Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
928 conjugacy classes of subgroups.
The subgroup lattice has 623 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722516 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | Q16×#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #64128⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q16×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11721238 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721237 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721231 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11720855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11720851 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11720844 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #11720840 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10594768 | — | 3 | 1 | no | maximal |
| 13 | #10594765 | — | 3 | 1 | no | maximal |
| 14 | Q8×#272 | C22 | 1 | 2 | yes | — |
| 15 | #88722 | C22 | 1 | 2 | yes | — |
| 16 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | — |
| 17 | #88650 | — | 2 | 2 | no | — |
| 18 | #88650 | C22 | 1 | 1 | yes | characteristic |
| 19 | #88649 | — | 2 | 2 | no | — |
| 20 | #88649 | C22 | 1 | 2 | yes | — |
| 21 | #88648 | — | 2 | 2 | no | — |
| 22 | #88648 | C22 | 1 | 2 | yes | — |
| 23 | ((C3⋊D3)⋊C3)⋊Q8 | — | 2 | 2 | no | — |
| 24 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 2 | yes | — |
| 25 | Q16×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 26 | #88550 | C22 | 1 | 2 | yes | — |
| 27 | #88530 | C22 | 1 | 1 | yes | characteristic |
| 28 | C8×#272 | C22 | 1 | 1 | yes | characteristic |
| 29 | #3755⋊C3 | C22 | 1 | 2 | yes | — |
| 30 | #3756⋊C3 | C22 | 1 | 2 | yes | — |
| 31 | #3745⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 32 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 33 | C8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 34 | #3746⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 35 | #88439 | C22 | 1 | 2 | yes | — |
| 36 | #88438 | C22 | 1 | 2 | yes | — |
| 37 | #88435 | C22 | 1 | 1 | yes | characteristic |
| 38 | #88431 | C22 | 1 | 2 | yes | — |
| 39 | #88430 | C22 | 1 | 1 | yes | characteristic |
| 40 | #88430 | C22 | 1 | 1 | yes | characteristic |
| 41 | #64316 | — | 3 | 2 | no | — |
| 42 | #64315 | — | 3 | 2 | no | — |
| 43 | #64128 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | Q16×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 45 | C3×#919 | — | 3 | 1 | no | — |
| 46 | C3×D3×Q16 | — | 3 | 1 | no | — |
| 47 | C3×D3×Q16 | — | 3 | 1 | no | — |
| 48 | C3×D3×Q16 | — | 3 | 1 | no | — |
| 49 | C3×D3×Q16 | — | 6 | 1 | no | — |
| 50 | #63951 | — | 3 | 2 | no | — |
| 51 | #63948 | — | 3 | 2 | no | — |
| 52 | #63948 | — | 3 | 2 | no | — |
| 53 | #63946 | — | 3 | 2 | no | — |
| 54 | #63945 | — | 3 | 2 | no | — |
| 55 | #63943 | — | 3 | 2 | no | — |
| 56 | #63810 | — | 3 | 1 | no | — |
| 57 | #63808 | — | 3 | 1 | no | — |
| 58 | #63808 | — | 3 | 1 | no | — |
| 59 | #63807 | — | 3 | 1 | no | — |
| 60 | #63803 | — | 3 | 1 | no | — |
| 61 | #63803 | — | 3 | 1 | no | — |
| 62 | #63802 | — | 3 | 1 | no | — |
| 63 | D3×Dic12 | — | 3 | 1 | no | — |
| 64 | Q8×H(3,𝔽3) | C23 | 1 | 2 | yes | — |
| 65 | C4×#272 | — | 2 | 2 | no | — |
| 66 | C4×#272 | C23 | 1 | 1 | yes | characteristic |
| 67 | #6229 | — | 2 | 2 | no | — |
| 68 | #6229 | C23 | 1 | 2 | yes | — |
| 69 | C4⋊((C3⋊D3)⋊C3) | — | 2 | 2 | no | — |
| 70 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 2 | yes | — |
| 71 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 72 | C4×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 73 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 75 | #634⋊C3 | — | 2 | 2 | no | — |
| 76 | #634⋊C3 | C23 | 1 | 2 | yes | — |
| 77 | #6200 | — | 2 | 2 | no | — |
| 78 | #6200 | D4 | 1 | 1 | yes | characteristic |
| 79 | #6200 | D4 | 1 | 1 | yes | characteristic |
| 80 | #6198 | — | 2 | 2 | no | — |
| 81 | #6198 | D4 | 1 | 1 | yes | characteristic |
| 82 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 83 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 84 | ((C3⋊D3)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 85 | #6196 | — | 2 | 2 | no | — |
| 86 | #6196 | D4 | 1 | 1 | yes | characteristic |
| 87 | C8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 88 | #6180 | C23 | 1 | 1 | yes | characteristic |
| 89 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 90 | (C3⋊(C3⋊C8))⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 91 | #5771 | — | 9 | 1 | no | — |
| 92 | #5766 | — | 9 | 1 | no | — |
| 93 | #5766 | — | 9 | 1 | no | — |
| 94 | #3832 | C2×D3 | 1 | 2 | yes | — |
| 95 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | — |
| 96 | C3×#239 | — | 3 | 2 | no | — |
| 97 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 98 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 99 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 100 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 101 | #3799 | — | 3 | 2 | no | — |
| 102 | #3799 | — | 3 | 2 | no | — |
| 103 | #3799 | — | 6 | 2 | no | — |
| 104 | #3799 | — | 6 | 2 | no | — |
| 105 | #3798 | — | 3 | 1 | no | — |
| 106 | #3798 | — | 3 | 1 | no | — |
| 107 | #3798 | — | 6 | 2 | no | — |
| 108 | #3798 | — | 6 | 2 | no | — |
| 109 | #3797 | — | 3 | 2 | no | — |
| 110 | #3797 | — | 6 | 2 | no | — |
| 111 | #3796 | — | 3 | 2 | no | — |
| 112 | #3796 | — | 6 | 2 | no | — |
| 113 | #3795 | — | 3 | 2 | no | — |
| 114 | #3795 | — | 6 | 2 | no | — |
| 115 | D3×Dic6 | — | 3 | 2 | no | — |
| 116 | D3×Dic6 | — | 6 | 2 | no | — |
| 117 | C32×Q16 | — | 2 | 1 | no | — |
| 118 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 119 | C32×Q16 | C2×D3 | 1 | 1 | yes | characteristic |
| 120 | #3756 | C2×D3 | 1 | 2 | yes | — |
| 121 | #3755 | C2×D3 | 1 | 2 | yes | — |
| 122 | #3746 | C2×D3 | 1 | 1 | yes | characteristic |
| 123 | #3745 | C2×D3 | 1 | 1 | yes | characteristic |
| 124 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 125 | C8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 126 | C3×#216 | — | 3 | 2 | no | — |
| 127 | C3×#216 | — | 3 | 2 | no | — |
| 128 | C3×#216 | — | 3 | 2 | no | — |
| 129 | C3×#216 | — | 6 | 2 | no | — |
| 130 | C3×#215 | — | 3 | 2 | no | — |
| 131 | C3×Dic12 | — | 3 | 1 | no | — |
| 132 | C3×Dic12 | — | 3 | 1 | no | — |
| 133 | C3×Dic12 | — | 3 | 1 | no | — |
| 134 | C3×Dic12 | — | 6 | 1 | no | — |
| 135 | C3×D24 | — | 3 | 1 | no | — |
| 136 | C3×D3×C8 | — | 3 | 1 | no | — |
| 137 | C3×D3×C8 | — | 3 | 1 | no | — |
| 138 | C3×D3×C8 | — | 3 | 1 | no | — |
| 139 | C3×D3×C8 | — | 3 | 1 | no | — |
| 140 | C3×D3×C8 | — | 6 | 1 | no | — |
| 141 | #3719 | — | 3 | 2 | no | — |
| 142 | #3718 | — | 3 | 2 | no | — |
| 143 | #3717 | — | 3 | 2 | no | — |
| 144 | #3717 | — | 3 | 2 | no | — |
| 145 | #3716 | — | 3 | 2 | no | — |
| 146 | #3715 | — | 3 | 2 | no | — |
| 147 | #3712 | — | 3 | 1 | no | — |
| 148 | #3712 | — | 3 | 1 | no | — |
| 149 | #3711 | — | 3 | 1 | no | — |
| 150 | #3711 | — | 3 | 1 | no | — |
| 151 | #3711 | — | 3 | 1 | no | — |
| 152 | #3711 | — | 3 | 1 | no | — |
| 153 | C2×#272 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×(C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 155 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C2×(C3⋊D3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C4×H(3,𝔽3) | — | 2 | 2 | no | — |
| 158 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 159 | #1084 | — | 2 | 2 | no | — |
| 160 | #1084 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | (C3⋊Dic3)⋊C3 | — | 2 | 2 | no | — |
| 162 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | (C3⋊Dic3)⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 164 | #1010 | — | 9 | 2 | no | — |
| 165 | #1007 | — | 9 | 2 | no | — |
| 166 | #1007 | — | 9 | 2 | no | — |
| 167 | C3×#135 | — | 9 | 1 | no | — |
| 168 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 169 | C2×C3×Q16 | — | 9 | 1 | no | — |
| 170 | #951 | — | 9 | 2 | no | — |
| 171 | #942 | — | 9 | 2 | no | — |
| 172 | #942 | — | 9 | 2 | no | — |
| 173 | #919 | — | 3 | 1 | no | — |
| 174 | #919 | — | 9 | 1 | no | — |
| 175 | #919 | — | 9 | 1 | no | — |
| 176 | #919 | — | 9 | 1 | no | — |
| 177 | #918 | — | 9 | 2 | no | — |
| 178 | #918 | — | 9 | 2 | no | — |
| 179 | #918 | — | 9 | 2 | no | — |
| 180 | #918 | — | 9 | 2 | no | — |
| 181 | D3×Q16 | — | 3 | 1 | no | — |
| 182 | D3×Q16 | — | 3 | 1 | no | — |
| 183 | D3×Q16 | — | 3 | 1 | no | — |
| 184 | D3×Q16 | — | 6 | 1 | no | — |
| 185 | D3×Q16 | — | 9 | 1 | no | — |
| 186 | D3×Q16 | — | 9 | 1 | no | — |
| 187 | D3×Q16 | — | 9 | 1 | no | — |
| 188 | #915 | — | 9 | 2 | no | — |
| 189 | #915 | — | 9 | 2 | no | — |
| 190 | #912 | — | 9 | 1 | no | — |
| 191 | #912 | — | 9 | 1 | no | — |
| 192 | C2×Dic12 | — | 9 | 1 | no | — |
| 193 | #904 | — | 9 | 1 | no | — |
| 194 | #904 | — | 9 | 1 | no | — |
| 195 | #901 | — | 9 | 1 | no | — |
| 196 | #901 | — | 9 | 1 | no | — |
| 197 | #901 | — | 9 | 1 | no | — |
| 198 | C32×Q8 | — | 2 | 2 | no | — |
| 199 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 200 | C32×Q8 | C22×D3 | 1 | 2 | yes | — |
| 201 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 202 | C4⋊(C3⋊D3) | C22×D3 | 1 | 2 | yes | — |
| 203 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 204 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 205 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 206 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 207 | #634 | — | 2 | 2 | no | — |
| 208 | #634 | C22×D3 | 1 | 2 | yes | — |
| 209 | C3×D12 | — | 3 | 2 | no | — |
| 210 | C3×D12 | — | 6 | 2 | no | — |
| 211 | C3×C4×D3 | — | 3 | 1 | no | — |
| 212 | C3×C4×D3 | — | 3 | 1 | no | — |
| 213 | C3×C4×D3 | — | 3 | 1 | no | — |
| 214 | C3×C4×D3 | — | 3 | 1 | no | — |
| 215 | C3×C4×D3 | — | 6 | 1 | no | — |
| 216 | C3×C4×D3 | — | 6 | 2 | no | — |
| 217 | C3×C4×D3 | — | 6 | 2 | no | — |
| 218 | C3×C4×D3 | — | 6 | 2 | no | — |
| 219 | C3×C4×D3 | — | 6 | 2 | no | — |
| 220 | C3×C4×D3 | — | 12 | 2 | no | — |
| 221 | C3×Dic6 | — | 3 | 2 | no | — |
| 222 | C3×Dic6 | — | 3 | 2 | no | — |
| 223 | C3×Dic6 | — | 3 | 2 | no | — |
| 224 | C3×Dic6 | — | 6 | 2 | no | — |
| 225 | C3×Dic6 | — | 6 | 2 | no | — |
| 226 | C3×Dic6 | — | 6 | 2 | no | — |
| 227 | C3×Dic6 | — | 6 | 2 | no | — |
| 228 | C3×Dic6 | — | 12 | 2 | no | — |
| 229 | #627 | — | 3 | 1 | no | — |
| 230 | #627 | — | 3 | 1 | no | — |
| 231 | #627 | — | 6 | 2 | no | — |
| 232 | #627 | — | 6 | 2 | no | — |
| 233 | #626 | — | 3 | 1 | no | — |
| 234 | #626 | — | 3 | 1 | no | — |
| 235 | #626 | — | 3 | 1 | no | — |
| 236 | #626 | — | 3 | 1 | no | — |
| 237 | #626 | — | 6 | 2 | no | — |
| 238 | #626 | — | 6 | 2 | no | — |
| 239 | #626 | — | 6 | 2 | no | — |
| 240 | #625 | — | 3 | 1 | no | — |
| 241 | #625 | — | 3 | 1 | no | — |
| 242 | #625 | — | 6 | 2 | no | — |
| 243 | #624 | — | 6 | 2 | no | — |
| 244 | #624 | — | 6 | 2 | no | — |
| 245 | #624 | — | 6 | 2 | no | — |
| 246 | D3×Dic3 | — | 6 | 2 | no | — |
| 247 | D3×Dic3 | — | 6 | 2 | no | — |
| 248 | D3×Dic3 | — | 6 | 2 | no | — |
| 249 | C32×C8 | — | 2 | 1 | no | — |
| 250 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 251 | C32×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 252 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 253 | C3⋊(C3⋊C8) | C22×D3 | 1 | 1 | yes | characteristic |
| 254 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 255 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 256 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 257 | C3×C3⋊C8 | — | 3 | 1 | no | — |
| 258 | C3×C3⋊C8 | — | 6 | 1 | no | — |
| 259 | #578 | — | 27 | 1 | no | Sylow |
| 260 | C2×H(3,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 261 | #272 | — | 2 | 1 | no | — |
| 262 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 263 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 264 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 265 | C3×#41 | — | 9 | 2 | no | — |
| 266 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 267 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 268 | #239 | — | 3 | 2 | no | — |
| 269 | #239 | — | 9 | 2 | no | — |
| 270 | #239 | — | 9 | 2 | no | — |
| 271 | #239 | — | 9 | 2 | no | — |
| 272 | #239 | — | 18 | 2 | no | — |
| 273 | #239 | — | 18 | 2 | no | — |
| 274 | D3×Q8 | — | 3 | 2 | no | — |
| 275 | D3×Q8 | — | 3 | 2 | no | — |
| 276 | D3×Q8 | — | 3 | 2 | no | — |
| 277 | D3×Q8 | — | 6 | 2 | no | — |
| 278 | D3×Q8 | — | 9 | 2 | no | — |
| 279 | D3×Q8 | — | 9 | 2 | no | — |
| 280 | D3×Q8 | — | 9 | 2 | no | — |
| 281 | D3×Q8 | — | 18 | 2 | no | — |
| 282 | D3×Q8 | — | 18 | 2 | no | — |
| 283 | #237 | — | 9 | 2 | no | — |
| 284 | #237 | — | 9 | 2 | no | — |
| 285 | #237 | — | 18 | 2 | no | — |
| 286 | #237 | — | 18 | 2 | no | — |
| 287 | #235 | — | 9 | 2 | no | — |
| 288 | #235 | — | 9 | 2 | no | — |
| 289 | #235 | — | 9 | 1 | no | — |
| 290 | #235 | — | 9 | 1 | no | — |
| 291 | #235 | — | 9 | 1 | no | — |
| 292 | #235 | — | 18 | 2 | no | — |
| 293 | #235 | — | 18 | 2 | no | — |
| 294 | #235 | — | 18 | 2 | no | — |
| 295 | #235 | — | 18 | 2 | no | — |
| 296 | #235 | — | 18 | 2 | no | — |
| 297 | C2×Dic6 | — | 9 | 2 | no | — |
| 298 | C2×Dic6 | — | 18 | 2 | no | — |
| 299 | C3×Q16 | — | 3 | 1 | no | — |
| 300 | C3×Q16 | — | 3 | 1 | no | — |
| 301 | C3×Q16 | — | 6 | 1 | no | — |
| 302 | C3×Q16 | — | 9 | 1 | no | — |
| 303 | C3×Q16 | — | 9 | 2 | no | — |
| 304 | C3×Q16 | — | 9 | 2 | no | — |
| 305 | C3×Q16 | — | 9 | 1 | no | — |
| 306 | C3×Q16 | D32 | 1 | 1 | yes | characteristic |
| 307 | C3×SD16 | — | 9 | 2 | no | — |
| 308 | C3×D8 | — | 9 | 1 | no | — |
| 309 | C2×C3×C8 | — | 9 | 1 | no | — |
| 310 | C2×C3×C8 | — | 9 | 1 | no | — |
| 311 | C2×C3×C8 | — | 9 | 1 | no | — |
| 312 | #216 | — | 3 | 2 | no | — |
| 313 | #216 | — | 3 | 2 | no | — |
| 314 | #216 | — | 3 | 2 | no | — |
| 315 | #216 | — | 6 | 2 | no | — |
| 316 | #216 | — | 9 | 2 | no | — |
| 317 | #216 | — | 9 | 2 | no | — |
| 318 | #216 | — | 9 | 2 | no | — |
| 319 | #215 | — | 3 | 2 | no | — |
| 320 | #215 | — | 9 | 2 | no | — |
| 321 | #215 | — | 9 | 2 | no | — |
| 322 | #215 | — | 9 | 2 | no | — |
| 323 | #214 | — | 9 | 2 | no | — |
| 324 | #214 | — | 9 | 2 | no | — |
| 325 | #208 | — | 9 | 1 | no | — |
| 326 | #208 | — | 9 | 1 | no | — |
| 327 | #208 | — | 9 | 1 | no | — |
| 328 | Dic12 | — | 3 | 1 | no | — |
| 329 | Dic12 | — | 3 | 1 | no | — |
| 330 | Dic12 | — | 3 | 1 | no | — |
| 331 | Dic12 | — | 6 | 1 | no | — |
| 332 | Dic12 | — | 9 | 1 | no | — |
| 333 | Dic12 | — | 9 | 2 | no | — |
| 334 | D24 | — | 3 | 1 | no | — |
| 335 | D24 | — | 9 | 1 | no | — |
| 336 | #204 | — | 9 | 2 | no | — |
| 337 | #204 | — | 9 | 2 | no | — |
| 338 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 339 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 340 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 341 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 342 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 343 | ΓL(1,𝔽25) | — | 9 | 1 | no | — |
| 344 | D3×C8 | — | 3 | 1 | no | — |
| 345 | D3×C8 | — | 3 | 1 | no | — |
| 346 | D3×C8 | — | 3 | 1 | no | — |
| 347 | D3×C8 | — | 3 | 1 | no | — |
| 348 | D3×C8 | — | 6 | 1 | no | — |
| 349 | D3×C8 | — | 9 | 1 | no | — |
| 350 | D3×C8 | — | 9 | 1 | no | — |
| 351 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 352 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 353 | C2×C3⋊D3 | D3×D4 | 1 | 1 | yes | characteristic |
| 354 | C2×C3×D3 | — | 3 | 1 | no | — |
| 355 | C2×C3×D3 | — | 3 | 1 | no | — |
| 356 | C2×C3×D3 | — | 3 | 1 | no | — |
| 357 | C2×C3×D3 | — | 3 | 1 | no | — |
| 358 | C2×C3×D3 | — | 6 | 1 | no | — |
| 359 | C2×C3×D3 | — | 6 | 2 | no | — |
| 360 | C32×C4 | — | 2 | 2 | no | — |
| 361 | C32×C4 | — | 2 | 2 | no | — |
| 362 | C32×C4 | — | 2 | 1 | no | — |
| 363 | C32×C4 | — | 4 | 2 | no | — |
| 364 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 365 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 366 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 367 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 368 | C3⋊Dic3 | D3×D4 | 1 | 1 | yes | characteristic |
| 369 | C3×Dic3 | — | 3 | 1 | no | — |
| 370 | C3×Dic3 | — | 3 | 1 | no | — |
| 371 | C3×Dic3 | — | 3 | 1 | no | — |
| 372 | C3×Dic3 | — | 3 | 1 | no | — |
| 373 | C3×Dic3 | — | 6 | 1 | no | — |
| 374 | C3×Dic3 | — | 6 | 2 | no | — |
| 375 | C3×Dic3 | — | 6 | 2 | no | — |
| 376 | C3×Dic3 | — | 6 | 2 | no | — |
| 377 | C3×Dic3 | — | 12 | 2 | no | — |
| 378 | 2−1+4 | — | 27 | 2 | no | — |
| 379 | #137 | — | 27 | 2 | no | — |
| 380 | #137 | — | 27 | 2 | no | — |
| 381 | #137 | — | 27 | 2 | no | — |
| 382 | #135 | — | 9 | 1 | no | — |
| 383 | #135 | — | 27 | 1 | no | — |
| 384 | #135 | — | 27 | 1 | no | — |
| 385 | C2×Q16 | — | 9 | 1 | no | — |
| 386 | C2×Q16 | — | 9 | 1 | no | — |
| 387 | C2×Q16 | — | 27 | 1 | no | — |
| 388 | #131 | — | 27 | 1 | no | — |
| 389 | H(3,𝔽3) | #578 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 390 | C3×Q8 | — | 3 | 2 | no | — |
| 391 | C3×Q8 | — | 3 | 2 | no | — |
| 392 | C3×Q8 | — | 6 | 2 | no | — |
| 393 | C3×Q8 | — | 9 | 2 | no | — |
| 394 | C3×Q8 | — | 9 | 2 | no | — |
| 395 | C3×Q8 | — | 18 | 2 | no | — |
| 396 | C3×Q8 | — | 18 | 2 | no | — |
| 397 | C3×Q8 | C2×D32 | 1 | 2 | yes | — |
| 398 | C3×D4 | — | 9 | 2 | no | — |
| 399 | C3×D4 | — | 18 | 2 | no | — |
| 400 | C2×C3×C4 | — | 9 | 1 | no | — |
| 401 | C2×C3×C4 | — | 9 | 1 | no | — |
| 402 | C2×C3×C4 | — | 9 | 1 | no | — |
| 403 | C2×C3×C4 | — | 18 | 2 | no | — |
| 404 | C2×C3×C4 | — | 18 | 2 | no | — |
| 405 | C2×C3×C4 | — | 18 | 2 | no | — |
| 406 | #67 | — | 9 | 1 | no | — |
| 407 | #67 | — | 9 | 1 | no | — |
| 408 | #67 | — | 9 | 1 | no | — |
| 409 | #67 | — | 9 | 1 | no | — |
| 410 | #67 | — | 9 | 1 | no | — |
| 411 | #67 | — | 9 | 1 | no | — |
| 412 | #67 | — | 18 | 2 | no | — |
| 413 | #67 | — | 18 | 2 | no | — |
| 414 | #67 | — | 18 | 2 | no | — |
| 415 | #67 | — | 18 | 2 | no | — |
| 416 | C2×Dic3 | — | 18 | 2 | no | — |
| 417 | C2×Dic3 | — | 18 | 2 | no | — |
| 418 | C2×Dic3 | — | 18 | 2 | no | — |
| 419 | D12 | — | 3 | 2 | no | — |
| 420 | D12 | — | 6 | 2 | no | — |
| 421 | D12 | — | 9 | 2 | no | — |
| 422 | D12 | — | 9 | 1 | no | — |
| 423 | D12 | — | 9 | 1 | no | — |
| 424 | D12 | — | 9 | 1 | no | — |
| 425 | D12 | — | 18 | 2 | no | — |
| 426 | D12 | — | 18 | 2 | no | — |
| 427 | D12 | — | 18 | 2 | no | — |
| 428 | C4×D3 | — | 3 | 1 | no | — |
| 429 | C4×D3 | — | 3 | 1 | no | — |
| 430 | C4×D3 | — | 3 | 1 | no | — |
| 431 | C4×D3 | — | 3 | 1 | no | — |
| 432 | C4×D3 | — | 6 | 1 | no | — |
| 433 | C4×D3 | — | 6 | 2 | no | — |
| 434 | C4×D3 | — | 6 | 2 | no | — |
| 435 | C4×D3 | — | 6 | 2 | no | — |
| 436 | C4×D3 | — | 6 | 2 | no | — |
| 437 | C4×D3 | — | 9 | 1 | no | — |
| 438 | C4×D3 | — | 9 | 1 | no | — |
| 439 | C4×D3 | — | 12 | 2 | no | — |
| 440 | C4×D3 | — | 18 | 2 | no | — |
| 441 | C4×D3 | — | 18 | 2 | no | — |
| 442 | C4×D3 | — | 18 | 2 | no | — |
| 443 | C4×D3 | — | 18 | 2 | no | — |
| 444 | C4×D3 | — | 18 | 2 | no | — |
| 445 | C4×D3 | — | 18 | 2 | no | — |
| 446 | C4×D3 | — | 18 | 2 | no | — |
| 447 | C4×D3 | — | 18 | 2 | no | — |
| 448 | Dic6 | — | 3 | 2 | no | — |
| 449 | Dic6 | — | 3 | 2 | no | — |
| 450 | Dic6 | — | 3 | 2 | no | — |
| 451 | Dic6 | — | 6 | 2 | no | — |
| 452 | Dic6 | — | 6 | 2 | no | — |
| 453 | Dic6 | — | 6 | 2 | no | — |
| 454 | Dic6 | — | 6 | 2 | no | — |
| 455 | Dic6 | — | 9 | 2 | no | — |
| 456 | Dic6 | — | 9 | 1 | no | — |
| 457 | Dic6 | — | 9 | 1 | no | — |
| 458 | Dic6 | — | 9 | 1 | no | — |
| 459 | Dic6 | — | 12 | 2 | no | — |
| 460 | Dic6 | — | 18 | 2 | no | — |
| 461 | Dic6 | — | 18 | 2 | no | — |
| 462 | Dic6 | — | 18 | 2 | no | — |
| 463 | Dic6 | — | 18 | 2 | no | — |
| 464 | C3×C8 | — | 3 | 1 | no | — |
| 465 | C3×C8 | — | 3 | 1 | no | — |
| 466 | C3×C8 | — | 6 | 1 | no | — |
| 467 | C3×C8 | — | 9 | 1 | no | — |
| 468 | C3×C8 | — | 9 | 1 | no | — |
| 469 | C3×C8 | — | 9 | 1 | no | — |
| 470 | C3×C8 | C2×D32 | 1 | 1 | yes | characteristic |
| 471 | C3⋊C8 | — | 3 | 1 | no | — |
| 472 | C3⋊C8 | — | 3 | 1 | no | — |
| 473 | C3⋊C8 | — | 3 | 1 | no | — |
| 474 | C3⋊C8 | — | 3 | 1 | no | — |
| 475 | C3⋊C8 | — | 6 | 1 | no | — |
| 476 | C3⋊C8 | — | 9 | 1 | no | — |
| 477 | C3⋊C8 | — | 9 | 1 | no | — |
| 478 | C2×C32 | — | 2 | 1 | no | — |
| 479 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 480 | C2×C32 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 481 | C3⋊D3 | — | 2 | 1 | no | — |
| 482 | C3⋊D3 | — | 2 | 1 | no | — |
| 483 | C3⋊D3 | — | 4 | 2 | no | — |
| 484 | C3×D3 | — | 6 | 2 | no | — |
| 485 | C3×D3 | — | 6 | 1 | no | — |
| 486 | C3×D3 | — | 6 | 1 | no | — |
| 487 | C3×D3 | — | 6 | 1 | no | — |
| 488 | C3×D3 | — | 6 | 1 | no | — |
| 489 | C3×D3 | — | 12 | 2 | no | — |
| 490 | #41 | — | 9 | 2 | no | — |
| 491 | #41 | — | 27 | 1 | no | — |
| 492 | #41 | — | 27 | 2 | no | — |
| 493 | #41 | — | 27 | 2 | no | — |
| 494 | #41 | — | 54 | 2 | no | — |
| 495 | #41 | — | 54 | 2 | no | — |
| 496 | #41 | — | 54 | 2 | no | — |
| 497 | C2×Q8 | — | 9 | 2 | no | — |
| 498 | C2×Q8 | — | 9 | 2 | no | — |
| 499 | C2×Q8 | — | 27 | 2 | no | — |
| 500 | C2×Q8 | — | 54 | 2 | no | — |
| 501 | Q16 | — | 9 | 2 | no | — |
| 502 | Q16 | — | 9 | 2 | no | — |
| 503 | Q16 | — | 9 | 1 | no | — |
| 504 | Q16 | — | 9 | 1 | no | — |
| 505 | Q16 | — | 27 | 2 | no | — |
| 506 | Q16 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 507 | SD16 | — | 9 | 2 | no | — |
| 508 | SD16 | — | 27 | 2 | no | — |
| 509 | SD16 | — | 27 | 2 | no | — |
| 510 | D8 | — | 9 | 1 | no | — |
| 511 | M16 | — | 27 | 1 | no | — |
| 512 | M16 | — | 27 | 1 | no | — |
| 513 | M16 | — | 27 | 1 | no | — |
| 514 | C2×C8 | — | 9 | 1 | no | — |
| 515 | C2×C8 | — | 9 | 1 | no | — |
| 516 | C2×C8 | — | 9 | 1 | no | — |
| 517 | C22×C3 | — | 9 | 1 | no | — |
| 518 | C22×C3 | — | 9 | 1 | no | — |
| 519 | C22×C3 | — | 9 | 1 | no | — |
| 520 | C22×C3 | — | 18 | 2 | no | — |
| 521 | C2×D3 | — | 3 | 1 | no | — |
| 522 | C2×D3 | — | 3 | 1 | no | — |
| 523 | C2×D3 | — | 3 | 1 | no | — |
| 524 | C2×D3 | — | 3 | 1 | no | — |
| 525 | C2×D3 | — | 6 | 1 | no | — |
| 526 | C2×D3 | — | 6 | 2 | no | — |
| 527 | C2×D3 | — | 9 | 1 | no | — |
| 528 | C2×D3 | — | 9 | 1 | no | — |
| 529 | C2×D3 | — | 18 | 2 | no | — |
| 530 | C3×C4 | — | 2 | 2 | no | — |
| 531 | C3×C4 | — | 3 | 1 | no | — |
| 532 | C3×C4 | — | 3 | 1 | no | — |
| 533 | C3×C4 | — | 6 | 2 | no | — |
| 534 | C3×C4 | — | 6 | 2 | no | — |
| 535 | C3×C4 | — | 6 | 1 | no | — |
| 536 | C3×C4 | — | 9 | 1 | no | — |
| 537 | C3×C4 | — | 9 | 1 | no | — |
| 538 | C3×C4 | — | 9 | 1 | no | — |
| 539 | C3×C4 | — | 12 | 2 | no | — |
| 540 | C3×C4 | — | 18 | 2 | no | — |
| 541 | C3×C4 | — | 18 | 2 | no | — |
| 542 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 543 | Dic3 | — | 3 | 1 | no | — |
| 544 | Dic3 | — | 3 | 1 | no | — |
| 545 | Dic3 | — | 3 | 1 | no | — |
| 546 | Dic3 | — | 3 | 1 | no | — |
| 547 | Dic3 | — | 6 | 1 | no | — |
| 548 | Dic3 | — | 6 | 2 | no | — |
| 549 | Dic3 | — | 6 | 2 | no | — |
| 550 | Dic3 | — | 6 | 2 | no | — |
| 551 | Dic3 | — | 9 | 1 | no | — |
| 552 | Dic3 | — | 9 | 1 | no | — |
| 553 | Dic3 | — | 12 | 2 | no | — |
| 554 | Dic3 | — | 18 | 2 | no | — |
| 555 | C32 | — | 2 | 1 | no | — |
| 556 | C32 | #5766 | 1 | 1 | yes | characteristic, complemented |
| 557 | C32 | #5771 | 1 | 1 | yes | characteristic, complemented |
| 558 | Q8 | — | 9 | 2 | no | — |
| 559 | Q8 | — | 9 | 2 | no | — |
| 560 | Q8 | — | 18 | 2 | no | — |
| 561 | Q8 | — | 18 | 2 | no | — |
| 562 | Q8 | — | 27 | 1 | no | — |
| 563 | Q8 | — | 54 | 2 | no | — |
| 564 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | — |
| 565 | D4 | — | 9 | 2 | no | — |
| 566 | D4 | — | 18 | 2 | no | — |
| 567 | D4 | — | 27 | 1 | no | — |
| 568 | D4 | — | 27 | 1 | no | — |
| 569 | D4 | — | 27 | 1 | no | — |
| 570 | D4 | — | 54 | 2 | no | — |
| 571 | D4 | — | 54 | 2 | no | — |
| 572 | C2×C4 | — | 9 | 1 | no | — |
| 573 | C2×C4 | — | 9 | 1 | no | — |
| 574 | C2×C4 | — | 9 | 1 | no | — |
| 575 | C2×C4 | — | 18 | 2 | no | — |
| 576 | C2×C4 | — | 18 | 2 | no | — |
| 577 | C2×C4 | — | 18 | 2 | no | — |
| 578 | C2×C4 | — | 54 | 2 | no | — |
| 579 | C2×C4 | — | 54 | 2 | no | — |
| 580 | C2×C4 | — | 54 | 2 | no | — |
| 581 | C8 | — | 9 | 1 | no | — |
| 582 | C8 | — | 9 | 1 | no | — |
| 583 | C8 | — | 9 | 1 | no | — |
| 584 | C8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 585 | C2×C3 | — | 3 | 1 | no | — |
| 586 | C2×C3 | — | 3 | 1 | no | — |
| 587 | C2×C3 | — | 6 | 1 | no | — |
| 588 | C2×C3 | — | 18 | 1 | no | — |
| 589 | C2×C3 | — | 18 | 1 | no | — |
| 590 | C2×C3 | — | 18 | 1 | no | — |
| 591 | C2×C3 | — | 36 | 2 | no | — |
| 592 | C2×C3 | D32×D4 | 1 | 1 | yes | characteristic |
| 593 | D3 | — | 6 | 1 | no | — |
| 594 | D3 | — | 6 | 1 | no | — |
| 595 | D3 | — | 6 | 2 | no | — |
| 596 | D3 | — | 6 | 1 | no | — |
| 597 | D3 | — | 6 | 1 | no | — |
| 598 | D3 | — | 12 | 2 | no | — |
| 599 | D3 | — | 18 | 1 | no | — |
| 600 | D3 | — | 18 | 1 | no | — |
| 601 | D3 | — | 36 | 2 | no | — |
| 602 | C22 | — | 9 | 1 | no | — |
| 603 | C22 | — | 9 | 1 | no | — |
| 604 | C22 | — | 9 | 1 | no | — |
| 605 | C22 | — | 18 | 2 | no | — |
| 606 | C4 | — | 2 | 2 | no | — |
| 607 | C4 | — | 9 | 1 | no | — |
| 608 | C4 | — | 9 | 1 | no | — |
| 609 | C4 | — | 9 | 1 | no | — |
| 610 | C4 | — | 18 | 2 | no | — |
| 611 | C4 | — | 18 | 2 | no | — |
| 612 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 613 | C3 | — | 3 | 1 | no | — |
| 614 | C3 | — | 3 | 1 | no | — |
| 615 | C3 | — | 6 | 1 | no | — |
| 616 | C3 | #10594768 | 1 | 1 | yes | characteristic |
| 617 | C2 | — | 18 | 1 | no | — |
| 618 | C2 | — | 18 | 1 | no | — |
| 619 | C2 | — | 18 | 1 | no | — |
| 620 | C2 | — | 36 | 2 | no | — |
| 621 | C2 | D4×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722516 | C2 | semidirect |
| 2. Q16×#272 | C2 | semidirect |
| 3. #64128⋊C3 | C2 | semidirect |
| 4. Q16×(C3⋊D3)⋊C3 | C2 | semidirect |
| 5. #11721238 | C2 | semidirect |
| 6. #11721237 | C2 | semidirect |
| 7. #11721231 | C2 | semidirect |
| 8. #11720855 | C2 | semidirect |
| 9. #11720851 | C2 | semidirect |
| 10. #11720844 | C2 | semidirect |
| 11. #11720840 | C2 | semidirect |
| 43. #64128 | D3 | semidirect |
| 44. Q16×C3⋊D3 | D3 | semidirect |
| 389. H(3,𝔽3) | #578 | semidirect |
| 556. C32 | #5766 | semidirect |
| 557. C32 | #5771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722516 | 2 |
| Q16×#272 | 2 |
| #64128⋊C3 | 2 |
| Q16×(C3⋊D3)⋊C3 | 2 |
| #11721238 | 2 |
| #11721237 | 2 |
| #11721231 | 2 |
| #11720855 | 2 |
| #11720851 | 2 |
| #11720844 | 2 |
| #11720840 | 2 |
| #10594768 | 3 |
| #10594765 | 3 |