no | — |
| 200 | C2×M16 | — | 3 | 2 | no | — |
| 201 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 202 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 203 | C4⋊Q8 | — | 2 | 1 | no | — |
| 204 | C4⋊Q8 | — | 2 | 1 | no | — |
| 205 | C4⋊Q8 | — | 2 | 2 | no | — |
| 206 | #127 | — | 6 | 1 | no | — |
| 207 | #127 | — | 6 | 1 | no | — |
| 208 | #127 | — | 6 | 2 | no | — |
| 209 | #124 | — | 6 | 2 | no | — |
| 210 | #124 | — | 6 | 2 | no | — |
| 211 | #124 | — | 6 | 4 | no | — |
| 212 | #121 | — | 6 | 4 | no | — |
| 213 | #121 | — | 6 | 4 | no | — |
| 214 | #121 | — | 6 | 4 | no | — |
| 215 | #121 | — | 6 | 4 | no | — |
| 216 | C4×D4 | — | 6 | 4 | no | — |
| 217 | C4×D4 | — | 6 | 4 | no | — |
| 218 | C4×D4 | — | 6 | 4 | no | — |
| 219 | C4×D4 | — | 6 | 4 | no | — |
| 220 | C2×C4⋊C4 | C4×D3 | 1 | 4 | yes | — |
| 221 | C2×C22⋊C4 | — | 3 | 8 | no | — |
| 222 | C2×C42 | — | 3 | 2 | no | — |
| 223 | C2×C42 | — | 3 | 1 | no | — |
| 224 | C2×C42 | — | 3 | 2 | no | — |
| 225 | C2×C42 | — | 3 | 2 | no | — |
| 226 | C2×C42 | — | 3 | 2 | no | — |
| 227 | C2×C42 | — | 3 | 2 | no | — |
| 228 | C2×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 229 | C4⋊C8 | — | 2 | 2 | no | — |
| 230 | C4⋊C8 | — | 6 | 4 | no | — |
| 231 | C4⋊C8 | — | 6 | 2 | no | — |
| 232 | #101 | — | 4 | 4 | no | — |
| 233 | #101 | — | 12 | 4 | no | — |
| 234 | #100 | — | 12 | 4 | no | — |
| 235 | #100 | — | 12 | 4 | no | — |
| 236 | C22⋊C8 | — | 6 | 4 | no | — |
| 237 | C22⋊C8 | — | 6 | 4 | no | — |
| 238 | #97 | — | 2 | 1 | no | — |
| 239 | #97 | — | 6 | 2 | no | — |
| 240 | #97 | — | 6 | 1 | no | — |
| 241 | C4×C8 | — | 2 | 1 | no | — |
| 242 | C4×C8 | — | 6 | 2 | no | — |
| 243 | C4×C8 | — | 6 | 1 | no | — |
| 244 | C23×C3 | C23×C4 | 1 | 1 | yes | characteristic |
| 245 | C22×D3 | — | 2 | 2 | no | — |
| 246 | C22×D3 | — | 2 | 4 | no | — |
| 247 | C22×D3 | — | 2 | 8 | no | — |
| 248 | C22×D3 | — | 4 | 2 | no | — |
| 249 | C22×D3 | — | 4 | 8 | no | — |
| 250 | C22×D3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 251 | C3×Q8 | — | 4 | 2 | no | — |
| 252 | C3×Q8 | — | 4 | 2 | no | — |
| 253 | C3×Q8 | — | 4 | 4 | no | — |
| 254 | C2×C3×C4 | — | 2 | 4 | no | — |
| 255 | C2×C3×C4 | — | 2 | 4 | no | — |
| 256 | C2×C3×C4 | — | 2 | 8 | no | — |
| 257 | C2×C3×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 258 | C2×C3×C4 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 259 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 262 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 263 | C2×Dic3 | — | 2 | 2 | no | — |
| 264 | C2×Dic3 | — | 4 | 2 | no | — |
| 265 | C2×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 266 | C2×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 267 | C2×Dic3 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 268 | D12 | — | 4 | 8 | no | — |
| 269 | D12 | — | 4 | 16 | no | — |
| 270 | D12 | — | 4 | 2 | no | — |
| 271 | D12 | — | 4 | 2 | no | — |
| 272 | D12 | — | 4 | 4 | no | — |
| 273 | D12 | — | 4 | 8 | no | — |
| 274 | C4×D3 | — | 2 | 2 | no | — |
| 275 | C4×D3 | — | 2 | 2 | no | — |
| 276 | C4×D3 | — | 2 | 4 | no | — |
| 277 | C4×D3 | — | 2 | 4 | no | — |
| 278 | C4×D3 | — | 2 | 4 | no | — |
| 279 | C4×D3 | — | 4 | 2 | no | — |
| 280 | C4×D3 | — | 4 | 2 | no | — |
| 281 | C4×D3 | — | 4 | 16 | no | — |
| 282 | C3×C8 | — | 4 | 2 | no | — |
| 283 | C3×C8 | — | 4 | 2 | no | — |
| 284 | C3⋊C8 | — | 4 | 2 | no | — |
| 285 | C3⋊C8 | — | 4 | 2 | no | — |
| 286 | C24 | — | 3 | 1 | no | — |
| 287 | C24 | — | 3 | 4 | no | — |
| 288 | #41 | — | 12 | 8 | no | — |
| 289 | #41 | — | 12 | 8 | no | — |
| 290 | #41 | — | 12 | 16 | no | — |
| 291 | C2×Q8 | — | 2 | 2 | no | — |
| 292 | C2×Q8 | — | 2 | 2 | no | — |
| 293 | C2×Q8 | — | 2 | 4 | no | — |
| 294 | C2×Q8 | — | 2 | 4 | no | — |
| 295 | C2×D4 | — | 6 | 8 | no | — |
| 296 | C2×D4 | — | 6 | 4 | no | — |
| 297 | C2×D4 | — | 6 | 4 | no | — |
| 298 | C2×D4 | — | 6 | 2 | no | — |
| 299 | C2×D4 | — | 6 | 2 | no | — |
| 300 | C2×D4 | — | 6 | 4 | no | — |
| 301 | C2×D4 | — | 6 | 4 | no | — |
| 302 | C2×D4 | — | 12 | 8 | no | — |
| 303 | C2×D4 | — | 12 | 8 | no | — |
| 304 | C22×C4 | — | 3 | 1 | no | — |
| 305 | C22×C4 | — | 3 | 2 | no | — |
| 306 | C22×C4 | — | 3 | 2 | no | — |
| 307 | C22×C4 | — | 3 | 2 | no | — |
| 308 | C22×C4 | — | 3 | 2 | no | — |
| 309 | C22×C4 | — | 3 | 2 | no | — |
| 310 | C22×C4 | — | 3 | 2 | no | — |
| 311 | C22×C4 | — | 3 | 2 | no | — |
| 312 | C22×C4 | — | 6 | 8 | no | — |
| 313 | C22×C4 | — | 6 | 2 | no | — |
| 314 | C22×C4 | — | 6 | 2 | no | — |
| 315 | C22×C4 | — | 12 | 4 | no | — |
| 316 | C22×C4 | — | 12 | 8 | no | — |
| 317 | C22×C4 | C2×C4×D3 | 1 | 4 | yes | — |
| 318 | C22×C4 | C2×C4×D3 | 1 | 2 | yes | — |
| 319 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 320 | M16 | — | 2 | 4 | no | — |
| 321 | M16 | — | 2 | 2 | no | — |
| 322 | M16 | — | 2 | 2 | no | — |
| 323 | M16 | — | 6 | 2 | no | — |
| 324 | M16 | — | 6 | 4 | no | — |
| 325 | M16 | — | 6 | 2 | no | — |
| 326 | C2×C8 | — | 2 | 2 | no | — |
| 327 | C2×C8 | — | 2 | 2 | no | — |
| 328 | C2×C8 | — | 6 | 2 | no | — |
| 329 | C2×C8 | — | 6 | 2 | no | — |
| 330 | C4⋊C4 | — | 2 | 4 | no | — |
| 331 | C4⋊C4 | — | 2 | 4 | no | — |
| 332 | C22⋊C4 | — | 6 | 8 | no | — |
| 333 | C22⋊C4 | — | 6 | 8 | no | — |
| 334 | C42 | — | 3 | 2 | no | — |
| 335 | C42 | — | 3 | 2 | no | — |
| 336 | C42 | — | 3 | 2 | no | — |
| 337 | C42 | — | 3 | 2 | no | — |
| 338 | C42 | — | 3 | 1 | no | — |
| 339 | C42 | — | 3 | 1 | no | — |
| 340 | C42 | — | 3 | 2 | no | — |
| 341 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 342 | C42 | D3×D4 | 1 | 1 | yes | characteristic |
| 343 | C42 | D3×D4 | 1 | 2 | yes | — |
| 344 | C22×C3 | — | 2 | 2 | no | — |
| 345 | C22×C3 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 346 | C22×C3 | #518 | 1 | 2 | yes | — |
| 347 | C2×D3 | — | 2 | 2 | no | — |
| 348 | C2×D3 | — | 2 | 2 | no | — |
| 349 | C2×D3 | — | 2 | 2 | no | — |
| 350 | C2×D3 | — | 4 | 4 | no | — |
| 351 | C2×D3 | — | 4 | 4 | no | — |
| 352 | C2×D3 | — | 4 | 8 | no | — |
| 353 | C2×D3 | — | 8 | 8 | no | — |
| 354 | C3×C4 | — | 2 | 2 | no | — |
| 355 | C3×C4 | — | 4 | 4 | no | — |
| 356 | C3×C4 | #413 | 1 | 4 | yes | — |
| 357 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 358 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 359 | C3×C4 | #535 | 1 | 2 | yes | — |
| 360 | Dic3 | — | 2 | 2 | no | — |
| 361 | Dic3 | — | 2 | 2 | no | — |
| 362 | Dic3 | — | 2 | 2 | no | — |
| 363 | C23 | — | 3 | 2 | no | — |
| 364 | C23 | — | 6 | 2 | no | — |
| 365 | C23 | — | 6 | 4 | no | — |
| 366 | C23 | — | 6 | 8 | no | — |
| 367 | C23 | — | 12 | 2 | no | — |
| 368 | C23 | — | 12 | 8 | no | — |
| 369 | C23 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 370 | Q8 | — | 4 | 2 | no | — |
| 371 | Q8 | — | 4 | 2 | no | — |
| 372 | Q8 | — | 4 | 4 | no | — |
| 373 | D4 | — | 12 | 8 | no | — |
| 374 | D4 | — | 12 | 16 | no | — |
| 375 | D4 | — | 12 | 2 | no | — |
| 376 | D4 | — | 12 | 2 | no | — |
| 377 | D4 | — | 12 | 8 | no | — |
| 378 | D4 | — | 12 | 4 | no | — |
| 379 | C2×C4 | — | 2 | 4 | no | — |
| 380 | C2×C4 | — | 2 | 4 | no | — |
| 381 | C2×C4 | — | 2 | 8 | no | — |
| 382 | C2×C4 | — | 3 | 2 | no | — |
| 383 | C2×C4 | — | 3 | 2 | no | — |
| 384 | C2×C4 | — | 3 | 2 | no | — |
| 385 | C2×C4 | — | 6 | 2 | no | — |
| 386 | C2×C4 | — | 6 | 2 | no | — |
| 387 | C2×C4 | — | 6 | 2 | no | — |
| 388 | C2×C4 | — | 6 | 4 | no | — |
| 389 | C2×C4 | — | 6 | 4 | no | — |
| 390 | C2×C4 | — | 6 | 4 | no | — |
| 391 | C2×C4 | — | 12 | 2 | no | — |
| 392 | C2×C4 | — | 12 | 2 | no | — |
| 393 | C2×C4 | — | 12 | 16 | no | — |
| 394 | C2×C4 | — | 12 | 2 | no | — |
| 395 | C2×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 396 | C2×C4 | D3×C22⋊C4 | 1 | 2 | yes | — |
| 397 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 399 | C2×C4 | #1004 | 1 | 2 | yes | — |
| 400 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 401 | C8 | — | 4 | 2 | no | — |
| 402 | C8 | — | 4 | 2 | no | — |
| 403 | C8 | — | 12 | 2 | no | — |
| 404 | C8 | — | 12 | 2 | no | — |
| 405 | C2×C3 | — | 2 | 2 | no | — |
| 406 | C2×C3 | #2309 | 1 | 1 | yes | characteristic |
| 407 | C2×C3 | C2×#413 | 1 | 2 | yes | — |
| 408 | D3 | — | 4 | 2 | no | — |
| 409 | D3 | — | 8 | 4 | no | — |
| 410 | C22 | — | 2 | 2 | no | — |
| 411 | C22 | — | 6 | 2 | no | — |
| 412 | C22 | — | 6 | 2 | no | — |
| 413 | C22 | — | 6 | 2 | no | — |
| 414 | C22 | — | 12 | 4 | no | — |
| 415 | C22 | — | 12 | 8 | no | — |
| 416 | C22 | — | 12 | 4 | no | — |
| 417 | C22 | — | 24 | 8 | no | — |
| 418 | C22 | C2×D3×C22⋊C4 | 1 | 1 | yes | characteristic |
| 419 | C22 | #5545 | 1 | 2 | yes | — |
| 420 | C4 | — | 2 | 2 | no | — |
| 421 | C4 | — | 4 | 4 | no | — |
| 422 | C4 | — | 6 | 2 | no | — |
| 423 | C4 | — | 6 | 2 | no | — |
| 424 | C4 | — | 6 | 2 | no | — |
| 425 | C4 | #4751 | 1 | 4 | yes | — |
| 426 | C4 | #5607 | 1 | 2 | yes | — |
| 427 | C4 | #5674 | 1 | 1 | yes | characteristic |
| 428 | C4 | #5715 | 1 | 1 | yes | characteristic |
| 429 | C3 | #21800 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 430 | C2 | — | 2 | 2 | no | — |
| 431 | C2 | — | 12 | 2 | no | — |
| 432 | C2 | — | 24 | 4 | no | — |
| 433 | C2 | #76428 | 1 | 1 | yes | characteristic |
| 434 | C2 | C2×#4751 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #79038 | C2 | semidirect |
| 3. #78517 | C2 | semidirect |
| 4. C3×#1966 | C2 | semidirect |
| 5. #71789 | C2 | semidirect |
| 6. #70521 | C2 | semidirect |
| 7. #70114 | C2 | semidirect |
| 8. #70099 | C2 | semidirect |
| 9. #69876 | C2 | semidirect |
| 43. #1966 | D3 | semidirect |
| 429. C3 | #21800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5725 | 2 |
| #79038 | 2 |
| #78517 | 2 |
| C3×#1966 | 2 |
| #71789 | 2 |
| #70521 | 2 |
| #70114 | 2 |
| #70099 | 2 |
| #69876 | 2 |
| #21800 | 3 |