Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4782 conjugacy classes of subgroups.
The subgroup lattice has 656 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#1010 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#3488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5836 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #84075 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #83427 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #83390 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #82933 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #82926 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C2×#5040 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #82624 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #82570 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #60374 | — | 3 | 1 | no | maximal, Sylow |
| 13 | C2×C3×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 14 | C22×C3×#41 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#1010 | — | 2 | 3 | no | — |
| 16 | C2×#1010 | — | 2 | 1 | no | — |
| 17 | C2×#1010 | — | 2 | 16 | no | — |
| 18 | C2×#1010 | C22 | 1 | 2 | yes | — |
| 19 | C2×#1010 | C22 | 1 | 6 | yes | complemented |
| 20 | C22×D3×Q8 | — | 2 | 1 | no | — |
| 21 | C22×#237 | — | 2 | 3 | no | — |
| 22 | C22×#235 | C22 | 1 | 3 | yes | complemented |
| 23 | C23×Dic6 | C22 | 1 | 3 | yes | complemented |
| 24 | C3×#550 | — | 2 | 1 | no | — |
| 25 | C3×#548 | — | 2 | 1 | no | — |
| 26 | C3×#546 | — | 2 | 3 | no | — |
| 27 | C3×D42 | — | 2 | 3 | no | — |
| 28 | C3×#537 | C22 | 1 | 3 | yes | complemented |
| 29 | C3×#535 | C22 | 1 | 3 | yes | complemented |
| 30 | C3×#525 | C22 | 1 | 3 | yes | — |
| 31 | C2×C3×#121 | C22 | 1 | 3 | yes | — |
| 32 | C3×#520 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #5836 | — | 2 | 16 | no | — |
| 34 | C2×#951 | C22 | 1 | 6 | yes | complemented |
| 35 | C2×#950 | C22 | 1 | 6 | yes | complemented |
| 36 | C2×#948 | C22 | 1 | 2 | yes | complemented |
| 37 | C22×#214 | C22 | 1 | 6 | yes | complemented |
| 38 | C2×#932 | C22 | 1 | 6 | yes | complemented |
| 39 | #5234 | C22 | 1 | 6 | yes | complemented |
| 40 | #5207 | C22 | 1 | 3 | yes | complemented |
| 41 | C2×#830 | C22 | 1 | 3 | yes | complemented |
| 42 | #5050 | C22 | 1 | 6 | yes | complemented |
| 43 | #5050 | C22 | 1 | 3 | yes | complemented |
| 44 | #5047 | C22 | 1 | 6 | yes | complemented |
| 45 | #5046 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #5040 | C22 | 1 | 6 | yes | complemented |
| 47 | #5040 | C22 | 1 | 12 | yes | complemented |
| 48 | #5040 | C22 | 1 | 6 | yes | complemented |
| 49 | #5040 | C22 | 1 | 3 | yes | complemented |
| 50 | #5037 | C22 | 1 | 6 | yes | complemented |
| 51 | #5037 | C22 | 1 | 12 | yes | complemented |
| 52 | #5036 | C22 | 1 | 3 | yes | complemented |
| 53 | #5004 | C22 | 1 | 6 | yes | complemented |
| 54 | #5002 | C22 | 1 | 6 | yes | complemented |
| 55 | C2×#810 | C22 | 1 | 6 | yes | complemented |
| 56 | #4966 | C22 | 1 | 6 | yes | complemented |
| 57 | C22×2−1+4 | — | 3 | 1 | no | — |
| 58 | C2×#577 | — | 3 | 2 | no | — |
| 59 | #3488 | D3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #3013 | — | 3 | 6 | no | — |
| 61 | #3010 | — | 3 | 6 | no | — |
| 62 | #3006 | — | 3 | 3 | no | — |
| 63 | #3004 | — | 3 | 3 | no | — |
| 64 | #3002 | — | 3 | 3 | no | — |
| 65 | C2×#448 | — | 3 | 3 | no | — |
| 66 | #2898 | — | 3 | 2 | no | — |
| 67 | #2880 | — | 3 | 1 | no | — |
| 68 | C3×H(5,𝔽2) | — | 2 | 8 | no | — |
| 69 | C2×C3×#41 | — | 2 | 8 | no | — |
| 70 | C2×C3×#41 | — | 2 | 1 | no | — |
| 71 | C2×C3×#41 | D4 | 1 | 3 | yes | — |
| 72 | C2×C3×#41 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 74 | C2×C3×#41 | C23 | 1 | 3 | yes | — |
| 75 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22×C3×Q8 | D4 | 1 | 1 | yes | characteristic |
| 77 | C22×C3×D4 | — | 2 | 3 | no | — |
| 78 | C22×C3×D4 | — | 2 | 3 | no | — |
| 79 | C22×C3×D4 | D4 | 1 | 3 | yes | — |
| 80 | C22×C3×D4 | C23 | 1 | 3 | yes | — |
| 81 | C23×C3×C4 | C23 | 1 | 3 | yes | — |
| 82 | C22×#67 | — | 2 | 3 | no | — |
| 83 | C23×Dic3 | — | 2 | 3 | no | — |
| 84 | #1010 | — | 2 | 16 | no | — |
| 85 | #1010 | — | 2 | 48 | no | — |
| 86 | #1010 | — | 2 | 8 | no | — |
| 87 | #1010 | — | 2 | 24 | no | — |
| 88 | #1010 | — | 2 | 24 | no | — |
| 89 | #1010 | D4 | 1 | 16 | yes | complemented |
| 90 | C2×D3×Q8 | — | 2 | 16 | no | — |
| 91 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 92 | C2×D3×Q8 | — | 2 | 6 | no | — |
| 93 | C2×#237 | — | 2 | 48 | no | — |
| 94 | C2×#237 | — | 2 | 6 | no | — |
| 95 | C2×#237 | — | 2 | 12 | no | — |
| 96 | C2×#237 | — | 2 | 6 | no | — |
| 97 | C2×#235 | — | 2 | 3 | no | — |
| 98 | C2×#235 | — | 2 | 3 | no | — |
| 99 | C2×#235 | — | 2 | 24 | no | — |
| 100 | C2×#235 | C23 | 1 | 6 | yes | — |
| 101 | C2×#235 | C23 | 1 | 6 | yes | — |
| 102 | C22×D12 | C23 | 1 | 1 | yes | characteristic |
| 103 | C22×C4×D3 | — | 2 | 3 | no | — |
| 104 | C22×Dic6 | — | 2 | 3 | no | — |
| 105 | C22×Dic6 | — | 2 | 3 | no | — |
| 106 | C22×Dic6 | — | 2 | 3 | no | — |
| 107 | C22×Dic6 | — | 2 | 24 | no | — |
| 108 | C22×Dic6 | C23 | 1 | 3 | yes | — |
| 109 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 110 | C22×Dic6 | C23 | 1 | 6 | yes | — |
| 111 | C3×#127 | — | 2 | 3 | no | — |
| 112 | C3×#124 | — | 2 | 3 | no | — |
| 113 | C3×#123 | — | 2 | 3 | no | — |
| 114 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 115 | C3×C22⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 116 | C3×C22⋊Q8 | C23 | 1 | 3 | yes | — |
| 117 | C3×#121 | — | 2 | 6 | no | — |
| 118 | C3×#121 | — | 2 | 3 | no | — |
| 119 | C3×#121 | — | 2 | 3 | no | — |
| 120 | C3×#121 | — | 2 | 3 | no | — |
| 121 | C3×#121 | C23 | 1 | 3 | yes | — |
| 122 | C3×#121 | C23 | 1 | 6 | yes | — |
| 123 | C3×#121 | C23 | 1 | 3 | yes | — |
| 124 | C3×#120 | — | 2 | 3 | no | — |
| 125 | C3×#120 | — | 2 | 6 | no | — |
| 126 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 127 | C3×C4×D4 | — | 2 | 3 | no | — |
| 128 | C3×C4×D4 | — | 2 | 3 | no | — |
| 129 | C3×C4×D4 | — | 2 | 3 | no | — |
| 130 | C3×#117 | C23 | 1 | 3 | yes | — |
| 131 | C2×C3×C4⋊C4 | C23 | 1 | 3 | yes | — |
| 132 | C2×C3×C22⋊C4 | — | 2 | 3 | no | — |
| 133 | #951 | — | 2 | 24 | no | — |
| 134 | #950 | — | 2 | 24 | no | — |
| 135 | #948 | — | 2 | 8 | no | — |
| 136 | C2×#216 | C23 | 1 | 6 | yes | — |
| 137 | C2×#215 | C23 | 1 | 2 | yes | — |
| 138 | C2×#214 | — | 2 | 24 | no | — |
| 139 | C2×#214 | C23 | 1 | 12 | yes | — |
| 140 | C2×#214 | C23 | 1 | 6 | yes | — |
| 141 | #932 | — | 2 | 24 | no | — |
| 142 | C2×#213 | C23 | 1 | 6 | yes | — |
| 143 | C2×#208 | C23 | 1 | 6 | yes | — |
| 144 | C22×C3⋊C8 | C23 | 1 | 6 | yes | — |
| 145 | #830 | C23 | 1 | 1 | yes | characteristic |
| 146 | #830 | C23 | 1 | 3 | yes | — |
| 147 | #830 | C23 | 1 | 6 | yes | — |
| 148 | #830 | C23 | 1 | 6 | yes | — |
| 149 | #810 | C23 | 1 | 12 | yes | — |
| 150 | #810 | C23 | 1 | 6 | yes | — |
| 151 | #810 | C23 | 1 | 6 | yes | — |
| 152 | #809 | C23 | 1 | 6 | yes | — |
| 153 | #809 | C23 | 1 | 2 | yes | — |
| 154 | C2×2−1+4 | — | 3 | 2 | no | — |
| 155 | C2×2−1+4 | — | 3 | 6 | no | — |
| 156 | C2×2−1+4 | — | 6 | 16 | no | — |
| 157 | C2×2−1+4 | — | 6 | 3 | no | — |
| 158 | C2×2−1+4 | — | 6 | 1 | no | — |
| 159 | C2×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 160 | C22×#41 | — | 3 | 3 | no | — |
| 161 | C22×#41 | — | 6 | 3 | no | — |
| 162 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 163 | C23×Q8 | — | 3 | 3 | no | — |
| 164 | C23×Q8 | — | 6 | 1 | no | — |
| 165 | #577 | — | 6 | 16 | no | — |
| 166 | C2×#137 | — | 3 | 6 | no | — |
| 167 | C2×AGL(1,ℤ/8) | — | 3 | 6 | no | — |
| 168 | C2×#135 | — | 3 | 6 | no | — |
| 169 | C22×SD16 | — | 3 | 6 | no | — |
| 170 | C2×#131 | — | 3 | 2 | no | — |
| 171 | #550 | — | 2 | 1 | no | — |
| 172 | #548 | — | 2 | 1 | no | — |
| 173 | #546 | — | 2 | 3 | no | — |
| 174 | D42 | — | 2 | 3 | no | — |
| 175 | #537 | C2×D3 | 1 | 3 | yes | complemented |
| 176 | #535 | C2×D3 | 1 | 3 | yes | complemented |
| 177 | #525 | C2×D3 | 1 | 3 | yes | — |
| 178 | C2×#121 | C2×D3 | 1 | 3 | yes | — |
| 179 | #520 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 180 | #452 | — | 3 | 6 | no | — |
| 181 | #451 | — | 3 | 3 | no | — |
| 182 | #451 | — | 3 | 6 | no | — |
| 183 | #450 | — | 3 | 1 | no | — |
| 184 | #449 | — | 3 | 6 | no | — |
| 185 | #449 | — | 3 | 12 | no | — |
| 186 | #448 | — | 3 | 3 | no | — |
| 187 | #448 | — | 3 | 6 | no | — |
| 188 | #448 | — | 3 | 12 | no | — |
| 189 | #448 | — | 3 | 6 | no | — |
| 190 | #447 | — | 3 | 3 | no | — |
| 191 | #419 | — | 3 | 6 | no | — |
| 192 | #417 | — | 3 | 6 | no | — |
| 193 | #416 | — | 3 | 6 | no | — |
| 194 | C2×#103 | — | 3 | 6 | no | — |
| 195 | #408 | — | 3 | 6 | no | — |
| 196 | #407 | — | 3 | 3 | no | — |
| 197 | C2×C22⋊C8 | — | 3 | 3 | no | — |
| 198 | C24×C3 | — | 2 | 3 | no | — |
| 199 | C24×C3 | C2×D4 | 1 | 3 | yes | — |
| 200 | C23×D3 | — | 2 | 1 | no | — |
| 201 | C3×#41 | — | 2 | 4 | no | — |
| 202 | C3×#41 | — | 2 | 12 | no | — |
| 203 | C3×#41 | — | 2 | 12 | no | — |
| 204 | C3×#41 | — | 2 | 12 | no | — |
| 205 | C3×#41 | — | 4 | 4 | no | — |
| 206 | C3×#41 | C2×D4 | 1 | 8 | yes | — |
| 207 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 208 | C2×C3×Q8 | C2×D4 | 1 | 3 | yes | — |
| 209 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C3×Q8 | C24 | 1 | 1 | yes | characteristic |
| 211 | C2×C3×D4 | — | 2 | 12 | no | — |
| 212 | C2×C3×D4 | — | 2 | 3 | no | — |
| 213 | C2×C3×D4 | — | 2 | 3 | no | — |
| 214 | C2×C3×D4 | — | 2 | 3 | no | — |
| 215 | C2×C3×D4 | — | 2 | 6 | no | — |
| 216 | C2×C3×D4 | — | 2 | 12 | no | — |
| 217 | C2×C3×D4 | — | 2 | 3 | no | — |
| 218 | C2×C3×D4 | — | 4 | 12 | no | — |
| 219 | C2×C3×D4 | — | 8 | 6 | no | — |
| 220 | C2×C3×D4 | C2×D4 | 1 | 6 | yes | — |
| 221 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 222 | C2×C3×D4 | C2×D4 | 1 | 3 | yes | — |
| 223 | C2×C3×D4 | C24 | 1 | 3 | yes | — |
| 224 | C22×C3×C4 | — | 2 | 12 | no | — |
| 225 | C22×C3×C4 | — | 2 | 3 | no | — |
| 226 | C22×C3×C4 | — | 2 | 3 | no | — |
| 227 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 228 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 229 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 230 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 231 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 232 | C22×C3×C4 | C24 | 1 | 3 | yes | — |
| 233 | C2×#67 | — | 2 | 24 | no | — |
| 234 | C2×#67 | — | 2 | 6 | no | — |
| 235 | C2×#67 | — | 2 | 6 | no | — |
| 236 | C22×Dic3 | — | 2 | 24 | no | — |
| 237 | C22×Dic3 | — | 2 | 3 | no | — |
| 238 | C22×Dic3 | — | 2 | 6 | no | — |
| 239 | C22×Dic3 | — | 2 | 6 | no | — |
| 240 | D3×Q8 | — | 2 | 48 | no | — |
| 241 | D3×Q8 | — | 2 | 16 | no | — |
| 242 | #237 | — | 2 | 96 | no | — |
| 243 | #237 | — | 2 | 48 | no | — |
| 244 | #237 | — | 2 | 48 | no | — |
| 245 | #235 | — | 2 | 24 | no | — |
| 246 | #235 | — | 2 | 24 | no | — |
| 247 | #235 | — | 2 | 12 | no | — |
| 248 | #235 | — | 2 | 12 | no | — |
| 249 | #235 | — | 2 | 12 | no | — |
| 250 | #235 | C2×D4 | 1 | 24 | yes | complemented |
| 251 | C2×D12 | — | 2 | 1 | no | — |
| 252 | C2×D12 | — | 2 | 4 | no | — |
| 253 | C2×D12 | C24 | 1 | 2 | yes | — |
| 254 | C2×C4×D3 | — | 2 | 24 | no | — |
| 255 | C2×C4×D3 | — | 2 | 6 | no | — |
| 256 | C2×C4×D3 | — | 2 | 6 | no | — |
| 257 | C2×Dic6 | — | 2 | 24 | no | — |
| 258 | C2×Dic6 | — | 2 | 24 | no | — |
| 259 | C2×Dic6 | — | 2 | 24 | no | — |
| 260 | C2×Dic6 | — | 2 | 3 | no | — |
| 261 | C2×Dic6 | — | 2 | 6 | no | — |
| 262 | C2×Dic6 | — | 2 | 6 | no | — |
| 263 | C2×Dic6 | — | 2 | 12 | no | — |
| 264 | C2×Dic6 | — | 2 | 12 | no | — |
| 265 | C2×Dic6 | — | 2 | 24 | no | — |
| 266 | C2×Dic6 | C2×D4 | 1 | 24 | yes | complemented |
| 267 | C2×Dic6 | C24 | 1 | 6 | yes | — |
| 268 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 269 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 270 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 271 | C3×C4⋊C4 | C24 | 1 | 3 | yes | — |
| 272 | C3×C4⋊C4 | C24 | 1 | 1 | yes | characteristic |
| 273 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 274 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 275 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 276 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 277 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 278 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 279 | C3×C42 | — | 2 | 3 | no | — |
| 280 | #216 | — | 2 | 12 | no | — |
| 281 | #215 | — | 2 | 4 | no | — |
| 282 | #214 | — | 2 | 24 | no | — |
| 283 | #214 | — | 2 | 12 | no | — |
| 284 | #213 | — | 2 | 12 | no | — |
| 285 | #208 | — | 2 | 12 | no | — |
| 286 | C2×C3⋊C8 | — | 2 | 12 | no | — |
| 287 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 288 | C2×C3⋊C8 | C24 | 1 | 6 | yes | — |
| 289 | 2−1+4 | — | 3 | 16 | no | — |
| 290 | 2−1+4 | — | 6 | 24 | no | — |
| 291 | 2−1+4 | — | 6 | 24 | no | — |
| 292 | 2−1+4 | — | 6 | 48 | no | — |
| 293 | 2−1+4 | — | 6 | 16 | no | — |
| 294 | 2−1+4 | — | 6 | 8 | no | — |
| 295 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 296 | C2×#41 | — | 2 | 8 | no | — |
| 297 | C2×#41 | — | 2 | 1 | no | — |
| 298 | C2×#41 | — | 3 | 6 | no | — |
| 299 | C2×#41 | — | 3 | 6 | no | — |
| 300 | C2×#41 | — | 6 | 24 | no | — |
| 301 | C2×#41 | — | 6 | 48 | no | — |
| 302 | C2×#41 | — | 6 | 12 | no | — |
| 303 | C2×#41 | — | 6 | 6 | no | — |
| 304 | C2×#41 | — | 6 | 6 | no | — |
| 305 | C2×#41 | — | 6 | 3 | no | — |
| 306 | C2×#41 | — | 6 | 3 | no | — |
| 307 | C2×#41 | #67 | 1 | 3 | yes | — |
| 308 | C2×#41 | #67 | 1 | 1 | yes | characteristic |
| 309 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 310 | C2×#41 | C22×D3 | 1 | 3 | yes | — |
| 311 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 312 | C22×Q8 | — | 3 | 6 | no | — |
| 313 | C22×Q8 | — | 3 | 3 | no | — |
| 314 | C22×Q8 | — | 3 | 6 | no | — |
| 315 | C22×Q8 | — | 6 | 24 | no | — |
| 316 | C22×Q8 | — | 6 | 16 | no | — |
| 317 | C22×Q8 | — | 6 | 6 | no | — |
| 318 | C22×Q8 | — | 6 | 2 | no | — |
| 319 | C22×Q8 | — | 6 | 3 | no | — |
| 320 | C22×Q8 | — | 6 | 3 | no | — |
| 321 | C22×Q8 | — | 6 | 3 | no | — |
| 322 | C22×Q8 | #67 | 1 | 1 | yes | characteristic |
| 323 | C22×D4 | — | 2 | 3 | no | — |
| 324 | C22×D4 | — | 2 | 3 | no | — |
| 325 | C22×D4 | — | 3 | 1 | no | — |
| 326 | C22×D4 | — | 6 | 3 | no | — |
| 327 | C22×D4 | #67 | 1 | 3 | yes | — |
| 328 | C22×D4 | C22×D3 | 1 | 3 | yes | — |
| 329 | C23×C4 | — | 6 | 3 | no | — |
| 330 | C23×C4 | — | 6 | 3 | no | — |
| 331 | C23×C4 | C22×D3 | 1 | 3 | yes | — |
| 332 | #137 | — | 6 | 24 | no | — |
| 333 | AGL(1,ℤ/8) | — | 6 | 24 | no | — |
| 334 | #135 | — | 6 | 24 | no | — |
| 335 | C2×Q16 | — | 3 | 6 | no | — |
| 336 | C2×SD16 | — | 3 | 2 | no | — |
| 337 | C2×SD16 | — | 3 | 6 | no | — |
| 338 | C2×SD16 | — | 3 | 12 | no | — |
| 339 | C2×SD16 | — | 6 | 24 | no | — |
| 340 | C2×D8 | — | 3 | 6 | no | — |
| 341 | #131 | — | 6 | 8 | no | — |
| 342 | C2×M16 | — | 3 | 6 | no | — |
| 343 | C22×C8 | — | 3 | 6 | no | — |
| 344 | #127 | — | 2 | 3 | no | — |
| 345 | #124 | — | 2 | 3 | no | — |
| 346 | #123 | — | 2 | 3 | no | — |
| 347 | C22⋊Q8 | — | 2 | 3 | no | — |
| 348 | C22⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 349 | C22⋊Q8 | C22×D3 | 1 | 3 | yes | — |
| 350 | #121 | — | 2 | 6 | no | — |
| 351 | #121 | — | 2 | 3 | no | — |
| 352 | #121 | — | 2 | 3 | no | — |
| 353 | #121 | — | 2 | 3 | no | — |
| 354 | #121 | C22×D3 | 1 | 3 | yes | — |
| 355 | #121 | C22×D3 | 1 | 6 | yes | — |
| 356 | #121 | C22×D3 | 1 | 3 | yes | — |
| 357 | #120 | — | 2 | 3 | no | — |
| 358 | #120 | — | 2 | 6 | no | — |
| 359 | C4×Q8 | — | 2 | 1 | no | — |
| 360 | C4×D4 | — | 2 | 3 | no | — |
| 361 | C4×D4 | — | 2 | 3 | no | — |
| 362 | C4×D4 | — | 2 | 3 | no | — |
| 363 | #117 | C22×D3 | 1 | 3 | yes | — |
| 364 | C2×C4⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 365 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 366 | #103 | — | 3 | 6 | no | — |
| 367 | #103 | — | 3 | 12 | no | — |
| 368 | #103 | — | 3 | 6 | no | — |
| 369 | #102 | — | 3 | 2 | no | — |
| 370 | #102 | — | 3 | 6 | no | — |
| 371 | C22⋊C8 | — | 3 | 1 | no | — |
| 372 | C22⋊C8 | — | 3 | 3 | no | — |
| 373 | C22⋊C8 | — | 3 | 6 | no | — |
| 374 | C22⋊C8 | — | 3 | 6 | no | — |
| 375 | C23×C3 | — | 2 | 6 | no | — |
| 376 | C23×C3 | — | 2 | 6 | no | — |
| 377 | C23×C3 | — | 2 | 3 | no | — |
| 378 | C23×C3 | — | 4 | 3 | no | — |
| 379 | C23×C3 | — | 4 | 6 | no | — |
| 380 | C23×C3 | — | 8 | 3 | no | — |
| 381 | C23×C3 | — | 8 | 3 | no | — |
| 382 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 383 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 384 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 385 | C22×D3 | — | 2 | 4 | no | — |
| 386 | C22×D3 | — | 2 | 2 | no | — |
| 387 | C22×D3 | — | 4 | 2 | no | — |
| 388 | C22×D3 | — | 4 | 2 | no | — |
| 389 | C3×Q8 | — | 2 | 6 | no | — |
| 390 | C3×Q8 | — | 2 | 2 | no | — |
| 391 | C3×Q8 | #120 | 1 | 4 | yes | — |
| 392 | C3×D4 | — | 2 | 12 | no | — |
| 393 | C3×D4 | — | 2 | 6 | no | — |
| 394 | C3×D4 | — | 2 | 6 | no | — |
| 395 | C3×D4 | — | 4 | 6 | no | — |
| 396 | C3×D4 | — | 4 | 6 | no | — |
| 397 | C3×D4 | — | 4 | 6 | no | — |
| 398 | C3×D4 | — | 8 | 3 | no | — |
| 399 | C3×D4 | — | 8 | 6 | no | — |
| 400 | C3×D4 | #120 | 1 | 12 | yes | — |
| 401 | C2×C3×C4 | — | 2 | 6 | no | — |
| 402 | C2×C3×C4 | — | 2 | 6 | no | — |
| 403 | C2×C3×C4 | — | 2 | 6 | no | — |
| 404 | C2×C3×C4 | — | 2 | 2 | no | — |
| 405 | C2×C3×C4 | — | 2 | 6 | no | — |
| 406 | C2×C3×C4 | — | 2 | 1 | no | — |
| 407 | C2×C3×C4 | — | 2 | 3 | no | — |
| 408 | C2×C3×C4 | — | 2 | 1 | no | — |
| 409 | C2×C3×C4 | — | 4 | 6 | no | — |
| 410 | C2×C3×C4 | — | 8 | 3 | no | — |
| 411 | C2×C3×C4 | C22×D4 | 1 | 12 | yes | — |
| 412 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 413 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 414 | C2×C3×C4 | C22×D4 | 1 | 3 | yes | — |
| 415 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 416 | #67 | — | 2 | 24 | no | — |
| 417 | #67 | — | 2 | 24 | no | — |
| 418 | C2×Dic3 | — | 2 | 12 | no | — |
| 419 | C2×Dic3 | — | 2 | 24 | no | — |
| 420 | C2×Dic3 | — | 2 | 24 | no | — |
| 421 | C2×Dic3 | — | 2 | 6 | no | — |
| 422 | D12 | — | 2 | 4 | no | — |
| 423 | D12 | — | 2 | 2 | no | — |
| 424 | D12 | C22×D4 | 1 | 4 | yes | — |
| 425 | C4×D3 | — | 2 | 24 | no | — |
| 426 | C4×D3 | — | 2 | 24 | no | — |
| 427 | Dic6 | — | 2 | 12 | no | — |
| 428 | Dic6 | — | 2 | 24 | no | — |
| 429 | Dic6 | — | 2 | 24 | no | — |
| 430 | Dic6 | — | 2 | 6 | no | — |
| 431 | Dic6 | C22×D4 | 1 | 12 | yes | — |
| 432 | C3⋊C8 | — | 2 | 2 | no | — |
| 433 | C3⋊C8 | — | 2 | 6 | no | — |
| 434 | C24 | — | 2 | 3 | no | — |
| 435 | C24 | — | 6 | 1 | no | — |
| 436 | C24 | C2×#67 | 1 | 3 | yes | — |
| 437 | #41 | — | 2 | 4 | no | — |
| 438 | #41 | — | 2 | 12 | no | — |
| 439 | #41 | — | 2 | 12 | no | — |
| 440 | #41 | — | 2 | 12 | no | — |
| 441 | #41 | — | 3 | 24 | no | — |
| 442 | #41 | — | 4 | 4 | no | — |
| 443 | #41 | — | 6 | 12 | no | — |
| 444 | #41 | — | 6 | 12 | no | — |
| 445 | #41 | — | 6 | 24 | no | — |
| 446 | #41 | — | 6 | 24 | no | — |
| 447 | #41 | — | 6 | 96 | no | — |
| 448 | #41 | — | 6 | 48 | no | — |
| 449 | #41 | — | 6 | 48 | no | — |
| 450 | #41 | — | 6 | 12 | no | — |
| 451 | #41 | D3×D4 | 1 | 8 | yes | — |
| 452 | C2×Q8 | — | 2 | 4 | no | — |
| 453 | C2×Q8 | — | 3 | 24 | no | — |
| 454 | C2×Q8 | — | 3 | 6 | no | — |
| 455 | C2×Q8 | — | 6 | 12 | no | — |
| 456 | C2×Q8 | — | 6 | 24 | no | — |
| 457 | C2×Q8 | — | 6 | 24 | no | — |
| 458 | C2×Q8 | — | 6 | 24 | no | — |
| 459 | C2×Q8 | — | 6 | 24 | no | — |
| 460 | C2×Q8 | — | 6 | 48 | no | — |
| 461 | C2×Q8 | — | 6 | 16 | no | — |
| 462 | C2×Q8 | — | 6 | 12 | no | — |
| 463 | C2×Q8 | — | 6 | 6 | no | — |
| 464 | C2×Q8 | — | 6 | 3 | no | — |
| 465 | C2×Q8 | — | 6 | 6 | no | — |
| 466 | C2×Q8 | C2×#67 | 1 | 3 | yes | — |
| 467 | C2×Q8 | C2×#67 | 1 | 1 | yes | characteristic |
| 468 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 469 | C2×D4 | — | 2 | 12 | no | — |
| 470 | C2×D4 | — | 2 | 3 | no | — |
| 471 | C2×D4 | — | 2 | 3 | no | — |
| 472 | C2×D4 | — | 2 | 3 | no | — |
| 473 | C2×D4 | — | 2 | 6 | no | — |
| 474 | C2×D4 | — | 2 | 12 | no | — |
| 475 | C2×D4 | — | 2 | 3 | no | — |
| 476 | C2×D4 | — | 3 | 2 | no | — |
| 477 | C2×D4 | — | 4 | 12 | no | — |
| 478 | C2×D4 | — | 6 | 4 | no | — |
| 479 | C2×D4 | — | 6 | 24 | no | — |
| 480 | C2×D4 | — | 6 | 6 | no | — |
| 481 | C2×D4 | — | 6 | 6 | no | — |
| 482 | C2×D4 | — | 6 | 1 | no | — |
| 483 | C2×D4 | — | 8 | 6 | no | — |
| 484 | C2×D4 | C2×#67 | 1 | 6 | yes | — |
| 485 | C2×D4 | C2×#67 | 1 | 3 | yes | — |
| 486 | C2×D4 | C2×#67 | 1 | 3 | yes | — |
| 487 | C2×D4 | C23×D3 | 1 | 3 | yes | — |
| 488 | C22×C4 | — | 2 | 12 | no | — |
| 489 | C22×C4 | — | 2 | 3 | no | — |
| 490 | C22×C4 | — | 2 | 3 | no | — |
| 491 | C22×C4 | — | 6 | 24 | no | — |
| 492 | C22×C4 | — | 6 | 24 | no | — |
| 493 | C22×C4 | — | 6 | 3 | no | — |
| 494 | C22×C4 | — | 6 | 6 | no | — |
| 495 | C22×C4 | — | 6 | 6 | no | — |
| 496 | C22×C4 | — | 6 | 6 | no | — |
| 497 | C22×C4 | — | 6 | 6 | no | — |
| 498 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 499 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 500 | C22×C4 | C2×#67 | 1 | 3 | yes | — |
| 501 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 502 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 503 | C22×C4 | C23×D3 | 1 | 3 | yes | — |
| 504 | Q16 | — | 6 | 12 | no | — |
| 505 | SD16 | — | 6 | 12 | no | — |
| 506 | SD16 | — | 6 | 24 | no | — |
| 507 | SD16 | — | 6 | 4 | no | — |
| 508 | D8 | — | 6 | 12 | no | — |
| 509 | M16 | — | 6 | 12 | no | — |
| 510 | C2×C8 | — | 3 | 2 | no | — |
| 511 | C2×C8 | — | 3 | 6 | no | — |
| 512 | C2×C8 | — | 6 | 12 | no | — |
| 513 | C4⋊C4 | — | 2 | 3 | no | — |
| 514 | C4⋊C4 | — | 2 | 1 | no | — |
| 515 | C4⋊C4 | — | 2 | 3 | no | — |
| 516 | C4⋊C4 | C23×D3 | 1 | 3 | yes | — |
| 517 | C4⋊C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 518 | C22⋊C4 | — | 2 | 3 | no | — |
| 519 | C22⋊C4 | — | 2 | 1 | no | — |
| 520 | C22⋊C4 | — | 2 | 3 | no | — |
| 521 | C22⋊C4 | — | 2 | 3 | no | — |
| 522 | C22⋊C4 | — | 2 | 6 | no | — |
| 523 | C22⋊C4 | — | 2 | 3 | no | — |
| 524 | C42 | — | 2 | 3 | no | — |
| 525 | C22×C3 | — | 2 | 1 | no | — |
| 526 | C22×C3 | — | 2 | 3 | no | — |
| 527 | C22×C3 | — | 2 | 1 | no | — |
| 528 | C22×C3 | — | 2 | 3 | no | — |
| 529 | C22×C3 | — | 2 | 3 | no | — |
| 530 | C22×C3 | — | 2 | 3 | no | — |
| 531 | C22×C3 | — | 2 | 3 | no | — |
| 532 | C22×C3 | — | 4 | 12 | no | — |
| 533 | C22×C3 | — | 4 | 3 | no | — |
| 534 | C22×C3 | — | 4 | 3 | no | — |
| 535 | C22×C3 | — | 4 | 3 | no | — |
| 536 | C22×C3 | — | 16 | 6 | no | — |
| 537 | C22×C3 | C2×#120 | 1 | 6 | yes | — |
| 538 | C22×C3 | #577 | 1 | 2 | yes | complemented |
| 539 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 540 | C2×D3 | — | 2 | 4 | no | — |
| 541 | C2×D3 | — | 4 | 8 | no | — |
| 542 | C2×D3 | — | 4 | 2 | no | — |
| 543 | C2×D3 | — | 4 | 2 | no | — |
| 544 | C3×C4 | — | 2 | 1 | no | — |
| 545 | C3×C4 | — | 2 | 3 | no | — |
| 546 | C3×C4 | — | 4 | 1 | no | — |
| 547 | C3×C4 | — | 4 | 1 | no | — |
| 548 | C3×C4 | — | 4 | 3 | no | — |
| 549 | C3×C4 | C2×#120 | 1 | 6 | yes | — |
| 550 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 551 | Dic3 | — | 2 | 12 | no | — |
| 552 | C23 | — | 2 | 6 | no | — |
| 553 | C23 | — | 2 | 6 | no | — |
| 554 | C23 | — | 2 | 3 | no | — |
| 555 | C23 | — | 4 | 3 | no | — |
| 556 | C23 | — | 4 | 6 | no | — |
| 557 | C23 | — | 6 | 4 | no | — |
| 558 | C23 | — | 6 | 2 | no | — |
| 559 | C23 | — | 8 | 3 | no | — |
| 560 | C23 | — | 8 | 3 | no | — |
| 561 | C23 | — | 12 | 2 | no | — |
| 562 | C23 | — | 12 | 2 | no | — |
| 563 | C23 | C22×#67 | 1 | 3 | yes | — |
| 564 | C23 | C22×#67 | 1 | 3 | yes | — |
| 565 | C23 | C22×#67 | 1 | 1 | yes | characteristic |
| 566 | Q8 | — | 2 | 6 | no | — |
| 567 | Q8 | — | 2 | 2 | no | — |
| 568 | Q8 | — | 3 | 12 | no | — |
| 569 | Q8 | — | 6 | 12 | no | — |
| 570 | Q8 | — | 6 | 24 | no | — |
| 571 | Q8 | — | 6 | 6 | no | — |
| 572 | Q8 | — | 6 | 24 | no | — |
| 573 | Q8 | #937 | 1 | 4 | yes | — |
| 574 | D4 | — | 2 | 12 | no | — |
| 575 | D4 | — | 2 | 6 | no | — |
| 576 | D4 | — | 2 | 6 | no | — |
| 577 | D4 | — | 3 | 4 | no | — |
| 578 | D4 | — | 4 | 6 | no | — |
| 579 | D4 | — | 4 | 6 | no | — |
| 580 | D4 | — | 4 | 6 | no | — |
| 581 | D4 | — | 6 | 4 | no | — |
| 582 | D4 | — | 6 | 24 | no | — |
| 583 | D4 | — | 6 | 24 | no | — |
| 584 | D4 | — | 6 | 2 | no | — |
| 585 | D4 | — | 8 | 6 | no | — |
| 586 | D4 | — | 8 | 3 | no | — |
| 587 | D4 | #937 | 1 | 12 | yes | — |
| 588 | C2×C4 | — | 2 | 6 | no | — |
| 589 | C2×C4 | — | 2 | 2 | no | — |
| 590 | C2×C4 | — | 2 | 6 | no | — |
| 591 | C2×C4 | — | 2 | 6 | no | — |
| 592 | C2×C4 | — | 2 | 6 | no | — |
| 593 | C2×C4 | — | 2 | 1 | no | — |
| 594 | C2×C4 | — | 2 | 3 | no | — |
| 595 | C2×C4 | — | 2 | 1 | no | — |
| 596 | C2×C4 | — | 4 | 6 | no | — |
| 597 | C2×C4 | — | 6 | 24 | no | — |
| 598 | C2×C4 | — | 6 | 12 | no | — |
| 599 | C2×C4 | — | 6 | 24 | no | — |
| 600 | C2×C4 | — | 6 | 6 | no | — |
| 601 | C2×C4 | — | 6 | 24 | no | — |
| 602 | C2×C4 | — | 6 | 24 | no | — |
| 603 | C2×C4 | — | 8 | 3 | no | — |
| 604 | C2×C4 | C2×D3×D4 | 1 | 12 | yes | — |
| 605 | C2×C4 | C22×#67 | 1 | 3 | yes | — |
| 606 | C2×C4 | C22×#67 | 1 | 1 | yes | characteristic |
| 607 | C2×C4 | C22×#67 | 1 | 3 | yes | — |
| 608 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 609 | C8 | — | 6 | 2 | no | — |
| 610 | C8 | — | 6 | 6 | no | — |
| 611 | C2×C3 | — | 2 | 2 | no | — |
| 612 | C2×C3 | — | 2 | 6 | no | — |
| 613 | C2×C3 | — | 4 | 3 | no | — |
| 614 | C2×C3 | — | 8 | 3 | no | — |
| 615 | C2×C3 | C22×#120 | 1 | 1 | yes | characteristic |
| 616 | C2×C3 | C2×#577 | 1 | 1 | yes | characteristic |
| 617 | C2×C3 | #3586 | 1 | 1 | yes | characteristic |
| 618 | D3 | — | 4 | 4 | no | — |
| 619 | C22 | — | 2 | 1 | no | — |
| 620 | C22 | — | 2 | 3 | no | — |
| 621 | C22 | — | 2 | 1 | no | — |
| 622 | C22 | — | 2 | 3 | no | — |
| 623 | C22 | — | 2 | 3 | no | — |
| 624 | C22 | — | 2 | 3 | no | — |
| 625 | C22 | — | 2 | 3 | no | — |
| 626 | C22 | — | 4 | 12 | no | — |
| 627 | C22 | — | 4 | 3 | no | — |
| 628 | C22 | — | 4 | 3 | no | — |
| 629 | C22 | — | 4 | 3 | no | — |
| 630 | C22 | — | 6 | 4 | no | — |
| 631 | C22 | — | 12 | 8 | no | — |
| 632 | C22 | — | 12 | 2 | no | — |
| 633 | C22 | — | 12 | 2 | no | — |
| 634 | C22 | — | 16 | 6 | no | — |
| 635 | C22 | C2×#937 | 1 | 6 | yes | — |
| 636 | C22 | #5836 | 1 | 2 | yes | complemented |
| 637 | C22 | C23×#67 | 1 | 1 | yes | characteristic |
| 638 | C4 | — | 2 | 1 | no | — |
| 639 | C4 | — | 2 | 3 | no | — |
| 640 | C4 | — | 4 | 1 | no | — |
| 641 | C4 | — | 4 | 1 | no | — |
| 642 | C4 | — | 4 | 3 | no | — |
| 643 | C4 | — | 6 | 12 | no | — |
| 644 | C4 | C2×#937 | 1 | 6 | yes | — |
| 645 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 646 | C3 | #60374 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 647 | C2 | — | 2 | 2 | no | — |
| 648 | C2 | — | 2 | 6 | no | — |
| 649 | C2 | — | 4 | 3 | no | — |
| 650 | C2 | — | 8 | 3 | no | — |
| 651 | C2 | — | 12 | 4 | no | — |
| 652 | C2 | C22×#937 | 1 | 1 | yes | characteristic |
| 653 | C2 | C2×#5836 | 1 | 1 | yes | characteristic |
| 654 | C2 | #87299 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#1010 | C2 | semidirect |
| 2. C3×#3488 | C2 | semidirect |
| 3. C2×#5836 | C2 | semidirect |
| 4. #84075 | C2 | semidirect |
| 5. #83427 | C2 | semidirect |
| 6. #83390 | C2 | semidirect |
| 7. #82933 | C2 | semidirect |
| 8. #82926 | C2 | semidirect |
| 9. C2×#5040 | C2 | semidirect |
| 10. #82624 | C2 | semidirect |
| 11. #82570 | C2 | semidirect |
| 13. C2×C3×H(5,𝔽2) | C22 | semidirect |
| 19. C2×#1010 | C22 | semidirect |
| 22. C22×#235 | C22 | semidirect |
| 23. C23×Dic6 | C22 | semidirect |
| 28. C3×#537 | C22 | semidirect |
| 29. C3×#535 | C22 | semidirect |
| 32. C3×#520 | C22 | semidirect |
| 34. C2×#951 | C22 | semidirect |
| 35. C2×#950 | C22 | semidirect |
| 36. C2×#948 | C22 | semidirect |
| 37. C22×#214 | C22 | semidirect |
| 38. C2×#932 | C22 | semidirect |
| 39. #5234 | C22 | semidirect |
| 40. #5207 | C22 | semidirect |
| 41. C2×#830 | C22 | semidirect |
| 42. #5050 | C22 | semidirect |
| 43. #5050 | C22 | semidirect |
| 44. #5047 | C22 | semidirect |
| 45. #5046 | C22 | semidirect |
| 46. #5040 | C22 | semidirect |
| 47. #5040 | C22 | semidirect |
| 48. #5040 | C22 | semidirect |
| 49. #5040 | C22 | semidirect |
| 50. #5037 | C22 | semidirect |
| 51. #5037 | C22 | semidirect |
| 52. #5036 | C22 | semidirect |
| 53. #5004 | C22 | semidirect |
| 54. #5002 | C22 | semidirect |
| 55. C2×#810 | C22 | semidirect |
| 56. #4966 | C22 | semidirect |
| 59. #3488 | D3 | semidirect |
| 89. #1010 | D4 | semidirect |
| 159. C2×H(5,𝔽2) | C2×D3 | semidirect |
| 175. #537 | C2×D3 | semidirect |
| 176. #535 | C2×D3 | semidirect |
| 179. #520 | C2×D3 | semidirect |
| 250. #235 | C2×D4 | semidirect |
| 266. C2×Dic6 | C2×D4 | semidirect |
| 538. C22×C3 | #577 | semidirect |
| 636. C22 | #5836 | semidirect |
| 646. C3 | #60374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#1010 | 2 |
| C3×#3488 | 2 |
| C2×#5836 | 2 |
| #84075 | 2 |
| #83427 | 2 |
| #83390 | 2 |
| #82933 | 2 |
| #82926 | 2 |
| C2×#5040 | 2 |
| #82624 | 2 |
| #82570 | 2 |
| #60374 | 3 |