Finite Group DatabasebetaFinite Group DatabasebetaOrder 5184.
600 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 34 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 | Dic3×PSU(3,𝔽2)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×C3⋊AGL(2,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #89092⋊C4 | — | 3 | 1 | no | maximal |
| 5 | C4×AGL(2,𝔽3) | — | 3 | 1 | no | maximal |
| 6 | C2×C3×PSU(3,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 7 | C3⋊AGL(2,𝔽3) | C4 | 1 | 2 | yes | complemented |
| 8 | (((C3⋊D3)⋊C3)⋊D3)⋊C4 | — | 4 | 1 | no | maximal |
| 9 | C2×#89092 | — | 3 | 1 | no | — |
| 10 | C2×AGL(2,𝔽3) | — | 3 | 1 | no | — |
| 11 | C2×AGL(2,𝔽3) | — | 6 | 1 | no | — |
| 12 | Dic3×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | #11724111 | — | 3 | 1 | no | — |
| 14 | #11724104 | — | 3 | 1 | no | — |
| 15 | #11724100 | — | 3 | 1 | no | — |
| 16 | C3×PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 17 | Dic3×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 18 | C4×PSU(3,𝔽2)⋊C3 | — | 3 | 1 | no | — |
| 19 | (PSU(3,𝔽2)⋊C3)⋊C4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C3×PSU(3,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×((C3⋊D3)⋊C3)⋊D3 | — | 4 | 1 | no | — |
| 22 | #10619901 | — | 4 | 1 | no | — |
| 23 | #10619890 | — | 4 | 1 | no | — |
| 24 | #10619885 | — | 4 | 1 | no | — |
| 25 | C3×((C3⋊D3)⋊C3)⋊C4 | — | 4 | 1 | no | — |
| 26 | #6289⋊C3 | — | 4 | 1 | no | — |
| 27 | Dic3×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 28 | C4×AΓL(1,𝔽9) | — | 9 | 1 | no | — |
| 29 | #10593214 | — | 9 | 1 | no | maximal |
| 30 | C2×C3×PSU(3,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 31 | C2×#157⋊D3 | — | 3 | 1 | no | — |
| 32 | C2×C3⋊AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 33 | C2×C3×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 34 | #89092 | — | 3 | 2 | no | — |
| 35 | #89092 | — | 3 | 2 | no | — |
| 36 | C2×PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 37 | C2×PSU(3,𝔽2)⋊C3 | C2×D3 | 1 | 1 | yes | characteristic |
| 38 | AGL(2,𝔽3) | — | 3 | 2 | no | — |
| 39 | AGL(2,𝔽3) | — | 6 | 2 | no | — |
| 40 | #88949 | — | 6 | 1 | no | — |
| 41 | D3×#624 | — | 12 | 1 | no | — |
| 42 | #88946 | — | 3 | 1 | no | — |
| 43 | #88932 | — | 6 | 1 | no | — |
| 44 | C3×#3773 | — | 3 | 1 | no | — |
| 45 | Dic3×#157 | — | 3 | 1 | no | — |
| 46 | C4×((C3⋊D3)⋊C3)⋊C2 | — | 12 | 1 | no | — |
| 47 | C2×C3⋊#272 | — | 4 | 1 | no | — |
| 48 | C2×C3⋊((C3⋊D3)⋊C3) | — | 4 | 1 | no | — |
| 49 | C2×C3×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 50 | ((C3⋊D3)⋊C3)⋊D3 | — | 4 | 2 | no | — |
| 51 | ((C3⋊D3)⋊C3)⋊D3 | — | 4 | 2 | no | — |
| 52 | C3×#1084 | — | 4 | 1 | no | — |
| 53 | C3⋊((C3⋊Dic3)⋊C3) | — | 4 | 1 | no | — |
| 54 | Dic3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 55 | C3×(C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 56 | C2×AΓL(1,𝔽9) | — | 9 | 1 | no | — |
| 57 | C2×C3⋊GL(2,𝔽3) | — | 9 | 1 | no | — |
| 58 | C4×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 59 | C4×GO+(4,𝔽2) | — | 9 | 1 | no | — |
| 60 | C4×AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 61 | AGL(1,𝔽9)⋊C4 | — | 9 | 1 | no | — |
| 62 | PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 63 | GO+(4,𝔽2)⋊C4 | — | 9 | 1 | no | — |
| 64 | Dic3×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 65 | C3×#859 | — | 9 | 1 | no | — |
| 66 | C2×#1113 | — | 6 | 1 | no | — |
| 67 | C2×D3×C3⋊D3 | — | 12 | 1 | no | — |
| 68 | C2×C3⋊#157 | — | 3 | 1 | no | — |
| 69 | C2×C3×#157 | — | 3 | 1 | no | — |
| 70 | C3×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 71 | C3×PSU(3,𝔽2) | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 72 | #157⋊D3 | — | 3 | 2 | no | — |
| 73 | #157⋊D3 | — | 6 | 1 | no | — |
| 74 | C3⋊AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 75 | C3×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 76 | PSU(3,𝔽2)⋊C3 | — | 2 | 1 | no | — |
| 77 | PSU(3,𝔽2)⋊C3 | C4×D3 | 1 | 1 | yes | characteristic, complemented |
| 78 | #6294 | — | 12 | 1 | no | — |
| 79 | #6289 | — | 4 | 1 | no | — |
| 80 | #6289 | — | 12 | 1 | no | — |
| 81 | Dic3×C3⋊D3 | — | 12 | 1 | no | — |
| 82 | Dic3×C3⋊D3 | S4 | 1 | 1 | yes | characteristic |
| 83 | C3×#624 | — | 6 | 1 | no | — |
| 84 | C3×#624 | — | 12 | 1 | no | — |
| 85 | C3×#624 | — | 12 | 1 | no | — |
| 86 | C3×#624 | — | 24 | 1 | no | — |
| 87 | C3×D3×Dic3 | — | 12 | 1 | no | — |
| 88 | C3×D3×Dic3 | — | 12 | 1 | no | — |
| 89 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 12 | 1 | no | — |
| 90 | C2×((C3⋊D3)⋊C3)⋊C2 | — | 24 | 1 | no | — |
| 91 | C4×#272 | — | 12 | 1 | no | — |
| 92 | C4×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 93 | C4×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 94 | #6199 | — | 12 | 1 | no | — |
| 95 | #6199 | — | 24 | 1 | no | — |
| 96 | ((C3⋊D3)⋊C3)⋊C4 | — | 4 | 1 | no | — |
| 97 | ((C3⋊D3)⋊C3)⋊C4 | — | 12 | 1 | no | — |
| 98 | C4×GL(2,𝔽3) | — | 27 | 1 | no | — |
| 99 | #4788 | — | 27 | 1 | no | — |
| 100 | C2×C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 101 | C3⋊#272 | — | 4 | 2 | no | — |
| 102 | C3⋊((C3⋊D3)⋊C3) | — | 4 | 2 | no | — |
| 103 | C3×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 104 | C3×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 105 | C2×PSU(3,𝔽2) | D32 | 1 | 1 | yes | characteristic |
| 106 | C2×GO+(4,𝔽2) | — | 9 | 1 | no | — |
| 107 | C2×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 108 | C2×AGL(1,𝔽9) | — | 9 | 1 | no | — |
| 109 | AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 110 | AΓL(1,𝔽9) | — | 9 | 2 | no | — |
| 111 | C2×C3×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 112 | C2×#624 | — | 36 | 1 | no | — |
| 113 | C4×D32 | — | 18 | 1 | no | — |
| 114 | C4×D32 | — | 36 | 1 | no | — |
| 115 | C4×D32 | — | 36 | 1 | no | — |
| 116 | C4×#157 | — | 9 | 1 | no | — |
| 117 | C3⋊GL(2,𝔽3) | — | 9 | 2 | no | — |
| 118 | #3777 | — | 9 | 1 | no | — |
| 119 | #3773 | — | 3 | 1 | no | — |
| 120 | D32⋊C4 | — | 18 | 1 | no | — |
| 121 | C2×C3⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 122 | C2×C3×C3⋊D3 | — | 12 | 1 | no | — |
| 123 | C2×C3×C3⋊D3 | — | 12 | 1 | no | — |
| 124 | C2×C3×C3⋊D3 | — | 24 | 1 | no | — |
| 125 | C2×C3×C3⋊D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 126 | C2×C32×D3 | — | 12 | 1 | no | — |
| 127 | #1113 | — | 6 | 2 | no | — |
| 128 | #1113 | — | 12 | 1 | no | — |
| 129 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 130 | D3×C3⋊D3 | — | 12 | 2 | no | — |
| 131 | C3⋊#157 | — | 6 | 1 | no | — |
| 132 | C3×#157 | — | 3 | 1 | no | — |
| 133 | C3×#157 | — | 3 | 1 | no | — |
| 134 | C3⋊(C3⋊Dic3) | GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 135 | C3×C3⋊Dic3 | — | 4 | 1 | no | — |
| 136 | C3×C3⋊Dic3 | — | 12 | 1 | no | — |
| 137 | C32×Dic3 | — | 4 | 1 | no | — |
| 138 | C32×Dic3 | — | 8 | 1 | no | — |
| 139 | C32×Dic3 | — | 12 | 1 | no | — |
| 140 | C32×Dic3 | — | 12 | 1 | no | — |
| 141 | C32×Dic3 | — | 24 | 1 | no | — |
| 142 | C32×Dic3 | GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 143 | C2×#272 | — | 12 | 1 | no | — |
| 144 | C2×#272 | — | 24 | 1 | no | — |
| 145 | C2×#272 | — | 24 | 1 | no | — |
| 146 | C2×#272 | — | 48 | 1 | no | — |
| 147 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 148 | C2×(C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 149 | C2×(C3⋊D3)⋊C3 | — | 12 | 1 | no | — |
| 150 | C2×(C3⋊D3)⋊C3 | — | 24 | 1 | no | — |
| 151 | ((C3⋊D3)⋊C3)⋊C2 | — | 12 | 2 | no | — |
| 152 | ((C3⋊D3)⋊C3)⋊C2 | — | 12 | 2 | no | — |
| 153 | ((C3⋊D3)⋊C3)⋊C2 | — | 24 | 2 | no | — |
| 154 | ((C3⋊D3)⋊C3)⋊C2 | — | 24 | 2 | no | — |
| 155 | C4×H(3,𝔽3) | — | 12 | 1 | no | — |
| 156 | #1084 | — | 4 | 1 | no | — |
| 157 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 158 | (C3⋊Dic3)⋊C3 | — | 8 | 1 | no | — |
| 159 | (C3⋊Dic3)⋊C3 | — | 12 | 1 | no | — |
| 160 | (C3⋊Dic3)⋊C3 | — | 24 | 1 | no | — |
| 161 | C2×GL(2,𝔽3) | — | 27 | 1 | no | — |
| 162 | C2×GL(2,𝔽3) | — | 54 | 1 | no | — |
| 163 | Q8×Dic3 | — | 9 | 1 | no | — |
| 164 | C2×#215 | — | 27 | 1 | no | — |
| 165 | #893 | — | 27 | 1 | no | — |
| 166 | C4×SL(2,𝔽3) | — | 27 | 1 | no | — |
| 167 | #859 | — | 9 | 1 | no | — |
| 168 | C3×#103 | — | 27 | 1 | no | — |
| 169 | #821 | — | 27 | 1 | no | — |
| 170 | C8×Dic3 | — | 27 | 1 | no | — |
| 171 | #808 | — | 27 | 1 | no | — |
| 172 | C3×H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 173 | C22×C3⋊D3 | — | 36 | 1 | no | — |
| 174 | C2×D32 | — | 18 | 1 | no | — |
| 175 | C2×D32 | — | 36 | 1 | no | — |
| 176 | C2×D32 | — | 36 | 1 | no | — |
| 177 | C2×D32 | — | 72 | 1 | no | — |
| 178 | C2×#157 | — | 3 | 1 | no | — |
| 179 | C2×#157 | — | 9 | 1 | no | — |
| 180 | PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 181 | PSU(3,𝔽2) | #624 | 1 | 1 | yes | characteristic, complemented |
| 182 | GO+(4,𝔽2) | — | 9 | 2 | no | — |
| 183 | GO+(4,𝔽2) | — | 18 | 1 | no | — |
| 184 | AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 185 | AGL(1,𝔽9) | — | 9 | 2 | no | — |
| 186 | C4×C3⋊D3 | — | 3 | 1 | no | — |
| 187 | C4×C3⋊D3 | — | 12 | 1 | no | — |
| 188 | C4×C3⋊D3 | — | 36 | 1 | no | — |
| 189 | C2×C3×Dic3 | — | 36 | 1 | no | — |
| 190 | C2×C3×Dic3 | — | 36 | 1 | no | — |
| 191 | C3×C4×D3 | — | 36 | 1 | no | — |
| 192 | C3×C4×D3 | — | 36 | 1 | no | — |
| 193 | C3×C4×D3 | — | 36 | 1 | no | — |
| 194 | C3×C4×D3 | — | 36 | 1 | no | — |
| 195 | C3×C4×D3 | — | 36 | 1 | no | — |
| 196 | C3×C4×D3 | — | 72 | 1 | no | — |
| 197 | C3×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 198 | #624 | — | 6 | 1 | no | — |
| 199 | #624 | — | 12 | 1 | no | — |
| 200 | #624 | — | 12 | 1 | no | — |
| 201 | #624 | — | 24 | 1 | no | — |
| 202 | #624 | — | 36 | 1 | no | — |
| 203 | #624 | — | 36 | 1 | no | — |
| 204 | #624 | — | 36 | 1 | no | — |
| 205 | #624 | — | 36 | 1 | no | — |
| 206 | #624 | — | 72 | 1 | no | — |
| 207 | D3×Dic3 | — | 12 | 1 | no | — |
| 208 | D3×Dic3 | — | 12 | 1 | no | — |
| 209 | D3×Dic3 | — | 36 | 1 | no | — |
| 210 | D3×Dic3 | — | 36 | 1 | no | — |
| 211 | D3×Dic3 | — | 36 | 1 | no | — |
| 212 | D3×Dic3 | — | 72 | 1 | no | — |
| 213 | C4×SD16 | — | 81 | 1 | no | Sylow |
| 214 | C2×C33 | — | 4 | 1 | no | — |
| 215 | C2×C33 | — | 8 | 1 | no | — |
| 216 | C2×C33 | C2×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 217 | C3⋊(C3⋊D3) | — | 4 | 2 | no | — |
| 218 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 219 | C3×C3⋊D3 | — | 12 | 2 | no | — |
| 220 | C3×C3⋊D3 | — | 24 | 2 | no | — |
| 221 | C3×C3⋊D3 | C4×S4 | 1 | 1 | yes | characteristic |
| 222 | C3×C3⋊D3 | #985 | 1 | 1 | yes | characteristic |
| 223 | C32×D3 | — | 12 | 1 | no | — |
| 224 | C32×D3 | — | 12 | 1 | no | — |
| 225 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 226 | C2×H(3,𝔽3) | — | 8 | 1 | no | — |
| 227 | C2×H(3,𝔽3) | — | 8 | 1 | no | — |
| 228 | C2×H(3,𝔽3) | — | 16 | 1 | no | — |
| 229 | #272 | — | 12 | 2 | no | — |
| 230 | #272 | — | 24 | 2 | no | — |
| 231 | #272 | — | 24 | 2 | no | — |
| 232 | #272 | — | 48 | 2 | no | — |
| 233 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 234 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 235 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 236 | (C3⋊D3)⋊C3 | — | 8 | 1 | no | — |
| 237 | (C3⋊D3)⋊C3 | — | 12 | 2 | no | — |
| 238 | (C3⋊D3)⋊C3 | — | 24 | 2 | no | — |
| 239 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 240 | C2×D12 | — | 27 | 1 | no | — |
| 241 | C2×C4×D3 | — | 54 | 1 | no | — |
| 242 | C2×C4×D3 | — | 108 | 1 | no | — |
| 243 | C2×C4×D3 | — | 108 | 1 | no | — |
| 244 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 245 | C2×SL(2,𝔽3) | — | 18 | 1 | no | — |
| 246 | GL(2,𝔽3) | — | 27 | 2 | no | — |
| 247 | GL(2,𝔽3) | — | 54 | 2 | no | — |
| 248 | C2×C3×C8 | — | 27 | 1 | no | — |
| 249 | C3×C4⋊C4 | — | 27 | 1 | no | — |
| 250 | #215 | — | 27 | 2 | no | — |
| 251 | #215 | — | 27 | 2 | no | — |
| 252 | (C2×D3)⋊C4 | — | 54 | 1 | no | — |
| 253 | C4⋊Dic3 | — | 27 | 1 | no | — |
| 254 | C4×Dic3 | — | 27 | 1 | no | — |
| 255 | C2×C3⋊C8 | — | 27 | 1 | no | — |
| 256 | C22×C32 | — | 36 | 1 | no | — |
| 257 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 258 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 259 | C2×C3⋊D3 | — | 12 | 1 | no | — |
| 260 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 261 | C2×C3⋊D3 | — | 24 | 1 | no | — |
| 262 | C2×C3⋊D3 | — | 36 | 1 | no | — |
| 263 | C2×C3⋊D3 | — | 36 | 2 | no | — |
| 264 | C2×C3⋊D3 | — | 36 | 2 | no | — |
| 265 | C2×C3⋊D3 | — | 72 | 1 | no | — |
| 266 | C2×C3⋊D3 | D3×S4 | 1 | 1 | yes | characteristic |
| 267 | C2×C3×D3 | — | 12 | 1 | no | — |
| 268 | C2×C3×D3 | — | 12 | 1 | no | — |
| 269 | C2×C3×D3 | — | 24 | 1 | no | — |
| 270 | C2×C3×D3 | — | 36 | 1 | no | — |
| 271 | C2×C3×D3 | — | 36 | 1 | no | — |
| 272 | C2×C3×D3 | — | 36 | 1 | no | — |
| 273 | C2×C3×D3 | — | 72 | 1 | no | — |
| 274 | C2×C3×D3 | — | 72 | 1 | no | — |
| 275 | C2×C3×D3 | — | 72 | 1 | no | — |
| 276 | C2×C3×D3 | — | 144 | 1 | no | — |
| 277 | D32 | — | 18 | 2 | no | — |
| 278 | D32 | — | 36 | 2 | no | — |
| 279 | D32 | — | 36 | 2 | no | — |
| 280 | D32 | — | 36 | 2 | no | — |
| 281 | D32 | — | 36 | 2 | no | — |
| 282 | D32 | — | 36 | 1 | no | — |
| 283 | D32 | — | 72 | 2 | no | — |
| 284 | D32 | — | 72 | 2 | no | — |
| 285 | #157 | — | 3 | 1 | no | — |
| 286 | #157 | — | 3 | 1 | no | — |
| 287 | #157 | — | 18 | 1 | no | — |
| 288 | C32×C4 | — | 3 | 1 | no | — |
| 289 | C32×C4 | — | 12 | 1 | no | — |
| 290 | C32×C4 | — | 24 | 1 | no | — |
| 291 | C32×C4 | — | 36 | 1 | no | — |
| 292 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 293 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 294 | C3⋊Dic3 | — | 12 | 1 | no | — |
| 295 | C3⋊Dic3 | — | 24 | 1 | no | — |
| 296 | C3×Dic3 | — | 4 | 1 | no | — |
| 297 | C3×Dic3 | — | 12 | 1 | no | — |
| 298 | C3×Dic3 | — | 12 | 1 | no | — |
| 299 | C3×Dic3 | — | 12 | 1 | no | — |
| 300 | C3×Dic3 | — | 12 | 1 | no | — |
| 301 | C3×Dic3 | — | 12 | 1 | no | — |
| 302 | C3×Dic3 | — | 24 | 1 | no | — |
| 303 | C3×Dic3 | — | 24 | 1 | no | — |
| 304 | C3×Dic3 | — | 24 | 1 | no | — |
| 305 | C3×Dic3 | — | 24 | 1 | no | — |
| 306 | C3×Dic3 | — | 24 | 1 | no | — |
| 307 | C3×Dic3 | — | 36 | 1 | no | — |
| 308 | C3×Dic3 | — | 36 | 1 | no | — |
| 309 | C3×Dic3 | — | 36 | 1 | no | — |
| 310 | C3×Dic3 | — | 48 | 1 | no | — |
| 311 | C3×Dic3 | — | 72 | 1 | no | — |
| 312 | C2×SD16 | — | 81 | 1 | no | — |
| 313 | C4×Q8 | — | 27 | 1 | no | — |
| 314 | C4×D4 | — | 81 | 1 | no | — |
| 315 | #106 | — | 81 | 1 | no | — |
| 316 | #103 | — | 27 | 1 | no | — |
| 317 | #102 | — | 81 | 1 | no | — |
| 318 | C4×C8 | — | 81 | 1 | no | — |
| 319 | C33 | — | 4 | 1 | no | — |
| 320 | C33 | — | 8 | 1 | no | — |
| 321 | C33 | C4×GL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 322 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 323 | H(3,𝔽3) | — | 8 | 1 | no | — |
| 324 | H(3,𝔽3) | — | 8 | 1 | no | — |
| 325 | H(3,𝔽3) | — | 16 | 1 | no | — |
| 326 | C22×D3 | — | 54 | 1 | no | — |
| 327 | C22×D3 | — | 108 | 1 | no | — |
| 328 | C22×D3 | — | 108 | 1 | no | — |
| 329 | C22×D3 | — | 216 | 1 | no | — |
| 330 | C3×Q8 | — | 9 | 1 | no | — |
| 331 | C3×Q8 | — | 27 | 1 | no | — |
| 332 | C2×C3×C4 | — | 27 | 1 | no | — |
| 333 | C2×C3×C4 | — | 54 | 1 | no | — |
| 334 | C2×C3×C4 | — | 108 | 1 | no | — |
| 335 | C2×C3×C4 | — | 108 | 1 | no | — |
| 336 | C2×Dic3 | — | 9 | 1 | no | — |
| 337 | C2×Dic3 | — | 27 | 1 | no | — |
| 338 | C2×Dic3 | — | 36 | 1 | no | — |
| 339 | C2×Dic3 | — | 108 | 1 | no | — |
| 340 | D12 | — | 27 | 2 | no | — |
| 341 | D12 | — | 54 | 1 | no | — |
| 342 | C4×D3 | — | 36 | 1 | no | — |
| 343 | C4×D3 | — | 36 | 1 | no | — |
| 344 | C4×D3 | — | 36 | 1 | no | — |
| 345 | C4×D3 | — | 36 | 1 | no | — |
| 346 | C4×D3 | — | 36 | 1 | no | — |
| 347 | C4×D3 | — | 72 | 1 | no | — |
| 348 | C4×D3 | — | 108 | 1 | no | — |
| 349 | C4×D3 | — | 108 | 1 | no | — |
| 350 | C4×D3 | — | 108 | 1 | no | — |
| 351 | C4×D3 | — | 108 | 1 | no | — |
| 352 | C4×D3 | — | 108 | 1 | no | — |
| 353 | C4×D3 | — | 216 | 1 | no | — |
| 354 | SL(2,𝔽3) | — | 9 | 1 | no | — |
| 355 | SL(2,𝔽3) | — | 18 | 1 | no | — |
| 356 | C3×C8 | — | 54 | 1 | no | — |
| 357 | C3⋊C8 | — | 27 | 2 | no | — |
| 358 | C2×C32 | — | 4 | 1 | no | — |
| 359 | C2×C32 | — | 4 | 1 | no | — |
| 360 | C2×C32 | — | 8 | 1 | no | — |
| 361 | C2×C32 | — | 8 | 1 | no | — |
| 362 | C2×C32 | — | 8 | 1 | no | — |
| 363 | C2×C32 | — | 12 | 1 | no | — |
| 364 | C2×C32 | — | 16 | 1 | no | — |
| 365 | C2×C32 | — | 24 | 1 | no | — |
| 366 | C2×C32 | — | 24 | 1 | no | — |
| 367 | C2×C32 | — | 36 | 1 | no | — |
| 368 | C2×C32 | — | 36 | 1 | no | — |
| 369 | C2×C32 | — | 48 | 1 | no | — |
| 370 | C2×C32 | D3×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 371 | C3⋊D3 | — | 12 | 2 | no | — |
| 372 | C3⋊D3 | — | 12 | 2 | no | — |
| 373 | C3⋊D3 | — | 12 | 2 | no | — |
| 374 | C3⋊D3 | — | 24 | 2 | no | — |
| 375 | C3⋊D3 | — | 24 | 2 | no | — |
| 376 | C3⋊D3 | — | 36 | 2 | no | — |
| 377 | C3⋊D3 | — | 72 | 2 | no | — |
| 378 | C3⋊D3 | #64198 | 1 | 1 | yes | characteristic |
| 379 | C3⋊D3 | (C3⋊S4)⋊C4 | 1 | 1 | yes | characteristic |
| 380 | C3×D3 | — | 12 | 1 | no | — |
| 381 | C3×D3 | — | 12 | 1 | no | — |
| 382 | C3×D3 | — | 12 | 1 | no | — |
| 383 | C3×D3 | — | 12 | 1 | no | — |
| 384 | C3×D3 | — | 24 | 1 | no | — |
| 385 | C3×D3 | — | 24 | 1 | no | — |
| 386 | C3×D3 | — | 36 | 2 | no | — |
| 387 | C3×D3 | — | 36 | 2 | no | — |
| 388 | C3×D3 | — | 36 | 2 | no | — |
| 389 | C3×D3 | — | 72 | 2 | no | — |
| 390 | C3×D3 | — | 72 | 2 | no | — |
| 391 | C3×D3 | — | 72 | 2 | no | — |
| 392 | C3×D3 | — | 144 | 2 | no | — |
| 393 | C2×Q8 | — | 9 | 1 | no | — |
| 394 | C2×D4 | — | 81 | 1 | no | — |
| 395 | C22×C4 | — | 162 | 1 | no | — |
| 396 | SD16 | — | 81 | 2 | no | — |
| 397 | SD16 | — | 81 | 2 | no | — |
| 398 | C2×C8 | — | 27 | 1 | no | — |
| 399 | C2×C8 | — | 81 | 1 | no | — |
| 400 | C4⋊C4 | — | 27 | 1 | no | — |
| 401 | C4⋊C4 | — | 81 | 1 | no | — |
| 402 | C22⋊C4 | — | 162 | 1 | no | — |
| 403 | C42 | — | 81 | 1 | no | — |
| 404 | C22×C3 | — | 9 | 1 | no | — |
| 405 | C22×C3 | — | 36 | 1 | no | — |
| 406 | C22×C3 | — | 72 | 1 | no | — |
| 407 | C22×C3 | — | 108 | 1 | no | — |
| 408 | C2×D3 | — | 12 | 1 | no | — |
| 409 | C2×D3 | — | 36 | 1 | no | — |
| 410 | C2×D3 | — | 36 | 1 | no | — |
| 411 | C2×D3 | — | 36 | 1 | no | — |
| 412 | C2×D3 | — | 54 | 2 | no | — |
| 413 | C2×D3 | — | 72 | 1 | no | — |
| 414 | C2×D3 | — | 72 | 1 | no | — |
| 415 | C2×D3 | — | 72 | 1 | no | — |
| 416 | C2×D3 | — | 108 | 2 | no | — |
| 417 | C2×D3 | — | 108 | 1 | no | — |
| 418 | C2×D3 | — | 108 | 2 | no | — |
| 419 | C2×D3 | — | 108 | 1 | no | — |
| 420 | C2×D3 | — | 108 | 2 | no | — |
| 421 | C2×D3 | — | 108 | 2 | no | — |
| 422 | C2×D3 | — | 144 | 1 | no | — |
| 423 | C2×D3 | — | 216 | 2 | no | — |
| 424 | C2×D3 | — | 216 | 1 | no | — |
| 425 | C2×D3 | — | 216 | 2 | no | — |
| 426 | C3×C4 | — | 12 | 1 | no | — |
| 427 | C3×C4 | — | 27 | 1 | no | — |
| 428 | C3×C4 | — | 27 | 1 | no | — |
| 429 | C3×C4 | — | 36 | 1 | no | — |
| 430 | C3×C4 | — | 36 | 1 | no | — |
| 431 | C3×C4 | — | 36 | 1 | no | — |
| 432 | C3×C4 | — | 72 | 1 | no | — |
| 433 | C3×C4 | — | 72 | 1 | no | — |
| 434 | C3×C4 | — | 108 | 1 | no | — |
| 435 | Dic3 | — | 9 | 1 | no | — |
| 436 | Dic3 | — | 12 | 1 | no | — |
| 437 | Dic3 | — | 12 | 1 | no | — |
| 438 | Dic3 | — | 24 | 1 | no | — |
| 439 | Dic3 | — | 36 | 1 | no | — |
| 440 | Dic3 | — | 36 | 1 | no | — |
| 441 | Dic3 | — | 54 | 1 | no | — |
| 442 | Dic3 | — | 72 | 1 | no | — |
| 443 | Dic3 | AGL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 444 | C32 | — | 4 | 1 | no | — |
| 445 | C32 | — | 4 | 1 | no | — |
| 446 | C32 | — | 8 | 1 | no | — |
| 447 | C32 | — | 8 | 1 | no | — |
| 448 | C32 | — | 8 | 1 | no | — |
| 449 | C32 | — | 12 | 1 | no | — |
| 450 | C32 | — | 16 | 1 | no | — |
| 451 | C32 | — | 24 | 1 | no | — |
| 452 | C32 | — | 24 | 1 | no | — |
| 453 | C32 | — | 48 | 1 | no | — |
| 454 | C32 | #10593214 | 1 | 1 | yes | characteristic, complemented |
| 455 | C23 | — | 162 | 1 | no | — |
| 456 | Q8 | — | 9 | 1 | no | — |
| 457 | Q8 | — | 27 | 1 | no | — |
| 458 | D4 | — | 81 | 2 | no | — |
| 459 | D4 | — | 162 | 1 | no | — |
| 460 | C2×C4 | — | 27 | 1 | no | — |
| 461 | C2×C4 | — | 27 | 1 | no | — |
| 462 | C2×C4 | — | 54 | 1 | no | — |
| 463 | C2×C4 | — | 324 | 1 | no | — |
| 464 | C2×C4 | — | 81 | 1 | no | — |
| 465 | C2×C4 | — | 108 | 1 | no | — |
| 466 | C8 | — | 54 | 1 | no | — |
| 467 | C8 | — | 81 | 2 | no | — |
| 468 | C2×C3 | — | 4 | 1 | no | — |
| 469 | C2×C3 | — | 8 | 1 | no | — |
| 470 | C2×C3 | — | 9 | 1 | no | — |
| 471 | C2×C3 | — | 9 | 1 | no | — |
| 472 | C2×C3 | — | 12 | 1 | no | — |
| 473 | C2×C3 | — | 24 | 1 | no | — |
| 474 | C2×C3 | — | 24 | 1 | no | — |
| 475 | C2×C3 | — | 36 | 1 | no | — |
| 476 | C2×C3 | — | 36 | 1 | no | — |
| 477 | C2×C3 | — | 48 | 1 | no | — |
| 478 | C2×C3 | — | 72 | 1 | no | — |
| 479 | C2×C3 | — | 72 | 1 | no | — |
| 480 | C2×C3 | — | 108 | 2 | no | — |
| 481 | C2×C3 | C2×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 482 | D3 | — | 12 | 1 | no | — |
| 483 | D3 | — | 12 | 1 | no | — |
| 484 | D3 | — | 36 | 2 | no | — |
| 485 | D3 | — | 36 | 2 | no | — |
| 486 | D3 | — | 36 | 2 | no | — |
| 487 | D3 | — | 72 | 2 | no | — |
| 488 | D3 | — | 72 | 2 | no | — |
| 489 | D3 | — | 72 | 2 | no | — |
| 490 | D3 | — | 108 | 2 | no | — |
| 491 | D3 | — | 144 | 2 | no | — |
| 492 | D3 | — | 216 | 2 | no | — |
| 493 | C22 | — | 9 | 1 | no | — |
| 494 | C22 | — | 324 | 1 | no | — |
| 495 | C22 | — | 108 | 1 | no | — |
| 496 | C22 | — | 162 | 2 | no | — |
| 497 | C4 | — | 3 | 1 | no | — |
| 498 | C4 | — | 27 | 1 | no | — |
| 499 | C4 | — | 27 | 1 | no | — |
| 500 | C4 | — | 27 | 1 | no | — |
| 501 | C4 | — | 36 | 1 | no | — |
| 502 | C4 | — | 162 | 1 | no | — |
| 503 | C3 | — | 4 | 1 | no | — |
| 504 | C3 | — | 8 | 1 | no | — |
| 505 | C3 | — | 12 | 1 | no | — |
| 506 | C3 | — | 24 | 1 | no | — |
| 507 | C3 | — | 24 | 1 | no | — |
| 508 | C3 | — | 48 | 1 | no | — |
| 509 | C3 | C4×AGL(2,𝔽3) | 1 | 1 | yes | characteristic, complemented |
| 510 | C2 | — | 9 | 1 | no | — |
| 511 | C2 | — | 9 | 1 | no | — |
| 512 | C2 | — | 108 | 2 | no | — |
| 513 | C2 | D3×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Dic3×PSU(3,𝔽2)⋊C3 | C2 | semidirect |
| 2. C3×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | semidirect |
| 7. C3⋊AGL(2,𝔽3) | C4 | semidirect |
| 12. Dic3×PSU(3,𝔽2) | D3 | semidirect |
| 19. (PSU(3,𝔽2)⋊C3)⋊C4 | D3 | semidirect |
| 20. C3×PSU(3,𝔽2)⋊C3 | C2×C4 | semidirect |
| 71. C3×PSU(3,𝔽2) | C4×D3 | semidirect |
| 77. PSU(3,𝔽2)⋊C3 | C4×D3 | semidirect |
| 134. C3⋊(C3⋊Dic3) | GL(2,𝔽3) | semidirect |
| 142. C32×Dic3 | GL(2,𝔽3) | semidirect |
| 181. PSU(3,𝔽2) | #624 | semidirect |
| 321. C33 | C4×GL(2,𝔽3) | semidirect |
| 443. Dic3 | AGL(2,𝔽3) | semidirect |
| 454. C32 | #10593214 | semidirect |
| 509. C3 | C4×AGL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Dic3×PSU(3,𝔽2)⋊C3 | 2 |
| C3×(PSU(3,𝔽2)⋊C3)⋊C4 | 2 |
| C2×C3⋊AGL(2,𝔽3) | 2 |
| #89092⋊C4 | 3 |
| C4×AGL(2,𝔽3) | 3 |
| (((C3⋊D3)⋊C3)⋊D3)⋊C4 | 4 |
| #10593214 | 9 |