Finite Group DatabasebetaFinite Group DatabasebetaOrder 5832.
908 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #72228414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10620045⋊C3 | — | 3 | 1 | no | maximal |
| 3 | #14518094 | — | 3 | 1 | no | maximal |
| 4 | C3×#10619762 | — | 3 | 1 | no | maximal |
| 5 | #14518090 | — | 3 | 1 | no | maximal |
| 6 | #10619751⋊C3 | — | 3 | 1 | no | maximal |
| 7 | (#66366⋊C2)⋊C3 | — | 3 | 1 | no | maximal |
| 8 | (#66366⋊C2)⋊C3 | — | 3 | 1 | no | maximal |
| 9 | (#66365⋊C2)⋊C3 | — | 3 | 1 | no | maximal |
| 10 | (#66365⋊C2)⋊C3 | — | 3 | 1 | no | maximal |
| 11 | #10619757⋊C3 | — | 3 | 1 | no | maximal |
| 12 | #10619762⋊C3 | — | 3 | 1 | no | maximal |
| 13 | #10619755⋊C3 | — | 3 | 1 | no | maximal |
| 14 | C3×#10619679 | — | 3 | 1 | no | maximal |
| 15 | #13091120 | — | 4 | 1 | no | maximal |
| 16 | #11758104 | D3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C22×C3×AΣL(1,𝔽27) | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C2×C3×#4183 | — | 3 | 1 | no | — |
| 19 | #11757866 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#66368 | D3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #11757864 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11757851 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #11757851 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #11757850 | D3 | 1 | 1 | yes | characteristic, complemented |
| 25 | #11757850 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | #11757849 | D3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #11757841 | D3 | 1 | 1 | yes | characteristic, complemented |
| 28 | #11757837 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | #11757836 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×#66330 | — | 3 | 1 | no | — |
| 31 | #10624749 | — | 4 | 1 | no | Sylow |
| 32 | C32×#638 | — | 9 | 1 | no | — |
| 33 | C3⋊#6258 | — | 3 | 1 | no | — |
| 34 | A4⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 35 | #66440⋊C2 | — | 3 | 1 | no | — |
| 36 | #66440⋊C2 | — | 3 | 1 | no | — |
| 37 | #10620045 | — | 3 | 1 | no | — |
| 38 | C3×(C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 39 | C3×(C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 40 | C3×(C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 41 | C3×(C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 42 | C3×((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 43 | C3×((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 44 | C3×((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 45 | C3×((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 46 | C3×((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 47 | C3×#611⋊C3 | — | 9 | 1 | no | — |
| 48 | C3×#611⋊C3 | — | 9 | 1 | no | — |
| 49 | C3×#638⋊C3 | — | 9 | 1 | no | — |
| 50 | #10619762 | — | 3 | 1 | no | — |
| 51 | #10619762 | — | 3 | 1 | no | — |
| 52 | #10619761 | — | 3 | 1 | no | — |
| 53 | #66365⋊C2 | — | 3 | 1 | no | — |
| 54 | #66365⋊C2 | — | 3 | 1 | no | — |
| 55 | #66366⋊C2 | — | 3 | 1 | no | — |
| 56 | #66366⋊C2 | — | 3 | 1 | no | — |
| 57 | #10619757 | — | 3 | 1 | no | — |
| 58 | #10619755 | — | 3 | 1 | no | — |
| 59 | #10619751 | — | 3 | 1 | no | — |
| 60 | #10619679 | — | 3 | 1 | no | — |
| 61 | #4207⋊C3 | — | 12 | 1 | no | — |
| 62 | C2×C3×AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 63 | #92333 | — | 12 | 1 | no | — |
| 64 | #4184⋊C3 | — | 12 | 1 | no | — |
| 65 | #4184⋊C3 | — | 12 | 1 | no | — |
| 66 | #4184⋊C3 | — | 12 | 1 | no | — |
| 67 | #4183⋊C3 | — | 12 | 1 | no | — |
| 68 | #4183⋊C3 | — | 12 | 1 | no | — |
| 69 | #4183⋊C3 | — | 12 | 1 | no | — |
| 70 | #4183⋊C3 | — | 12 | 1 | no | — |
| 71 | C3×#4183 | — | 6 | 1 | no | — |
| 72 | C3×#4183 | — | 12 | 1 | no | — |
| 73 | #92302 | — | 12 | 1 | no | — |
| 74 | #92300 | — | 12 | 1 | no | — |
| 75 | C22×C34 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 76 | C2×C32×C3⋊D3 | — | 9 | 1 | no | — |
| 77 | C32×C3⋊Dic3 | — | 9 | 1 | no | — |
| 78 | C22×C3×3−1+2 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 79 | C22×C3×3−1+2 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 80 | C22×C3×H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 81 | C2×C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 82 | C2×C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 83 | C2×C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 84 | C3×C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 85 | C3×C22⋊H(3,𝔽3) | — | 6 | 1 | no | — |
| 86 | C3×C22⋊H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 87 | C3×C22⋊H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 88 | C3×C22⋊H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 89 | C3×C22⋊H(3,𝔽3) | C3⋊D3 | 1 | 1 | yes | characteristic |
| 90 | C3×#1094 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 91 | C3×#1094 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 92 | C3×#1094 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 93 | C3×#1094 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 94 | C3×#1094 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 95 | #66440 | — | 3 | 1 | no | — |
| 96 | #66440 | — | 3 | 1 | no | — |
| 97 | #66440 | — | 6 | 1 | no | — |
| 98 | #66440 | — | 6 | 1 | no | — |
| 99 | A4×3−1+2 | — | 3 | 1 | no | — |
| 100 | A4×3−1+2 | — | 6 | 1 | no | — |
| 101 | #66436 | — | 3 | 1 | no | — |
| 102 | #66436 | — | 6 | 1 | no | — |
| 103 | C3×3−1+2⋊C4 | — | 9 | 1 | no | — |
| 104 | C3×3−1+2⋊C4 | — | 9 | 1 | no | — |
| 105 | C3×(C3⋊Dic3)⋊C3 | — | 9 | 1 | no | — |
| 106 | C22×AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 107 | C22×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 108 | C2×#4183 | — | 3 | 1 | no | — |
| 109 | #66368 | — | 3 | 1 | no | — |
| 110 | #66368 | — | 3 | 1 | no | — |
| 111 | #66368 | — | 6 | 1 | no | — |
| 112 | #66368 | — | 6 | 1 | no | — |
| 113 | C32⋊(C22⋊C9) | — | 3 | 1 | no | — |
| 114 | C32⋊(C22⋊C9) | — | 6 | 1 | no | — |
| 115 | #66366 | — | 3 | 1 | no | — |
| 116 | #66366 | — | 3 | 1 | no | — |
| 117 | #66366 | — | 6 | 1 | no | — |
| 118 | #66366 | — | 6 | 1 | no | — |
| 119 | #66365 | — | 3 | 1 | no | — |
| 120 | #66365 | — | 3 | 1 | no | — |
| 121 | #66365 | — | 6 | 1 | no | — |
| 122 | #66365 | — | 6 | 1 | no | — |
| 123 | #66363 | — | 3 | 1 | no | — |
| 124 | #66363 | — | 6 | 1 | no | — |
| 125 | #66362 | — | 3 | 1 | no | — |
| 126 | #66362 | — | 6 | 1 | no | — |
| 127 | #66357 | — | 3 | 1 | no | — |
| 128 | #66357 | — | 6 | 1 | no | — |
| 129 | #66330 | — | 3 | 1 | no | — |
| 130 | 3−1+4 | — | 4 | 1 | no | — |
| 131 | #6911 | — | 4 | 1 | no | — |
| 132 | #6910 | — | 4 | 1 | no | — |
| 133 | #6910 | — | 4 | 1 | no | — |
| 134 | #6910 | — | 4 | 1 | no | — |
| 135 | #6909 | — | 4 | 1 | no | — |
| 136 | #6909 | — | 4 | 1 | no | — |
| 137 | #6909 | — | 4 | 1 | no | — |
| 138 | #6909 | — | 4 | 1 | no | — |
| 139 | C3×AΣL(1,𝔽27) | — | 4 | 1 | no | — |
| 140 | C3×AΣL(1,𝔽27) | S4 | 1 | 1 | yes | characteristic, complemented |
| 141 | #6891 | — | 4 | 1 | no | — |
| 142 | C32⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 143 | C3×C3⋊S4 | — | 9 | 1 | no | — |
| 144 | C3×C3⋊S4 | — | 9 | 1 | no | — |
| 145 | C3×C3⋊S4 | — | 9 | 1 | no | — |
| 146 | C3×C3⋊S4 | — | 9 | 1 | no | — |
| 147 | C3×#638 | — | 9 | 1 | no | — |
| 148 | C3×#638 | — | 9 | 1 | no | — |
| 149 | C3×#638 | — | 9 | 1 | no | — |
| 150 | C3×#638 | — | 9 | 1 | no | — |
| 151 | C3×#638 | — | 9 | 1 | no | — |
| 152 | C32×#67 | — | 27 | 3 | no | — |
| 153 | C32×#67 | — | 27 | 1 | no | — |
| 154 | #6258 | — | 27 | 3 | no | — |
| 155 | C9⋊S4 | — | 3 | 1 | no | — |
| 156 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 157 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 158 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 159 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 160 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 161 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 162 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 163 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 164 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 165 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 166 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 167 | (C3⋊S4)⋊C3 | — | 9 | 1 | no | — |
| 168 | C3×(C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 169 | C3×(C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 170 | C3×(C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 171 | C3×(C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 172 | C3×(C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 173 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 174 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 175 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 176 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 177 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 178 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 179 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 180 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 181 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 182 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 183 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 184 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 185 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 186 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 187 | ((C22⋊C9)⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 188 | #611⋊C3 | — | 9 | 1 | no | — |
| 189 | #611⋊C3 | — | 9 | 1 | no | — |
| 190 | #611⋊C3 | — | 9 | 1 | no | — |
| 191 | #611⋊C3 | — | 9 | 1 | no | — |
| 192 | #611⋊C3 | — | 9 | 1 | no | — |
| 193 | #611⋊C3 | — | 9 | 1 | no | — |
| 194 | #638⋊C3 | — | 9 | 1 | no | — |
| 195 | #638⋊C3 | — | 9 | 1 | no | — |
| 196 | #638⋊C3 | — | 9 | 1 | no | — |
| 197 | C3×#611 | — | 9 | 1 | no | — |
| 198 | C3×#611 | — | 9 | 1 | no | — |
| 199 | C2×C34 | — | 3 | 1 | no | — |
| 200 | C32×C3⋊D3 | — | 18 | 1 | no | — |
| 201 | C2×C3×3−1+2 | — | 3 | 1 | no | — |
| 202 | C2×C3×3−1+2 | — | 3 | 1 | no | — |
| 203 | C2×C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 204 | C3⋊#272 | — | 12 | 1 | no | — |
| 205 | #4207 | — | 12 | 1 | no | — |
| 206 | #4207 | — | 12 | 1 | no | — |
| 207 | #4207 | — | 12 | 1 | no | — |
| 208 | C3⋊AGL(1,ℤ/9) | — | 12 | 1 | no | — |
| 209 | C3×AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 210 | C3×AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 211 | C3×AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 212 | C3×AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 213 | C3×AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 214 | C3×AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 215 | C3×AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 216 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 217 | C3×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 218 | C3×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 219 | C3×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 220 | C3×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 221 | C2×AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 222 | C2×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 223 | C2×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 224 | C2×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 225 | C2×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 226 | #4185 | — | 12 | 1 | no | — |
| 227 | #4184 | — | 12 | 1 | no | — |
| 228 | #4184 | — | 12 | 1 | no | — |
| 229 | #4184 | — | 12 | 1 | no | — |
| 230 | #4183 | — | 6 | 1 | no | — |
| 231 | #4183 | — | 12 | 1 | no | — |
| 232 | #4183 | — | 12 | 1 | no | — |
| 233 | #4183 | — | 12 | 1 | no | — |
| 234 | #4183 | — | 12 | 1 | no | — |
| 235 | #4183 | — | 12 | 1 | no | — |
| 236 | #4181 | — | 12 | 1 | no | — |
| 237 | C22×C33 | — | 3 | 1 | no | — |
| 238 | C22×C33 | — | 3 | 1 | no | — |
| 239 | C22×C33 | — | 3 | 1 | no | — |
| 240 | C22×C33 | — | 3 | 1 | no | — |
| 241 | C22×C33 | — | 3 | 1 | no | — |
| 242 | C22×C33 | — | 9 | 3 | no | — |
| 243 | C22×C33 | C3⋊(C3⋊D3) | 1 | 1 | yes | characteristic |
| 244 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 245 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 246 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 247 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 248 | C2×C3×C3⋊D3 | — | 9 | 1 | no | — |
| 249 | C2×C32×D3 | — | 27 | 1 | no | — |
| 250 | C2×C32×D3 | — | 27 | 3 | no | — |
| 251 | C32×A4 | — | 2 | 1 | no | — |
| 252 | C32×A4 | — | 3 | 1 | no | — |
| 253 | C32×A4 | — | 3 | 1 | no | — |
| 254 | C32×A4 | — | 3 | 1 | no | — |
| 255 | C32×A4 | #272 | 1 | 1 | yes | characteristic |
| 256 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 257 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 258 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 259 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 260 | C3×C3⋊Dic3 | — | 9 | 1 | no | — |
| 261 | C32×Dic3 | — | 27 | 1 | no | — |
| 262 | C32×Dic3 | — | 27 | 3 | no | — |
| 263 | C22×3−1+2 | — | 2 | 1 | no | — |
| 264 | C22×3−1+2 | — | 3 | 1 | no | — |
| 265 | C22×3−1+2 | — | 3 | 1 | no | — |
| 266 | C22×3−1+2 | — | 3 | 1 | no | — |
| 267 | C22×3−1+2 | — | 3 | 1 | no | — |
| 268 | C22×3−1+2 | — | 3 | 1 | no | — |
| 269 | C22×3−1+2 | #272 | 1 | 1 | yes | characteristic, complemented |
| 270 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 271 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 272 | C22×H(3,𝔽3) | — | 3 | 1 | no | — |
| 273 | C22×C3×C9 | — | 3 | 1 | no | — |
| 274 | C22×C3×C9 | — | 3 | 1 | no | — |
| 275 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 276 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 277 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 278 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 279 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 280 | C2×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 281 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 282 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 283 | C2×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 284 | C2×C3×D9 | — | 9 | 1 | no | — |
| 285 | C2×C3×D9 | — | 9 | 1 | no | — |
| 286 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 287 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 288 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 289 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 290 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 291 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 292 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 293 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 294 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 295 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 296 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 297 | C22⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 298 | C22⋊H(3,𝔽3) | — | 9 | 3 | no | — |
| 299 | C22⋊H(3,𝔽3) | — | 18 | 3 | no | — |
| 300 | #1094 | — | 2 | 1 | no | — |
| 301 | #1094 | — | 3 | 1 | no | — |
| 302 | #1094 | — | 3 | 1 | no | — |
| 303 | #1094 | — | 3 | 1 | no | — |
| 304 | #1094 | — | 3 | 1 | no | — |
| 305 | #1094 | — | 3 | 1 | no | — |
| 306 | #1094 | — | 3 | 1 | no | — |
| 307 | #1094 | — | 3 | 1 | no | — |
| 308 | #1094 | — | 3 | 1 | no | — |
| 309 | #1094 | — | 3 | 1 | no | — |
| 310 | #1094 | — | 3 | 1 | no | — |
| 311 | #1094 | — | 3 | 1 | no | — |
| 312 | #1094 | — | 3 | 1 | no | — |
| 313 | #1094 | — | 3 | 1 | no | — |
| 314 | #1094 | — | 3 | 1 | no | — |
| 315 | #1094 | #272 | 1 | 1 | yes | characteristic, complemented |
| 316 | C3×C22⋊C9 | — | 2 | 1 | no | — |
| 317 | C3×C22⋊C9 | — | 3 | 1 | no | — |
| 318 | C3×C22⋊C9 | — | 3 | 1 | no | — |
| 319 | C3×C22⋊C9 | — | 3 | 1 | no | — |
| 320 | C3×C22⋊C9 | — | 3 | 1 | no | — |
| 321 | C3×C22⋊C9 | #272 | 1 | 1 | yes | characteristic, complemented |
| 322 | C9⋊A4 | — | 6 | 1 | no | — |
| 323 | C9⋊A4 | — | 6 | 1 | no | — |
| 324 | C9⋊A4 | — | 6 | 1 | no | — |
| 325 | C9⋊A4 | — | 6 | 1 | no | — |
| 326 | C9⋊A4 | — | 6 | 1 | no | — |
| 327 | C9⋊A4 | — | 6 | 1 | no | — |
| 328 | C9⋊A4 | — | 6 | 1 | no | — |
| 329 | C9⋊A4 | — | 6 | 2 | no | — |
| 330 | C9×A4 | — | 3 | 1 | no | — |
| 331 | C9×A4 | — | 6 | 1 | no | — |
| 332 | C9×A4 | — | 6 | 1 | no | — |
| 333 | C9×A4 | — | 6 | 1 | no | — |
| 334 | C9×A4 | — | 6 | 1 | no | — |
| 335 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 336 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 337 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 338 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 339 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 340 | 3−1+2⋊C4 | — | 9 | 1 | no | — |
| 341 | (C3⋊Dic3)⋊C3 | — | 9 | 1 | no | — |
| 342 | (C3⋊Dic3)⋊C3 | — | 9 | 1 | no | — |
| 343 | (C3⋊Dic3)⋊C3 | — | 9 | 1 | no | — |
| 344 | C3×Dic9 | — | 9 | 1 | no | — |
| 345 | C3×Dic9 | — | 9 | 1 | no | — |
| 346 | C34 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 347 | #737 | — | 12 | 1 | no | — |
| 348 | #737 | — | 12 | 1 | no | — |
| 349 | #737 | — | 12 | 1 | no | — |
| 350 | #737 | — | 24 | 1 | no | — |
| 351 | #737 | — | 24 | 1 | no | — |
| 352 | #737 | — | 24 | 1 | no | — |
| 353 | C3×3−1+2 | — | 4 | 1 | no | — |
| 354 | C3×3−1+2 | — | 4 | 1 | no | — |
| 355 | C3×3−1+2 | — | 4 | 1 | no | — |
| 356 | C3×3−1+2 | — | 4 | 1 | no | — |
| 357 | C3×3−1+2 | — | 4 | 1 | no | — |
| 358 | C3×3−1+2 | — | 12 | 1 | no | — |
| 359 | C3×3−1+2 | — | 24 | 1 | no | — |
| 360 | C3×3−1+2 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 361 | C3×3−1+2 | C3⋊S4 | 1 | 1 | yes | characteristic |
| 362 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 363 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 364 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 365 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 366 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 367 | C3×H(3,𝔽3) | — | 24 | 1 | no | — |
| 368 | C3×H(3,𝔽3) | C3⋊S4 | 1 | 1 | yes | characteristic |
| 369 | #732 | — | 12 | 1 | no | — |
| 370 | #732 | — | 24 | 1 | no | — |
| 371 | #731 | — | 12 | 1 | no | — |
| 372 | #731 | — | 12 | 1 | no | — |
| 373 | #731 | — | 12 | 1 | no | — |
| 374 | #731 | — | 24 | 1 | no | — |
| 375 | #731 | — | 24 | 1 | no | — |
| 376 | #731 | — | 24 | 1 | no | — |
| 377 | AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 378 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 379 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 380 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 381 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 382 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 383 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 384 | AΣL(1,𝔽27) | — | 24 | 1 | no | — |
| 385 | AΣL(1,𝔽27) | — | 24 | 1 | no | — |
| 386 | AΣL(1,𝔽27) | — | 24 | 1 | no | — |
| 387 | AΣL(1,𝔽27) | — | 24 | 1 | no | — |
| 388 | AΣL(1,𝔽27) | — | 24 | 1 | no | — |
| 389 | C32⋊C9 | — | 12 | 1 | no | — |
| 390 | C32⋊C9 | — | 24 | 1 | no | — |
| 391 | C3⋊S4 | — | 9 | 1 | no | — |
| 392 | C3⋊S4 | — | 9 | 1 | no | — |
| 393 | C3⋊S4 | — | 9 | 1 | no | — |
| 394 | C3⋊S4 | — | 9 | 1 | no | — |
| 395 | C3×S4 | — | 81 | 1 | no | — |
| 396 | C3×S4 | — | 81 | 1 | no | — |
| 397 | C3×S4 | — | 81 | 1 | no | — |
| 398 | C3×S4 | — | 81 | 1 | no | — |
| 399 | C32×D4 | — | 81 | 1 | no | — |
| 400 | #638 | — | 9 | 1 | no | — |
| 401 | #638 | — | 9 | 1 | no | — |
| 402 | C3×#67 | — | 27 | 3 | no | — |
| 403 | C3×#67 | — | 27 | 3 | no | — |
| 404 | C3×#67 | — | 27 | 3 | no | — |
| 405 | C3×#67 | — | 27 | 3 | no | — |
| 406 | C3×#67 | — | 27 | 1 | no | — |
| 407 | C3×#67 | — | 27 | 1 | no | — |
| 408 | C3×#67 | — | 27 | 1 | no | — |
| 409 | C3×#67 | — | 27 | 1 | no | — |
| 410 | C3×#67 | — | 81 | 1 | no | — |
| 411 | (C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 412 | (C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 413 | (C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 414 | (C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 415 | (C22⋊C9)⋊C2 | — | 9 | 1 | no | — |
| 416 | #611 | — | 9 | 1 | no | — |
| 417 | #611 | — | 9 | 1 | no | — |
| 418 | C2×C33 | — | 3 | 1 | no | — |
| 419 | C2×C33 | — | 3 | 1 | no | — |
| 420 | C2×C33 | — | 6 | 1 | no | — |
| 421 | C2×C33 | — | 9 | 1 | no | — |
| 422 | C2×C33 | — | 9 | 1 | no | — |
| 423 | C2×C33 | — | 9 | 1 | no | — |
| 424 | C2×C33 | — | 9 | 1 | no | — |
| 425 | C2×C33 | — | 9 | 3 | no | — |
| 426 | C2×C33 | — | 18 | 3 | no | — |
| 427 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 428 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 429 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 430 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 431 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 432 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 433 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 434 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 435 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 436 | C32×D3 | — | 54 | 3 | no | — |
| 437 | C32×D3 | — | 54 | 1 | no | — |
| 438 | C2×3−1+2 | — | 3 | 1 | no | — |
| 439 | C2×3−1+2 | — | 3 | 1 | no | — |
| 440 | C2×3−1+2 | — | 6 | 1 | no | — |
| 441 | C2×3−1+2 | — | 6 | 1 | no | — |
| 442 | C2×3−1+2 | — | 9 | 1 | no | — |
| 443 | C2×3−1+2 | — | 9 | 1 | no | — |
| 444 | C2×3−1+2 | — | 9 | 1 | no | — |
| 445 | C2×3−1+2 | — | 9 | 1 | no | — |
| 446 | C2×H(3,𝔽3) | — | 3 | 1 | no | — |
| 447 | C2×H(3,𝔽3) | — | 6 | 1 | no | — |
| 448 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 449 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 450 | C2×C3×C9 | — | 9 | 1 | no | — |
| 451 | C2×C3×C9 | — | 9 | 1 | no | — |
| 452 | #272 | — | 108 | 3 | no | — |
| 453 | C3⋊D9 | — | 12 | 1 | no | — |
| 454 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 455 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 456 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 457 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 458 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 459 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 460 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 461 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 462 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 463 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 464 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 465 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 466 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 467 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 468 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 469 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 470 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 471 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 472 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 473 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 474 | AGL(1,ℤ/9) | — | 36 | 1 | no | — |
| 475 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 476 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 477 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 478 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 479 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 480 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 481 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 482 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 483 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 484 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 485 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 486 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 487 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 488 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 489 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 490 | C3×D9 | — | 18 | 1 | no | — |
| 491 | C3×D9 | — | 18 | 1 | no | — |
| 492 | C3×D9 | — | 36 | 1 | no | — |
| 493 | C3×D9 | — | 36 | 1 | no | — |
| 494 | C3×D9 | — | 36 | 1 | no | — |
| 495 | C3×D9 | — | 36 | 1 | no | — |
| 496 | C3×D9 | — | 36 | 1 | no | — |
| 497 | C22×C32 | — | 3 | 3 | no | — |
| 498 | C22×C32 | — | 3 | 3 | no | — |
| 499 | C22×C32 | — | 9 | 1 | no | — |
| 500 | C22×C32 | — | 9 | 3 | no | — |
| 501 | C22×C32 | — | 9 | 3 | no | — |
| 502 | C22×C32 | — | 9 | 1 | no | — |
| 503 | C22×C32 | — | 9 | 1 | no | — |
| 504 | C22×C32 | — | 18 | 1 | no | — |
| 505 | C22×C32 | — | 18 | 1 | no | — |
| 506 | C22×C32 | — | 27 | 1 | no | — |
| 507 | C22×C32 | — | 81 | 1 | no | — |
| 508 | C22×C32 | C3⋊#272 | 1 | 1 | yes | characteristic |
| 509 | C22×C32 | C3⋊#272 | 1 | 1 | yes | characteristic |
| 510 | C22×C32 | C3⋊#272 | 1 | 1 | yes | characteristic |
| 511 | C22×C32 | C3⋊#272 | 1 | 1 | yes | characteristic |
| 512 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 513 | C2×C3⋊D3 | — | 9 | 1 | no | — |
| 514 | C2×C3×D3 | — | 27 | 1 | no | — |
| 515 | C2×C3×D3 | — | 27 | 1 | no | — |
| 516 | C2×C3×D3 | — | 27 | 1 | no | — |
| 517 | C2×C3×D3 | — | 27 | 1 | no | — |
| 518 | C2×C3×D3 | — | 27 | 3 | no | — |
| 519 | C2×C3×D3 | — | 27 | 3 | no | — |
| 520 | C2×C3×D3 | — | 27 | 3 | no | — |
| 521 | C2×C3×D3 | — | 27 | 3 | no | — |
| 522 | C2×C3×D3 | — | 81 | 1 | no | — |
| 523 | C3×A4 | — | 3 | 1 | no | — |
| 524 | C3×A4 | — | 6 | 1 | no | — |
| 525 | C3×A4 | — | 9 | 1 | no | — |
| 526 | C3×A4 | — | 9 | 1 | no | — |
| 527 | C3×A4 | — | 9 | 1 | no | — |
| 528 | C3×A4 | — | 9 | 1 | no | — |
| 529 | C3×A4 | — | 9 | 1 | no | — |
| 530 | C3×A4 | — | 9 | 1 | no | — |
| 531 | C3×A4 | — | 18 | 1 | no | — |
| 532 | C3×A4 | — | 18 | 1 | no | — |
| 533 | C3×A4 | — | 18 | 1 | no | — |
| 534 | C3×A4 | — | 27 | 1 | no | — |
| 535 | C32×C4 | — | 81 | 1 | no | — |
| 536 | C3⋊Dic3 | — | 9 | 1 | no | — |
| 537 | C3⋊Dic3 | — | 9 | 1 | no | — |
| 538 | C3×Dic3 | — | 27 | 1 | no | — |
| 539 | C3×Dic3 | — | 27 | 1 | no | — |
| 540 | C3×Dic3 | — | 27 | 1 | no | — |
| 541 | C3×Dic3 | — | 27 | 1 | no | — |
| 542 | C3×Dic3 | — | 27 | 3 | no | — |
| 543 | C3×Dic3 | — | 27 | 3 | no | — |
| 544 | C3×Dic3 | — | 27 | 3 | no | — |
| 545 | C3×Dic3 | — | 27 | 3 | no | — |
| 546 | C3×Dic3 | — | 81 | 1 | no | — |
| 547 | C22×C9 | — | 3 | 1 | no | — |
| 548 | C22×C9 | — | 6 | 1 | no | — |
| 549 | C22×C9 | — | 9 | 1 | no | — |
| 550 | C2×D9 | — | 9 | 1 | no | — |
| 551 | C2×D9 | — | 9 | 1 | no | — |
| 552 | C22⋊C9 | — | 3 | 1 | no | — |
| 553 | C22⋊C9 | — | 3 | 1 | no | — |
| 554 | C22⋊C9 | — | 6 | 1 | no | — |
| 555 | C22⋊C9 | — | 6 | 1 | no | — |
| 556 | C22⋊C9 | — | 9 | 1 | no | — |
| 557 | C22⋊C9 | — | 9 | 1 | no | — |
| 558 | C22⋊C9 | — | 9 | 1 | no | — |
| 559 | Dic9 | — | 9 | 1 | no | — |
| 560 | Dic9 | — | 9 | 1 | no | — |
| 561 | C33 | — | 3 | 1 | no | — |
| 562 | C33 | — | 3 | 1 | no | — |
| 563 | C33 | — | 3 | 1 | no | — |
| 564 | C33 | — | 3 | 1 | no | — |
| 565 | C33 | — | 3 | 1 | no | — |
| 566 | C33 | — | 4 | 1 | no | — |
| 567 | C33 | — | 8 | 1 | no | — |
| 568 | C33 | — | 9 | 3 | no | — |
| 569 | C33 | — | 12 | 1 | no | — |
| 570 | C33 | — | 12 | 1 | no | — |
| 571 | C33 | — | 12 | 1 | no | — |
| 572 | C33 | C3⋊(C3⋊S4) | 1 | 1 | yes | characteristic |
| 573 | 3−1+2 | — | 2 | 1 | no | — |
| 574 | 3−1+2 | — | 3 | 1 | no | — |
| 575 | 3−1+2 | — | 3 | 1 | no | — |
| 576 | 3−1+2 | — | 3 | 1 | no | — |
| 577 | 3−1+2 | — | 3 | 1 | no | — |
| 578 | 3−1+2 | — | 3 | 1 | no | — |
| 579 | 3−1+2 | — | 4 | 1 | no | — |
| 580 | 3−1+2 | — | 8 | 1 | no | — |
| 581 | 3−1+2 | — | 12 | 1 | no | — |
| 582 | 3−1+2 | — | 12 | 1 | no | — |
| 583 | 3−1+2 | — | 12 | 1 | no | — |
| 584 | 3−1+2 | — | 12 | 1 | no | — |
| 585 | 3−1+2 | — | 12 | 1 | no | — |
| 586 | 3−1+2 | — | 12 | 1 | no | — |
| 587 | 3−1+2 | — | 12 | 1 | no | — |
| 588 | 3−1+2 | — | 12 | 1 | no | — |
| 589 | 3−1+2 | — | 12 | 1 | no | — |
| 590 | 3−1+2 | — | 12 | 1 | no | — |
| 591 | 3−1+2 | — | 12 | 1 | no | — |
| 592 | 3−1+2 | — | 12 | 1 | no | — |
| 593 | 3−1+2 | — | 12 | 1 | no | — |
| 594 | 3−1+2 | — | 12 | 1 | no | — |
| 595 | 3−1+2 | — | 24 | 1 | no | — |
| 596 | 3−1+2 | — | 24 | 1 | no | — |
| 597 | 3−1+2 | — | 24 | 1 | no | — |
| 598 | 3−1+2 | — | 24 | 1 | no | — |
| 599 | 3−1+2 | — | 24 | 1 | no | — |
| 600 | 3−1+2 | — | 24 | 1 | no | — |
| 601 | 3−1+2 | — | 24 | 1 | no | — |
| 602 | 3−1+2 | — | 24 | 2 | no | — |
| 603 | 3−1+2 | #6258 | 1 | 1 | yes | characteristic, complemented |
| 604 | H(3,𝔽3) | — | 3 | 1 | no | — |
| 605 | H(3,𝔽3) | — | 3 | 1 | no | — |
| 606 | H(3,𝔽3) | — | 3 | 1 | no | — |
| 607 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 608 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 609 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 610 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 611 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 612 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 613 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 614 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 615 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 616 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 617 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 618 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 619 | H(3,𝔽3) | — | 36 | 3 | no | — |
| 620 | H(3,𝔽3) | — | 72 | 3 | no | — |
| 621 | C3×C9 | — | 3 | 1 | no | — |
| 622 | C3×C9 | — | 3 | 1 | no | — |
| 623 | C3×C9 | — | 4 | 1 | no | — |
| 624 | C3×C9 | — | 8 | 1 | no | — |
| 625 | C3×C9 | — | 12 | 1 | no | — |
| 626 | C3×C9 | — | 12 | 1 | no | — |
| 627 | C3×C9 | — | 12 | 1 | no | — |
| 628 | C3×C9 | — | 12 | 1 | no | — |
| 629 | C3×C9 | — | 12 | 1 | no | — |
| 630 | C3×C9 | — | 24 | 1 | no | — |
| 631 | C3×C9 | — | 24 | 1 | no | — |
| 632 | C3×C9 | — | 24 | 1 | no | — |
| 633 | C3×C9 | — | 24 | 1 | no | — |
| 634 | S4 | — | 81 | 1 | no | — |
| 635 | S4 | — | 81 | 1 | no | — |
| 636 | S4 | — | 81 | 1 | no | — |
| 637 | S4 | — | 81 | 1 | no | — |
| 638 | C3×D4 | — | 81 | 1 | no | — |
| 639 | C3×D4 | — | 81 | 1 | no | — |
| 640 | C3×D4 | — | 81 | 1 | no | — |
| 641 | C3×D4 | — | 81 | 1 | no | — |
| 642 | #67 | — | 27 | 3 | no | — |
| 643 | #67 | — | 27 | 1 | no | — |
| 644 | #67 | — | 81 | 1 | no | — |
| 645 | C2×C32 | — | 3 | 1 | no | — |
| 646 | C2×C32 | — | 3 | 1 | no | — |
| 647 | C2×C32 | — | 3 | 1 | no | — |
| 648 | C2×C32 | — | 3 | 1 | no | — |
| 649 | C2×C32 | — | 9 | 1 | no | — |
| 650 | C2×C32 | — | 9 | 1 | no | — |
| 651 | C2×C32 | — | 9 | 3 | no | — |
| 652 | C2×C32 | — | 9 | 1 | no | — |
| 653 | C2×C32 | — | 9 | 3 | no | — |
| 654 | C2×C32 | — | 9 | 3 | no | — |
| 655 | C2×C32 | — | 9 | 3 | no | — |
| 656 | C2×C32 | — | 18 | 1 | no | — |
| 657 | C2×C32 | — | 18 | 1 | no | — |
| 658 | C2×C32 | — | 18 | 1 | no | — |
| 659 | C2×C32 | — | 18 | 3 | no | — |
| 660 | C2×C32 | — | 18 | 3 | no | — |
| 661 | C2×C32 | — | 18 | 3 | no | — |
| 662 | C2×C32 | — | 18 | 3 | no | — |
| 663 | C2×C32 | — | 27 | 1 | no | — |
| 664 | C2×C32 | — | 54 | 1 | no | — |
| 665 | C2×C32 | — | 162 | 1 | no | — |
| 666 | C3⋊D3 | — | 18 | 1 | no | — |
| 667 | C3⋊D3 | — | 18 | 1 | no | — |
| 668 | C3⋊D3 | — | 36 | 1 | no | — |
| 669 | C3⋊D3 | — | 36 | 1 | no | — |
| 670 | C3⋊D3 | — | 36 | 1 | no | — |
| 671 | C3⋊D3 | — | 36 | 1 | no | — |
| 672 | C3×D3 | — | 54 | 3 | no | — |
| 673 | C3×D3 | — | 54 | 3 | no | — |
| 674 | C3×D3 | — | 54 | 3 | no | — |
| 675 | C3×D3 | — | 54 | 3 | no | — |
| 676 | C3×D3 | — | 54 | 1 | no | — |
| 677 | C3×D3 | — | 54 | 1 | no | — |
| 678 | C3×D3 | — | 54 | 1 | no | — |
| 679 | C3×D3 | — | 54 | 1 | no | — |
| 680 | C3×D3 | — | 324 | 1 | no | — |
| 681 | C3×D3 | — | 324 | 1 | no | — |
| 682 | C3×D3 | — | 324 | 1 | no | — |
| 683 | C3×D3 | — | 324 | 1 | no | — |
| 684 | C3×D3 | — | 162 | 1 | no | — |
| 685 | C2×C9 | — | 9 | 1 | no | — |
| 686 | C2×C9 | — | 9 | 1 | no | — |
| 687 | C2×C9 | — | 18 | 1 | no | — |
| 688 | C2×C9 | — | 18 | 1 | no | — |
| 689 | D9 | — | 18 | 1 | no | — |
| 690 | D9 | — | 18 | 1 | no | — |
| 691 | D9 | — | 36 | 1 | no | — |
| 692 | D9 | — | 36 | 1 | no | — |
| 693 | D9 | — | 36 | 1 | no | — |
| 694 | D9 | — | 36 | 1 | no | — |
| 695 | D9 | — | 36 | 1 | no | — |
| 696 | C22×C3 | — | 3 | 1 | no | — |
| 697 | C22×C3 | — | 3 | 1 | no | — |
| 698 | C22×C3 | — | 3 | 1 | no | — |
| 699 | C22×C3 | — | 3 | 1 | no | — |
| 700 | C22×C3 | — | 9 | 3 | no | — |
| 701 | C22×C3 | — | 27 | 1 | no | — |
| 702 | C22×C3 | — | 81 | 1 | no | — |
| 703 | C22×C3 | — | 81 | 1 | no | — |
| 704 | C22×C3 | — | 81 | 1 | no | — |
| 705 | C22×C3 | — | 81 | 1 | no | — |
| 706 | C22×C3 | #92338 | 1 | 1 | yes | characteristic |
| 707 | C2×D3 | — | 27 | 1 | no | — |
| 708 | C2×D3 | — | 27 | 3 | no | — |
| 709 | C2×D3 | — | 81 | 1 | no | — |
| 710 | A4 | — | 9 | 1 | no | — |
| 711 | A4 | — | 18 | 1 | no | — |
| 712 | A4 | — | 27 | 1 | no | — |
| 713 | A4 | — | 27 | 1 | no | — |
| 714 | A4 | — | 27 | 1 | no | — |
| 715 | C3×C4 | — | 81 | 1 | no | — |
| 716 | C3×C4 | — | 81 | 1 | no | — |
| 717 | C3×C4 | — | 81 | 1 | no | — |
| 718 | C3×C4 | — | 81 | 1 | no | — |
| 719 | Dic3 | — | 27 | 1 | no | — |
| 720 | Dic3 | — | 27 | 3 | no | — |
| 721 | Dic3 | — | 81 | 1 | no | — |
| 722 | C32 | — | 3 | 3 | no | — |
| 723 | C32 | — | 3 | 3 | no | — |
| 724 | C32 | — | 9 | 1 | no | — |
| 725 | C32 | — | 9 | 3 | no | — |
| 726 | C32 | — | 9 | 3 | no | — |
| 727 | C32 | — | 9 | 1 | no | — |
| 728 | C32 | — | 9 | 1 | no | — |
| 729 | C32 | — | 12 | 1 | no | — |
| 730 | C32 | — | 18 | 1 | no | — |
| 731 | C32 | — | 18 | 1 | no | — |
| 732 | C32 | — | 24 | 1 | no | — |
| 733 | C32 | — | 27 | 1 | no | — |
| 734 | C32 | — | 36 | 1 | no | — |
| 735 | C32 | — | 36 | 1 | no | — |
| 736 | C32 | — | 36 | 1 | no | — |
| 737 | C32 | — | 36 | 1 | no | — |
| 738 | C32 | — | 36 | 1 | no | — |
| 739 | C32 | — | 36 | 1 | no | — |
| 740 | C32 | — | 72 | 1 | no | — |
| 741 | C32 | — | 72 | 1 | no | — |
| 742 | C32 | — | 72 | 1 | no | — |
| 743 | C32 | — | 108 | 1 | no | — |
| 744 | C32 | A4⋊#272 | 1 | 1 | yes | characteristic |
| 745 | C32 | A4⋊#272 | 1 | 1 | yes | characteristic |
| 746 | C32 | A4⋊#272 | 1 | 1 | yes | characteristic |
| 747 | C32 | C3⋊#6258 | 1 | 1 | yes | characteristic |
| 748 | C9 | — | 3 | 1 | no | — |
| 749 | C9 | — | 6 | 1 | no | — |
| 750 | C9 | — | 9 | 1 | no | — |
| 751 | C9 | — | 12 | 1 | no | — |
| 752 | C9 | — | 12 | 1 | no | — |
| 753 | C9 | — | 24 | 1 | no | — |
| 754 | C9 | — | 24 | 1 | no | — |
| 755 | C9 | — | 36 | 1 | no | — |
| 756 | C9 | — | 36 | 1 | no | — |
| 757 | C9 | — | 36 | 1 | no | — |
| 758 | D4 | — | 81 | 1 | no | Sylow |
| 759 | C2×C3 | — | 3 | 1 | no | — |
| 760 | C2×C3 | — | 3 | 1 | no | — |
| 761 | C2×C3 | — | 6 | 1 | no | — |
| 762 | C2×C3 | — | 9 | 1 | no | — |
| 763 | C2×C3 | — | 9 | 1 | no | — |
| 764 | C2×C3 | — | 9 | 1 | no | — |
| 765 | C2×C3 | — | 9 | 3 | no | — |
| 766 | C2×C3 | — | 18 | 3 | no | — |
| 767 | C2×C3 | — | 27 | 1 | no | — |
| 768 | C2×C3 | — | 54 | 1 | no | — |
| 769 | C2×C3 | — | 162 | 1 | no | — |
| 770 | C2×C3 | — | 162 | 1 | no | — |
| 771 | C2×C3 | — | 162 | 1 | no | — |
| 772 | C2×C3 | — | 162 | 1 | no | — |
| 773 | D3 | — | 54 | 3 | no | — |
| 774 | D3 | — | 54 | 1 | no | — |
| 775 | D3 | — | 324 | 1 | no | — |
| 776 | D3 | — | 324 | 1 | no | — |
| 777 | D3 | — | 324 | 1 | no | — |
| 778 | D3 | — | 324 | 1 | no | — |
| 779 | D3 | — | 162 | 1 | no | — |
| 780 | C22 | — | 81 | 1 | no | — |
| 781 | C22 | #13091120 | 1 | 1 | yes | characteristic, complemented |
| 782 | C4 | — | 81 | 1 | no | — |
| 783 | C3 | — | 3 | 1 | no | — |
| 784 | C3 | — | 3 | 1 | no | — |
| 785 | C3 | — | 3 | 1 | no | — |
| 786 | C3 | — | 3 | 1 | no | — |
| 787 | C3 | — | 9 | 3 | no | — |
| 788 | C3 | — | 27 | 1 | no | — |
| 789 | C3 | — | 36 | 1 | no | — |
| 790 | C3 | — | 72 | 1 | no | — |
| 791 | C3 | — | 108 | 1 | no | — |
| 792 | C3 | — | 108 | 1 | no | — |
| 793 | C3 | — | 108 | 1 | no | — |
| 794 | C3 | #14518118 | 1 | 1 | yes | characteristic |
| 795 | C2 | — | 3 | 1 | no | — |
| 796 | C2 | — | 162 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #72228414 | C2 |
| Frattini | C33 | C3⋊(C3⋊S4) |
| Fitting | C22×C3×AΣL(1,𝔽27) | D3 |
| socle | C22×C3 | #92338 |
| LCS | G ▷ #72228414 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72228414 | C2 | semidirect |
| 16. #11758104 | D3 | semidirect |
| 17. C22×C3×AΣL(1,𝔽27) | D3 | semidirect |
| 19. #11757866 | D3 | semidirect |
| 20. C3×#66368 | D3 | semidirect |
| 21. #11757864 | D3 | semidirect |
| 22. #11757851 | D3 | semidirect |
| 23. #11757851 | D3 | semidirect |
| 24. #11757850 | D3 | semidirect |
| 25. #11757850 | D3 | semidirect |
| 26. #11757849 | D3 | semidirect |
| 27. #11757841 | D3 | semidirect |
| 28. #11757837 | D3 | semidirect |
| 29. #11757836 | D3 | semidirect |
| 140. C3×AΣL(1,𝔽27) | S4 | semidirect |
| 269. C22×3−1+2 | #272 | semidirect |
| 315. #1094 | #272 | semidirect |
| 321. C3×C22⋊C9 | #272 | semidirect |
| 603. 3−1+2 | #6258 | semidirect |
| 781. C22 | #13091120 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72228414 | 2 |
| #10620045⋊C3 | 3 |
| #14518094 | 3 |
| C3×#10619762 | 3 |
| #14518090 | 3 |
| #10619751⋊C3 | 3 |
| (#66366⋊C2)⋊C3 | 3 |
| (#66365⋊C2)⋊C3 | 3 |
| #10619757⋊C3 | 3 |
| #10619762⋊C3 | 3 |
| #10619755⋊C3 | 3 |
| C3×#10619679 | 3 |
| #13091120 | 4 |