Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1014 conjugacy classes of subgroups.
The subgroup lattice has 692 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722482 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64159⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #64160⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721231 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721226 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721192 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11721189 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#88439 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11721074 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11721064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10595467 | — | 3 | 1 | no | maximal |
| 13 | #10595465 | — | 3 | 1 | no | maximal |
| 14 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | Q8×#272 | C22 | 1 | 2 | yes | — |
| 16 | #88744 | — | 2 | 2 | no | — |
| 17 | #88744 | C22 | 1 | 2 | yes | — |
| 18 | #88740 | — | 2 | 1 | no | — |
| 19 | #88740 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#6229 | — | 2 | 1 | no | — |
| 21 | C2×#6229 | C22 | 1 | 1 | yes | characteristic |
| 22 | #3828⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#634⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 24 | #88671 | — | 2 | 2 | no | — |
| 25 | #88652 | — | 2 | 1 | no | — |
| 26 | #88651 | C22 | 1 | 2 | yes | — |
| 27 | #88649 | C22 | 1 | 2 | yes | — |
| 28 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 1 | no | — |
| 29 | #3755⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 30 | #3756⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 31 | #3756⋊C3 | C22 | 1 | 2 | yes | — |
| 32 | #3753⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 33 | #3754⋊C3 | C22 | 1 | 2 | yes | — |
| 34 | #3754⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 35 | #3748⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×(C3⋊(C3⋊C8))⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 37 | #88439 | C22 | 1 | 2 | yes | — |
| 38 | #88439 | C22 | 1 | 2 | yes | — |
| 39 | #88439 | C22 | 1 | 2 | yes | — |
| 40 | #88438 | C22 | 1 | 2 | yes | — |
| 41 | #88435 | C22 | 1 | 2 | yes | — |
| 42 | #88434 | C22 | 1 | 2 | yes | — |
| 43 | C3×#1010 | — | 3 | 1 | no | — |
| 44 | C3×#1010 | — | 3 | 1 | no | — |
| 45 | C3×#1010 | — | 6 | 1 | no | — |
| 46 | #64298 | — | 3 | 1 | no | — |
| 47 | #64297 | — | 3 | 1 | no | — |
| 48 | #64160 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #64159 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C3×#951 | — | 3 | 1 | no | — |
| 51 | C3×#950 | — | 3 | 1 | no | — |
| 52 | #63948 | — | 3 | 2 | no | — |
| 53 | #63946 | — | 3 | 2 | no | — |
| 54 | D3×#216 | — | 3 | 2 | no | — |
| 55 | D3×#216 | — | 3 | 2 | no | — |
| 56 | #63935 | — | 3 | 2 | no | — |
| 57 | #63933 | — | 3 | 2 | no | — |
| 58 | #63929 | — | 3 | 2 | no | — |
| 59 | #63929 | — | 3 | 2 | no | — |
| 60 | C2×#3719 | — | 3 | 1 | no | — |
| 61 | C2×#3718 | — | 3 | 1 | no | — |
| 62 | #63833 | — | 3 | 1 | no | — |
| 63 | #63827 | — | 3 | 1 | no | — |
| 64 | #63815 | — | 3 | 1 | no | — |
| 65 | #63814 | — | 3 | 1 | no | — |
| 66 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 67 | D4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 68 | D4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 70 | C2×C4×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 71 | #6235 | — | 2 | 2 | no | — |
| 72 | #6235 | D4 | 1 | 2 | yes | — |
| 73 | C2×#1084 | — | 2 | 1 | no | — |
| 74 | C2×#1084 | — | 2 | 2 | no | — |
| 75 | C4⋊#272 | D4 | 1 | 1 | yes | characteristic |
| 76 | C4×#272 | — | 2 | 2 | no | — |
| 77 | C4×#272 | C23 | 1 | 2 | yes | — |
| 78 | #6229 | — | 2 | 1 | no | — |
| 79 | #6229 | — | 2 | 2 | no | — |
| 80 | #6229 | D4 | 1 | 1 | yes | characteristic |
| 81 | #6229 | C23 | 1 | 2 | yes | — |
| 82 | #638⋊C3 | — | 2 | 1 | no | — |
| 83 | C2×(C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 84 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 86 | #634⋊C3 | — | 2 | 1 | no | — |
| 87 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 88 | #634⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 89 | #6200 | — | 2 | 2 | no | — |
| 90 | #6199 | — | 2 | 2 | no | — |
| 91 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 92 | #6196 | — | 2 | 2 | no | — |
| 93 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 94 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 2 | yes | — |
| 95 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 96 | #5838 | — | 9 | 1 | no | — |
| 97 | #5779 | — | 9 | 1 | no | — |
| 98 | #5771 | — | 9 | 1 | no | — |
| 99 | C32×#41 | — | 2 | 1 | no | — |
| 100 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 102 | #3828 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | C2×#634 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 105 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 106 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 107 | C3×#237 | — | 3 | 2 | no | — |
| 108 | C3×#237 | — | 3 | 2 | no | — |
| 109 | C3×#237 | — | 6 | 2 | no | — |
| 110 | C3×#237 | — | 6 | 2 | no | — |
| 111 | C3×#237 | — | 6 | 2 | no | — |
| 112 | C3×#237 | — | 6 | 4 | no | — |
| 113 | C3×#235 | — | 3 | 1 | no | — |
| 114 | C3×#235 | — | 3 | 1 | no | — |
| 115 | C3×#235 | — | 3 | 1 | no | — |
| 116 | C3×#235 | — | 6 | 1 | no | — |
| 117 | C3×#235 | — | 6 | 1 | no | — |
| 118 | C3×#235 | — | 6 | 1 | no | — |
| 119 | C3×#235 | — | 6 | 2 | no | — |
| 120 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 121 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 122 | C2×C3×Dic6 | — | 3 | 1 | no | — |
| 123 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 124 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 125 | C2×C3×Dic6 | — | 6 | 1 | no | — |
| 126 | C2×C3×Dic6 | — | 6 | 2 | no | — |
| 127 | #3805 | — | 6 | 2 | no | — |
| 128 | #3804 | — | 6 | 2 | no | — |
| 129 | #3799 | — | 3 | 2 | no | — |
| 130 | #3797 | — | 6 | 1 | no | — |
| 131 | #3796 | — | 6 | 1 | no | — |
| 132 | #3795 | — | 3 | 2 | no | — |
| 133 | #3795 | — | 6 | 1 | no | — |
| 134 | D3×Dic6 | — | 3 | 2 | no | — |
| 135 | D3×Dic6 | — | 3 | 2 | no | — |
| 136 | D3×Dic6 | — | 6 | 1 | no | — |
| 137 | #3756 | C2×D3 | 1 | 1 | yes | characteristic |
| 138 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 139 | #3755 | C2×D3 | 1 | 1 | yes | characteristic |
| 140 | #3754 | C2×D3 | 1 | 1 | yes | characteristic |
| 141 | #3754 | C2×D3 | 1 | 2 | yes | — |
| 142 | #3753 | C2×D3 | 1 | 1 | yes | characteristic |
| 143 | #3748 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×C3⋊(C3⋊C8) | C2×D3 | 1 | 1 | yes | characteristic |
| 145 | C3×#216 | — | 3 | 1 | no | — |
| 146 | C3×#216 | — | 3 | 2 | no | — |
| 147 | C3×#215 | — | 3 | 1 | no | — |
| 148 | C3×#214 | — | 3 | 1 | no | — |
| 149 | C3×#214 | — | 3 | 2 | no | — |
| 150 | C3×#213 | — | 3 | 1 | no | — |
| 151 | C3×#208 | — | 3 | 1 | no | — |
| 152 | C2×C3×C3⋊C8 | — | 3 | 1 | no | — |
| 153 | #3719 | — | 3 | 2 | no | — |
| 154 | #3719 | — | 3 | 2 | no | — |
| 155 | #3719 | — | 3 | 2 | no | — |
| 156 | #3718 | — | 3 | 2 | no | — |
| 157 | #3718 | — | 3 | 2 | no | — |
| 158 | #3718 | — | 3 | 2 | no | — |
| 159 | #3717 | — | 3 | 2 | no | — |
| 160 | #3715 | — | 3 | 2 | no | — |
| 161 | #3711 | — | 3 | 2 | no | — |
| 162 | #3711 | — | 3 | 2 | no | — |
| 163 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 164 | D3×C3⋊C8 | — | 3 | 2 | no | — |
| 165 | C22×H(3,𝔽3) | — | 2 | 1 | no | — |
| 166 | C22×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×#272 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 169 | C4×H(3,𝔽3) | — | 2 | 1 | no | — |
| 170 | C4×H(3,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 172 | #1084 | — | 2 | 2 | no | — |
| 173 | #1084 | C2×D4 | 1 | 2 | yes | — |
| 174 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 175 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 176 | C3×2−1+4 | — | 9 | 1 | no | — |
| 177 | #1010 | — | 3 | 1 | no | — |
| 178 | #1010 | — | 3 | 1 | no | — |
| 179 | #1010 | — | 6 | 1 | no | — |
| 180 | #1010 | — | 9 | 1 | no | — |
| 181 | #1010 | — | 9 | 1 | no | — |
| 182 | #1007 | — | 9 | 1 | no | — |
| 183 | C3×#137 | — | 9 | 1 | no | — |
| 184 | C3×#135 | — | 9 | 1 | no | — |
| 185 | #951 | — | 3 | 1 | no | — |
| 186 | #951 | — | 9 | 1 | no | — |
| 187 | #951 | — | 9 | 2 | no | — |
| 188 | #951 | — | 9 | 1 | no | — |
| 189 | #950 | — | 3 | 1 | no | — |
| 190 | #950 | — | 9 | 1 | no | — |
| 191 | #950 | — | 9 | 2 | no | — |
| 192 | #948 | — | 9 | 1 | no | — |
| 193 | C2×#216 | — | 9 | 1 | no | — |
| 194 | C2×#216 | — | 9 | 2 | no | — |
| 195 | C2×#216 | — | 9 | 1 | no | — |
| 196 | #942 | — | 9 | 1 | no | — |
| 197 | #942 | — | 9 | 2 | no | — |
| 198 | #918 | — | 9 | 2 | no | — |
| 199 | D3×Q16 | — | 9 | 2 | no | — |
| 200 | D3×Q16 | — | 9 | 2 | no | — |
| 201 | #916 | — | 9 | 2 | no | — |
| 202 | #915 | — | 9 | 2 | no | — |
| 203 | #915 | — | 9 | 2 | no | — |
| 204 | #915 | — | 9 | 2 | no | — |
| 205 | #912 | — | 9 | 2 | no | — |
| 206 | #909 | — | 9 | 1 | no | — |
| 207 | #907 | — | 9 | 1 | no | — |
| 208 | C2×Dic12 | — | 9 | 1 | no | — |
| 209 | #901 | — | 9 | 1 | no | — |
| 210 | C32×Q8 | — | 2 | 1 | no | — |
| 211 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 212 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 213 | C32×D4 | — | 2 | 2 | no | — |
| 214 | C32×D4 | — | 2 | 1 | no | — |
| 215 | C32×D4 | — | 2 | 1 | no | — |
| 216 | C32×D4 | — | 2 | 1 | no | — |
| 217 | C32×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 218 | C32×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 219 | C2×C32×C4 | — | 2 | 2 | no | — |
| 220 | C2×C32×C4 | — | 2 | 1 | no | — |
| 221 | C2×C32×C4 | — | 2 | 1 | no | — |
| 222 | C2×C32×C4 | — | 2 | 1 | no | — |
| 223 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 224 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 225 | #638 | — | 2 | 1 | no | — |
| 226 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 227 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 228 | C4×C3⋊D3 | — | 2 | 1 | no | — |
| 229 | #634 | — | 2 | 1 | no | — |
| 230 | #634 | C22×D3 | 1 | 1 | yes | characteristic |
| 231 | #634 | C22×D3 | 1 | 2 | yes | — |
| 232 | C3×#67 | — | 3 | 2 | no | — |
| 233 | C3×#67 | — | 3 | 2 | no | — |
| 234 | C3×#67 | — | 6 | 2 | no | — |
| 235 | C3×#67 | — | 6 | 2 | no | — |
| 236 | C3×#67 | — | 6 | 2 | no | — |
| 237 | C3×#67 | — | 6 | 4 | no | — |
| 238 | C3×#67 | — | 6 | 1 | no | — |
| 239 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 240 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 241 | C2×C3×Dic3 | — | 6 | 4 | no | — |
| 242 | C2×C3×Dic3 | — | 6 | 2 | no | — |
| 243 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 244 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 245 | C2×C3×Dic3 | — | 6 | 1 | no | — |
| 246 | C3×D12 | — | 3 | 1 | no | — |
| 247 | C3×D12 | — | 3 | 1 | no | — |
| 248 | C3×D12 | — | 3 | 1 | no | — |
| 249 | C3×D12 | — | 6 | 1 | no | — |
| 250 | C3×C4×D3 | — | 3 | 2 | no | — |
| 251 | C3×C4×D3 | — | 3 | 2 | no | — |
| 252 | C3×C4×D3 | — | 6 | 2 | no | — |
| 253 | C3×C4×D3 | — | 6 | 2 | no | — |
| 254 | C3×C4×D3 | — | 6 | 2 | no | — |
| 255 | C3×C4×D3 | — | 6 | 4 | no | — |
| 256 | C3×C4×D3 | — | 6 | 1 | no | — |
| 257 | C3×Dic6 | — | 3 | 1 | no | — |
| 258 | C3×Dic6 | — | 3 | 1 | no | — |
| 259 | C3×Dic6 | — | 3 | 1 | no | — |
| 260 | C3×Dic6 | — | 3 | 2 | no | — |
| 261 | C3×Dic6 | — | 3 | 2 | no | — |
| 262 | C3×Dic6 | — | 3 | 2 | no | — |
| 263 | C3×Dic6 | — | 6 | 1 | no | — |
| 264 | C3×Dic6 | — | 6 | 2 | no | — |
| 265 | C3×Dic6 | — | 6 | 2 | no | — |
| 266 | C3×Dic6 | — | 6 | 2 | no | — |
| 267 | C3×Dic6 | — | 6 | 2 | no | — |
| 268 | C3×Dic6 | — | 6 | 4 | no | — |
| 269 | C3×Dic6 | — | 6 | 1 | no | — |
| 270 | C3×Dic6 | — | 6 | 1 | no | — |
| 271 | C3×Dic6 | — | 6 | 1 | no | — |
| 272 | #627 | — | 6 | 2 | no | — |
| 273 | #627 | — | 6 | 2 | no | — |
| 274 | #626 | — | 6 | 2 | no | — |
| 275 | #625 | — | 6 | 2 | no | — |
| 276 | #624 | — | 6 | 2 | no | — |
| 277 | D3×Dic3 | — | 6 | 2 | no | — |
| 278 | D3×Dic3 | — | 6 | 2 | no | — |
| 279 | D3×Dic3 | — | 6 | 2 | no | — |
| 280 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 281 | C3⋊(C3⋊C8) | C22×D3 | 1 | 2 | yes | — |
| 282 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 283 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 284 | C3×C3⋊C8 | — | 3 | 2 | no | — |
| 285 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 286 | #578 | — | 27 | 1 | no | Sylow |
| 287 | C2×H(3,𝔽3) | — | 2 | 1 | no | — |
| 288 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 289 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 290 | #272 | — | 2 | 2 | no | — |
| 291 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 292 | C3×#41 | — | 3 | 1 | no | — |
| 293 | C3×#41 | — | 3 | 1 | no | — |
| 294 | C3×#41 | — | 6 | 1 | no | — |
| 295 | C3×#41 | — | 9 | 1 | no | — |
| 296 | C3×#41 | — | 9 | 1 | no | — |
| 297 | C3×#41 | — | 9 | 2 | no | — |
| 298 | C3×#41 | — | 18 | 1 | no | — |
| 299 | C3×#41 | — | 18 | 2 | no | — |
| 300 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 301 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 302 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 303 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 304 | C2×C3×Q8 | — | 18 | 1 | no | — |
| 305 | #239 | — | 9 | 2 | no | — |
| 306 | #239 | — | 18 | 1 | no | — |
| 307 | D3×Q8 | — | 3 | 2 | no | — |
| 308 | D3×Q8 | — | 3 | 2 | no | — |
| 309 | D3×Q8 | — | 6 | 2 | no | — |
| 310 | D3×Q8 | — | 9 | 2 | no | — |
| 311 | D3×Q8 | — | 9 | 2 | no | — |
| 312 | D3×Q8 | — | 18 | 1 | no | — |
| 313 | D3×Q8 | — | 18 | 1 | no | — |
| 314 | #237 | — | 3 | 2 | no | — |
| 315 | #237 | — | 3 | 2 | no | — |
| 316 | #237 | — | 6 | 2 | no | — |
| 317 | #237 | — | 6 | 2 | no | — |
| 318 | #237 | — | 6 | 2 | no | — |
| 319 | #237 | — | 6 | 4 | no | — |
| 320 | #237 | — | 9 | 2 | no | — |
| 321 | #237 | — | 18 | 1 | no | — |
| 322 | #237 | — | 18 | 2 | no | — |
| 323 | #237 | — | 18 | 2 | no | — |
| 324 | #235 | — | 3 | 1 | no | — |
| 325 | #235 | — | 3 | 1 | no | — |
| 326 | #235 | — | 3 | 1 | no | — |
| 327 | #235 | — | 6 | 1 | no | — |
| 328 | #235 | — | 6 | 1 | no | — |
| 329 | #235 | — | 6 | 1 | no | — |
| 330 | #235 | — | 6 | 2 | no | — |
| 331 | #235 | — | 9 | 1 | no | — |
| 332 | #235 | — | 9 | 2 | no | — |
| 333 | #235 | — | 18 | 1 | no | — |
| 334 | #235 | — | 18 | 2 | no | — |
| 335 | C2×Dic6 | — | 3 | 1 | no | — |
| 336 | C2×Dic6 | — | 3 | 1 | no | — |
| 337 | C2×Dic6 | — | 3 | 1 | no | — |
| 338 | C2×Dic6 | — | 6 | 1 | no | — |
| 339 | C2×Dic6 | — | 6 | 1 | no | — |
| 340 | C2×Dic6 | — | 6 | 1 | no | — |
| 341 | C2×Dic6 | — | 6 | 2 | no | — |
| 342 | C2×Dic6 | — | 9 | 1 | no | — |
| 343 | C2×Dic6 | — | 9 | 2 | no | — |
| 344 | C2×Dic6 | — | 18 | 1 | no | — |
| 345 | C3×Q16 | — | 9 | 1 | no | — |
| 346 | C3×Q16 | — | 9 | 2 | no | — |
| 347 | C3×SD16 | — | 9 | 1 | no | — |
| 348 | C3×SD16 | — | 9 | 2 | no | — |
| 349 | C3×SD16 | — | 9 | 1 | no | — |
| 350 | C3×D8 | — | 9 | 1 | no | — |
| 351 | C3×M16 | — | 9 | 1 | no | — |
| 352 | C2×C3×C8 | — | 9 | 1 | no | — |
| 353 | #216 | — | 3 | 2 | no | — |
| 354 | #216 | — | 3 | 1 | no | — |
| 355 | #216 | — | 9 | 2 | no | — |
| 356 | #216 | — | 9 | 1 | no | — |
| 357 | #216 | — | 9 | 2 | no | — |
| 358 | #216 | — | 9 | 2 | no | — |
| 359 | #216 | — | 9 | 2 | no | — |
| 360 | #216 | — | 9 | 2 | no | — |
| 361 | #216 | — | 9 | 2 | no | — |
| 362 | #216 | — | 9 | 2 | no | — |
| 363 | #215 | — | 3 | 1 | no | — |
| 364 | #215 | — | 9 | 1 | no | — |
| 365 | #215 | — | 9 | 2 | no | — |
| 366 | #214 | — | 3 | 1 | no | — |
| 367 | #214 | — | 3 | 2 | no | — |
| 368 | #214 | — | 9 | 2 | no | — |
| 369 | #214 | — | 9 | 1 | no | — |
| 370 | #214 | — | 9 | 2 | no | — |
| 371 | #213 | — | 3 | 1 | no | — |
| 372 | #213 | — | 9 | 1 | no | — |
| 373 | #208 | — | 3 | 1 | no | — |
| 374 | #208 | — | 9 | 1 | no | — |
| 375 | #208 | — | 9 | 2 | no | — |
| 376 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 377 | C2×C3⋊C8 | — | 9 | 1 | no | — |
| 378 | C2×C3⋊C8 | — | 9 | 2 | no | — |
| 379 | Dic12 | — | 9 | 2 | no | — |
| 380 | Dic12 | — | 9 | 2 | no | — |
| 381 | Dic12 | — | 9 | 2 | no | — |
| 382 | #204 | — | 9 | 2 | no | — |
| 383 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 384 | ΓL(1,𝔽25) | — | 9 | 2 | no | — |
| 385 | D3×C8 | — | 9 | 2 | no | — |
| 386 | D3×C8 | — | 9 | 2 | no | — |
| 387 | C22×C32 | — | 2 | 2 | no | — |
| 388 | C22×C32 | — | 2 | 1 | no | — |
| 389 | C22×C32 | — | 2 | 1 | no | — |
| 390 | C22×C32 | — | 2 | 1 | no | — |
| 391 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 392 | C22×C32 | D3×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 394 | C2×C3×D3 | — | 3 | 2 | no | — |
| 395 | C2×C3×D3 | — | 3 | 2 | no | — |
| 396 | C2×C3×D3 | — | 6 | 2 | no | — |
| 397 | C2×C3×D3 | — | 6 | 1 | no | — |
| 398 | C32×C4 | — | 2 | 2 | no | — |
| 399 | C32×C4 | — | 2 | 1 | no | — |
| 400 | C32×C4 | — | 2 | 1 | no | — |
| 401 | C32×C4 | — | 2 | 1 | no | — |
| 402 | C32×C4 | — | 2 | 1 | no | — |
| 403 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 404 | C32×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 405 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 406 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 407 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 408 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 409 | C3×Dic3 | — | 3 | 2 | no | — |
| 410 | C3×Dic3 | — | 3 | 2 | no | — |
| 411 | C3×Dic3 | — | 6 | 2 | no | — |
| 412 | C3×Dic3 | — | 6 | 4 | no | — |
| 413 | C3×Dic3 | — | 6 | 1 | no | — |
| 414 | C3×Dic3 | — | 6 | 2 | no | — |
| 415 | C3×Dic3 | — | 6 | 2 | no | — |
| 416 | C3×Dic3 | — | 6 | 2 | no | — |
| 417 | 2−1+4 | — | 9 | 1 | no | — |
| 418 | 2−1+4 | — | 27 | 1 | no | — |
| 419 | #137 | — | 9 | 1 | no | — |
| 420 | #137 | — | 27 | 1 | no | — |
| 421 | #137 | — | 27 | 2 | no | — |
| 422 | #137 | — | 27 | 2 | no | — |
| 423 | #135 | — | 9 | 1 | no | — |
| 424 | #135 | — | 27 | 2 | no | — |
| 425 | C2×Q16 | — | 27 | 1 | no | — |
| 426 | C2×Q16 | — | 27 | 2 | no | — |
| 427 | #131 | — | 27 | 1 | no | — |
| 428 | H(3,𝔽3) | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 429 | C3×Q8 | — | 3 | 1 | no | — |
| 430 | C3×Q8 | — | 3 | 1 | no | — |
| 431 | C3×Q8 | — | 6 | 1 | no | — |
| 432 | C3×Q8 | — | 9 | 1 | no | — |
| 433 | C3×Q8 | — | 9 | 2 | no | — |
| 434 | C3×Q8 | — | 9 | 1 | no | — |
| 435 | C3×Q8 | — | 9 | 2 | no | — |
| 436 | C3×Q8 | — | 18 | 2 | no | — |
| 437 | C3×Q8 | — | 18 | 1 | no | — |
| 438 | C3×Q8 | — | 18 | 1 | no | — |
| 439 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 440 | C3×D4 | — | 2 | 1 | no | — |
| 441 | C3×D4 | — | 3 | 1 | no | — |
| 442 | C3×D4 | — | 3 | 1 | no | — |
| 443 | C3×D4 | — | 6 | 1 | no | — |
| 444 | C3×D4 | — | 6 | 1 | no | — |
| 445 | C3×D4 | — | 6 | 2 | no | — |
| 446 | C3×D4 | — | 6 | 1 | no | — |
| 447 | C3×D4 | — | 9 | 1 | no | — |
| 448 | C3×D4 | — | 9 | 2 | no | — |
| 449 | C3×D4 | — | 9 | 1 | no | — |
| 450 | C3×D4 | — | 18 | 2 | no | — |
| 451 | C3×D4 | — | 18 | 1 | no | — |
| 452 | C3×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 453 | C2×C3×C4 | — | 2 | 1 | no | — |
| 454 | C2×C3×C4 | — | 3 | 1 | no | — |
| 455 | C2×C3×C4 | — | 3 | 1 | no | — |
| 456 | C2×C3×C4 | — | 6 | 1 | no | — |
| 457 | C2×C3×C4 | — | 6 | 1 | no | — |
| 458 | C2×C3×C4 | — | 6 | 2 | no | — |
| 459 | C2×C3×C4 | — | 6 | 1 | no | — |
| 460 | C2×C3×C4 | — | 9 | 2 | no | — |
| 461 | C2×C3×C4 | — | 18 | 2 | no | — |
| 462 | C2×C3×C4 | — | 18 | 1 | no | — |
| 463 | C2×C3×C4 | — | 18 | 2 | no | — |
| 464 | C2×C3×C4 | — | 18 | 1 | no | — |
| 465 | C2×C3×C4 | — | 18 | 1 | no | — |
| 466 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 467 | #67 | — | 3 | 2 | no | — |
| 468 | #67 | — | 3 | 2 | no | — |
| 469 | #67 | — | 6 | 2 | no | — |
| 470 | #67 | — | 6 | 2 | no | — |
| 471 | #67 | — | 6 | 2 | no | — |
| 472 | #67 | — | 6 | 4 | no | — |
| 473 | #67 | — | 6 | 1 | no | — |
| 474 | #67 | — | 18 | 1 | no | — |
| 475 | #67 | — | 18 | 2 | no | — |
| 476 | #67 | — | 18 | 2 | no | — |
| 477 | C2×Dic3 | — | 6 | 2 | no | — |
| 478 | C2×Dic3 | — | 6 | 2 | no | — |
| 479 | C2×Dic3 | — | 6 | 1 | no | — |
| 480 | C2×Dic3 | — | 6 | 1 | no | — |
| 481 | C2×Dic3 | — | 6 | 4 | no | — |
| 482 | C2×Dic3 | — | 6 | 2 | no | — |
| 483 | C2×Dic3 | — | 6 | 1 | no | — |
| 484 | C2×Dic3 | — | 18 | 1 | no | — |
| 485 | C2×Dic3 | — | 18 | 2 | no | — |
| 486 | C2×Dic3 | — | 18 | 2 | no | — |
| 487 | D12 | — | 3 | 1 | no | — |
| 488 | D12 | — | 3 | 1 | no | — |
| 489 | D12 | — | 3 | 1 | no | — |
| 490 | D12 | — | 6 | 1 | no | — |
| 491 | D12 | — | 9 | 1 | no | — |
| 492 | D12 | — | 18 | 2 | no | — |
| 493 | C4×D3 | — | 3 | 2 | no | — |
| 494 | C4×D3 | — | 3 | 2 | no | — |
| 495 | C4×D3 | — | 6 | 2 | no | — |
| 496 | C4×D3 | — | 6 | 2 | no | — |
| 497 | C4×D3 | — | 6 | 2 | no | — |
| 498 | C4×D3 | — | 6 | 4 | no | — |
| 499 | C4×D3 | — | 6 | 1 | no | — |
| 500 | C4×D3 | — | 18 | 1 | no | — |
| 501 | C4×D3 | — | 18 | 2 | no | — |
| 502 | C4×D3 | — | 18 | 2 | no | — |
| 503 | C4×D3 | — | 18 | 2 | no | — |
| 504 | C4×D3 | — | 18 | 2 | no | — |
| 505 | Dic6 | — | 3 | 1 | no | — |
| 506 | Dic6 | — | 3 | 1 | no | — |
| 507 | Dic6 | — | 3 | 2 | no | — |
| 508 | Dic6 | — | 3 | 2 | no | — |
| 509 | Dic6 | — | 3 | 2 | no | — |
| 510 | Dic6 | — | 3 | 1 | no | — |
| 511 | Dic6 | — | 6 | 1 | no | — |
| 512 | Dic6 | — | 6 | 2 | no | — |
| 513 | Dic6 | — | 6 | 2 | no | — |
| 514 | Dic6 | — | 6 | 2 | no | — |
| 515 | Dic6 | — | 6 | 1 | no | — |
| 516 | Dic6 | — | 6 | 1 | no | — |
| 517 | Dic6 | — | 6 | 2 | no | — |
| 518 | Dic6 | — | 6 | 4 | no | — |
| 519 | Dic6 | — | 6 | 1 | no | — |
| 520 | Dic6 | — | 9 | 2 | no | — |
| 521 | Dic6 | — | 9 | 1 | no | — |
| 522 | Dic6 | — | 18 | 1 | no | — |
| 523 | Dic6 | — | 18 | 2 | no | — |
| 524 | Dic6 | — | 18 | 2 | no | — |
| 525 | Dic6 | — | 18 | 2 | no | — |
| 526 | C3×C8 | — | 9 | 1 | no | — |
| 527 | C3×C8 | — | 9 | 2 | no | — |
| 528 | C3×C8 | — | 9 | 1 | no | — |
| 529 | C3⋊C8 | — | 3 | 1 | no | — |
| 530 | C3⋊C8 | — | 3 | 1 | no | — |
| 531 | C3⋊C8 | — | 3 | 2 | no | — |
| 532 | C3⋊C8 | — | 9 | 1 | no | — |
| 533 | C3⋊C8 | — | 9 | 2 | no | — |
| 534 | C3⋊C8 | — | 9 | 1 | no | — |
| 535 | C2×C32 | — | 2 | 1 | no | — |
| 536 | C2×C32 | — | 2 | 1 | no | — |
| 537 | C2×C32 | — | 2 | 1 | no | — |
| 538 | C2×C32 | — | 4 | 1 | no | — |
| 539 | C2×C32 | — | 4 | 2 | no | — |
| 540 | C2×C32 | — | 4 | 1 | no | — |
| 541 | C2×C32 | — | 4 | 1 | no | — |
| 542 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 543 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 544 | C3⋊D3 | — | 4 | 1 | no | — |
| 545 | C3×D3 | — | 6 | 2 | no | — |
| 546 | C3×D3 | — | 6 | 2 | no | — |
| 547 | C3×D3 | — | 12 | 2 | no | — |
| 548 | C3×D3 | — | 12 | 1 | no | — |
| 549 | #41 | — | 9 | 1 | no | — |
| 550 | #41 | — | 9 | 2 | no | — |
| 551 | #41 | — | 9 | 1 | no | — |
| 552 | #41 | — | 18 | 1 | no | — |
| 553 | #41 | — | 18 | 2 | no | — |
| 554 | #41 | — | 27 | 2 | no | — |
| 555 | #41 | — | 54 | 2 | no | — |
| 556 | #41 | — | 54 | 1 | no | — |
| 557 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 558 | C2×Q8 | — | 9 | 2 | no | — |
| 559 | C2×Q8 | — | 9 | 1 | no | — |
| 560 | C2×Q8 | — | 9 | 1 | no | — |
| 561 | C2×Q8 | — | 18 | 1 | no | — |
| 562 | C2×Q8 | — | 27 | 2 | no | — |
| 563 | C2×Q8 | — | 54 | 1 | no | — |
| 564 | Q16 | — | 9 | 1 | no | — |
| 565 | Q16 | — | 9 | 2 | no | — |
| 566 | Q16 | — | 27 | 2 | no | — |
| 567 | Q16 | — | 27 | 2 | no | — |
| 568 | Q16 | — | 27 | 2 | no | — |
| 569 | SD16 | — | 9 | 1 | no | — |
| 570 | SD16 | — | 9 | 1 | no | — |
| 571 | SD16 | — | 9 | 2 | no | — |
| 572 | SD16 | — | 27 | 2 | no | — |
| 573 | D8 | — | 9 | 1 | no | — |
| 574 | M16 | — | 9 | 1 | no | — |
| 575 | M16 | — | 27 | 2 | no | — |
| 576 | C2×C8 | — | 9 | 1 | no | — |
| 577 | C2×C8 | — | 27 | 2 | no | — |
| 578 | C22×C3 | — | 2 | 1 | no | — |
| 579 | C22×C3 | — | 3 | 1 | no | — |
| 580 | C22×C3 | — | 3 | 1 | no | — |
| 581 | C22×C3 | — | 6 | 1 | no | — |
| 582 | C22×C3 | — | 6 | 1 | no | — |
| 583 | C22×C3 | — | 6 | 2 | no | — |
| 584 | C22×C3 | — | 6 | 1 | no | — |
| 585 | C22×C3 | — | 9 | 2 | no | — |
| 586 | C22×C3 | — | 18 | 1 | no | — |
| 587 | C22×C3 | #3811 | 1 | 1 | yes | characteristic |
| 588 | C2×D3 | — | 3 | 2 | no | — |
| 589 | C2×D3 | — | 3 | 2 | no | — |
| 590 | C2×D3 | — | 6 | 2 | no | — |
| 591 | C2×D3 | — | 6 | 1 | no | — |
| 592 | C2×D3 | — | 18 | 1 | no | — |
| 593 | C3×C4 | — | 2 | 1 | no | — |
| 594 | C3×C4 | — | 3 | 1 | no | — |
| 595 | C3×C4 | — | 3 | 1 | no | — |
| 596 | C3×C4 | — | 3 | 1 | no | — |
| 597 | C3×C4 | — | 3 | 1 | no | — |
| 598 | C3×C4 | — | 6 | 1 | no | — |
| 599 | C3×C4 | — | 6 | 1 | no | — |
| 600 | C3×C4 | — | 6 | 2 | no | — |
| 601 | C3×C4 | — | 6 | 1 | no | — |
| 602 | C3×C4 | — | 6 | 1 | no | — |
| 603 | C3×C4 | — | 9 | 2 | no | — |
| 604 | C3×C4 | — | 18 | 1 | no | — |
| 605 | C3×C4 | — | 18 | 2 | no | — |
| 606 | C3×C4 | — | 18 | 2 | no | — |
| 607 | C3×C4 | #3811 | 1 | 1 | yes | characteristic |
| 608 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 609 | Dic3 | — | 3 | 2 | no | — |
| 610 | Dic3 | — | 3 | 2 | no | — |
| 611 | Dic3 | — | 6 | 2 | no | — |
| 612 | Dic3 | — | 6 | 2 | no | — |
| 613 | Dic3 | — | 6 | 2 | no | — |
| 614 | Dic3 | — | 6 | 4 | no | — |
| 615 | Dic3 | — | 6 | 2 | no | — |
| 616 | Dic3 | — | 6 | 1 | no | — |
| 617 | Dic3 | — | 18 | 1 | no | — |
| 618 | Dic3 | — | 18 | 2 | no | — |
| 619 | C32 | — | 2 | 1 | no | — |
| 620 | C32 | #5771 | 1 | 1 | yes | characteristic, complemented |
| 621 | C32 | #5779 | 1 | 1 | yes | characteristic, complemented |
| 622 | Q8 | — | 9 | 1 | no | — |
| 623 | Q8 | — | 9 | 2 | no | — |
| 624 | Q8 | — | 9 | 1 | no | — |
| 625 | Q8 | — | 9 | 2 | no | — |
| 626 | Q8 | — | 18 | 2 | no | — |
| 627 | Q8 | — | 18 | 1 | no | — |
| 628 | Q8 | — | 18 | 1 | no | — |
| 629 | Q8 | — | 54 | 2 | no | — |
| 630 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 631 | D4 | — | 2 | 1 | no | — |
| 632 | D4 | — | 9 | 2 | no | — |
| 633 | D4 | — | 9 | 1 | no | — |
| 634 | D4 | — | 9 | 1 | no | — |
| 635 | D4 | — | 18 | 2 | no | — |
| 636 | D4 | — | 18 | 1 | no | — |
| 637 | D4 | — | 54 | 2 | no | — |
| 638 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | — | 2 | 1 | no | — |
| 640 | C2×C4 | — | 9 | 2 | no | — |
| 641 | C2×C4 | — | 18 | 2 | no | — |
| 642 | C2×C4 | — | 18 | 2 | no | — |
| 643 | C2×C4 | — | 18 | 1 | no | — |
| 644 | C2×C4 | — | 18 | 1 | no | — |
| 645 | C2×C4 | — | 18 | 1 | no | — |
| 646 | C2×C4 | — | 54 | 2 | no | — |
| 647 | C2×C4 | — | 54 | 2 | no | — |
| 648 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 649 | C8 | — | 9 | 1 | no | — |
| 650 | C8 | — | 9 | 1 | no | — |
| 651 | C8 | — | 9 | 2 | no | — |
| 652 | C2×C3 | — | 2 | 1 | no | — |
| 653 | C2×C3 | — | 3 | 1 | no | — |
| 654 | C2×C3 | — | 3 | 1 | no | — |
| 655 | C2×C3 | — | 4 | 1 | no | — |
| 656 | C2×C3 | — | 6 | 1 | no | — |
| 657 | C2×C3 | — | 6 | 1 | no | — |
| 658 | C2×C3 | — | 6 | 1 | no | — |
| 659 | C2×C3 | — | 12 | 1 | no | — |
| 660 | C2×C3 | — | 12 | 1 | no | — |
| 661 | C2×C3 | — | 12 | 1 | no | — |
| 662 | C2×C3 | — | 12 | 2 | no | — |
| 663 | C2×C3 | — | 18 | 2 | no | — |
| 664 | C2×C3 | — | 36 | 1 | no | — |
| 665 | C2×C3 | C2×#3811 | 1 | 1 | yes | characteristic |
| 666 | D3 | — | 6 | 2 | no | — |
| 667 | D3 | — | 6 | 2 | no | — |
| 668 | D3 | — | 12 | 2 | no | — |
| 669 | D3 | — | 12 | 1 | no | — |
| 670 | D3 | — | 36 | 1 | no | — |
| 671 | C22 | — | 2 | 1 | no | — |
| 672 | C22 | — | 9 | 2 | no | — |
| 673 | C22 | — | 18 | 1 | no | — |
| 674 | C22 | #88677 | 1 | 1 | yes | characteristic |
| 675 | C4 | — | 2 | 1 | no | — |
| 676 | C4 | — | 9 | 2 | no | — |
| 677 | C4 | — | 18 | 2 | no | — |
| 678 | C4 | — | 18 | 1 | no | — |
| 679 | C4 | — | 18 | 2 | no | — |
| 680 | C4 | #88677 | 1 | 1 | yes | characteristic |
| 681 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 682 | C3 | — | 3 | 1 | no | — |
| 683 | C3 | — | 3 | 1 | no | — |
| 684 | C3 | — | 6 | 1 | no | — |
| 685 | C3 | #10595472 | 1 | 1 | yes | characteristic |
| 686 | C2 | — | 2 | 1 | no | — |
| 687 | C2 | — | 4 | 1 | no | — |
| 688 | C2 | — | 18 | 2 | no | — |
| 689 | C2 | — | 36 | 1 | no | — |
| 690 | C2 | C2×#88677 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722676 | C2 | semidirect |
| 2. #11722482 | C2 | semidirect |
| 3. #64159⋊C3 | C2 | semidirect |
| 4. #64160⋊C3 | C2 | semidirect |
| 5. #11721231 | C2 | semidirect |
| 6. #11721226 | C2 | semidirect |
| 7. #11721192 | C2 | semidirect |
| 8. #11721189 | C2 | semidirect |
| 9. C2×#88439 | C2 | semidirect |
| 10. #11721074 | C2 | semidirect |
| 11. #11721064 | C2 | semidirect |
| 48. #64160 | D3 | semidirect |
| 49. #64159 | D3 | semidirect |
| 428. H(3,𝔽3) | #578 | semidirect |
| 620. C32 | #5771 | semidirect |
| 621. C32 | #5779 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722676 | 2 |
| #11722482 | 2 |
| #64159⋊C3 | 2 |
| #64160⋊C3 | 2 |
| #11721231 | 2 |
| #11721226 | 2 |
| #11721192 | 2 |
| #11721189 | 2 |
| C2×#88439 | 2 |
| #11721074 | 2 |
| #11721064 | 2 |
| #10595467 | 3 |
| #10595465 | 3 |