Finite Group DatabasebetaFinite Group DatabasebetaOrder 6912.
1004 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #72220484 | — | 3 | 1 | no | maximal |
| 2 | #72220123 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C2×D4×PSU(3,𝔽2)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C23×PSU(3,𝔽2)⋊C3 | C4 | 1 | 2 | yes | — |
| 5 | D4×PSU(3,𝔽2)⋊C3 | — | 2 | 2 | no | — |
| 6 | C2×C4×PSU(3,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 7 | (PSU(3,𝔽2)⋊C3)⋊C8 | — | 2 | 2 | no | — |
| 8 | #13140565 | — | 4 | 1 | no | maximal |
| 9 | C2×D4×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 10 | #11785131 | — | 3 | 1 | no | — |
| 11 | #11776370 | — | 3 | 2 | no | — |
| 12 | #11774597 | — | 3 | 2 | no | — |
| 13 | #11773820 | — | 3 | 1 | no | — |
| 14 | C22×PSU(3,𝔽2)⋊C3 | — | 2 | 2 | no | — |
| 15 | C22×PSU(3,𝔽2)⋊C3 | — | 4 | 2 | no | — |
| 16 | C22×PSU(3,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 17 | C4×PSU(3,𝔽2)⋊C3 | D4 | 1 | 2 | yes | — |
| 18 | C2×D4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 19 | #11721053 | — | 4 | 2 | no | — |
| 20 | #11720579 | — | 4 | 1 | no | — |
| 21 | #63660⋊C3 | — | 4 | 1 | no | — |
| 22 | #11720320 | — | 4 | 2 | no | — |
| 23 | #11711035 | — | 9 | 1 | no | maximal |
| 24 | C23×PSU(3,𝔽2) | Dic3 | 1 | 2 | yes | — |
| 25 | C2×D4×#157 | — | 3 | 1 | no | — |
| 26 | C2×C22⋊PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 27 | D4×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 28 | D4×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 29 | C2×C4⋊PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 30 | C2×C4×PSU(3,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 31 | #10596484 | — | 3 | 2 | no | — |
| 32 | #10593328 | — | 3 | 2 | no | — |
| 33 | #10593272 | — | 6 | 2 | no | — |
| 34 | #10593158 | — | 6 | 4 | no | — |
| 35 | PSU(3,𝔽2)⋊C8 | — | 6 | 2 | no | — |
| 36 | PSU(3,𝔽2)⋊C8 | — | 6 | 2 | no | — |
| 37 | #10591503 | — | 6 | 1 | no | — |
| 38 | D3×#833 | — | 12 | 1 | no | — |
| 39 | #10590053 | — | 6 | 1 | no | — |
| 40 | C2×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 41 | C2×PSU(3,𝔽2)⋊C3 | — | 4 | 2 | no | — |
| 42 | C2×PSU(3,𝔽2)⋊C3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 43 | C23×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 44 | C2×D4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 45 | C2×#638⋊C3 | — | 4 | 2 | no | — |
| 46 | D4×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 47 | D4×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 48 | C2×C4⋊((C3⋊D3)⋊C3) | — | 4 | 1 | no | — |
| 49 | C2×C4×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 50 | #88538 | — | 4 | 2 | no | — |
| 51 | #3748⋊C3 | — | 4 | 2 | no | — |
| 52 | #88430 | — | 8 | 2 | no | — |
| 53 | ((C3⋊D3)⋊C3)⋊C8 | — | 8 | 2 | no | — |
| 54 | C2×D4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 55 | #73055 | — | 9 | 2 | no | — |
| 56 | C23×#157 | — | 3 | 2 | no | — |
| 57 | C22×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 58 | C22×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 59 | C22×PSU(3,𝔽2) | — | 4 | 2 | no | — |
| 60 | C22×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 61 | C22×PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 62 | C22×PSU(3,𝔽2) | C2×Dic3 | 1 | 1 | yes | characteristic |
| 63 | C2×D4×C3⋊D3 | S4 | 1 | 1 | yes | characteristic |
| 64 | C2×C3×D3×D4 | — | 12 | 1 | no | — |
| 65 | C2×C22⋊#157 | — | 3 | 2 | no | — |
| 66 | D4×#157 | — | 6 | 2 | no | — |
| 67 | D4×#157 | — | 6 | 2 | no | — |
| 68 | C2×C4⋊#157 | — | 3 | 1 | no | — |
| 69 | C2×C4×#157 | — | 3 | 1 | no | — |
| 70 | C22⋊PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 71 | C22⋊PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 72 | C2×#3777 | — | 3 | 1 | no | — |
| 73 | C2×#3777 | — | 6 | 1 | no | — |
| 74 | C4⋊PSU(3,𝔽2) | — | 3 | 4 | no | — |
| 75 | C4⋊PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 76 | C4×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 77 | C4×PSU(3,𝔽2) | #67 | 1 | 2 | yes | — |
| 78 | C22⋊AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 79 | C4⋊AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 80 | C4×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 81 | #63818 | — | 6 | 2 | no | — |
| 82 | D3×#208 | — | 12 | 2 | no | — |
| 83 | #63732 | — | 6 | 2 | no | — |
| 84 | #63732 | — | 6 | 2 | no | — |
| 85 | #63660 | — | 4 | 1 | no | — |
| 86 | C3×#833 | — | 12 | 1 | no | — |
| 87 | C3×#833 | — | 12 | 1 | no | — |
| 88 | C3×#833 | — | 24 | 1 | no | — |
| 89 | #63559 | — | 12 | 1 | no | — |
| 90 | #63558 | — | 12 | 2 | no | — |
| 91 | #8391 | — | 27 | 1 | no | Sylow |
| 92 | PSU(3,𝔽2)⋊C3 | #100 | 1 | 1 | yes | characteristic, complemented |
| 93 | C23×H(3,𝔽3) | — | 4 | 2 | no | — |
| 94 | C22×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 95 | C22×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 96 | C22×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 97 | C22×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 98 | C22×(C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 99 | C22×(C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 100 | D4×H(3,𝔽3) | — | 8 | 2 | no | — |
| 101 | C2×C4×H(3,𝔽3) | — | 4 | 1 | no | — |
| 102 | #638⋊C3 | — | 8 | 4 | no | — |
| 103 | C2×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 104 | C4⋊((C3⋊D3)⋊C3) | — | 8 | 2 | no | — |
| 105 | C4×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 106 | C4×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 107 | #6180 | — | 8 | 2 | no | — |
| 108 | (C3⋊(C3⋊C8))⋊C3 | — | 8 | 2 | no | — |
| 109 | C23×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 110 | D4×SL(2,𝔽3) | — | 18 | 2 | no | — |
| 111 | C2×C4×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 112 | C2×#833 | — | 36 | 1 | no | — |
| 113 | D3×#100 | — | 36 | 1 | no | — |
| 114 | SL(2,𝔽3)⋊C8 | — | 18 | 2 | no | — |
| 115 | C23×C3⋊D3 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 116 | C23×C3×D3 | — | 12 | 2 | no | — |
| 117 | C22×#157 | — | 3 | 1 | no | — |
| 118 | C22×#157 | — | 3 | 1 | no | — |
| 119 | C22×#157 | — | 3 | 2 | no | — |
| 120 | C22×#157 | — | 6 | 2 | no | — |
| 121 | C22×#157 | — | 6 | 2 | no | — |
| 122 | C22×#157 | — | 12 | 2 | no | — |
| 123 | C22×#157 | — | 12 | 2 | no | — |
| 124 | C2×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 125 | C2×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 126 | C2×PSU(3,𝔽2) | — | 3 | 4 | no | — |
| 127 | C2×PSU(3,𝔽2) | — | 4 | 2 | no | — |
| 128 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 129 | C2×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 130 | C2×PSU(3,𝔽2) | — | 12 | 4 | no | — |
| 131 | C2×PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 132 | C2×PSU(3,𝔽2) | — | 12 | 4 | no | — |
| 133 | C2×PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 134 | C2×PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 135 | C2×PSU(3,𝔽2) | #217 | 1 | 1 | yes | characteristic |
| 136 | C2×AGL(1,𝔽9) | — | 12 | 2 | no | — |
| 137 | C2×C32×D4 | — | 4 | 1 | no | — |
| 138 | C2×C32×D4 | — | 8 | 1 | no | — |
| 139 | C2×C32×D4 | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 140 | C2×#638 | #226 | 1 | 2 | yes | — |
| 141 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 142 | D4×C3⋊D3 | — | 2 | 2 | no | — |
| 143 | C2×C4⋊(C3⋊D3) | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 144 | C2×C4×C3⋊D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 145 | C2×C3×#67 | — | 12 | 2 | no | — |
| 146 | C3×D3×D4 | — | 24 | 2 | no | — |
| 147 | C3×D3×D4 | — | 24 | 2 | no | — |
| 148 | C2×C3×D12 | — | 12 | 1 | no | — |
| 149 | C2×C3×C4×D3 | — | 12 | 1 | no | — |
| 150 | C22⋊#157 | — | 6 | 4 | no | — |
| 151 | C4⋊#157 | — | 6 | 2 | no | — |
| 152 | C4×#157 | — | 3 | 2 | no | — |
| 153 | C4×#157 | — | 3 | 2 | no | — |
| 154 | #3777 | — | 3 | 2 | no | — |
| 155 | #3777 | — | 6 | 1 | no | — |
| 156 | #3777 | — | 6 | 4 | no | — |
| 157 | #3748 | — | 4 | 2 | no | — |
| 158 | C3×#208 | — | 12 | 2 | no | — |
| 159 | C3×#208 | — | 12 | 2 | no | — |
| 160 | C3×#208 | — | 24 | 2 | no | — |
| 161 | #3712 | — | 12 | 2 | no | — |
| 162 | #3711 | — | 24 | 2 | no | — |
| 163 | #3710 | — | 12 | 2 | no | — |
| 164 | D3×C3⋊C8 | — | 24 | 2 | no | — |
| 165 | C2×D4×Q8 | — | 9 | 1 | no | — |
| 166 | #1800 | — | 27 | 1 | no | — |
| 167 | #1548 | — | 27 | 2 | no | — |
| 168 | #1487 | — | 27 | 2 | no | — |
| 169 | #1460 | — | 27 | 1 | no | — |
| 170 | C22×H(3,𝔽3) | — | 4 | 1 | no | — |
| 171 | C22×H(3,𝔽3) | — | 8 | 2 | no | — |
| 172 | C22×H(3,𝔽3) | — | 16 | 2 | no | — |
| 173 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 174 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 175 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 176 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 177 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 178 | C2×(C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 179 | C2×(C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 180 | C2×(C3⋊D3)⋊C3 | — | 16 | 4 | no | — |
| 181 | C2×(C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 182 | C4×H(3,𝔽3) | — | 4 | 2 | no | — |
| 183 | (C3⋊Dic3)⋊C3 | — | 4 | 2 | no | — |
| 184 | C22×C3×D4 | — | 36 | 1 | no | — |
| 185 | C2×D3×D4 | — | 12 | 1 | no | — |
| 186 | C22×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 187 | C22×SL(2,𝔽3) | — | 18 | 2 | no | — |
| 188 | C22×SL(2,𝔽3) | — | 36 | 2 | no | — |
| 189 | C2×#208 | — | 36 | 2 | no | — |
| 190 | D3×M16 | — | 36 | 2 | no | — |
| 191 | C4×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 192 | C3×#100 | — | 36 | 1 | no | — |
| 193 | #833 | — | 12 | 1 | no | — |
| 194 | #833 | — | 12 | 1 | no | — |
| 195 | #833 | — | 24 | 1 | no | — |
| 196 | #833 | — | 36 | 1 | no | — |
| 197 | #833 | — | 36 | 2 | no | — |
| 198 | #823 | — | 36 | 2 | no | — |
| 199 | C23×C32 | — | 4 | 2 | no | — |
| 200 | C23×C32 | — | 8 | 2 | no | — |
| 201 | C23×C32 | #859 | 1 | 2 | yes | — |
| 202 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 203 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 204 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 205 | C22×C3⋊D3 | — | 4 | 2 | no | — |
| 206 | C22×C3⋊D3 | #859 | 1 | 2 | yes | — |
| 207 | C22×C3⋊D3 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 208 | C22×C3×D3 | — | 12 | 1 | no | — |
| 209 | C22×C3×D3 | — | 12 | 2 | no | — |
| 210 | C22×C3×D3 | — | 24 | 2 | no | — |
| 211 | C22×C3×D3 | — | 24 | 2 | no | — |
| 212 | C22×C3×D3 | — | 48 | 2 | no | — |
| 213 | C22×C3×D3 | — | 48 | 2 | no | — |
| 214 | C2×#157 | — | 3 | 1 | no | — |
| 215 | C2×#157 | — | 3 | 2 | no | — |
| 216 | C2×#157 | — | 3 | 1 | no | — |
| 217 | C2×#157 | — | 6 | 1 | no | — |
| 218 | C2×#157 | — | 6 | 1 | no | — |
| 219 | C2×#157 | — | 6 | 2 | no | — |
| 220 | C2×#157 | — | 12 | 2 | no | — |
| 221 | C2×#157 | — | 12 | 2 | no | — |
| 222 | C2×#157 | — | 12 | 1 | no | — |
| 223 | C2×#157 | — | 12 | 4 | no | — |
| 224 | C2×#157 | — | 12 | 2 | no | — |
| 225 | PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 226 | PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 227 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 228 | PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 229 | PSU(3,𝔽2) | — | 12 | 2 | no | — |
| 230 | PSU(3,𝔽2) | — | 12 | 4 | no | — |
| 231 | PSU(3,𝔽2) | #833 | 1 | 1 | yes | characteristic, complemented |
| 232 | AGL(1,𝔽9) | — | 24 | 2 | no | — |
| 233 | C32×D4 | — | 2 | 2 | no | — |
| 234 | C32×D4 | — | 8 | 2 | no | — |
| 235 | C32×D4 | — | 16 | 2 | no | — |
| 236 | C2×C32×C4 | — | 4 | 1 | no | — |
| 237 | C2×C32×C4 | — | 8 | 1 | no | — |
| 238 | C2×C32×C4 | C2×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 239 | #638 | — | 2 | 4 | no | — |
| 240 | C2×C3⋊Dic3 | C2×#226 | 1 | 1 | yes | characteristic |
| 241 | C4⋊(C3⋊D3) | — | 2 | 2 | no | — |
| 242 | C4×C3⋊D3 | #983 | 1 | 2 | yes | — |
| 243 | C4×C3⋊D3 | GL(2,ℤ/4) | 1 | 2 | yes | — |
| 244 | C3×#67 | — | 24 | 4 | no | — |
| 245 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 246 | C3×D12 | — | 24 | 2 | no | — |
| 247 | C3×C4×D3 | — | 12 | 2 | no | — |
| 248 | C3×C4×D3 | — | 12 | 2 | no | — |
| 249 | C3⋊(C3⋊C8) | — | 8 | 2 | no | — |
| 250 | C3×C3⋊C8 | — | 24 | 2 | no | — |
| 251 | C3×C3⋊C8 | — | 24 | 2 | no | — |
| 252 | C3×C3⋊C8 | — | 48 | 2 | no | — |
| 253 | C23×Q8 | — | 9 | 2 | no | — |
| 254 | D4×Q8 | — | 18 | 2 | no | — |
| 255 | D4×Q8 | — | 54 | 2 | no | — |
| 256 | C2×C4⋊Q8 | — | 27 | 1 | no | — |
| 257 | C2×C22⋊Q8 | — | 27 | 2 | no | — |
| 258 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 259 | C2×C4×D4 | — | 27 | 1 | no | — |
| 260 | #431 | — | 27 | 2 | no | — |
| 261 | #423 | — | 27 | 2 | no | — |
| 262 | C2×#100 | — | 54 | 1 | no | — |
| 263 | #343 | — | 54 | 1 | no | — |
| 264 | #333 | — | 54 | 4 | no | — |
| 265 | Q8⋊C8 | — | 54 | 2 | no | — |
| 266 | Q8⋊C8 | — | 54 | 2 | no | — |
| 267 | #323 | — | 54 | 2 | no | — |
| 268 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 269 | C2×H(3,𝔽3) | — | 8 | 1 | no | — |
| 270 | C2×H(3,𝔽3) | — | 16 | 2 | no | — |
| 271 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 272 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 273 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 274 | (C3⋊D3)⋊C3 | — | 16 | 2 | no | — |
| 275 | C24×C3 | — | 36 | 2 | no | — |
| 276 | C23×D3 | — | 12 | 2 | no | — |
| 277 | C2×C3×D4 | — | 4 | 1 | no | — |
| 278 | C2×C3×D4 | — | 12 | 1 | no | — |
| 279 | C2×C3×D4 | — | 24 | 1 | no | — |
| 280 | C2×C3×D4 | — | 36 | 1 | no | — |
| 281 | C2×C3×D4 | — | 36 | 2 | no | — |
| 282 | C2×C3×D4 | — | 72 | 2 | no | — |
| 283 | C2×C3×D4 | — | 72 | 2 | no | — |
| 284 | C22×C3×C4 | — | 36 | 1 | no | — |
| 285 | C2×#67 | — | 12 | 2 | no | — |
| 286 | D3×D4 | — | 24 | 2 | no | — |
| 287 | D3×D4 | — | 24 | 2 | no | — |
| 288 | C2×D12 | — | 12 | 1 | no | — |
| 289 | C2×C4×D3 | — | 12 | 1 | no | — |
| 290 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 291 | C2×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 292 | C2×SL(2,𝔽3) | — | 36 | 2 | no | — |
| 293 | C3×M16 | — | 36 | 2 | no | — |
| 294 | #208 | — | 12 | 2 | no | — |
| 295 | #208 | — | 12 | 2 | no | — |
| 296 | #208 | — | 24 | 2 | no | — |
| 297 | #208 | — | 36 | 2 | no | — |
| 298 | #208 | — | 72 | 2 | no | — |
| 299 | C2×C3⋊C8 | — | 72 | 2 | no | — |
| 300 | ΓL(1,𝔽25) | — | 72 | 2 | no | — |
| 301 | D3×C8 | — | 72 | 2 | no | — |
| 302 | C22×C32 | — | 2 | 2 | no | — |
| 303 | C22×C32 | — | 4 | 1 | no | — |
| 304 | C22×C32 | — | 4 | 2 | no | — |
| 305 | C22×C32 | — | 8 | 1 | no | — |
| 306 | C22×C32 | — | 8 | 2 | no | — |
| 307 | C22×C32 | — | 16 | 2 | no | — |
| 308 | C22×C32 | — | 16 | 2 | no | — |
| 309 | C22×C32 | — | 32 | 2 | no | — |
| 310 | C22×C32 | C2×#859 | 1 | 1 | yes | characteristic |
| 311 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 312 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 313 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 314 | C2×C3⋊D3 | — | 4 | 4 | no | — |
| 315 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 316 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 317 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 318 | C2×C3⋊D3 | #5420 | 1 | 1 | yes | characteristic |
| 319 | C2×C3⋊D3 | #5432 | 1 | 1 | yes | characteristic |
| 320 | C2×C3×D3 | — | 12 | 1 | no | — |
| 321 | C2×C3×D3 | — | 12 | 1 | no | — |
| 322 | C2×C3×D3 | — | 24 | 1 | no | — |
| 323 | C2×C3×D3 | — | 24 | 1 | no | — |
| 324 | C2×C3×D3 | — | 24 | 2 | no | — |
| 325 | C2×C3×D3 | — | 48 | 2 | no | — |
| 326 | C2×C3×D3 | — | 48 | 2 | no | — |
| 327 | C2×C3×D3 | — | 48 | 4 | no | — |
| 328 | C2×C3×D3 | — | 48 | 2 | no | — |
| 329 | #157 | — | 3 | 1 | no | — |
| 330 | #157 | — | 3 | 1 | no | — |
| 331 | #157 | — | 6 | 1 | no | — |
| 332 | #157 | — | 6 | 2 | no | — |
| 333 | #157 | — | 12 | 2 | no | — |
| 334 | C32×C4 | — | 4 | 2 | no | — |
| 335 | C32×C4 | — | 8 | 2 | no | — |
| 336 | C32×C4 | #5421 | 1 | 2 | yes | — |
| 337 | C3⋊Dic3 | #5419 | 1 | 2 | yes | — |
| 338 | C3×Dic3 | — | 12 | 2 | no | — |
| 339 | C22×Q8 | — | 9 | 1 | no | — |
| 340 | C22×Q8 | — | 18 | 2 | no | — |
| 341 | C22×Q8 | — | 27 | 2 | no | — |
| 342 | C22×Q8 | — | 36 | 2 | no | — |
| 343 | C22×Q8 | — | 54 | 2 | no | — |
| 344 | C22×Q8 | — | 108 | 2 | no | — |
| 345 | C22×D4 | — | 9 | 1 | no | — |
| 346 | C23×C4 | — | 27 | 2 | no | — |
| 347 | C2×M16 | — | 54 | 2 | no | — |
| 348 | C4⋊Q8 | — | 27 | 4 | no | — |
| 349 | C4⋊Q8 | — | 54 | 2 | no | — |
| 350 | C22⋊Q8 | — | 54 | 4 | no | — |
| 351 | C22⋊Q8 | — | 54 | 4 | no | — |
| 352 | C4×Q8 | — | 9 | 2 | no | — |
| 353 | C4×Q8 | — | 27 | 2 | no | — |
| 354 | C4×D4 | — | 54 | 2 | no | — |
| 355 | C4×D4 | — | 54 | 2 | no | — |
| 356 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 357 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 358 | C2×C4⋊C4 | — | 54 | 1 | no | — |
| 359 | C2×C22⋊C4 | — | 27 | 2 | no | — |
| 360 | C2×C42 | — | 27 | 1 | no | — |
| 361 | C4⋊C8 | — | 54 | 2 | no | — |
| 362 | C4⋊C8 | — | 54 | 2 | no | — |
| 363 | C4⋊C8 | — | 54 | 2 | no | — |
| 364 | #100 | — | 36 | 1 | no | — |
| 365 | #100 | — | 108 | 1 | no | — |
| 366 | C22⋊C8 | — | 54 | 2 | no | — |
| 367 | C4×C8 | — | 54 | 2 | no | — |
| 368 | H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 369 | C23×C3 | — | 4 | 2 | no | — |
| 370 | C23×C3 | — | 12 | 2 | no | — |
| 371 | C23×C3 | — | 24 | 2 | no | — |
| 372 | C23×C3 | — | 36 | 1 | no | — |
| 373 | C23×C3 | — | 36 | 2 | no | — |
| 374 | C23×C3 | — | 72 | 2 | no | — |
| 375 | C23×C3 | — | 72 | 2 | no | — |
| 376 | C23×C3 | — | 144 | 2 | no | — |
| 377 | C23×C3 | — | 144 | 2 | no | — |
| 378 | C22×D3 | — | 12 | 1 | no | — |
| 379 | C22×D3 | — | 12 | 2 | no | — |
| 380 | C22×D3 | — | 24 | 2 | no | — |
| 381 | C22×D3 | — | 24 | 2 | no | — |
| 382 | C22×D3 | — | 48 | 2 | no | — |
| 383 | C22×D3 | — | 48 | 2 | no | — |
| 384 | C3×D4 | — | 8 | 2 | no | — |
| 385 | C3×D4 | — | 24 | 2 | no | — |
| 386 | C3×D4 | — | 48 | 2 | no | — |
| 387 | C3×D4 | — | 72 | 2 | no | — |
| 388 | C3×D4 | — | 72 | 4 | no | — |
| 389 | C2×C3×C4 | — | 4 | 1 | no | — |
| 390 | C2×C3×C4 | — | 12 | 1 | no | — |
| 391 | C2×C3×C4 | — | 24 | 1 | no | — |
| 392 | C2×C3×C4 | — | 36 | 2 | no | — |
| 393 | C2×C3×C4 | — | 36 | 2 | no | — |
| 394 | C2×C3×C4 | — | 36 | 1 | no | — |
| 395 | #67 | — | 24 | 4 | no | — |
| 396 | C2×Dic3 | — | 12 | 1 | no | — |
| 397 | D12 | — | 24 | 2 | no | — |
| 398 | C4×D3 | — | 12 | 2 | no | — |
| 399 | C4×D3 | — | 12 | 2 | no | — |
| 400 | SL(2,𝔽3) | — | 9 | 1 | no | — |
| 401 | C3×C8 | — | 72 | 2 | no | — |
| 402 | C3⋊C8 | — | 24 | 2 | no | — |
| 403 | C3⋊C8 | — | 24 | 2 | no | — |
| 404 | C3⋊C8 | — | 48 | 2 | no | — |
| 405 | C3⋊C8 | — | 72 | 2 | no | — |
| 406 | C2×C32 | — | 2 | 1 | no | — |
| 407 | C2×C32 | — | 4 | 1 | no | — |
| 408 | C2×C32 | — | 4 | 2 | no | — |
| 409 | C2×C32 | — | 8 | 1 | no | — |
| 410 | C2×C32 | — | 8 | 1 | no | — |
| 411 | C2×C32 | — | 16 | 1 | no | — |
| 412 | C2×C32 | — | 16 | 2 | no | — |
| 413 | C2×C32 | — | 32 | 2 | no | — |
| 414 | C2×C32 | #73148 | 1 | 1 | yes | characteristic |
| 415 | C3⋊D3 | — | 2 | 1 | no | — |
| 416 | C3⋊D3 | — | 4 | 2 | no | — |
| 417 | C3⋊D3 | #73143 | 1 | 1 | yes | characteristic |
| 418 | C3⋊D3 | #73154 | 1 | 1 | yes | characteristic |
| 419 | C3×D3 | — | 12 | 1 | no | — |
| 420 | C3×D3 | — | 12 | 1 | no | — |
| 421 | C3×D3 | — | 24 | 1 | no | — |
| 422 | C3×D3 | — | 48 | 2 | no | — |
| 423 | C24 | — | 9 | 2 | no | — |
| 424 | C2×Q8 | — | 9 | 1 | no | — |
| 425 | C2×Q8 | — | 18 | 1 | no | — |
| 426 | C2×Q8 | — | 27 | 1 | no | — |
| 427 | C2×Q8 | — | 27 | 4 | no | — |
| 428 | C2×Q8 | — | 36 | 2 | no | — |
| 429 | C2×Q8 | — | 54 | 2 | no | — |
| 430 | C2×Q8 | — | 54 | 1 | no | — |
| 431 | C2×Q8 | — | 108 | 2 | no | — |
| 432 | C2×Q8 | — | 108 | 2 | no | — |
| 433 | C2×Q8 | — | 108 | 4 | no | — |
| 434 | C2×Q8 | — | 108 | 2 | no | — |
| 435 | C2×Q8 | — | 108 | 4 | no | — |
| 436 | C2×D4 | — | 9 | 2 | no | — |
| 437 | C2×D4 | — | 9 | 1 | no | — |
| 438 | C2×D4 | — | 18 | 2 | no | — |
| 439 | C2×D4 | — | 18 | 2 | no | — |
| 440 | C2×D4 | AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 441 | C22×C4 | — | 9 | 1 | no | — |
| 442 | C22×C4 | — | 27 | 1 | no | — |
| 443 | C22×C4 | — | 27 | 1 | no | — |
| 444 | C22×C4 | — | 27 | 2 | no | — |
| 445 | C22×C4 | — | 54 | 2 | no | — |
| 446 | C22×C4 | — | 54 | 2 | no | — |
| 447 | C22×C4 | — | 108 | 2 | no | — |
| 448 | C22×C4 | — | 108 | 2 | no | — |
| 449 | M16 | — | 36 | 2 | no | — |
| 450 | M16 | — | 108 | 2 | no | — |
| 451 | C2×C8 | — | 108 | 2 | no | — |
| 452 | C2×C8 | — | 108 | 2 | no | — |
| 453 | C4⋊C4 | — | 27 | 2 | no | — |
| 454 | C4⋊C4 | — | 54 | 2 | no | — |
| 455 | C4⋊C4 | — | 54 | 1 | no | — |
| 456 | C4⋊C4 | — | 54 | 4 | no | — |
| 457 | C22⋊C4 | — | 54 | 4 | no | — |
| 458 | C42 | — | 27 | 2 | no | — |
| 459 | C42 | — | 27 | 2 | no | — |
| 460 | C22×C3 | — | 4 | 1 | no | — |
| 461 | C22×C3 | — | 8 | 2 | no | — |
| 462 | C22×C3 | — | 12 | 1 | no | — |
| 463 | C22×C3 | — | 16 | 2 | no | — |
| 464 | C22×C3 | — | 24 | 2 | no | — |
| 465 | C22×C3 | — | 24 | 1 | no | — |
| 466 | C22×C3 | — | 36 | 1 | no | — |
| 467 | C22×C3 | — | 36 | 1 | no | — |
| 468 | C22×C3 | — | 48 | 2 | no | — |
| 469 | C22×C3 | — | 48 | 2 | no | — |
| 470 | C22×C3 | — | 72 | 2 | no | — |
| 471 | C22×C3 | — | 72 | 1 | no | — |
| 472 | C22×C3 | — | 72 | 1 | no | — |
| 473 | C22×C3 | — | 96 | 2 | no | — |
| 474 | C22×C3 | — | 144 | 2 | no | — |
| 475 | C22×C3 | — | 144 | 2 | no | — |
| 476 | C22×C3 | — | 144 | 2 | no | — |
| 477 | C22×C3 | — | 144 | 4 | no | — |
| 478 | C2×D3 | — | 12 | 1 | no | — |
| 479 | C2×D3 | — | 12 | 1 | no | — |
| 480 | C2×D3 | — | 24 | 1 | no | — |
| 481 | C2×D3 | — | 24 | 1 | no | — |
| 482 | C2×D3 | — | 24 | 2 | no | — |
| 483 | C2×D3 | — | 48 | 2 | no | — |
| 484 | C2×D3 | — | 48 | 2 | no | — |
| 485 | C2×D3 | — | 48 | 4 | no | — |
| 486 | C2×D3 | — | 48 | 2 | no | — |
| 487 | C3×C4 | — | 4 | 2 | no | — |
| 488 | C3×C4 | — | 12 | 2 | no | — |
| 489 | C3×C4 | — | 24 | 2 | no | — |
| 490 | C3×C4 | — | 36 | 2 | no | — |
| 491 | Dic3 | — | 12 | 2 | no | — |
| 492 | C32 | — | 4 | 1 | no | — |
| 493 | C32 | — | 8 | 1 | no | — |
| 494 | C32 | #11711035 | 1 | 1 | yes | characteristic, complemented |
| 495 | C23 | — | 9 | 1 | no | — |
| 496 | C23 | — | 9 | 2 | no | — |
| 497 | C23 | — | 18 | 2 | no | — |
| 498 | C23 | — | 18 | 2 | no | — |
| 499 | C23 | — | 36 | 2 | no | — |
| 500 | C23 | — | 36 | 2 | no | — |
| 501 | C23 | (PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 2 | yes | — |
| 502 | Q8 | — | 9 | 1 | no | — |
| 503 | Q8 | — | 27 | 1 | no | — |
| 504 | Q8 | — | 27 | 2 | no | — |
| 505 | Q8 | — | 54 | 1 | no | — |
| 506 | Q8 | — | 108 | 2 | no | — |
| 507 | Q8 | — | 108 | 2 | no | — |
| 508 | Q8 | — | 108 | 4 | no | — |
| 509 | D4 | — | 2 | 2 | no | — |
| 510 | D4 | — | 18 | 4 | no | — |
| 511 | D4 | — | 18 | 2 | no | — |
| 512 | C2×C4 | — | 9 | 1 | no | — |
| 513 | C2×C4 | — | 9 | 2 | no | — |
| 514 | C2×C4 | — | 9 | 2 | no | — |
| 515 | C2×C4 | — | 27 | 1 | no | — |
| 516 | C2×C4 | — | 27 | 2 | no | — |
| 517 | C2×C4 | — | 27 | 1 | no | — |
| 518 | C2×C4 | — | 54 | 1 | no | — |
| 519 | C2×C4 | — | 54 | 1 | no | — |
| 520 | C2×C4 | — | 54 | 2 | no | — |
| 521 | C2×C4 | — | 108 | 2 | no | — |
| 522 | C2×C4 | — | 108 | 2 | no | — |
| 523 | C2×C4 | — | 108 | 1 | no | — |
| 524 | C2×C4 | — | 108 | 4 | no | — |
| 525 | C2×C4 | — | 108 | 2 | no | — |
| 526 | C2×C4 | C2×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 527 | C8 | — | 72 | 2 | no | — |
| 528 | C8 | — | 216 | 2 | no | — |
| 529 | C2×C3 | — | 4 | 1 | no | — |
| 530 | C2×C3 | — | 8 | 1 | no | — |
| 531 | C2×C3 | — | 12 | 1 | no | — |
| 532 | C2×C3 | — | 16 | 2 | no | — |
| 533 | C2×C3 | — | 24 | 1 | no | — |
| 534 | C2×C3 | — | 24 | 1 | no | — |
| 535 | C2×C3 | — | 36 | 1 | no | — |
| 536 | C2×C3 | — | 36 | 1 | no | — |
| 537 | C2×C3 | — | 48 | 1 | no | — |
| 538 | C2×C3 | — | 48 | 2 | no | — |
| 539 | C2×C3 | — | 72 | 1 | no | — |
| 540 | C2×C3 | — | 96 | 2 | no | — |
| 541 | C2×C3 | — | 144 | 2 | no | — |
| 542 | D3 | — | 12 | 1 | no | — |
| 543 | D3 | — | 12 | 1 | no | — |
| 544 | D3 | — | 24 | 1 | no | — |
| 545 | D3 | — | 48 | 2 | no | — |
| 546 | C22 | — | 2 | 2 | no | — |
| 547 | C22 | — | 4 | 2 | no | — |
| 548 | C22 | — | 9 | 1 | no | — |
| 549 | C22 | — | 9 | 1 | no | — |
| 550 | C22 | — | 18 | 1 | no | — |
| 551 | C22 | — | 18 | 1 | no | — |
| 552 | C22 | — | 18 | 2 | no | — |
| 553 | C22 | — | 36 | 2 | no | — |
| 554 | C22 | — | 36 | 2 | no | — |
| 555 | C22 | — | 36 | 2 | no | — |
| 556 | C22 | — | 36 | 4 | no | — |
| 557 | C22 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 1 | yes | characteristic |
| 558 | C4 | — | 9 | 2 | no | — |
| 559 | C4 | — | 27 | 1 | no | — |
| 560 | C4 | — | 27 | 1 | no | — |
| 561 | C4 | — | 54 | 2 | no | — |
| 562 | C4 | — | 54 | 1 | no | — |
| 563 | C4 | — | 108 | 2 | no | — |
| 564 | C4 | #13180131 | 1 | 2 | yes | — |
| 565 | C3 | — | 4 | 1 | no | — |
| 566 | C3 | — | 12 | 1 | no | — |
| 567 | C3 | — | 24 | 1 | no | — |
| 568 | C2 | — | 2 | 1 | no | — |
| 569 | C2 | — | 4 | 2 | no | — |
| 570 | C2 | — | 9 | 1 | no | — |
| 571 | C2 | — | 9 | 1 | no | — |
| 572 | C2 | — | 18 | 1 | no | — |
| 573 | C2 | — | 36 | 2 | no | — |
| 574 | C2 | #72220407 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72220123 | C2 | semidirect |
| 92. PSU(3,𝔽2)⋊C3 | #100 | semidirect |
| 231. PSU(3,𝔽2) | #833 | semidirect |
| 494. C32 | #11711035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220484 | 3 |
| #72220123 | 2 |
| C2×D4×PSU(3,𝔽2)⋊C3 | 2 |
| #13140565 | 4 |
| #11711035 | 9 |