Finite Group DatabasebetaFinite Group Databasebeta← C3×((C3⋊D3)⋊C3)⋊D9 #72269340
Order 2916.
757 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 757 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C3×C9⋊#272 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#92297 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×C9×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#66431 | — | 3 | 1 | no | maximal |
| 5 | C3×((C3⋊D3)⋊C3)⋊D3 | — | 3 | 1 | no | maximal |
| 6 | C3×D3×C3⋊D9 | — | 3 | 1 | no | maximal |
| 7 | ((C3⋊D3)⋊C3)⋊D9 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 8 | C3×((C3⋊D3)⋊C9)⋊C2 | — | 3 | 1 | no | maximal |
| 9 | C3×((C3⋊D3)⋊C9)⋊C2 | — | 3 | 1 | no | maximal |
| 10 | C3×C9×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C3×C3⋊#272 | — | 3 | 1 | no | — |
| 12 | C3×C3⋊(C3⋊D9) | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 14 | C3×C9×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C32×C3⋊D9 | — | 3 | 1 | no | — |
| 16 | C32×C3⋊D9 | — | 3 | 1 | no | — |
| 17 | C32×C3⋊D9 | — | 3 | 1 | no | — |
| 18 | C32×C3⋊D9 | — | 6 | 1 | no | — |
| 19 | C32×(C3⋊D3)⋊C3 | D3 | 1 | 1 | yes | characteristic |
| 20 | C32×D3×C9 | — | 3 | 1 | no | — |
| 21 | C9⋊#272 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 22 | #92297 | — | 2 | 1 | no | — |
| 23 | #92297 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 24 | C3×#4181 | — | 3 | 1 | no | — |
| 25 | C3×#4181 | — | 3 | 1 | no | — |
| 26 | C3×#4181 | — | 6 | 1 | no | — |
| 27 | C3×#4181 | — | 6 | 1 | no | — |
| 28 | C3×#4181 | — | 6 | 1 | no | — |
| 29 | C9×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 30 | C9×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 31 | C9×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 32 | C9×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 33 | C9×(C3⋊D3)⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3×#4169 | — | 3 | 1 | no | — |
| 35 | C3×#4169 | — | 3 | 1 | no | — |
| 36 | C3×(C3⋊D3)⋊C9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×(C3⋊D3)⋊C9 | D3 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×#1113 | — | 9 | 1 | no | — |
| 39 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 40 | C2×C3×C3⋊D9 | — | 9 | 1 | no | — |
| 41 | #66431 | — | 3 | 1 | no | — |
| 42 | ((C3⋊D3)⋊C3)⋊D3 | — | 3 | 1 | no | — |
| 43 | D3×C3⋊D9 | — | 3 | 1 | no | — |
| 44 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 45 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 46 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 47 | C3×D3×D9 | — | 9 | 1 | no | — |
| 48 | C3×D3×D9 | — | 9 | 1 | no | — |
| 49 | C3×D3×D9 | — | 9 | 1 | no | — |
| 50 | C3×D3×D9 | — | 9 | 1 | no | — |
| 51 | ((C3⋊D3)⋊C9)⋊C2 | — | 3 | 1 | no | — |
| 52 | ((C3⋊D3)⋊C9)⋊C2 | — | 3 | 1 | no | — |
| 53 | C32×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 54 | C33×C9 | — | 2 | 1 | no | — |
| 55 | C33×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 56 | C33×C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 58 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 59 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 60 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 61 | C9×H(3,𝔽3) | — | 2 | 1 | no | — |
| 62 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 63 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 64 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 65 | C9×H(3,𝔽3) | — | 4 | 1 | no | — |
| 66 | C9×H(3,𝔽3) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 68 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 69 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 70 | C3×C32⋊C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 71 | C3×C32⋊C9 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 72 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 73 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 74 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 75 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 76 | C32×C3⋊D3 | — | 18 | 1 | no | — |
| 77 | C32×C3⋊D3 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 78 | C33×D3 | — | 3 | 1 | no | — |
| 79 | C2×C32×C9 | — | 9 | 1 | no | — |
| 80 | C3⋊#272 | — | 3 | 1 | no | — |
| 81 | C3⋊(C3⋊D9) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | C3×#272 | — | 9 | 1 | no | — |
| 83 | C3×#272 | — | 9 | 1 | no | — |
| 84 | C3×#272 | — | 9 | 1 | no | — |
| 85 | C3×#272 | — | 18 | 1 | no | — |
| 86 | C3×#272 | — | 18 | 1 | no | — |
| 87 | C3×#272 | — | 18 | 1 | no | — |
| 88 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 89 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 90 | C9×C3⋊D3 | — | 2 | 1 | no | — |
| 91 | C9×C3⋊D3 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 92 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 93 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 94 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 95 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 96 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 97 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 98 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 99 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 100 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 101 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 102 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 103 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 104 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 105 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 106 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 107 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 108 | C3×C3⋊D9 | — | 18 | 1 | no | — |
| 109 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 110 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 111 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 112 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 113 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 114 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 115 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 116 | C3×(C3⋊D3)⋊C3 | D9 | 1 | 1 | yes | characteristic, complemented |
| 117 | C3×(C3⋊D3)⋊C3 | D9 | 1 | 1 | yes | characteristic, complemented |
| 118 | C3×(C3⋊D3)⋊C3 | D9 | 1 | 1 | yes | characteristic, complemented |
| 119 | C3×(C3⋊D3)⋊C3 | C3×D3 | 1 | 1 | yes | characteristic |
| 120 | C3×D3×C9 | — | 3 | 1 | no | — |
| 121 | C3×D3×C9 | — | 3 | 1 | no | — |
| 122 | C3×D3×C9 | — | 3 | 1 | no | — |
| 123 | C3×D3×C9 | — | 3 | 1 | no | — |
| 124 | C3×D3×C9 | — | 6 | 1 | no | — |
| 125 | C3×D3×C9 | — | 6 | 1 | no | — |
| 126 | C3×D3×C9 | — | 6 | 1 | no | — |
| 127 | C3×D3×C9 | — | 6 | 1 | no | — |
| 128 | C3×D3×C9 | — | 18 | 1 | no | — |
| 129 | C32×D9 | — | 9 | 1 | no | — |
| 130 | C32×D9 | — | 9 | 1 | no | — |
| 131 | C32×D9 | — | 9 | 1 | no | — |
| 132 | C32×D9 | — | 9 | 1 | no | — |
| 133 | C32×D9 | — | 18 | 1 | no | — |
| 134 | C32×D9 | — | 18 | 1 | no | — |
| 135 | C32×D9 | — | 18 | 1 | no | — |
| 136 | C32×D9 | — | 18 | 1 | no | — |
| 137 | #4181 | — | 3 | 1 | no | — |
| 138 | #4181 | — | 3 | 1 | no | — |
| 139 | #4181 | — | 6 | 1 | no | — |
| 140 | #4181 | — | 6 | 1 | no | — |
| 141 | #4181 | — | 6 | 1 | no | — |
| 142 | #4169 | — | 3 | 1 | no | — |
| 143 | #4169 | — | 3 | 1 | no | — |
| 144 | #4169 | — | 6 | 1 | no | — |
| 145 | #4169 | — | 6 | 1 | no | — |
| 146 | (C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 147 | (C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 148 | (C3⋊D3)⋊C9 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 149 | (C3⋊D3)⋊C9 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 150 | C2×C3×C3⋊D3 | — | 27 | 1 | no | — |
| 151 | #1113 | — | 9 | 1 | no | — |
| 152 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 153 | C3×D32 | — | 27 | 1 | no | — |
| 154 | C3×D32 | — | 27 | 1 | no | — |
| 155 | C3×D32 | — | 27 | 1 | no | — |
| 156 | C3×D32 | — | 27 | 1 | no | — |
| 157 | C3×D32 | — | 27 | 1 | no | — |
| 158 | C3×D32 | — | 27 | 1 | no | — |
| 159 | C2×C3⋊D9 | — | 9 | 1 | no | — |
| 160 | C2×C3×D9 | — | 27 | 1 | no | — |
| 161 | C2×C3×D9 | — | 27 | 1 | no | — |
| 162 | C2×C3×D9 | — | 27 | 1 | no | — |
| 163 | ((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 164 | ((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 165 | ((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 166 | D3×D9 | — | 9 | 1 | no | — |
| 167 | D3×D9 | — | 9 | 1 | no | — |
| 168 | D3×D9 | — | 9 | 1 | no | — |
| 169 | D3×D9 | — | 9 | 1 | no | — |
| 170 | C34 | — | 2 | 1 | no | — |
| 171 | C34 | D32 | 1 | 1 | yes | characteristic |
| 172 | C34 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 173 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 174 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 175 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 176 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 177 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 178 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 179 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 180 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 181 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 182 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 183 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 184 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 185 | C3×H(3,𝔽3) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 186 | C3×H(3,𝔽3) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 187 | C3×H(3,𝔽3) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 188 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 189 | C32×C9 | — | 2 | 1 | no | — |
| 190 | C32×C9 | — | 2 | 1 | no | — |
| 191 | C32×C9 | — | 2 | 1 | no | — |
| 192 | C32×C9 | — | 2 | 1 | no | — |
| 193 | C32×C9 | — | 2 | 1 | no | — |
| 194 | C32×C9 | — | 2 | 1 | no | — |
| 195 | C32×C9 | — | 2 | 1 | no | — |
| 196 | C32×C9 | — | 2 | 1 | no | — |
| 197 | C32×C9 | — | 2 | 1 | no | — |
| 198 | C32×C9 | — | 2 | 1 | no | — |
| 199 | C32×C9 | — | 3 | 1 | no | — |
| 200 | C32×C9 | — | 4 | 1 | no | — |
| 201 | C32×C9 | — | 4 | 1 | no | — |
| 202 | C32×C9 | — | 4 | 1 | no | — |
| 203 | C32×C9 | — | 4 | 1 | no | — |
| 204 | C32×C9 | — | 4 | 1 | no | — |
| 205 | C32×C9 | — | 6 | 1 | no | — |
| 206 | C32×C9 | — | 6 | 1 | no | — |
| 207 | C32×C9 | — | 6 | 1 | no | — |
| 208 | C32×C9 | — | 6 | 1 | no | — |
| 209 | C32×C9 | — | 6 | 1 | no | — |
| 210 | C32×C9 | — | 12 | 1 | no | — |
| 211 | C32×C9 | — | 12 | 1 | no | — |
| 212 | C32×C9 | — | 12 | 1 | no | — |
| 213 | C32×C9 | — | 12 | 1 | no | — |
| 214 | C32×C9 | — | 12 | 1 | no | — |
| 215 | C32×C9 | — | 12 | 1 | no | — |
| 216 | C32×C9 | — | 12 | 1 | no | — |
| 217 | C32×C9 | — | 12 | 1 | no | — |
| 218 | C32×C9 | D32 | 1 | 1 | yes | characteristic |
| 219 | C32×C9 | D32 | 1 | 1 | yes | characteristic |
| 220 | C32×C9 | D32 | 1 | 1 | yes | characteristic |
| 221 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 222 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 223 | C32⋊C9 | — | 2 | 1 | no | — |
| 224 | C32⋊C9 | — | 2 | 1 | no | — |
| 225 | C32⋊C9 | — | 2 | 1 | no | — |
| 226 | C32⋊C9 | — | 2 | 1 | no | — |
| 227 | C32⋊C9 | — | 2 | 1 | no | — |
| 228 | C32⋊C9 | — | 2 | 1 | no | — |
| 229 | C32⋊C9 | — | 2 | 1 | no | — |
| 230 | C32⋊C9 | — | 4 | 1 | no | — |
| 231 | C32⋊C9 | — | 4 | 1 | no | — |
| 232 | C32⋊C9 | — | 4 | 1 | no | — |
| 233 | C32⋊C9 | — | 4 | 1 | no | — |
| 234 | C32⋊C9 | — | 4 | 1 | no | — |
| 235 | C32⋊C9 | — | 4 | 1 | no | — |
| 236 | C32⋊C9 | — | 4 | 1 | no | — |
| 237 | C32⋊C9 | — | 4 | 1 | no | — |
| 238 | C32⋊C9 | — | 4 | 1 | no | — |
| 239 | C32⋊C9 | — | 4 | 1 | no | — |
| 240 | C32⋊C9 | — | 4 | 1 | no | — |
| 241 | C32⋊C9 | — | 4 | 1 | no | — |
| 242 | C32⋊C9 | — | 4 | 1 | no | — |
| 243 | C32⋊C9 | — | 4 | 1 | no | — |
| 244 | C32⋊C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 245 | C32⋊C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 246 | C2×C33 | — | 9 | 1 | no | — |
| 247 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 248 | C3×C3⋊D3 | — | 2 | 1 | no | — |
| 249 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 250 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 251 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 252 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 253 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 254 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 255 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 256 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 257 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 258 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 259 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 260 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 261 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 262 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 263 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 264 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 265 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 266 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 267 | C3×C3⋊D3 | C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 268 | C3×C3⋊D3 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 269 | C32×D3 | — | 3 | 1 | no | — |
| 270 | C32×D3 | — | 3 | 1 | no | — |
| 271 | C32×D3 | — | 3 | 1 | no | — |
| 272 | C32×D3 | — | 3 | 1 | no | — |
| 273 | C32×D3 | — | 3 | 1 | no | — |
| 274 | C32×D3 | — | 6 | 1 | no | — |
| 275 | C32×D3 | — | 6 | 1 | no | — |
| 276 | C32×D3 | — | 6 | 1 | no | — |
| 277 | C32×D3 | — | 6 | 1 | no | — |
| 278 | C32×D3 | — | 18 | 1 | no | — |
| 279 | C32×D3 | — | 27 | 1 | no | — |
| 280 | C32×D3 | — | 27 | 1 | no | — |
| 281 | C32×D3 | — | 27 | 1 | no | — |
| 282 | C32×D3 | — | 27 | 1 | no | — |
| 283 | C32×D3 | — | 27 | 1 | no | — |
| 284 | C32×D3 | — | 27 | 1 | no | — |
| 285 | C32×D3 | — | 27 | 1 | no | — |
| 286 | C32×D3 | — | 54 | 1 | no | — |
| 287 | C32×D3 | — | 54 | 1 | no | — |
| 288 | C32×D3 | — | 54 | 1 | no | — |
| 289 | C32×D3 | — | 54 | 1 | no | — |
| 290 | C32×D3 | — | 54 | 1 | no | — |
| 291 | C2×C3×C9 | — | 9 | 1 | no | — |
| 292 | C2×C3×C9 | — | 9 | 1 | no | — |
| 293 | C2×C3×C9 | — | 9 | 1 | no | — |
| 294 | C2×C3×C9 | — | 9 | 1 | no | — |
| 295 | C2×C3×C9 | — | 18 | 1 | no | — |
| 296 | C2×C3×C9 | — | 18 | 1 | no | — |
| 297 | C2×C3×C9 | — | 18 | 1 | no | — |
| 298 | C2×C3×C9 | — | 18 | 1 | no | — |
| 299 | #272 | — | 9 | 1 | no | — |
| 300 | #272 | — | 9 | 1 | no | — |
| 301 | #272 | — | 9 | 1 | no | — |
| 302 | #272 | — | 18 | 1 | no | — |
| 303 | #272 | — | 18 | 1 | no | — |
| 304 | #272 | — | 18 | 1 | no | — |
| 305 | C3⋊D9 | — | 3 | 1 | no | — |
| 306 | C3⋊D9 | — | 3 | 1 | no | — |
| 307 | C3⋊D9 | — | 3 | 1 | no | — |
| 308 | C3⋊D9 | — | 3 | 1 | no | — |
| 309 | C3⋊D9 | — | 3 | 1 | no | — |
| 310 | C3⋊D9 | — | 6 | 1 | no | — |
| 311 | C3⋊D9 | — | 9 | 1 | no | — |
| 312 | C3⋊D9 | — | 18 | 1 | no | — |
| 313 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 314 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 315 | (C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 316 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 317 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 318 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 319 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 320 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 321 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 322 | (C3⋊D3)⋊C3 | C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 323 | (C3⋊D3)⋊C3 | C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 324 | (C3⋊D3)⋊C3 | C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 325 | D3×C9 | — | 3 | 1 | no | — |
| 326 | D3×C9 | — | 3 | 1 | no | — |
| 327 | D3×C9 | — | 3 | 1 | no | — |
| 328 | D3×C9 | — | 6 | 1 | no | — |
| 329 | D3×C9 | — | 6 | 1 | no | — |
| 330 | D3×C9 | — | 6 | 1 | no | — |
| 331 | D3×C9 | — | 18 | 1 | no | — |
| 332 | D3×C9 | — | 18 | 1 | no | — |
| 333 | C3×D9 | — | 9 | 1 | no | — |
| 334 | C3×D9 | — | 9 | 1 | no | — |
| 335 | C3×D9 | — | 9 | 1 | no | — |
| 336 | C3×D9 | — | 9 | 1 | no | — |
| 337 | C3×D9 | — | 9 | 1 | no | — |
| 338 | C3×D9 | — | 9 | 1 | no | — |
| 339 | C3×D9 | — | 9 | 1 | no | — |
| 340 | C3×D9 | — | 9 | 1 | no | — |
| 341 | C3×D9 | — | 18 | 1 | no | — |
| 342 | C3×D9 | — | 18 | 1 | no | — |
| 343 | C3×D9 | — | 18 | 1 | no | — |
| 344 | C3×D9 | — | 18 | 1 | no | — |
| 345 | C3×D9 | — | 18 | 1 | no | — |
| 346 | C3×D9 | — | 18 | 1 | no | — |
| 347 | C3×D9 | — | 18 | 1 | no | — |
| 348 | C3×D9 | — | 18 | 1 | no | — |
| 349 | C3×D9 | — | 18 | 1 | no | — |
| 350 | C3×D9 | — | 18 | 1 | no | — |
| 351 | C3×D9 | — | 18 | 1 | no | — |
| 352 | C3×D9 | — | 18 | 1 | no | — |
| 353 | C3×D9 | — | 18 | 1 | no | — |
| 354 | C3×D9 | — | 18 | 1 | no | — |
| 355 | C3×D9 | — | 18 | 1 | no | — |
| 356 | C3×D9 | — | 18 | 1 | no | — |
| 357 | C3×D9 | — | 18 | 1 | no | — |
| 358 | C3×D9 | — | 18 | 1 | no | — |
| 359 | C3×D9 | — | 18 | 1 | no | — |
| 360 | C3×D9 | — | 18 | 1 | no | — |
| 361 | C3×D9 | — | 27 | 1 | no | — |
| 362 | C3×D9 | — | 27 | 1 | no | — |
| 363 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 364 | C2×C3×D3 | — | 81 | 1 | no | — |
| 365 | C2×C3×D3 | — | 81 | 1 | no | — |
| 366 | C2×C3×D3 | — | 81 | 1 | no | — |
| 367 | C2×C3×D3 | — | 81 | 1 | no | — |
| 368 | C2×C3×D3 | — | 81 | 1 | no | — |
| 369 | C2×C3×D3 | — | 81 | 1 | no | — |
| 370 | D32 | — | 27 | 1 | no | — |
| 371 | D32 | — | 27 | 1 | no | — |
| 372 | D32 | — | 27 | 1 | no | — |
| 373 | D32 | — | 27 | 1 | no | — |
| 374 | D32 | — | 27 | 1 | no | — |
| 375 | D32 | — | 27 | 1 | no | — |
| 376 | C2×D9 | — | 27 | 1 | no | — |
| 377 | C2×D9 | — | 27 | 1 | no | — |
| 378 | C2×D9 | — | 27 | 1 | no | — |
| 379 | C33 | — | 2 | 1 | no | — |
| 380 | C33 | — | 2 | 1 | no | — |
| 381 | C33 | — | 2 | 1 | no | — |
| 382 | C33 | — | 2 | 1 | no | — |
| 383 | C33 | — | 2 | 1 | no | — |
| 384 | C33 | — | 2 | 1 | no | — |
| 385 | C33 | — | 2 | 1 | no | — |
| 386 | C33 | — | 2 | 1 | no | — |
| 387 | C33 | — | 2 | 1 | no | — |
| 388 | C33 | — | 2 | 1 | no | — |
| 389 | C33 | — | 2 | 1 | no | — |
| 390 | C33 | — | 4 | 1 | no | — |
| 391 | C33 | — | 4 | 1 | no | — |
| 392 | C33 | — | 4 | 1 | no | — |
| 393 | C33 | — | 4 | 1 | no | — |
| 394 | C33 | — | 4 | 1 | no | — |
| 395 | C33 | — | 6 | 1 | no | — |
| 396 | C33 | — | 6 | 1 | no | — |
| 397 | C33 | — | 6 | 1 | no | — |
| 398 | C33 | — | 12 | 1 | no | — |
| 399 | C33 | — | 12 | 1 | no | — |
| 400 | C33 | — | 12 | 1 | no | — |
| 401 | C33 | — | 12 | 1 | no | — |
| 402 | C33 | — | 12 | 1 | no | — |
| 403 | C33 | — | 12 | 1 | no | — |
| 404 | C33 | — | 12 | 1 | no | — |
| 405 | C33 | — | 12 | 1 | no | — |
| 406 | C33 | — | 12 | 1 | no | — |
| 407 | C33 | — | 12 | 1 | no | — |
| 408 | C33 | — | 12 | 1 | no | — |
| 409 | C33 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 410 | C33 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 411 | C33 | D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 412 | C33 | C2×C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 413 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 414 | C33 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 415 | C33 | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 416 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 417 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 418 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 419 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 420 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 421 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 422 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 423 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 424 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 425 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 426 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 427 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 428 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 429 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 430 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 431 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 432 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 433 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 434 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 435 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 436 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 437 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 438 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 439 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 440 | H(3,𝔽3) | C2×C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 441 | H(3,𝔽3) | C2×C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 442 | H(3,𝔽3) | C2×C3×D9 | 1 | 1 | yes | characteristic, complemented |
| 443 | C3×C9 | — | 2 | 1 | no | — |
| 444 | C3×C9 | — | 2 | 1 | no | — |
| 445 | C3×C9 | — | 2 | 1 | no | — |
| 446 | C3×C9 | — | 2 | 1 | no | — |
| 447 | C3×C9 | — | 2 | 1 | no | — |
| 448 | C3×C9 | — | 2 | 1 | no | — |
| 449 | C3×C9 | — | 2 | 1 | no | — |
| 450 | C3×C9 | — | 2 | 1 | no | — |
| 451 | C3×C9 | — | 3 | 1 | no | — |
| 452 | C3×C9 | — | 3 | 1 | no | — |
| 453 | C3×C9 | — | 3 | 1 | no | — |
| 454 | C3×C9 | — | 4 | 1 | no | — |
| 455 | C3×C9 | — | 4 | 1 | no | — |
| 456 | C3×C9 | — | 4 | 1 | no | — |
| 457 | C3×C9 | — | 4 | 1 | no | — |
| 458 | C3×C9 | — | 6 | 1 | no | — |
| 459 | C3×C9 | — | 6 | 1 | no | — |
| 460 | C3×C9 | — | 6 | 1 | no | — |
| 461 | C3×C9 | — | 6 | 1 | no | — |
| 462 | C3×C9 | — | 6 | 1 | no | — |
| 463 | C3×C9 | — | 6 | 1 | no | — |
| 464 | C3×C9 | — | 6 | 1 | no | — |
| 465 | C3×C9 | — | 6 | 1 | no | — |
| 466 | C3×C9 | — | 6 | 1 | no | — |
| 467 | C3×C9 | — | 6 | 1 | no | — |
| 468 | C3×C9 | — | 12 | 1 | no | — |
| 469 | C3×C9 | — | 12 | 1 | no | — |
| 470 | C3×C9 | — | 12 | 1 | no | — |
| 471 | C3×C9 | — | 12 | 1 | no | — |
| 472 | C3×C9 | — | 12 | 1 | no | — |
| 473 | C3×C9 | — | 12 | 1 | no | — |
| 474 | C3×C9 | — | 12 | 1 | no | — |
| 475 | C3×C9 | — | 12 | 2 | no | — |
| 476 | C3×C9 | — | 12 | 1 | no | — |
| 477 | C3×C9 | — | 12 | 1 | no | — |
| 478 | C3×C9 | — | 12 | 1 | no | — |
| 479 | C3×C9 | — | 12 | 1 | no | — |
| 480 | C3×C9 | — | 12 | 1 | no | — |
| 481 | C3×C9 | — | 12 | 1 | no | — |
| 482 | C3×C9 | — | 12 | 1 | no | — |
| 483 | C3×C9 | — | 12 | 1 | no | — |
| 484 | C3×C9 | — | 12 | 1 | no | — |
| 485 | C3×C9 | — | 12 | 1 | no | — |
| 486 | C3×C9 | — | 12 | 1 | no | — |
| 487 | C3×C9 | — | 12 | 1 | no | — |
| 488 | C3×C9 | — | 12 | 1 | no | — |
| 489 | C3×C9 | — | 12 | 2 | no | — |
| 490 | C3×C9 | — | 12 | 1 | no | — |
| 491 | C3×C9 | — | 12 | 1 | no | — |
| 492 | C3×C9 | — | 12 | 1 | no | — |
| 493 | C3×C9 | — | 12 | 1 | no | — |
| 494 | C3×C9 | — | 12 | 1 | no | — |
| 495 | C3×C9 | — | 12 | 1 | no | — |
| 496 | C3×C9 | — | 12 | 1 | no | — |
| 497 | C3×C9 | — | 12 | 1 | no | — |
| 498 | C3×C9 | — | 12 | 1 | no | — |
| 499 | C3×C9 | — | 12 | 1 | no | — |
| 500 | C3×C9 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 501 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 502 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 503 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 504 | C2×C32 | — | 9 | 1 | no | — |
| 505 | C2×C32 | — | 9 | 1 | no | — |
| 506 | C2×C32 | — | 9 | 1 | no | — |
| 507 | C2×C32 | — | 9 | 1 | no | — |
| 508 | C2×C32 | — | 9 | 1 | no | — |
| 509 | C2×C32 | — | 18 | 1 | no | — |
| 510 | C2×C32 | — | 18 | 1 | no | — |
| 511 | C2×C32 | — | 18 | 1 | no | — |
| 512 | C2×C32 | — | 18 | 1 | no | — |
| 513 | C2×C32 | — | 81 | 1 | no | — |
| 514 | C2×C32 | — | 81 | 1 | no | — |
| 515 | C3⋊D3 | — | 9 | 1 | no | — |
| 516 | C3⋊D3 | — | 9 | 1 | no | — |
| 517 | C3⋊D3 | — | 9 | 1 | no | — |
| 518 | C3⋊D3 | — | 9 | 1 | no | — |
| 519 | C3⋊D3 | — | 9 | 1 | no | — |
| 520 | C3⋊D3 | — | 9 | 1 | no | — |
| 521 | C3⋊D3 | — | 18 | 1 | no | — |
| 522 | C3⋊D3 | — | 54 | 1 | no | — |
| 523 | C3⋊D3 | — | 54 | 1 | no | — |
| 524 | C3⋊D3 | C3×C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 525 | C3×D3 | — | 3 | 1 | no | — |
| 526 | C3×D3 | — | 3 | 1 | no | — |
| 527 | C3×D3 | — | 3 | 1 | no | — |
| 528 | C3×D3 | — | 3 | 1 | no | — |
| 529 | C3×D3 | — | 3 | 1 | no | — |
| 530 | C3×D3 | — | 6 | 1 | no | — |
| 531 | C3×D3 | — | 6 | 1 | no | — |
| 532 | C3×D3 | — | 6 | 1 | no | — |
| 533 | C3×D3 | — | 6 | 1 | no | — |
| 534 | C3×D3 | — | 18 | 1 | no | — |
| 535 | C3×D3 | — | 18 | 1 | no | — |
| 536 | C3×D3 | — | 18 | 1 | no | — |
| 537 | C3×D3 | — | 27 | 1 | no | — |
| 538 | C3×D3 | — | 27 | 1 | no | — |
| 539 | C3×D3 | — | 27 | 1 | no | — |
| 540 | C3×D3 | — | 27 | 1 | no | — |
| 541 | C3×D3 | — | 27 | 1 | no | — |
| 542 | C3×D3 | — | 27 | 1 | no | — |
| 543 | C3×D3 | — | 27 | 1 | no | — |
| 544 | C3×D3 | — | 27 | 1 | no | — |
| 545 | C3×D3 | — | 27 | 1 | no | — |
| 546 | C3×D3 | — | 27 | 1 | no | — |
| 547 | C3×D3 | — | 27 | 1 | no | — |
| 548 | C3×D3 | — | 27 | 1 | no | — |
| 549 | C3×D3 | — | 27 | 1 | no | — |
| 550 | C3×D3 | — | 27 | 1 | no | — |
| 551 | C3×D3 | — | 54 | 1 | no | — |
| 552 | C3×D3 | — | 54 | 1 | no | — |
| 553 | C3×D3 | — | 54 | 1 | no | — |
| 554 | C3×D3 | — | 54 | 1 | no | — |
| 555 | C3×D3 | — | 54 | 1 | no | — |
| 556 | C3×D3 | — | 54 | 1 | no | — |
| 557 | C3×D3 | — | 54 | 1 | no | — |
| 558 | C3×D3 | — | 54 | 1 | no | — |
| 559 | C3×D3 | — | 54 | 1 | no | — |
| 560 | C3×D3 | — | 54 | 1 | no | — |
| 561 | C3×D3 | — | 54 | 1 | no | — |
| 562 | C3×D3 | — | 54 | 1 | no | — |
| 563 | C3×D3 | — | 54 | 1 | no | — |
| 564 | C3×D3 | — | 54 | 1 | no | — |
| 565 | C3×D3 | — | 54 | 1 | no | — |
| 566 | C3×D3 | — | 54 | 1 | no | — |
| 567 | C3×D3 | — | 54 | 1 | no | — |
| 568 | C3×D3 | — | 54 | 1 | no | — |
| 569 | C3×D3 | — | 54 | 1 | no | — |
| 570 | C3×D3 | — | 54 | 1 | no | — |
| 571 | C3×D3 | — | 54 | 1 | no | — |
| 572 | C3×D3 | — | 54 | 1 | no | — |
| 573 | C3×D3 | — | 54 | 1 | no | — |
| 574 | C3×D3 | — | 54 | 2 | no | — |
| 575 | C3×D3 | — | 54 | 1 | no | — |
| 576 | C3×D3 | — | 54 | 1 | no | — |
| 577 | C3×D3 | — | 81 | 1 | no | — |
| 578 | C3×D3 | — | 81 | 1 | no | — |
| 579 | C3×D3 | — | 81 | 1 | no | — |
| 580 | C2×C9 | — | 9 | 1 | no | — |
| 581 | C2×C9 | — | 9 | 1 | no | — |
| 582 | C2×C9 | — | 9 | 1 | no | — |
| 583 | C2×C9 | — | 18 | 1 | no | — |
| 584 | C2×C9 | — | 18 | 1 | no | — |
| 585 | C2×C9 | — | 18 | 1 | no | — |
| 586 | D9 | — | 9 | 1 | no | — |
| 587 | D9 | — | 9 | 1 | no | — |
| 588 | D9 | — | 9 | 1 | no | — |
| 589 | D9 | — | 9 | 1 | no | — |
| 590 | D9 | — | 18 | 1 | no | — |
| 591 | D9 | — | 18 | 1 | no | — |
| 592 | D9 | — | 18 | 1 | no | — |
| 593 | D9 | — | 18 | 1 | no | — |
| 594 | D9 | — | 27 | 1 | no | — |
| 595 | D9 | — | 27 | 1 | no | — |
| 596 | C22×C3 | — | 243 | 1 | no | — |
| 597 | C2×D3 | — | 81 | 1 | no | — |
| 598 | C2×D3 | — | 81 | 1 | no | — |
| 599 | C2×D3 | — | 81 | 1 | no | — |
| 600 | C2×D3 | — | 81 | 1 | no | — |
| 601 | C2×D3 | — | 81 | 1 | no | — |
| 602 | C2×D3 | — | 81 | 1 | no | — |
| 603 | C32 | — | 2 | 1 | no | — |
| 604 | C32 | — | 2 | 1 | no | — |
| 605 | C32 | — | 2 | 1 | no | — |
| 606 | C32 | — | 2 | 1 | no | — |
| 607 | C32 | — | 2 | 1 | no | — |
| 608 | C32 | — | 2 | 1 | no | — |
| 609 | C32 | — | 2 | 1 | no | — |
| 610 | C32 | — | 2 | 1 | no | — |
| 611 | C32 | — | 2 | 1 | no | — |
| 612 | C32 | — | 2 | 1 | no | — |
| 613 | C32 | — | 2 | 1 | no | — |
| 614 | C32 | — | 3 | 1 | no | — |
| 615 | C32 | — | 3 | 1 | no | — |
| 616 | C32 | — | 3 | 1 | no | — |
| 617 | C32 | — | 4 | 1 | no | — |
| 618 | C32 | — | 4 | 1 | no | — |
| 619 | C32 | — | 4 | 1 | no | — |
| 620 | C32 | — | 4 | 1 | no | — |
| 621 | C32 | — | 4 | 1 | no | — |
| 622 | C32 | — | 6 | 1 | no | — |
| 623 | C32 | — | 6 | 1 | no | — |
| 624 | C32 | — | 6 | 1 | no | — |
| 625 | C32 | — | 6 | 1 | no | — |
| 626 | C32 | — | 6 | 1 | no | — |
| 627 | C32 | — | 6 | 1 | no | — |
| 628 | C32 | — | 6 | 1 | no | — |
| 629 | C32 | — | 6 | 1 | no | — |
| 630 | C32 | — | 6 | 1 | no | — |
| 631 | C32 | — | 12 | 1 | no | — |
| 632 | C32 | — | 12 | 1 | no | — |
| 633 | C32 | — | 12 | 1 | no | — |
| 634 | C32 | — | 12 | 1 | no | — |
| 635 | C32 | — | 12 | 1 | no | — |
| 636 | C32 | — | 12 | 1 | no | — |
| 637 | C32 | — | 12 | 1 | no | — |
| 638 | C32 | — | 12 | 1 | no | — |
| 639 | C32 | — | 12 | 1 | no | — |
| 640 | C32 | — | 12 | 1 | no | — |
| 641 | C32 | — | 12 | 1 | no | — |
| 642 | C32 | — | 12 | 1 | no | — |
| 643 | C32 | — | 12 | 1 | no | — |
| 644 | C32 | — | 12 | 1 | no | — |
| 645 | C32 | — | 12 | 2 | no | — |
| 646 | C32 | — | 12 | 1 | no | — |
| 647 | C32 | — | 12 | 1 | no | — |
| 648 | C32 | — | 12 | 1 | no | — |
| 649 | C32 | — | 12 | 1 | no | — |
| 650 | C32 | — | 12 | 2 | no | — |
| 651 | C32 | — | 12 | 1 | no | — |
| 652 | C32 | — | 12 | 1 | no | — |
| 653 | C32 | — | 12 | 1 | no | — |
| 654 | C32 | — | 12 | 1 | no | — |
| 655 | C32 | — | 12 | 1 | no | — |
| 656 | C32 | — | 12 | 1 | no | — |
| 657 | C32 | — | 12 | 1 | no | — |
| 658 | C32 | — | 12 | 1 | no | — |
| 659 | C32 | — | 12 | 1 | no | — |
| 660 | C32 | — | 12 | 2 | no | — |
| 661 | C32 | — | 12 | 1 | no | — |
| 662 | C32 | — | 12 | 1 | no | — |
| 663 | C32 | — | 12 | 1 | no | — |
| 664 | C32 | — | 12 | 1 | no | — |
| 665 | C32 | — | 12 | 1 | no | — |
| 666 | C32 | — | 12 | 1 | no | — |
| 667 | C32 | — | 12 | 1 | no | — |
| 668 | C32 | — | 12 | 1 | no | — |
| 669 | C32 | — | 12 | 1 | no | — |
| 670 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 671 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 672 | C32 | C3×D3×D9 | 1 | 1 | yes | characteristic, complemented |
| 673 | C32 | D3×C3⋊D9 | 1 | 1 | yes | characteristic |
| 674 | C32 | ((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 675 | C32 | C2×C3×C3⋊D9 | 1 | 1 | yes | characteristic, complemented |
| 676 | C32 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 677 | C9 | — | 2 | 1 | no | — |
| 678 | C9 | — | 2 | 1 | no | — |
| 679 | C9 | — | 3 | 1 | no | — |
| 680 | C9 | — | 3 | 1 | no | — |
| 681 | C9 | — | 4 | 1 | no | — |
| 682 | C9 | — | 6 | 1 | no | — |
| 683 | C9 | — | 6 | 1 | no | — |
| 684 | C9 | — | 12 | 1 | no | — |
| 685 | C9 | — | 12 | 1 | no | — |
| 686 | C9 | — | 12 | 1 | no | — |
| 687 | C9 | — | 12 | 1 | no | — |
| 688 | C9 | — | 12 | 1 | no | — |
| 689 | C9 | — | 12 | 1 | no | — |
| 690 | C9 | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 691 | C2×C3 | — | 9 | 1 | no | — |
| 692 | C2×C3 | — | 9 | 1 | no | — |
| 693 | C2×C3 | — | 9 | 1 | no | — |
| 694 | C2×C3 | — | 9 | 1 | no | — |
| 695 | C2×C3 | — | 9 | 1 | no | — |
| 696 | C2×C3 | — | 18 | 1 | no | — |
| 697 | C2×C3 | — | 18 | 1 | no | — |
| 698 | C2×C3 | — | 18 | 1 | no | — |
| 699 | C2×C3 | — | 18 | 1 | no | — |
| 700 | C2×C3 | — | 81 | 1 | no | — |
| 701 | C2×C3 | — | 81 | 1 | no | — |
| 702 | C2×C3 | — | 81 | 1 | no | — |
| 703 | C2×C3 | — | 81 | 1 | no | — |
| 704 | C2×C3 | — | 162 | 1 | no | — |
| 705 | C2×C3 | — | 162 | 1 | no | — |
| 706 | D3 | — | 3 | 1 | no | — |
| 707 | D3 | — | 18 | 1 | no | — |
| 708 | D3 | — | 27 | 1 | no | — |
| 709 | D3 | — | 27 | 1 | no | — |
| 710 | D3 | — | 27 | 1 | no | — |
| 711 | D3 | — | 27 | 1 | no | — |
| 712 | D3 | — | 27 | 1 | no | — |
| 713 | D3 | — | 27 | 1 | no | — |
| 714 | D3 | — | 27 | 1 | no | — |
| 715 | D3 | — | 54 | 1 | no | — |
| 716 | D3 | — | 54 | 1 | no | — |
| 717 | D3 | — | 54 | 1 | no | — |
| 718 | D3 | — | 54 | 1 | no | — |
| 719 | D3 | — | 54 | 1 | no | — |
| 720 | D3 | — | 81 | 1 | no | — |
| 721 | D3 | — | 162 | 1 | no | — |
| 722 | D3 | — | 162 | 1 | no | — |
| 723 | C22 | — | 243 | 1 | no | Sylow |
| 724 | C3 | — | 2 | 1 | no | — |
| 725 | C3 | — | 2 | 1 | no | — |
| 726 | C3 | — | 2 | 1 | no | — |
| 727 | C3 | — | 3 | 1 | no | — |
| 728 | C3 | — | 4 | 1 | no | — |
| 729 | C3 | — | 6 | 1 | no | — |
| 730 | C3 | — | 6 | 1 | no | — |
| 731 | C3 | — | 6 | 1 | no | — |
| 732 | C3 | — | 6 | 1 | no | — |
| 733 | C3 | — | 6 | 1 | no | — |
| 734 | C3 | — | 12 | 1 | no | — |
| 735 | C3 | — | 12 | 1 | no | — |
| 736 | C3 | — | 12 | 1 | no | — |
| 737 | C3 | — | 12 | 1 | no | — |
| 738 | C3 | — | 12 | 1 | no | — |
| 739 | C3 | — | 12 | 1 | no | — |
| 740 | C3 | — | 12 | 1 | no | — |
| 741 | C3 | — | 12 | 1 | no | — |
| 742 | C3 | — | 12 | 1 | no | — |
| 743 | C3 | — | 12 | 1 | no | — |
| 744 | C3 | ((C3⋊D3)⋊C3)⋊D9 | 1 | 1 | yes | characteristic, direct product factor |
| 745 | C3 | C3×D3×C3⋊D9 | 1 | 1 | yes | characteristic |
| 746 | C3 | C3×((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 747 | C2 | — | 9 | 1 | no | — |
| 748 | C2 | — | 81 | 1 | no | — |
| 749 | C2 | — | 81 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | ((C3⋊D3)⋊C3)⋊D9 |
| commutator, cosocle, hypocenter | C9×H(3,𝔽3) | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×C9×H(3,𝔽3) | C22 |
| socle | C33 | D3×C3⋊D3 |
| LCS | G ▷ C9×H(3,𝔽3) | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C9⋊#272 | C2 | semidirect |
| 2. C3×#92297 | C2 | semidirect |
| 3. C3×C9×(C3⋊D3)⋊C3 | C2 | semidirect |
| 7. ((C3⋊D3)⋊C3)⋊D9 | C3 | direct (N × H) |
| 10. C3×C9×H(3,𝔽3) | C22 | semidirect |
| 12. C3×C3⋊(C3⋊D9) | D3 | semidirect |
| 14. C3×C9×C3⋊D3 | D3 | semidirect |
| 21. C9⋊#272 | C2×C3 | semidirect |
| 23. #92297 | C2×C3 | semidirect |
| 33. C9×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 36. C3×(C3⋊D3)⋊C9 | D3 | semidirect |
| 37. C3×(C3⋊D3)⋊C9 | D3 | semidirect |
| 55. C33×C9 | C2×D3 | semidirect |
| 56. C33×C9 | C2×D3 | semidirect |
| 66. C9×H(3,𝔽3) | C22×C3 | semidirect |
| 70. C3×C32⋊C9 | C2×D3 | semidirect |
| 71. C3×C32⋊C9 | C2×D3 | semidirect |
| 81. C3⋊(C3⋊D9) | C3×D3 | semidirect |
| 91. C9×C3⋊D3 | C3×D3 | semidirect |
| 116. C3×(C3⋊D3)⋊C3 | D9 | semidirect |
| 117. C3×(C3⋊D3)⋊C3 | D9 | semidirect |
| 118. C3×(C3⋊D3)⋊C3 | D9 | semidirect |
| 148. (C3⋊D3)⋊C9 | C3×D3 | semidirect |
| 149. (C3⋊D3)⋊C9 | C3×D3 | semidirect |
| 185. C3×H(3,𝔽3) | C2×D9 | semidirect |
| 186. C3×H(3,𝔽3) | C2×D9 | semidirect |
| 187. C3×H(3,𝔽3) | C2×D9 | semidirect |
| 221. C32×C9 | C2×C3×D3 | semidirect |
| 222. C32×C9 | C2×C3×D3 | semidirect |
| 244. C32⋊C9 | C2×C3×D3 | semidirect |
| 245. C32⋊C9 | C2×C3×D3 | semidirect |
| 267. C3×C3⋊D3 | C3⋊D9 | semidirect |
| 322. (C3⋊D3)⋊C3 | C3×D9 | semidirect |
| 323. (C3⋊D3)⋊C3 | C3×D9 | semidirect |
| 324. (C3⋊D3)⋊C3 | C3×D9 | semidirect |
| 409. C33 | D3×D9 | semidirect |
| 410. C33 | D3×D9 | semidirect |
| 411. C33 | D3×D9 | semidirect |
| 412. C33 | C2×C3⋊D9 | semidirect |
| 440. H(3,𝔽3) | C2×C3×D9 | semidirect |
| 441. H(3,𝔽3) | C2×C3×D9 | semidirect |
| 442. H(3,𝔽3) | C2×C3×D9 | semidirect |
| 500. C3×C9 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 524. C3⋊D3 | C3×C3⋊D9 | semidirect |
| 670. C32 | C3×D3×D9 | semidirect |
| 671. C32 | C3×D3×D9 | semidirect |
| 672. C32 | C3×D3×D9 | semidirect |
| 675. C32 | C2×C3×C3⋊D9 | semidirect |
| 690. C9 | C3×((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 744. C3 | ((C3⋊D3)⋊C3)⋊D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9⋊#272 | 2 |
| C3×#92297 | 2 |
| C3×C9×(C3⋊D3)⋊C3 | 2 |
| C3×#66431 | 3 |
| C3×((C3⋊D3)⋊C3)⋊D3 | 3 |
| C3×D3×C3⋊D9 | 3 |
| ((C3⋊D3)⋊C3)⋊D9 | 3 |
| C3×((C3⋊D3)⋊C9)⋊C2 | 3 |