Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
728 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 67 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⋊#92303 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3⋊(D9⋊H(3,𝔽3)) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#92262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3⋊D3×C3⋊D9 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | maximal |
| 6 | C3⋊D3×(C3⋊D3)⋊C3 | — | 3 | 1 | no | maximal |
| 7 | D9⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | maximal |
| 8 | D9⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | maximal |
| 9 | D9⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | maximal |
| 10 | C3×C9⋊H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | C3⋊(C3⋊(C3⋊D9)) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3⋊(C3⋊AGL(1,ℤ/9)) | — | 3 | 1 | no | — |
| 13 | C3⋊(C3⋊((C3⋊D3)⋊C3)) | — | 3 | 1 | no | — |
| 14 | C3×C3⋊AGL(1,ℤ/9) | — | 2 | 1 | no | — |
| 15 | C3×C3⋊AGL(1,ℤ/9) | D3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C3⋊D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 17 | C3×C9×C3⋊D3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C32×C3⋊D9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×D3×3−1+2 | — | 3 | 1 | no | — |
| 20 | C32×(C3⋊D3)⋊C3 | D3 | 1 | 1 | yes | characteristic |
| 21 | #92303 | — | 3 | 1 | no | — |
| 22 | #92303 | — | 3 | 1 | no | — |
| 23 | #92303 | — | 3 | 1 | no | — |
| 24 | #92303 | — | 6 | 1 | no | — |
| 25 | #92303 | — | 6 | 1 | no | — |
| 26 | #92303 | — | 6 | 1 | no | — |
| 27 | C3⋊#4169 | — | 6 | 1 | no | — |
| 28 | #92262 | — | 2 | 1 | no | — |
| 29 | #92262 | — | 2 | 1 | no | — |
| 30 | #92262 | — | 2 | 1 | no | — |
| 31 | #92262 | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #92262 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #92262 | D3 | 1 | 1 | yes | characteristic, complemented |
| 34 | D9⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 35 | D9⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 36 | D9⋊H(3,𝔽3) | — | 3 | 1 | no | — |
| 37 | C3×(C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 38 | C3⋊D32 | — | 3 | 1 | no | — |
| 39 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 40 | C2×C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 41 | D3×C3⋊D9 | — | 3 | 1 | no | — |
| 42 | D3×C3⋊D9 | — | 9 | 1 | no | — |
| 43 | D9×C3⋊D3 | — | 3 | 1 | no | — |
| 44 | D9×C3⋊D3 | — | 3 | 1 | no | — |
| 45 | D9×C3⋊D3 | — | 3 | 1 | no | — |
| 46 | D3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 47 | D3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 48 | D3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 49 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 50 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 51 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 52 | D3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 53 | C32×3−1+2 | — | 2 | 1 | no | — |
| 54 | C32×3−1+2 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 55 | C32×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C33×C9 | C22×C3 | 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) | — | 2 | 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) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C9⋊H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 68 | C9⋊H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 70 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 71 | C3×C32⋊C9 | — | 4 | 1 | no | — |
| 72 | C3⋊(C3⋊(C3⋊D3)) | — | 3 | 1 | no | — |
| 73 | C3×C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 74 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 75 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 76 | C32×C3⋊D3 | — | 6 | 1 | no | — |
| 77 | C32×C3⋊D3 | C3×D3 | 1 | 1 | yes | characteristic |
| 78 | C33×D3 | — | 3 | 1 | no | — |
| 79 | C2×C3×3−1+2 | — | 9 | 1 | no | — |
| 80 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 81 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 82 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 83 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 84 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 85 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 86 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 87 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 88 | C3⋊(C3⋊D9) | — | 9 | 1 | no | — |
| 89 | C3⋊(C3⋊D9) | — | 18 | 1 | no | — |
| 90 | C3⋊(C3⋊D9) | — | 18 | 1 | no | — |
| 91 | C3⋊(C3⋊D9) | — | 18 | 1 | no | — |
| 92 | C3⋊(C3⋊D9) | — | 18 | 1 | no | — |
| 93 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 94 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 95 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 96 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 97 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 98 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 99 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 100 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 101 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 102 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 103 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 104 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 105 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 106 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 107 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 108 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 109 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 110 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 111 | C9×C3⋊D3 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | C9×C3⋊D3 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 113 | C9×C3⋊D3 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 114 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 115 | C3×C3⋊D9 | C3×D3 | 1 | 1 | yes | characteristic |
| 116 | D3×3−1+2 | — | 3 | 1 | no | — |
| 117 | D3×3−1+2 | — | 3 | 1 | no | — |
| 118 | D3×3−1+2 | — | 3 | 1 | no | — |
| 119 | D3×3−1+2 | — | 6 | 1 | no | — |
| 120 | D3×3−1+2 | — | 6 | 1 | no | — |
| 121 | D3×3−1+2 | — | 6 | 1 | no | — |
| 122 | C3×AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 123 | C3×AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 124 | C3×AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 125 | C3×AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 126 | C3×AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 127 | C3×AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 128 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 129 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 130 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 131 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 132 | C3×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 133 | C3×(C3⋊D3)⋊C3 | — | 3 | 1 | no | — |
| 134 | C3×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 135 | C3×(C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 136 | C3×(C3⋊D3)⋊C3 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 137 | C3×D3×C9 | — | 3 | 1 | no | — |
| 138 | C3×D3×C9 | — | 6 | 1 | no | — |
| 139 | C3×D3×C9 | — | 9 | 1 | no | — |
| 140 | C32×D9 | — | 3 | 1 | no | — |
| 141 | C32×D9 | — | 3 | 1 | no | — |
| 142 | C32×D9 | — | 3 | 1 | no | — |
| 143 | #4169 | — | 18 | 1 | no | — |
| 144 | #4169 | — | 18 | 1 | no | — |
| 145 | #4169 | — | 18 | 1 | no | — |
| 146 | (C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 147 | (C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 148 | (C3⋊D3)⋊C9 | — | 2 | 1 | no | — |
| 149 | C2×C3×C3⋊D3 | — | 27 | 1 | no | — |
| 150 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 151 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 152 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 153 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 154 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 155 | D3×C3⋊D3 | — | 27 | 1 | no | — |
| 156 | C3×D32 | — | 27 | 1 | no | — |
| 157 | C3×D32 | — | 27 | 1 | no | — |
| 158 | C3×D32 | — | 27 | 1 | no | — |
| 159 | C3×D32 | — | 27 | 1 | no | — |
| 160 | C2×C3⋊D9 | — | 9 | 1 | no | — |
| 161 | C2×AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 162 | C2×AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 163 | C2×AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 164 | C2×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 165 | D3×D9 | — | 9 | 1 | no | — |
| 166 | D3×D9 | — | 9 | 1 | no | — |
| 167 | D3×D9 | — | 9 | 1 | no | — |
| 168 | D3×D9 | — | 27 | 1 | no | — |
| 169 | D3×D9 | — | 27 | 1 | no | — |
| 170 | D3×D9 | — | 27 | 1 | no | — |
| 171 | C34 | — | 2 | 1 | no | — |
| 172 | C34 | D32 | 1 | 1 | yes | characteristic |
| 173 | C34 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 174 | C3×3−1+2 | — | 2 | 1 | no | — |
| 175 | C3×3−1+2 | — | 2 | 1 | no | — |
| 176 | C3×3−1+2 | — | 2 | 1 | no | — |
| 177 | C3×3−1+2 | — | 2 | 1 | no | — |
| 178 | C3×3−1+2 | — | 2 | 1 | no | — |
| 179 | C3×3−1+2 | — | 2 | 1 | no | — |
| 180 | C3×3−1+2 | — | 4 | 1 | no | — |
| 181 | C3×3−1+2 | — | 4 | 1 | no | — |
| 182 | C3×3−1+2 | — | 4 | 1 | no | — |
| 183 | C3×3−1+2 | — | 6 | 1 | no | — |
| 184 | C3×3−1+2 | — | 6 | 1 | no | — |
| 185 | C3×3−1+2 | — | 6 | 1 | no | — |
| 186 | C3×3−1+2 | — | 12 | 1 | no | — |
| 187 | C3×3−1+2 | — | 12 | 1 | no | — |
| 188 | C3×3−1+2 | — | 12 | 1 | no | — |
| 189 | C3×3−1+2 | — | 12 | 1 | no | — |
| 190 | C3×3−1+2 | — | 12 | 1 | no | — |
| 191 | C3×3−1+2 | — | 12 | 1 | no | — |
| 192 | C3×3−1+2 | — | 12 | 1 | no | — |
| 193 | C3×3−1+2 | D32 | 1 | 1 | yes | characteristic, complemented |
| 194 | C3×3−1+2 | D32 | 1 | 1 | yes | characteristic, complemented |
| 195 | C3×3−1+2 | D32 | 1 | 1 | yes | characteristic, complemented |
| 196 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 197 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 198 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 199 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 200 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 201 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 202 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 203 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 204 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 205 | C3×H(3,𝔽3) | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 206 | C32×C9 | — | 2 | 1 | no | — |
| 207 | C32×C9 | — | 2 | 1 | no | — |
| 208 | C32×C9 | — | 2 | 1 | no | — |
| 209 | C32×C9 | — | 2 | 1 | no | — |
| 210 | C32×C9 | — | 2 | 1 | no | — |
| 211 | C32×C9 | — | 3 | 1 | no | — |
| 212 | C32×C9 | — | 4 | 1 | no | — |
| 213 | C32×C9 | — | 6 | 1 | no | — |
| 214 | C32×C9 | — | 6 | 1 | no | — |
| 215 | C32×C9 | — | 6 | 1 | no | — |
| 216 | C32×C9 | — | 6 | 1 | no | — |
| 217 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 218 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 219 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 220 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 221 | C32⋊C9 | — | 2 | 1 | no | — |
| 222 | C32⋊C9 | — | 2 | 1 | no | — |
| 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 | — | 4 | 1 | no | — |
| 228 | C32⋊C9 | — | 4 | 1 | no | — |
| 229 | C32⋊C9 | — | 4 | 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 | C2×C33 | — | 9 | 1 | no | — |
| 243 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 244 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 245 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 246 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 247 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 248 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 249 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 250 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 251 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 252 | C3⋊(C3⋊D3) | — | 27 | 1 | no | — |
| 253 | C3⋊(C3⋊D3) | — | 54 | 1 | no | — |
| 254 | C3⋊(C3⋊D3) | — | 54 | 1 | no | — |
| 255 | C3⋊(C3⋊D3) | — | 54 | 1 | no | — |
| 256 | C3⋊(C3⋊D3) | — | 54 | 1 | no | — |
| 257 | C3×C3⋊D3 | — | 3 | 1 | no | — |
| 258 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 259 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 260 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 261 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 262 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 263 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 264 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 265 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 266 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 267 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 268 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 269 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 270 | C3×C3⋊D3 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 271 | C3×C3⋊D3 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 272 | C3×C3⋊D3 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 273 | C3×C3⋊D3 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 274 | C32×D3 | — | 3 | 1 | no | — |
| 275 | C32×D3 | — | 3 | 1 | no | — |
| 276 | C32×D3 | — | 6 | 1 | no | — |
| 277 | C32×D3 | — | 9 | 1 | no | — |
| 278 | C32×D3 | — | 9 | 1 | no | — |
| 279 | C32×D3 | — | 9 | 1 | no | — |
| 280 | C32×D3 | — | 9 | 1 | no | — |
| 281 | C32×D3 | — | 9 | 1 | no | — |
| 282 | C32×D3 | — | 9 | 1 | no | — |
| 283 | C32×D3 | — | 9 | 1 | no | — |
| 284 | C32×D3 | — | 9 | 1 | no | — |
| 285 | C32×D3 | — | 9 | 1 | no | — |
| 286 | C32×D3 | — | 9 | 1 | no | — |
| 287 | C32×D3 | — | 9 | 1 | no | — |
| 288 | C32×D3 | — | 18 | 1 | no | — |
| 289 | C32×D3 | — | 18 | 1 | no | — |
| 290 | C32×D3 | — | 18 | 1 | no | — |
| 291 | C32×D3 | — | 18 | 1 | no | — |
| 292 | C32×D3 | — | 18 | 1 | no | — |
| 293 | C2×3−1+2 | — | 9 | 1 | no | — |
| 294 | C2×3−1+2 | — | 9 | 1 | no | — |
| 295 | C2×3−1+2 | — | 9 | 1 | no | — |
| 296 | C2×3−1+2 | — | 18 | 1 | no | — |
| 297 | C2×3−1+2 | — | 18 | 1 | no | — |
| 298 | C2×3−1+2 | — | 18 | 1 | no | — |
| 299 | C2×H(3,𝔽3) | — | 27 | 1 | no | — |
| 300 | C2×C3×C9 | — | 9 | 1 | no | — |
| 301 | C2×C3×C9 | — | 18 | 1 | no | — |
| 302 | C3⋊D9 | — | 9 | 1 | no | — |
| 303 | C3⋊D9 | — | 9 | 1 | no | — |
| 304 | C3⋊D9 | — | 9 | 1 | no | — |
| 305 | C3⋊D9 | — | 9 | 1 | no | — |
| 306 | C3⋊D9 | — | 18 | 1 | no | — |
| 307 | C3⋊D9 | — | 18 | 1 | no | — |
| 308 | C3⋊D9 | — | 18 | 1 | no | — |
| 309 | C3⋊D9 | — | 18 | 1 | no | — |
| 310 | C3⋊D9 | — | 18 | 1 | no | — |
| 311 | C3⋊D9 | — | 18 | 1 | no | — |
| 312 | C3⋊D9 | — | 18 | 1 | no | — |
| 313 | C3⋊D9 | — | 27 | 1 | no | — |
| 314 | C3⋊D9 | — | 27 | 1 | no | — |
| 315 | C3⋊D9 | — | 27 | 1 | no | — |
| 316 | C3⋊D9 | — | 54 | 1 | no | — |
| 317 | C3⋊D9 | — | 54 | 1 | no | — |
| 318 | C3⋊D9 | — | 54 | 1 | no | — |
| 319 | C3⋊D9 | — | 54 | 2 | no | — |
| 320 | C3⋊D9 | — | 54 | 2 | no | — |
| 321 | C3⋊D9 | — | 54 | 2 | no | — |
| 322 | C3⋊D9 | — | 54 | 1 | no | — |
| 323 | C3⋊D9 | — | 54 | 1 | no | — |
| 324 | C3⋊D9 | — | 54 | 1 | no | — |
| 325 | C3⋊D9 | — | 54 | 1 | no | — |
| 326 | C3⋊D9 | — | 54 | 2 | no | — |
| 327 | C3⋊D9 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 328 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 329 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 330 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 331 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 332 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 333 | AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 334 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 335 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 336 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 337 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 338 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 339 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 340 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 341 | (C3⋊D3)⋊C3 | — | 6 | 1 | no | — |
| 342 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 343 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 344 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 345 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 346 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 347 | D3×C9 | — | 3 | 1 | no | — |
| 348 | D3×C9 | — | 3 | 1 | no | — |
| 349 | D3×C9 | — | 3 | 1 | no | — |
| 350 | D3×C9 | — | 6 | 1 | no | — |
| 351 | D3×C9 | — | 6 | 1 | no | — |
| 352 | D3×C9 | — | 6 | 1 | no | — |
| 353 | D3×C9 | — | 9 | 1 | no | — |
| 354 | D3×C9 | — | 9 | 1 | no | — |
| 355 | D3×C9 | — | 9 | 1 | no | — |
| 356 | C3×D9 | — | 3 | 1 | no | — |
| 357 | C3×D9 | — | 3 | 1 | no | — |
| 358 | C3×D9 | — | 3 | 1 | no | — |
| 359 | C3×D9 | — | 9 | 1 | no | — |
| 360 | C3×D9 | — | 9 | 1 | no | — |
| 361 | C3×D9 | — | 9 | 1 | no | — |
| 362 | C2×C3⋊D3 | — | 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 | D32 | — | 27 | 1 | no | — |
| 370 | D32 | — | 27 | 1 | no | — |
| 371 | D32 | — | 27 | 1 | no | — |
| 372 | D32 | — | 27 | 1 | no | — |
| 373 | D32 | — | 81 | 1 | no | — |
| 374 | D32 | — | 81 | 1 | no | — |
| 375 | D32 | — | 81 | 1 | no | — |
| 376 | D32 | — | 81 | 1 | no | — |
| 377 | C2×D9 | — | 27 | 1 | no | — |
| 378 | C2×D9 | — | 27 | 1 | no | — |
| 379 | C2×D9 | — | 27 | 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 | — | 3 | 1 | no | — |
| 387 | C33 | — | 3 | 1 | no | — |
| 388 | C33 | — | 3 | 1 | no | — |
| 389 | C33 | — | 3 | 1 | no | — |
| 390 | C33 | — | 4 | 1 | no | — |
| 391 | C33 | — | 6 | 1 | no | — |
| 392 | C33 | — | 6 | 1 | no | — |
| 393 | C33 | — | 6 | 1 | no | — |
| 394 | C33 | — | 6 | 1 | no | — |
| 395 | C33 | — | 6 | 1 | no | — |
| 396 | C33 | — | 6 | 1 | no | — |
| 397 | C33 | — | 6 | 1 | no | — |
| 398 | C33 | — | 6 | 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 | C2×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 409 | C33 | C2×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 410 | C33 | C2×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 411 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 412 | C33 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 413 | C33 | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 414 | 3−1+2 | — | 6 | 1 | no | — |
| 415 | 3−1+2 | — | 6 | 1 | no | — |
| 416 | 3−1+2 | — | 6 | 1 | no | — |
| 417 | 3−1+2 | — | 6 | 1 | no | — |
| 418 | 3−1+2 | — | 6 | 1 | no | — |
| 419 | 3−1+2 | — | 6 | 1 | no | — |
| 420 | 3−1+2 | — | 6 | 1 | no | — |
| 421 | 3−1+2 | — | 6 | 1 | no | — |
| 422 | 3−1+2 | — | 12 | 1 | no | — |
| 423 | 3−1+2 | — | 12 | 1 | no | — |
| 424 | 3−1+2 | — | 12 | 1 | no | — |
| 425 | 3−1+2 | — | 12 | 2 | no | — |
| 426 | 3−1+2 | — | 12 | 2 | no | — |
| 427 | 3−1+2 | — | 12 | 2 | no | — |
| 428 | 3−1+2 | — | 12 | 1 | no | — |
| 429 | 3−1+2 | — | 12 | 1 | no | — |
| 430 | 3−1+2 | — | 12 | 1 | no | — |
| 431 | 3−1+2 | — | 12 | 1 | no | — |
| 432 | 3−1+2 | — | 12 | 1 | no | — |
| 433 | 3−1+2 | — | 12 | 1 | no | — |
| 434 | 3−1+2 | — | 12 | 1 | no | — |
| 435 | 3−1+2 | — | 12 | 1 | no | — |
| 436 | 3−1+2 | — | 12 | 1 | no | — |
| 437 | 3−1+2 | — | 12 | 1 | no | — |
| 438 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 439 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 440 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 441 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 442 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 443 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 444 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 445 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 446 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 447 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 448 | C3×C9 | — | 2 | 1 | no | — |
| 449 | C3×C9 | — | 2 | 1 | no | — |
| 450 | C3×C9 | — | 2 | 1 | no | — |
| 451 | C3×C9 | — | 2 | 1 | no | — |
| 452 | C3×C9 | — | 2 | 1 | no | — |
| 453 | C3×C9 | — | 2 | 1 | no | — |
| 454 | C3×C9 | — | 2 | 1 | no | — |
| 455 | C3×C9 | — | 2 | 1 | no | — |
| 456 | C3×C9 | — | 2 | 1 | no | — |
| 457 | C3×C9 | — | 2 | 1 | no | — |
| 458 | C3×C9 | — | 3 | 1 | no | — |
| 459 | C3×C9 | — | 3 | 1 | no | — |
| 460 | C3×C9 | — | 3 | 1 | no | — |
| 461 | C3×C9 | — | 4 | 1 | no | — |
| 462 | C3×C9 | — | 4 | 1 | no | — |
| 463 | C3×C9 | — | 4 | 1 | no | — |
| 464 | C3×C9 | — | 6 | 2 | no | — |
| 465 | C3×C9 | — | 6 | 2 | no | — |
| 466 | C3×C9 | — | 6 | 2 | no | — |
| 467 | C3×C9 | — | 6 | 1 | no | — |
| 468 | C3×C9 | — | 6 | 1 | no | — |
| 469 | C3×C9 | — | 6 | 1 | no | — |
| 470 | C3×C9 | — | 6 | 2 | no | — |
| 471 | C3×C9 | — | 6 | 1 | no | — |
| 472 | C3×C9 | — | 6 | 1 | no | — |
| 473 | C3×C9 | — | 6 | 1 | no | — |
| 474 | C3×C9 | — | 6 | 1 | no | — |
| 475 | C3×C9 | — | 6 | 1 | no | — |
| 476 | C3×C9 | — | 12 | 1 | no | — |
| 477 | C3×C9 | — | 12 | 2 | no | — |
| 478 | C3×C9 | — | 12 | 1 | no | — |
| 479 | C3×C9 | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 480 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 481 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 482 | C3×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 483 | C2×C32 | — | 9 | 1 | no | — |
| 484 | C2×C32 | — | 9 | 1 | no | — |
| 485 | C2×C32 | — | 18 | 1 | no | — |
| 486 | C2×C32 | — | 27 | 1 | no | — |
| 487 | C2×C32 | — | 27 | 1 | no | — |
| 488 | C2×C32 | — | 27 | 1 | no | — |
| 489 | C2×C32 | — | 54 | 1 | no | — |
| 490 | C2×C32 | — | 54 | 1 | no | — |
| 491 | C2×C32 | — | 54 | 1 | no | — |
| 492 | C3⋊D3 | — | 3 | 1 | no | — |
| 493 | C3⋊D3 | — | 27 | 1 | no | — |
| 494 | C3⋊D3 | — | 27 | 1 | no | — |
| 495 | C3⋊D3 | — | 27 | 1 | no | — |
| 496 | C3⋊D3 | — | 27 | 1 | no | — |
| 497 | C3⋊D3 | — | 27 | 1 | no | — |
| 498 | C3⋊D3 | — | 27 | 1 | no | — |
| 499 | C3⋊D3 | — | 54 | 1 | no | — |
| 500 | C3⋊D3 | — | 54 | 1 | no | — |
| 501 | C3⋊D3 | — | 54 | 1 | no | — |
| 502 | C3⋊D3 | — | 54 | 1 | no | — |
| 503 | C3⋊D3 | — | 54 | 1 | no | — |
| 504 | C3⋊D3 | — | 54 | 1 | no | — |
| 505 | C3⋊D3 | — | 54 | 1 | no | — |
| 506 | C3⋊D3 | — | 54 | 1 | no | — |
| 507 | C3⋊D3 | — | 81 | 1 | no | — |
| 508 | C3⋊D3 | — | 81 | 1 | no | — |
| 509 | C3⋊D3 | — | 81 | 1 | no | — |
| 510 | C3⋊D3 | — | 81 | 1 | no | — |
| 511 | C3⋊D3 | — | 162 | 1 | no | — |
| 512 | C3⋊D3 | — | 162 | 1 | no | — |
| 513 | C3⋊D3 | — | 162 | 1 | no | — |
| 514 | C3⋊D3 | — | 162 | 1 | no | — |
| 515 | C3⋊D3 | — | 162 | 2 | no | — |
| 516 | C3⋊D3 | — | 162 | 2 | no | — |
| 517 | C3⋊D3 | — | 162 | 2 | no | — |
| 518 | C3⋊D3 | — | 162 | 2 | no | — |
| 519 | C3⋊D3 | — | 162 | 1 | no | — |
| 520 | C3⋊D3 | — | 162 | 1 | no | — |
| 521 | C3⋊D3 | — | 162 | 1 | no | — |
| 522 | C3⋊D3 | — | 162 | 1 | no | — |
| 523 | C3⋊D3 | C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 524 | C3×D3 | — | 3 | 1 | no | — |
| 525 | C3×D3 | — | 3 | 1 | no | — |
| 526 | C3×D3 | — | 3 | 1 | no | — |
| 527 | C3×D3 | — | 3 | 1 | no | — |
| 528 | C3×D3 | — | 9 | 1 | no | — |
| 529 | C3×D3 | — | 9 | 1 | no | — |
| 530 | C3×D3 | — | 9 | 1 | no | — |
| 531 | C3×D3 | — | 9 | 1 | no | — |
| 532 | C3×D3 | — | 9 | 1 | no | — |
| 533 | C3×D3 | — | 9 | 1 | no | — |
| 534 | C3×D3 | — | 9 | 1 | no | — |
| 535 | C3×D3 | — | 9 | 1 | no | — |
| 536 | C3×D3 | — | 18 | 1 | no | — |
| 537 | C3×D3 | — | 18 | 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 | — | 54 | 1 | no | — |
| 545 | C3×D3 | — | 54 | 1 | no | — |
| 546 | C3×D3 | — | 54 | 1 | no | — |
| 547 | C3×D3 | — | 54 | 1 | no | — |
| 548 | C3×D3 | — | 54 | 1 | no | — |
| 549 | C3×D3 | — | 54 | 1 | no | — |
| 550 | C3×D3 | — | 81 | 1 | no | — |
| 551 | C3×D3 | — | 81 | 1 | no | — |
| 552 | C3×D3 | — | 81 | 1 | no | — |
| 553 | C3×D3 | — | 81 | 1 | no | — |
| 554 | C3×D3 | — | 81 | 1 | no | — |
| 555 | C3×D3 | — | 162 | 1 | no | — |
| 556 | C3×D3 | — | 162 | 1 | no | — |
| 557 | C3×D3 | — | 162 | 1 | no | — |
| 558 | C3×D3 | — | 162 | 1 | no | — |
| 559 | C2×C9 | — | 9 | 1 | no | — |
| 560 | C2×C9 | — | 9 | 1 | no | — |
| 561 | C2×C9 | — | 9 | 1 | no | — |
| 562 | C2×C9 | — | 18 | 1 | no | — |
| 563 | C2×C9 | — | 18 | 1 | no | — |
| 564 | C2×C9 | — | 18 | 1 | no | — |
| 565 | D9 | — | 3 | 1 | no | — |
| 566 | D9 | — | 3 | 1 | no | — |
| 567 | D9 | — | 3 | 1 | no | — |
| 568 | D9 | — | 27 | 1 | no | — |
| 569 | D9 | — | 27 | 1 | no | — |
| 570 | D9 | — | 27 | 1 | no | — |
| 571 | D9 | — | 54 | 1 | no | — |
| 572 | D9 | — | 54 | 1 | no | — |
| 573 | D9 | — | 54 | 1 | no | — |
| 574 | D9 | — | 162 | 1 | no | — |
| 575 | D9 | — | 162 | 1 | no | — |
| 576 | D9 | — | 162 | 1 | no | — |
| 577 | C22×C3 | — | 243 | 1 | no | — |
| 578 | C2×D3 | — | 81 | 1 | no | — |
| 579 | C2×D3 | — | 81 | 1 | no | — |
| 580 | C2×D3 | — | 81 | 1 | no | — |
| 581 | C2×D3 | — | 81 | 1 | no | — |
| 582 | C2×D3 | — | 81 | 1 | no | — |
| 583 | C2×D3 | — | 243 | 1 | no | — |
| 584 | C32 | — | 2 | 1 | no | — |
| 585 | C32 | — | 2 | 1 | no | — |
| 586 | C32 | — | 2 | 1 | no | — |
| 587 | C32 | — | 2 | 1 | no | — |
| 588 | C32 | — | 2 | 1 | no | — |
| 589 | C32 | — | 2 | 1 | no | — |
| 590 | C32 | — | 2 | 1 | no | — |
| 591 | C32 | — | 2 | 1 | no | — |
| 592 | C32 | — | 3 | 1 | no | — |
| 593 | C32 | — | 3 | 1 | no | — |
| 594 | C32 | — | 3 | 1 | no | — |
| 595 | C32 | — | 3 | 1 | no | — |
| 596 | C32 | — | 3 | 1 | no | — |
| 597 | C32 | — | 6 | 1 | no | — |
| 598 | C32 | — | 6 | 1 | no | — |
| 599 | C32 | — | 6 | 1 | no | — |
| 600 | C32 | — | 6 | 1 | no | — |
| 601 | C32 | — | 6 | 2 | no | — |
| 602 | C32 | — | 6 | 2 | no | — |
| 603 | C32 | — | 6 | 2 | no | — |
| 604 | C32 | — | 6 | 2 | no | — |
| 605 | C32 | — | 6 | 1 | no | — |
| 606 | C32 | — | 6 | 1 | no | — |
| 607 | C32 | — | 6 | 1 | no | — |
| 608 | C32 | — | 6 | 1 | no | — |
| 609 | C32 | — | 6 | 1 | no | — |
| 610 | C32 | — | 6 | 1 | no | — |
| 611 | C32 | — | 6 | 1 | no | — |
| 612 | C32 | — | 6 | 1 | no | — |
| 613 | C32 | — | 9 | 1 | no | — |
| 614 | C32 | — | 12 | 1 | no | — |
| 615 | C32 | — | 12 | 1 | no | — |
| 616 | C32 | — | 12 | 1 | no | — |
| 617 | C32 | — | 12 | 2 | no | — |
| 618 | C32 | — | 12 | 1 | no | — |
| 619 | C32 | — | 12 | 1 | no | — |
| 620 | C32 | — | 12 | 1 | no | — |
| 621 | C32 | — | 18 | 1 | no | — |
| 622 | C32 | — | 18 | 1 | no | — |
| 623 | C32 | — | 36 | 1 | no | — |
| 624 | C32 | — | 36 | 1 | no | — |
| 625 | C32 | — | 36 | 1 | no | — |
| 626 | C32 | — | 36 | 1 | no | — |
| 627 | C32 | — | 36 | 1 | no | — |
| 628 | C32 | — | 36 | 1 | no | — |
| 629 | C32 | — | 36 | 1 | no | — |
| 630 | C32 | — | 36 | 1 | no | — |
| 631 | C32 | — | 36 | 1 | no | — |
| 632 | C32 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 633 | C32 | D3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 634 | C32 | D3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 635 | C32 | D3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 636 | C32 | C2×C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 637 | C32 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 638 | C9 | — | 2 | 1 | no | — |
| 639 | C9 | — | 2 | 1 | no | — |
| 640 | C9 | — | 2 | 1 | no | — |
| 641 | C9 | — | 6 | 1 | no | — |
| 642 | C9 | — | 6 | 1 | no | — |
| 643 | C9 | — | 6 | 1 | no | — |
| 644 | C9 | — | 6 | 1 | no | — |
| 645 | C9 | — | 12 | 1 | no | — |
| 646 | C9 | — | 12 | 1 | no | — |
| 647 | C9 | — | 12 | 1 | no | — |
| 648 | C9 | — | 12 | 1 | no | — |
| 649 | C9 | — | 12 | 1 | no | — |
| 650 | C9 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 651 | C9 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 652 | C9 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 653 | C2×C3 | — | 9 | 1 | no | — |
| 654 | C2×C3 | — | 9 | 1 | no | — |
| 655 | C2×C3 | — | 9 | 1 | no | — |
| 656 | C2×C3 | — | 9 | 1 | no | — |
| 657 | C2×C3 | — | 27 | 1 | no | — |
| 658 | C2×C3 | — | 54 | 1 | no | — |
| 659 | C2×C3 | — | 54 | 1 | no | — |
| 660 | C2×C3 | — | 81 | 1 | no | — |
| 661 | C2×C3 | — | 162 | 1 | no | — |
| 662 | C2×C3 | — | 162 | 1 | no | — |
| 663 | C2×C3 | — | 243 | 1 | no | — |
| 664 | D3 | — | 3 | 1 | no | — |
| 665 | D3 | — | 9 | 1 | no | — |
| 666 | D3 | — | 9 | 1 | no | — |
| 667 | D3 | — | 9 | 1 | no | — |
| 668 | D3 | — | 9 | 1 | no | — |
| 669 | D3 | — | 9 | 1 | no | — |
| 670 | D3 | — | 81 | 1 | no | — |
| 671 | D3 | — | 81 | 1 | no | — |
| 672 | D3 | — | 81 | 1 | no | — |
| 673 | D3 | — | 81 | 1 | no | — |
| 674 | D3 | — | 81 | 1 | no | — |
| 675 | D3 | — | 162 | 1 | no | — |
| 676 | D3 | — | 162 | 1 | no | — |
| 677 | D3 | — | 162 | 1 | no | — |
| 678 | D3 | — | 162 | 1 | no | — |
| 679 | D3 | — | 486 | 1 | no | — |
| 680 | D3 | — | 486 | 1 | no | — |
| 681 | D3 | — | 486 | 1 | no | — |
| 682 | D3 | — | 486 | 1 | no | — |
| 683 | D3 | — | 243 | 1 | no | — |
| 684 | C22 | — | 243 | 1 | no | Sylow |
| 685 | C3 | — | 2 | 1 | no | — |
| 686 | C3 | — | 2 | 1 | no | — |
| 687 | C3 | — | 2 | 1 | no | — |
| 688 | C3 | — | 2 | 1 | no | — |
| 689 | C3 | — | 3 | 1 | no | — |
| 690 | C3 | — | 6 | 1 | no | — |
| 691 | C3 | — | 6 | 1 | no | — |
| 692 | C3 | — | 6 | 1 | no | — |
| 693 | C3 | — | 6 | 1 | no | — |
| 694 | C3 | — | 18 | 1 | no | — |
| 695 | C3 | — | 18 | 1 | no | — |
| 696 | C3 | — | 18 | 1 | no | — |
| 697 | C3 | — | 36 | 1 | no | — |
| 698 | C3 | D9⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic, complemented |
| 699 | C3 | D9⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic, complemented |
| 700 | C3 | D9⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic, complemented |
| 701 | C3 | C3⋊D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 702 | C3 | D3×C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 703 | C2 | — | 9 | 1 | no | — |
| 704 | C2 | — | 27 | 1 | no | — |
| 705 | C2 | — | 243 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C33×C9 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×C9⋊H(3,𝔽3) | C22 |
| socle | C33 | C3×D32 |
| LCS | G ▷ C33×C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊#92303 | C2 | semidirect |
| 2. C3⋊(D9⋊H(3,𝔽3)) | C2 | semidirect |
| 3. C3×#92262 | C2 | semidirect |
| 4. C3⋊D3×C3⋊D9 | C3 | semidirect |
| 10. C3×C9⋊H(3,𝔽3) | C22 | semidirect |
| 11. C3⋊(C3⋊(C3⋊D9)) | C2×C3 | semidirect |
| 15. C3×C3⋊AGL(1,ℤ/9) | D3 | semidirect |
| 17. C3×C9×C3⋊D3 | C2×C3 | semidirect |
| 18. C32×C3⋊D9 | C2×C3 | semidirect |
| 31. #92262 | D3 | semidirect |
| 32. #92262 | D3 | semidirect |
| 33. #92262 | D3 | semidirect |
| 54. C32×3−1+2 | C2×D3 | semidirect |
| 56. C33×C9 | C22×C3 | semidirect |
| 66. C9⋊H(3,𝔽3) | C2×D3 | semidirect |
| 67. C9⋊H(3,𝔽3) | C2×D3 | semidirect |
| 68. C9⋊H(3,𝔽3) | C2×D3 | semidirect |
| 111. C9×C3⋊D3 | C3×D3 | semidirect |
| 112. C9×C3⋊D3 | C3×D3 | semidirect |
| 113. C9×C3⋊D3 | C3×D3 | semidirect |
| 193. C3×3−1+2 | D32 | semidirect |
| 194. C3×3−1+2 | D32 | semidirect |
| 195. C3×3−1+2 | D32 | semidirect |
| 218. C32×C9 | C2×C3×D3 | semidirect |
| 219. C32×C9 | C2×C3×D3 | semidirect |
| 220. C32×C9 | C2×C3×D3 | semidirect |
| 270. C3×C3⋊D3 | AGL(1,ℤ/9) | semidirect |
| 271. C3×C3⋊D3 | AGL(1,ℤ/9) | semidirect |
| 272. C3×C3⋊D3 | AGL(1,ℤ/9) | semidirect |
| 327. C3⋊D9 | (C3⋊D3)⋊C3 | semidirect |
| 408. C33 | C2×AGL(1,ℤ/9) | semidirect |
| 409. C33 | C2×AGL(1,ℤ/9) | semidirect |
| 410. C33 | C2×AGL(1,ℤ/9) | semidirect |
| 479. C3×C9 | C2×(C3⋊D3)⋊C3 | semidirect |
| 523. C3⋊D3 | C3⋊AGL(1,ℤ/9) | semidirect |
| 636. C32 | C2×C3⋊AGL(1,ℤ/9) | semidirect |
| 650. C9 | D3×(C3⋊D3)⋊C3 | semidirect |
| 651. C9 | D3×(C3⋊D3)⋊C3 | semidirect |
| 652. C9 | D3×(C3⋊D3)⋊C3 | semidirect |
| 698. C3 | D9⋊((C3⋊D3)⋊C3) | semidirect |
| 699. C3 | D9⋊((C3⋊D3)⋊C3) | semidirect |
| 700. C3 | D9⋊((C3⋊D3)⋊C3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊#92303 | 2 |
| C3⋊(D9⋊H(3,𝔽3)) | 2 |
| C3×#92262 | 2 |
| C3⋊D3×C3⋊D9 | 3 |
| D3×C3⋊AGL(1,ℤ/9) | 3 |
| C3⋊D3×(C3⋊D3)⋊C3 | 3 |
| D9⋊((C3⋊D3)⋊C3) | 3 |