Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
1458 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 1458 conjugacy classes of subgroups — too many to draw. Only its 75 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 | D3×#4175⋊C3 | — | 3 | 1 | no | maximal |
| 2 | #72243906 | C3 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#66432⋊C3 | — | 3 | 1 | no | maximal |
| 4 | #72243679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72243630 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72221974 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72221895 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #14554344 | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3×#92391 | — | 3 | 1 | no | — |
| 10 | C3×#92391 | — | 3 | 1 | no | — |
| 11 | C3×#92392 | D3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#92283 | — | 2 | 1 | no | — |
| 13 | C3×#4177⋊C3 | — | 6 | 1 | no | — |
| 14 | C3⋊(#4183⋊C3) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C3×#92281 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3⋊(#4175⋊C3) | — | 2 | 1 | no | — |
| 17 | C3⋊(#4175⋊C3) | D3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C3⋊(#4175⋊C3) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#4175⋊C3 | — | 3 | 1 | no | — |
| 20 | D3×#6909 | — | 3 | 1 | no | — |
| 21 | #13091158 | — | 2 | 3 | no | — |
| 22 | #13091158 | C2×C3 | 1 | 3 | yes | complemented |
| 23 | #13091156 | C2×C3 | 1 | 3 | yes | complemented |
| 24 | #13091154 | — | 2 | 3 | no | — |
| 25 | #13091154 | C2×C3 | 1 | 3 | yes | complemented |
| 26 | #66432⋊C3 | — | 3 | 3 | no | — |
| 27 | C3×#66432 | — | 3 | 1 | no | — |
| 28 | D3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 29 | C32×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 30 | C3×D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 31 | C3×D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 32 | C2×#4175⋊C3 | — | 9 | 1 | no | — |
| 33 | #11757735 | C32 | 1 | 1 | yes | characteristic, complemented |
| 34 | (#4174⋊C2)⋊C3 | — | 9 | 1 | no | — |
| 35 | D3×#4175 | — | 3 | 3 | no | — |
| 36 | C3×H(5,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#6910 | — | 2 | 1 | no | — |
| 38 | C3×#6910 | — | 2 | 1 | no | — |
| 39 | C3×#6910 | — | 4 | 1 | no | — |
| 40 | C3×#6909 | — | 2 | 1 | no | — |
| 41 | C3×#6909 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | C3×#6909 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 43 | #10624761 | — | 2 | 3 | no | — |
| 44 | #10624761 | — | 2 | 3 | no | — |
| 45 | #10624761 | — | 4 | 3 | no | — |
| 46 | #10624761 | C22×C3 | 1 | 3 | yes | complemented |
| 47 | C3⋊(C3⋊((C3⋊D3)⋊C3)) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | #92392 | — | 6 | 1 | no | — |
| 49 | #92392 | C3×D3 | 1 | 3 | yes | — |
| 50 | #92391 | — | 3 | 3 | no | — |
| 51 | #92391 | — | 3 | 3 | no | — |
| 52 | #92391 | — | 6 | 3 | no | — |
| 53 | #92391 | — | 6 | 3 | no | — |
| 54 | C3×C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 55 | C32×#272 | — | 3 | 1 | no | — |
| 56 | C32×#272 | C3×D3 | 1 | 1 | yes | characteristic |
| 57 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 58 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 59 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 60 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 61 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 62 | C3×C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 63 | C3×C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 64 | C3×D3×3−1+2 | — | 6 | 1 | no | — |
| 65 | C3×D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 66 | C3×D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 67 | C3×D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 68 | C32×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 69 | C32×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 70 | C32×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 71 | C32×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 72 | C32×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 73 | C32×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 74 | C2×#6909 | — | 9 | 1 | no | — |
| 75 | C3⋊#4183 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 76 | #4183⋊C3 | — | 9 | 1 | no | — |
| 77 | #4183⋊C3 | — | 18 | 1 | no | — |
| 78 | C3⋊#4175 | — | 2 | 3 | no | — |
| 79 | C3⋊#4175 | — | 2 | 1 | no | — |
| 80 | C3⋊#4175 | C3×D3 | 1 | 3 | yes | complemented |
| 81 | C3⋊#4175 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 82 | #4177⋊C3 | — | 6 | 3 | no | — |
| 83 | #4177⋊C3 | — | 6 | 1 | no | — |
| 84 | #4177⋊C3 | — | 6 | 3 | no | — |
| 85 | #4177⋊C3 | — | 6 | 2 | no | — |
| 86 | #92283 | — | 2 | 3 | no | — |
| 87 | #92283 | — | 6 | 1 | no | — |
| 88 | #92283 | — | 6 | 1 | no | — |
| 89 | #4175⋊C3 | — | 3 | 1 | no | — |
| 90 | #4175⋊C3 | — | 6 | 3 | no | — |
| 91 | #4175⋊C3 | — | 6 | 1 | no | — |
| 92 | #4175⋊C3 | — | 9 | 1 | no | — |
| 93 | #4175⋊C3 | — | 9 | 1 | no | — |
| 94 | #4175⋊C3 | — | 18 | 1 | no | — |
| 95 | #92281 | — | 3 | 1 | no | — |
| 96 | #92281 | — | 6 | 1 | no | — |
| 97 | C3×#4177 | — | 6 | 3 | no | — |
| 98 | C3×#4176 | — | 6 | 1 | no | — |
| 99 | D3×AΣL(1,𝔽27) | — | 3 | 3 | no | — |
| 100 | D3×AΣL(1,𝔽27) | — | 6 | 3 | no | — |
| 101 | C3×#4175 | — | 3 | 3 | no | — |
| 102 | C3×#4174 | — | 2 | 1 | no | — |
| 103 | C3×#4174 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 104 | D3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 105 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 106 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 107 | C32×D32 | — | 27 | 1 | no | — |
| 108 | C32×D32 | — | 27 | 1 | no | — |
| 109 | C2×C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 110 | C2×C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 111 | #66432 | — | 3 | 1 | no | — |
| 112 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 3 | no | — |
| 113 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 114 | D3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 115 | D3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 116 | D3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 117 | C2×#4175 | — | 9 | 3 | no | — |
| 118 | #4174⋊C2 | — | 9 | 1 | no | — |
| 119 | H(5,𝔽3) | — | 2 | 3 | no | — |
| 120 | H(5,𝔽3) | — | 6 | 1 | no | — |
| 121 | H(5,𝔽3) | — | 6 | 3 | no | — |
| 122 | H(5,𝔽3) | — | 12 | 1 | no | — |
| 123 | H(5,𝔽3) | — | 12 | 3 | no | — |
| 124 | H(5,𝔽3) | C2×C3×D3 | 1 | 3 | yes | — |
| 125 | C32×3−1+2 | — | 2 | 1 | no | — |
| 126 | C32×3−1+2 | — | 2 | 1 | no | — |
| 127 | C32×3−1+2 | — | 4 | 1 | no | — |
| 128 | C32×H(3,𝔽3) | — | 2 | 1 | no | — |
| 129 | C32×H(3,𝔽3) | — | 3 | 1 | no | — |
| 130 | C32×H(3,𝔽3) | — | 3 | 1 | no | — |
| 131 | C32×H(3,𝔽3) | — | 6 | 1 | no | — |
| 132 | C32×H(3,𝔽3) | — | 6 | 1 | no | — |
| 133 | C32×H(3,𝔽3) | — | 6 | 1 | no | — |
| 134 | C32×H(3,𝔽3) | — | 12 | 1 | no | — |
| 135 | C32×H(3,𝔽3) | D32 | 1 | 1 | yes | characteristic |
| 136 | C32×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 137 | C32×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 138 | #6910 | — | 2 | 3 | no | — |
| 139 | #6910 | — | 2 | 3 | no | — |
| 140 | #6910 | — | 4 | 3 | no | — |
| 141 | #6910 | — | 4 | 3 | no | — |
| 142 | #6910 | — | 4 | 6 | no | — |
| 143 | #6910 | — | 4 | 3 | no | — |
| 144 | #6910 | — | 6 | 1 | no | — |
| 145 | #6910 | — | 6 | 2 | no | — |
| 146 | #6910 | — | 6 | 3 | no | — |
| 147 | #6910 | — | 6 | 1 | no | — |
| 148 | #6910 | — | 6 | 1 | no | — |
| 149 | #6910 | — | 12 | 1 | no | — |
| 150 | #6910 | — | 12 | 1 | no | — |
| 151 | #6910 | — | 12 | 1 | no | — |
| 152 | #6910 | — | 12 | 3 | no | — |
| 153 | #6910 | — | 12 | 2 | no | — |
| 154 | #6909 | — | 3 | 1 | no | — |
| 155 | #6909 | — | 3 | 1 | no | — |
| 156 | #6909 | — | 6 | 3 | no | — |
| 157 | #6909 | — | 6 | 1 | no | — |
| 158 | #6909 | — | 6 | 1 | no | — |
| 159 | #6909 | — | 6 | 1 | no | — |
| 160 | #6909 | — | 6 | 1 | no | — |
| 161 | #6909 | — | 12 | 1 | no | — |
| 162 | #6909 | — | 12 | 3 | no | — |
| 163 | #6909 | — | 12 | 1 | no | — |
| 164 | C3×#731 | — | 6 | 1 | no | — |
| 165 | C3×#731 | — | 6 | 3 | no | — |
| 166 | C3×#731 | — | 12 | 1 | no | — |
| 167 | C3×#731 | — | 12 | 3 | no | — |
| 168 | C3×AΣL(1,𝔽27) | — | 2 | 3 | no | — |
| 169 | C3×AΣL(1,𝔽27) | — | 2 | 1 | no | — |
| 170 | C3×AΣL(1,𝔽27) | — | 2 | 3 | no | — |
| 171 | C3×AΣL(1,𝔽27) | — | 2 | 1 | no | — |
| 172 | C3×AΣL(1,𝔽27) | — | 4 | 1 | no | — |
| 173 | C3×AΣL(1,𝔽27) | — | 4 | 3 | no | — |
| 174 | C3×AΣL(1,𝔽27) | C2×C3×D3 | 1 | 3 | yes | complemented |
| 175 | C3×AΣL(1,𝔽27) | C22×C32 | 1 | 1 | yes | characteristic, complemented |
| 176 | C3⋊(C3⋊(C3⋊D3)) | C32×D3 | 1 | 1 | yes | characteristic, complemented |
| 177 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 178 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 179 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 180 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 181 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 182 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 183 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 184 | C32×C3⋊D3 | — | 18 | 1 | no | — |
| 185 | C32×C3⋊D3 | — | 18 | 1 | no | — |
| 186 | C33×D3 | — | 3 | 1 | no | — |
| 187 | C33×D3 | — | 3 | 1 | no | — |
| 188 | C33×D3 | — | 6 | 1 | no | — |
| 189 | C33×D3 | — | 9 | 1 | no | — |
| 190 | C33×D3 | — | 9 | 1 | no | — |
| 191 | C33×D3 | — | 9 | 1 | no | — |
| 192 | C33×D3 | — | 18 | 1 | no | — |
| 193 | C33×D3 | — | 27 | 1 | no | — |
| 194 | C33×D3 | — | 27 | 1 | no | — |
| 195 | C2×C3×3−1+2 | — | 18 | 1 | no | — |
| 196 | C2×C3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 197 | C2×C3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 198 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 199 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 200 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 201 | C3×#272 | — | 2 | 1 | no | — |
| 202 | C3×#272 | — | 3 | 3 | no | — |
| 203 | C3×#272 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 204 | C3×#272 | C32×D3 | 1 | 1 | yes | characteristic |
| 205 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 3 | no | — |
| 206 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 3 | no | — |
| 207 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 208 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 209 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 210 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 211 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 3 | no | — |
| 212 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 213 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 3 | no | — |
| 214 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 215 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 216 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 217 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 218 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 219 | D3×3−1+2 | — | 6 | 3 | no | — |
| 220 | D3×3−1+2 | — | 18 | 1 | no | — |
| 221 | D3×3−1+2 | — | 18 | 1 | no | — |
| 222 | C3×AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 223 | D3×H(3,𝔽3) | — | 3 | 3 | no | — |
| 224 | D3×H(3,𝔽3) | — | 9 | 3 | no | — |
| 225 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 226 | D3×H(3,𝔽3) | — | 18 | 1 | no | — |
| 227 | D3×H(3,𝔽3) | — | 18 | 1 | no | — |
| 228 | D3×H(3,𝔽3) | — | 18 | 3 | no | — |
| 229 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 230 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 231 | C3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 232 | C3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 233 | C3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 234 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 235 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 236 | C3×(C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 237 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 238 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 239 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 240 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 241 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 242 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 243 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 244 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 245 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 246 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 247 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 248 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 249 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 250 | C3×(C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 251 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 252 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 253 | C3×(C3⋊D3)⋊C3 | — | 18 | 6 | no | — |
| 254 | C3×(C3⋊D3)⋊C3 | — | 18 | 6 | no | — |
| 255 | C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 256 | C3×D3×C9 | — | 18 | 1 | no | — |
| 257 | C2×AΣL(1,𝔽27) | — | 9 | 3 | no | — |
| 258 | C2×AΣL(1,𝔽27) | — | 18 | 3 | no | — |
| 259 | #4183 | — | 9 | 1 | no | — |
| 260 | #4183 | — | 18 | 1 | no | — |
| 261 | #4177 | — | 6 | 3 | no | — |
| 262 | #4177 | — | 6 | 6 | no | — |
| 263 | #4176 | — | 6 | 3 | no | — |
| 264 | #4175 | — | 3 | 3 | no | — |
| 265 | #4175 | — | 6 | 3 | no | — |
| 266 | #4175 | — | 9 | 1 | no | — |
| 267 | #4175 | — | 9 | 3 | no | — |
| 268 | #4175 | — | 18 | 1 | no | — |
| 269 | #4175 | — | 18 | 3 | no | — |
| 270 | #4174 | — | 3 | 1 | no | — |
| 271 | #4174 | — | 6 | 1 | no | — |
| 272 | C2×C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 273 | C2×C3×C3⋊D3 | — | 27 | 1 | no | — |
| 274 | C2×C32×D3 | — | 81 | 1 | no | — |
| 275 | C2×C32×D3 | — | 81 | 1 | no | — |
| 276 | C2×C32×D3 | — | 81 | 1 | no | — |
| 277 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 278 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 279 | D3×C3⋊D3 | — | 27 | 1 | no | — |
| 280 | D3×C3⋊D3 | — | 81 | 1 | no | — |
| 281 | C3×D32 | — | 27 | 1 | no | — |
| 282 | C3×D32 | — | 27 | 3 | no | — |
| 283 | C3×D32 | — | 27 | 3 | no | — |
| 284 | C3×D32 | — | 27 | 1 | no | — |
| 285 | C3×D32 | — | 81 | 1 | no | — |
| 286 | C3×D32 | — | 81 | 1 | no | — |
| 287 | C2×(C3⋊D3)⋊C3 | — | 27 | 3 | no | — |
| 288 | C2×(C3⋊D3)⋊C3 | — | 81 | 1 | no | — |
| 289 | ((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 290 | C34 | — | 2 | 1 | no | — |
| 291 | C34 | — | 3 | 1 | no | — |
| 292 | C34 | — | 3 | 1 | no | — |
| 293 | C34 | — | 3 | 1 | no | — |
| 294 | C34 | — | 6 | 1 | no | — |
| 295 | C34 | — | 6 | 1 | no | — |
| 296 | C34 | — | 6 | 1 | no | — |
| 297 | C34 | — | 12 | 1 | no | — |
| 298 | C34 | C3×D32 | 1 | 1 | yes | characteristic |
| 299 | C34 | C2×C32×D3 | 1 | 1 | yes | characteristic, complemented |
| 300 | C3×3−1+2 | — | 2 | 3 | no | — |
| 301 | C3×3−1+2 | — | 2 | 1 | no | — |
| 302 | C3×3−1+2 | — | 4 | 1 | no | — |
| 303 | C3×3−1+2 | — | 4 | 3 | no | — |
| 304 | C3×3−1+2 | — | 6 | 1 | no | — |
| 305 | C3×3−1+2 | — | 6 | 1 | no | — |
| 306 | C3×3−1+2 | — | 6 | 1 | no | — |
| 307 | C3×3−1+2 | — | 6 | 1 | no | — |
| 308 | C3×3−1+2 | — | 6 | 1 | no | — |
| 309 | C3×3−1+2 | — | 6 | 1 | no | — |
| 310 | C3×3−1+2 | — | 12 | 1 | no | — |
| 311 | C3×3−1+2 | — | 12 | 1 | no | — |
| 312 | C3×3−1+2 | — | 12 | 1 | no | — |
| 313 | C3×3−1+2 | — | 12 | 1 | no | — |
| 314 | C3×3−1+2 | — | 12 | 1 | no | — |
| 315 | C3×3−1+2 | — | 12 | 1 | no | — |
| 316 | C3×3−1+2 | — | 12 | 1 | no | — |
| 317 | C3×3−1+2 | — | 12 | 1 | no | — |
| 318 | C3×3−1+2 | — | 12 | 1 | no | — |
| 319 | C3×3−1+2 | — | 12 | 1 | no | — |
| 320 | C3×3−1+2 | — | 12 | 1 | no | — |
| 321 | C3×3−1+2 | — | 12 | 1 | no | — |
| 322 | C3×3−1+2 | — | 12 | 1 | no | — |
| 323 | C3×3−1+2 | — | 12 | 1 | no | — |
| 324 | C3×3−1+2 | — | 12 | 1 | no | — |
| 325 | C3×3−1+2 | — | 12 | 1 | no | — |
| 326 | C3×3−1+2 | — | 12 | 1 | no | — |
| 327 | C3×3−1+2 | — | 12 | 1 | no | — |
| 328 | C3×3−1+2 | — | 12 | 1 | no | — |
| 329 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 330 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 331 | C3×H(3,𝔽3) | — | 2 | 3 | no | — |
| 332 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 333 | C3×H(3,𝔽3) | — | 2 | 3 | no | — |
| 334 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 335 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 336 | C3×H(3,𝔽3) | — | 3 | 3 | no | — |
| 337 | C3×H(3,𝔽3) | — | 3 | 3 | no | — |
| 338 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 339 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 340 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 341 | C3×H(3,𝔽3) | — | 4 | 3 | no | — |
| 342 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 343 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 344 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 345 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 346 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 347 | C3×H(3,𝔽3) | — | 6 | 6 | no | — |
| 348 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 349 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 350 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 351 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 352 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 353 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 354 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 355 | C3×H(3,𝔽3) | — | 6 | 6 | no | — |
| 356 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 357 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 358 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 359 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 360 | C3×H(3,𝔽3) | — | 6 | 3 | no | — |
| 361 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 362 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 363 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 364 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 365 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 366 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 367 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 368 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 369 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 370 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 371 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 372 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 373 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 374 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 375 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 376 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 377 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 378 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 379 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 380 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 381 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 382 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 383 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 384 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 385 | C3×H(3,𝔽3) | — | 12 | 6 | no | — |
| 386 | C3×H(3,𝔽3) | — | 12 | 3 | no | — |
| 387 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 388 | C3×H(3,𝔽3) | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 389 | C3×H(3,𝔽3) | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 390 | C3×H(3,𝔽3) | C3×D32 | 1 | 3 | yes | — |
| 391 | C3×H(3,𝔽3) | C2×C32×D3 | 1 | 1 | yes | characteristic |
| 392 | C32×C9 | — | 6 | 1 | no | — |
| 393 | C32×C9 | — | 6 | 1 | no | — |
| 394 | C32×C9 | — | 12 | 1 | no | — |
| 395 | #731 | — | 6 | 6 | no | — |
| 396 | #731 | — | 6 | 3 | no | — |
| 397 | #731 | — | 6 | 3 | no | — |
| 398 | #731 | — | 12 | 3 | no | — |
| 399 | #731 | — | 12 | 3 | no | — |
| 400 | #731 | — | 12 | 3 | no | — |
| 401 | #731 | — | 12 | 3 | no | — |
| 402 | #731 | — | 12 | 6 | no | — |
| 403 | #731 | — | 12 | 3 | no | — |
| 404 | #731 | — | 12 | 6 | no | — |
| 405 | #731 | — | 12 | 6 | no | — |
| 406 | #731 | — | 12 | 12 | no | — |
| 407 | #731 | — | 12 | 3 | no | — |
| 408 | AΣL(1,𝔽27) | — | 3 | 3 | no | — |
| 409 | AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 410 | AΣL(1,𝔽27) | — | 6 | 3 | no | — |
| 411 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 412 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 413 | AΣL(1,𝔽27) | — | 6 | 3 | no | — |
| 414 | AΣL(1,𝔽27) | — | 6 | 3 | no | — |
| 415 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 416 | AΣL(1,𝔽27) | — | 12 | 3 | no | — |
| 417 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 418 | AΣL(1,𝔽27) | — | 12 | 3 | no | — |
| 419 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 420 | AΣL(1,𝔽27) | — | 12 | 2 | no | — |
| 421 | AΣL(1,𝔽27) | — | 12 | 6 | no | — |
| 422 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 423 | AΣL(1,𝔽27) | — | 12 | 3 | no | — |
| 424 | C2×C33 | — | 9 | 1 | no | — |
| 425 | C2×C33 | — | 9 | 1 | no | — |
| 426 | C2×C33 | — | 18 | 1 | no | — |
| 427 | C2×C33 | — | 27 | 1 | no | — |
| 428 | C2×C33 | — | 81 | 1 | no | — |
| 429 | C2×C33 | — | 81 | 1 | no | — |
| 430 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 431 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 432 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 433 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 434 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 435 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 436 | C3⋊(C3⋊D3) | — | 81 | 1 | no | — |
| 437 | C3×C3⋊D3 | — | 9 | 3 | no | — |
| 438 | C3×C3⋊D3 | — | 9 | 3 | no | — |
| 439 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 440 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 441 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 442 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 443 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 444 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 445 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 446 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 447 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 448 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 449 | C3×C3⋊D3 | — | 18 | 3 | no | — |
| 450 | C3×C3⋊D3 | — | 18 | 3 | no | — |
| 451 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 452 | C3×C3⋊D3 | — | 81 | 1 | no | — |
| 453 | C3×C3⋊D3 | — | 81 | 1 | no | — |
| 454 | C3×C3⋊D3 | — | 81 | 1 | no | — |
| 455 | C32×D3 | — | 3 | 1 | no | — |
| 456 | C32×D3 | — | 3 | 1 | no | — |
| 457 | C32×D3 | — | 6 | 1 | no | — |
| 458 | C32×D3 | — | 9 | 1 | no | — |
| 459 | C32×D3 | — | 9 | 3 | no | — |
| 460 | C32×D3 | — | 9 | 1 | no | — |
| 461 | C32×D3 | — | 9 | 1 | no | — |
| 462 | C32×D3 | — | 9 | 3 | no | — |
| 463 | C32×D3 | — | 18 | 1 | no | — |
| 464 | C32×D3 | — | 18 | 1 | no | — |
| 465 | C32×D3 | — | 18 | 3 | no | — |
| 466 | C32×D3 | — | 27 | 1 | no | — |
| 467 | C32×D3 | — | 27 | 1 | no | — |
| 468 | C32×D3 | — | 27 | 1 | no | — |
| 469 | C32×D3 | — | 27 | 1 | no | — |
| 470 | C32×D3 | — | 27 | 1 | no | — |
| 471 | C32×D3 | — | 27 | 1 | no | — |
| 472 | C32×D3 | — | 27 | 1 | no | — |
| 473 | C32×D3 | — | 27 | 3 | no | — |
| 474 | C32×D3 | — | 27 | 3 | no | — |
| 475 | C32×D3 | — | 27 | 1 | no | — |
| 476 | C32×D3 | — | 27 | 1 | no | — |
| 477 | C32×D3 | — | 54 | 1 | no | — |
| 478 | C32×D3 | — | 54 | 1 | no | — |
| 479 | C32×D3 | — | 54 | 1 | no | — |
| 480 | C32×D3 | — | 54 | 1 | no | — |
| 481 | C32×D3 | — | 54 | 1 | no | — |
| 482 | C32×D3 | — | 54 | 1 | no | — |
| 483 | C32×D3 | — | 54 | 1 | no | — |
| 484 | C32×D3 | — | 54 | 3 | no | — |
| 485 | C32×D3 | — | 54 | 3 | no | — |
| 486 | C32×D3 | — | 54 | 1 | no | — |
| 487 | C32×D3 | — | 54 | 1 | no | — |
| 488 | C32×D3 | — | 81 | 1 | no | — |
| 489 | C32×D3 | — | 81 | 1 | no | — |
| 490 | C32×D3 | — | 81 | 1 | no | — |
| 491 | C32×D3 | — | 81 | 1 | no | — |
| 492 | C32×D3 | — | 162 | 1 | no | — |
| 493 | C32×D3 | — | 162 | 1 | no | — |
| 494 | C2×3−1+2 | — | 18 | 3 | no | — |
| 495 | C2×3−1+2 | — | 54 | 1 | no | — |
| 496 | C2×3−1+2 | — | 54 | 1 | no | — |
| 497 | C2×H(3,𝔽3) | — | 9 | 3 | no | — |
| 498 | C2×H(3,𝔽3) | — | 27 | 1 | no | — |
| 499 | C2×H(3,𝔽3) | — | 54 | 1 | no | — |
| 500 | C2×H(3,𝔽3) | — | 54 | 1 | no | — |
| 501 | C2×C3×C9 | — | 54 | 1 | no | — |
| 502 | #272 | C3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 503 | C3⋊D9 | — | 6 | 1 | no | — |
| 504 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 505 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 506 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 507 | (C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 508 | (C3⋊D3)⋊C3 | — | 9 | 3 | no | — |
| 509 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 510 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 511 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 512 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 513 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 514 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 515 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 516 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 517 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 518 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 519 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 520 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 521 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 522 | (C3⋊D3)⋊C3 | — | 18 | 2 | no | — |
| 523 | (C3⋊D3)⋊C3 | — | 18 | 2 | no | — |
| 524 | (C3⋊D3)⋊C3 | — | 18 | 3 | no | — |
| 525 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 526 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 527 | (C3⋊D3)⋊C3 | — | 81 | 1 | no | — |
| 528 | D3×C9 | — | 18 | 3 | no | — |
| 529 | C3×D9 | — | 54 | 1 | no | — |
| 530 | C22×C32 | — | 243 | 1 | no | — |
| 531 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 532 | C2×C3⋊D3 | — | 81 | 1 | no | — |
| 533 | C2×C3⋊D3 | — | 243 | 1 | no | — |
| 534 | C2×C3×D3 | — | 81 | 1 | no | — |
| 535 | C2×C3×D3 | — | 81 | 1 | no | — |
| 536 | C2×C3×D3 | — | 81 | 1 | no | — |
| 537 | C2×C3×D3 | — | 81 | 3 | no | — |
| 538 | C2×C3×D3 | — | 81 | 3 | no | — |
| 539 | C2×C3×D3 | — | 81 | 3 | no | — |
| 540 | C2×C3×D3 | — | 243 | 1 | no | — |
| 541 | D32 | — | 27 | 1 | no | — |
| 542 | D32 | — | 27 | 1 | no | — |
| 543 | D32 | — | 81 | 1 | no | — |
| 544 | D32 | — | 81 | 1 | no | — |
| 545 | D32 | — | 243 | 1 | no | — |
| 546 | C33 | — | 2 | 1 | no | — |
| 547 | C33 | — | 2 | 1 | no | — |
| 548 | C33 | — | 2 | 1 | no | — |
| 549 | C33 | — | 3 | 1 | no | — |
| 550 | C33 | — | 3 | 3 | no | — |
| 551 | C33 | — | 3 | 1 | no | — |
| 552 | C33 | — | 3 | 3 | no | — |
| 553 | C33 | — | 3 | 1 | no | — |
| 554 | C33 | — | 3 | 1 | no | — |
| 555 | C33 | — | 3 | 1 | no | — |
| 556 | C33 | — | 4 | 1 | no | — |
| 557 | C33 | — | 6 | 3 | no | — |
| 558 | C33 | — | 6 | 1 | no | — |
| 559 | C33 | — | 6 | 3 | no | — |
| 560 | C33 | — | 6 | 1 | no | — |
| 561 | C33 | — | 6 | 3 | no | — |
| 562 | C33 | — | 6 | 3 | no | — |
| 563 | C33 | — | 6 | 1 | no | — |
| 564 | C33 | — | 6 | 1 | no | — |
| 565 | C33 | — | 6 | 3 | no | — |
| 566 | C33 | — | 6 | 1 | no | — |
| 567 | C33 | — | 6 | 1 | no | — |
| 568 | C33 | — | 6 | 1 | no | — |
| 569 | C33 | — | 6 | 1 | no | — |
| 570 | C33 | — | 12 | 1 | no | — |
| 571 | C33 | — | 12 | 1 | no | — |
| 572 | C33 | — | 12 | 3 | no | — |
| 573 | C33 | — | 12 | 3 | no | — |
| 574 | C33 | — | 12 | 3 | no | — |
| 575 | C33 | — | 12 | 3 | no | — |
| 576 | C33 | — | 12 | 6 | no | — |
| 577 | C33 | — | 12 | 1 | no | — |
| 578 | C33 | — | 27 | 1 | no | — |
| 579 | C33 | — | 27 | 1 | no | — |
| 580 | C33 | — | 27 | 1 | no | — |
| 581 | C33 | — | 27 | 1 | no | — |
| 582 | C33 | — | 27 | 1 | no | — |
| 583 | C33 | — | 54 | 1 | no | — |
| 584 | C33 | — | 54 | 1 | no | — |
| 585 | C33 | — | 54 | 1 | no | — |
| 586 | C33 | — | 54 | 1 | no | — |
| 587 | C33 | — | 54 | 1 | no | — |
| 588 | C33 | — | 54 | 1 | no | — |
| 589 | C33 | — | 54 | 1 | no | — |
| 590 | C33 | — | 54 | 1 | no | — |
| 591 | C33 | — | 54 | 1 | no | — |
| 592 | C33 | — | 108 | 1 | no | — |
| 593 | C33 | — | 108 | 1 | no | — |
| 594 | C33 | — | 108 | 1 | no | — |
| 595 | C33 | — | 108 | 1 | no | — |
| 596 | C33 | — | 108 | 1 | no | — |
| 597 | C33 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 598 | C33 | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 599 | C33 | C32×D32 | 1 | 1 | yes | characteristic |
| 600 | 3−1+2 | — | 6 | 1 | no | — |
| 601 | 3−1+2 | — | 6 | 3 | no | — |
| 602 | 3−1+2 | — | 12 | 1 | no | — |
| 603 | 3−1+2 | — | 12 | 3 | no | — |
| 604 | 3−1+2 | — | 12 | 3 | no | — |
| 605 | 3−1+2 | — | 12 | 2 | no | — |
| 606 | 3−1+2 | — | 12 | 1 | no | — |
| 607 | 3−1+2 | — | 12 | 3 | no | — |
| 608 | 3−1+2 | — | 12 | 3 | no | — |
| 609 | 3−1+2 | — | 18 | 1 | no | — |
| 610 | 3−1+2 | — | 18 | 1 | no | — |
| 611 | 3−1+2 | — | 18 | 1 | no | — |
| 612 | 3−1+2 | — | 18 | 1 | no | — |
| 613 | 3−1+2 | — | 36 | 1 | no | — |
| 614 | 3−1+2 | — | 36 | 1 | no | — |
| 615 | 3−1+2 | — | 36 | 1 | no | — |
| 616 | 3−1+2 | — | 36 | 1 | no | — |
| 617 | 3−1+2 | — | 36 | 1 | no | — |
| 618 | 3−1+2 | — | 36 | 1 | no | — |
| 619 | 3−1+2 | — | 36 | 1 | no | — |
| 620 | 3−1+2 | — | 36 | 1 | no | — |
| 621 | 3−1+2 | — | 36 | 1 | no | — |
| 622 | 3−1+2 | — | 36 | 1 | no | — |
| 623 | H(3,𝔽3) | — | 2 | 3 | no | — |
| 624 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 625 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 626 | H(3,𝔽3) | — | 2 | 3 | no | — |
| 627 | H(3,𝔽3) | — | 4 | 3 | no | — |
| 628 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 629 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 630 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 631 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 632 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 633 | H(3,𝔽3) | — | 6 | 2 | no | — |
| 634 | H(3,𝔽3) | — | 6 | 2 | no | — |
| 635 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 636 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 637 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 638 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 639 | H(3,𝔽3) | — | 6 | 3 | no | — |
| 640 | H(3,𝔽3) | — | 9 | 1 | no | — |
| 641 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 642 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 643 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 644 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 645 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 646 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 647 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 648 | H(3,𝔽3) | — | 12 | 6 | no | — |
| 649 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 650 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 651 | H(3,𝔽3) | — | 12 | 2 | no | — |
| 652 | H(3,𝔽3) | — | 12 | 2 | no | — |
| 653 | H(3,𝔽3) | — | 12 | 6 | no | — |
| 654 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 655 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 656 | H(3,𝔽3) | — | 12 | 6 | no | — |
| 657 | H(3,𝔽3) | — | 12 | 3 | no | — |
| 658 | H(3,𝔽3) | — | 18 | 1 | no | — |
| 659 | H(3,𝔽3) | — | 18 | 1 | no | — |
| 660 | H(3,𝔽3) | — | 36 | 1 | no | — |
| 661 | H(3,𝔽3) | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 662 | H(3,𝔽3) | C2×C3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 663 | C3×C9 | — | 6 | 3 | no | — |
| 664 | C3×C9 | — | 6 | 1 | no | — |
| 665 | C3×C9 | — | 12 | 3 | no | — |
| 666 | C3×C9 | — | 12 | 1 | no | — |
| 667 | C3×C9 | — | 18 | 1 | no | — |
| 668 | C3×C9 | — | 18 | 1 | no | — |
| 669 | C3×C9 | — | 36 | 1 | no | — |
| 670 | C3×C9 | — | 36 | 1 | no | — |
| 671 | C3×C9 | — | 36 | 1 | no | — |
| 672 | C3×C9 | — | 36 | 1 | no | — |
| 673 | C3×C9 | — | 36 | 1 | no | — |
| 674 | C2×C32 | — | 9 | 1 | no | — |
| 675 | C2×C32 | — | 9 | 1 | no | — |
| 676 | C2×C32 | — | 18 | 1 | no | — |
| 677 | C2×C32 | — | 27 | 3 | no | — |
| 678 | C2×C32 | — | 27 | 1 | no | — |
| 679 | C2×C32 | — | 54 | 1 | no | — |
| 680 | C2×C32 | — | 81 | 1 | no | — |
| 681 | C2×C32 | — | 81 | 1 | no | — |
| 682 | C2×C32 | — | 81 | 1 | no | — |
| 683 | C2×C32 | — | 81 | 1 | no | — |
| 684 | C2×C32 | — | 81 | 1 | no | — |
| 685 | C2×C32 | — | 81 | 1 | no | — |
| 686 | C2×C32 | — | 81 | 1 | no | — |
| 687 | C2×C32 | — | 81 | 3 | no | — |
| 688 | C2×C32 | — | 81 | 3 | no | — |
| 689 | C2×C32 | — | 162 | 1 | no | — |
| 690 | C2×C32 | — | 162 | 1 | no | — |
| 691 | C2×C32 | — | 162 | 1 | no | — |
| 692 | C2×C32 | — | 162 | 1 | no | — |
| 693 | C2×C32 | — | 162 | 3 | no | — |
| 694 | C2×C32 | — | 162 | 3 | no | — |
| 695 | C3⋊D3 | — | 9 | 1 | no | — |
| 696 | C3⋊D3 | — | 9 | 1 | no | — |
| 697 | C3⋊D3 | — | 9 | 1 | no | — |
| 698 | C3⋊D3 | — | 9 | 1 | no | — |
| 699 | C3⋊D3 | — | 18 | 1 | no | — |
| 700 | C3⋊D3 | — | 18 | 1 | no | — |
| 701 | C3⋊D3 | — | 27 | 1 | no | — |
| 702 | C3⋊D3 | — | 81 | 1 | no | — |
| 703 | C3⋊D3 | — | 81 | 1 | no | — |
| 704 | C3⋊D3 | — | 81 | 1 | no | — |
| 705 | C3⋊D3 | — | 81 | 1 | no | — |
| 706 | C3⋊D3 | — | 486 | 1 | no | — |
| 707 | C3⋊D3 | — | 243 | 1 | no | — |
| 708 | C3⋊D3 | — | 243 | 1 | no | — |
| 709 | C3×D3 | — | 3 | 1 | no | — |
| 710 | C3×D3 | — | 9 | 1 | no | — |
| 711 | C3×D3 | — | 9 | 1 | no | — |
| 712 | C3×D3 | — | 9 | 1 | no | — |
| 713 | C3×D3 | — | 9 | 1 | no | — |
| 714 | C3×D3 | — | 18 | 1 | no | — |
| 715 | C3×D3 | — | 18 | 1 | no | — |
| 716 | C3×D3 | — | 27 | 3 | no | — |
| 717 | C3×D3 | — | 27 | 1 | no | — |
| 718 | C3×D3 | — | 27 | 1 | no | — |
| 719 | C3×D3 | — | 27 | 3 | no | — |
| 720 | C3×D3 | — | 27 | 1 | no | — |
| 721 | C3×D3 | — | 27 | 3 | no | — |
| 722 | C3×D3 | — | 27 | 3 | no | — |
| 723 | C3×D3 | — | 27 | 1 | no | — |
| 724 | C3×D3 | — | 27 | 1 | no | — |
| 725 | C3×D3 | — | 27 | 1 | no | — |
| 726 | C3×D3 | — | 54 | 1 | no | — |
| 727 | C3×D3 | — | 54 | 1 | no | — |
| 728 | C3×D3 | — | 54 | 3 | no | — |
| 729 | C3×D3 | — | 54 | 1 | no | — |
| 730 | C3×D3 | — | 54 | 3 | no | — |
| 731 | C3×D3 | — | 54 | 1 | no | — |
| 732 | C3×D3 | — | 54 | 3 | no | — |
| 733 | C3×D3 | — | 81 | 1 | no | — |
| 734 | C3×D3 | — | 81 | 1 | no | — |
| 735 | C3×D3 | — | 81 | 1 | no | — |
| 736 | C3×D3 | — | 81 | 1 | no | — |
| 737 | C3×D3 | — | 81 | 1 | no | — |
| 738 | C3×D3 | — | 81 | 1 | no | — |
| 739 | C3×D3 | — | 81 | 3 | no | — |
| 740 | C3×D3 | — | 81 | 3 | no | — |
| 741 | C3×D3 | — | 162 | 1 | no | — |
| 742 | C3×D3 | — | 162 | 1 | no | — |
| 743 | C3×D3 | — | 162 | 1 | no | — |
| 744 | C3×D3 | — | 162 | 1 | no | — |
| 745 | C3×D3 | — | 162 | 3 | no | — |
| 746 | C3×D3 | — | 162 | 3 | no | — |
| 747 | C3×D3 | — | 243 | 1 | no | — |
| 748 | C2×C9 | — | 54 | 3 | no | — |
| 749 | D9 | — | 54 | 1 | no | — |
| 750 | C22×C3 | — | 243 | 1 | no | — |
| 751 | C22×C3 | — | 243 | 3 | no | — |
| 752 | C2×D3 | — | 81 | 1 | no | — |
| 753 | C2×D3 | — | 81 | 1 | no | — |
| 754 | C2×D3 | — | 81 | 1 | no | — |
| 755 | C2×D3 | — | 729 | 1 | no | — |
| 756 | C2×D3 | — | 243 | 1 | no | — |
| 757 | C32 | — | 2 | 1 | no | — |
| 758 | C32 | — | 2 | 1 | no | — |
| 759 | C32 | — | 2 | 1 | no | — |
| 760 | C32 | — | 3 | 1 | no | — |
| 761 | C32 | — | 3 | 3 | no | — |
| 762 | C32 | — | 4 | 1 | no | — |
| 763 | C32 | — | 6 | 1 | no | — |
| 764 | C32 | — | 6 | 3 | no | — |
| 765 | C32 | — | 6 | 3 | no | — |
| 766 | C32 | — | 6 | 1 | no | — |
| 767 | C32 | — | 9 | 1 | no | — |
| 768 | C32 | — | 9 | 1 | no | — |
| 769 | C32 | — | 9 | 1 | no | — |
| 770 | C32 | — | 9 | 1 | no | — |
| 771 | C32 | — | 9 | 1 | no | — |
| 772 | C32 | — | 9 | 1 | no | — |
| 773 | C32 | — | 12 | 3 | no | — |
| 774 | C32 | — | 12 | 1 | no | — |
| 775 | C32 | — | 18 | 1 | no | — |
| 776 | C32 | — | 18 | 1 | no | — |
| 777 | C32 | — | 18 | 1 | no | — |
| 778 | C32 | — | 18 | 1 | no | — |
| 779 | C32 | — | 18 | 1 | no | — |
| 780 | C32 | — | 18 | 1 | no | — |
| 781 | C32 | — | 18 | 1 | no | — |
| 782 | C32 | — | 18 | 1 | no | — |
| 783 | C32 | — | 18 | 1 | no | — |
| 784 | C32 | — | 27 | 1 | no | — |
| 785 | C32 | — | 27 | 3 | no | — |
| 786 | C32 | — | 27 | 1 | no | — |
| 787 | C32 | — | 27 | 1 | no | — |
| 788 | C32 | — | 27 | 3 | no | — |
| 789 | C32 | — | 36 | 1 | no | — |
| 790 | C32 | — | 36 | 1 | no | — |
| 791 | C32 | — | 36 | 1 | no | — |
| 792 | C32 | — | 36 | 1 | no | — |
| 793 | C32 | — | 36 | 1 | no | — |
| 794 | C32 | — | 36 | 1 | no | — |
| 795 | C32 | — | 36 | 1 | no | — |
| 796 | C32 | — | 54 | 1 | no | — |
| 797 | C32 | — | 54 | 1 | no | — |
| 798 | C32 | — | 54 | 1 | no | — |
| 799 | C32 | — | 54 | 3 | no | — |
| 800 | C32 | — | 54 | 1 | no | — |
| 801 | C32 | — | 54 | 3 | no | — |
| 802 | C32 | — | 54 | 1 | no | — |
| 803 | C32 | — | 54 | 3 | no | — |
| 804 | C32 | — | 54 | 3 | no | — |
| 805 | C32 | — | 54 | 3 | no | — |
| 806 | C32 | — | 108 | 1 | no | — |
| 807 | C32 | — | 108 | 1 | no | — |
| 808 | C32 | — | 108 | 3 | no | — |
| 809 | C32 | — | 108 | 3 | no | — |
| 810 | C32 | — | 108 | 3 | no | — |
| 811 | C32 | — | 108 | 3 | no | — |
| 812 | C32 | — | 108 | 6 | no | — |
| 813 | C32 | (((C3⋊D3)⋊C3)⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 814 | C32 | C3×D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 815 | C32 | C32×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 816 | C9 | — | 18 | 1 | no | — |
| 817 | C9 | — | 18 | 3 | no | — |
| 818 | C9 | — | 36 | 1 | no | — |
| 819 | C9 | — | 36 | 3 | no | — |
| 820 | C2×C3 | — | 9 | 1 | no | — |
| 821 | C2×C3 | — | 27 | 1 | no | — |
| 822 | C2×C3 | — | 27 | 1 | no | — |
| 823 | C2×C3 | — | 54 | 1 | no | — |
| 824 | C2×C3 | — | 81 | 3 | no | — |
| 825 | C2×C3 | — | 81 | 1 | no | — |
| 826 | C2×C3 | — | 81 | 1 | no | — |
| 827 | C2×C3 | — | 81 | 1 | no | — |
| 828 | C2×C3 | — | 81 | 1 | no | — |
| 829 | C2×C3 | — | 81 | 1 | no | — |
| 830 | C2×C3 | — | 81 | 3 | no | — |
| 831 | C2×C3 | — | 81 | 3 | no | — |
| 832 | C2×C3 | — | 162 | 1 | no | — |
| 833 | C2×C3 | — | 162 | 1 | no | — |
| 834 | C2×C3 | — | 162 | 1 | no | — |
| 835 | C2×C3 | — | 162 | 3 | no | — |
| 836 | C2×C3 | — | 162 | 3 | no | — |
| 837 | D3 | — | 3 | 1 | no | — |
| 838 | D3 | — | 9 | 1 | no | — |
| 839 | D3 | — | 27 | 1 | no | — |
| 840 | D3 | — | 27 | 1 | no | — |
| 841 | D3 | — | 81 | 1 | no | — |
| 842 | D3 | — | 81 | 1 | no | — |
| 843 | D3 | — | 81 | 1 | no | — |
| 844 | D3 | — | 81 | 1 | no | — |
| 845 | D3 | — | 162 | 1 | no | — |
| 846 | D3 | — | 162 | 1 | no | — |
| 847 | D3 | — | 729 | 1 | no | — |
| 848 | D3 | — | 243 | 1 | no | — |
| 849 | C22 | — | 243 | 1 | no | Sylow |
| 850 | C3 | — | 3 | 1 | no | — |
| 851 | C3 | — | 3 | 1 | no | — |
| 852 | C3 | — | 3 | 1 | no | — |
| 853 | C3 | — | 6 | 1 | no | — |
| 854 | C3 | — | 6 | 1 | no | — |
| 855 | C3 | — | 6 | 1 | no | — |
| 856 | C3 | — | 9 | 1 | no | — |
| 857 | C3 | — | 9 | 3 | no | — |
| 858 | C3 | — | 12 | 1 | no | — |
| 859 | C3 | — | 18 | 1 | no | — |
| 860 | C3 | — | 18 | 1 | no | — |
| 861 | C3 | — | 18 | 3 | no | — |
| 862 | C3 | — | 18 | 3 | no | — |
| 863 | C3 | — | 27 | 1 | no | — |
| 864 | C3 | — | 36 | 1 | no | — |
| 865 | C3 | — | 36 | 3 | no | — |
| 866 | C3 | — | 54 | 1 | no | — |
| 867 | C3 | C3×(((C3⋊D3)⋊C3)⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 868 | C2 | — | 9 | 1 | no | — |
| 869 | C2 | — | 81 | 1 | no | — |
| 870 | C2 | — | 81 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×AΣL(1,𝔽27) | C22×C32 |
| Frattini | C33 | C32×D32 |
| Fitting | #14554344 | C22 |
| socle | C3 | C3×(((C3⋊D3)⋊C3)⋊D3)⋊C3 |
| LCS | G ▷ C3×AΣL(1,𝔽27) | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72243906 | C3 | semidirect |
| 4. #72243679 | C2 | semidirect |
| 5. #72243630 | C2 | semidirect |
| 6. #72221974 | C3 | semidirect |
| 7. #72221895 | C2 | semidirect |
| 8. #14554344 | C22 | semidirect |
| 11. C3×#92392 | D3 | semidirect |
| 14. C3⋊(#4183⋊C3) | C2×C3 | semidirect |
| 15. C3×#92281 | C2×C3 | semidirect |
| 17. C3⋊(#4175⋊C3) | D3 | semidirect |
| 18. C3⋊(#4175⋊C3) | C2×C3 | semidirect |
| 22. #13091158 | C2×C3 | semidirect |
| 23. #13091156 | C2×C3 | semidirect |
| 25. #13091154 | C2×C3 | semidirect |
| 33. #11757735 | C32 | semidirect |
| 36. C3×H(5,𝔽3) | C2×D3 | semidirect |
| 41. C3×#6909 | C2×D3 | semidirect |
| 42. C3×#6909 | C22×C3 | semidirect |
| 46. #10624761 | C22×C3 | semidirect |
| 47. C3⋊(C3⋊((C3⋊D3)⋊C3)) | C3×D3 | semidirect |
| 75. C3⋊#4183 | C2×C32 | semidirect |
| 80. C3⋊#4175 | C3×D3 | semidirect |
| 81. C3⋊#4175 | C2×C32 | semidirect |
| 103. C3×#4174 | C2×C32 | semidirect |
| 137. C32×H(3,𝔽3) | C2×C3×D3 | semidirect |
| 174. C3×AΣL(1,𝔽27) | C2×C3×D3 | semidirect |
| 175. C3×AΣL(1,𝔽27) | C22×C32 | semidirect |
| 176. C3⋊(C3⋊(C3⋊D3)) | C32×D3 | semidirect |
| 299. C34 | C2×C32×D3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#4175⋊C3 | 3 |
| #72243906 | 3 |
| C3×#66432⋊C3 | 3 |
| #72243679 | 2 |
| #72243630 | 2 |
| #72221974 | 3 |
| #72221895 | 2 |