Finite Group DatabasebetaFinite Group DatabasebetaOrder 7776.
862 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 862 conjugacy classes of subgroups — too many to draw. Only its 37 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 | #72224532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72224531 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #72224523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72214344 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72214189 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#13049804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #72214042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72210346 | — | 3 | 1 | no | maximal |
| 9 | #14519547 | — | 2 | 1 | no | — |
| 10 | C3⋊#10620211 | — | 2 | 1 | no | — |
| 11 | C3⋊#10620211 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C3×#10620211 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #14519528 | C22 | 1 | 1 | yes | characteristic |
| 14 | #14519527 | — | 2 | 1 | no | — |
| 15 | C3×#10620206 | C22 | 1 | 1 | yes | characteristic |
| 16 | #14519512 | — | 2 | 1 | no | — |
| 17 | #14519512 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3⋊#10620192 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#10620193 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #13049818 | — | 3 | 1 | no | — |
| 21 | #13049813 | — | 3 | 1 | no | — |
| 22 | #13049804 | — | 3 | 1 | no | — |
| 23 | #13049804 | D3 | 1 | 1 | yes | characteristic, complemented |
| 24 | #13049803 | — | 3 | 1 | no | — |
| 25 | #13049803 | — | 3 | 1 | no | — |
| 26 | #13049788 | — | 3 | 1 | no | — |
| 27 | #11758168 | — | 2 | 1 | no | — |
| 28 | #11758168 | D4 | 1 | 1 | yes | characteristic |
| 29 | C3×C3⋊#1113 | — | 4 | 2 | no | — |
| 30 | C3×C3⋊D32 | — | 2 | 1 | no | — |
| 31 | C3⋊#66472 | — | 2 | 1 | no | — |
| 32 | C3⋊#66472 | D4 | 1 | 1 | yes | characteristic |
| 33 | C3×#66472 | — | 2 | 1 | no | — |
| 34 | C3×#66472 | C23 | 1 | 1 | yes | characteristic |
| 35 | D3×AΓL(1,𝔽9) | — | 9 | 2 | no | maximal |
| 36 | #10620215 | — | 6 | 1 | no | — |
| 37 | D3×#1113 | — | 12 | 2 | 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 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 47 | #10620192 | — | 3 | 1 | no | — |
| 48 | C3×C3⋊(C3⋊(C3⋊D3)) | C2×D4 | 1 | 1 | yes | characteristic |
| 49 | C32×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 50 | C32×C3⋊(C3⋊D3) | SD16 | 1 | 2 | yes | complemented |
| 51 | C33×C3⋊D3 | — | 4 | 1 | no | — |
| 52 | D3×PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 53 | D3×GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 54 | AGL(1,𝔽9)⋊D3 | — | 9 | 2 | no | — |
| 55 | #89092 | — | 9 | 2 | no | — |
| 56 | #89092 | — | 18 | 1 | no | — |
| 57 | #89091 | — | 9 | 2 | no | — |
| 58 | #89091 | — | 18 | 1 | no | — |
| 59 | C3×AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 60 | D3×AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 61 | C3⋊#1113 | — | 4 | 2 | no | — |
| 62 | C3⋊#1113 | — | 12 | 2 | no | — |
| 63 | C3⋊#1113 | — | 12 | 2 | no | — |
| 64 | C3⋊#1113 | — | 24 | 1 | no | — |
| 65 | C3⋊D32 | — | 2 | 1 | no | — |
| 66 | C3⋊D32 | — | 3 | 1 | no | — |
| 67 | C3⋊D32 | — | 6 | 1 | no | — |
| 68 | C3×#1113 | — | 12 | 2 | no | — |
| 69 | C3×#1113 | — | 12 | 2 | no | — |
| 70 | C3×#1113 | — | 24 | 2 | no | — |
| 71 | C3×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 72 | C3×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 73 | C3×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 74 | C3×D3×C3⋊D3 | — | 24 | 1 | no | — |
| 75 | #66472 | — | 2 | 1 | no | — |
| 76 | #66472 | — | 3 | 1 | no | — |
| 77 | #66472 | — | 6 | 1 | no | — |
| 78 | #66472 | C22×D3 | 1 | 1 | yes | characteristic |
| 79 | C2×AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 80 | C35 | C2×SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 81 | C2×#1113 | — | 36 | 1 | no | — |
| 82 | D33 | — | 18 | 2 | no | — |
| 83 | D33 | — | 36 | 1 | no | — |
| 84 | D33 | — | 36 | 2 | no | — |
| 85 | C3⋊PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 86 | C3⋊PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 87 | C3⋊PSU(3,𝔽2) | — | 18 | 2 | no | — |
| 88 | C3⋊PSU(3,𝔽2) | — | 36 | 1 | no | — |
| 89 | C3×PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 90 | C3×PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 91 | #157⋊D3 | — | 9 | 2 | no | — |
| 92 | #157⋊D3 | — | 18 | 1 | no | — |
| 93 | D32⋊D3 | — | 18 | 2 | no | — |
| 94 | D32⋊D3 | — | 36 | 1 | no | — |
| 95 | C3×GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 96 | C3×GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 97 | D3×#157 | — | 9 | 2 | no | — |
| 98 | D3×#157 | — | 18 | 2 | no | — |
| 99 | C3⋊AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 100 | C3⋊AGL(1,𝔽9) | — | 18 | 1 | no | — |
| 101 | C3⋊AGL(1,𝔽9) | — | 18 | 1 | no | — |
| 102 | C3⋊AGL(1,𝔽9) | — | 36 | 1 | no | — |
| 103 | C3×AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 104 | C3⋊(C3⋊(C3⋊D3)) | D3×D4 | 1 | 1 | yes | characteristic |
| 105 | C3×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 106 | C3×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 107 | C3×C3⋊(C3⋊D3) | — | 8 | 1 | no | — |
| 108 | C3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 109 | C3×C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 110 | C3×C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 111 | C3×C3⋊(C3⋊D3) | — | 48 | 1 | no | — |
| 112 | C32×C3⋊D3 | — | 3 | 2 | no | — |
| 113 | C32×C3⋊D3 | — | 4 | 2 | no | — |
| 114 | C32×C3⋊D3 | — | 4 | 1 | no | — |
| 115 | C32×C3⋊D3 | — | 8 | 1 | no | — |
| 116 | C32×C3⋊D3 | — | 8 | 2 | no | — |
| 117 | C32×C3⋊D3 | — | 12 | 2 | no | — |
| 118 | C32×C3⋊D3 | — | 12 | 2 | no | — |
| 119 | C32×C3⋊D3 | — | 12 | 1 | no | — |
| 120 | C32×C3⋊D3 | — | 16 | 1 | no | — |
| 121 | C32×C3⋊D3 | — | 24 | 1 | no | — |
| 122 | C32×C3⋊D3 | — | 24 | 2 | no | — |
| 123 | C32×C3⋊D3 | — | 24 | 2 | no | — |
| 124 | C32×C3⋊D3 | — | 48 | 1 | no | — |
| 125 | C33×D3 | — | 12 | 2 | no | — |
| 126 | C33×D3 | — | 24 | 1 | no | — |
| 127 | C2×PSU(3,𝔽2) | — | 27 | 2 | no | — |
| 128 | C2×GO+(4,𝔽2) | — | 27 | 2 | no | — |
| 129 | C2×AGL(1,𝔽9) | — | 27 | 2 | no | — |
| 130 | AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 131 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 132 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 133 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 134 | AΓL(1,𝔽9) | — | 54 | 1 | no | — |
| 135 | AΓL(1,𝔽9) | — | 54 | 1 | no | — |
| 136 | C2×C3×C3⋊D3 | — | 36 | 1 | no | — |
| 137 | C2×C3×C3⋊D3 | — | 36 | 2 | no | — |
| 138 | #1113 | — | 12 | 2 | no | — |
| 139 | #1113 | — | 12 | 2 | no | — |
| 140 | #1113 | — | 18 | 2 | no | — |
| 141 | #1113 | — | 24 | 2 | no | — |
| 142 | #1113 | — | 36 | 1 | no | — |
| 143 | #1113 | — | 36 | 1 | no | — |
| 144 | #1113 | — | 36 | 1 | no | — |
| 145 | #1113 | — | 36 | 1 | no | — |
| 146 | #1113 | — | 36 | 1 | no | — |
| 147 | #1113 | — | 72 | 1 | no | — |
| 148 | #1113 | — | 72 | 2 | no | — |
| 149 | D3×C3⋊D3 | — | 9 | 2 | no | — |
| 150 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 151 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 152 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 153 | D3×C3⋊D3 | — | 24 | 1 | no | — |
| 154 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 155 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 156 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 157 | D3×C3⋊D3 | — | 72 | 1 | no | — |
| 158 | C3×D32 | — | 18 | 2 | no | — |
| 159 | C3×D32 | — | 36 | 2 | no | — |
| 160 | C3×D32 | — | 36 | 1 | no | — |
| 161 | C3×D32 | — | 36 | 2 | no | — |
| 162 | C3×D32 | — | 36 | 2 | no | — |
| 163 | C3×D32 | — | 36 | 2 | no | — |
| 164 | C3×D32 | — | 36 | 1 | no | — |
| 165 | C3×D32 | — | 36 | 1 | no | — |
| 166 | C3×D32 | — | 36 | 2 | no | — |
| 167 | C3×D32 | — | 72 | 2 | no | — |
| 168 | C3×D32 | — | 72 | 2 | no | — |
| 169 | C3×D32 | — | 72 | 2 | no | — |
| 170 | C3⋊#157 | — | 9 | 2 | no | — |
| 171 | C3⋊#157 | — | 18 | 2 | no | — |
| 172 | C3⋊#157 | — | 36 | 1 | no | — |
| 173 | C3⋊#157 | — | 36 | 1 | no | — |
| 174 | C3⋊#157 | — | 36 | 1 | no | — |
| 175 | C3⋊#157 | — | 36 | 1 | no | — |
| 176 | C3⋊#157 | — | 72 | 1 | no | — |
| 177 | C3×#157 | — | 9 | 2 | no | — |
| 178 | C3×#157 | — | 18 | 1 | no | — |
| 179 | C3×#157 | — | 18 | 1 | no | — |
| 180 | C3×#157 | — | 18 | 2 | no | — |
| 181 | C3×#157 | — | 36 | 1 | no | — |
| 182 | C3×#157 | — | 36 | 1 | no | — |
| 183 | C3×#157 | — | 36 | 1 | no | — |
| 184 | C3×#157 | — | 72 | 1 | no | — |
| 185 | D3×SD16 | — | 81 | 1 | no | — |
| 186 | C34 | — | 4 | 2 | no | — |
| 187 | C34 | — | 8 | 1 | no | — |
| 188 | C34 | — | 8 | 1 | no | — |
| 189 | C34 | — | 8 | 2 | no | — |
| 190 | C34 | — | 16 | 1 | no | — |
| 191 | C34 | — | 16 | 1 | no | — |
| 192 | C34 | — | 16 | 1 | no | — |
| 193 | C34 | — | 32 | 1 | no | — |
| 194 | C34 | D3×SD16 | 1 | 1 | yes | characteristic, complemented |
| 195 | C2×D32 | — | 54 | 2 | no | — |
| 196 | C2×D32 | — | 108 | 1 | no | — |
| 197 | C2×D32 | — | 108 | 1 | no | — |
| 198 | C2×D32 | — | 108 | 2 | no | — |
| 199 | C2×#157 | — | 27 | 2 | no | — |
| 200 | C2×#157 | — | 54 | 2 | no | — |
| 201 | PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 202 | PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 203 | PSU(3,𝔽2) | — | 27 | 2 | no | — |
| 204 | PSU(3,𝔽2) | — | 54 | 2 | no | — |
| 205 | PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 206 | PSU(3,𝔽2) | — | 108 | 1 | no | — |
| 207 | GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 208 | GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 209 | GO+(4,𝔽2) | — | 27 | 2 | no | — |
| 210 | GO+(4,𝔽2) | — | 54 | 2 | no | — |
| 211 | GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 212 | GO+(4,𝔽2) | — | 108 | 1 | no | — |
| 213 | AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 214 | AGL(1,𝔽9) | — | 27 | 2 | no | — |
| 215 | AGL(1,𝔽9) | — | 54 | 1 | no | — |
| 216 | AGL(1,𝔽9) | — | 54 | 1 | no | — |
| 217 | AGL(1,𝔽9) | — | 108 | 1 | no | — |
| 218 | C2×C33 | — | 36 | 1 | no | — |
| 219 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 220 | C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 221 | C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 222 | C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 223 | C3⋊(C3⋊D3) | — | 48 | 1 | no | — |
| 224 | C3⋊(C3⋊D3) | AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 225 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 226 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 227 | C3×C3⋊D3 | — | 8 | 1 | no | — |
| 228 | C3×C3⋊D3 | — | 8 | 2 | no | — |
| 229 | C3×C3⋊D3 | — | 9 | 2 | no | — |
| 230 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 231 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 232 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 233 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 234 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 235 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 236 | C3×C3⋊D3 | — | 16 | 1 | no | — |
| 237 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 238 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 239 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 240 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 241 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 242 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 243 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 244 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 245 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 246 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 247 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 248 | C3×C3⋊D3 | — | 24 | 1 | no | — |
| 249 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 250 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 251 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 252 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 253 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 254 | C3×C3⋊D3 | — | 48 | 2 | no | — |
| 255 | C3×C3⋊D3 | — | 48 | 2 | no | — |
| 256 | C3×C3⋊D3 | — | 48 | 2 | no | — |
| 257 | C3×C3⋊D3 | — | 48 | 1 | no | — |
| 258 | C3×C3⋊D3 | — | 48 | 1 | no | — |
| 259 | C3×C3⋊D3 | — | 72 | 1 | no | — |
| 260 | C3×C3⋊D3 | — | 72 | 2 | no | — |
| 261 | C3×C3⋊D3 | — | 72 | 2 | no | — |
| 262 | C3×C3⋊D3 | — | 72 | 1 | no | — |
| 263 | C3×C3⋊D3 | — | 72 | 1 | no | — |
| 264 | C3×C3⋊D3 | — | 144 | 2 | no | — |
| 265 | C3×C3⋊D3 | — | 144 | 1 | no | — |
| 266 | C32×D3 | — | 9 | 2 | no | — |
| 267 | C32×D3 | — | 12 | 2 | no | — |
| 268 | C32×D3 | — | 12 | 2 | no | — |
| 269 | C32×D3 | — | 12 | 2 | no | — |
| 270 | C32×D3 | — | 24 | 2 | no | — |
| 271 | C32×D3 | — | 24 | 2 | no | — |
| 272 | C32×D3 | — | 24 | 2 | no | — |
| 273 | C32×D3 | — | 24 | 1 | no | — |
| 274 | C32×D3 | — | 24 | 2 | no | — |
| 275 | C32×D3 | — | 24 | 1 | no | — |
| 276 | C32×D3 | — | 24 | 1 | no | — |
| 277 | C32×D3 | — | 36 | 2 | no | — |
| 278 | C32×D3 | — | 36 | 1 | no | — |
| 279 | C32×D3 | — | 36 | 2 | no | — |
| 280 | C32×D3 | — | 48 | 2 | no | — |
| 281 | C32×D3 | — | 48 | 2 | no | — |
| 282 | C32×D3 | — | 48 | 1 | no | — |
| 283 | C32×D3 | — | 48 | 1 | no | — |
| 284 | C32×D3 | — | 72 | 1 | no | — |
| 285 | C32×D3 | — | 72 | 2 | no | — |
| 286 | C32×D3 | — | 72 | 2 | no | — |
| 287 | C32×D3 | — | 144 | 1 | no | — |
| 288 | D3×Q8 | — | 81 | 1 | no | — |
| 289 | D3×D4 | — | 81 | 1 | no | — |
| 290 | C3×SD16 | — | 81 | 1 | no | — |
| 291 | #215 | — | 81 | 1 | no | — |
| 292 | #214 | — | 81 | 1 | no | — |
| 293 | #204 | — | 81 | 1 | no | — |
| 294 | D3×C8 | — | 81 | 1 | no | — |
| 295 | C2×C3⋊D3 | — | 27 | 2 | no | — |
| 296 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 297 | C2×C3⋊D3 | — | 36 | 2 | no | — |
| 298 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 299 | C2×C3×D3 | — | 108 | 2 | no | — |
| 300 | C2×C3×D3 | — | 108 | 2 | no | — |
| 301 | C2×C3×D3 | — | 108 | 2 | no | — |
| 302 | C2×C3×D3 | — | 108 | 2 | no | — |
| 303 | C2×C3×D3 | — | 108 | 2 | no | — |
| 304 | C2×C3×D3 | — | 216 | 2 | no | — |
| 305 | C2×C3×D3 | — | 216 | 1 | no | — |
| 306 | D32 | — | 18 | 2 | no | — |
| 307 | D32 | — | 36 | 1 | no | — |
| 308 | D32 | — | 36 | 2 | no | — |
| 309 | D32 | — | 36 | 2 | no | — |
| 310 | D32 | — | 36 | 2 | no | — |
| 311 | D32 | — | 36 | 2 | no | — |
| 312 | D32 | — | 36 | 2 | no | — |
| 313 | D32 | — | 36 | 1 | no | — |
| 314 | D32 | — | 36 | 1 | no | — |
| 315 | D32 | — | 54 | 2 | no | — |
| 316 | D32 | — | 72 | 2 | no | — |
| 317 | D32 | — | 72 | 2 | no | — |
| 318 | D32 | — | 72 | 2 | no | — |
| 319 | D32 | — | 108 | 1 | no | — |
| 320 | D32 | — | 108 | 1 | no | — |
| 321 | D32 | — | 108 | 1 | no | — |
| 322 | D32 | — | 108 | 2 | no | — |
| 323 | D32 | — | 108 | 2 | no | — |
| 324 | D32 | — | 108 | 1 | no | — |
| 325 | D32 | — | 108 | 1 | no | — |
| 326 | D32 | — | 216 | 1 | no | — |
| 327 | D32 | — | 216 | 2 | no | — |
| 328 | D32 | — | 216 | 1 | no | — |
| 329 | #157 | — | 9 | 2 | no | — |
| 330 | #157 | — | 18 | 1 | no | — |
| 331 | #157 | — | 18 | 1 | no | — |
| 332 | #157 | — | 18 | 2 | no | — |
| 333 | #157 | — | 27 | 2 | no | — |
| 334 | #157 | — | 36 | 1 | no | — |
| 335 | #157 | — | 36 | 1 | no | — |
| 336 | #157 | — | 36 | 1 | no | — |
| 337 | #157 | — | 54 | 2 | no | — |
| 338 | #157 | — | 72 | 1 | no | — |
| 339 | #157 | — | 108 | 1 | no | — |
| 340 | #157 | — | 108 | 1 | no | — |
| 341 | #157 | — | 108 | 1 | no | — |
| 342 | #157 | — | 108 | 1 | no | — |
| 343 | #157 | — | 216 | 1 | no | — |
| 344 | C2×SD16 | — | 243 | 1 | no | Sylow |
| 345 | C33 | — | 2 | 1 | no | — |
| 346 | C33 | — | 2 | 1 | no | — |
| 347 | C33 | — | 4 | 1 | no | — |
| 348 | C33 | — | 4 | 1 | no | — |
| 349 | C33 | — | 4 | 2 | no | — |
| 350 | C33 | — | 4 | 1 | no | — |
| 351 | C33 | — | 4 | 1 | no | — |
| 352 | C33 | — | 4 | 1 | no | — |
| 353 | C33 | — | 8 | 1 | no | — |
| 354 | C33 | — | 8 | 1 | no | — |
| 355 | C33 | — | 8 | 1 | no | — |
| 356 | C33 | — | 8 | 2 | no | — |
| 357 | C33 | — | 8 | 2 | no | — |
| 358 | C33 | — | 8 | 2 | no | — |
| 359 | C33 | — | 8 | 2 | no | — |
| 360 | C33 | — | 8 | 2 | no | — |
| 361 | C33 | — | 8 | 1 | no | — |
| 362 | C33 | — | 8 | 1 | no | — |
| 363 | C33 | — | 16 | 1 | no | — |
| 364 | C33 | — | 16 | 1 | no | — |
| 365 | C33 | — | 16 | 1 | no | — |
| 366 | C33 | — | 16 | 2 | no | — |
| 367 | C33 | — | 16 | 1 | no | — |
| 368 | C33 | — | 16 | 1 | no | — |
| 369 | C33 | — | 16 | 1 | no | — |
| 370 | C33 | — | 16 | 1 | no | — |
| 371 | C33 | — | 16 | 2 | no | — |
| 372 | C33 | — | 16 | 2 | no | — |
| 373 | C33 | — | 16 | 2 | no | — |
| 374 | C33 | — | 16 | 2 | no | — |
| 375 | C33 | — | 16 | 2 | no | — |
| 376 | C33 | — | 16 | 1 | no | — |
| 377 | C33 | — | 32 | 1 | no | — |
| 378 | C33 | — | 32 | 1 | no | — |
| 379 | C33 | — | 32 | 2 | no | — |
| 380 | C33 | — | 32 | 1 | no | — |
| 381 | C33 | — | 32 | 2 | no | — |
| 382 | C33 | — | 32 | 2 | no | — |
| 383 | C33 | — | 32 | 1 | no | — |
| 384 | C33 | — | 32 | 1 | no | — |
| 385 | C33 | — | 32 | 1 | no | — |
| 386 | C33 | — | 32 | 1 | no | — |
| 387 | C33 | — | 32 | 2 | no | — |
| 388 | C33 | — | 32 | 2 | no | — |
| 389 | C33 | — | 32 | 2 | no | — |
| 390 | C33 | — | 32 | 1 | no | — |
| 391 | C33 | — | 32 | 1 | no | — |
| 392 | C33 | — | 32 | 2 | no | — |
| 393 | C33 | C2×AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 394 | C22×D3 | — | 324 | 2 | no | — |
| 395 | C22×D3 | — | 162 | 1 | no | — |
| 396 | C3×Q8 | — | 81 | 1 | no | — |
| 397 | C3×D4 | — | 81 | 1 | no | — |
| 398 | #67 | — | 162 | 1 | no | — |
| 399 | D12 | — | 81 | 1 | no | — |
| 400 | C4×D3 | — | 81 | 1 | no | — |
| 401 | C4×D3 | — | 162 | 1 | no | — |
| 402 | Dic6 | — | 81 | 1 | no | — |
| 403 | Dic6 | — | 162 | 1 | no | — |
| 404 | C3×C8 | — | 81 | 1 | no | — |
| 405 | C3⋊C8 | — | 81 | 1 | no | — |
| 406 | C2×C32 | — | 27 | 2 | no | — |
| 407 | C2×C32 | — | 36 | 1 | no | — |
| 408 | C2×C32 | — | 36 | 2 | no | — |
| 409 | C2×C32 | — | 72 | 1 | no | — |
| 410 | C2×C32 | — | 72 | 2 | no | — |
| 411 | C2×C32 | — | 108 | 1 | no | — |
| 412 | C2×C32 | — | 144 | 1 | no | — |
| 413 | C3⋊D3 | — | 3 | 2 | no | — |
| 414 | C3⋊D3 | — | 4 | 1 | no | — |
| 415 | C3⋊D3 | — | 9 | 2 | no | — |
| 416 | C3⋊D3 | — | 12 | 2 | no | — |
| 417 | C3⋊D3 | — | 12 | 1 | no | — |
| 418 | C3⋊D3 | — | 12 | 2 | no | — |
| 419 | C3⋊D3 | — | 18 | 1 | no | — |
| 420 | C3⋊D3 | — | 18 | 1 | no | — |
| 421 | C3⋊D3 | — | 24 | 1 | no | — |
| 422 | C3⋊D3 | — | 24 | 2 | no | — |
| 423 | C3⋊D3 | — | 24 | 2 | no | — |
| 424 | C3⋊D3 | — | 36 | 1 | no | — |
| 425 | C3⋊D3 | — | 36 | 1 | no | — |
| 426 | C3⋊D3 | — | 36 | 1 | no | — |
| 427 | C3⋊D3 | — | 36 | 1 | no | — |
| 428 | C3⋊D3 | — | 36 | 1 | no | — |
| 429 | C3⋊D3 | — | 48 | 1 | no | — |
| 430 | C3⋊D3 | — | 72 | 1 | no | — |
| 431 | C3⋊D3 | — | 72 | 2 | no | — |
| 432 | C3⋊D3 | — | 72 | 2 | no | — |
| 433 | C3⋊D3 | — | 72 | 1 | no | — |
| 434 | C3⋊D3 | — | 72 | 1 | no | — |
| 435 | C3⋊D3 | — | 144 | 2 | no | — |
| 436 | C3⋊D3 | — | 144 | 1 | no | — |
| 437 | C3×D3 | — | 12 | 2 | no | — |
| 438 | C3×D3 | — | 12 | 2 | no | — |
| 439 | C3×D3 | — | 12 | 2 | no | — |
| 440 | C3×D3 | — | 24 | 2 | no | — |
| 441 | C3×D3 | — | 24 | 2 | no | — |
| 442 | C3×D3 | — | 24 | 2 | no | — |
| 443 | C3×D3 | — | 24 | 1 | no | — |
| 444 | C3×D3 | — | 24 | 2 | no | — |
| 445 | C3×D3 | — | 24 | 1 | no | — |
| 446 | C3×D3 | — | 24 | 1 | no | — |
| 447 | C3×D3 | — | 36 | 2 | no | — |
| 448 | C3×D3 | — | 36 | 2 | no | — |
| 449 | C3×D3 | — | 36 | 2 | no | — |
| 450 | C3×D3 | — | 36 | 2 | no | — |
| 451 | C3×D3 | — | 36 | 2 | no | — |
| 452 | C3×D3 | — | 36 | 2 | no | — |
| 453 | C3×D3 | — | 48 | 2 | no | — |
| 454 | C3×D3 | — | 48 | 2 | no | — |
| 455 | C3×D3 | — | 48 | 1 | no | — |
| 456 | C3×D3 | — | 48 | 1 | no | — |
| 457 | C3×D3 | — | 72 | 2 | no | — |
| 458 | C3×D3 | — | 72 | 1 | no | — |
| 459 | C3×D3 | — | 72 | 2 | no | — |
| 460 | C3×D3 | — | 72 | 2 | no | — |
| 461 | C3×D3 | — | 72 | 2 | no | — |
| 462 | C3×D3 | — | 72 | 2 | no | — |
| 463 | C3×D3 | — | 72 | 2 | no | — |
| 464 | C3×D3 | — | 72 | 2 | no | — |
| 465 | C3×D3 | — | 72 | 1 | no | — |
| 466 | C3×D3 | — | 72 | 1 | no | — |
| 467 | C3×D3 | — | 108 | 2 | no | — |
| 468 | C3×D3 | — | 144 | 2 | no | — |
| 469 | C3×D3 | — | 144 | 2 | no | — |
| 470 | C3×D3 | — | 144 | 2 | no | — |
| 471 | C3×D3 | — | 144 | 1 | no | — |
| 472 | C3×D3 | — | 144 | 1 | no | — |
| 473 | C3×D3 | — | 432 | 1 | no | — |
| 474 | C3×D3 | — | 216 | 1 | no | — |
| 475 | C3×D3 | — | 216 | 1 | no | — |
| 476 | C2×Q8 | — | 243 | 1 | no | — |
| 477 | C2×D4 | — | 243 | 1 | no | — |
| 478 | SD16 | — | 81 | 1 | no | — |
| 479 | SD16 | — | 243 | 1 | no | — |
| 480 | SD16 | — | 243 | 1 | no | — |
| 481 | SD16 | — | 243 | 1 | no | — |
| 482 | C2×C8 | — | 243 | 1 | no | — |
| 483 | C22×C3 | — | 324 | 2 | no | — |
| 484 | C22×C3 | — | 162 | 1 | no | — |
| 485 | C2×D3 | — | 324 | 2 | no | — |
| 486 | C2×D3 | — | 324 | 2 | no | — |
| 487 | C2×D3 | — | 81 | 1 | no | — |
| 488 | C2×D3 | — | 108 | 2 | no | — |
| 489 | C2×D3 | — | 108 | 2 | no | — |
| 490 | C2×D3 | — | 108 | 2 | no | — |
| 491 | C2×D3 | — | 108 | 2 | no | — |
| 492 | C2×D3 | — | 108 | 2 | no | — |
| 493 | C2×D3 | — | 648 | 1 | no | — |
| 494 | C2×D3 | — | 162 | 1 | no | — |
| 495 | C2×D3 | — | 216 | 2 | no | — |
| 496 | C2×D3 | — | 216 | 1 | no | — |
| 497 | C3×C4 | — | 81 | 1 | no | — |
| 498 | C3×C4 | — | 162 | 1 | no | — |
| 499 | Dic3 | — | 81 | 1 | no | — |
| 500 | Dic3 | — | 162 | 1 | no | — |
| 501 | C32 | — | 2 | 1 | no | — |
| 502 | C32 | — | 2 | 1 | no | — |
| 503 | C32 | — | 4 | 1 | no | — |
| 504 | C32 | — | 4 | 1 | no | — |
| 505 | C32 | — | 4 | 2 | no | — |
| 506 | C32 | — | 4 | 1 | no | — |
| 507 | C32 | — | 4 | 1 | no | — |
| 508 | C32 | — | 4 | 1 | no | — |
| 509 | C32 | — | 8 | 1 | no | — |
| 510 | C32 | — | 8 | 2 | no | — |
| 511 | C32 | — | 8 | 2 | no | — |
| 512 | C32 | — | 8 | 2 | no | — |
| 513 | C32 | — | 8 | 2 | no | — |
| 514 | C32 | — | 8 | 2 | no | — |
| 515 | C32 | — | 8 | 1 | no | — |
| 516 | C32 | — | 8 | 1 | no | — |
| 517 | C32 | — | 8 | 1 | no | — |
| 518 | C32 | — | 8 | 1 | no | — |
| 519 | C32 | — | 16 | 2 | no | — |
| 520 | C32 | — | 16 | 2 | no | — |
| 521 | C32 | — | 16 | 2 | no | — |
| 522 | C32 | — | 16 | 2 | no | — |
| 523 | C32 | — | 16 | 1 | no | — |
| 524 | C32 | — | 16 | 1 | no | — |
| 525 | C32 | — | 16 | 1 | no | — |
| 526 | C32 | — | 16 | 2 | no | — |
| 527 | C32 | — | 16 | 2 | no | — |
| 528 | C32 | — | 16 | 1 | no | — |
| 529 | C32 | — | 16 | 1 | no | — |
| 530 | C32 | — | 16 | 1 | no | — |
| 531 | C32 | — | 16 | 1 | no | — |
| 532 | C32 | — | 16 | 1 | no | — |
| 533 | C32 | — | 32 | 2 | no | — |
| 534 | C32 | — | 32 | 2 | no | — |
| 535 | C32 | — | 32 | 1 | no | — |
| 536 | C32 | — | 32 | 2 | no | — |
| 537 | C32 | — | 32 | 2 | no | — |
| 538 | C32 | — | 32 | 2 | no | — |
| 539 | C32 | — | 32 | 2 | no | — |
| 540 | C32 | — | 32 | 1 | no | — |
| 541 | C32 | — | 32 | 1 | no | — |
| 542 | C32 | — | 32 | 1 | no | — |
| 543 | C32 | — | 32 | 1 | no | — |
| 544 | C32 | — | 32 | 2 | no | — |
| 545 | C32 | — | 32 | 1 | no | — |
| 546 | C32 | — | 32 | 1 | no | — |
| 547 | C32 | — | 32 | 1 | no | — |
| 548 | C32 | — | 32 | 1 | no | — |
| 549 | C32 | D3×AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 550 | C23 | — | 486 | 1 | no | — |
| 551 | Q8 | — | 81 | 1 | no | — |
| 552 | Q8 | — | 486 | 1 | no | — |
| 553 | Q8 | — | 243 | 1 | no | — |
| 554 | D4 | — | 81 | 1 | no | — |
| 555 | D4 | — | 486 | 1 | no | — |
| 556 | D4 | — | 243 | 1 | no | — |
| 557 | C2×C4 | — | 486 | 1 | no | — |
| 558 | C2×C4 | — | 243 | 1 | no | — |
| 559 | C8 | — | 81 | 1 | no | — |
| 560 | C8 | — | 243 | 1 | no | — |
| 561 | C2×C3 | — | 36 | 2 | no | — |
| 562 | C2×C3 | — | 36 | 1 | no | — |
| 563 | C2×C3 | — | 72 | 1 | no | — |
| 564 | C2×C3 | — | 72 | 2 | no | — |
| 565 | C2×C3 | — | 81 | 1 | no | — |
| 566 | C2×C3 | — | 108 | 2 | no | — |
| 567 | C2×C3 | — | 108 | 2 | no | — |
| 568 | C2×C3 | — | 144 | 1 | no | — |
| 569 | C2×C3 | — | 216 | 1 | no | — |
| 570 | D3 | — | 9 | 2 | no | — |
| 571 | D3 | — | 12 | 2 | no | — |
| 572 | D3 | — | 24 | 1 | no | — |
| 573 | D3 | — | 36 | 2 | no | — |
| 574 | D3 | — | 36 | 2 | no | — |
| 575 | D3 | — | 36 | 1 | no | — |
| 576 | D3 | — | 72 | 2 | no | — |
| 577 | D3 | — | 72 | 1 | no | — |
| 578 | D3 | — | 72 | 2 | no | — |
| 579 | D3 | — | 108 | 2 | no | — |
| 580 | D3 | — | 144 | 1 | no | — |
| 581 | D3 | — | 432 | 1 | no | — |
| 582 | D3 | — | 216 | 1 | no | — |
| 583 | D3 | — | 216 | 1 | no | — |
| 584 | C22 | — | 324 | 2 | no | — |
| 585 | C22 | — | 162 | 1 | no | — |
| 586 | C22 | — | 486 | 1 | no | — |
| 587 | C22 | — | 243 | 1 | no | — |
| 588 | C4 | — | 81 | 1 | no | — |
| 589 | C4 | — | 162 | 1 | no | — |
| 590 | C4 | — | 486 | 1 | no | — |
| 591 | C4 | — | 243 | 1 | no | — |
| 592 | C3 | — | 4 | 2 | no | — |
| 593 | C3 | — | 8 | 1 | no | — |
| 594 | C3 | — | 8 | 2 | no | — |
| 595 | C3 | — | 8 | 1 | no | — |
| 596 | C3 | — | 16 | 1 | no | — |
| 597 | C3 | — | 16 | 1 | no | — |
| 598 | C3 | — | 16 | 1 | no | — |
| 599 | C3 | — | 32 | 1 | no | — |
| 600 | C3 | #72210346 | 1 | 1 | yes | characteristic, complemented |
| 601 | C2 | — | 27 | 2 | no | — |
| 602 | C2 | — | 36 | 1 | no | — |
| 603 | C2 | — | 81 | 1 | no | — |
| 604 | C2 | — | 108 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×#66472 | C23 |
| Fitting, socle, hypocenter | C35 | C2×SD16 |
| prime radical | #72224531 | C2 |
| LCS | G ▷ C3×#66472 ▷ C3×C3⋊(C3⋊(C3⋊D3)) ▷ C35 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72224532 | C2 | semidirect |
| 3. #72224523 | C2 | semidirect |
| 4. #72214344 | C2 | semidirect |
| 5. #72214189 | C2 | semidirect |
| 6. C3×#13049804 | C2 | semidirect |
| 7. #72214042 | C2 | semidirect |
| 11. C3⋊#10620211 | C22 | semidirect |
| 12. C3×#10620211 | C22 | semidirect |
| 18. C3⋊#10620192 | C22 | semidirect |
| 19. C3×#10620193 | C22 | semidirect |
| 23. #13049804 | D3 | semidirect |
| 40. #10620211 | C2×D3 | semidirect |
| 46. #10620193 | C2×D3 | semidirect |
| 50. C32×C3⋊(C3⋊D3) | SD16 | semidirect |
| 80. C35 | C2×SD16 | semidirect |
| 194. C34 | D3×SD16 | semidirect |
| 224. C3⋊(C3⋊D3) | AΓL(1,𝔽9) | semidirect |
| 393. C33 | C2×AΓL(1,𝔽9) | semidirect |
| 549. C32 | D3×AΓL(1,𝔽9) | semidirect |
| 600. C3 | #72210346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72224532 | 2 |
| #72224531 | 2 |
| #72224523 | 2 |
| #72214344 | 2 |
| #72214189 | 2 |
| C3×#13049804 | 2 |
| #72214042 | 2 |
| #72210346 | 3 |
| D3×AΓL(1,𝔽9) | 9 |