Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
636 conjugacy classes of subgroups.
The subgroup lattice has 634 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #84018 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #84017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #82041 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #80947 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#2195 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71506 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #71499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #71096 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #69273 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #69270 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #69245 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #69238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #69129 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #69122 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #33860 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C3×#578 | C22 | 1 | 1 | yes | characteristic |
| 18 | #5838 | — | 2 | 1 | no | — |
| 19 | #5779 | — | 2 | 1 | no | — |
| 20 | #5771 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5766 | C22 | 1 | 1 | yes | characteristic |
| 22 | #5753 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×#510 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C3×Q32 | C22 | 1 | 1 | yes | characteristic |
| 25 | C3×#473 | C22 | 1 | 1 | yes | characteristic |
| 26 | #5246 | — | 2 | 1 | no | — |
| 27 | #5205 | — | 2 | 1 | no | — |
| 28 | #5205 | — | 2 | 1 | no | — |
| 29 | #5204 | — | 2 | 1 | no | — |
| 30 | #5196 | C22 | 1 | 1 | yes | characteristic |
| 31 | #5195 | — | 2 | 1 | no | — |
| 32 | #5195 | C22 | 1 | 1 | yes | characteristic |
| 33 | #5194 | — | 2 | 1 | no | — |
| 34 | #5194 | C22 | 1 | 1 | yes | characteristic |
| 35 | #5192 | C22 | 1 | 1 | yes | characteristic |
| 36 | #5183 | C22 | 1 | 1 | yes | characteristic |
| 37 | #5183 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#829 | — | 2 | 1 | no | — |
| 39 | C2×#829 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#829 | C22 | 1 | 1 | yes | characteristic |
| 41 | #5179 | — | 2 | 1 | no | — |
| 42 | #5179 | C22 | 1 | 1 | yes | characteristic |
| 43 | #5144 | C22 | 1 | 1 | yes | characteristic |
| 44 | #5143 | C22 | 1 | 1 | yes | characteristic |
| 45 | #5140 | C22 | 1 | 1 | yes | characteristic |
| 46 | #4918 | — | 2 | 1 | no | — |
| 47 | D3×Q32 | — | 2 | 1 | no | — |
| 48 | #4916 | — | 2 | 1 | no | — |
| 49 | #4915 | — | 2 | 1 | no | — |
| 50 | #4909 | C22 | 1 | 1 | yes | characteristic |
| 51 | #4907 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×Dic24 | C22 | 1 | 1 | yes | characteristic |
| 53 | #4896 | C22 | 1 | 1 | yes | characteristic |
| 54 | #4895 | C22 | 1 | 1 | yes | characteristic |
| 55 | #4755 | — | 2 | 1 | no | — |
| 56 | #4752 | — | 2 | 1 | no | — |
| 57 | C3×#362 | C22 | 1 | 1 | yes | characteristic |
| 58 | C3×#359 | C22 | 1 | 1 | yes | characteristic |
| 59 | C3×#350 | C22 | 1 | 1 | yes | characteristic |
| 60 | #4565 | C22 | 1 | 1 | yes | characteristic |
| 61 | #4517 | C22 | 1 | 1 | yes | characteristic |
| 62 | #4511 | C22 | 1 | 1 | yes | characteristic |
| 63 | #4510 | C22 | 1 | 1 | yes | characteristic |
| 64 | #4508 | C22 | 1 | 1 | yes | characteristic |
| 65 | Dic3×C16 | C22 | 1 | 1 | yes | characteristic |
| 66 | #4496 | C22 | 1 | 1 | yes | characteristic |
| 67 | #4493 | C22 | 1 | 1 | yes | characteristic |
| 68 | #3417 | — | 3 | 1 | no | — |
| 69 | #3417 | — | 3 | 1 | no | — |
| 70 | #3293 | — | 3 | 1 | no | — |
| 71 | #3293 | — | 3 | 1 | no | — |
| 72 | #2247 | — | 3 | 1 | no | — |
| 73 | #2222 | — | 3 | 1 | no | — |
| 74 | #2222 | — | 3 | 1 | no | — |
| 75 | #2214 | — | 3 | 1 | no | — |
| 76 | #2214 | — | 3 | 1 | no | — |
| 77 | #2195 | — | 3 | 1 | no | — |
| 78 | #2195 | — | 3 | 1 | no | — |
| 79 | #2195 | — | 3 | 1 | no | — |
| 80 | #2195 | D3 | 1 | 1 | yes | characteristic, complemented |
| 81 | #2178 | — | 3 | 1 | no | — |
| 82 | #2170 | — | 3 | 1 | no | — |
| 83 | C3×2−1+4 | — | 2 | 1 | no | — |
| 84 | #1010 | — | 2 | 1 | no | — |
| 85 | #1010 | — | 2 | 1 | no | — |
| 86 | #1007 | — | 2 | 1 | no | — |
| 87 | C3×#137 | — | 2 | 1 | no | — |
| 88 | C3×#137 | — | 2 | 1 | no | — |
| 89 | C3×#137 | — | 4 | 1 | no | — |
| 90 | C3×#135 | — | 2 | 1 | no | — |
| 91 | C3×#135 | C23 | 1 | 1 | yes | characteristic |
| 92 | C2×C3×Q16 | — | 2 | 1 | no | — |
| 93 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C3×Q16 | C23 | 1 | 1 | yes | characteristic |
| 95 | C3×#131 | C23 | 1 | 1 | yes | characteristic |
| 96 | #951 | — | 2 | 1 | no | — |
| 97 | #951 | — | 2 | 1 | no | — |
| 98 | #951 | — | 4 | 1 | no | — |
| 99 | #950 | — | 4 | 1 | no | — |
| 100 | #950 | D4 | 1 | 1 | yes | characteristic |
| 101 | #948 | — | 2 | 1 | no | — |
| 102 | #944 | — | 2 | 1 | no | — |
| 103 | #944 | — | 2 | 1 | no | — |
| 104 | C2×#216 | — | 2 | 1 | no | — |
| 105 | C2×#216 | — | 2 | 1 | no | — |
| 106 | C2×#216 | — | 4 | 1 | no | — |
| 107 | #942 | — | 2 | 1 | no | — |
| 108 | #942 | — | 2 | 1 | no | — |
| 109 | #942 | — | 4 | 1 | no | — |
| 110 | #919 | — | 2 | 1 | no | — |
| 111 | #918 | — | 4 | 1 | no | — |
| 112 | #918 | — | 4 | 1 | no | — |
| 113 | D3×Q16 | — | 2 | 1 | no | — |
| 114 | D3×Q16 | — | 2 | 1 | no | — |
| 115 | D3×Q16 | — | 4 | 1 | no | — |
| 116 | #916 | — | 4 | 1 | no | — |
| 117 | #915 | — | 4 | 1 | no | — |
| 118 | #915 | — | 4 | 1 | no | — |
| 119 | #912 | — | 2 | 1 | no | — |
| 120 | #909 | — | 2 | 1 | no | — |
| 121 | #909 | — | 2 | 1 | no | — |
| 122 | #909 | — | 4 | 1 | no | — |
| 123 | #907 | — | 2 | 1 | no | — |
| 124 | C2×Dic12 | — | 2 | 1 | no | — |
| 125 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 127 | #904 | — | 2 | 1 | no | — |
| 128 | #904 | C23 | 1 | 1 | yes | characteristic |
| 129 | #901 | C23 | 1 | 1 | yes | characteristic |
| 130 | C3×Q32 | — | 2 | 1 | no | — |
| 131 | C3×Q32 | — | 4 | 1 | no | — |
| 132 | C3×SD32 | — | 2 | 1 | no | — |
| 133 | C3×M32 | C23 | 1 | 1 | yes | characteristic |
| 134 | C2×C3×C16 | C23 | 1 | 1 | yes | characteristic |
| 135 | C3×#108 | C23 | 1 | 1 | yes | characteristic |
| 136 | C3×#101 | — | 2 | 1 | no | — |
| 137 | #837 | — | 2 | 1 | no | — |
| 138 | #837 | D4 | 1 | 1 | yes | characteristic |
| 139 | #836 | — | 2 | 1 | no | — |
| 140 | #829 | — | 2 | 1 | no | — |
| 141 | #829 | — | 2 | 1 | no | — |
| 142 | #829 | — | 2 | 1 | no | — |
| 143 | #829 | — | 2 | 1 | no | — |
| 144 | #829 | — | 2 | 1 | no | — |
| 145 | #829 | — | 2 | 1 | no | — |
| 146 | #829 | D4 | 1 | 1 | yes | characteristic |
| 147 | #828 | — | 2 | 1 | no | — |
| 148 | #828 | D4 | 1 | 1 | yes | characteristic |
| 149 | #827 | — | 2 | 1 | no | — |
| 150 | #827 | D4 | 1 | 1 | yes | characteristic |
| 151 | #826 | D4 | 1 | 1 | yes | characteristic |
| 152 | #825 | — | 2 | 1 | no | — |
| 153 | #825 | D4 | 1 | 1 | yes | characteristic |
| 154 | #824 | — | 2 | 1 | no | — |
| 155 | #824 | — | 2 | 1 | no | — |
| 156 | #822 | D4 | 1 | 1 | yes | characteristic |
| 157 | #819 | C23 | 1 | 1 | yes | characteristic |
| 158 | C8×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 159 | #812 | — | 2 | 1 | no | — |
| 160 | #812 | C23 | 1 | 1 | yes | characteristic |
| 161 | C2×C3⋊C16 | — | 2 | 1 | no | — |
| 162 | C2×C3⋊C16 | C23 | 1 | 1 | yes | characteristic |
| 163 | Dic24 | — | 2 | 1 | no | — |
| 164 | Dic24 | — | 4 | 1 | no | — |
| 165 | #800 | — | 2 | 1 | no | — |
| 166 | #798 | — | 2 | 1 | no | — |
| 167 | D3×C16 | — | 2 | 1 | no | — |
| 168 | #578 | — | 3 | 1 | no | — |
| 169 | #578 | — | 3 | 1 | no | — |
| 170 | #578 | — | 3 | 1 | no | — |
| 171 | #578 | — | 6 | 1 | no | — |
| 172 | #578 | — | 6 | 1 | no | — |
| 173 | #578 | C2×D3 | 1 | 1 | yes | characteristic |
| 174 | #510 | — | 3 | 1 | no | — |
| 175 | #510 | — | 3 | 1 | no | — |
| 176 | #510 | — | 3 | 1 | no | — |
| 177 | #510 | — | 6 | 1 | no | — |
| 178 | #510 | — | 6 | 1 | no | — |
| 179 | #510 | — | 6 | 1 | no | — |
| 180 | #510 | — | 6 | 1 | no | — |
| 181 | #510 | C2×D3 | 1 | 1 | yes | characteristic |
| 182 | #508 | — | 3 | 1 | no | — |
| 183 | #508 | — | 6 | 1 | no | — |
| 184 | #508 | — | 6 | 1 | no | — |
| 185 | C2×Q32 | — | 3 | 1 | no | — |
| 186 | C2×Q32 | — | 3 | 1 | no | — |
| 187 | C2×Q32 | — | 3 | 1 | no | — |
| 188 | C2×Q32 | — | 6 | 1 | no | — |
| 189 | C2×Q32 | — | 6 | 1 | no | — |
| 190 | C2×Q32 | C2×D3 | 1 | 1 | yes | characteristic |
| 191 | #504 | — | 3 | 1 | no | — |
| 192 | #504 | — | 3 | 1 | no | — |
| 193 | #494 | — | 3 | 1 | no | — |
| 194 | #494 | — | 3 | 1 | no | — |
| 195 | #473 | — | 3 | 1 | no | — |
| 196 | #473 | — | 3 | 1 | no | — |
| 197 | #473 | — | 3 | 1 | no | — |
| 198 | #473 | — | 6 | 1 | no | — |
| 199 | #473 | — | 6 | 1 | no | — |
| 200 | #473 | C2×D3 | 1 | 1 | yes | characteristic |
| 201 | #456 | — | 6 | 1 | no | — |
| 202 | #456 | — | 6 | 1 | no | — |
| 203 | #456 | — | 6 | 1 | no | — |
| 204 | #456 | — | 6 | 1 | no | — |
| 205 | #443 | — | 3 | 1 | no | — |
| 206 | #443 | — | 3 | 1 | no | — |
| 207 | #443 | — | 3 | 1 | no | — |
| 208 | #368 | — | 3 | 1 | no | — |
| 209 | #364 | — | 3 | 1 | no | — |
| 210 | #362 | — | 3 | 1 | no | — |
| 211 | #362 | — | 3 | 1 | no | — |
| 212 | #362 | — | 3 | 1 | no | — |
| 213 | #362 | C2×D3 | 1 | 1 | yes | characteristic |
| 214 | #359 | — | 3 | 1 | no | — |
| 215 | #359 | C2×D3 | 1 | 1 | yes | characteristic |
| 216 | #350 | — | 3 | 1 | no | — |
| 217 | #350 | C2×D3 | 1 | 1 | yes | characteristic |
| 218 | C4×C16 | — | 3 | 1 | no | — |
| 219 | C3×#41 | — | 2 | 1 | no | — |
| 220 | C3×#41 | — | 4 | 1 | no | — |
| 221 | C3×#41 | — | 4 | 1 | no | — |
| 222 | C3×#41 | — | 8 | 1 | no | — |
| 223 | C3×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 225 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 226 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 227 | C2×C3×Q8 | — | 4 | 1 | no | — |
| 228 | #239 | — | 4 | 1 | no | — |
| 229 | #239 | — | 4 | 1 | no | — |
| 230 | D3×Q8 | — | 4 | 1 | no | — |
| 231 | D3×Q8 | — | 4 | 1 | no | — |
| 232 | D3×Q8 | — | 4 | 1 | no | — |
| 233 | D3×Q8 | — | 4 | 1 | no | — |
| 234 | #237 | — | 4 | 1 | no | — |
| 235 | #237 | — | 4 | 1 | no | — |
| 236 | #237 | — | 8 | 1 | no | — |
| 237 | #237 | — | 8 | 1 | no | — |
| 238 | #235 | — | 2 | 1 | no | — |
| 239 | #235 | — | 4 | 1 | no | — |
| 240 | #235 | — | 4 | 1 | no | — |
| 241 | #235 | — | 8 | 1 | no | — |
| 242 | #235 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×Dic6 | — | 2 | 1 | no | — |
| 244 | C2×Dic6 | — | 2 | 1 | no | — |
| 245 | C2×Dic6 | — | 4 | 1 | no | — |
| 246 | C2×Dic6 | — | 4 | 1 | no | — |
| 247 | C3×Q16 | — | 2 | 1 | no | — |
| 248 | C3×Q16 | — | 2 | 1 | no | — |
| 249 | C3×Q16 | — | 2 | 1 | no | — |
| 250 | C3×Q16 | — | 2 | 1 | no | — |
| 251 | C3×Q16 | — | 4 | 1 | no | — |
| 252 | C3×Q16 | — | 4 | 1 | no | — |
| 253 | C3×Q16 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C3×SD16 | — | 2 | 1 | no | — |
| 255 | C3×SD16 | — | 4 | 1 | no | — |
| 256 | C3×SD16 | — | 4 | 1 | no | — |
| 257 | C3×D8 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C3×M16 | — | 2 | 1 | no | — |
| 259 | C3×M16 | — | 2 | 1 | no | — |
| 260 | C3×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 261 | C2×C3×C8 | — | 2 | 1 | no | — |
| 262 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 263 | #216 | — | 4 | 1 | no | — |
| 264 | #216 | — | 4 | 1 | no | — |
| 265 | #216 | — | 4 | 1 | no | — |
| 266 | #216 | — | 4 | 1 | no | — |
| 267 | #216 | — | 4 | 1 | no | — |
| 268 | #216 | — | 4 | 1 | no | — |
| 269 | #216 | — | 4 | 1 | no | — |
| 270 | #216 | — | 4 | 1 | no | — |
| 271 | #216 | D8 | 1 | 1 | yes | characteristic |
| 272 | #215 | — | 4 | 1 | no | — |
| 273 | #215 | — | 4 | 1 | no | — |
| 274 | #215 | D8 | 1 | 1 | yes | characteristic |
| 275 | #214 | — | 4 | 1 | no | — |
| 276 | #214 | — | 4 | 1 | no | — |
| 277 | #214 | D8 | 1 | 1 | yes | characteristic |
| 278 | #213 | D8 | 1 | 1 | yes | characteristic |
| 279 | Dic3⋊C4 | — | 8 | 1 | no | — |
| 280 | Dic3⋊C4 | — | 8 | 1 | no | — |
| 281 | C4×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | #208 | — | 2 | 1 | no | — |
| 283 | #208 | — | 4 | 1 | no | — |
| 284 | #208 | C2×D4 | 1 | 1 | yes | characteristic |
| 285 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 286 | C2×C3⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 287 | Dic12 | — | 2 | 1 | no | — |
| 288 | Dic12 | — | 2 | 1 | no | — |
| 289 | Dic12 | — | 2 | 1 | no | — |
| 290 | Dic12 | — | 2 | 1 | no | — |
| 291 | Dic12 | — | 4 | 1 | no | — |
| 292 | Dic12 | — | 4 | 1 | no | — |
| 293 | Dic12 | C2×D4 | 1 | 1 | yes | characteristic |
| 294 | D24 | C2×D4 | 1 | 1 | yes | characteristic |
| 295 | #204 | — | 2 | 1 | no | — |
| 296 | #204 | — | 4 | 1 | no | — |
| 297 | #204 | — | 4 | 1 | no | — |
| 298 | ΓL(1,𝔽25) | — | 2 | 1 | no | — |
| 299 | ΓL(1,𝔽25) | — | 4 | 1 | no | — |
| 300 | D3×C8 | — | 2 | 1 | no | — |
| 301 | D3×C8 | — | 4 | 1 | no | — |
| 302 | C3×C16 | — | 2 | 1 | no | — |
| 303 | C3×C16 | — | 2 | 1 | no | — |
| 304 | C3⋊C16 | — | 2 | 1 | no | — |
| 305 | C3⋊C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 306 | C3⋊C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | 2−1+4 | — | 2 | 1 | no | — |
| 308 | 2−1+4 | — | 6 | 1 | no | — |
| 309 | 2−1+4 | — | 6 | 1 | no | — |
| 310 | 2−1+4 | — | 6 | 1 | no | — |
| 311 | #137 | — | 2 | 1 | no | — |
| 312 | #137 | — | 2 | 1 | no | — |
| 313 | #137 | — | 4 | 1 | no | — |
| 314 | #137 | — | 6 | 1 | no | — |
| 315 | #137 | — | 6 | 1 | no | — |
| 316 | #137 | — | 6 | 1 | no | — |
| 317 | #137 | — | 6 | 1 | no | — |
| 318 | #137 | — | 6 | 1 | no | — |
| 319 | #137 | — | 6 | 1 | no | — |
| 320 | #137 | — | 12 | 1 | no | — |
| 321 | #137 | — | 12 | 1 | no | — |
| 322 | #137 | — | 12 | 1 | no | — |
| 323 | #137 | — | 12 | 1 | no | — |
| 324 | #137 | — | 12 | 1 | no | — |
| 325 | #137 | — | 12 | 1 | no | — |
| 326 | #137 | — | 12 | 1 | no | — |
| 327 | #135 | — | 2 | 1 | no | — |
| 328 | #135 | — | 3 | 1 | no | — |
| 329 | #135 | — | 3 | 1 | no | — |
| 330 | #135 | — | 6 | 1 | no | — |
| 331 | #135 | — | 6 | 1 | no | — |
| 332 | #135 | — | 6 | 1 | no | — |
| 333 | #135 | — | 12 | 1 | no | — |
| 334 | #135 | — | 12 | 1 | no | — |
| 335 | #135 | C22×D3 | 1 | 1 | yes | characteristic |
| 336 | C2×Q16 | — | 2 | 1 | no | — |
| 337 | C2×Q16 | — | 3 | 1 | no | — |
| 338 | C2×Q16 | — | 3 | 1 | no | — |
| 339 | C2×Q16 | — | 6 | 1 | no | — |
| 340 | C2×Q16 | — | 6 | 1 | no | — |
| 341 | C2×Q16 | — | 6 | 1 | no | — |
| 342 | C2×Q16 | — | 6 | 1 | no | — |
| 343 | C2×Q16 | — | 6 | 1 | no | — |
| 344 | C2×Q16 | — | 12 | 1 | no | — |
| 345 | C2×Q16 | — | 12 | 1 | no | — |
| 346 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 347 | C2×Q16 | C22×D3 | 1 | 1 | yes | characteristic |
| 348 | #131 | — | 3 | 1 | no | — |
| 349 | #131 | — | 6 | 1 | no | — |
| 350 | #131 | — | 6 | 1 | no | — |
| 351 | #131 | C22×D3 | 1 | 1 | yes | characteristic |
| 352 | C4⋊Q8 | — | 6 | 1 | no | — |
| 353 | C4⋊Q8 | — | 6 | 1 | no | — |
| 354 | Q32 | — | 2 | 1 | no | — |
| 355 | Q32 | — | 3 | 1 | no | — |
| 356 | Q32 | — | 4 | 1 | no | — |
| 357 | Q32 | — | 6 | 1 | no | — |
| 358 | Q32 | — | 6 | 1 | no | — |
| 359 | Q32 | — | 6 | 1 | no | — |
| 360 | Q32 | — | 6 | 1 | no | — |
| 361 | Q32 | — | 6 | 1 | no | — |
| 362 | Q32 | — | 6 | 1 | no | — |
| 363 | Q32 | — | 6 | 1 | no | — |
| 364 | Q32 | — | 12 | 1 | no | — |
| 365 | SD32 | — | 2 | 1 | no | — |
| 366 | SD32 | — | 3 | 1 | no | — |
| 367 | SD32 | — | 3 | 1 | no | — |
| 368 | SD32 | — | 6 | 1 | no | — |
| 369 | SD32 | — | 6 | 1 | no | — |
| 370 | SD32 | — | 6 | 1 | no | — |
| 371 | D16 | — | 3 | 1 | no | — |
| 372 | M32 | — | 3 | 1 | no | — |
| 373 | M32 | — | 6 | 1 | no | — |
| 374 | M32 | — | 6 | 1 | no | — |
| 375 | M32 | C22×D3 | 1 | 1 | yes | characteristic |
| 376 | C2×C16 | — | 3 | 1 | no | — |
| 377 | C2×C16 | — | 6 | 1 | no | — |
| 378 | C2×C16 | — | 6 | 1 | no | — |
| 379 | C2×C16 | C22×D3 | 1 | 1 | yes | characteristic |
| 380 | #108 | — | 3 | 1 | no | — |
| 381 | #108 | — | 3 | 1 | no | — |
| 382 | #108 | C22×D3 | 1 | 1 | yes | characteristic |
| 383 | #104 | — | 3 | 1 | no | — |
| 384 | #104 | — | 3 | 1 | no | — |
| 385 | #104 | — | 6 | 1 | no | — |
| 386 | #104 | — | 6 | 1 | no | — |
| 387 | #101 | — | 2 | 1 | no | — |
| 388 | #101 | — | 6 | 1 | no | — |
| 389 | #101 | — | 6 | 1 | no | — |
| 390 | #101 | — | 6 | 1 | no | — |
| 391 | C4×C8 | — | 3 | 1 | no | — |
| 392 | C3×Q8 | — | 2 | 1 | no | — |
| 393 | C3×Q8 | — | 4 | 1 | no | — |
| 394 | C3×Q8 | — | 4 | 1 | no | — |
| 395 | C3×Q8 | — | 4 | 1 | no | — |
| 396 | C3×Q8 | — | 4 | 1 | no | — |
| 397 | C3×Q8 | — | 8 | 1 | no | — |
| 398 | C3×Q8 | C2×D8 | 1 | 1 | yes | characteristic |
| 399 | C3×D4 | — | 2 | 1 | no | — |
| 400 | C3×D4 | — | 2 | 1 | no | — |
| 401 | C3×D4 | — | 4 | 1 | no | — |
| 402 | C3×D4 | — | 8 | 1 | no | — |
| 403 | C3×D4 | C2×D8 | 1 | 1 | yes | characteristic |
| 404 | C2×C3×C4 | — | 2 | 1 | no | — |
| 405 | C2×C3×C4 | — | 4 | 1 | no | — |
| 406 | C2×C3×C4 | — | 4 | 1 | no | — |
| 407 | C2×C3×C4 | — | 4 | 1 | no | — |
| 408 | C2×C3×C4 | — | 8 | 1 | no | — |
| 409 | C2×C3×C4 | — | 8 | 1 | no | — |
| 410 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 411 | #67 | — | 2 | 1 | no | — |
| 412 | #67 | — | 4 | 1 | no | — |
| 413 | #67 | — | 8 | 1 | no | — |
| 414 | #67 | — | 8 | 1 | no | — |
| 415 | C2×Dic3 | — | 2 | 1 | no | — |
| 416 | C2×Dic3 | — | 4 | 1 | no | — |
| 417 | C2×Dic3 | — | 4 | 1 | no | — |
| 418 | C2×Dic3 | — | 8 | 1 | no | — |
| 419 | C2×Dic3 | — | 8 | 1 | no | — |
| 420 | D12 | — | 2 | 1 | no | — |
| 421 | D12 | — | 8 | 1 | no | — |
| 422 | D12 | C2×D8 | 1 | 1 | yes | characteristic |
| 423 | C4×D3 | — | 2 | 1 | no | — |
| 424 | C4×D3 | — | 4 | 1 | no | — |
| 425 | C4×D3 | — | 8 | 1 | no | — |
| 426 | C4×D3 | — | 8 | 1 | no | — |
| 427 | C4×D3 | — | 8 | 1 | no | — |
| 428 | C4×D3 | — | 8 | 1 | no | — |
| 429 | Dic6 | — | 2 | 1 | no | — |
| 430 | Dic6 | — | 4 | 1 | no | — |
| 431 | Dic6 | — | 4 | 1 | no | — |
| 432 | Dic6 | — | 4 | 1 | no | — |
| 433 | Dic6 | — | 4 | 1 | no | — |
| 434 | Dic6 | — | 8 | 1 | no | — |
| 435 | Dic6 | — | 8 | 1 | no | — |
| 436 | Dic6 | — | 8 | 1 | no | — |
| 437 | Dic6 | C2×D8 | 1 | 1 | yes | characteristic |
| 438 | C3×C8 | — | 2 | 1 | no | — |
| 439 | C3×C8 | — | 4 | 1 | no | — |
| 440 | C3×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 441 | C3×C8 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 442 | C3⋊C8 | — | 2 | 1 | no | — |
| 443 | C3⋊C8 | — | 4 | 1 | no | — |
| 444 | C3⋊C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 445 | C3⋊C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 446 | #41 | — | 2 | 1 | no | — |
| 447 | #41 | — | 3 | 1 | no | — |
| 448 | #41 | — | 4 | 1 | no | — |
| 449 | #41 | — | 4 | 1 | no | — |
| 450 | #41 | — | 6 | 1 | no | — |
| 451 | #41 | — | 8 | 1 | no | — |
| 452 | #41 | — | 12 | 1 | no | — |
| 453 | #41 | — | 12 | 1 | no | — |
| 454 | #41 | — | 12 | 1 | no | — |
| 455 | #41 | — | 12 | 1 | no | — |
| 456 | #41 | — | 12 | 1 | no | — |
| 457 | #41 | — | 12 | 1 | no | — |
| 458 | #41 | — | 24 | 1 | no | — |
| 459 | #41 | — | 24 | 1 | no | — |
| 460 | #41 | — | 24 | 1 | no | — |
| 461 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 462 | C2×Q8 | — | 2 | 1 | no | — |
| 463 | C2×Q8 | — | 2 | 1 | no | — |
| 464 | C2×Q8 | — | 4 | 1 | no | — |
| 465 | C2×Q8 | — | 4 | 1 | no | — |
| 466 | C2×Q8 | — | 6 | 1 | no | — |
| 467 | C2×Q8 | — | 6 | 1 | no | — |
| 468 | C2×Q8 | — | 12 | 1 | no | — |
| 469 | C2×Q8 | — | 12 | 1 | no | — |
| 470 | C2×Q8 | — | 12 | 1 | no | — |
| 471 | C2×Q8 | — | 12 | 1 | no | — |
| 472 | C2×Q8 | — | 12 | 1 | no | — |
| 473 | C2×Q8 | — | 12 | 1 | no | — |
| 474 | Q16 | — | 2 | 1 | no | — |
| 475 | Q16 | — | 2 | 1 | no | — |
| 476 | Q16 | — | 2 | 1 | no | — |
| 477 | Q16 | — | 2 | 1 | no | — |
| 478 | Q16 | — | 3 | 1 | no | — |
| 479 | Q16 | — | 3 | 1 | no | — |
| 480 | Q16 | — | 4 | 1 | no | — |
| 481 | Q16 | — | 4 | 1 | no | — |
| 482 | Q16 | — | 6 | 1 | no | — |
| 483 | Q16 | — | 6 | 1 | no | — |
| 484 | Q16 | — | 6 | 1 | no | — |
| 485 | Q16 | — | 6 | 1 | no | — |
| 486 | Q16 | — | 12 | 1 | no | — |
| 487 | Q16 | — | 12 | 1 | no | — |
| 488 | Q16 | — | 12 | 1 | no | — |
| 489 | Q16 | — | 12 | 1 | no | — |
| 490 | Q16 | — | 12 | 1 | no | — |
| 491 | Q16 | — | 12 | 1 | no | — |
| 492 | Q16 | — | 12 | 1 | no | — |
| 493 | Q16 | — | 12 | 1 | no | — |
| 494 | Q16 | — | 12 | 1 | no | — |
| 495 | Q16 | — | 12 | 1 | no | — |
| 496 | Q16 | D3×D4 | 1 | 1 | yes | characteristic |
| 497 | SD16 | — | 2 | 1 | no | — |
| 498 | SD16 | — | 3 | 1 | no | — |
| 499 | SD16 | — | 3 | 1 | no | — |
| 500 | SD16 | — | 4 | 1 | no | — |
| 501 | SD16 | — | 4 | 1 | no | — |
| 502 | SD16 | — | 6 | 1 | no | — |
| 503 | SD16 | — | 12 | 1 | no | — |
| 504 | SD16 | — | 12 | 1 | no | — |
| 505 | SD16 | — | 12 | 1 | no | — |
| 506 | SD16 | — | 12 | 1 | no | — |
| 507 | SD16 | — | 12 | 1 | no | — |
| 508 | SD16 | — | 12 | 1 | no | — |
| 509 | D8 | — | 3 | 1 | no | — |
| 510 | D8 | — | 3 | 1 | no | — |
| 511 | D8 | D3×D4 | 1 | 1 | yes | characteristic |
| 512 | M16 | — | 2 | 1 | no | — |
| 513 | M16 | — | 2 | 1 | no | — |
| 514 | M16 | — | 3 | 1 | no | — |
| 515 | M16 | — | 6 | 1 | no | — |
| 516 | M16 | — | 6 | 1 | no | — |
| 517 | M16 | — | 12 | 1 | no | — |
| 518 | M16 | — | 12 | 1 | no | — |
| 519 | M16 | D3×D4 | 1 | 1 | yes | characteristic |
| 520 | C2×C8 | — | 2 | 1 | no | — |
| 521 | C2×C8 | — | 3 | 1 | no | — |
| 522 | C2×C8 | — | 6 | 1 | no | — |
| 523 | C2×C8 | — | 12 | 1 | no | — |
| 524 | C2×C8 | — | 12 | 1 | no | — |
| 525 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 526 | C4⋊C4 | — | 24 | 1 | no | — |
| 527 | C4⋊C4 | — | 24 | 1 | no | — |
| 528 | C42 | — | 3 | 1 | no | — |
| 529 | C16 | — | 2 | 1 | no | — |
| 530 | C16 | — | 2 | 1 | no | — |
| 531 | C16 | — | 3 | 1 | no | — |
| 532 | C16 | — | 3 | 1 | no | — |
| 533 | C16 | — | 6 | 1 | no | — |
| 534 | C22×C3 | — | 2 | 1 | no | — |
| 535 | C22×C3 | — | 4 | 1 | no | — |
| 536 | C22×C3 | #576 | 1 | 1 | yes | characteristic |
| 537 | C2×D3 | — | 2 | 1 | no | — |
| 538 | C2×D3 | — | 4 | 1 | no | — |
| 539 | C3×C4 | — | 2 | 1 | no | — |
| 540 | C3×C4 | — | 4 | 1 | no | — |
| 541 | C3×C4 | — | 8 | 1 | no | — |
| 542 | C3×C4 | — | 8 | 1 | no | — |
| 543 | C3×C4 | D42 | 1 | 1 | yes | characteristic |
| 544 | C3×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 545 | Dic3 | — | 2 | 2 | no | — |
| 546 | Dic3 | — | 2 | 1 | no | — |
| 547 | Dic3 | — | 4 | 1 | no | — |
| 548 | Dic3 | — | 8 | 1 | no | — |
| 549 | Dic3 | — | 8 | 1 | no | — |
| 550 | Q8 | — | 2 | 1 | no | — |
| 551 | Q8 | — | 3 | 1 | no | — |
| 552 | Q8 | — | 4 | 1 | no | — |
| 553 | Q8 | — | 4 | 1 | no | — |
| 554 | Q8 | — | 4 | 1 | no | — |
| 555 | Q8 | — | 4 | 1 | no | — |
| 556 | Q8 | — | 6 | 1 | no | — |
| 557 | Q8 | — | 8 | 1 | no | — |
| 558 | Q8 | — | 12 | 1 | no | — |
| 559 | Q8 | — | 12 | 1 | no | — |
| 560 | Q8 | — | 12 | 1 | no | — |
| 561 | Q8 | — | 12 | 1 | no | — |
| 562 | Q8 | — | 24 | 1 | no | — |
| 563 | Q8 | — | 24 | 1 | no | — |
| 564 | Q8 | — | 24 | 1 | no | — |
| 565 | Q8 | D3×D8 | 1 | 1 | yes | characteristic |
| 566 | D4 | — | 2 | 1 | no | — |
| 567 | D4 | — | 2 | 1 | no | — |
| 568 | D4 | — | 3 | 1 | no | — |
| 569 | D4 | — | 4 | 1 | no | — |
| 570 | D4 | — | 6 | 1 | no | — |
| 571 | D4 | — | 6 | 1 | no | — |
| 572 | D4 | — | 8 | 1 | no | — |
| 573 | D4 | — | 12 | 1 | no | — |
| 574 | D4 | — | 24 | 1 | no | — |
| 575 | D4 | — | 24 | 1 | no | — |
| 576 | D4 | — | 24 | 1 | no | — |
| 577 | D4 | D3×D8 | 1 | 1 | yes | characteristic |
| 578 | C2×C4 | — | 2 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 1 | no | — |
| 580 | C2×C4 | — | 4 | 1 | no | — |
| 581 | C2×C4 | — | 4 | 1 | no | — |
| 582 | C2×C4 | — | 6 | 1 | no | — |
| 583 | C2×C4 | — | 6 | 1 | no | — |
| 584 | C2×C4 | — | 8 | 1 | no | — |
| 585 | C2×C4 | — | 8 | 1 | no | — |
| 586 | C2×C4 | — | 12 | 1 | no | — |
| 587 | C2×C4 | — | 12 | 1 | no | — |
| 588 | C2×C4 | — | 12 | 1 | no | — |
| 589 | C2×C4 | — | 24 | 1 | no | — |
| 590 | C2×C4 | — | 24 | 1 | no | — |
| 591 | C2×C4 | — | 24 | 1 | no | — |
| 592 | C2×C4 | — | 24 | 1 | no | — |
| 593 | C2×C4 | — | 24 | 1 | no | — |
| 594 | C2×C4 | — | 24 | 1 | no | — |
| 595 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 596 | C8 | — | 2 | 1 | no | — |
| 597 | C8 | — | 3 | 1 | no | — |
| 598 | C8 | — | 3 | 1 | no | — |
| 599 | C8 | — | 4 | 1 | no | — |
| 600 | C8 | — | 6 | 1 | no | — |
| 601 | C8 | — | 12 | 1 | no | — |
| 602 | C8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 603 | C8 | #1004 | 1 | 1 | yes | characteristic |
| 604 | C2×C3 | — | 2 | 1 | no | — |
| 605 | C2×C3 | — | 4 | 1 | no | — |
| 606 | C2×C3 | — | 8 | 1 | no | — |
| 607 | C2×C3 | D4×D8 | 1 | 1 | yes | characteristic |
| 608 | D3 | — | 4 | 1 | no | — |
| 609 | D3 | — | 8 | 1 | no | — |
| 610 | C22 | — | 2 | 1 | no | — |
| 611 | C22 | — | 4 | 1 | no | — |
| 612 | C22 | — | 6 | 1 | no | — |
| 613 | C22 | — | 12 | 1 | no | — |
| 614 | C22 | #5774 | 1 | 1 | yes | characteristic |
| 615 | C4 | — | 2 | 1 | no | — |
| 616 | C4 | — | 4 | 1 | no | — |
| 617 | C4 | — | 6 | 2 | no | — |
| 618 | C4 | — | 6 | 1 | no | — |
| 619 | C4 | — | 8 | 1 | no | — |
| 620 | C4 | — | 8 | 1 | no | — |
| 621 | C4 | — | 12 | 1 | no | — |
| 622 | C4 | — | 24 | 1 | no | — |
| 623 | C4 | — | 24 | 1 | no | — |
| 624 | C4 | #5590 | 1 | 1 | yes | characteristic |
| 625 | C4 | C2×D3×D8 | 1 | 1 | yes | characteristic |
| 626 | C3 | #33860 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 627 | C2 | — | 2 | 1 | no | — |
| 628 | C2 | — | 4 | 1 | no | — |
| 629 | C2 | — | 8 | 1 | no | — |
| 630 | C2 | — | 12 | 1 | no | — |
| 631 | C2 | — | 24 | 1 | no | — |
| 632 | C2 | #80024 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #84018 | C2 | semidirect |
| 2. #84017 | C2 | semidirect |
| 3. #82041 | C2 | semidirect |
| 4. #80947 | C2 | semidirect |
| 5. C3×#2195 | C2 | semidirect |
| 6. #71520 | C2 | semidirect |
| 7. #71506 | C2 | semidirect |
| 8. #71499 | C2 | semidirect |
| 9. #71096 | C2 | semidirect |
| 10. #69273 | C2 | semidirect |
| 11. #69270 | C2 | semidirect |
| 12. #69245 | C2 | semidirect |
| 13. #69238 | C2 | semidirect |
| 14. #69129 | C2 | semidirect |
| 15. #69122 | C2 | semidirect |
| 80. #2195 | D3 | semidirect |
| 626. C3 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #84018 | 2 |
| #84017 | 2 |
| #82041 | 2 |
| #80947 | 2 |
| C3×#2195 | 2 |
| #71520 | 2 |
| #71506 | 2 |
| #71499 | 2 |
| #71096 | 2 |
| #69273 | 2 |
| #69270 | 2 |
| #69245 | 2 |
| #69238 | 2 |
| #69129 | 2 |
| #69122 | 2 |
| #33860 | 3 |