Finite Group DatabasebetaFinite Group DatabasebetaOrder 7776.
1540 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 38 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 | #72224523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D3×#10620193 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72224521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D3×#10620206 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #72214225 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#13049804 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | D3×#10620211 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#13049804 | — | 3 | 1 | no | maximal |
| 9 | D3×C3⋊D32 | — | 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 | D3×#66472 | — | 2 | 1 | no | — |
| 17 | D3×#66472 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3⋊#10620193 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | C3×#10620193 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#10620211 | — | 3 | 1 | no | — |
| 21 | C2×#10620206 | — | 3 | 1 | no | — |
| 22 | C2×#10620193 | — | 3 | 1 | no | — |
| 23 | #13049804 | — | 3 | 1 | no | — |
| 24 | #13049804 | — | 3 | 1 | no | — |
| 25 | #13049804 | — | 3 | 1 | no | — |
| 26 | #13049804 | D3 | 1 | 1 | yes | characteristic, direct product factor |
| 27 | #11758168 | — | 2 | 1 | no | — |
| 28 | C3⋊D3×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 29 | D3×C3⋊(C3⋊(C3⋊D3)) | D4 | 1 | 1 | yes | characteristic |
| 30 | C3×C3⋊D32 | — | 2 | 1 | no | — |
| 31 | C32×D3×C3⋊D3 | — | 4 | 1 | no | — |
| 32 | C3⋊#66472 | — | 2 | 1 | no | — |
| 33 | C3⋊#66472 | D4 | 1 | 1 | yes | characteristic |
| 34 | C3×#66472 | — | 2 | 1 | no | — |
| 35 | C3×#66472 | C23 | 1 | 1 | yes | characteristic |
| 36 | D3×AΓL(1,𝔽9) | — | 9 | 2 | no | maximal |
| 37 | C2×C3⋊D32 | — | 6 | 1 | no | — |
| 38 | C2×#66472 | — | 3 | 1 | no | — |
| 39 | C2×#66472 | — | 6 | 1 | no | — |
| 40 | D32×C3⋊D3 | — | 12 | 2 | no | — |
| 41 | D32×C3⋊D3 | — | 12 | 2 | no | — |
| 42 | #10620211 | — | 3 | 1 | no | — |
| 43 | #10620211 | — | 6 | 1 | no | — |
| 44 | #10620211 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 45 | #10620206 | — | 3 | 1 | no | — |
| 46 | #10620206 | — | 6 | 1 | no | — |
| 47 | #10620206 | C2×D3 | 1 | 1 | yes | characteristic |
| 48 | #10620193 | — | 3 | 1 | no | — |
| 49 | #10620193 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C3⋊(C3⋊(C3⋊(C3⋊D3))) | SD16 | 1 | 1 | yes | characteristic, complemented |
| 51 | C3×C3⋊(C3⋊(C3⋊D3)) | C2×D4 | 1 | 1 | yes | characteristic |
| 52 | C32×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 53 | C33×C3⋊D3 | — | 4 | 1 | no | — |
| 54 | C34×D3 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 55 | D3×PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 56 | D3×PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 57 | D3×GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 58 | D3×GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 59 | AGL(1,𝔽9)⋊D3 | — | 9 | 2 | no | — |
| 60 | #89092 | — | 9 | 2 | no | — |
| 61 | #89091 | — | 9 | 2 | no | — |
| 62 | C3×AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 63 | D3×AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 64 | C2×C3⋊(C3⋊(C3⋊D3)) | — | 3 | 1 | no | — |
| 65 | C2×C32×C3⋊D3 | — | 12 | 1 | no | — |
| 66 | C3⋊#1113 | — | 12 | 2 | no | — |
| 67 | C3⋊#1113 | — | 12 | 2 | no | — |
| 68 | C3⋊D32 | — | 2 | 1 | no | — |
| 69 | C3⋊D32 | — | 6 | 1 | no | — |
| 70 | C3⋊D32 | — | 12 | 1 | no | — |
| 71 | C3⋊D32 | — | 12 | 2 | no | — |
| 72 | C3⋊D32 | — | 12 | 2 | no | — |
| 73 | C3⋊D32 | — | 24 | 2 | no | — |
| 74 | C3⋊D32 | — | 24 | 2 | no | — |
| 75 | D3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 76 | D3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 77 | D3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 78 | D3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 79 | D3×C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 80 | D3×C3⋊(C3⋊D3) | — | 24 | 2 | no | — |
| 81 | C3×D3×C3⋊D3 | — | 4 | 2 | no | — |
| 82 | C3×D3×C3⋊D3 | — | 4 | 2 | no | — |
| 83 | C3×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 84 | C3×D3×C3⋊D3 | — | 12 | 2 | no | — |
| 85 | C32×D32 | — | 12 | 2 | no | — |
| 86 | C32×D32 | — | 12 | 2 | no | — |
| 87 | #66472 | — | 2 | 1 | no | — |
| 88 | #66472 | — | 3 | 1 | no | — |
| 89 | #66472 | — | 6 | 1 | no | — |
| 90 | #66472 | C22×D3 | 1 | 1 | yes | characteristic |
| 91 | C2×AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 92 | C35 | C2×SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 93 | C2×D3×C3⋊D3 | — | 36 | 1 | no | — |
| 94 | C2×D3×C3⋊D3 | — | 36 | 2 | no | — |
| 95 | C2×D3×C3⋊D3 | — | 36 | 2 | no | — |
| 96 | D33 | — | 18 | 2 | no | — |
| 97 | D33 | — | 18 | 2 | no | — |
| 98 | D33 | — | 36 | 1 | no | — |
| 99 | D33 | — | 36 | 4 | no | — |
| 100 | D33 | — | 36 | 1 | no | — |
| 101 | C3⋊PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 102 | C3⋊PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 103 | C3⋊PSU(3,𝔽2) | — | 18 | 2 | no | — |
| 104 | C3⋊PSU(3,𝔽2) | — | 18 | 2 | no | — |
| 105 | C3×PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 106 | C3×PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 107 | #157⋊D3 | — | 9 | 2 | no | — |
| 108 | #157⋊D3 | — | 18 | 1 | no | — |
| 109 | D32⋊D3 | — | 18 | 2 | no | — |
| 110 | D32⋊D3 | — | 18 | 2 | no | — |
| 111 | C3×GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 112 | C3×GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 113 | D3×#157 | — | 9 | 2 | no | — |
| 114 | D3×#157 | — | 18 | 1 | no | — |
| 115 | D3×#157 | — | 18 | 1 | no | — |
| 116 | D3×#157 | — | 18 | 2 | no | — |
| 117 | D3×#157 | — | 18 | 2 | no | — |
| 118 | D3×#157 | — | 36 | 1 | no | — |
| 119 | D3×#157 | — | 36 | 2 | no | — |
| 120 | D3×#157 | — | 36 | 1 | no | — |
| 121 | C3⋊AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 122 | C3×AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 123 | C2×C34 | — | 3 | 1 | no | — |
| 124 | C3⋊(C3⋊(C3⋊D3)) | — | 3 | 1 | no | — |
| 125 | C3⋊(C3⋊(C3⋊D3)) | — | 12 | 2 | no | — |
| 126 | C3⋊(C3⋊(C3⋊D3)) | — | 12 | 2 | no | — |
| 127 | C3⋊(C3⋊(C3⋊D3)) | — | 24 | 1 | no | — |
| 128 | C3⋊(C3⋊(C3⋊D3)) | — | 24 | 2 | no | — |
| 129 | C3⋊(C3⋊(C3⋊D3)) | — | 24 | 2 | no | — |
| 130 | C3⋊(C3⋊(C3⋊D3)) | — | 24 | 2 | no | — |
| 131 | C3⋊(C3⋊(C3⋊D3)) | — | 48 | 1 | no | — |
| 132 | C3⋊(C3⋊(C3⋊D3)) | — | 48 | 2 | no | — |
| 133 | C3⋊(C3⋊(C3⋊D3)) | D3×D4 | 1 | 1 | yes | characteristic |
| 134 | C3×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 135 | C3×C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 136 | C3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 137 | C3×C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 138 | C3×C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 139 | C3×C3⋊(C3⋊D3) | — | 24 | 2 | no | — |
| 140 | C32×C3⋊D3 | — | 4 | 1 | no | — |
| 141 | C32×C3⋊D3 | — | 4 | 2 | no | — |
| 142 | C32×C3⋊D3 | — | 4 | 2 | no | — |
| 143 | C32×C3⋊D3 | — | 8 | 2 | no | — |
| 144 | C32×C3⋊D3 | — | 8 | 2 | no | — |
| 145 | C32×C3⋊D3 | — | 12 | 1 | no | — |
| 146 | C32×C3⋊D3 | — | 12 | 2 | no | — |
| 147 | C32×C3⋊D3 | — | 12 | 2 | no | — |
| 148 | C32×C3⋊D3 | — | 24 | 2 | no | — |
| 149 | C32×C3⋊D3 | — | 24 | 2 | no | — |
| 150 | C33×D3 | — | 4 | 2 | no | — |
| 151 | C33×D3 | — | 4 | 2 | no | — |
| 152 | C33×D3 | — | 8 | 1 | no | — |
| 153 | C33×D3 | — | 8 | 2 | no | — |
| 154 | C33×D3 | — | 12 | 2 | no | — |
| 155 | C33×D3 | — | 12 | 2 | no | — |
| 156 | C2×PSU(3,𝔽2) | — | 27 | 2 | no | — |
| 157 | C2×PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 158 | C2×GO+(4,𝔽2) | — | 27 | 2 | no | — |
| 159 | C2×GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 160 | C2×AGL(1,𝔽9) | — | 27 | 2 | no | — |
| 161 | AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 162 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 163 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 164 | AΓL(1,𝔽9) | — | 27 | 2 | no | — |
| 165 | C2×C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 166 | C2×C3⋊(C3⋊D3) | — | 36 | 2 | no | — |
| 167 | C2×C3⋊(C3⋊D3) | — | 36 | 2 | no | — |
| 168 | C2×C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 169 | C2×C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 170 | C2×C3×C3⋊D3 | — | 12 | 2 | no | — |
| 171 | C2×C3×C3⋊D3 | — | 12 | 2 | no | — |
| 172 | C2×C3×C3⋊D3 | — | 36 | 1 | no | — |
| 173 | C2×C32×D3 | — | 36 | 1 | no | — |
| 174 | C2×C32×D3 | — | 36 | 2 | no | — |
| 175 | C2×C32×D3 | — | 36 | 2 | no | — |
| 176 | #1113 | — | 18 | 2 | no | — |
| 177 | #1113 | — | 18 | 2 | no | — |
| 178 | #1113 | — | 36 | 1 | no | — |
| 179 | #1113 | — | 36 | 4 | no | — |
| 180 | #1113 | — | 36 | 1 | no | — |
| 181 | D3×C3⋊D3 | — | 4 | 1 | no | — |
| 182 | D3×C3⋊D3 | — | 9 | 2 | no | — |
| 183 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 184 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 185 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 186 | D3×C3⋊D3 | — | 18 | 1 | no | — |
| 187 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 188 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 189 | D3×C3⋊D3 | — | 36 | 4 | no | — |
| 190 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 191 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 192 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 193 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 194 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 195 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 196 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 197 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 198 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 199 | D3×C3⋊D3 | — | 36 | 4 | no | — |
| 200 | D3×C3⋊D3 | — | 36 | 4 | no | — |
| 201 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 202 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 203 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 204 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 205 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 206 | D3×C3⋊D3 | — | 36 | 2 | no | — |
| 207 | D3×C3⋊D3 | — | 36 | 1 | no | — |
| 208 | D3×C3⋊D3 | — | 72 | 1 | no | — |
| 209 | D3×C3⋊D3 | — | 72 | 4 | no | — |
| 210 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 211 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 212 | D3×C3⋊D3 | — | 72 | 1 | no | — |
| 213 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 214 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 215 | D3×C3⋊D3 | — | 72 | 4 | no | — |
| 216 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 217 | D3×C3⋊D3 | — | 72 | 4 | no | — |
| 218 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 219 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 220 | D3×C3⋊D3 | — | 72 | 2 | no | — |
| 221 | C3×D32 | — | 12 | 2 | no | — |
| 222 | C3×D32 | — | 12 | 2 | no | — |
| 223 | C3×D32 | — | 12 | 4 | no | — |
| 224 | C3×D32 | — | 12 | 4 | no | — |
| 225 | C3×D32 | — | 12 | 2 | no | — |
| 226 | C3×D32 | — | 12 | 2 | no | — |
| 227 | C3×D32 | — | 18 | 2 | no | — |
| 228 | C3×D32 | — | 18 | 2 | no | — |
| 229 | C3×D32 | — | 36 | 1 | no | — |
| 230 | C3×D32 | — | 36 | 4 | no | — |
| 231 | C3×D32 | — | 36 | 1 | no | — |
| 232 | C3⋊#157 | — | 9 | 2 | no | — |
| 233 | C3⋊#157 | — | 18 | 1 | no | — |
| 234 | C3⋊#157 | — | 18 | 1 | no | — |
| 235 | C3⋊#157 | — | 18 | 2 | no | — |
| 236 | C3⋊#157 | — | 18 | 2 | no | — |
| 237 | C3⋊#157 | — | 36 | 1 | no | — |
| 238 | C3⋊#157 | — | 36 | 2 | no | — |
| 239 | C3⋊#157 | — | 36 | 1 | no | — |
| 240 | C3×#157 | — | 9 | 2 | no | — |
| 241 | C3×#157 | — | 18 | 1 | no | — |
| 242 | C3×#157 | — | 18 | 1 | no | — |
| 243 | C3×#157 | — | 18 | 2 | no | — |
| 244 | C3×#157 | — | 18 | 2 | no | — |
| 245 | C3×#157 | — | 36 | 1 | no | — |
| 246 | C3×#157 | — | 36 | 2 | no | — |
| 247 | C3×#157 | — | 36 | 1 | no | — |
| 248 | D3×SD16 | — | 81 | 1 | no | — |
| 249 | C34 | — | 4 | 2 | no | — |
| 250 | C34 | — | 4 | 2 | no | — |
| 251 | C34 | — | 8 | 1 | no | — |
| 252 | C34 | — | 8 | 2 | no | — |
| 253 | C34 | — | 8 | 2 | no | — |
| 254 | C34 | — | 8 | 2 | no | — |
| 255 | C34 | — | 16 | 2 | no | — |
| 256 | C34 | — | 16 | 1 | no | — |
| 257 | C34 | D3×SD16 | 1 | 1 | yes | characteristic, complemented |
| 258 | C22×C3⋊D3 | — | 108 | 1 | no | — |
| 259 | C2×D32 | — | 54 | 2 | no | — |
| 260 | C2×D32 | — | 54 | 2 | no | — |
| 261 | C2×D32 | — | 108 | 1 | no | — |
| 262 | C2×D32 | — | 108 | 4 | no | — |
| 263 | C2×D32 | — | 108 | 1 | no | — |
| 264 | C2×D32 | — | 108 | 2 | no | — |
| 265 | C2×D32 | — | 108 | 2 | no | — |
| 266 | C2×#157 | — | 27 | 2 | no | — |
| 267 | C2×#157 | — | 54 | 2 | no | — |
| 268 | C2×#157 | — | 54 | 2 | no | — |
| 269 | C2×#157 | — | 54 | 1 | no | — |
| 270 | C2×#157 | — | 54 | 1 | no | — |
| 271 | C2×#157 | — | 108 | 2 | no | — |
| 272 | C2×#157 | — | 108 | 1 | no | — |
| 273 | C2×#157 | — | 108 | 1 | no | — |
| 274 | PSU(3,𝔽2) | — | 9 | 2 | no | — |
| 275 | PSU(3,𝔽2) | — | 18 | 1 | no | — |
| 276 | PSU(3,𝔽2) | — | 27 | 2 | no | — |
| 277 | PSU(3,𝔽2) | — | 54 | 2 | no | — |
| 278 | PSU(3,𝔽2) | — | 54 | 2 | no | — |
| 279 | PSU(3,𝔽2) | — | 54 | 1 | no | — |
| 280 | GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 281 | GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 282 | GO+(4,𝔽2) | — | 27 | 2 | no | — |
| 283 | GO+(4,𝔽2) | — | 54 | 2 | no | — |
| 284 | GO+(4,𝔽2) | — | 54 | 2 | no | — |
| 285 | GO+(4,𝔽2) | — | 54 | 1 | no | — |
| 286 | AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 287 | AGL(1,𝔽9) | — | 27 | 2 | no | — |
| 288 | C2×C33 | — | 12 | 2 | no | — |
| 289 | C2×C33 | — | 12 | 2 | no | — |
| 290 | C2×C33 | — | 24 | 1 | no | — |
| 291 | C2×C33 | — | 24 | 2 | no | — |
| 292 | C2×C33 | — | 36 | 1 | no | — |
| 293 | C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 294 | C3⋊(C3⋊D3) | — | 9 | 2 | no | — |
| 295 | C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 296 | C3⋊(C3⋊D3) | — | 12 | 2 | no | — |
| 297 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 298 | C3⋊(C3⋊D3) | — | 18 | 1 | no | — |
| 299 | C3⋊(C3⋊D3) | — | 24 | 1 | no | — |
| 300 | C3⋊(C3⋊D3) | — | 24 | 2 | no | — |
| 301 | C3⋊(C3⋊D3) | — | 36 | 2 | no | — |
| 302 | C3⋊(C3⋊D3) | — | 36 | 2 | no | — |
| 303 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 304 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 305 | C3⋊(C3⋊D3) | — | 36 | 4 | no | — |
| 306 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 307 | C3⋊(C3⋊D3) | — | 36 | 2 | no | — |
| 308 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 309 | C3⋊(C3⋊D3) | — | 36 | 1 | no | — |
| 310 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 311 | C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 312 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 313 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 314 | C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 315 | C3⋊(C3⋊D3) | — | 72 | 4 | no | — |
| 316 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 317 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 318 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 319 | C3⋊(C3⋊D3) | — | 72 | 4 | no | — |
| 320 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 321 | C3⋊(C3⋊D3) | — | 72 | 4 | no | — |
| 322 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 323 | C3⋊(C3⋊D3) | — | 72 | 2 | no | — |
| 324 | C3⋊(C3⋊D3) | — | 72 | 1 | no | — |
| 325 | C3⋊(C3⋊D3) | — | 144 | 1 | no | — |
| 326 | C3⋊(C3⋊D3) | — | 144 | 1 | no | — |
| 327 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 328 | C3⋊(C3⋊D3) | — | 144 | 1 | no | — |
| 329 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 330 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 331 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 332 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 333 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 334 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 335 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 336 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 337 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 338 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 339 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 340 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 341 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 342 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 343 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 344 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 345 | C3⋊(C3⋊D3) | — | 144 | 4 | no | — |
| 346 | C3⋊(C3⋊D3) | — | 144 | 2 | no | — |
| 347 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 348 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 349 | C3×C3⋊D3 | — | 4 | 2 | no | — |
| 350 | C3×C3⋊D3 | — | 8 | 2 | no | — |
| 351 | C3×C3⋊D3 | — | 8 | 2 | no | — |
| 352 | C3×C3⋊D3 | — | 9 | 2 | no | — |
| 353 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 354 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 355 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 356 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 357 | C3×C3⋊D3 | — | 12 | 4 | no | — |
| 358 | C3×C3⋊D3 | — | 12 | 4 | no | — |
| 359 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 360 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 361 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 362 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 363 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 364 | C3×C3⋊D3 | — | 24 | 4 | no | — |
| 365 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 366 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 367 | C3×C3⋊D3 | — | 24 | 4 | no | — |
| 368 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 369 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 370 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 371 | C3×C3⋊D3 | — | 36 | 4 | no | — |
| 372 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 373 | C3×C3⋊D3 | — | 36 | 2 | no | — |
| 374 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 375 | C3×C3⋊D3 | — | 36 | 1 | no | — |
| 376 | C3×C3⋊D3 | — | 72 | 1 | no | — |
| 377 | C3×C3⋊D3 | — | 72 | 4 | no | — |
| 378 | C3×C3⋊D3 | — | 72 | 2 | no | — |
| 379 | C3×C3⋊D3 | — | 72 | 2 | no | — |
| 380 | C3×C3⋊D3 | — | 72 | 1 | no | — |
| 381 | C32×D3 | — | 2 | 1 | no | — |
| 382 | C32×D3 | — | 2 | 1 | no | — |
| 383 | C32×D3 | — | 4 | 1 | no | — |
| 384 | C32×D3 | — | 4 | 1 | no | — |
| 385 | C32×D3 | — | 4 | 4 | no | — |
| 386 | C32×D3 | — | 4 | 1 | no | — |
| 387 | C32×D3 | — | 4 | 2 | no | — |
| 388 | C32×D3 | — | 4 | 1 | no | — |
| 389 | C32×D3 | — | 4 | 1 | no | — |
| 390 | C32×D3 | — | 8 | 4 | no | — |
| 391 | C32×D3 | — | 8 | 1 | no | — |
| 392 | C32×D3 | — | 8 | 2 | no | — |
| 393 | C32×D3 | — | 8 | 2 | no | — |
| 394 | C32×D3 | — | 8 | 1 | no | — |
| 395 | C32×D3 | — | 12 | 2 | no | — |
| 396 | C32×D3 | — | 12 | 2 | no | — |
| 397 | C32×D3 | — | 12 | 2 | no | — |
| 398 | C32×D3 | — | 12 | 2 | no | — |
| 399 | C32×D3 | — | 12 | 4 | no | — |
| 400 | C32×D3 | — | 12 | 4 | no | — |
| 401 | C32×D3 | — | 12 | 2 | no | — |
| 402 | C32×D3 | — | 12 | 2 | no | — |
| 403 | C32×D3 | — | 24 | 2 | no | — |
| 404 | C32×D3 | — | 24 | 4 | no | — |
| 405 | C32×D3 | — | 24 | 2 | no | — |
| 406 | C32×D3 | — | 24 | 2 | no | — |
| 407 | C32×D3 | — | 24 | 4 | no | — |
| 408 | C32×D3 | — | 24 | 2 | no | — |
| 409 | C32×D3 | — | 36 | 1 | no | — |
| 410 | C32×D3 | — | 36 | 2 | no | — |
| 411 | C32×D3 | — | 36 | 2 | no | — |
| 412 | C32×D3 | — | 72 | 2 | no | — |
| 413 | C32×D3 | — | 72 | 2 | no | — |
| 414 | C32×D3 | AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 415 | D3×Q8 | — | 81 | 1 | no | — |
| 416 | D3×D4 | — | 81 | 1 | no | — |
| 417 | C3×SD16 | — | 81 | 1 | no | — |
| 418 | #215 | — | 81 | 1 | no | — |
| 419 | #214 | — | 81 | 1 | no | — |
| 420 | #204 | — | 81 | 1 | no | — |
| 421 | D3×C8 | — | 81 | 1 | no | — |
| 422 | C22×C32 | — | 108 | 1 | no | — |
| 423 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 424 | C2×C3⋊D3 | — | 27 | 2 | no | — |
| 425 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 426 | C2×C3⋊D3 | — | 54 | 1 | no | — |
| 427 | C2×C3⋊D3 | — | 54 | 1 | no | — |
| 428 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 429 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 430 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 431 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 432 | C2×C3⋊D3 | — | 108 | 2 | no | — |
| 433 | C2×C3⋊D3 | — | 108 | 2 | no | — |
| 434 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 435 | C2×C3⋊D3 | — | 108 | 4 | no | — |
| 436 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 437 | C2×C3⋊D3 | — | 108 | 2 | no | — |
| 438 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 439 | C2×C3⋊D3 | — | 108 | 1 | no | — |
| 440 | C2×C3⋊D3 | — | 216 | 1 | no | — |
| 441 | C2×C3⋊D3 | — | 216 | 4 | no | — |
| 442 | C2×C3⋊D3 | — | 216 | 2 | no | — |
| 443 | C2×C3⋊D3 | — | 216 | 2 | no | — |
| 444 | C2×C3⋊D3 | — | 216 | 2 | no | — |
| 445 | C2×C3⋊D3 | — | 216 | 2 | no | — |
| 446 | C2×C3⋊D3 | — | 216 | 1 | no | — |
| 447 | C2×C3×D3 | — | 36 | 2 | no | — |
| 448 | C2×C3×D3 | — | 36 | 2 | no | — |
| 449 | C2×C3×D3 | — | 36 | 2 | no | — |
| 450 | C2×C3×D3 | — | 36 | 2 | no | — |
| 451 | C2×C3×D3 | — | 36 | 2 | no | — |
| 452 | C2×C3×D3 | — | 36 | 4 | no | — |
| 453 | C2×C3×D3 | — | 36 | 4 | no | — |
| 454 | C2×C3×D3 | — | 36 | 2 | no | — |
| 455 | C2×C3×D3 | — | 108 | 2 | no | — |
| 456 | C2×C3×D3 | — | 108 | 2 | no | — |
| 457 | D32 | — | 12 | 2 | no | — |
| 458 | D32 | — | 12 | 2 | no | — |
| 459 | D32 | — | 18 | 2 | no | — |
| 460 | D32 | — | 18 | 2 | no | — |
| 461 | D32 | — | 36 | 1 | no | — |
| 462 | D32 | — | 36 | 4 | no | — |
| 463 | D32 | — | 36 | 1 | no | — |
| 464 | D32 | — | 54 | 2 | no | — |
| 465 | D32 | — | 54 | 2 | no | — |
| 466 | D32 | — | 108 | 2 | no | — |
| 467 | D32 | — | 108 | 2 | no | — |
| 468 | D32 | — | 108 | 2 | no | — |
| 469 | D32 | — | 108 | 2 | no | — |
| 470 | D32 | — | 108 | 2 | no | — |
| 471 | D32 | — | 108 | 4 | no | — |
| 472 | D32 | — | 108 | 4 | no | — |
| 473 | D32 | — | 108 | 2 | no | — |
| 474 | D32 | — | 108 | 1 | no | — |
| 475 | D32 | — | 108 | 4 | no | — |
| 476 | D32 | — | 108 | 1 | no | — |
| 477 | D32 | — | 108 | 2 | no | — |
| 478 | D32 | — | 108 | 2 | no | — |
| 479 | D32 | — | 108 | 2 | no | — |
| 480 | D32 | — | 108 | 2 | no | — |
| 481 | D32 | — | 216 | 2 | no | — |
| 482 | D32 | — | 216 | 4 | no | — |
| 483 | D32 | — | 216 | 4 | no | — |
| 484 | D32 | — | 216 | 2 | no | — |
| 485 | D32 | — | 216 | 2 | no | — |
| 486 | D32 | — | 216 | 2 | no | — |
| 487 | D32 | — | 216 | 1 | no | — |
| 488 | D32 | — | 216 | 2 | no | — |
| 489 | #157 | — | 9 | 2 | no | — |
| 490 | #157 | — | 18 | 1 | no | — |
| 491 | #157 | — | 18 | 1 | no | — |
| 492 | #157 | — | 18 | 2 | no | — |
| 493 | #157 | — | 18 | 2 | no | — |
| 494 | #157 | — | 27 | 2 | no | — |
| 495 | #157 | — | 36 | 1 | no | — |
| 496 | #157 | — | 36 | 2 | no | — |
| 497 | #157 | — | 36 | 1 | no | — |
| 498 | #157 | — | 54 | 2 | no | — |
| 499 | #157 | — | 54 | 2 | no | — |
| 500 | #157 | — | 54 | 1 | no | — |
| 501 | #157 | — | 54 | 1 | no | — |
| 502 | #157 | — | 108 | 2 | no | — |
| 503 | #157 | — | 108 | 1 | no | — |
| 504 | #157 | — | 108 | 1 | no | — |
| 505 | C2×SD16 | — | 243 | 1 | no | Sylow |
| 506 | C33 | — | 2 | 1 | no | — |
| 507 | C33 | — | 2 | 1 | no | — |
| 508 | C33 | — | 4 | 2 | no | — |
| 509 | C33 | — | 4 | 1 | no | — |
| 510 | C33 | — | 4 | 2 | no | — |
| 511 | C33 | — | 4 | 1 | no | — |
| 512 | C33 | — | 4 | 4 | no | — |
| 513 | C33 | — | 4 | 1 | no | — |
| 514 | C33 | — | 4 | 2 | no | — |
| 515 | C33 | — | 4 | 1 | no | — |
| 516 | C33 | — | 4 | 1 | no | — |
| 517 | C33 | — | 8 | 1 | no | — |
| 518 | C33 | — | 8 | 2 | no | — |
| 519 | C33 | — | 8 | 2 | no | — |
| 520 | C33 | — | 8 | 4 | no | — |
| 521 | C33 | — | 8 | 1 | no | — |
| 522 | C33 | — | 8 | 2 | no | — |
| 523 | C33 | — | 8 | 4 | no | — |
| 524 | C33 | — | 8 | 2 | no | — |
| 525 | C33 | — | 8 | 2 | no | — |
| 526 | C33 | — | 8 | 4 | no | — |
| 527 | C33 | — | 8 | 2 | no | — |
| 528 | C33 | — | 8 | 2 | no | — |
| 529 | C33 | — | 8 | 2 | no | — |
| 530 | C33 | — | 8 | 1 | no | — |
| 531 | C33 | — | 8 | 2 | no | — |
| 532 | C33 | — | 16 | 1 | no | — |
| 533 | C33 | — | 16 | 2 | no | — |
| 534 | C33 | — | 16 | 2 | no | — |
| 535 | C33 | — | 16 | 4 | no | — |
| 536 | C33 | — | 16 | 1 | no | — |
| 537 | C33 | — | 16 | 1 | no | — |
| 538 | C33 | — | 16 | 2 | no | — |
| 539 | C33 | — | 16 | 2 | no | — |
| 540 | C33 | — | 16 | 4 | no | — |
| 541 | C33 | — | 16 | 2 | no | — |
| 542 | C33 | — | 16 | 4 | no | — |
| 543 | C33 | — | 16 | 2 | no | — |
| 544 | C33 | — | 16 | 2 | no | — |
| 545 | C33 | — | 16 | 4 | no | — |
| 546 | C33 | — | 16 | 4 | no | — |
| 547 | C33 | — | 16 | 2 | no | — |
| 548 | C33 | — | 16 | 2 | no | — |
| 549 | C33 | — | 16 | 4 | no | — |
| 550 | C33 | — | 16 | 2 | no | — |
| 551 | C33 | — | 16 | 4 | no | — |
| 552 | C33 | — | 16 | 2 | no | — |
| 553 | C33 | — | 16 | 2 | no | — |
| 554 | C33 | C2×AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 555 | C22×D3 | — | 324 | 2 | no | — |
| 556 | C22×D3 | — | 324 | 2 | no | — |
| 557 | C22×D3 | — | 162 | 1 | no | — |
| 558 | C3×Q8 | — | 81 | 1 | no | — |
| 559 | C3×D4 | — | 81 | 1 | no | — |
| 560 | #67 | — | 162 | 1 | no | — |
| 561 | D12 | — | 81 | 1 | no | — |
| 562 | C4×D3 | — | 81 | 1 | no | — |
| 563 | C4×D3 | — | 162 | 1 | no | — |
| 564 | Dic6 | — | 81 | 1 | no | — |
| 565 | Dic6 | — | 162 | 1 | no | — |
| 566 | C3×C8 | — | 81 | 1 | no | — |
| 567 | C3⋊C8 | — | 81 | 1 | no | — |
| 568 | C2×C32 | — | 3 | 2 | no | — |
| 569 | C2×C32 | — | 6 | 1 | no | — |
| 570 | C2×C32 | — | 6 | 1 | no | — |
| 571 | C2×C32 | — | 12 | 1 | no | — |
| 572 | C2×C32 | — | 12 | 1 | no | — |
| 573 | C2×C32 | — | 12 | 4 | no | — |
| 574 | C2×C32 | — | 12 | 1 | no | — |
| 575 | C2×C32 | — | 12 | 2 | no | — |
| 576 | C2×C32 | — | 12 | 1 | no | — |
| 577 | C2×C32 | — | 12 | 1 | no | — |
| 578 | C2×C32 | — | 24 | 1 | no | — |
| 579 | C2×C32 | — | 24 | 4 | no | — |
| 580 | C2×C32 | — | 24 | 2 | no | — |
| 581 | C2×C32 | — | 24 | 2 | no | — |
| 582 | C2×C32 | — | 24 | 1 | no | — |
| 583 | C2×C32 | — | 36 | 1 | no | — |
| 584 | C2×C32 | — | 36 | 2 | no | — |
| 585 | C2×C32 | — | 36 | 2 | no | — |
| 586 | C2×C32 | — | 72 | 2 | no | — |
| 587 | C2×C32 | — | 72 | 2 | no | — |
| 588 | C2×C32 | — | 108 | 1 | no | — |
| 589 | C3⋊D3 | — | 4 | 1 | no | — |
| 590 | C3⋊D3 | — | 9 | 2 | no | — |
| 591 | C3⋊D3 | — | 12 | 1 | no | — |
| 592 | C3⋊D3 | — | 12 | 2 | no | — |
| 593 | C3⋊D3 | — | 12 | 2 | no | — |
| 594 | C3⋊D3 | — | 18 | 1 | no | — |
| 595 | C3⋊D3 | — | 18 | 1 | no | — |
| 596 | C3⋊D3 | — | 24 | 2 | no | — |
| 597 | C3⋊D3 | — | 24 | 2 | no | — |
| 598 | C3⋊D3 | — | 27 | 2 | no | — |
| 599 | C3⋊D3 | — | 36 | 1 | no | — |
| 600 | C3⋊D3 | — | 36 | 1 | no | — |
| 601 | C3⋊D3 | — | 36 | 4 | no | — |
| 602 | C3⋊D3 | — | 36 | 1 | no | — |
| 603 | C3⋊D3 | — | 36 | 2 | no | — |
| 604 | C3⋊D3 | — | 36 | 1 | no | — |
| 605 | C3⋊D3 | — | 36 | 1 | no | — |
| 606 | C3⋊D3 | — | 54 | 1 | no | — |
| 607 | C3⋊D3 | — | 54 | 1 | no | — |
| 608 | C3⋊D3 | — | 72 | 1 | no | — |
| 609 | C3⋊D3 | — | 72 | 4 | no | — |
| 610 | C3⋊D3 | — | 72 | 2 | no | — |
| 611 | C3⋊D3 | — | 72 | 2 | no | — |
| 612 | C3⋊D3 | — | 72 | 1 | no | — |
| 613 | C3⋊D3 | — | 108 | 1 | no | — |
| 614 | C3⋊D3 | — | 108 | 1 | no | — |
| 615 | C3⋊D3 | — | 108 | 4 | no | — |
| 616 | C3⋊D3 | — | 108 | 1 | no | — |
| 617 | C3⋊D3 | — | 108 | 2 | no | — |
| 618 | C3⋊D3 | — | 108 | 2 | no | — |
| 619 | C3⋊D3 | — | 108 | 2 | no | — |
| 620 | C3⋊D3 | — | 108 | 1 | no | — |
| 621 | C3⋊D3 | — | 108 | 1 | no | — |
| 622 | C3⋊D3 | — | 432 | 2 | no | — |
| 623 | C3⋊D3 | — | 432 | 2 | no | — |
| 624 | C3⋊D3 | — | 432 | 4 | no | — |
| 625 | C3⋊D3 | — | 432 | 4 | no | — |
| 626 | C3⋊D3 | — | 432 | 2 | no | — |
| 627 | C3⋊D3 | — | 432 | 2 | no | — |
| 628 | C3⋊D3 | — | 432 | 4 | no | — |
| 629 | C3⋊D3 | — | 432 | 4 | no | — |
| 630 | C3⋊D3 | — | 432 | 2 | no | — |
| 631 | C3⋊D3 | — | 432 | 2 | no | — |
| 632 | C3⋊D3 | — | 432 | 2 | no | — |
| 633 | C3⋊D3 | — | 432 | 2 | no | — |
| 634 | C3⋊D3 | — | 432 | 2 | no | — |
| 635 | C3⋊D3 | — | 432 | 1 | no | — |
| 636 | C3⋊D3 | — | 432 | 1 | no | — |
| 637 | C3⋊D3 | — | 432 | 4 | no | — |
| 638 | C3⋊D3 | — | 432 | 4 | no | — |
| 639 | C3⋊D3 | — | 432 | 4 | no | — |
| 640 | C3⋊D3 | — | 432 | 2 | no | — |
| 641 | C3⋊D3 | — | 432 | 2 | no | — |
| 642 | C3⋊D3 | — | 432 | 2 | no | — |
| 643 | C3⋊D3 | — | 432 | 1 | no | — |
| 644 | C3⋊D3 | — | 216 | 2 | no | — |
| 645 | C3⋊D3 | — | 216 | 2 | no | — |
| 646 | C3⋊D3 | — | 216 | 4 | no | — |
| 647 | C3⋊D3 | — | 216 | 4 | no | — |
| 648 | C3⋊D3 | — | 216 | 1 | no | — |
| 649 | C3⋊D3 | — | 216 | 2 | no | — |
| 650 | C3⋊D3 | — | 216 | 1 | no | — |
| 651 | C3⋊D3 | — | 216 | 4 | no | — |
| 652 | C3⋊D3 | — | 216 | 2 | no | — |
| 653 | C3⋊D3 | — | 216 | 2 | no | — |
| 654 | C3⋊D3 | — | 216 | 2 | no | — |
| 655 | C3⋊D3 | — | 216 | 2 | no | — |
| 656 | C3⋊D3 | — | 216 | 2 | no | — |
| 657 | C3⋊D3 | — | 216 | 2 | no | — |
| 658 | C3⋊D3 | — | 216 | 1 | no | — |
| 659 | C3×D3 | — | 4 | 2 | no | — |
| 660 | C3×D3 | — | 4 | 2 | no | — |
| 661 | C3×D3 | — | 8 | 1 | no | — |
| 662 | C3×D3 | — | 8 | 2 | no | — |
| 663 | C3×D3 | — | 12 | 2 | no | — |
| 664 | C3×D3 | — | 12 | 2 | no | — |
| 665 | C3×D3 | — | 12 | 2 | no | — |
| 666 | C3×D3 | — | 12 | 2 | no | — |
| 667 | C3×D3 | — | 12 | 4 | no | — |
| 668 | C3×D3 | — | 12 | 4 | no | — |
| 669 | C3×D3 | — | 12 | 2 | no | — |
| 670 | C3×D3 | — | 12 | 2 | no | — |
| 671 | C3×D3 | — | 24 | 2 | no | — |
| 672 | C3×D3 | — | 24 | 2 | no | — |
| 673 | C3×D3 | — | 24 | 2 | no | — |
| 674 | C3×D3 | — | 24 | 4 | no | — |
| 675 | C3×D3 | — | 24 | 4 | no | — |
| 676 | C3×D3 | — | 24 | 2 | no | — |
| 677 | C3×D3 | — | 36 | 2 | no | — |
| 678 | C3×D3 | — | 36 | 2 | no | — |
| 679 | C3×D3 | — | 36 | 2 | no | — |
| 680 | C3×D3 | — | 36 | 2 | no | — |
| 681 | C3×D3 | — | 36 | 4 | no | — |
| 682 | C3×D3 | — | 36 | 4 | no | — |
| 683 | C3×D3 | — | 36 | 2 | no | — |
| 684 | C3×D3 | — | 36 | 2 | no | — |
| 685 | C3×D3 | — | 72 | 2 | no | — |
| 686 | C3×D3 | — | 72 | 2 | no | — |
| 687 | C3×D3 | — | 72 | 2 | no | — |
| 688 | C3×D3 | — | 72 | 4 | no | — |
| 689 | C3×D3 | — | 72 | 4 | no | — |
| 690 | C3×D3 | — | 72 | 2 | no | — |
| 691 | C3×D3 | — | 108 | 2 | no | — |
| 692 | C3×D3 | — | 108 | 2 | no | — |
| 693 | C3×D3 | — | 216 | 1 | no | — |
| 694 | C3×D3 | — | 216 | 2 | no | — |
| 695 | C2×Q8 | — | 243 | 1 | no | — |
| 696 | C2×D4 | — | 243 | 1 | no | — |
| 697 | SD16 | — | 81 | 1 | no | — |
| 698 | SD16 | — | 243 | 1 | no | — |
| 699 | SD16 | — | 243 | 1 | no | — |
| 700 | SD16 | — | 243 | 1 | no | — |
| 701 | C2×C8 | — | 243 | 1 | no | — |
| 702 | C22×C3 | — | 108 | 2 | no | — |
| 703 | C22×C3 | — | 108 | 2 | no | — |
| 704 | C22×C3 | — | 162 | 1 | no | — |
| 705 | C2×D3 | — | 36 | 2 | no | — |
| 706 | C2×D3 | — | 36 | 2 | no | — |
| 707 | C2×D3 | — | 36 | 1 | no | — |
| 708 | C2×D3 | — | 324 | 2 | no | — |
| 709 | C2×D3 | — | 324 | 2 | no | — |
| 710 | C2×D3 | — | 324 | 2 | no | — |
| 711 | C2×D3 | — | 324 | 2 | no | — |
| 712 | C2×D3 | — | 324 | 1 | no | — |
| 713 | C2×D3 | — | 324 | 2 | no | — |
| 714 | C2×D3 | — | 324 | 2 | no | — |
| 715 | C2×D3 | — | 324 | 2 | no | — |
| 716 | C2×D3 | — | 324 | 2 | no | — |
| 717 | C2×D3 | — | 81 | 1 | no | — |
| 718 | C2×D3 | — | 108 | 2 | no | — |
| 719 | C2×D3 | — | 108 | 2 | no | — |
| 720 | C2×D3 | — | 648 | 2 | no | — |
| 721 | C2×D3 | — | 648 | 2 | no | — |
| 722 | C2×D3 | — | 648 | 1 | no | — |
| 723 | C2×D3 | — | 648 | 2 | no | — |
| 724 | C2×D3 | — | 162 | 1 | no | — |
| 725 | C3×C4 | — | 81 | 1 | no | — |
| 726 | C3×C4 | — | 162 | 1 | no | — |
| 727 | Dic3 | — | 81 | 1 | no | — |
| 728 | Dic3 | — | 162 | 1 | no | — |
| 729 | C32 | — | 2 | 1 | no | — |
| 730 | C32 | — | 2 | 1 | no | — |
| 731 | C32 | — | 4 | 1 | no | — |
| 732 | C32 | — | 4 | 1 | no | — |
| 733 | C32 | — | 4 | 4 | no | — |
| 734 | C32 | — | 4 | 1 | no | — |
| 735 | C32 | — | 4 | 2 | no | — |
| 736 | C32 | — | 4 | 2 | no | — |
| 737 | C32 | — | 4 | 2 | no | — |
| 738 | C32 | — | 4 | 1 | no | — |
| 739 | C32 | — | 4 | 1 | no | — |
| 740 | C32 | — | 8 | 4 | no | — |
| 741 | C32 | — | 8 | 1 | no | — |
| 742 | C32 | — | 8 | 2 | no | — |
| 743 | C32 | — | 8 | 2 | no | — |
| 744 | C32 | — | 8 | 2 | no | — |
| 745 | C32 | — | 8 | 2 | no | — |
| 746 | C32 | — | 8 | 2 | no | — |
| 747 | C32 | — | 8 | 2 | no | — |
| 748 | C32 | — | 8 | 2 | no | — |
| 749 | C32 | — | 8 | 4 | no | — |
| 750 | C32 | — | 8 | 4 | no | — |
| 751 | C32 | — | 8 | 2 | no | — |
| 752 | C32 | — | 8 | 1 | no | — |
| 753 | C32 | — | 8 | 1 | no | — |
| 754 | C32 | — | 8 | 2 | no | — |
| 755 | C32 | — | 16 | 2 | no | — |
| 756 | C32 | — | 16 | 4 | no | — |
| 757 | C32 | — | 16 | 4 | no | — |
| 758 | C32 | — | 16 | 2 | no | — |
| 759 | C32 | — | 16 | 2 | no | — |
| 760 | C32 | — | 16 | 2 | no | — |
| 761 | C32 | — | 16 | 1 | no | — |
| 762 | C32 | — | 16 | 4 | no | — |
| 763 | C32 | — | 16 | 1 | no | — |
| 764 | C32 | — | 16 | 4 | no | — |
| 765 | C32 | — | 16 | 4 | no | — |
| 766 | C32 | — | 16 | 2 | no | — |
| 767 | C32 | — | 16 | 2 | no | — |
| 768 | C32 | — | 16 | 2 | no | — |
| 769 | C32 | — | 16 | 4 | no | — |
| 770 | C32 | — | 16 | 2 | no | — |
| 771 | C32 | — | 16 | 4 | no | — |
| 772 | C32 | — | 16 | 1 | no | — |
| 773 | C32 | — | 16 | 2 | no | — |
| 774 | C32 | — | 16 | 2 | no | — |
| 775 | C32 | — | 16 | 2 | no | — |
| 776 | C32 | — | 16 | 2 | no | — |
| 777 | C32 | D3×AΓL(1,𝔽9) | 1 | 2 | yes | complemented |
| 778 | C23 | — | 486 | 1 | no | — |
| 779 | Q8 | — | 81 | 1 | no | — |
| 780 | Q8 | — | 486 | 1 | no | — |
| 781 | Q8 | — | 243 | 1 | no | — |
| 782 | D4 | — | 81 | 1 | no | — |
| 783 | D4 | — | 486 | 1 | no | — |
| 784 | D4 | — | 243 | 1 | no | — |
| 785 | C2×C4 | — | 486 | 1 | no | — |
| 786 | C2×C4 | — | 243 | 1 | no | — |
| 787 | C8 | — | 81 | 1 | no | — |
| 788 | C8 | — | 243 | 1 | no | — |
| 789 | C2×C3 | — | 12 | 2 | no | — |
| 790 | C2×C3 | — | 12 | 2 | no | — |
| 791 | C2×C3 | — | 24 | 1 | no | — |
| 792 | C2×C3 | — | 24 | 2 | no | — |
| 793 | C2×C3 | — | 36 | 2 | no | — |
| 794 | C2×C3 | — | 36 | 2 | no | — |
| 795 | C2×C3 | — | 36 | 1 | no | — |
| 796 | C2×C3 | — | 72 | 2 | no | — |
| 797 | C2×C3 | — | 72 | 2 | no | — |
| 798 | C2×C3 | — | 81 | 1 | no | — |
| 799 | C2×C3 | — | 108 | 2 | no | — |
| 800 | C2×C3 | — | 108 | 2 | no | — |
| 801 | D3 | — | 12 | 2 | no | — |
| 802 | D3 | — | 12 | 2 | no | — |
| 803 | D3 | — | 1296 | 1 | no | — |
| 804 | D3 | — | 1296 | 2 | no | — |
| 805 | D3 | — | 36 | 2 | no | — |
| 806 | D3 | — | 36 | 2 | no | — |
| 807 | D3 | — | 36 | 1 | no | — |
| 808 | D3 | — | 324 | 2 | no | — |
| 809 | D3 | — | 324 | 2 | no | — |
| 810 | D3 | — | 72 | 2 | no | — |
| 811 | D3 | — | 72 | 2 | no | — |
| 812 | D3 | — | 81 | 1 | no | — |
| 813 | D3 | — | 108 | 2 | no | — |
| 814 | D3 | — | 108 | 2 | no | — |
| 815 | D3 | — | 648 | 1 | no | — |
| 816 | D3 | — | 648 | 2 | no | — |
| 817 | D3 | — | 648 | 2 | no | — |
| 818 | D3 | — | 648 | 2 | no | — |
| 819 | D3 | — | 216 | 1 | no | — |
| 820 | D3 | — | 216 | 2 | no | — |
| 821 | D3 | #13049804 | 1 | 1 | yes | characteristic, direct product factor |
| 822 | C22 | — | 108 | 1 | no | — |
| 823 | C22 | — | 162 | 1 | no | — |
| 824 | C22 | — | 972 | 1 | no | — |
| 825 | C22 | — | 486 | 1 | no | — |
| 826 | C22 | — | 243 | 1 | no | — |
| 827 | C4 | — | 81 | 1 | no | — |
| 828 | C4 | — | 162 | 1 | no | — |
| 829 | C4 | — | 486 | 1 | no | — |
| 830 | C4 | — | 243 | 1 | no | — |
| 831 | C3 | — | 4 | 2 | no | — |
| 832 | C3 | — | 4 | 2 | no | — |
| 833 | C3 | — | 8 | 2 | no | — |
| 834 | C3 | — | 8 | 2 | no | — |
| 835 | C3 | — | 8 | 1 | no | — |
| 836 | C3 | — | 8 | 2 | no | — |
| 837 | C3 | — | 16 | 2 | no | — |
| 838 | C3 | — | 16 | 1 | no | — |
| 839 | C3 | C2×#13049804 | 1 | 1 | yes | characteristic, complemented |
| 840 | C2 | — | 3 | 1 | no | — |
| 841 | C2 | — | 36 | 1 | no | — |
| 842 | C2 | — | 81 | 1 | no | — |
| 843 | C2 | — | 108 | 1 | no | — |
| 844 | C2 | — | 243 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle | C3×#66472 | C23 |
| Fitting, socle, hypocenter | C35 | C2×SD16 |
| prime radical | D3×#10620206 | 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. #72224523 | C2 | semidirect |
| 2. D3×#10620193 | C2 | semidirect |
| 3. #72224521 | C2 | semidirect |
| 5. #72214225 | C2 | semidirect |
| 6. C3×#13049804 | C2 | semidirect |
| 7. D3×#10620211 | C2 | semidirect |
| 11. C3⋊#10620211 | C22 | semidirect |
| 12. C3×#10620211 | C22 | semidirect |
| 18. C3⋊#10620193 | C22 | semidirect |
| 19. C3×#10620193 | C22 | semidirect |
| 26. #13049804 | D3 | direct (N × H) |
| 44. #10620211 | C2×D3 | semidirect |
| 49. #10620193 | C2×D3 | semidirect |
| 50. C3⋊(C3⋊(C3⋊(C3⋊D3))) | SD16 | semidirect |
| 54. C34×D3 | SD16 | semidirect |
| 92. C35 | C2×SD16 | semidirect |
| 257. C34 | D3×SD16 | semidirect |
| 414. C32×D3 | AΓL(1,𝔽9) | semidirect |
| 554. C33 | C2×AΓL(1,𝔽9) | semidirect |
| 777. C32 | D3×AΓL(1,𝔽9) | semidirect |
| 821. D3 | #13049804 | direct (N × H) |
| 839. C3 | C2×#13049804 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72224523 | 2 |
| D3×#10620193 | 2 |
| #72224521 | 2 |
| D3×#10620206 | 2 |
| #72214225 | 2 |
| C3×#13049804 | 2 |
| D3×#10620211 | 2 |
| C2×#13049804 | 3 |
| D3×AΓL(1,𝔽9) | 9 |