Finite Group DatabasebetaFinite Group DatabasebetaOrder 4374.
624 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 79 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 | #14552545 | C2 | 1 | 1 | yes | maximal, characteristic, complemented, Sylow |
| 2 | C3×#92314 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3⋊#92264 | — | 3 | 1 | no | maximal |
| 4 | C3⋊#92264 | — | 3 | 1 | no | maximal |
| 5 | #13090669 | — | 3 | 1 | no | maximal |
| 6 | #13090669 | — | 3 | 1 | no | maximal |
| 7 | #13090629 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13090615 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #13090615 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C3×#6900 | C2×C3 | 1 | 1 | yes | characteristic |
| 11 | C3×#6896 | D3 | 1 | 1 | yes | characteristic |
| 12 | C3×#6896 | D3 | 1 | 1 | yes | characteristic |
| 13 | #10624575 | — | 2 | 1 | no | — |
| 14 | #10624575 | — | 2 | 1 | no | — |
| 15 | #10624575 | — | 2 | 1 | no | — |
| 16 | #10624575 | — | 2 | 1 | no | — |
| 17 | #10624572 | — | 2 | 1 | no | — |
| 18 | #10624572 | — | 2 | 1 | no | — |
| 19 | #10624567 | D3 | 1 | 1 | yes | characteristic |
| 20 | #10624567 | D3 | 1 | 1 | yes | characteristic |
| 21 | #10624565 | — | 2 | 1 | no | — |
| 22 | #10624565 | — | 2 | 1 | no | — |
| 23 | #10624561 | — | 2 | 1 | no | — |
| 24 | #10624561 | — | 2 | 1 | no | — |
| 25 | #10624561 | — | 2 | 1 | no | — |
| 26 | #10624561 | — | 2 | 1 | no | — |
| 27 | #10624560 | — | 2 | 1 | no | — |
| 28 | #10624560 | — | 2 | 1 | no | — |
| 29 | #10624550 | — | 2 | 1 | no | — |
| 30 | #10624550 | — | 2 | 1 | no | — |
| 31 | #10624550 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | C9×C9⋊C9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 33 | C9×C9⋊C9 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 34 | C3⋊D3×3−1+2 | — | 9 | 1 | no | — |
| 35 | C3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 36 | C3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 37 | C3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 38 | C3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 39 | #92314 | — | 3 | 1 | no | — |
| 40 | C3⋊(D9⋊C9) | — | 3 | 1 | no | — |
| 41 | C3⋊(D9⋊C9) | — | 3 | 1 | no | — |
| 42 | C3⋊(D9⋊C9) | — | 3 | 1 | no | — |
| 43 | C3⋊(D9⋊C9) | — | 3 | 1 | no | — |
| 44 | C3×C9⋊D9 | C32 | 1 | 1 | yes | characteristic |
| 45 | C9×C3⋊D9 | — | 3 | 1 | no | — |
| 46 | C9×C3⋊D9 | — | 3 | 1 | no | — |
| 47 | #92264 | — | 9 | 1 | no | — |
| 48 | #92264 | — | 9 | 1 | no | — |
| 49 | #92264 | — | 9 | 2 | no | — |
| 50 | #92264 | — | 9 | 1 | no | — |
| 51 | #92264 | — | 9 | 1 | no | — |
| 52 | #92158 | — | 3 | 1 | no | — |
| 53 | #92158 | — | 3 | 1 | no | — |
| 54 | #92158 | — | 3 | 1 | no | — |
| 55 | #92158 | — | 3 | 1 | no | — |
| 56 | #92158 | — | 3 | 1 | no | — |
| 57 | #92158 | — | 3 | 1 | no | — |
| 58 | C32×3−1+2 | C3×D3 | 1 | 1 | yes | characteristic |
| 59 | C32×3−1+2 | C3×D3 | 1 | 1 | yes | characteristic |
| 60 | C32×3−1+2 | C3×D3 | 1 | 1 | yes | characteristic |
| 61 | C32×3−1+2 | C3×D3 | 1 | 1 | yes | characteristic |
| 62 | C32×3−1+2 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 63 | #6900 | — | 3 | 1 | no | — |
| 64 | #6900 | — | 6 | 1 | no | — |
| 65 | #6900 | — | 6 | 1 | no | — |
| 66 | #6900 | — | 6 | 1 | no | — |
| 67 | #6900 | — | 6 | 1 | no | — |
| 68 | #6896 | — | 3 | 1 | no | — |
| 69 | #6896 | — | 3 | 1 | no | — |
| 70 | #6896 | — | 6 | 2 | no | — |
| 71 | #6896 | — | 6 | 2 | no | — |
| 72 | #6896 | — | 6 | 1 | no | — |
| 73 | #6896 | — | 6 | 1 | no | — |
| 74 | #6896 | — | 6 | 1 | no | — |
| 75 | #6896 | — | 6 | 1 | no | — |
| 76 | #6896 | — | 6 | 1 | no | — |
| 77 | #6896 | — | 6 | 1 | no | — |
| 78 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 79 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 80 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 81 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 82 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 83 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 84 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 85 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 86 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 87 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 88 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 89 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 90 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 91 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 92 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 93 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 94 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 95 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 96 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 97 | C3×C9⋊C9 | — | 2 | 1 | no | — |
| 98 | C3×C9⋊C9 | C3×D3 | 1 | 1 | yes | characteristic |
| 99 | C3×C9⋊C9 | C3×D3 | 1 | 1 | yes | characteristic |
| 100 | C3×C9⋊C9 | C3×D3 | 1 | 1 | yes | characteristic |
| 101 | C3×C9⋊C9 | C3×D3 | 1 | 1 | yes | characteristic |
| 102 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 103 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 104 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 105 | C3×C32⋊C9 | — | 2 | 1 | no | — |
| 106 | C3×C92 | — | 2 | 1 | no | — |
| 107 | C3×C92 | — | 2 | 1 | no | — |
| 108 | C3×C92 | C3×D3 | 1 | 1 | yes | characteristic |
| 109 | C3×C92 | C3×D3 | 1 | 1 | yes | characteristic |
| 110 | C3×C92 | C2×C32 | 1 | 1 | yes | characteristic |
| 111 | #6855 | — | 2 | 1 | no | — |
| 112 | #6855 | — | 2 | 1 | no | — |
| 113 | #6855 | — | 2 | 1 | no | — |
| 114 | #6855 | — | 2 | 1 | no | — |
| 115 | #6855 | — | 2 | 1 | no | — |
| 116 | #6855 | — | 2 | 1 | no | — |
| 117 | #6855 | — | 2 | 1 | no | — |
| 118 | #6855 | — | 2 | 1 | no | — |
| 119 | #6855 | — | 2 | 1 | no | — |
| 120 | #6855 | — | 2 | 1 | no | — |
| 121 | #6855 | — | 2 | 1 | no | — |
| 122 | #6855 | — | 2 | 1 | no | — |
| 123 | #6855 | — | 2 | 1 | no | — |
| 124 | #6855 | — | 2 | 1 | no | — |
| 125 | #6855 | — | 2 | 1 | no | — |
| 126 | #6855 | — | 2 | 1 | no | — |
| 127 | #6855 | — | 2 | 1 | no | — |
| 128 | #6855 | — | 2 | 1 | no | — |
| 129 | #6855 | — | 2 | 1 | no | — |
| 130 | #6855 | — | 2 | 1 | no | — |
| 131 | #6855 | — | 2 | 1 | no | — |
| 132 | #6855 | — | 2 | 1 | no | — |
| 133 | #6855 | — | 2 | 1 | no | — |
| 134 | #6855 | — | 2 | 1 | no | — |
| 135 | #6855 | — | 2 | 1 | no | — |
| 136 | #6855 | — | 2 | 1 | no | — |
| 137 | #6855 | — | 2 | 1 | no | — |
| 138 | #6855 | — | 2 | 1 | no | — |
| 139 | #6855 | — | 2 | 1 | no | — |
| 140 | #6855 | — | 2 | 1 | no | — |
| 141 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 142 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 143 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 144 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 145 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 146 | #6855 | C3×D3 | 1 | 1 | yes | characteristic |
| 147 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 148 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 149 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 150 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 151 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 152 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 153 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 154 | C9×C3⋊D3 | — | 9 | 1 | no | — |
| 155 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 156 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 157 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 158 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 159 | D3×3−1+2 | — | 27 | 1 | no | — |
| 160 | D3×3−1+2 | — | 27 | 1 | no | — |
| 161 | D3×3−1+2 | — | 27 | 1 | no | — |
| 162 | D3×3−1+2 | — | 27 | 1 | no | — |
| 163 | C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 164 | C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 165 | C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 166 | C3×AGL(1,ℤ/9) | — | 9 | 2 | no | — |
| 167 | C3×AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 168 | C3×AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 169 | C3×AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 170 | C9⋊D9 | 3−1+2 | 1 | 1 | yes | characteristic, complemented |
| 171 | D9⋊C9 | — | 9 | 1 | no | — |
| 172 | D9⋊C9 | — | 9 | 1 | no | — |
| 173 | D9⋊C9 | — | 9 | 1 | no | — |
| 174 | D9⋊C9 | — | 9 | 1 | no | — |
| 175 | D9⋊C9 | — | 9 | 2 | no | — |
| 176 | D9⋊C9 | — | 9 | 1 | no | — |
| 177 | D9⋊C9 | — | 9 | 1 | no | — |
| 178 | D9⋊C9 | — | 9 | 2 | no | — |
| 179 | D9⋊C9 | — | 9 | 1 | no | — |
| 180 | D9⋊C9 | — | 9 | 1 | no | — |
| 181 | C9×D9 | — | 9 | 2 | no | — |
| 182 | C9×D9 | — | 9 | 1 | no | — |
| 183 | C9×D9 | — | 9 | 1 | no | — |
| 184 | C9×D9 | — | 9 | 1 | no | — |
| 185 | C9×D9 | — | 9 | 1 | no | — |
| 186 | C34 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 187 | C3×3−1+2 | — | 3 | 1 | no | — |
| 188 | C3×3−1+2 | — | 3 | 1 | no | — |
| 189 | C3×3−1+2 | — | 3 | 1 | no | — |
| 190 | C3×3−1+2 | — | 3 | 1 | no | — |
| 191 | C3×3−1+2 | — | 3 | 1 | no | — |
| 192 | C3×3−1+2 | — | 6 | 1 | no | — |
| 193 | C3×3−1+2 | — | 6 | 1 | no | — |
| 194 | C3×3−1+2 | — | 6 | 1 | no | — |
| 195 | C3×3−1+2 | — | 6 | 1 | no | — |
| 196 | C3×3−1+2 | — | 6 | 2 | no | — |
| 197 | C3×3−1+2 | — | 6 | 1 | no | — |
| 198 | C3×3−1+2 | — | 6 | 1 | no | — |
| 199 | C3×3−1+2 | — | 6 | 1 | no | — |
| 200 | C3×3−1+2 | — | 6 | 1 | no | — |
| 201 | C3×3−1+2 | — | 6 | 1 | no | — |
| 202 | C3×3−1+2 | — | 6 | 1 | no | — |
| 203 | C3×3−1+2 | — | 6 | 1 | no | — |
| 204 | C3×3−1+2 | — | 6 | 1 | no | — |
| 205 | C3×3−1+2 | — | 6 | 1 | no | — |
| 206 | C3×3−1+2 | — | 6 | 1 | no | — |
| 207 | C3×3−1+2 | — | 6 | 2 | no | — |
| 208 | C3×3−1+2 | — | 6 | 1 | no | — |
| 209 | C3×3−1+2 | — | 9 | 1 | no | — |
| 210 | C3×3−1+2 | — | 9 | 1 | no | — |
| 211 | C3×3−1+2 | — | 9 | 1 | no | — |
| 212 | C3×3−1+2 | — | 18 | 1 | no | — |
| 213 | C3×3−1+2 | — | 18 | 1 | no | — |
| 214 | C3×3−1+2 | — | 18 | 1 | no | — |
| 215 | C32×C9 | — | 2 | 1 | no | — |
| 216 | C32×C9 | — | 2 | 1 | no | — |
| 217 | C32×C9 | — | 2 | 1 | no | — |
| 218 | C32×C9 | — | 2 | 1 | no | — |
| 219 | C32×C9 | — | 2 | 1 | no | — |
| 220 | C32×C9 | — | 2 | 1 | no | — |
| 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 | — | 2 | 1 | no | — |
| 228 | C32×C9 | — | 2 | 1 | no | — |
| 229 | C32×C9 | — | 2 | 1 | no | — |
| 230 | C32×C9 | — | 2 | 1 | no | — |
| 231 | C32×C9 | C32×D3 | 1 | 1 | yes | characteristic |
| 232 | C32×C9 | C32×D3 | 1 | 1 | yes | characteristic |
| 233 | C32×C9 | C32×D3 | 1 | 1 | yes | characteristic |
| 234 | C32×C9 | C32×D3 | 1 | 1 | yes | characteristic |
| 235 | C32×C9 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 236 | C32×C9 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 237 | C32×C9 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 238 | C9⋊C9 | — | 2 | 2 | no | — |
| 239 | C9⋊C9 | — | 2 | 1 | no | — |
| 240 | C9⋊C9 | — | 2 | 1 | no | — |
| 241 | C9⋊C9 | — | 2 | 1 | no | — |
| 242 | C9⋊C9 | — | 2 | 1 | no | — |
| 243 | C9⋊C9 | — | 3 | 1 | no | — |
| 244 | C9⋊C9 | — | 3 | 1 | no | — |
| 245 | C9⋊C9 | — | 3 | 1 | no | — |
| 246 | C9⋊C9 | — | 6 | 1 | no | — |
| 247 | C9⋊C9 | — | 6 | 1 | no | — |
| 248 | C9⋊C9 | — | 6 | 1 | no | — |
| 249 | C9⋊C9 | — | 6 | 1 | no | — |
| 250 | C9⋊C9 | — | 6 | 1 | no | — |
| 251 | C9⋊C9 | — | 6 | 1 | no | — |
| 252 | C9⋊C9 | — | 6 | 2 | no | — |
| 253 | C9⋊C9 | — | 6 | 1 | no | — |
| 254 | C9⋊C9 | — | 6 | 1 | no | — |
| 255 | C9⋊C9 | — | 6 | 2 | no | — |
| 256 | C9⋊C9 | — | 6 | 1 | no | — |
| 257 | C9⋊C9 | — | 6 | 1 | no | — |
| 258 | C9⋊C9 | — | 6 | 2 | no | — |
| 259 | C9⋊C9 | — | 6 | 1 | no | — |
| 260 | C9⋊C9 | — | 6 | 1 | no | — |
| 261 | C9⋊C9 | — | 6 | 1 | no | — |
| 262 | C9⋊C9 | — | 6 | 1 | no | — |
| 263 | C9⋊C9 | — | 6 | 2 | no | — |
| 264 | C9⋊C9 | — | 6 | 1 | no | — |
| 265 | C9⋊C9 | — | 6 | 1 | no | — |
| 266 | C9⋊C9 | — | 6 | 2 | no | — |
| 267 | C9⋊C9 | — | 6 | 2 | no | — |
| 268 | C9⋊C9 | — | 6 | 2 | no | — |
| 269 | C9⋊C9 | — | 6 | 2 | no | — |
| 270 | C9⋊C9 | — | 6 | 2 | no | — |
| 271 | C9⋊C9 | — | 6 | 2 | no | — |
| 272 | C9⋊C9 | — | 6 | 1 | no | — |
| 273 | C9⋊C9 | — | 6 | 2 | no | — |
| 274 | C9⋊C9 | — | 6 | 1 | no | — |
| 275 | C9⋊C9 | — | 6 | 1 | no | — |
| 276 | C9⋊C9 | — | 6 | 1 | no | — |
| 277 | C9⋊C9 | — | 6 | 1 | no | — |
| 278 | C9⋊C9 | — | 6 | 1 | no | — |
| 279 | C9⋊C9 | — | 6 | 1 | no | — |
| 280 | C9⋊C9 | — | 18 | 1 | no | — |
| 281 | C9⋊C9 | — | 18 | 1 | no | — |
| 282 | C9⋊C9 | — | 18 | 1 | no | — |
| 283 | C9⋊C9 | — | 18 | 1 | no | — |
| 284 | C9⋊C9 | — | 18 | 1 | no | — |
| 285 | C9⋊C9 | — | 18 | 1 | no | — |
| 286 | C9⋊C9 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 287 | C9⋊C9 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 288 | C9⋊C9 | AGL(1,ℤ/9) | 1 | 2 | yes | complemented |
| 289 | C9⋊C9 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 290 | C9⋊C9 | AGL(1,ℤ/9) | 1 | 1 | yes | characteristic, complemented |
| 291 | C32⋊C9 | — | 6 | 1 | no | — |
| 292 | C32⋊C9 | — | 6 | 1 | no | — |
| 293 | C32⋊C9 | — | 6 | 1 | no | — |
| 294 | C32⋊C9 | — | 6 | 1 | no | — |
| 295 | C32⋊C9 | — | 6 | 2 | no | — |
| 296 | C32⋊C9 | — | 18 | 1 | no | — |
| 297 | C32⋊C9 | — | 18 | 1 | no | — |
| 298 | C92 | — | 2 | 1 | no | — |
| 299 | C92 | — | 2 | 1 | no | — |
| 300 | C92 | — | 2 | 1 | no | — |
| 301 | C92 | — | 2 | 1 | no | — |
| 302 | C92 | — | 3 | 2 | no | — |
| 303 | C92 | — | 6 | 1 | no | — |
| 304 | C92 | — | 6 | 1 | no | — |
| 305 | C92 | — | 6 | 2 | no | — |
| 306 | C92 | — | 6 | 1 | no | — |
| 307 | C92 | — | 6 | 1 | no | — |
| 308 | C92 | — | 6 | 1 | no | — |
| 309 | C92 | — | 6 | 1 | no | — |
| 310 | C92 | — | 6 | 1 | no | — |
| 311 | C92 | — | 6 | 1 | no | — |
| 312 | C92 | C2×3−1+2 | 1 | 1 | yes | characteristic, complemented |
| 313 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 314 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 315 | C32×D3 | — | 27 | 1 | no | — |
| 316 | C32×D3 | — | 27 | 1 | no | — |
| 317 | C32×D3 | — | 27 | 1 | no | — |
| 318 | C32×D3 | — | 27 | 1 | no | — |
| 319 | C2×3−1+2 | — | 81 | 1 | no | — |
| 320 | C3⋊D9 | — | 3 | 1 | no | — |
| 321 | C3⋊D9 | — | 3 | 1 | no | — |
| 322 | C3⋊D9 | — | 3 | 1 | no | — |
| 323 | C3⋊D9 | — | 3 | 1 | no | — |
| 324 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 325 | AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 326 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 327 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 328 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 329 | AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 330 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 331 | AGL(1,ℤ/9) | — | 27 | 1 | no | — |
| 332 | AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 333 | D3×C9 | — | 27 | 1 | no | — |
| 334 | D3×C9 | — | 27 | 1 | no | — |
| 335 | D3×C9 | — | 27 | 1 | no | — |
| 336 | D3×C9 | — | 27 | 1 | no | — |
| 337 | D3×C9 | — | 27 | 1 | no | — |
| 338 | D3×C9 | — | 27 | 1 | no | — |
| 339 | D3×C9 | — | 27 | 1 | no | — |
| 340 | D3×C9 | — | 27 | 1 | no | — |
| 341 | D3×C9 | — | 27 | 1 | no | — |
| 342 | D3×C9 | — | 27 | 1 | no | — |
| 343 | D3×C9 | — | 27 | 1 | no | — |
| 344 | D3×C9 | — | 27 | 1 | no | — |
| 345 | C3×D9 | — | 9 | 2 | no | — |
| 346 | C3×D9 | — | 9 | 1 | no | — |
| 347 | C3×D9 | — | 9 | 1 | no | — |
| 348 | C3×D9 | — | 9 | 1 | no | — |
| 349 | C3×D9 | — | 9 | 1 | no | — |
| 350 | C3×D9 | — | 27 | 1 | no | — |
| 351 | C3×D9 | — | 27 | 1 | no | — |
| 352 | C33 | — | 3 | 1 | no | — |
| 353 | C33 | — | 3 | 1 | no | — |
| 354 | C33 | — | 3 | 1 | no | — |
| 355 | C33 | — | 3 | 1 | no | — |
| 356 | C33 | — | 6 | 1 | no | — |
| 357 | C33 | — | 6 | 1 | no | — |
| 358 | C33 | — | 6 | 1 | no | — |
| 359 | C33 | — | 6 | 1 | no | — |
| 360 | C33 | — | 6 | 1 | no | — |
| 361 | C33 | C32×C3⋊D3 | 1 | 1 | yes | characteristic |
| 362 | 3−1+2 | — | 9 | 2 | no | — |
| 363 | 3−1+2 | — | 9 | 1 | no | — |
| 364 | 3−1+2 | — | 9 | 1 | no | — |
| 365 | 3−1+2 | — | 18 | 2 | no | — |
| 366 | 3−1+2 | — | 18 | 1 | no | — |
| 367 | 3−1+2 | — | 18 | 1 | no | — |
| 368 | 3−1+2 | — | 18 | 1 | no | — |
| 369 | 3−1+2 | — | 18 | 1 | no | — |
| 370 | 3−1+2 | — | 18 | 1 | no | — |
| 371 | 3−1+2 | — | 18 | 1 | no | — |
| 372 | 3−1+2 | — | 18 | 1 | no | — |
| 373 | 3−1+2 | — | 18 | 2 | no | — |
| 374 | 3−1+2 | — | 18 | 1 | no | — |
| 375 | 3−1+2 | — | 18 | 2 | no | — |
| 376 | 3−1+2 | — | 18 | 3 | no | — |
| 377 | 3−1+2 | — | 18 | 3 | no | — |
| 378 | 3−1+2 | — | 18 | 2 | no | — |
| 379 | 3−1+2 | — | 18 | 1 | no | — |
| 380 | 3−1+2 | — | 18 | 1 | no | — |
| 381 | 3−1+2 | — | 18 | 1 | no | — |
| 382 | C3×C9 | — | 2 | 1 | no | — |
| 383 | C3×C9 | — | 2 | 1 | no | — |
| 384 | C3×C9 | — | 2 | 1 | no | — |
| 385 | C3×C9 | — | 2 | 1 | no | — |
| 386 | C3×C9 | — | 2 | 2 | no | — |
| 387 | C3×C9 | — | 2 | 1 | no | — |
| 388 | C3×C9 | — | 2 | 1 | no | — |
| 389 | C3×C9 | — | 2 | 1 | no | — |
| 390 | C3×C9 | — | 2 | 1 | no | — |
| 391 | C3×C9 | — | 2 | 1 | no | — |
| 392 | C3×C9 | — | 2 | 1 | no | — |
| 393 | C3×C9 | — | 2 | 2 | no | — |
| 394 | C3×C9 | — | 2 | 1 | no | — |
| 395 | C3×C9 | — | 2 | 1 | no | — |
| 396 | C3×C9 | — | 2 | 1 | no | — |
| 397 | C3×C9 | — | 2 | 1 | no | — |
| 398 | C3×C9 | — | 3 | 1 | no | — |
| 399 | C3×C9 | — | 3 | 1 | no | — |
| 400 | C3×C9 | — | 3 | 1 | no | — |
| 401 | C3×C9 | — | 3 | 1 | no | — |
| 402 | C3×C9 | — | 3 | 1 | no | — |
| 403 | C3×C9 | — | 3 | 1 | no | — |
| 404 | C3×C9 | — | 3 | 1 | no | — |
| 405 | C3×C9 | — | 3 | 1 | no | — |
| 406 | C3×C9 | — | 6 | 1 | no | — |
| 407 | C3×C9 | — | 6 | 1 | no | — |
| 408 | C3×C9 | — | 6 | 1 | no | — |
| 409 | C3×C9 | — | 6 | 1 | no | — |
| 410 | C3×C9 | — | 6 | 1 | no | — |
| 411 | C3×C9 | — | 6 | 1 | no | — |
| 412 | C3×C9 | — | 6 | 1 | no | — |
| 413 | C3×C9 | — | 6 | 1 | no | — |
| 414 | C3×C9 | — | 6 | 1 | no | — |
| 415 | C3×C9 | — | 6 | 1 | no | — |
| 416 | C3×C9 | — | 6 | 1 | no | — |
| 417 | C3×C9 | — | 6 | 1 | no | — |
| 418 | C3×C9 | — | 6 | 1 | no | — |
| 419 | C3×C9 | — | 6 | 1 | no | — |
| 420 | C3×C9 | — | 6 | 1 | no | — |
| 421 | C3×C9 | — | 6 | 1 | no | — |
| 422 | C3×C9 | — | 6 | 1 | no | — |
| 423 | C3×C9 | — | 6 | 1 | no | — |
| 424 | C3×C9 | — | 6 | 1 | no | — |
| 425 | C3×C9 | — | 6 | 1 | no | — |
| 426 | C3×C9 | — | 6 | 1 | no | — |
| 427 | C3×C9 | — | 6 | 1 | no | — |
| 428 | C3×C9 | — | 6 | 1 | no | — |
| 429 | C3×C9 | — | 6 | 1 | no | — |
| 430 | C3×C9 | — | 6 | 1 | no | — |
| 431 | C3×C9 | — | 6 | 1 | no | — |
| 432 | C3×C9 | — | 6 | 1 | no | — |
| 433 | C3×C9 | — | 6 | 1 | no | — |
| 434 | C3×C9 | — | 6 | 1 | no | — |
| 435 | C3×C9 | — | 6 | 1 | no | — |
| 436 | C3×C9 | — | 6 | 1 | no | — |
| 437 | C3×C9 | — | 6 | 1 | no | — |
| 438 | C3×C9 | — | 6 | 1 | no | — |
| 439 | C3×C9 | — | 6 | 1 | no | — |
| 440 | C3×C9 | — | 6 | 1 | no | — |
| 441 | C3×C9 | — | 6 | 1 | no | — |
| 442 | C3×C9 | — | 6 | 1 | no | — |
| 443 | C3×C9 | — | 6 | 1 | no | — |
| 444 | C3×C9 | — | 6 | 1 | no | — |
| 445 | C3×C9 | — | 6 | 1 | no | — |
| 446 | C3×C9 | — | 6 | 1 | no | — |
| 447 | C3×C9 | — | 6 | 1 | no | — |
| 448 | C3×C9 | — | 6 | 1 | no | — |
| 449 | C3×C9 | — | 6 | 1 | no | — |
| 450 | C3×C9 | — | 6 | 2 | no | — |
| 451 | C3×C9 | — | 6 | 2 | no | — |
| 452 | C3×C9 | — | 6 | 1 | no | — |
| 453 | C3×C9 | — | 6 | 1 | no | — |
| 454 | C3×C9 | — | 6 | 1 | no | — |
| 455 | C3×C9 | — | 6 | 1 | no | — |
| 456 | C3×C9 | — | 6 | 1 | no | — |
| 457 | C3×C9 | — | 6 | 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 | — | 6 | 1 | no | — |
| 469 | C3×C9 | — | 6 | 1 | no | — |
| 470 | C3×C9 | — | 6 | 1 | no | — |
| 471 | C3×C9 | — | 6 | 1 | no | — |
| 472 | C3×C9 | C3×AGL(1,ℤ/9) | 1 | 2 | yes | — |
| 473 | C3×C9 | C3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 474 | C3×C9 | C3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 475 | C3×C9 | C3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 476 | C3×C9 | C3×AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 477 | C3×C9 | D3×3−1+2 | 1 | 1 | yes | characteristic |
| 478 | C3×C9 | D3×3−1+2 | 1 | 1 | yes | characteristic |
| 479 | C3×C9 | D3×3−1+2 | 1 | 1 | yes | characteristic |
| 480 | C3×C9 | D3×3−1+2 | 1 | 1 | yes | characteristic |
| 481 | C3×C9 | C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 482 | C3×C9 | C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 483 | C2×C32 | — | 81 | 1 | no | — |
| 484 | C3⋊D3 | — | 9 | 1 | no | — |
| 485 | C3×D3 | — | 27 | 1 | no | — |
| 486 | C3×D3 | — | 27 | 1 | no | — |
| 487 | C3×D3 | — | 27 | 1 | no | — |
| 488 | C3×D3 | — | 27 | 1 | no | — |
| 489 | C3×D3 | — | 81 | 1 | no | — |
| 490 | C3×D3 | — | 81 | 1 | no | — |
| 491 | C3×D3 | — | 81 | 1 | no | — |
| 492 | C3×D3 | — | 81 | 1 | no | — |
| 493 | C2×C9 | — | 81 | 1 | no | — |
| 494 | C2×C9 | — | 81 | 1 | no | — |
| 495 | C2×C9 | — | 81 | 1 | no | — |
| 496 | D9 | — | 9 | 1 | no | — |
| 497 | D9 | — | 9 | 2 | no | — |
| 498 | D9 | — | 9 | 1 | no | — |
| 499 | D9 | — | 9 | 1 | no | — |
| 500 | D9 | — | 9 | 1 | no | — |
| 501 | D9 | — | 27 | 1 | no | — |
| 502 | D9 | — | 27 | 1 | no | — |
| 503 | C32 | — | 2 | 1 | no | — |
| 504 | C32 | — | 2 | 1 | no | — |
| 505 | C32 | — | 2 | 1 | no | — |
| 506 | C32 | — | 2 | 1 | no | — |
| 507 | C32 | — | 9 | 1 | no | — |
| 508 | C32 | — | 9 | 1 | no | — |
| 509 | C32 | — | 9 | 1 | no | — |
| 510 | C32 | — | 9 | 1 | no | — |
| 511 | C32 | — | 18 | 1 | no | — |
| 512 | C32 | — | 18 | 1 | no | — |
| 513 | C32 | — | 18 | 1 | no | — |
| 514 | C32 | — | 18 | 1 | no | — |
| 515 | C32 | — | 18 | 1 | no | — |
| 516 | C32 | C3×C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 517 | C32 | C3×C3⋊AGL(1,ℤ/9) | 1 | 1 | yes | characteristic |
| 518 | C32 | C3⋊D3×3−1+2 | 1 | 1 | yes | characteristic |
| 519 | C32 | #4207⋊C3 | 1 | 1 | yes | characteristic |
| 520 | C32 | #4207⋊C3 | 1 | 1 | yes | characteristic |
| 521 | C9 | — | 2 | 2 | no | — |
| 522 | C9 | — | 2 | 1 | no | — |
| 523 | C9 | — | 2 | 1 | no | — |
| 524 | C9 | — | 2 | 1 | no | — |
| 525 | C9 | — | 2 | 1 | no | — |
| 526 | C9 | — | 3 | 1 | no | — |
| 527 | C9 | — | 3 | 1 | no | — |
| 528 | C9 | — | 3 | 1 | no | — |
| 529 | C9 | — | 6 | 1 | no | — |
| 530 | C9 | — | 6 | 1 | no | — |
| 531 | C9 | — | 6 | 1 | no | — |
| 532 | C9 | — | 6 | 1 | no | — |
| 533 | C9 | — | 6 | 2 | no | — |
| 534 | C9 | — | 6 | 1 | no | — |
| 535 | C9 | — | 6 | 1 | no | — |
| 536 | C9 | — | 6 | 1 | no | — |
| 537 | C9 | — | 6 | 1 | no | — |
| 538 | C9 | — | 6 | 1 | no | — |
| 539 | C9 | — | 9 | 1 | no | — |
| 540 | C9 | — | 18 | 1 | no | — |
| 541 | C9 | — | 18 | 1 | no | — |
| 542 | C9 | — | 18 | 1 | no | — |
| 543 | C9 | — | 18 | 1 | no | — |
| 544 | C9 | — | 18 | 1 | no | — |
| 545 | C9 | — | 18 | 1 | no | — |
| 546 | C9 | — | 18 | 1 | no | — |
| 547 | C9 | — | 18 | 1 | no | — |
| 548 | C9 | — | 18 | 1 | no | — |
| 549 | C9 | — | 18 | 1 | no | — |
| 550 | C9 | — | 18 | 1 | no | — |
| 551 | C9 | — | 18 | 1 | no | — |
| 552 | C9 | — | 18 | 1 | no | — |
| 553 | C9 | — | 18 | 1 | no | — |
| 554 | C9 | #92264 | 1 | 1 | yes | characteristic, complemented |
| 555 | C9 | #92264 | 1 | 2 | yes | complemented |
| 556 | C9 | #92264 | 1 | 1 | yes | characteristic, complemented |
| 557 | C9 | #92264 | 1 | 1 | yes | characteristic, complemented |
| 558 | C9 | #92264 | 1 | 1 | yes | characteristic, complemented |
| 559 | C2×C3 | — | 81 | 1 | no | — |
| 560 | C2×C3 | — | 243 | 1 | no | — |
| 561 | D3 | — | 27 | 1 | no | — |
| 562 | D3 | — | 27 | 1 | no | — |
| 563 | D3 | — | 27 | 1 | no | — |
| 564 | D3 | — | 27 | 1 | no | — |
| 565 | C3 | — | 2 | 1 | no | — |
| 566 | C3 | — | 2 | 1 | no | — |
| 567 | C3 | — | 2 | 1 | no | — |
| 568 | C3 | — | 2 | 1 | no | — |
| 569 | C3 | — | 54 | 1 | no | — |
| 570 | C3 | C3⋊#92264 | 1 | 1 | yes | characteristic |
| 571 | C3 | C3⋊#92264 | 1 | 1 | yes | characteristic |
| 572 | C3 | #13091482 | 1 | 1 | yes | characteristic |
| 573 | C3 | #13091482 | 1 | 1 | yes | characteristic |
| 574 | C3 | #13091521 | 1 | 1 | yes | characteristic |
| 575 | C2 | — | 81 | 1 | no | Sylow |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #13091521 |
| commutator, cosocle | C3×C92 | C2×C32 |
| Frattini, socle | C33 | C32×C3⋊D3 |
| Fitting | #14552545 | C2 |
| prime radical | C3×#92314 | C3 |
| hypocenter | C92 | C2×3−1+2 |
| LCS | G ▷ C3×C92 ▷ C92 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14552545 | C2 | semidirect |
| 7. #13090629 | C3 | semidirect |
| 8. #13090615 | C3 | semidirect |
| 9. #13090615 | C3 | semidirect |
| 31. #10624550 | C2×C3 | semidirect |
| 32. C9×C9⋊C9 | C2×C3 | semidirect |
| 33. C9×C9⋊C9 | C2×C3 | semidirect |
| 170. C9⋊D9 | 3−1+2 | semidirect |
| 286. C9⋊C9 | AGL(1,ℤ/9) | semidirect |
| 287. C9⋊C9 | AGL(1,ℤ/9) | semidirect |
| 288. C9⋊C9 | AGL(1,ℤ/9) | semidirect |
| 289. C9⋊C9 | AGL(1,ℤ/9) | semidirect |
| 290. C9⋊C9 | AGL(1,ℤ/9) | semidirect |
| 312. C92 | C2×3−1+2 | semidirect |
| 554. C9 | #92264 | semidirect |
| 555. C9 | #92264 | semidirect |
| 556. C9 | #92264 | semidirect |
| 557. C9 | #92264 | semidirect |
| 558. C9 | #92264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14552545 | 2 |
| C3×#92314 | 3 |
| C3⋊#92264 | 3 |
| #13090669 | 3 |
| #13090629 | 3 |
| #13090615 | 3 |