Finite Group DatabasebetaFinite Group DatabasebetaOrder 11664.
13161 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 13161 conjugacy classes of subgroups — too many to draw. Only its 407 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 | C22×#11758090 | — | 3 | 4 | no | maximal |
| 2 | C22×#13091502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C22×#13091503 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#72214331 | C2 | 1 | 12 | yes | maximal, direct product factor |
| 5 | C22×H(3,𝔽3)2 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×#13091502 | C22 | 1 | 6 | yes | complemented |
| 7 | C2×#13091503 | C22 | 1 | 12 | yes | complemented |
| 8 | #72214331 | C22 | 1 | 16 | yes | direct product factor |
| 9 | C22×#11757731 | — | 3 | 4 | no | maximal |
| 10 | C22×C3×C3⋊#272 | — | 3 | 4 | no | — |
| 11 | C22×C3×C3⋊#272 | — | 6 | 2 | no | — |
| 12 | C22×C3⋊(C3⋊((C3⋊D3)⋊C3)) | D3 | 1 | 4 | yes | complemented |
| 13 | C22×C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 4 | no | — |
| 14 | C2×#11758090 | — | 3 | 48 | no | — |
| 15 | C22×#92338 | — | 3 | 4 | no | — |
| 16 | C22×#92338 | — | 6 | 2 | no | — |
| 17 | C22×#92338 | — | 6 | 8 | no | — |
| 18 | C22×#92338 | — | 6 | 4 | no | — |
| 19 | C22×#92301 | D3 | 1 | 4 | yes | complemented |
| 20 | C22×#92258 | — | 3 | 4 | no | — |
| 21 | C2×#11757731 | — | 3 | 48 | no | — |
| 22 | #13091503 | C23 | 1 | 8 | yes | complemented |
| 23 | #13091502 | C23 | 1 | 4 | yes | complemented |
| 24 | C2×H(3,𝔽3)2 | C23 | 1 | 3 | yes | complemented |
| 25 | C22×C3⋊#1113 | — | 9 | 2 | no | — |
| 26 | C22×C3⋊D32 | — | 9 | 2 | no | — |
| 27 | C22×#66432 | — | 9 | 2 | no | — |
| 28 | C22×#66432 | — | 9 | 8 | no | — |
| 29 | C22×#66432 | — | 9 | 4 | no | — |
| 30 | C22×((C3⋊D3)⋊C3)⋊D3 | — | 9 | 4 | no | — |
| 31 | C22×C32×H(3,𝔽3) | — | 2 | 2 | no | — |
| 32 | C22×C32×H(3,𝔽3) | C2×D3 | 1 | 4 | yes | complemented |
| 33 | C2×C3×C3⋊#272 | — | 3 | 24 | no | — |
| 34 | C2×C3×C3⋊#272 | — | 6 | 12 | no | — |
| 35 | C2×C3⋊(C3⋊((C3⋊D3)⋊C3)) | C2×D3 | 1 | 24 | yes | complemented |
| 36 | C2×C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 24 | no | — |
| 37 | #11758090 | — | 3 | 64 | no | — |
| 38 | C22×C32⋊H(3,𝔽3) | — | 2 | 2 | no | — |
| 39 | C22×C32⋊H(3,𝔽3) | — | 2 | 8 | no | — |
| 40 | C22×C32⋊H(3,𝔽3) | — | 2 | 4 | no | — |
| 41 | C22×C32⋊H(3,𝔽3) | C2×D3 | 1 | 4 | yes | complemented |
| 42 | C2×#92338 | — | 3 | 24 | no | — |
| 43 | C2×#92338 | — | 6 | 48 | no | — |
| 44 | C2×#92338 | — | 6 | 24 | no | — |
| 45 | C2×#92338 | — | 6 | 12 | no | — |
| 46 | C2×#92301 | C2×D3 | 1 | 24 | yes | complemented |
| 47 | C2×#92258 | — | 3 | 24 | no | — |
| 48 | #11757731 | — | 3 | 64 | no | — |
| 49 | H(3,𝔽3)2 | C24 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 50 | C22×C3⋊(C3⋊(C3⋊D3)) | C3⋊D3 | 1 | 2 | yes | complemented |
| 51 | C22×C3×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 52 | C22×C32×C3⋊D3 | — | 9 | 2 | no | — |
| 53 | C22×C32×C3⋊D3 | — | 9 | 2 | no | — |
| 54 | C22×C32×C3⋊D3 | — | 9 | 2 | no | — |
| 55 | C22×C32×C3⋊D3 | — | 18 | 4 | no | — |
| 56 | C22×C32×C3⋊D3 | — | 18 | 2 | no | — |
| 57 | C2×C3⋊#1113 | — | 9 | 24 | no | — |
| 58 | C2×C3⋊D32 | — | 9 | 24 | no | — |
| 59 | C22×C3⋊#272 | — | 3 | 4 | no | — |
| 60 | C22×C3⋊#272 | — | 6 | 2 | no | — |
| 61 | C22×C3×#272 | — | 9 | 2 | no | — |
| 62 | C22×C3×#272 | — | 9 | 4 | no | — |
| 63 | C22×C3×#272 | — | 9 | 8 | no | — |
| 64 | C22×C3×#272 | — | 18 | 8 | no | — |
| 65 | C22×C3×#272 | — | 18 | 8 | no | — |
| 66 | C22×C3×#272 | — | 18 | 4 | no | — |
| 67 | C22×C3×#272 | — | 18 | 8 | no | — |
| 68 | C22×C3×#272 | — | 18 | 2 | no | — |
| 69 | C22×C3×#272 | — | 18 | 8 | no | — |
| 70 | C22×C3×#272 | — | 18 | 4 | no | — |
| 71 | C22×C3×#272 | — | 18 | 8 | no | — |
| 72 | C22×C3⋊((C3⋊D3)⋊C3) | — | 3 | 4 | no | — |
| 73 | C22×C3⋊((C3⋊D3)⋊C3) | — | 3 | 8 | no | — |
| 74 | C22×C3⋊((C3⋊D3)⋊C3) | — | 3 | 8 | no | — |
| 75 | C22×C3⋊((C3⋊D3)⋊C3) | — | 3 | 8 | no | — |
| 76 | C22×C3⋊((C3⋊D3)⋊C3) | — | 9 | 4 | no | — |
| 77 | C22×C3⋊((C3⋊D3)⋊C3) | — | 18 | 4 | no | — |
| 78 | C22×C3×(C3⋊D3)⋊C3 | — | 9 | 4 | no | — |
| 79 | C22×C3×(C3⋊D3)⋊C3 | — | 18 | 4 | no | — |
| 80 | C2×#66432 | — | 9 | 24 | no | — |
| 81 | C2×#66432 | — | 9 | 96 | no | — |
| 82 | C2×#66432 | — | 9 | 48 | no | — |
| 83 | C2×((C3⋊D3)⋊C3)⋊D3 | — | 9 | 48 | no | — |
| 84 | C2×C32×H(3,𝔽3) | — | 2 | 6 | no | — |
| 85 | C2×C32×H(3,𝔽3) | C22×D3 | 1 | 12 | yes | complemented |
| 86 | C3×C3⋊#272 | — | 3 | 16 | no | — |
| 87 | C3×C3⋊#272 | — | 6 | 8 | no | — |
| 88 | C3⋊(C3⋊((C3⋊D3)⋊C3)) | C22×D3 | 1 | 16 | yes | complemented |
| 89 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 16 | no | — |
| 90 | C2×C32⋊H(3,𝔽3) | — | 2 | 6 | no | — |
| 91 | C2×C32⋊H(3,𝔽3) | — | 2 | 12 | no | — |
| 92 | C2×C32⋊H(3,𝔽3) | — | 2 | 24 | no | — |
| 93 | C2×C32⋊H(3,𝔽3) | C22×D3 | 1 | 12 | yes | complemented |
| 94 | #92338 | — | 3 | 16 | no | — |
| 95 | #92338 | — | 6 | 16 | no | — |
| 96 | #92338 | — | 6 | 32 | no | — |
| 97 | #92338 | — | 6 | 8 | no | — |
| 98 | #92301 | C22×D3 | 1 | 16 | yes | complemented |
| 99 | #92258 | — | 3 | 16 | no | — |
| 100 | C22×#1113 | — | 27 | 4 | no | — |
| 101 | C22×#1113 | — | 27 | 4 | no | — |
| 102 | C22×D3×C3⋊D3 | — | 27 | 4 | no | — |
| 103 | C22×D3×C3⋊D3 | — | 27 | 4 | no | — |
| 104 | C22×D3×C3⋊D3 | — | 27 | 4 | no | — |
| 105 | C22×D3×C3⋊D3 | — | 27 | 4 | no | — |
| 106 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 2 | no | — |
| 107 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 8 | no | — |
| 108 | C22×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 4 | no | — |
| 109 | C22×C34 | — | 2 | 2 | no | — |
| 110 | C22×C34 | — | 2 | 4 | no | — |
| 111 | C22×C34 | D32 | 1 | 2 | yes | complemented |
| 112 | C22×C34 | C2×C3⋊D3 | 1 | 2 | yes | complemented |
| 113 | C2×C3⋊(C3⋊(C3⋊D3)) | C2×C3⋊D3 | 1 | 12 | yes | complemented |
| 114 | C2×C3×C3⋊(C3⋊D3) | — | 3 | 24 | no | — |
| 115 | C2×C32×C3⋊D3 | — | 9 | 12 | no | — |
| 116 | C2×C32×C3⋊D3 | — | 9 | 12 | no | — |
| 117 | C2×C32×C3⋊D3 | — | 9 | 12 | no | — |
| 118 | C2×C32×C3⋊D3 | — | 18 | 24 | no | — |
| 119 | C2×C32×C3⋊D3 | — | 18 | 12 | no | — |
| 120 | C3⋊#1113 | — | 9 | 32 | no | — |
| 121 | C3⋊D32 | — | 9 | 32 | no | — |
| 122 | C22×C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 123 | C22×C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 124 | C22×C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 125 | C22×C3×H(3,𝔽3) | — | 2 | 4 | no | — |
| 126 | C22×C3×H(3,𝔽3) | — | 2 | 2 | no | — |
| 127 | C22×C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 128 | C22×C3×H(3,𝔽3) | — | 2 | 4 | no | — |
| 129 | C22×C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 130 | C22×C3×H(3,𝔽3) | — | 3 | 4 | no | — |
| 131 | C22×C3×H(3,𝔽3) | — | 6 | 4 | no | — |
| 132 | C22×C3×H(3,𝔽3) | — | 6 | 4 | no | — |
| 133 | C22×C3×H(3,𝔽3) | — | 6 | 2 | no | — |
| 134 | C22×C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 135 | C22×C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 136 | C22×C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 137 | C22×C3×H(3,𝔽3) | D32 | 1 | 2 | yes | — |
| 138 | C22×C3×H(3,𝔽3) | D32 | 1 | 8 | yes | complemented |
| 139 | C22×C3×H(3,𝔽3) | D32 | 1 | 4 | yes | complemented |
| 140 | C2×C3⋊#272 | — | 3 | 24 | no | — |
| 141 | C2×C3⋊#272 | — | 6 | 12 | no | — |
| 142 | C2×C3×#272 | — | 9 | 12 | no | — |
| 143 | C2×C3×#272 | — | 9 | 48 | no | — |
| 144 | C2×C3×#272 | — | 9 | 24 | no | — |
| 145 | C2×C3×#272 | — | 18 | 48 | no | — |
| 146 | C2×C3×#272 | — | 18 | 24 | no | — |
| 147 | C2×C3×#272 | — | 18 | 48 | no | — |
| 148 | C2×C3×#272 | — | 18 | 48 | no | — |
| 149 | C2×C3×#272 | — | 18 | 48 | no | — |
| 150 | C2×C3×#272 | — | 18 | 24 | no | — |
| 151 | C2×C3×#272 | — | 18 | 48 | no | — |
| 152 | C2×C3×#272 | — | 18 | 12 | no | — |
| 153 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 24 | no | — |
| 154 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 48 | no | — |
| 155 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 48 | no | — |
| 156 | C2×C3⋊((C3⋊D3)⋊C3) | — | 3 | 48 | no | — |
| 157 | C2×C3⋊((C3⋊D3)⋊C3) | — | 9 | 24 | no | — |
| 158 | C2×C3⋊((C3⋊D3)⋊C3) | — | 18 | 24 | no | — |
| 159 | C2×C3×(C3⋊D3)⋊C3 | — | 9 | 24 | no | — |
| 160 | C2×C3×(C3⋊D3)⋊C3 | — | 18 | 24 | no | — |
| 161 | #66432 | — | 9 | 32 | no | — |
| 162 | #66432 | — | 9 | 128 | no | — |
| 163 | #66432 | — | 9 | 64 | no | — |
| 164 | ((C3⋊D3)⋊C3)⋊D3 | — | 9 | 64 | no | — |
| 165 | C32×H(3,𝔽3) | — | 2 | 2 | no | — |
| 166 | C32×H(3,𝔽3) | C23×D3 | 1 | 4 | yes | complemented |
| 167 | C32⋊H(3,𝔽3) | — | 2 | 2 | no | — |
| 168 | C32⋊H(3,𝔽3) | — | 2 | 8 | no | — |
| 169 | C32⋊H(3,𝔽3) | — | 2 | 4 | no | — |
| 170 | C32⋊H(3,𝔽3) | C23×D3 | 1 | 4 | yes | complemented |
| 171 | C22×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 172 | C22×C3⋊(C3⋊D3) | — | 3 | 4 | no | — |
| 173 | C22×C3⋊(C3⋊D3) | — | 9 | 4 | no | — |
| 174 | C22×C3⋊(C3⋊D3) | — | 18 | 4 | no | — |
| 175 | C22×C3⋊(C3⋊D3) | — | 27 | 4 | no | — |
| 176 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 177 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 178 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 179 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 180 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 181 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 182 | C22×C3×C3⋊D3 | — | 9 | 4 | no | — |
| 183 | C22×C3×C3⋊D3 | — | 18 | 4 | no | — |
| 184 | C22×C3×C3⋊D3 | — | 18 | 4 | no | — |
| 185 | C22×C3×C3⋊D3 | — | 18 | 4 | no | — |
| 186 | C22×C3×C3⋊D3 | — | 18 | 4 | no | — |
| 187 | C22×C3×C3⋊D3 | — | 18 | 8 | no | — |
| 188 | C22×C3×C3⋊D3 | — | 18 | 2 | no | — |
| 189 | C22×C3×C3⋊D3 | — | 18 | 2 | no | — |
| 190 | C22×C3×C3⋊D3 | — | 27 | 4 | no | — |
| 191 | C22×C3×C3⋊D3 | — | 27 | 8 | no | — |
| 192 | C22×C32×D3 | — | 27 | 4 | no | — |
| 193 | C22×C32×D3 | — | 27 | 4 | no | — |
| 194 | C22×C32×D3 | — | 27 | 4 | no | — |
| 195 | C22×C32×D3 | — | 27 | 4 | no | — |
| 196 | C22×C32×D3 | — | 54 | 2 | no | — |
| 197 | C22×C32×D3 | — | 54 | 2 | no | — |
| 198 | C22×C32×D3 | — | 54 | 8 | no | — |
| 199 | C22×C32×D3 | — | 54 | 4 | no | — |
| 200 | C2×#1113 | — | 27 | 48 | no | — |
| 201 | C2×#1113 | — | 27 | 48 | no | — |
| 202 | C2×D3×C3⋊D3 | — | 27 | 48 | no | — |
| 203 | C2×D3×C3⋊D3 | — | 27 | 48 | no | — |
| 204 | C2×D3×C3⋊D3 | — | 27 | 48 | no | — |
| 205 | C2×D3×C3⋊D3 | — | 27 | 48 | no | — |
| 206 | C22×#272 | — | 9 | 8 | no | — |
| 207 | C22×#272 | — | 9 | 4 | no | — |
| 208 | C22×#272 | — | 9 | 2 | no | — |
| 209 | C22×#272 | — | 18 | 8 | no | — |
| 210 | C22×#272 | — | 18 | 4 | no | — |
| 211 | C22×#272 | — | 18 | 8 | no | — |
| 212 | C22×#272 | — | 18 | 8 | no | — |
| 213 | C22×#272 | — | 18 | 8 | no | — |
| 214 | C22×#272 | — | 18 | 8 | no | — |
| 215 | C22×#272 | — | 18 | 2 | no | — |
| 216 | C22×#272 | — | 18 | 4 | no | — |
| 217 | C22×(C3⋊D3)⋊C3 | — | 9 | 8 | no | — |
| 218 | C22×(C3⋊D3)⋊C3 | — | 9 | 4 | no | — |
| 219 | C22×(C3⋊D3)⋊C3 | — | 18 | 4 | no | — |
| 220 | C22×(C3⋊D3)⋊C3 | — | 18 | 8 | no | — |
| 221 | C22×(C3⋊D3)⋊C3 | — | 27 | 8 | no | — |
| 222 | C22×(C3⋊D3)⋊C3 | — | 27 | 8 | no | — |
| 223 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 24 | no | — |
| 224 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 96 | no | — |
| 225 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 48 | no | — |
| 226 | C2×C34 | — | 2 | 6 | no | — |
| 227 | C2×C34 | — | 2 | 12 | no | — |
| 228 | C2×C34 | C2×D32 | 1 | 6 | yes | complemented |
| 229 | C2×C34 | C22×C3⋊D3 | 1 | 6 | yes | complemented |
| 230 | C3⋊(C3⋊(C3⋊D3)) | C22×C3⋊D3 | 1 | 8 | yes | complemented |
| 231 | C3×C3⋊(C3⋊D3) | — | 3 | 16 | no | — |
| 232 | C32×C3⋊D3 | — | 9 | 8 | no | — |
| 233 | C32×C3⋊D3 | — | 9 | 8 | no | — |
| 234 | C32×C3⋊D3 | — | 9 | 8 | no | — |
| 235 | C32×C3⋊D3 | — | 18 | 16 | no | — |
| 236 | C32×C3⋊D3 | — | 18 | 8 | no | — |
| 237 | C2×C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 238 | C2×C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 239 | C2×C3×H(3,𝔽3) | — | 2 | 12 | no | — |
| 240 | C2×C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 241 | C2×C3×H(3,𝔽3) | — | 2 | 6 | no | — |
| 242 | C2×C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 243 | C2×C3×H(3,𝔽3) | — | 2 | 12 | no | — |
| 244 | C2×C3×H(3,𝔽3) | — | 2 | 24 | no | — |
| 245 | C2×C3×H(3,𝔽3) | — | 3 | 12 | no | — |
| 246 | C2×C3×H(3,𝔽3) | — | 6 | 12 | no | — |
| 247 | C2×C3×H(3,𝔽3) | — | 6 | 12 | no | — |
| 248 | C2×C3×H(3,𝔽3) | — | 6 | 6 | no | — |
| 249 | C2×C3×H(3,𝔽3) | — | 12 | 12 | no | — |
| 250 | C2×C3×H(3,𝔽3) | — | 12 | 12 | no | — |
| 251 | C2×C3×H(3,𝔽3) | — | 12 | 12 | no | — |
| 252 | C2×C3×H(3,𝔽3) | C2×D32 | 1 | 6 | yes | — |
| 253 | C2×C3×H(3,𝔽3) | C2×D32 | 1 | 24 | yes | complemented |
| 254 | C2×C3×H(3,𝔽3) | C2×D32 | 1 | 12 | yes | complemented |
| 255 | C3⋊#272 | — | 3 | 16 | no | — |
| 256 | C3⋊#272 | — | 6 | 8 | no | — |
| 257 | C3×#272 | — | 9 | 8 | no | — |
| 258 | C3×#272 | — | 9 | 16 | no | — |
| 259 | C3×#272 | — | 9 | 32 | no | — |
| 260 | C3×#272 | — | 18 | 32 | no | — |
| 261 | C3×#272 | — | 18 | 32 | no | — |
| 262 | C3×#272 | — | 18 | 32 | no | — |
| 263 | C3×#272 | — | 18 | 16 | no | — |
| 264 | C3×#272 | — | 18 | 16 | no | — |
| 265 | C3×#272 | — | 18 | 32 | no | — |
| 266 | C3×#272 | — | 18 | 8 | no | — |
| 267 | C3×#272 | — | 18 | 32 | no | — |
| 268 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 16 | no | — |
| 269 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 32 | no | — |
| 270 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 32 | no | — |
| 271 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 32 | no | — |
| 272 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 16 | no | — |
| 273 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 16 | no | — |
| 274 | C3×(C3⋊D3)⋊C3 | — | 9 | 16 | no | — |
| 275 | C3×(C3⋊D3)⋊C3 | — | 18 | 16 | no | — |
| 276 | C23×C3⋊D3 | — | 81 | 1 | no | — |
| 277 | C23×C3⋊D3 | — | 81 | 2 | no | — |
| 278 | C22×D32 | — | 81 | 4 | no | — |
| 279 | C22×D32 | — | 81 | 4 | no | — |
| 280 | C22×D32 | — | 81 | 8 | no | — |
| 281 | C22×D32 | — | 81 | 8 | no | — |
| 282 | C22×D32 | — | 81 | 8 | no | — |
| 283 | C22×D32 | — | 81 | 2 | no | — |
| 284 | C22×C33 | — | 2 | 2 | no | — |
| 285 | C22×C33 | — | 2 | 2 | no | — |
| 286 | C22×C33 | — | 2 | 8 | no | — |
| 287 | C22×C33 | — | 2 | 4 | no | — |
| 288 | C22×C33 | — | 3 | 4 | no | — |
| 289 | C22×C33 | — | 3 | 4 | no | — |
| 290 | C22×C33 | — | 6 | 4 | no | — |
| 291 | C22×C33 | — | 6 | 4 | no | — |
| 292 | C22×C33 | — | 6 | 4 | no | — |
| 293 | C22×C33 | — | 6 | 4 | no | — |
| 294 | C22×C33 | — | 6 | 4 | no | — |
| 295 | C22×C33 | — | 9 | 4 | no | — |
| 296 | C22×C33 | — | 9 | 4 | no | — |
| 297 | C22×C33 | — | 12 | 4 | no | — |
| 298 | C22×C33 | — | 12 | 4 | no | — |
| 299 | C22×C33 | — | 12 | 4 | no | — |
| 300 | C22×C33 | — | 18 | 8 | no | — |
| 301 | C22×C33 | — | 18 | 2 | no | — |
| 302 | C22×C33 | — | 18 | 2 | no | — |
| 303 | C22×C33 | D3×C3⋊D3 | 1 | 4 | yes | — |
| 304 | C22×C33 | D3×C3⋊D3 | 1 | 4 | yes | — |
| 305 | C2×C3⋊(C3⋊D3) | — | 3 | 24 | no | — |
| 306 | C2×C3⋊(C3⋊D3) | — | 3 | 24 | no | — |
| 307 | C2×C3⋊(C3⋊D3) | — | 9 | 24 | no | — |
| 308 | C2×C3⋊(C3⋊D3) | — | 18 | 24 | no | — |
| 309 | C2×C3⋊(C3⋊D3) | — | 27 | 24 | no | — |
| 310 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 311 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 312 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 313 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 314 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 315 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 316 | C2×C3×C3⋊D3 | — | 9 | 24 | no | — |
| 317 | C2×C3×C3⋊D3 | — | 18 | 24 | no | — |
| 318 | C2×C3×C3⋊D3 | — | 18 | 24 | no | — |
| 319 | C2×C3×C3⋊D3 | — | 18 | 24 | no | — |
| 320 | C2×C3×C3⋊D3 | — | 18 | 24 | no | — |
| 321 | C2×C3×C3⋊D3 | — | 18 | 48 | no | — |
| 322 | C2×C3×C3⋊D3 | — | 18 | 12 | no | — |
| 323 | C2×C3×C3⋊D3 | — | 18 | 12 | no | — |
| 324 | C2×C3×C3⋊D3 | — | 27 | 24 | no | — |
| 325 | C2×C3×C3⋊D3 | — | 27 | 48 | no | — |
| 326 | C2×C32×D3 | — | 27 | 24 | no | — |
| 327 | C2×C32×D3 | — | 27 | 24 | no | — |
| 328 | C2×C32×D3 | — | 27 | 24 | no | — |
| 329 | C2×C32×D3 | — | 27 | 24 | no | — |
| 330 | C2×C32×D3 | — | 54 | 48 | no | — |
| 331 | C2×C32×D3 | — | 54 | 24 | no | — |
| 332 | C2×C32×D3 | — | 54 | 12 | no | — |
| 333 | C2×C32×D3 | — | 54 | 12 | no | — |
| 334 | #1113 | — | 27 | 64 | no | — |
| 335 | #1113 | — | 27 | 64 | no | — |
| 336 | D3×C3⋊D3 | — | 27 | 64 | no | — |
| 337 | D3×C3⋊D3 | — | 27 | 64 | no | — |
| 338 | D3×C3⋊D3 | — | 27 | 64 | no | — |
| 339 | D3×C3⋊D3 | — | 27 | 64 | no | — |
| 340 | C22×H(3,𝔽3) | — | 2 | 4 | no | — |
| 341 | C22×H(3,𝔽3) | — | 3 | 8 | no | — |
| 342 | C22×H(3,𝔽3) | — | 4 | 2 | no | — |
| 343 | C22×H(3,𝔽3) | — | 6 | 8 | no | — |
| 344 | C22×H(3,𝔽3) | — | 6 | 8 | no | — |
| 345 | C22×H(3,𝔽3) | — | 6 | 8 | no | — |
| 346 | C22×H(3,𝔽3) | — | 6 | 4 | no | — |
| 347 | C22×H(3,𝔽3) | — | 6 | 8 | no | — |
| 348 | C22×H(3,𝔽3) | — | 9 | 4 | no | — |
| 349 | C22×H(3,𝔽3) | — | 12 | 4 | no | — |
| 350 | C22×H(3,𝔽3) | — | 12 | 8 | no | — |
| 351 | C22×H(3,𝔽3) | — | 12 | 8 | no | — |
| 352 | C22×H(3,𝔽3) | — | 12 | 8 | no | — |
| 353 | C22×H(3,𝔽3) | — | 18 | 8 | no | — |
| 354 | C22×H(3,𝔽3) | — | 18 | 8 | no | — |
| 355 | C22×H(3,𝔽3) | — | 18 | 2 | no | — |
| 356 | C22×H(3,𝔽3) | — | 18 | 4 | no | — |
| 357 | C22×H(3,𝔽3) | ((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | complemented |
| 358 | C2×#272 | — | 9 | 48 | no | — |
| 359 | C2×#272 | — | 9 | 24 | no | — |
| 360 | C2×#272 | — | 9 | 12 | no | — |
| 361 | C2×#272 | — | 18 | 48 | no | — |
| 362 | C2×#272 | — | 18 | 24 | no | — |
| 363 | C2×#272 | — | 18 | 48 | no | — |
| 364 | C2×#272 | — | 18 | 48 | no | — |
| 365 | C2×#272 | — | 18 | 48 | no | — |
| 366 | C2×#272 | — | 18 | 48 | no | — |
| 367 | C2×#272 | — | 18 | 12 | no | — |
| 368 | C2×#272 | — | 18 | 24 | no | — |
| 369 | C2×(C3⋊D3)⋊C3 | — | 9 | 48 | no | — |
| 370 | C2×(C3⋊D3)⋊C3 | — | 9 | 24 | no | — |
| 371 | C2×(C3⋊D3)⋊C3 | — | 18 | 24 | no | — |
| 372 | C2×(C3⋊D3)⋊C3 | — | 18 | 48 | no | — |
| 373 | C2×(C3⋊D3)⋊C3 | — | 27 | 48 | no | — |
| 374 | C2×(C3⋊D3)⋊C3 | — | 27 | 48 | no | — |
| 375 | ((C3⋊D3)⋊C3)⋊C2 | — | 27 | 32 | no | — |
| 376 | ((C3⋊D3)⋊C3)⋊C2 | — | 27 | 128 | no | — |
| 377 | ((C3⋊D3)⋊C3)⋊C2 | — | 27 | 64 | no | — |
| 378 | C34 | — | 2 | 2 | no | — |
| 379 | C34 | — | 2 | 4 | no | — |
| 380 | C34 | C22×D32 | 1 | 2 | yes | complemented |
| 381 | C34 | C23×C3⋊D3 | 1 | 2 | yes | complemented |
| 382 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 383 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 384 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 385 | C3×H(3,𝔽3) | — | 2 | 4 | no | — |
| 386 | C3×H(3,𝔽3) | — | 2 | 2 | no | — |
| 387 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 388 | C3×H(3,𝔽3) | — | 2 | 4 | no | — |
| 389 | C3×H(3,𝔽3) | — | 2 | 8 | no | — |
| 390 | C3×H(3,𝔽3) | — | 3 | 4 | no | — |
| 391 | C3×H(3,𝔽3) | — | 6 | 4 | no | — |
| 392 | C3×H(3,𝔽3) | — | 6 | 4 | no | — |
| 393 | C3×H(3,𝔽3) | — | 6 | 2 | no | — |
| 394 | C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 395 | C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 396 | C3×H(3,𝔽3) | — | 12 | 4 | no | — |
| 397 | C3×H(3,𝔽3) | C22×D32 | 1 | 2 | yes | — |
| 398 | C3×H(3,𝔽3) | C22×D32 | 1 | 8 | yes | complemented |
| 399 | C3×H(3,𝔽3) | C22×D32 | 1 | 4 | yes | complemented |
| 400 | C23×C32 | — | 81 | 2 | no | — |
| 401 | C23×C32 | — | 81 | 1 | no | — |
| 402 | C22×C3⋊D3 | — | 9 | 2 | no | — |
| 403 | C22×C3⋊D3 | — | 9 | 2 | no | — |
| 404 | C22×C3⋊D3 | — | 9 | 2 | no | — |
| 405 | C22×C3⋊D3 | — | 9 | 4 | no | — |
| 406 | C22×C3⋊D3 | — | 18 | 4 | no | — |
| 407 | C22×C3⋊D3 | — | 18 | 4 | no | — |
| 408 | C22×C3⋊D3 | — | 18 | 2 | no | — |
| 409 | C22×C3⋊D3 | — | 27 | 4 | no | — |
| 410 | C22×C3⋊D3 | — | 27 | 8 | no | — |
| 411 | C22×C3⋊D3 | — | 27 | 8 | no | — |
| 412 | C22×C3⋊D3 | — | 27 | 8 | no | — |
| 413 | C22×C3⋊D3 | — | 81 | 2 | no | — |
| 414 | C22×C3⋊D3 | — | 81 | 12 | no | — |
| 415 | C22×C3⋊D3 | — | 81 | 24 | no | — |
| 416 | C22×C3⋊D3 | — | 162 | 4 | no | — |
| 417 | C22×C3⋊D3 | — | 162 | 4 | no | — |
| 418 | C22×C3×D3 | — | 27 | 8 | no | — |
| 419 | C22×C3×D3 | — | 27 | 8 | no | — |
| 420 | C22×C3×D3 | — | 27 | 8 | no | — |
| 421 | C22×C3×D3 | — | 27 | 8 | no | — |
| 422 | C22×C3×D3 | — | 27 | 4 | no | — |
| 423 | C22×C3×D3 | — | 27 | 8 | no | — |
| 424 | C22×C3×D3 | — | 27 | 4 | no | — |
| 425 | C22×C3×D3 | — | 27 | 8 | no | — |
| 426 | C22×C3×D3 | — | 27 | 4 | no | — |
| 427 | C22×C3×D3 | — | 27 | 4 | no | — |
| 428 | C22×C3×D3 | — | 54 | 2 | no | — |
| 429 | C22×C3×D3 | — | 54 | 8 | no | — |
| 430 | C22×C3×D3 | — | 54 | 4 | no | — |
| 431 | C22×C3×D3 | — | 54 | 4 | no | — |
| 432 | C22×C3×D3 | — | 54 | 4 | no | — |
| 433 | C22×C3×D3 | — | 54 | 8 | no | — |
| 434 | C22×C3×D3 | — | 54 | 8 | no | — |
| 435 | C22×C3×D3 | — | 54 | 4 | no | — |
| 436 | C22×C3×D3 | — | 54 | 16 | no | — |
| 437 | C22×C3×D3 | — | 54 | 2 | no | — |
| 438 | C22×C3×D3 | — | 54 | 4 | no | — |
| 439 | C22×C3×D3 | — | 81 | 4 | no | — |
| 440 | C22×C3×D3 | — | 162 | 4 | no | — |
| 441 | C2×D32 | — | 81 | 48 | no | — |
| 442 | C2×D32 | — | 81 | 96 | no | — |
| 443 | C2×D32 | — | 81 | 96 | no | — |
| 444 | C2×D32 | — | 81 | 48 | no | — |
| 445 | C2×D32 | — | 81 | 96 | no | — |
| 446 | C2×D32 | — | 81 | 24 | no | — |
| 447 | C2×C33 | — | 2 | 6 | no | — |
| 448 | C2×C33 | — | 2 | 6 | no | — |
| 449 | C2×C33 | — | 2 | 24 | no | — |
| 450 | C2×C33 | — | 2 | 12 | no | — |
| 451 | C2×C33 | — | 3 | 12 | no | — |
| 452 | C2×C33 | — | 3 | 12 | no | — |
| 453 | C2×C33 | — | 6 | 12 | no | — |
| 454 | C2×C33 | — | 6 | 12 | no | — |
| 455 | C2×C33 | — | 6 | 12 | no | — |
| 456 | C2×C33 | — | 6 | 12 | no | — |
| 457 | C2×C33 | — | 6 | 12 | no | — |
| 458 | C2×C33 | — | 9 | 12 | no | — |
| 459 | C2×C33 | — | 9 | 12 | no | — |
| 460 | C2×C33 | — | 12 | 12 | no | — |
| 461 | C2×C33 | — | 12 | 12 | no | — |
| 462 | C2×C33 | — | 12 | 12 | no | — |
| 463 | C2×C33 | — | 18 | 24 | no | — |
| 464 | C2×C33 | — | 18 | 6 | no | — |
| 465 | C2×C33 | — | 18 | 6 | no | — |
| 466 | C2×C33 | C2×D3×C3⋊D3 | 1 | 12 | yes | — |
| 467 | C2×C33 | C2×D3×C3⋊D3 | 1 | 12 | yes | — |
| 468 | C3⋊(C3⋊D3) | — | 3 | 16 | no | — |
| 469 | C3⋊(C3⋊D3) | — | 3 | 16 | no | — |
| 470 | C3⋊(C3⋊D3) | — | 9 | 16 | no | — |
| 471 | C3⋊(C3⋊D3) | — | 18 | 16 | no | — |
| 472 | C3⋊(C3⋊D3) | — | 27 | 16 | no | — |
| 473 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 474 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 475 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 476 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 477 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 478 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 479 | C3×C3⋊D3 | — | 9 | 16 | no | — |
| 480 | C3×C3⋊D3 | — | 18 | 16 | no | — |
| 481 | C3×C3⋊D3 | — | 18 | 16 | no | — |
| 482 | C3×C3⋊D3 | — | 18 | 32 | no | — |
| 483 | C3×C3⋊D3 | — | 18 | 16 | no | — |
| 484 | C3×C3⋊D3 | — | 18 | 16 | no | — |
| 485 | C3×C3⋊D3 | — | 18 | 8 | no | — |
| 486 | C3×C3⋊D3 | — | 18 | 8 | no | — |
| 487 | C3×C3⋊D3 | — | 27 | 16 | no | — |
| 488 | C3×C3⋊D3 | — | 27 | 32 | no | — |
| 489 | C32×D3 | — | 27 | 16 | no | — |
| 490 | C32×D3 | — | 27 | 16 | no | — |
| 491 | C32×D3 | — | 27 | 16 | no | — |
| 492 | C32×D3 | — | 27 | 16 | no | — |
| 493 | C32×D3 | — | 54 | 16 | no | — |
| 494 | C32×D3 | — | 54 | 32 | no | — |
| 495 | C32×D3 | — | 54 | 8 | no | — |
| 496 | C32×D3 | — | 54 | 8 | no | — |
| 497 | C2×H(3,𝔽3) | — | 2 | 12 | no | — |
| 498 | C2×H(3,𝔽3) | — | 3 | 24 | no | — |
| 499 | C2×H(3,𝔽3) | — | 4 | 6 | no | — |
| 500 | C2×H(3,𝔽3) | — | 6 | 24 | no | — |
| 501 | C2×H(3,𝔽3) | — | 6 | 24 | no | — |
| 502 | C2×H(3,𝔽3) | — | 6 | 24 | no | — |
| 503 | C2×H(3,𝔽3) | — | 6 | 12 | no | — |
| 504 | C2×H(3,𝔽3) | — | 6 | 24 | no | — |
| 505 | C2×H(3,𝔽3) | — | 9 | 12 | no | — |
| 506 | C2×H(3,𝔽3) | — | 12 | 12 | no | — |
| 507 | C2×H(3,𝔽3) | — | 12 | 24 | no | — |
| 508 | C2×H(3,𝔽3) | — | 12 | 24 | no | — |
| 509 | C2×H(3,𝔽3) | — | 12 | 24 | no | — |
| 510 | C2×H(3,𝔽3) | — | 18 | 24 | no | — |
| 511 | C2×H(3,𝔽3) | — | 18 | 24 | no | — |
| 512 | C2×H(3,𝔽3) | — | 18 | 6 | no | — |
| 513 | C2×H(3,𝔽3) | — | 18 | 12 | no | — |
| 514 | C2×H(3,𝔽3) | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 6 | yes | complemented |
| 515 | #272 | — | 9 | 32 | no | — |
| 516 | #272 | — | 9 | 16 | no | — |
| 517 | #272 | — | 9 | 8 | no | — |
| 518 | #272 | — | 18 | 32 | no | — |
| 519 | #272 | — | 18 | 16 | no | — |
| 520 | #272 | — | 18 | 32 | no | — |
| 521 | #272 | — | 18 | 32 | no | — |
| 522 | #272 | — | 18 | 32 | no | — |
| 523 | #272 | — | 18 | 32 | no | — |
| 524 | #272 | — | 18 | 8 | no | — |
| 525 | #272 | — | 18 | 16 | no | — |
| 526 | (C3⋊D3)⋊C3 | — | 9 | 32 | no | — |
| 527 | (C3⋊D3)⋊C3 | — | 9 | 16 | no | — |
| 528 | (C3⋊D3)⋊C3 | — | 18 | 16 | no | — |
| 529 | (C3⋊D3)⋊C3 | — | 18 | 32 | no | — |
| 530 | (C3⋊D3)⋊C3 | — | 27 | 32 | no | — |
| 531 | (C3⋊D3)⋊C3 | — | 27 | 32 | no | — |
| 532 | C23×D3 | — | 243 | 2 | no | — |
| 533 | C23×D3 | — | 243 | 2 | no | — |
| 534 | C23×D3 | — | 243 | 4 | no | — |
| 535 | C23×D3 | — | 243 | 4 | no | — |
| 536 | C22×C32 | — | 2 | 4 | no | — |
| 537 | C22×C32 | — | 2 | 2 | no | — |
| 538 | C22×C32 | — | 3 | 4 | no | — |
| 539 | C22×C32 | — | 3 | 8 | no | — |
| 540 | C22×C32 | — | 3 | 8 | no | — |
| 541 | C22×C32 | — | 3 | 8 | no | — |
| 542 | C22×C32 | — | 4 | 2 | no | — |
| 543 | C22×C32 | — | 6 | 2 | no | — |
| 544 | C22×C32 | — | 6 | 4 | no | — |
| 545 | C22×C32 | — | 6 | 8 | no | — |
| 546 | C22×C32 | — | 6 | 4 | no | — |
| 547 | C22×C32 | — | 6 | 8 | no | — |
| 548 | C22×C32 | — | 6 | 8 | no | — |
| 549 | C22×C32 | — | 6 | 4 | no | — |
| 550 | C22×C32 | — | 6 | 4 | no | — |
| 551 | C22×C32 | — | 6 | 4 | no | — |
| 552 | C22×C32 | — | 6 | 16 | no | — |
| 553 | C22×C32 | — | 9 | 2 | no | — |
| 554 | C22×C32 | — | 9 | 2 | no | — |
| 555 | C22×C32 | — | 18 | 4 | no | — |
| 556 | C22×C32 | — | 18 | 4 | no | — |
| 557 | C22×C32 | — | 18 | 4 | no | — |
| 558 | C22×C32 | — | 18 | 4 | no | — |
| 559 | C22×C32 | — | 18 | 2 | no | — |
| 560 | C22×C32 | — | 36 | 4 | no | — |
| 561 | C22×C32 | — | 36 | 4 | no | — |
| 562 | C22×C32 | — | 36 | 2 | no | — |
| 563 | C22×C32 | — | 36 | 4 | no | — |
| 564 | C22×C32 | — | 36 | 8 | no | — |
| 565 | C22×C32 | — | 36 | 4 | no | — |
| 566 | C22×C32 | — | 81 | 12 | no | — |
| 567 | C22×C32 | — | 81 | 6 | no | — |
| 568 | C22×C32 | ((C3⋊D3)⋊C3)⋊D3 | 1 | 4 | yes | complemented |
| 569 | C22×C32 | C3⋊D32 | 1 | 1 | yes | characteristic |
| 570 | C2×C3⋊D3 | — | 9 | 12 | no | — |
| 571 | C2×C3⋊D3 | — | 9 | 12 | no | — |
| 572 | C2×C3⋊D3 | — | 9 | 12 | no | — |
| 573 | C2×C3⋊D3 | — | 9 | 24 | no | — |
| 574 | C2×C3⋊D3 | — | 18 | 24 | no | — |
| 575 | C2×C3⋊D3 | — | 18 | 24 | no | — |
| 576 | C2×C3⋊D3 | — | 18 | 12 | no | — |
| 577 | C2×C3⋊D3 | — | 27 | 24 | no | — |
| 578 | C2×C3⋊D3 | — | 27 | 48 | no | — |
| 579 | C2×C3⋊D3 | — | 27 | 48 | no | — |
| 580 | C2×C3⋊D3 | — | 27 | 48 | no | — |
| 581 | C2×C3⋊D3 | — | 81 | 12 | no | — |
| 582 | C2×C3⋊D3 | — | 81 | 16 | no | — |
| 583 | C2×C3⋊D3 | — | 81 | 32 | no | — |
| 584 | C2×C3⋊D3 | — | 162 | 24 | no | — |
| 585 | C2×C3⋊D3 | — | 162 | 24 | no | — |
| 586 | C2×C3×D3 | — | 27 | 48 | no | — |
| 587 | C2×C3×D3 | — | 27 | 48 | no | — |
| 588 | C2×C3×D3 | — | 27 | 48 | no | — |
| 589 | C2×C3×D3 | — | 27 | 48 | no | — |
| 590 | C2×C3×D3 | — | 27 | 24 | no | — |
| 591 | C2×C3×D3 | — | 27 | 48 | no | — |
| 592 | C2×C3×D3 | — | 27 | 24 | no | — |
| 593 | C2×C3×D3 | — | 27 | 48 | no | — |
| 594 | C2×C3×D3 | — | 27 | 24 | no | — |
| 595 | C2×C3×D3 | — | 27 | 24 | no | — |
| 596 | C2×C3×D3 | — | 54 | 12 | no | — |
| 597 | C2×C3×D3 | — | 54 | 48 | no | — |
| 598 | C2×C3×D3 | — | 54 | 24 | no | — |
| 599 | C2×C3×D3 | — | 54 | 24 | no | — |
| 600 | C2×C3×D3 | — | 54 | 24 | no | — |
| 601 | C2×C3×D3 | — | 54 | 48 | no | — |
| 602 | C2×C3×D3 | — | 54 | 48 | no | — |
| 603 | C2×C3×D3 | — | 54 | 24 | no | — |
| 604 | C2×C3×D3 | — | 54 | 96 | no | — |
| 605 | C2×C3×D3 | — | 54 | 12 | no | — |
| 606 | C2×C3×D3 | — | 54 | 24 | no | — |
| 607 | C2×C3×D3 | — | 81 | 24 | no | — |
| 608 | C2×C3×D3 | — | 162 | 24 | no | — |
| 609 | D32 | — | 81 | 64 | no | — |
| 610 | D32 | — | 81 | 128 | no | — |
| 611 | D32 | — | 81 | 128 | no | — |
| 612 | D32 | — | 81 | 64 | no | — |
| 613 | D32 | — | 81 | 128 | no | — |
| 614 | D32 | — | 81 | 32 | no | — |
| 615 | C33 | — | 2 | 2 | no | — |
| 616 | C33 | — | 2 | 2 | no | — |
| 617 | C33 | — | 2 | 4 | no | — |
| 618 | C33 | — | 2 | 8 | no | — |
| 619 | C33 | — | 3 | 4 | no | — |
| 620 | C33 | — | 3 | 4 | no | — |
| 621 | C33 | — | 6 | 4 | no | — |
| 622 | C33 | — | 6 | 4 | no | — |
| 623 | C33 | — | 6 | 4 | no | — |
| 624 | C33 | — | 6 | 4 | no | — |
| 625 | C33 | — | 6 | 4 | no | — |
| 626 | C33 | — | 9 | 4 | no | — |
| 627 | C33 | — | 9 | 4 | no | — |
| 628 | C33 | — | 12 | 4 | no | — |
| 629 | C33 | — | 12 | 4 | no | — |
| 630 | C33 | — | 12 | 4 | no | — |
| 631 | C33 | — | 18 | 8 | no | — |
| 632 | C33 | — | 18 | 2 | no | — |
| 633 | C33 | — | 18 | 2 | no | — |
| 634 | C33 | C22×D3×C3⋊D3 | 1 | 4 | yes | — |
| 635 | C33 | C22×D3×C3⋊D3 | 1 | 4 | yes | — |
| 636 | H(3,𝔽3) | — | 2 | 4 | no | — |
| 637 | H(3,𝔽3) | — | 3 | 8 | no | — |
| 638 | H(3,𝔽3) | — | 4 | 2 | no | — |
| 639 | H(3,𝔽3) | — | 6 | 8 | no | — |
| 640 | H(3,𝔽3) | — | 6 | 8 | no | — |
| 641 | H(3,𝔽3) | — | 6 | 8 | no | — |
| 642 | H(3,𝔽3) | — | 6 | 4 | no | — |
| 643 | H(3,𝔽3) | — | 6 | 8 | no | — |
| 644 | H(3,𝔽3) | — | 9 | 4 | no | — |
| 645 | H(3,𝔽3) | — | 12 | 4 | no | — |
| 646 | H(3,𝔽3) | — | 12 | 8 | no | — |
| 647 | H(3,𝔽3) | — | 12 | 8 | no | — |
| 648 | H(3,𝔽3) | — | 12 | 8 | no | — |
| 649 | H(3,𝔽3) | — | 18 | 8 | no | — |
| 650 | H(3,𝔽3) | — | 18 | 8 | no | — |
| 651 | H(3,𝔽3) | — | 18 | 2 | no | — |
| 652 | H(3,𝔽3) | — | 18 | 4 | no | — |
| 653 | H(3,𝔽3) | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 2 | yes | complemented |
| 654 | C23×C3 | — | 81 | 4 | no | — |
| 655 | C23×C3 | — | 81 | 4 | no | — |
| 656 | C23×C3 | — | 81 | 2 | no | — |
| 657 | C23×C3 | — | 81 | 2 | no | — |
| 658 | C22×D3 | — | 27 | 4 | no | — |
| 659 | C22×D3 | — | 27 | 4 | no | — |
| 660 | C22×D3 | — | 27 | 4 | no | — |
| 661 | C22×D3 | — | 27 | 4 | no | — |
| 662 | C22×D3 | — | 54 | 2 | no | — |
| 663 | C22×D3 | — | 54 | 2 | no | — |
| 664 | C22×D3 | — | 54 | 8 | no | — |
| 665 | C22×D3 | — | 54 | 4 | no | — |
| 666 | C22×D3 | — | 81 | 4 | no | — |
| 667 | C22×D3 | — | 162 | 4 | no | — |
| 668 | C22×D3 | — | 243 | 4 | no | — |
| 669 | C22×D3 | — | 243 | 24 | no | — |
| 670 | C22×D3 | — | 243 | 24 | no | — |
| 671 | C22×D3 | — | 243 | 48 | no | — |
| 672 | C22×D3 | — | 243 | 48 | no | — |
| 673 | C2×C32 | — | 2 | 12 | no | — |
| 674 | C2×C32 | — | 2 | 6 | no | — |
| 675 | C2×C32 | — | 3 | 12 | no | — |
| 676 | C2×C32 | — | 3 | 24 | no | — |
| 677 | C2×C32 | — | 3 | 24 | no | — |
| 678 | C2×C32 | — | 3 | 24 | no | — |
| 679 | C2×C32 | — | 4 | 6 | no | — |
| 680 | C2×C32 | — | 6 | 6 | no | — |
| 681 | C2×C32 | — | 6 | 12 | no | — |
| 682 | C2×C32 | — | 6 | 24 | no | — |
| 683 | C2×C32 | — | 6 | 12 | no | — |
| 684 | C2×C32 | — | 6 | 24 | no | — |
| 685 | C2×C32 | — | 6 | 24 | no | — |
| 686 | C2×C32 | — | 6 | 12 | no | — |
| 687 | C2×C32 | — | 6 | 12 | no | — |
| 688 | C2×C32 | — | 6 | 12 | no | — |
| 689 | C2×C32 | — | 6 | 48 | no | — |
| 690 | C2×C32 | — | 9 | 6 | no | — |
| 691 | C2×C32 | — | 9 | 6 | no | — |
| 692 | C2×C32 | — | 18 | 12 | no | — |
| 693 | C2×C32 | — | 18 | 12 | no | — |
| 694 | C2×C32 | — | 18 | 12 | no | — |
| 695 | C2×C32 | — | 18 | 12 | no | — |
| 696 | C2×C32 | — | 18 | 6 | no | — |
| 697 | C2×C32 | — | 36 | 12 | no | — |
| 698 | C2×C32 | — | 36 | 12 | no | — |
| 699 | C2×C32 | — | 36 | 6 | no | — |
| 700 | C2×C32 | — | 36 | 12 | no | — |
| 701 | C2×C32 | — | 36 | 24 | no | — |
| 702 | C2×C32 | — | 36 | 12 | no | — |
| 703 | C2×C32 | — | 81 | 8 | no | — |
| 704 | C2×C32 | — | 81 | 4 | no | — |
| 705 | C2×C32 | C2×((C3⋊D3)⋊C3)⋊D3 | 1 | 12 | yes | complemented |
| 706 | C2×C32 | C2×C3⋊D32 | 1 | 3 | yes | — |
| 707 | C3⋊D3 | — | 9 | 8 | no | — |
| 708 | C3⋊D3 | — | 9 | 8 | no | — |
| 709 | C3⋊D3 | — | 9 | 8 | no | — |
| 710 | C3⋊D3 | — | 9 | 16 | no | — |
| 711 | C3⋊D3 | — | 18 | 16 | no | — |
| 712 | C3⋊D3 | — | 18 | 16 | no | — |
| 713 | C3⋊D3 | — | 18 | 8 | no | — |
| 714 | C3⋊D3 | — | 27 | 16 | no | — |
| 715 | C3⋊D3 | — | 27 | 32 | no | — |
| 716 | C3⋊D3 | — | 27 | 32 | no | — |
| 717 | C3⋊D3 | — | 27 | 32 | no | — |
| 718 | C3⋊D3 | — | 81 | 8 | no | — |
| 719 | C3⋊D3 | — | 162 | 16 | no | — |
| 720 | C3⋊D3 | — | 162 | 16 | no | — |
| 721 | C3×D3 | — | 27 | 32 | no | — |
| 722 | C3×D3 | — | 27 | 32 | no | — |
| 723 | C3×D3 | — | 27 | 32 | no | — |
| 724 | C3×D3 | — | 27 | 32 | no | — |
| 725 | C3×D3 | — | 27 | 32 | no | — |
| 726 | C3×D3 | — | 27 | 16 | no | — |
| 727 | C3×D3 | — | 27 | 16 | no | — |
| 728 | C3×D3 | — | 27 | 32 | no | — |
| 729 | C3×D3 | — | 27 | 16 | no | — |
| 730 | C3×D3 | — | 27 | 16 | no | — |
| 731 | C3×D3 | — | 54 | 8 | no | — |
| 732 | C3×D3 | — | 54 | 16 | no | — |
| 733 | C3×D3 | — | 54 | 32 | no | — |
| 734 | C3×D3 | — | 54 | 16 | no | — |
| 735 | C3×D3 | — | 54 | 16 | no | — |
| 736 | C3×D3 | — | 54 | 16 | no | — |
| 737 | C3×D3 | — | 54 | 64 | no | — |
| 738 | C3×D3 | — | 54 | 32 | no | — |
| 739 | C3×D3 | — | 54 | 32 | no | — |
| 740 | C3×D3 | — | 54 | 16 | no | — |
| 741 | C3×D3 | — | 54 | 8 | no | — |
| 742 | C3×D3 | — | 81 | 16 | no | — |
| 743 | C3×D3 | — | 162 | 16 | no | — |
| 744 | C24 | — | 729 | 1 | no | Sylow |
| 745 | C22×C3 | — | 3 | 4 | no | — |
| 746 | C22×C3 | — | 6 | 2 | no | — |
| 747 | C22×C3 | — | 6 | 4 | no | — |
| 748 | C22×C3 | — | 9 | 4 | no | — |
| 749 | C22×C3 | — | 12 | 2 | no | — |
| 750 | C22×C3 | — | 18 | 2 | no | — |
| 751 | C22×C3 | — | 18 | 8 | no | — |
| 752 | C22×C3 | — | 18 | 4 | no | — |
| 753 | C22×C3 | — | 81 | 24 | no | — |
| 754 | C22×C3 | — | 81 | 24 | no | — |
| 755 | C22×C3 | — | 81 | 12 | no | — |
| 756 | C22×C3 | — | 81 | 12 | no | — |
| 757 | C22×C3 | #11758084 | 1 | 2 | yes | — |
| 758 | C22×C3 | #11758086 | 1 | 2 | yes | — |
| 759 | C2×D3 | — | 27 | 24 | no | — |
| 760 | C2×D3 | — | 27 | 24 | no | — |
| 761 | C2×D3 | — | 27 | 24 | no | — |
| 762 | C2×D3 | — | 27 | 24 | no | — |
| 763 | C2×D3 | — | 54 | 12 | no | — |
| 764 | C2×D3 | — | 54 | 12 | no | — |
| 765 | C2×D3 | — | 54 | 48 | no | — |
| 766 | C2×D3 | — | 54 | 24 | no | — |
| 767 | C2×D3 | — | 81 | 24 | no | — |
| 768 | C2×D3 | — | 162 | 24 | no | — |
| 769 | C2×D3 | — | 243 | 24 | no | — |
| 770 | C2×D3 | — | 243 | 32 | no | — |
| 771 | C2×D3 | — | 243 | 32 | no | — |
| 772 | C2×D3 | — | 243 | 64 | no | — |
| 773 | C2×D3 | — | 243 | 64 | no | — |
| 774 | C32 | — | 2 | 2 | no | — |
| 775 | C32 | — | 2 | 4 | no | — |
| 776 | C32 | — | 3 | 8 | no | — |
| 777 | C32 | — | 3 | 4 | no | — |
| 778 | C32 | — | 3 | 8 | no | — |
| 779 | C32 | — | 3 | 8 | no | — |
| 780 | C32 | — | 4 | 2 | no | — |
| 781 | C32 | — | 6 | 4 | no | — |
| 782 | C32 | — | 6 | 2 | no | — |
| 783 | C32 | — | 6 | 4 | no | — |
| 784 | C32 | — | 6 | 4 | no | — |
| 785 | C32 | — | 6 | 4 | no | — |
| 786 | C32 | — | 6 | 16 | no | — |
| 787 | C32 | — | 6 | 8 | no | — |
| 788 | C32 | — | 6 | 4 | no | — |
| 789 | C32 | — | 6 | 8 | no | — |
| 790 | C32 | — | 6 | 8 | no | — |
| 791 | C32 | — | 9 | 2 | no | — |
| 792 | C32 | — | 9 | 2 | no | — |
| 793 | C32 | — | 18 | 4 | no | — |
| 794 | C32 | — | 18 | 4 | no | — |
| 795 | C32 | — | 18 | 4 | no | — |
| 796 | C32 | — | 18 | 4 | no | — |
| 797 | C32 | — | 18 | 2 | no | — |
| 798 | C32 | — | 36 | 4 | no | — |
| 799 | C32 | — | 36 | 2 | no | — |
| 800 | C32 | — | 36 | 4 | no | — |
| 801 | C32 | — | 36 | 4 | no | — |
| 802 | C32 | — | 36 | 8 | no | — |
| 803 | C32 | — | 36 | 4 | no | — |
| 804 | C32 | C22×((C3⋊D3)⋊C3)⋊D3 | 1 | 4 | yes | complemented |
| 805 | C32 | C22×C3⋊D32 | 1 | 1 | yes | characteristic |
| 806 | C23 | — | 81 | 1 | no | — |
| 807 | C23 | — | 81 | 2 | no | — |
| 808 | C23 | — | 729 | 12 | no | — |
| 809 | C2×C3 | — | 3 | 12 | no | — |
| 810 | C2×C3 | — | 6 | 6 | no | — |
| 811 | C2×C3 | — | 6 | 12 | no | — |
| 812 | C2×C3 | — | 9 | 12 | no | — |
| 813 | C2×C3 | — | 12 | 6 | no | — |
| 814 | C2×C3 | — | 18 | 6 | no | — |
| 815 | C2×C3 | — | 18 | 24 | no | — |
| 816 | C2×C3 | — | 18 | 12 | no | — |
| 817 | C2×C3 | — | 81 | 16 | no | — |
| 818 | C2×C3 | — | 81 | 16 | no | — |
| 819 | C2×C3 | — | 81 | 8 | no | — |
| 820 | C2×C3 | — | 81 | 8 | no | — |
| 821 | C2×C3 | C2×#11758084 | 1 | 6 | yes | — |
| 822 | C2×C3 | C2×#11758086 | 1 | 6 | yes | — |
| 823 | D3 | — | 27 | 16 | no | — |
| 824 | D3 | — | 27 | 16 | no | — |
| 825 | D3 | — | 27 | 16 | no | — |
| 826 | D3 | — | 27 | 16 | no | — |
| 827 | D3 | — | 54 | 8 | no | — |
| 828 | D3 | — | 54 | 8 | no | — |
| 829 | D3 | — | 54 | 32 | no | — |
| 830 | D3 | — | 54 | 16 | no | — |
| 831 | D3 | — | 81 | 16 | no | — |
| 832 | D3 | — | 162 | 16 | no | — |
| 833 | D3 | — | 243 | 16 | no | — |
| 834 | C22 | — | 81 | 6 | no | — |
| 835 | C22 | — | 81 | 12 | no | — |
| 836 | C22 | — | 729 | 16 | no | — |
| 837 | C22 | #72214331 | 1 | 1 | yes | characteristic, direct product factor |
| 838 | C3 | — | 3 | 4 | no | — |
| 839 | C3 | — | 6 | 2 | no | — |
| 840 | C3 | — | 6 | 4 | no | — |
| 841 | C3 | — | 9 | 4 | no | — |
| 842 | C3 | — | 12 | 2 | no | — |
| 843 | C3 | — | 18 | 2 | no | — |
| 844 | C3 | — | 18 | 4 | no | — |
| 845 | C3 | — | 18 | 8 | no | — |
| 846 | C3 | C22×#11758086 | 1 | 2 | yes | — |
| 847 | C3 | C22×#11758084 | 1 | 2 | yes | — |
| 848 | C2 | — | 81 | 4 | no | — |
| 849 | C2 | — | 81 | 8 | no | — |
| 850 | C2 | C2×#72214331 | 1 | 3 | yes | direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #72214331 |
| commutator, cosocle, hypocenter | H(3,𝔽3)2 | C24 |
| Frattini | C32 | C22×C3⋊D32 |
| Fitting | C22×H(3,𝔽3)2 | C22 |
| socle | C22×C32 | C3⋊D32 |
| LCS | G ▷ H(3,𝔽3)2 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#11758090 | 3 |
| C22×#13091502 | 2 |
| C22×#13091503 | 2 |
| C2×#72214331 | 2 |
| C22×#11757731 | 3 |