Finite Group DatabasebetaFinite Group DatabasebetaOrder 7776.
473 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 473 conjugacy classes of subgroups — too many to draw. Only its 33 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 | #72222006 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72222004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72222001 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72221995 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72221986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #72221982 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72221972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72210346 | — | 3 | 1 | no | maximal |
| 9 | ((((C3⋊D3)⋊C3)⋊D3)⋊C3)⋊C2 | — | 2 | 1 | no | — |
| 10 | #14517942 | — | 2 | 1 | no | — |
| 11 | #14517942 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #14517936 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #14517930 | C22 | 1 | 1 | yes | characteristic |
| 14 | #14517925 | — | 2 | 1 | no | — |
| 15 | #10620206⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 16 | #14517916 | — | 2 | 1 | no | — |
| 17 | #14517916 | C22 | 1 | 1 | yes | characteristic |
| 18 | #14517911 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #10620192⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #13049818 | — | 3 | 1 | no | — |
| 21 | #13049813 | — | 3 | 1 | no | — |
| 22 | #13049804 | — | 3 | 1 | no | — |
| 23 | #13049804 | — | 3 | 1 | no | — |
| 24 | #13049803 | — | 3 | 1 | no | — |
| 25 | #13049803 | D3 | 1 | 1 | yes | characteristic, complemented |
| 26 | #13049788 | — | 3 | 1 | no | — |
| 27 | #11757749 | — | 2 | 1 | no | — |
| 28 | #11757731 | D4 | 1 | 1 | yes | characteristic |
| 29 | #11757730 | — | 4 | 1 | no | — |
| 30 | (((C3⋊D3)⋊C3)⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 31 | #11757702 | — | 2 | 1 | no | — |
| 32 | #11757689 | — | 2 | 1 | no | — |
| 33 | #11757689 | D4 | 1 | 1 | yes | characteristic |
| 34 | #66472⋊C3 | — | 2 | 1 | no | — |
| 35 | #66472⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 36 | D3×AΓL(1,𝔽9) | — | 9 | 1 | no | maximal |
| 37 | #10620215 | — | 6 | 1 | no | — |
| 38 | #10620211 | — | 3 | 1 | no | — |
| 39 | #10620211 | — | 6 | 1 | no | — |
| 40 | #10620211 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | #10620206 | — | 3 | 1 | no | — |
| 42 | #10620206 | — | 6 | 1 | no | — |
| 43 | #10620206 | C2×D3 | 1 | 1 | yes | characteristic |
| 44 | #10620198 | — | 3 | 1 | no | — |
| 45 | #10620198 | — | 6 | 1 | no | — |
| 46 | #10620193 | — | 3 | 1 | no | — |
| 47 | #10620192 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 48 | D3×((C3⋊D3)⋊C3)⋊C2 | — | 12 | 1 | no | — |
| 49 | #92338 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 50 | #92301 | C2×D4 | 1 | 1 | yes | characteristic |
| 51 | #92300 | — | 4 | 1 | no | — |
| 52 | #92258 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 53 | (C3⋊D3)⋊H(3,𝔽3) | — | 4 | 1 | no | — |
| 54 | D3×PSU(3,𝔽2) | — | 9 | 1 | no | — |
| 55 | D3×GO+(4,𝔽2) | — | 9 | 1 | no | — |
| 56 | AGL(1,𝔽9)⋊D3 | — | 9 | 1 | no | — |
| 57 | #89092 | — | 9 | 1 | no | — |
| 58 | #89091 | — | 9 | 1 | no | — |
| 59 | C3×AΓL(1,𝔽9) | — | 9 | 1 | no | — |
| 60 | D3×AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 61 | C3⋊D32 | — | 2 | 1 | no | — |
| 62 | C3⋊D32 | — | 3 | 1 | no | — |
| 63 | C3⋊D32 | — | 6 | 1 | no | — |
| 64 | C3×#1113 | — | 12 | 1 | no | — |
| 65 | C3×#1113 | — | 12 | 1 | no | — |
| 66 | #66472 | — | 2 | 1 | no | — |
| 67 | #66472 | — | 3 | 1 | no | — |
| 68 | #66472 | — | 6 | 1 | no | — |
| 69 | #66472 | C22×D3 | 1 | 1 | yes | characteristic |
| 70 | #66432 | — | 12 | 1 | no | — |
| 71 | D3×#272 | — | 12 | 1 | no | — |
| 72 | ((C3⋊D3)⋊C3)⋊D3 | — | 4 | 1 | no | — |
| 73 | ((C3⋊D3)⋊C3)⋊D3 | — | 12 | 1 | no | — |
| 74 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 12 | 1 | no | — |
| 75 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 24 | 1 | no | — |
| 76 | D3×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 77 | D3×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 78 | C2×AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 79 | C2×AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 80 | C32⋊H(3,𝔽3) | C2×SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 81 | D33 | — | 18 | 1 | no | — |
| 82 | D33 | — | 36 | 1 | no | — |
| 83 | D33 | — | 36 | 1 | no | — |
| 84 | C3⋊PSU(3,𝔽2) | — | 9 | 1 | no | — |
| 85 | C3⋊PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 86 | C3×PSU(3,𝔽2) | — | 9 | 1 | no | — |
| 87 | #157⋊D3 | — | 9 | 1 | no | — |
| 88 | D32⋊D3 | — | 18 | 1 | no | — |
| 89 | C3×GO+(4,𝔽2) | — | 9 | 1 | no | — |
| 90 | D3×#157 | — | 9 | 1 | no | — |
| 91 | D3×#157 | — | 18 | 1 | no | — |
| 92 | C3⋊AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 93 | C3×AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 94 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 36 | 1 | no | — |
| 95 | C3⋊(C3⋊(C3⋊D3)) | D3×D4 | 1 | 1 | yes | characteristic |
| 96 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 97 | C32×C3⋊D3 | — | 3 | 1 | no | — |
| 98 | C32×C3⋊D3 | — | 4 | 1 | no | — |
| 99 | C32×C3⋊D3 | — | 12 | 1 | no | — |
| 100 | C3⋊#272 | — | 4 | 1 | no | — |
| 101 | C3×#272 | — | 12 | 1 | no | — |
| 102 | C3×#272 | — | 24 | 1 | no | — |
| 103 | C3⋊((C3⋊D3)⋊C3) | — | 4 | 1 | no | — |
| 104 | C3⋊((C3⋊D3)⋊C3) | — | 12 | 1 | no | — |
| 105 | D3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 106 | C3×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 107 | C3×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 108 | C3×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 109 | C3×(C3⋊D3)⋊C3 | — | 24 | 1 | no | — |
| 110 | C2×PSU(3,𝔽2) | — | 27 | 1 | no | — |
| 111 | C2×PSU(3,𝔽2) | — | 27 | 1 | no | — |
| 112 | C2×GO+(4,𝔽2) | — | 27 | 1 | no | — |
| 113 | C2×GO+(4,𝔽2) | — | 27 | 1 | no | — |
| 114 | C2×AGL(1,𝔽9) | — | 27 | 1 | no | — |
| 115 | C2×AGL(1,𝔽9) | — | 27 | 1 | no | — |
| 116 | AΓL(1,𝔽9) | — | 9 | 1 | no | — |
| 117 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 118 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 119 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 120 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 121 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 122 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 123 | AΓL(1,𝔽9) | — | 27 | 1 | no | — |
| 124 | AΓL(1,𝔽9) | — | 54 | 1 | no | — |
| 125 | #1113 | — | 12 | 1 | no | — |
| 126 | #1113 | — | 12 | 1 | no | — |
| 127 | #1113 | — | 18 | 1 | no | — |
| 128 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 129 | D3×C3⋊D3 | — | 12 | 1 | no | — |
| 130 | D3×C3⋊D3 | — | 12 | 1 | no | — |
| 131 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 132 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 133 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 134 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 135 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 136 | D3×C3⋊D3 | — | 72 | 1 | no | — |
| 137 | C3×D32 | — | 18 | 1 | no | — |
| 138 | C3×D32 | — | 36 | 1 | no | — |
| 139 | C3×D32 | — | 36 | 1 | no | — |
| 140 | C3×D32 | — | 36 | 1 | no | — |
| 141 | C3×D32 | — | 36 | 1 | no | — |
| 142 | C3×D32 | — | 36 | 1 | no | — |
| 143 | C3×D32 | — | 36 | 1 | no | — |
| 144 | C3×D32 | — | 36 | 1 | no | — |
| 145 | C3×D32 | — | 72 | 1 | no | — |
| 146 | C3⋊#157 | — | 9 | 1 | no | — |
| 147 | C3⋊#157 | — | 18 | 1 | no | — |
| 148 | C3×#157 | — | 9 | 1 | no | — |
| 149 | C3×#157 | — | 18 | 1 | no | — |
| 150 | C2×#272 | — | 36 | 1 | no | — |
| 151 | C2×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 152 | C2×(C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 153 | ((C3⋊D3)⋊C3)⋊C2 | — | 12 | 1 | no | — |
| 154 | ((C3⋊D3)⋊C3)⋊C2 | — | 24 | 1 | no | — |
| 155 | ((C3⋊D3)⋊C3)⋊C2 | — | 36 | 1 | no | — |
| 156 | ((C3⋊D3)⋊C3)⋊C2 | — | 36 | 1 | no | — |
| 157 | ((C3⋊D3)⋊C3)⋊C2 | — | 36 | 1 | no | — |
| 158 | ((C3⋊D3)⋊C3)⋊C2 | — | 72 | 1 | no | — |
| 159 | D3×SD16 | — | 81 | 1 | no | — |
| 160 | C34 | D3×SD16 | 1 | 1 | yes | characteristic, complemented |
| 161 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 162 | C3×H(3,𝔽3) | — | 8 | 1 | no | — |
| 163 | C2×D32 | — | 54 | 1 | no | — |
| 164 | C2×D32 | — | 54 | 1 | no | — |
| 165 | C2×D32 | — | 108 | 1 | no | — |
| 166 | C2×D32 | — | 108 | 1 | no | — |
| 167 | C2×D32 | — | 108 | 1 | no | — |
| 168 | C2×#157 | — | 27 | 1 | no | — |
| 169 | C2×#157 | — | 27 | 1 | no | — |
| 170 | C2×#157 | — | 54 | 1 | no | — |
| 171 | C2×#157 | — | 54 | 1 | no | — |
| 172 | PSU(3,𝔽2) | — | 9 | 1 | no | — |
| 173 | PSU(3,𝔽2) | — | 27 | 1 | no | — |
| 174 | PSU(3,𝔽2) | — | 27 | 1 | no | — |
| 175 | PSU(3,𝔽2) | — | 27 | 1 | no | — |
| 176 | PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 177 | PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 178 | PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 179 | PSU(3,𝔽2) | — | 108 | 1 | no | — |
| 180 | GO+(4,𝔽2) | — | 9 | 1 | no | — |
| 181 | GO+(4,𝔽2) | — | 27 | 1 | no | — |
| 182 | GO+(4,𝔽2) | — | 27 | 1 | no | — |
| 183 | GO+(4,𝔽2) | — | 27 | 1 | no | — |
| 184 | GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 185 | GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 186 | GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 187 | GO+(4,𝔽2) | — | 108 | 1 | no | — |
| 188 | AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 189 | AGL(1,𝔽9) | — | 27 | 1 | no | — |
| 190 | AGL(1,𝔽9) | — | 27 | 1 | no | — |
| 191 | AGL(1,𝔽9) | — | 27 | 1 | no | — |
| 192 | AGL(1,𝔽9) | — | 54 | 1 | no | — |
| 193 | C3⋊(C3⋊D3) | — | 12 | 1 | no | — |
| 194 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 195 | C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 196 | C3⋊(C3⋊D3) | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 197 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 198 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 199 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 200 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 201 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 202 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 203 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 204 | C3×C3⋊D3 | — | 12 | 1 | no | — |
| 205 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 206 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 207 | C32×D3 | — | 9 | 1 | no | — |
| 208 | C32×D3 | — | 12 | 1 | no | — |
| 209 | C32×D3 | — | 12 | 1 | no | — |
| 210 | C32×D3 | — | 24 | 1 | no | — |
| 211 | C32×D3 | — | 36 | 1 | no | — |
| 212 | C32×D3 | — | 36 | 1 | no | — |
| 213 | C32×D3 | — | 36 | 1 | no | — |
| 214 | C32×D3 | — | 36 | 1 | no | — |
| 215 | C32×D3 | — | 36 | 1 | no | — |
| 216 | C32×D3 | — | 72 | 1 | no | — |
| 217 | C32×D3 | — | 72 | 1 | no | — |
| 218 | C2×H(3,𝔽3) | — | 36 | 1 | no | — |
| 219 | #272 | — | 12 | 1 | no | — |
| 220 | #272 | — | 24 | 1 | no | — |
| 221 | #272 | — | 36 | 1 | no | — |
| 222 | #272 | — | 72 | 1 | no | — |
| 223 | (C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 224 | (C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 225 | (C3⋊D3)⋊C3 | — | 24 | 1 | no | — |
| 226 | (C3⋊D3)⋊C3 | — | 24 | 1 | no | — |
| 227 | (C3⋊D3)⋊C3 | — | 24 | 1 | no | — |
| 228 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 229 | (C3⋊D3)⋊C3 | — | 36 | 1 | no | — |
| 230 | (C3⋊D3)⋊C3 | — | 48 | 1 | no | — |
| 231 | (C3⋊D3)⋊C3 | — | 72 | 1 | no | — |
| 232 | D3×Q8 | — | 81 | 1 | no | — |
| 233 | D3×D4 | — | 81 | 1 | no | — |
| 234 | C3×SD16 | — | 81 | 1 | no | — |
| 235 | #215 | — | 81 | 1 | no | — |
| 236 | #214 | — | 81 | 1 | no | — |
| 237 | #204 | — | 81 | 1 | no | — |
| 238 | D3×C8 | — | 81 | 1 | no | — |
| 239 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 240 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 241 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 242 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 243 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 244 | C2×C3×D3 | — | 108 | 1 | no | — |
| 245 | C2×C3×D3 | — | 108 | 1 | no | — |
| 246 | C2×C3×D3 | — | 108 | 1 | no | — |
| 247 | C2×C3×D3 | — | 108 | 1 | no | — |
| 248 | C2×C3×D3 | — | 108 | 1 | no | — |
| 249 | C2×C3×D3 | — | 108 | 1 | no | — |
| 250 | C2×C3×D3 | — | 108 | 1 | no | — |
| 251 | C2×C3×D3 | — | 108 | 1 | no | — |
| 252 | C2×C3×D3 | — | 216 | 1 | no | — |
| 253 | D32 | — | 18 | 1 | no | — |
| 254 | D32 | — | 36 | 1 | no | — |
| 255 | D32 | — | 36 | 1 | no | — |
| 256 | D32 | — | 36 | 1 | no | — |
| 257 | D32 | — | 36 | 1 | no | — |
| 258 | D32 | — | 36 | 1 | no | — |
| 259 | D32 | — | 36 | 1 | no | — |
| 260 | D32 | — | 36 | 1 | no | — |
| 261 | D32 | — | 54 | 1 | no | — |
| 262 | D32 | — | 54 | 1 | no | — |
| 263 | D32 | — | 54 | 1 | no | — |
| 264 | D32 | — | 72 | 1 | no | — |
| 265 | D32 | — | 108 | 1 | no | — |
| 266 | D32 | — | 108 | 1 | no | — |
| 267 | D32 | — | 108 | 1 | no | — |
| 268 | D32 | — | 108 | 1 | no | — |
| 269 | D32 | — | 108 | 1 | no | — |
| 270 | D32 | — | 108 | 1 | no | — |
| 271 | D32 | — | 108 | 1 | no | — |
| 272 | D32 | — | 108 | 1 | no | — |
| 273 | D32 | — | 108 | 1 | no | — |
| 274 | D32 | — | 108 | 1 | no | — |
| 275 | D32 | — | 216 | 1 | no | — |
| 276 | D32 | — | 216 | 1 | no | — |
| 277 | D32 | — | 216 | 1 | no | — |
| 278 | #157 | — | 9 | 1 | no | — |
| 279 | #157 | — | 18 | 1 | no | — |
| 280 | #157 | — | 27 | 1 | no | — |
| 281 | #157 | — | 27 | 1 | no | — |
| 282 | #157 | — | 27 | 1 | no | — |
| 283 | #157 | — | 54 | 1 | no | — |
| 284 | #157 | — | 54 | 1 | no | — |
| 285 | #157 | — | 54 | 1 | no | — |
| 286 | #157 | — | 54 | 1 | no | — |
| 287 | #157 | — | 108 | 1 | no | — |
| 288 | #157 | — | 108 | 1 | no | — |
| 289 | #157 | — | 108 | 1 | no | — |
| 290 | #157 | — | 108 | 1 | no | — |
| 291 | #157 | — | 108 | 1 | no | — |
| 292 | #157 | — | 216 | 1 | no | — |
| 293 | C2×SD16 | — | 243 | 1 | no | Sylow |
| 294 | C33 | — | 4 | 1 | no | — |
| 295 | C33 | — | 8 | 1 | no | — |
| 296 | C33 | — | 12 | 1 | no | — |
| 297 | C33 | — | 24 | 1 | no | — |
| 298 | C33 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 299 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 300 | H(3,𝔽3) | — | 24 | 1 | no | — |
| 301 | H(3,𝔽3) | — | 24 | 1 | no | — |
| 302 | H(3,𝔽3) | — | 48 | 1 | no | — |
| 303 | C22×D3 | — | 324 | 1 | no | — |
| 304 | C22×D3 | — | 324 | 1 | no | — |
| 305 | C22×D3 | — | 162 | 1 | no | — |
| 306 | C3×Q8 | — | 81 | 1 | no | — |
| 307 | C3×D4 | — | 81 | 1 | no | — |
| 308 | #67 | — | 162 | 1 | no | — |
| 309 | D12 | — | 81 | 1 | no | — |
| 310 | C4×D3 | — | 81 | 1 | no | — |
| 311 | C4×D3 | — | 162 | 1 | no | — |
| 312 | Dic6 | — | 81 | 1 | no | — |
| 313 | Dic6 | — | 162 | 1 | no | — |
| 314 | C3×C8 | — | 81 | 1 | no | — |
| 315 | C3⋊C8 | — | 81 | 1 | no | — |
| 316 | C2×C32 | — | 27 | 1 | no | — |
| 317 | C2×C32 | — | 27 | 1 | no | — |
| 318 | C2×C32 | — | 36 | 1 | no | — |
| 319 | C2×C32 | — | 36 | 1 | no | — |
| 320 | C2×C32 | — | 72 | 1 | no | — |
| 321 | C2×C32 | — | 108 | 1 | no | — |
| 322 | C3⋊D3 | — | 3 | 1 | no | — |
| 323 | C3⋊D3 | — | 3 | 1 | no | — |
| 324 | C3⋊D3 | — | 4 | 1 | no | — |
| 325 | C3⋊D3 | — | 9 | 1 | no | — |
| 326 | C3⋊D3 | — | 12 | 1 | no | — |
| 327 | C3⋊D3 | — | 12 | 1 | no | — |
| 328 | C3⋊D3 | — | 24 | 1 | no | — |
| 329 | C3⋊D3 | — | 27 | 1 | no | — |
| 330 | C3⋊D3 | — | 36 | 1 | no | — |
| 331 | C3⋊D3 | — | 36 | 1 | no | — |
| 332 | C3⋊D3 | — | 54 | 1 | no | — |
| 333 | C3⋊D3 | — | 72 | 1 | no | — |
| 334 | C3⋊D3 | — | 108 | 1 | no | — |
| 335 | C3⋊D3 | — | 108 | 1 | no | — |
| 336 | C3⋊D3 | — | 108 | 1 | no | — |
| 337 | C3⋊D3 | — | 216 | 1 | no | — |
| 338 | C3⋊D3 | — | 216 | 1 | no | — |
| 339 | C3⋊D3 | — | 216 | 1 | no | — |
| 340 | C3×D3 | — | 12 | 1 | no | — |
| 341 | C3×D3 | — | 36 | 1 | no | — |
| 342 | C3×D3 | — | 36 | 1 | no | — |
| 343 | C3×D3 | — | 36 | 1 | no | — |
| 344 | C3×D3 | — | 36 | 1 | no | — |
| 345 | C3×D3 | — | 36 | 1 | no | — |
| 346 | C3×D3 | — | 36 | 1 | no | — |
| 347 | C3×D3 | — | 36 | 1 | no | — |
| 348 | C3×D3 | — | 36 | 1 | no | — |
| 349 | C3×D3 | — | 36 | 1 | no | — |
| 350 | C3×D3 | — | 36 | 1 | no | — |
| 351 | C3×D3 | — | 36 | 1 | no | — |
| 352 | C3×D3 | — | 36 | 1 | no | — |
| 353 | C3×D3 | — | 36 | 1 | no | — |
| 354 | C3×D3 | — | 72 | 1 | no | — |
| 355 | C3×D3 | — | 72 | 1 | no | — |
| 356 | C3×D3 | — | 72 | 1 | no | — |
| 357 | C3×D3 | — | 72 | 1 | no | — |
| 358 | C3×D3 | — | 72 | 1 | no | — |
| 359 | C3×D3 | — | 72 | 1 | no | — |
| 360 | C3×D3 | — | 72 | 1 | no | — |
| 361 | C3×D3 | — | 72 | 1 | no | — |
| 362 | C3×D3 | — | 72 | 1 | no | — |
| 363 | C3×D3 | — | 72 | 1 | no | — |
| 364 | C3×D3 | — | 72 | 1 | no | — |
| 365 | C3×D3 | — | 72 | 1 | no | — |
| 366 | C3×D3 | — | 108 | 1 | no | — |
| 367 | C3×D3 | — | 108 | 1 | no | — |
| 368 | C3×D3 | — | 144 | 1 | no | — |
| 369 | C3×D3 | — | 216 | 1 | no | — |
| 370 | C2×Q8 | — | 243 | 1 | no | — |
| 371 | C2×D4 | — | 243 | 1 | no | — |
| 372 | SD16 | — | 81 | 1 | no | — |
| 373 | SD16 | — | 243 | 1 | no | — |
| 374 | SD16 | — | 243 | 1 | no | — |
| 375 | SD16 | — | 243 | 1 | no | — |
| 376 | C2×C8 | — | 243 | 1 | no | — |
| 377 | C22×C3 | — | 324 | 1 | no | — |
| 378 | C22×C3 | — | 324 | 1 | no | — |
| 379 | C22×C3 | — | 162 | 1 | no | — |
| 380 | C2×D3 | — | 324 | 1 | no | — |
| 381 | C2×D3 | — | 324 | 1 | no | — |
| 382 | C2×D3 | — | 324 | 1 | no | — |
| 383 | C2×D3 | — | 324 | 1 | no | — |
| 384 | C2×D3 | — | 324 | 1 | no | — |
| 385 | C2×D3 | — | 324 | 1 | no | — |
| 386 | C2×D3 | — | 81 | 1 | no | — |
| 387 | C2×D3 | — | 108 | 1 | no | — |
| 388 | C2×D3 | — | 108 | 1 | no | — |
| 389 | C2×D3 | — | 108 | 1 | no | — |
| 390 | C2×D3 | — | 108 | 1 | no | — |
| 391 | C2×D3 | — | 108 | 1 | no | — |
| 392 | C2×D3 | — | 108 | 1 | no | — |
| 393 | C2×D3 | — | 108 | 1 | no | — |
| 394 | C2×D3 | — | 108 | 1 | no | — |
| 395 | C2×D3 | — | 648 | 1 | no | — |
| 396 | C2×D3 | — | 162 | 1 | no | — |
| 397 | C2×D3 | — | 216 | 1 | no | — |
| 398 | C3×C4 | — | 81 | 1 | no | — |
| 399 | C3×C4 | — | 162 | 1 | no | — |
| 400 | Dic3 | — | 81 | 1 | no | — |
| 401 | Dic3 | — | 162 | 1 | no | — |
| 402 | C32 | — | 3 | 1 | no | — |
| 403 | C32 | — | 4 | 1 | no | — |
| 404 | C32 | — | 6 | 1 | no | — |
| 405 | C32 | — | 8 | 1 | no | — |
| 406 | C32 | — | 12 | 1 | no | — |
| 407 | C32 | — | 12 | 1 | no | — |
| 408 | C32 | — | 12 | 1 | no | — |
| 409 | C32 | — | 12 | 1 | no | — |
| 410 | C32 | — | 24 | 1 | no | — |
| 411 | C32 | — | 24 | 1 | no | — |
| 412 | C32 | — | 24 | 1 | no | — |
| 413 | C32 | — | 24 | 1 | no | — |
| 414 | C32 | — | 24 | 1 | no | — |
| 415 | C32 | — | 48 | 1 | no | — |
| 416 | C32 | D3×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic |
| 417 | C23 | — | 486 | 1 | no | — |
| 418 | Q8 | — | 81 | 1 | no | — |
| 419 | Q8 | — | 486 | 1 | no | — |
| 420 | Q8 | — | 243 | 1 | no | — |
| 421 | D4 | — | 81 | 1 | no | — |
| 422 | D4 | — | 486 | 1 | no | — |
| 423 | D4 | — | 243 | 1 | no | — |
| 424 | C2×C4 | — | 486 | 1 | no | — |
| 425 | C2×C4 | — | 243 | 1 | no | — |
| 426 | C8 | — | 81 | 1 | no | — |
| 427 | C8 | — | 243 | 1 | no | — |
| 428 | C2×C3 | — | 36 | 1 | no | — |
| 429 | C2×C3 | — | 81 | 1 | no | — |
| 430 | C2×C3 | — | 108 | 1 | no | — |
| 431 | C2×C3 | — | 108 | 1 | no | — |
| 432 | C2×C3 | — | 108 | 1 | no | — |
| 433 | C2×C3 | — | 108 | 1 | no | — |
| 434 | C2×C3 | — | 108 | 1 | no | — |
| 435 | C2×C3 | — | 108 | 1 | no | — |
| 436 | C2×C3 | — | 216 | 1 | no | — |
| 437 | C2×C3 | — | 216 | 1 | no | — |
| 438 | D3 | — | 9 | 1 | no | — |
| 439 | D3 | — | 12 | 1 | no | — |
| 440 | D3 | — | 36 | 1 | no | — |
| 441 | D3 | — | 36 | 1 | no | — |
| 442 | D3 | — | 36 | 1 | no | — |
| 443 | D3 | — | 36 | 1 | no | — |
| 444 | D3 | — | 36 | 1 | no | — |
| 445 | D3 | — | 324 | 1 | no | — |
| 446 | D3 | — | 72 | 1 | no | — |
| 447 | D3 | — | 72 | 1 | no | — |
| 448 | D3 | — | 81 | 1 | no | — |
| 449 | D3 | — | 108 | 1 | no | — |
| 450 | D3 | — | 108 | 1 | no | — |
| 451 | D3 | — | 648 | 1 | no | — |
| 452 | D3 | — | 216 | 1 | no | — |
| 453 | C22 | — | 324 | 1 | no | — |
| 454 | C22 | — | 324 | 1 | no | — |
| 455 | C22 | — | 162 | 1 | no | — |
| 456 | C22 | — | 486 | 1 | no | — |
| 457 | C22 | — | 243 | 1 | no | — |
| 458 | C4 | — | 81 | 1 | no | — |
| 459 | C4 | — | 162 | 1 | no | — |
| 460 | C4 | — | 486 | 1 | no | — |
| 461 | C4 | — | 243 | 1 | no | — |
| 462 | C3 | — | 4 | 1 | no | — |
| 463 | C3 | — | 9 | 1 | no | — |
| 464 | C3 | — | 12 | 1 | no | — |
| 465 | C3 | — | 24 | 1 | no | — |
| 466 | C3 | — | 72 | 1 | no | — |
| 467 | C2 | — | 27 | 1 | no | — |
| 468 | C2 | — | 27 | 1 | no | — |
| 469 | C2 | — | 36 | 1 | no | — |
| 470 | C2 | — | 81 | 1 | no | — |
| 471 | C2 | — | 108 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle | #66472⋊C3 | C23 |
| Frattini, socle | C32 | D3×AΓL(1,𝔽9) |
| Fitting, hypocenter | C32⋊H(3,𝔽3) | C2×SD16 |
| prime radical | #72221995 | C2 |
| LCS | G ▷ #66472⋊C3 ▷ #92301 ▷ C32⋊H(3,𝔽3) | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72222006 | C2 | semidirect |
| 2. #72222004 | C2 | semidirect |
| 3. #72222001 | C2 | semidirect |
| 5. #72221986 | C2 | semidirect |
| 6. #72221982 | C2 | semidirect |
| 7. #72221972 | C2 | semidirect |
| 11. #14517942 | C22 | semidirect |
| 12. #14517936 | C22 | semidirect |
| 18. #14517911 | C22 | semidirect |
| 19. #10620192⋊C3 | C22 | semidirect |
| 25. #13049803 | D3 | semidirect |
| 40. #10620211 | C2×D3 | semidirect |
| 47. #10620192 | C2×D3 | semidirect |
| 49. #92338 | SD16 | semidirect |
| 52. #92258 | SD16 | semidirect |
| 80. C32⋊H(3,𝔽3) | C2×SD16 | semidirect |
| 160. C34 | D3×SD16 | semidirect |
| 196. C3⋊(C3⋊D3) | AΓL(1,𝔽9) | semidirect |
| 298. C33 | C2×AΓL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72222006 | 2 |
| #72222004 | 2 |
| #72222001 | 2 |
| #72221995 | 2 |
| #72221986 | 2 |
| #72221982 | 2 |
| #72221972 | 2 |
| #72210346 | 3 |
| D3×AΓL(1,𝔽9) | 9 |