Finite Group DatabasebetaFinite Group DatabasebetaOrder 8748.
1102 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 62 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 | #72243896 | — | 3 | 1 | no | maximal |
| 2 | #72243894 | — | 3 | 1 | no | maximal |
| 3 | D3×#92330 | — | 3 | 1 | no | maximal |
| 4 | #72243888 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72243766 | — | 3 | 1 | no | maximal |
| 6 | #72243665 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72243619 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72221903 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #72214622 | — | 3 | 1 | no | maximal |
| 10 | #14554857 | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 11 | #13091664 | — | 2 | 1 | no | — |
| 12 | #13091663 | — | 6 | 1 | no | — |
| 13 | #13091652 | — | 3 | 1 | no | — |
| 14 | #13091650 | D3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #13091649 | — | 3 | 1 | no | — |
| 16 | #13091649 | — | 3 | 1 | no | — |
| 17 | #13091649 | — | 3 | 1 | no | — |
| 18 | #13091648 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3⋊#92344 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×#92280 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3⋊#92330 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C3⋊#92330 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#92330 | — | 3 | 1 | no | — |
| 24 | D3×#6908 | — | 3 | 1 | no | — |
| 25 | #13091163 | — | 6 | 1 | no | — |
| 26 | #13091162 | — | 2 | 1 | no | — |
| 27 | #13091153 | — | 3 | 1 | no | — |
| 28 | #13091150 | — | 3 | 1 | no | — |
| 29 | #13091147 | D3 | 1 | 1 | yes | characteristic, complemented |
| 30 | #13091137 | — | 6 | 1 | no | — |
| 31 | #13091135 | — | 2 | 1 | no | — |
| 32 | #13091127 | — | 6 | 1 | no | — |
| 33 | #13091125 | — | 2 | 1 | no | — |
| 34 | #13091110 | — | 3 | 1 | no | — |
| 35 | #13091108 | — | 3 | 1 | no | — |
| 36 | #13091106 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | #13091042 | — | 2 | 1 | no | — |
| 38 | #11758094 | — | 3 | 1 | no | — |
| 39 | D3×C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 40 | #66432⋊C3 | — | 9 | 1 | no | — |
| 41 | D3×#4207 | — | 9 | 1 | no | — |
| 42 | C2×#92330 | — | 9 | 1 | no | — |
| 43 | #92280⋊C2 | — | 9 | 1 | no | — |
| 44 | #92280⋊C2 | — | 9 | 2 | no | — |
| 45 | #11757741 | — | 3 | 1 | no | — |
| 46 | #11757738 | — | 3 | 1 | no | — |
| 47 | #11757735 | — | 3 | 1 | no | — |
| 48 | (#4176⋊C2)⋊C3 | — | 9 | 2 | no | — |
| 49 | D3×#4179 | — | 9 | 1 | no | — |
| 50 | D3×#4177 | — | 9 | 1 | no | — |
| 51 | D3×#4177 | — | 9 | 1 | no | — |
| 52 | C3×#4176⋊C2 | — | 9 | 1 | no | — |
| 53 | D3×#4175 | — | 9 | 1 | no | — |
| 54 | #10624935 | — | 2 | 1 | no | — |
| 55 | #10624935 | — | 2 | 1 | no | — |
| 56 | #10624931 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 57 | #10624931 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 58 | C3×#6908 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 59 | C3×#6908 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 60 | #10624764 | — | 4 | 1 | no | — |
| 61 | #10624763 | — | 2 | 1 | no | — |
| 62 | #10624763 | — | 2 | 1 | no | — |
| 63 | #10624760 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 64 | #10624756 | — | 2 | 1 | no | — |
| 65 | #10624756 | — | 2 | 1 | no | — |
| 66 | #10624756 | — | 4 | 1 | no | — |
| 67 | #10624756 | — | 4 | 1 | no | — |
| 68 | #10624752 | — | 2 | 1 | no | — |
| 69 | #10624752 | — | 2 | 1 | no | — |
| 70 | #10624749 | — | 4 | 1 | no | — |
| 71 | UT(4,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | #10624731 | — | 2 | 1 | no | — |
| 73 | C3⋊(C3⋊(C3⋊D9)) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 74 | C3⋊#4207 | — | 3 | 1 | no | — |
| 75 | C3⋊#4207 | — | 3 | 1 | no | — |
| 76 | C3⋊#4207 | — | 3 | 1 | no | — |
| 77 | C3⋊#4207 | — | 6 | 1 | no | — |
| 78 | C3×C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 79 | #92394 | — | 2 | 1 | no | — |
| 80 | #4207⋊C3 | — | 18 | 1 | no | — |
| 81 | #92392 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 82 | #92391 | — | 9 | 1 | no | — |
| 83 | #92391 | — | 9 | 1 | no | — |
| 84 | C3×#4208 | C3×D3 | 1 | 1 | yes | characteristic |
| 85 | C3×#4207 | — | 9 | 1 | no | — |
| 86 | D3×#737 | — | 3 | 1 | no | — |
| 87 | D3×#737 | — | 6 | 1 | no | — |
| 88 | C32×D3×C9 | — | 3 | 1 | no | — |
| 89 | C2×#6908 | — | 9 | 1 | no | — |
| 90 | #92344 | — | 9 | 1 | no | — |
| 91 | #92344 | — | 9 | 2 | no | — |
| 92 | #92344 | — | 18 | 1 | no | — |
| 93 | #92344 | — | 18 | 2 | no | — |
| 94 | C3⋊(#733⋊C2) | — | 6 | 1 | no | — |
| 95 | C3⋊#4185 | — | 3 | 1 | no | — |
| 96 | C3⋊#4184 | — | 3 | 1 | no | — |
| 97 | C3⋊#4184 | — | 6 | 1 | no | — |
| 98 | C3⋊#4183 | — | 3 | 1 | no | — |
| 99 | C3⋊#4183 | — | 6 | 1 | no | — |
| 100 | #4184⋊C3 | — | 9 | 2 | no | — |
| 101 | #4184⋊C3 | — | 18 | 2 | no | — |
| 102 | #92330 | — | 3 | 1 | no | — |
| 103 | #92330 | — | 6 | 1 | no | — |
| 104 | #92330 | — | 6 | 1 | no | — |
| 105 | #92330 | — | 6 | 2 | no | — |
| 106 | #92330 | — | 9 | 1 | no | — |
| 107 | #92330 | — | 9 | 1 | no | — |
| 108 | #92330 | — | 9 | 2 | no | — |
| 109 | #92330 | — | 18 | 1 | no | — |
| 110 | C3⋊#4179 | — | 3 | 1 | no | — |
| 111 | C3⋊#4179 | — | 3 | 1 | no | — |
| 112 | C3⋊#4177 | — | 3 | 1 | no | — |
| 113 | C3⋊#4177 | — | 3 | 1 | no | — |
| 114 | C3⋊#4177 | — | 3 | 1 | no | — |
| 115 | C3⋊#4177 | — | 6 | 1 | no | — |
| 116 | C3⋊#4177 | — | 6 | 1 | no | — |
| 117 | C3⋊#4177 | — | 6 | 1 | no | — |
| 118 | C3⋊#4177 | — | 6 | 1 | no | — |
| 119 | C3×#4184 | — | 9 | 1 | no | — |
| 120 | C3×#4184 | — | 18 | 1 | no | — |
| 121 | C3⋊#4175 | — | 3 | 1 | no | — |
| 122 | C3⋊#4175 | — | 3 | 1 | no | — |
| 123 | #92301 | — | 6 | 1 | no | — |
| 124 | #6913⋊C2 | — | 6 | 2 | no | — |
| 125 | #4179⋊C3 | — | 18 | 1 | no | — |
| 126 | #92285 | — | 2 | 1 | no | — |
| 127 | #4177⋊C3 | — | 9 | 2 | no | — |
| 128 | #4177⋊C3 | — | 18 | 1 | no | — |
| 129 | #4177⋊C3 | — | 18 | 1 | no | — |
| 130 | #92283 | — | 2 | 1 | no | — |
| 131 | #92283 | — | 3 | 2 | no | — |
| 132 | #4175⋊C3 | — | 18 | 1 | no | — |
| 133 | #92281 | — | 2 | 1 | no | — |
| 134 | #92280 | — | 3 | 1 | no | — |
| 135 | #92280 | — | 3 | 2 | no | — |
| 136 | #92280 | — | 6 | 1 | no | — |
| 137 | D3×#733 | — | 6 | 1 | no | — |
| 138 | D3×#732 | — | 3 | 1 | no | — |
| 139 | C3×#4179 | — | 9 | 1 | no | — |
| 140 | C3×#4178 | C3×D3 | 1 | 1 | yes | characteristic |
| 141 | D3×#731 | — | 3 | 1 | no | — |
| 142 | D3×#731 | — | 6 | 1 | no | — |
| 143 | D3×#731 | — | 9 | 1 | no | — |
| 144 | C3×#4177 | — | 9 | 1 | no | — |
| 145 | C3×#4177 | — | 9 | 1 | no | — |
| 146 | C3×#4177 | — | 9 | 1 | no | — |
| 147 | C3×#4176 | — | 3 | 1 | no | — |
| 148 | C3×#4176 | C3×D3 | 1 | 1 | yes | characteristic |
| 149 | D3×AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 150 | D3×AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 151 | C3×#4175 | — | 9 | 1 | no | — |
| 152 | C3×#4174 | C3×D3 | 1 | 1 | yes | characteristic |
| 153 | D3×C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 154 | C2×C3⋊(C3⋊D9) | — | 9 | 1 | no | — |
| 155 | C2×#4207 | — | 27 | 1 | no | — |
| 156 | #4207⋊C2 | — | 27 | 1 | no | — |
| 157 | #66432 | — | 9 | 1 | no | — |
| 158 | D3×C3⋊D9 | — | 9 | 1 | no | — |
| 159 | D3×C3⋊D9 | — | 9 | 1 | no | — |
| 160 | D3×C3⋊D9 | — | 9 | 1 | no | — |
| 161 | D3×C3⋊D9 | — | 9 | 1 | no | — |
| 162 | D3×C3⋊D9 | — | 27 | 1 | no | — |
| 163 | D3×C3⋊D9 | — | 27 | 2 | no | — |
| 164 | D3×AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 165 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 27 | 1 | no | — |
| 166 | D3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 167 | D3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 168 | C3×D3×D9 | — | 27 | 1 | no | — |
| 169 | C2×#4179 | — | 27 | 1 | no | — |
| 170 | C2×#4177 | — | 27 | 1 | no | — |
| 171 | C2×#4175 | — | 27 | 1 | no | — |
| 172 | #4178⋊C2 | — | 27 | 1 | no | — |
| 173 | #4176⋊C2 | — | 9 | 1 | no | — |
| 174 | #4176⋊C2 | — | 9 | 2 | no | — |
| 175 | #4174⋊C2 | — | 27 | 1 | no | — |
| 176 | 3−1+4 | — | 2 | 1 | no | — |
| 177 | 3−1+4 | — | 2 | 1 | no | — |
| 178 | 3−1+4 | — | 4 | 1 | no | — |
| 179 | H(5,𝔽3) | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 180 | C3×#737 | — | 2 | 1 | no | — |
| 181 | C3×#737 | — | 2 | 1 | no | — |
| 182 | C3×#737 | D32 | 1 | 1 | yes | characteristic |
| 183 | C3×#737 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 184 | C33×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 185 | #6913 | — | 6 | 2 | no | — |
| 186 | #6913 | — | 12 | 1 | no | — |
| 187 | #6913 | — | 12 | 2 | no | — |
| 188 | #6913 | — | 12 | 2 | no | — |
| 189 | #6912 | — | 4 | 1 | no | — |
| 190 | #6912 | — | 4 | 1 | no | — |
| 191 | #6912 | — | 4 | 1 | no | — |
| 192 | #6912 | — | 4 | 1 | no | — |
| 193 | #6911 | — | 2 | 1 | no | — |
| 194 | #6911 | — | 2 | 1 | no | — |
| 195 | #6911 | — | 4 | 1 | no | — |
| 196 | #6910 | — | 2 | 1 | no | — |
| 197 | #6910 | — | 2 | 1 | no | — |
| 198 | #6910 | — | 3 | 2 | no | — |
| 199 | #6910 | — | 4 | 1 | no | — |
| 200 | #6910 | — | 4 | 1 | no | — |
| 201 | #6910 | — | 4 | 1 | no | — |
| 202 | #6910 | — | 4 | 1 | no | — |
| 203 | #6910 | — | 4 | 1 | no | — |
| 204 | #6910 | — | 6 | 1 | no | — |
| 205 | #6910 | — | 6 | 2 | no | — |
| 206 | #6910 | — | 12 | 1 | no | — |
| 207 | #6909 | — | 2 | 1 | no | — |
| 208 | #6909 | — | 2 | 1 | no | — |
| 209 | #6909 | — | 4 | 1 | no | — |
| 210 | #6909 | — | 4 | 1 | no | — |
| 211 | #6909 | — | 4 | 1 | no | — |
| 212 | #6909 | — | 4 | 1 | no | — |
| 213 | #6909 | — | 4 | 1 | no | — |
| 214 | #6908 | — | 3 | 1 | no | — |
| 215 | #6908 | — | 3 | 2 | no | — |
| 216 | #6908 | — | 3 | 1 | no | — |
| 217 | #6908 | — | 6 | 1 | no | — |
| 218 | #6908 | — | 6 | 2 | no | — |
| 219 | #6908 | — | 6 | 1 | no | — |
| 220 | #6908 | — | 6 | 1 | no | — |
| 221 | #6908 | — | 6 | 2 | no | — |
| 222 | #6908 | — | 6 | 1 | no | — |
| 223 | #6908 | — | 6 | 1 | no | — |
| 224 | #6908 | — | 12 | 1 | no | — |
| 225 | #6908 | — | 12 | 1 | no | — |
| 226 | C3×#733 | — | 2 | 1 | no | — |
| 227 | C3×#733 | — | 2 | 1 | no | — |
| 228 | C3×#732 | D32 | 1 | 1 | yes | characteristic |
| 229 | C3×#732 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 230 | C3×#731 | — | 2 | 1 | no | — |
| 231 | C3×#731 | — | 2 | 1 | no | — |
| 232 | C3×#731 | — | 2 | 1 | no | — |
| 233 | C3×#731 | — | 2 | 1 | no | — |
| 234 | C3×#731 | — | 2 | 1 | no | — |
| 235 | C3×#731 | — | 3 | 1 | no | — |
| 236 | C3×#731 | — | 3 | 1 | no | — |
| 237 | C3×#731 | — | 4 | 1 | no | — |
| 238 | C3×#731 | — | 4 | 1 | no | — |
| 239 | C3×#731 | — | 4 | 1 | no | — |
| 240 | C3×#731 | — | 6 | 1 | no | — |
| 241 | C3×#731 | — | 6 | 1 | no | — |
| 242 | C3×#731 | D32 | 1 | 1 | yes | characteristic |
| 243 | C3×#731 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 244 | C3×AΣL(1,𝔽27) | — | 2 | 1 | no | — |
| 245 | C3×AΣL(1,𝔽27) | — | 2 | 1 | no | — |
| 246 | C3×AΣL(1,𝔽27) | D32 | 1 | 1 | yes | characteristic |
| 247 | C3×AΣL(1,𝔽27) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 248 | #6891 | — | 4 | 1 | no | — |
| 249 | C32⋊H(3,𝔽3) | — | 2 | 1 | no | — |
| 250 | C3⋊(C3⋊(C3⋊D3)) | — | 3 | 1 | no | — |
| 251 | C3×C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 252 | C33×D3 | — | 3 | 1 | no | — |
| 253 | C2×#737 | — | 9 | 1 | no | — |
| 254 | C2×#737 | — | 18 | 1 | no | — |
| 255 | C2×C32×C9 | — | 9 | 1 | no | — |
| 256 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 257 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 258 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 259 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 260 | C3⋊(C3⋊D9) | — | 3 | 1 | no | — |
| 261 | C3⋊(C3⋊D9) | — | 6 | 1 | no | — |
| 262 | C3⋊(C3⋊D9) | — | 9 | 1 | no | — |
| 263 | C3⋊(C3⋊D9) | — | 9 | 1 | no | — |
| 264 | C3⋊(C3⋊D9) | — | 9 | 2 | no | — |
| 265 | C3⋊(C3⋊D9) | — | 18 | 1 | no | — |
| 266 | C3⋊(C3⋊D9) | — | 54 | 1 | no | — |
| 267 | #4208 | — | 3 | 1 | no | — |
| 268 | #4208 | — | 6 | 1 | no | — |
| 269 | #4207 | — | 9 | 1 | no | — |
| 270 | #4207 | — | 18 | 1 | no | — |
| 271 | #4207 | — | 18 | 1 | no | — |
| 272 | #4207 | — | 18 | 2 | no | — |
| 273 | #4207 | — | 27 | 1 | no | — |
| 274 | #4207 | — | 27 | 1 | no | — |
| 275 | #4207 | — | 27 | 1 | no | — |
| 276 | #4207 | — | 54 | 1 | no | — |
| 277 | #4207 | — | 54 | 1 | no | — |
| 278 | #4207 | — | 54 | 1 | no | — |
| 279 | #4207 | — | 54 | 1 | no | — |
| 280 | #4207 | — | 54 | 2 | no | — |
| 281 | C3⋊AGL(1,ℤ/9) | — | 9 | 2 | no | — |
| 282 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 283 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 284 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 285 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 286 | C3×#272 | — | 3 | 1 | no | — |
| 287 | C3×#272 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 288 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 289 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 290 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 291 | C3⋊((C3⋊D3)⋊C3) | — | 9 | 1 | no | — |
| 292 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 293 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 294 | C3⋊((C3⋊D3)⋊C3) | — | 18 | 1 | no | — |
| 295 | C3⋊((C3⋊D3)⋊C3) | — | 54 | 1 | no | — |
| 296 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 297 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 298 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 299 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 300 | C3×C3⋊D9 | — | 9 | 1 | no | — |
| 301 | C3×C3⋊D9 | — | 27 | 1 | no | — |
| 302 | C3×C3⋊D9 | — | 27 | 2 | no | — |
| 303 | D3×3−1+2 | — | 6 | 1 | no | — |
| 304 | D3×3−1+2 | — | 6 | 1 | no | — |
| 305 | D3×3−1+2 | — | 6 | 1 | no | — |
| 306 | D3×3−1+2 | — | 9 | 2 | no | — |
| 307 | D3×3−1+2 | — | 18 | 2 | no | — |
| 308 | D3×3−1+2 | — | 18 | 1 | no | — |
| 309 | C3×AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 310 | C3×AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 311 | C3×AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 312 | D3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 313 | D3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 314 | D3×H(3,𝔽3) | — | 9 | 1 | no | — |
| 315 | C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 316 | C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 317 | C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 318 | C3×(C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 319 | C3×(C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 320 | C3×(C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 321 | C3×D3×C9 | — | 3 | 1 | no | — |
| 322 | C3×D3×C9 | — | 3 | 1 | no | — |
| 323 | C3×D3×C9 | — | 3 | 1 | no | — |
| 324 | C3×D3×C9 | — | 9 | 1 | no | — |
| 325 | C3×D3×C9 | — | 9 | 2 | no | — |
| 326 | C3×D3×C9 | — | 9 | 1 | no | — |
| 327 | C3×D3×C9 | — | 9 | 1 | no | — |
| 328 | C3×D3×C9 | — | 18 | 1 | no | — |
| 329 | C32×D9 | — | 27 | 1 | no | — |
| 330 | C2×#733 | — | 18 | 1 | no | — |
| 331 | C2×#732 | — | 9 | 1 | no | — |
| 332 | C2×#731 | — | 9 | 1 | no | — |
| 333 | C2×#731 | — | 18 | 1 | no | — |
| 334 | C2×AΣL(1,𝔽27) | — | 9 | 1 | no | — |
| 335 | C2×AΣL(1,𝔽27) | — | 18 | 1 | no | — |
| 336 | #733⋊C2 | — | 54 | 1 | no | — |
| 337 | #733⋊C2 | — | 54 | 2 | no | — |
| 338 | #4185 | — | 27 | 1 | no | — |
| 339 | #4185 | — | 54 | 1 | no | — |
| 340 | #4184 | — | 9 | 1 | no | — |
| 341 | #4184 | — | 9 | 2 | no | — |
| 342 | #4184 | — | 18 | 1 | no | — |
| 343 | #4184 | — | 18 | 2 | no | — |
| 344 | #4184 | — | 54 | 1 | no | — |
| 345 | #4184 | — | 54 | 2 | no | — |
| 346 | #4183 | — | 27 | 1 | no | — |
| 347 | #4183 | — | 54 | 1 | no | — |
| 348 | #4183 | — | 54 | 1 | no | — |
| 349 | #4183 | — | 54 | 2 | no | — |
| 350 | #4179 | — | 9 | 1 | no | — |
| 351 | #4179 | — | 18 | 1 | no | — |
| 352 | #4179 | — | 18 | 1 | no | — |
| 353 | #4179 | — | 18 | 2 | no | — |
| 354 | #4179 | — | 27 | 1 | no | — |
| 355 | #4179 | — | 27 | 1 | no | — |
| 356 | #4178 | — | 3 | 1 | no | — |
| 357 | #4178 | — | 6 | 1 | no | — |
| 358 | #4177 | — | 9 | 1 | no | — |
| 359 | #4177 | — | 9 | 1 | no | — |
| 360 | #4177 | — | 9 | 1 | no | — |
| 361 | #4177 | — | 9 | 2 | no | — |
| 362 | #4177 | — | 18 | 1 | no | — |
| 363 | #4177 | — | 18 | 1 | no | — |
| 364 | #4177 | — | 18 | 1 | no | — |
| 365 | #4177 | — | 18 | 1 | no | — |
| 366 | #4177 | — | 18 | 1 | no | — |
| 367 | #4177 | — | 18 | 2 | no | — |
| 368 | #4177 | — | 18 | 2 | no | — |
| 369 | #4177 | — | 18 | 2 | no | — |
| 370 | #4177 | — | 54 | 1 | no | — |
| 371 | #4176 | — | 6 | 1 | no | — |
| 372 | #4176 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 373 | #4176 | (C3⋊D3)⋊C3 | 1 | 2 | yes | complemented |
| 374 | #4175 | — | 9 | 1 | no | — |
| 375 | #4175 | — | 18 | 1 | no | — |
| 376 | #4175 | — | 18 | 1 | no | — |
| 377 | #4175 | — | 18 | 2 | no | — |
| 378 | #4175 | — | 27 | 1 | no | — |
| 379 | #4175 | — | 27 | 1 | no | — |
| 380 | #4174 | — | 3 | 1 | no | — |
| 381 | #4174 | — | 6 | 1 | no | — |
| 382 | C2×C3⋊(C3⋊D3) | — | 27 | 1 | no | — |
| 383 | D3×C3⋊D3 | — | 27 | 1 | no | — |
| 384 | D3×C3⋊D3 | — | 27 | 1 | no | — |
| 385 | D3×C3⋊D3 | — | 81 | 1 | no | — |
| 386 | D3×C3⋊D3 | — | 81 | 3 | no | — |
| 387 | C3×D32 | — | 81 | 1 | no | — |
| 388 | C3×D32 | — | 81 | 1 | no | — |
| 389 | C2×C3⋊D9 | — | 27 | 1 | no | — |
| 390 | C2×C3⋊D9 | — | 27 | 1 | no | — |
| 391 | C2×C3⋊D9 | — | 27 | 1 | no | — |
| 392 | C2×C3⋊D9 | — | 81 | 1 | no | — |
| 393 | C2×C3⋊D9 | — | 81 | 2 | no | — |
| 394 | C2×AGL(1,ℤ/9) | — | 81 | 2 | no | — |
| 395 | C2×(C3⋊D3)⋊C3 | — | 81 | 1 | no | — |
| 396 | C2×C3×D9 | — | 81 | 1 | no | — |
| 397 | ((C3⋊D3)⋊C3)⋊C2 | — | 27 | 1 | no | — |
| 398 | D3×D9 | — | 27 | 1 | no | — |
| 399 | D3×D9 | — | 27 | 2 | no | — |
| 400 | D3×D9 | — | 81 | 1 | no | — |
| 401 | D3×D9 | — | 81 | 1 | no | — |
| 402 | D3×D9 | — | 81 | 1 | no | — |
| 403 | C34 | C3×D32 | 1 | 1 | yes | characteristic |
| 404 | #737 | — | 3 | 1 | no | — |
| 405 | #737 | — | 3 | 1 | no | — |
| 406 | #737 | — | 6 | 1 | no | — |
| 407 | #737 | — | 6 | 1 | no | — |
| 408 | #737 | — | 6 | 1 | no | — |
| 409 | #737 | — | 6 | 2 | no | — |
| 410 | #737 | — | 6 | 1 | no | — |
| 411 | #737 | — | 6 | 2 | no | — |
| 412 | #737 | — | 6 | 1 | no | — |
| 413 | #737 | — | 6 | 1 | no | — |
| 414 | #737 | — | 12 | 1 | no | — |
| 415 | #737 | — | 12 | 1 | no | — |
| 416 | #737 | — | 12 | 2 | no | — |
| 417 | #737 | — | 12 | 1 | no | — |
| 418 | #737 | — | 12 | 1 | no | — |
| 419 | #737 | — | 12 | 2 | no | — |
| 420 | #737 | — | 18 | 1 | no | — |
| 421 | #737 | — | 18 | 1 | no | — |
| 422 | #737 | — | 36 | 1 | no | — |
| 423 | #737 | — | 36 | 1 | no | — |
| 424 | #737 | — | 36 | 1 | no | — |
| 425 | #737 | — | 36 | 1 | no | — |
| 426 | #737 | — | 36 | 1 | no | — |
| 427 | C3×3−1+2 | — | 2 | 1 | no | — |
| 428 | C3×3−1+2 | — | 2 | 1 | no | — |
| 429 | C3×3−1+2 | — | 2 | 1 | no | — |
| 430 | C3×3−1+2 | — | 2 | 1 | no | — |
| 431 | C3×3−1+2 | — | 2 | 1 | no | — |
| 432 | C3×3−1+2 | — | 2 | 1 | no | — |
| 433 | C3×3−1+2 | — | 3 | 2 | no | — |
| 434 | C3×3−1+2 | — | 4 | 1 | no | — |
| 435 | C3×3−1+2 | — | 4 | 1 | no | — |
| 436 | C3×3−1+2 | — | 4 | 1 | no | — |
| 437 | C3×3−1+2 | — | 6 | 1 | no | — |
| 438 | C3×3−1+2 | — | 6 | 2 | no | — |
| 439 | C3×3−1+2 | — | 6 | 1 | no | — |
| 440 | C3×3−1+2 | — | 6 | 2 | no | — |
| 441 | C3×3−1+2 | — | 6 | 1 | no | — |
| 442 | C3×3−1+2 | — | 12 | 1 | no | — |
| 443 | C3×3−1+2 | — | 12 | 1 | no | — |
| 444 | C3×3−1+2 | — | 36 | 1 | no | — |
| 445 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 446 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 447 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 448 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 449 | C3×H(3,𝔽3) | — | 3 | 1 | no | — |
| 450 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 451 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 452 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 453 | C3×H(3,𝔽3) | — | 18 | 1 | no | — |
| 454 | C3×H(3,𝔽3) | — | 18 | 1 | no | — |
| 455 | C3×H(3,𝔽3) | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 456 | C3×H(3,𝔽3) | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 457 | C32×C9 | — | 3 | 1 | no | — |
| 458 | C32×C9 | — | 3 | 1 | no | — |
| 459 | C32×C9 | — | 3 | 2 | no | — |
| 460 | C32×C9 | — | 3 | 1 | no | — |
| 461 | C32×C9 | — | 3 | 1 | no | — |
| 462 | C32×C9 | — | 6 | 1 | no | — |
| 463 | C32×C9 | — | 6 | 1 | no | — |
| 464 | C32×C9 | — | 6 | 1 | no | — |
| 465 | C32×C9 | — | 18 | 1 | no | — |
| 466 | C32×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 467 | C32×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 468 | C32×C9 | C3×D32 | 1 | 1 | yes | characteristic |
| 469 | #733 | — | 6 | 2 | no | — |
| 470 | #733 | — | 6 | 1 | no | — |
| 471 | #733 | — | 6 | 1 | no | — |
| 472 | #733 | — | 12 | 1 | no | — |
| 473 | #733 | — | 12 | 2 | no | — |
| 474 | #733 | — | 12 | 1 | no | — |
| 475 | #733 | — | 12 | 1 | no | — |
| 476 | #733 | — | 12 | 2 | no | — |
| 477 | #733 | — | 36 | 1 | no | — |
| 478 | #733 | — | 36 | 1 | no | — |
| 479 | #732 | — | 3 | 1 | no | — |
| 480 | #732 | — | 3 | 1 | no | — |
| 481 | #732 | — | 6 | 1 | no | — |
| 482 | #732 | — | 6 | 1 | no | — |
| 483 | #732 | — | 6 | 2 | no | — |
| 484 | #732 | — | 6 | 1 | no | — |
| 485 | #732 | — | 6 | 1 | no | — |
| 486 | #732 | — | 12 | 1 | no | — |
| 487 | #732 | — | 36 | 1 | no | — |
| 488 | #731 | — | 2 | 1 | no | — |
| 489 | #731 | — | 2 | 2 | no | — |
| 490 | #731 | — | 2 | 1 | no | — |
| 491 | #731 | — | 2 | 1 | no | — |
| 492 | #731 | — | 4 | 1 | no | — |
| 493 | #731 | — | 6 | 2 | no | — |
| 494 | #731 | — | 6 | 2 | no | — |
| 495 | #731 | — | 6 | 1 | no | — |
| 496 | #731 | — | 6 | 1 | no | — |
| 497 | #731 | — | 6 | 1 | no | — |
| 498 | #731 | — | 6 | 2 | no | — |
| 499 | #731 | — | 6 | 1 | no | — |
| 500 | #731 | — | 6 | 2 | no | — |
| 501 | #731 | — | 6 | 1 | no | — |
| 502 | #731 | — | 6 | 1 | no | — |
| 503 | #731 | — | 12 | 1 | no | — |
| 504 | #731 | — | 12 | 2 | no | — |
| 505 | #731 | — | 12 | 1 | no | — |
| 506 | #731 | — | 12 | 1 | no | — |
| 507 | #731 | — | 12 | 1 | no | — |
| 508 | #731 | — | 12 | 2 | no | — |
| 509 | #731 | — | 12 | 2 | no | — |
| 510 | #731 | — | 12 | 2 | no | — |
| 511 | #731 | — | 12 | 1 | no | — |
| 512 | #731 | — | 12 | 1 | no | — |
| 513 | #731 | — | 18 | 1 | no | — |
| 514 | #731 | — | 36 | 1 | no | — |
| 515 | #731 | — | 36 | 1 | no | — |
| 516 | #731 | — | 36 | 1 | no | — |
| 517 | #731 | — | 36 | 1 | no | — |
| 518 | #731 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 519 | #731 | C2×(C3⋊D3)⋊C3 | 1 | 2 | yes | — |
| 520 | #731 | C2×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 521 | AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 522 | AΣL(1,𝔽27) | — | 3 | 1 | no | — |
| 523 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 524 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 525 | AΣL(1,𝔽27) | — | 6 | 2 | no | — |
| 526 | AΣL(1,𝔽27) | — | 6 | 2 | no | — |
| 527 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 528 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 529 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 530 | AΣL(1,𝔽27) | — | 6 | 1 | no | — |
| 531 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 532 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 533 | AΣL(1,𝔽27) | — | 12 | 2 | no | — |
| 534 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 535 | AΣL(1,𝔽27) | — | 12 | 1 | no | — |
| 536 | AΣL(1,𝔽27) | — | 12 | 2 | no | — |
| 537 | AΣL(1,𝔽27) | — | 36 | 1 | no | — |
| 538 | AΣL(1,𝔽27) | — | 36 | 1 | no | — |
| 539 | AΣL(1,𝔽27) | — | 36 | 1 | no | — |
| 540 | C32⋊C9 | — | 36 | 1 | no | — |
| 541 | C2×C33 | — | 9 | 1 | no | — |
| 542 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 543 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 544 | C3⋊(C3⋊D3) | — | 9 | 1 | no | — |
| 545 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 546 | C3⋊(C3⋊D3) | — | 27 | 1 | no | — |
| 547 | C3⋊(C3⋊D3) | — | 27 | 1 | no | — |
| 548 | C3⋊(C3⋊D3) | — | 54 | 1 | no | — |
| 549 | C3⋊(C3⋊D3) | — | 81 | 3 | no | — |
| 550 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 551 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 552 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 553 | C3×C3⋊D3 | — | 27 | 1 | no | — |
| 554 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 555 | C3×C3⋊D3 | — | 54 | 1 | no | — |
| 556 | C3×C3⋊D3 | — | 81 | 1 | no | — |
| 557 | C3×C3⋊D3 | — | 81 | 3 | no | — |
| 558 | C32×D3 | — | 3 | 1 | no | — |
| 559 | C32×D3 | — | 9 | 1 | no | — |
| 560 | C32×D3 | — | 9 | 1 | no | — |
| 561 | C32×D3 | — | 9 | 3 | no | — |
| 562 | C32×D3 | — | 9 | 1 | no | — |
| 563 | C32×D3 | — | 18 | 1 | no | — |
| 564 | C32×D3 | — | 27 | 1 | no | — |
| 565 | C32×D3 | — | 81 | 1 | no | — |
| 566 | C32×D3 | — | 81 | 1 | no | — |
| 567 | C2×3−1+2 | — | 18 | 1 | no | — |
| 568 | C2×3−1+2 | — | 18 | 1 | no | — |
| 569 | C2×3−1+2 | — | 18 | 1 | no | — |
| 570 | C2×3−1+2 | — | 27 | 2 | no | — |
| 571 | C2×3−1+2 | — | 54 | 2 | no | — |
| 572 | C2×H(3,𝔽3) | — | 9 | 1 | no | — |
| 573 | C2×H(3,𝔽3) | — | 18 | 1 | no | — |
| 574 | C2×C3×C9 | — | 9 | 1 | no | — |
| 575 | C2×C3×C9 | — | 9 | 1 | no | — |
| 576 | C2×C3×C9 | — | 9 | 1 | no | — |
| 577 | C2×C3×C9 | — | 27 | 1 | no | — |
| 578 | C2×C3×C9 | — | 27 | 2 | no | — |
| 579 | C2×C3×C9 | — | 27 | 1 | no | — |
| 580 | C2×C3×C9 | — | 54 | 1 | no | — |
| 581 | #272 | C3⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic |
| 582 | C3⋊D9 | — | 9 | 1 | no | — |
| 583 | C3⋊D9 | — | 9 | 1 | no | — |
| 584 | C3⋊D9 | — | 9 | 1 | no | — |
| 585 | C3⋊D9 | — | 9 | 2 | no | — |
| 586 | C3⋊D9 | — | 9 | 1 | no | — |
| 587 | C3⋊D9 | — | 9 | 1 | no | — |
| 588 | C3⋊D9 | — | 18 | 1 | no | — |
| 589 | C3⋊D9 | — | 18 | 1 | no | — |
| 590 | C3⋊D9 | — | 18 | 1 | no | — |
| 591 | C3⋊D9 | — | 18 | 1 | no | — |
| 592 | C3⋊D9 | — | 27 | 1 | no | — |
| 593 | C3⋊D9 | — | 27 | 2 | no | — |
| 594 | C3⋊D9 | — | 27 | 1 | no | — |
| 595 | C3⋊D9 | — | 27 | 1 | no | — |
| 596 | C3⋊D9 | — | 27 | 1 | no | — |
| 597 | C3⋊D9 | — | 27 | 1 | no | — |
| 598 | C3⋊D9 | — | 27 | 1 | no | — |
| 599 | C3⋊D9 | — | 54 | 1 | no | — |
| 600 | C3⋊D9 | — | 54 | 2 | no | — |
| 601 | C3⋊D9 | — | 54 | 1 | no | — |
| 602 | C3⋊D9 | — | 54 | 1 | no | — |
| 603 | C3⋊D9 | — | 54 | 1 | no | — |
| 604 | C3⋊D9 | — | 54 | 1 | no | — |
| 605 | C3⋊D9 | — | 81 | 1 | no | — |
| 606 | C3⋊D9 | — | 81 | 2 | no | — |
| 607 | C3⋊D9 | — | 162 | 1 | no | — |
| 608 | C3⋊D9 | — | 162 | 2 | no | — |
| 609 | AGL(1,ℤ/9) | — | 27 | 2 | no | — |
| 610 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 611 | AGL(1,ℤ/9) | — | 54 | 1 | no | — |
| 612 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 613 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 614 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 615 | AGL(1,ℤ/9) | — | 54 | 2 | no | — |
| 616 | AGL(1,ℤ/9) | — | 81 | 2 | no | — |
| 617 | AGL(1,ℤ/9) | — | 162 | 1 | no | — |
| 618 | AGL(1,ℤ/9) | — | 162 | 1 | no | — |
| 619 | AGL(1,ℤ/9) | — | 162 | 1 | no | — |
| 620 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 621 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 622 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 623 | (C3⋊D3)⋊C3 | — | 27 | 1 | no | — |
| 624 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 625 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 626 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 627 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 628 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 629 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 630 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 631 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 632 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 633 | (C3⋊D3)⋊C3 | — | 54 | 1 | no | — |
| 634 | (C3⋊D3)⋊C3 | — | 162 | 1 | no | — |
| 635 | (C3⋊D3)⋊C3 | — | 162 | 3 | no | — |
| 636 | D3×C9 | — | 3 | 1 | no | — |
| 637 | D3×C9 | — | 3 | 2 | no | — |
| 638 | D3×C9 | — | 9 | 1 | no | — |
| 639 | D3×C9 | — | 9 | 1 | no | — |
| 640 | D3×C9 | — | 18 | 1 | no | — |
| 641 | D3×C9 | — | 18 | 1 | no | — |
| 642 | D3×C9 | — | 18 | 1 | no | — |
| 643 | D3×C9 | — | 27 | 1 | no | — |
| 644 | D3×C9 | — | 54 | 1 | no | — |
| 645 | C3×D9 | — | 27 | 1 | no | — |
| 646 | C3×D9 | — | 27 | 1 | no | — |
| 647 | C3×D9 | — | 27 | 2 | no | — |
| 648 | C3×D9 | — | 54 | 1 | no | — |
| 649 | C3×D9 | — | 54 | 1 | no | — |
| 650 | C3×D9 | — | 54 | 2 | no | — |
| 651 | C3×D9 | — | 81 | 1 | no | — |
| 652 | C3×D9 | — | 81 | 1 | no | — |
| 653 | C3×D9 | — | 81 | 1 | no | — |
| 654 | C3×D9 | — | 81 | 1 | no | — |
| 655 | C2×C3⋊D3 | — | 81 | 1 | no | — |
| 656 | C2×C3⋊D3 | — | 243 | 1 | no | — |
| 657 | C2×C3⋊D3 | — | 243 | 3 | no | — |
| 658 | C2×C3×D3 | — | 243 | 1 | no | — |
| 659 | C2×C3×D3 | — | 243 | 1 | no | — |
| 660 | C2×C3×D3 | — | 243 | 1 | no | — |
| 661 | D32 | — | 81 | 1 | no | — |
| 662 | D32 | — | 81 | 1 | no | — |
| 663 | D32 | — | 243 | 1 | no | — |
| 664 | D32 | — | 243 | 3 | no | — |
| 665 | D32 | — | 243 | 1 | no | — |
| 666 | C2×D9 | — | 81 | 1 | no | — |
| 667 | C2×D9 | — | 81 | 2 | no | — |
| 668 | C2×D9 | — | 243 | 1 | no | — |
| 669 | C2×D9 | — | 243 | 1 | no | — |
| 670 | C33 | — | 3 | 1 | no | — |
| 671 | C33 | — | 3 | 1 | no | — |
| 672 | C33 | — | 3 | 1 | no | — |
| 673 | C33 | — | 3 | 1 | no | — |
| 674 | C33 | — | 6 | 1 | no | — |
| 675 | C33 | — | 6 | 1 | no | — |
| 676 | C33 | — | 6 | 1 | no | — |
| 677 | C33 | — | 6 | 1 | no | — |
| 678 | C33 | — | 9 | 1 | no | — |
| 679 | C33 | — | 9 | 3 | no | — |
| 680 | C33 | — | 12 | 1 | no | — |
| 681 | C33 | — | 18 | 1 | no | — |
| 682 | C33 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 683 | 3−1+2 | — | 2 | 2 | no | — |
| 684 | 3−1+2 | — | 2 | 1 | no | — |
| 685 | 3−1+2 | — | 2 | 1 | no | — |
| 686 | 3−1+2 | — | 4 | 1 | no | — |
| 687 | 3−1+2 | — | 6 | 1 | no | — |
| 688 | 3−1+2 | — | 6 | 1 | no | — |
| 689 | 3−1+2 | — | 6 | 1 | no | — |
| 690 | 3−1+2 | — | 6 | 1 | no | — |
| 691 | 3−1+2 | — | 9 | 2 | no | — |
| 692 | 3−1+2 | — | 12 | 1 | no | — |
| 693 | 3−1+2 | — | 12 | 1 | no | — |
| 694 | 3−1+2 | — | 12 | 1 | no | — |
| 695 | 3−1+2 | — | 12 | 1 | no | — |
| 696 | 3−1+2 | — | 12 | 1 | no | — |
| 697 | 3−1+2 | — | 12 | 1 | no | — |
| 698 | 3−1+2 | — | 12 | 1 | no | — |
| 699 | 3−1+2 | — | 12 | 1 | no | — |
| 700 | 3−1+2 | — | 12 | 1 | no | — |
| 701 | 3−1+2 | — | 12 | 1 | no | — |
| 702 | 3−1+2 | — | 12 | 1 | no | — |
| 703 | 3−1+2 | — | 12 | 1 | no | — |
| 704 | 3−1+2 | — | 12 | 1 | no | — |
| 705 | 3−1+2 | — | 12 | 1 | no | — |
| 706 | 3−1+2 | — | 12 | 1 | no | — |
| 707 | 3−1+2 | — | 18 | 2 | no | — |
| 708 | 3−1+2 | — | 18 | 2 | no | — |
| 709 | 3−1+2 | — | 18 | 1 | no | — |
| 710 | 3−1+2 | — | 18 | 2 | no | — |
| 711 | 3−1+2 | — | 18 | 2 | no | — |
| 712 | 3−1+2 | — | 18 | 2 | no | — |
| 713 | 3−1+2 | — | 36 | 2 | no | — |
| 714 | 3−1+2 | — | 36 | 1 | no | — |
| 715 | 3−1+2 | — | 36 | 2 | no | — |
| 716 | 3−1+2 | — | 36 | 2 | no | — |
| 717 | 3−1+2 | — | 36 | 2 | no | — |
| 718 | 3−1+2 | — | 36 | 2 | no | — |
| 719 | 3−1+2 | — | 36 | 1 | no | — |
| 720 | 3−1+2 | — | 36 | 1 | no | — |
| 721 | 3−1+2 | — | 36 | 1 | no | — |
| 722 | 3−1+2 | — | 36 | 1 | no | — |
| 723 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 724 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 725 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 726 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 727 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 728 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 729 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 730 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 731 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 732 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 733 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 734 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 735 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 736 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 737 | H(3,𝔽3) | — | 18 | 1 | no | — |
| 738 | H(3,𝔽3) | — | 18 | 1 | no | — |
| 739 | H(3,𝔽3) | — | 18 | 1 | no | — |
| 740 | H(3,𝔽3) | — | 54 | 3 | no | — |
| 741 | H(3,𝔽3) | ((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 742 | H(3,𝔽3) | C2×C3⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic |
| 743 | C3×C9 | — | 2 | 1 | no | — |
| 744 | C3×C9 | — | 3 | 1 | no | — |
| 745 | C3×C9 | — | 3 | 1 | no | — |
| 746 | C3×C9 | — | 3 | 1 | no | — |
| 747 | C3×C9 | — | 3 | 1 | no | — |
| 748 | C3×C9 | — | 6 | 1 | no | — |
| 749 | C3×C9 | — | 6 | 1 | no | — |
| 750 | C3×C9 | — | 6 | 1 | no | — |
| 751 | C3×C9 | — | 6 | 1 | no | — |
| 752 | C3×C9 | — | 6 | 1 | no | — |
| 753 | C3×C9 | — | 6 | 1 | no | — |
| 754 | C3×C9 | — | 6 | 1 | no | — |
| 755 | C3×C9 | — | 6 | 1 | no | — |
| 756 | C3×C9 | — | 6 | 1 | no | — |
| 757 | C3×C9 | — | 9 | 1 | no | — |
| 758 | C3×C9 | — | 9 | 2 | no | — |
| 759 | C3×C9 | — | 9 | 1 | no | — |
| 760 | C3×C9 | — | 9 | 1 | no | — |
| 761 | C3×C9 | — | 12 | 1 | no | — |
| 762 | C3×C9 | — | 12 | 1 | no | — |
| 763 | C3×C9 | — | 12 | 1 | no | — |
| 764 | C3×C9 | — | 18 | 1 | no | — |
| 765 | C3×C9 | — | 18 | 2 | no | — |
| 766 | C3×C9 | — | 18 | 1 | no | — |
| 767 | C3×C9 | — | 18 | 2 | no | — |
| 768 | C3×C9 | — | 18 | 1 | no | — |
| 769 | C3×C9 | — | 18 | 1 | no | — |
| 770 | C3×C9 | — | 18 | 1 | no | — |
| 771 | C3×C9 | — | 18 | 1 | no | — |
| 772 | C3×C9 | — | 18 | 1 | no | — |
| 773 | C3×C9 | — | 18 | 2 | no | — |
| 774 | C3×C9 | — | 36 | 1 | no | — |
| 775 | C3×C9 | — | 36 | 1 | no | — |
| 776 | C3×C9 | — | 36 | 2 | no | — |
| 777 | C3×C9 | — | 36 | 1 | no | — |
| 778 | C3×C9 | D3×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 779 | C3×C9 | D3×(C3⋊D3)⋊C3 | 1 | 2 | yes | — |
| 780 | C3×C9 | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 781 | C2×C32 | — | 9 | 1 | no | — |
| 782 | C2×C32 | — | 27 | 1 | no | — |
| 783 | C2×C32 | — | 27 | 1 | no | — |
| 784 | C2×C32 | — | 27 | 3 | no | — |
| 785 | C2×C32 | — | 54 | 1 | no | — |
| 786 | C2×C32 | — | 243 | 1 | no | — |
| 787 | C2×C32 | — | 243 | 1 | no | — |
| 788 | C3⋊D3 | — | 27 | 1 | no | — |
| 789 | C3⋊D3 | — | 27 | 1 | no | — |
| 790 | C3⋊D3 | — | 27 | 1 | no | — |
| 791 | C3⋊D3 | — | 27 | 1 | no | — |
| 792 | C3⋊D3 | — | 54 | 1 | no | — |
| 793 | C3⋊D3 | — | 54 | 1 | no | — |
| 794 | C3⋊D3 | — | 81 | 1 | no | — |
| 795 | C3⋊D3 | — | 81 | 3 | no | — |
| 796 | C3⋊D3 | — | 162 | 1 | no | — |
| 797 | C3⋊D3 | — | 162 | 3 | no | — |
| 798 | C3⋊D3 | — | 486 | 1 | no | — |
| 799 | C3⋊D3 | — | 486 | 2 | no | — |
| 800 | C3⋊D3 | — | 243 | 1 | no | — |
| 801 | C3⋊D3 | — | 243 | 3 | no | — |
| 802 | C3⋊D3 | — | 243 | 3 | no | — |
| 803 | C3⋊D3 | — | 243 | 1 | no | — |
| 804 | C3⋊D3 | — | 243 | 1 | no | — |
| 805 | C3×D3 | — | 3 | 1 | no | — |
| 806 | C3×D3 | — | 9 | 1 | no | — |
| 807 | C3×D3 | — | 9 | 3 | no | — |
| 808 | C3×D3 | — | 9 | 1 | no | — |
| 809 | C3×D3 | — | 27 | 1 | no | — |
| 810 | C3×D3 | — | 27 | 1 | no | — |
| 811 | C3×D3 | — | 54 | 1 | no | — |
| 812 | C3×D3 | — | 81 | 1 | no | — |
| 813 | C3×D3 | — | 81 | 1 | no | — |
| 814 | C3×D3 | — | 81 | 1 | no | — |
| 815 | C3×D3 | — | 81 | 1 | no | — |
| 816 | C3×D3 | — | 81 | 1 | no | — |
| 817 | C3×D3 | — | 162 | 1 | no | — |
| 818 | C3×D3 | — | 162 | 1 | no | — |
| 819 | C3×D3 | — | 486 | 1 | no | — |
| 820 | C3×D3 | — | 486 | 1 | no | — |
| 821 | C3×D3 | — | 243 | 1 | no | — |
| 822 | C3×D3 | — | 243 | 3 | no | — |
| 823 | C3×D3 | — | 243 | 1 | no | — |
| 824 | C3×D3 | — | 243 | 1 | no | — |
| 825 | C3×D3 | — | 243 | 1 | no | — |
| 826 | C2×C9 | — | 9 | 1 | no | — |
| 827 | C2×C9 | — | 9 | 2 | no | — |
| 828 | C2×C9 | — | 27 | 1 | no | — |
| 829 | C2×C9 | — | 27 | 1 | no | — |
| 830 | C2×C9 | — | 54 | 1 | no | — |
| 831 | C2×C9 | — | 54 | 1 | no | — |
| 832 | C2×C9 | — | 54 | 1 | no | — |
| 833 | D9 | — | 27 | 1 | no | — |
| 834 | D9 | — | 27 | 2 | no | — |
| 835 | D9 | — | 54 | 1 | no | — |
| 836 | D9 | — | 54 | 2 | no | — |
| 837 | D9 | — | 81 | 1 | no | — |
| 838 | D9 | — | 81 | 1 | no | — |
| 839 | D9 | — | 81 | 1 | no | — |
| 840 | D9 | — | 81 | 2 | no | — |
| 841 | D9 | — | 81 | 1 | no | — |
| 842 | D9 | — | 162 | 1 | no | — |
| 843 | D9 | — | 162 | 1 | no | — |
| 844 | D9 | — | 162 | 1 | no | — |
| 845 | D9 | — | 243 | 1 | no | — |
| 846 | C22×C3 | — | 729 | 1 | no | — |
| 847 | C2×D3 | — | 729 | 3 | no | — |
| 848 | C2×D3 | — | 729 | 1 | no | — |
| 849 | C2×D3 | — | 243 | 1 | no | — |
| 850 | C2×D3 | — | 243 | 1 | no | — |
| 851 | C2×D3 | — | 243 | 1 | no | — |
| 852 | C32 | — | 2 | 1 | no | — |
| 853 | C32 | — | 3 | 1 | no | — |
| 854 | C32 | — | 3 | 1 | no | — |
| 855 | C32 | — | 6 | 3 | no | — |
| 856 | C32 | — | 6 | 1 | no | — |
| 857 | C32 | — | 6 | 1 | no | — |
| 858 | C32 | — | 9 | 1 | no | — |
| 859 | C32 | — | 9 | 3 | no | — |
| 860 | C32 | — | 9 | 3 | no | — |
| 861 | C32 | — | 9 | 1 | no | — |
| 862 | C32 | — | 18 | 2 | no | — |
| 863 | C32 | — | 18 | 1 | no | — |
| 864 | C32 | — | 18 | 1 | no | — |
| 865 | C32 | — | 18 | 1 | no | — |
| 866 | C32 | — | 27 | 1 | no | — |
| 867 | C32 | — | 27 | 1 | no | — |
| 868 | C32 | — | 36 | 1 | no | — |
| 869 | C32 | — | 54 | 1 | no | — |
| 870 | C32 | — | 54 | 1 | no | — |
| 871 | C32 | — | 54 | 1 | no | — |
| 872 | C32 | — | 81 | 1 | no | — |
| 873 | C32 | — | 108 | 1 | no | — |
| 874 | C32 | — | 162 | 1 | no | — |
| 875 | C32 | D3×C3⋊((C3⋊D3)⋊C3) | 1 | 1 | yes | characteristic |
| 876 | C32 | C3×((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 877 | C9 | — | 3 | 1 | no | — |
| 878 | C9 | — | 3 | 2 | no | — |
| 879 | C9 | — | 3 | 1 | no | — |
| 880 | C9 | — | 6 | 1 | no | — |
| 881 | C9 | — | 6 | 2 | no | — |
| 882 | C9 | — | 6 | 1 | no | — |
| 883 | C9 | — | 6 | 1 | no | — |
| 884 | C9 | — | 9 | 1 | no | — |
| 885 | C9 | — | 12 | 1 | no | — |
| 886 | C9 | — | 18 | 1 | no | — |
| 887 | C9 | — | 18 | 1 | no | — |
| 888 | C9 | — | 18 | 1 | no | — |
| 889 | C9 | — | 18 | 1 | no | — |
| 890 | C9 | — | 36 | 1 | no | — |
| 891 | C9 | — | 36 | 1 | no | — |
| 892 | C9 | — | 36 | 1 | no | — |
| 893 | C2×C3 | — | 9 | 1 | no | — |
| 894 | C2×C3 | — | 27 | 1 | no | — |
| 895 | C2×C3 | — | 27 | 3 | no | — |
| 896 | C2×C3 | — | 81 | 1 | no | — |
| 897 | C2×C3 | — | 162 | 1 | no | — |
| 898 | C2×C3 | — | 486 | 1 | no | — |
| 899 | C2×C3 | — | 486 | 1 | no | — |
| 900 | C2×C3 | — | 243 | 1 | no | — |
| 901 | C2×C3 | — | 243 | 1 | no | — |
| 902 | C2×C3 | — | 243 | 1 | no | — |
| 903 | C2×C3 | — | 243 | 1 | no | — |
| 904 | D3 | — | 3 | 1 | no | — |
| 905 | D3 | — | 9 | 1 | no | — |
| 906 | D3 | — | 81 | 1 | no | — |
| 907 | D3 | — | 81 | 1 | no | — |
| 908 | D3 | — | 1458 | 1 | no | — |
| 909 | D3 | — | 729 | 3 | no | — |
| 910 | D3 | — | 486 | 1 | no | — |
| 911 | D3 | — | 486 | 1 | no | — |
| 912 | D3 | — | 243 | 1 | no | — |
| 913 | D3 | — | 243 | 1 | no | — |
| 914 | D3 | — | 243 | 1 | no | — |
| 915 | D3 | — | 243 | 3 | no | — |
| 916 | D3 | — | 243 | 1 | no | — |
| 917 | C22 | — | 729 | 1 | no | Sylow |
| 918 | C3 | — | 3 | 1 | no | — |
| 919 | C3 | — | 3 | 1 | no | — |
| 920 | C3 | — | 6 | 1 | no | — |
| 921 | C3 | — | 9 | 1 | no | — |
| 922 | C3 | — | 9 | 3 | no | — |
| 923 | C3 | — | 9 | 1 | no | — |
| 924 | C3 | — | 18 | 1 | no | — |
| 925 | C3 | — | 18 | 1 | no | — |
| 926 | C3 | — | 54 | 1 | no | — |
| 927 | C3 | — | 54 | 1 | no | — |
| 928 | C3 | — | 54 | 1 | no | — |
| 929 | C3 | — | 108 | 1 | no | — |
| 930 | C3 | #72214370 | 1 | 1 | yes | characteristic |
| 931 | C2 | — | 9 | 1 | no | — |
| 932 | C2 | — | 243 | 1 | no | — |
| 933 | C2 | — | 243 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#6908 | C22×C3 |
| Frattini | C33 | C3×D3×C3⋊D3 |
| Fitting | #14554857 | C22 |
| socle | C3 | #72214370 |
| LCS | G ▷ C3×#6908 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #72243888 | C3 | semidirect |
| 6. #72243665 | C2 | semidirect |
| 7. #72243619 | C2 | semidirect |
| 8. #72221903 | C2 | semidirect |
| 10. #14554857 | C22 | semidirect |
| 14. #13091650 | D3 | semidirect |
| 18. #13091648 | D3 | semidirect |
| 19. C3⋊#92344 | C2×C3 | semidirect |
| 20. C3×#92280 | C2×C3 | semidirect |
| 21. C3⋊#92330 | D3 | semidirect |
| 22. C3⋊#92330 | C2×C3 | semidirect |
| 29. #13091147 | D3 | semidirect |
| 36. #13091106 | D3 | semidirect |
| 56. #10624931 | C2×D3 | semidirect |
| 57. #10624931 | C2×D3 | semidirect |
| 58. C3×#6908 | C2×D3 | semidirect |
| 59. C3×#6908 | C22×C3 | semidirect |
| 63. #10624760 | C2×D3 | semidirect |
| 73. C3⋊(C3⋊(C3⋊D9)) | C3×D3 | semidirect |
| 184. C33×C9 | C2×C3×D3 | semidirect |
| 372. #4176 | (C3⋊D3)⋊C3 | semidirect |
| 373. #4176 | (C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72243896 | 3 |
| #72243894 | 3 |
| D3×#92330 | 3 |
| #72243888 | 3 |
| #72243766 | 3 |
| #72243665 | 2 |
| #72243619 | 2 |
| #72221903 | 2 |
| #72214622 | 3 |