Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
821 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 821 conjugacy classes of subgroups — too many to draw. Only its 50 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 | C2×A4×PSU(3,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#157⋊S4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×A4⋊AGL(1,𝔽9) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13181780 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 5 | C2×#10596418 | — | 3 | 1 | no | maximal |
| 6 | C2×#89101 | — | 2 | 1 | no | — |
| 7 | C2×A4×#157 | — | 2 | 1 | no | — |
| 8 | C2×A4×#157 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#89092 | — | 4 | 1 | no | maximal |
| 10 | A4×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 11 | A4×PSU(3,𝔽2) | C22 | 1 | 2 | yes | complemented |
| 12 | #157⋊S4 | — | 2 | 1 | no | — |
| 13 | #157⋊S4 | C22 | 1 | 2 | yes | — |
| 14 | A4⋊AGL(1,𝔽9) | C22 | 1 | 2 | yes | complemented |
| 15 | C23×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C22×AΓL(1,𝔽9) | — | 3 | 1 | no | — |
| 17 | C22×AΓL(1,𝔽9) | — | 3 | 1 | no | — |
| 18 | C2×#64242 | — | 3 | 1 | no | — |
| 19 | C2×C22⋊AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 20 | #10596418 | — | 3 | 4 | no | — |
| 21 | #10596418 | — | 3 | 4 | no | — |
| 22 | C2×PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 23 | C2×PSU(3,𝔽2)⋊C4 | — | 3 | 1 | no | — |
| 24 | C2×A4×C3⋊D3 | D4 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×C3⋊S4 | — | 4 | 1 | no | — |
| 26 | C2×C3×PSU(3,𝔽2) | — | 4 | 1 | no | — |
| 27 | C2×#157⋊D3 | — | 4 | 1 | no | — |
| 28 | C2×C3⋊AGL(1,𝔽9) | — | 4 | 1 | no | — |
| 29 | #89101 | — | 2 | 2 | no | — |
| 30 | #89101 | — | 4 | 1 | no | — |
| 31 | A4×#157 | — | 2 | 2 | no | — |
| 32 | A4×#157 | D4 | 1 | 1 | yes | characteristic |
| 33 | A4×#157 | C23 | 1 | 1 | yes | characteristic |
| 34 | #89092 | — | 4 | 4 | no | — |
| 35 | C2×#5417 | — | 9 | 1 | no | maximal |
| 36 | C23×#157 | — | 2 | 1 | no | — |
| 37 | C23×#157 | C2×D3 | 1 | 1 | yes | characteristic |
| 38 | C22×PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 39 | C22×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 40 | C22×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 41 | C22×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 42 | C22×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 43 | C22×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 44 | C22×PSU(3,𝔽2) | C2×D3 | 1 | 2 | yes | complemented |
| 45 | C22×GO+(4,𝔽2) | — | 3 | 1 | no | — |
| 46 | C22×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 47 | C22×AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 48 | C2×D3×S4 | — | 12 | 1 | no | — |
| 49 | C2×AΓL(1,𝔽9) | — | 3 | 4 | no | — |
| 50 | C2×AΓL(1,𝔽9) | — | 3 | 4 | no | — |
| 51 | C2×AΓL(1,𝔽9) | — | 6 | 2 | no | — |
| 52 | C2×AΓL(1,𝔽9) | — | 6 | 2 | no | — |
| 53 | C2×AΓL(1,𝔽9) | — | 6 | 2 | no | — |
| 54 | C2×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 55 | C2×AΓL(1,𝔽9) | — | 6 | 1 | no | — |
| 56 | C2×#3811 | — | 6 | 1 | no | — |
| 57 | #64242 | — | 3 | 2 | no | — |
| 58 | #64242 | — | 3 | 2 | no | — |
| 59 | #64242 | — | 6 | 1 | no | — |
| 60 | #64242 | — | 6 | 1 | no | — |
| 61 | C2×#3773 | — | 3 | 1 | no | — |
| 62 | C2×D32⋊C4 | — | 6 | 1 | no | — |
| 63 | C22⋊AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 64 | C22⋊AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 65 | PSU(3,𝔽2)⋊C4 | — | 3 | 4 | no | — |
| 66 | PSU(3,𝔽2)⋊C4 | — | 3 | 4 | no | — |
| 67 | C2×C32×A4 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 68 | C2×#1113 | — | 8 | 1 | no | — |
| 69 | C2×C3×#157 | — | 4 | 1 | no | — |
| 70 | C2×C3×#157 | — | 8 | 1 | no | — |
| 71 | A4×C3⋊D3 | SD16 | 1 | 1 | yes | characteristic, complemented |
| 72 | A4×C3⋊D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C3×C3⋊S4 | — | 4 | 2 | no | — |
| 74 | C3×PSU(3,𝔽2) | — | 4 | 2 | no | — |
| 75 | C3×PSU(3,𝔽2) | — | 8 | 1 | no | — |
| 76 | #157⋊D3 | — | 4 | 2 | no | — |
| 77 | #157⋊D3 | — | 8 | 1 | no | — |
| 78 | C3⋊AGL(1,𝔽9) | — | 4 | 2 | no | — |
| 79 | C2×Q8×A4 | — | 9 | 1 | no | — |
| 80 | C2×C4⋊S4 | — | 9 | 1 | no | — |
| 81 | #5417 | — | 9 | 4 | no | — |
| 82 | C2×A4⋊C8 | — | 9 | 1 | no | — |
| 83 | C23×C3⋊D3 | #67 | 1 | 1 | yes | characteristic |
| 84 | C22×D32 | — | 6 | 1 | no | — |
| 85 | C22×#157 | — | 2 | 2 | no | — |
| 86 | C22×#157 | — | 3 | 1 | no | — |
| 87 | C22×#157 | — | 3 | 1 | no | — |
| 88 | C22×#157 | — | 3 | 1 | no | — |
| 89 | C22×#157 | — | 3 | 1 | no | — |
| 90 | C22×#157 | — | 6 | 1 | no | — |
| 91 | C22×#157 | — | 6 | 2 | no | — |
| 92 | C22×#157 | — | 6 | 1 | no | — |
| 93 | C22×#157 | #67 | 1 | 1 | yes | characteristic |
| 94 | C22×#157 | C22×D3 | 1 | 1 | yes | characteristic |
| 95 | C2×D3×A4 | — | 12 | 1 | no | — |
| 96 | C2×C3⋊S4 | — | 4 | 1 | no | — |
| 97 | C2×C3×S4 | — | 12 | 1 | no | — |
| 98 | C2×C3×S4 | — | 24 | 1 | no | — |
| 99 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 100 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 101 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 102 | C2×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 103 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 104 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 105 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 106 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 107 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 108 | C2×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 109 | C2×PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 110 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 111 | C2×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 112 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 113 | C2×PSU(3,𝔽2) | S4 | 1 | 1 | yes | characteristic, complemented |
| 114 | C2×GO+(4,𝔽2) | — | 3 | 2 | no | — |
| 115 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 116 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 117 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 118 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 119 | C2×GO+(4,𝔽2) | — | 6 | 1 | no | — |
| 120 | C2×AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 121 | C2×AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 122 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 123 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 124 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 125 | C2×AGL(1,𝔽9) | — | 6 | 1 | no | — |
| 126 | D3×S4 | — | 12 | 2 | no | — |
| 127 | D3×S4 | — | 12 | 2 | no | — |
| 128 | AΓL(1,𝔽9) | — | 6 | 8 | no | — |
| 129 | AΓL(1,𝔽9) | — | 6 | 4 | no | — |
| 130 | AΓL(1,𝔽9) | — | 6 | 4 | no | — |
| 131 | C2×C3×#67 | — | 12 | 1 | no | — |
| 132 | #3811 | — | 6 | 2 | no | — |
| 133 | #3811 | — | 6 | 2 | no | — |
| 134 | #3811 | — | 12 | 1 | no | — |
| 135 | #3811 | — | 12 | 1 | no | — |
| 136 | C2×#626 | — | 12 | 1 | no | — |
| 137 | C2×#624 | — | 6 | 1 | no | — |
| 138 | #3773 | — | 3 | 2 | no | — |
| 139 | #3773 | — | 6 | 1 | no | — |
| 140 | D32⋊C4 | — | 6 | 2 | no | — |
| 141 | D32⋊C4 | — | 6 | 2 | no | — |
| 142 | C2×#448 | — | 27 | 1 | no | Sylow |
| 143 | C2×C3×C3⋊D3 | — | 4 | 1 | no | — |
| 144 | C2×C3×C3⋊D3 | — | 16 | 1 | no | — |
| 145 | C32×A4 | C2×SD16 | 1 | 1 | yes | characteristic, complemented |
| 146 | #1113 | — | 8 | 2 | no | — |
| 147 | #1113 | — | 16 | 1 | no | — |
| 148 | C3×#157 | — | 4 | 1 | no | — |
| 149 | C3×#157 | — | 4 | 1 | no | — |
| 150 | C3×#157 | — | 8 | 2 | no | — |
| 151 | C22×S4 | — | 18 | 1 | no | — |
| 152 | C2×D3×D4 | — | 36 | 1 | no | — |
| 153 | Q8×A4 | — | 9 | 2 | no | — |
| 154 | Q8×A4 | — | 18 | 1 | no | — |
| 155 | C2×C4×A4 | — | 9 | 1 | no | — |
| 156 | C2×C4×A4 | — | 18 | 1 | no | — |
| 157 | C4⋊S4 | — | 9 | 2 | no | — |
| 158 | C4⋊S4 | — | 18 | 1 | no | — |
| 159 | C2×#215 | — | 36 | 1 | no | — |
| 160 | A4⋊C8 | — | 9 | 2 | no | — |
| 161 | C23×C32 | #215 | 1 | 1 | yes | characteristic, complemented |
| 162 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 163 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 164 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 165 | C22×C3⋊D3 | — | 3 | 1 | no | — |
| 166 | C22×C3⋊D3 | #215 | 1 | 1 | yes | characteristic, complemented |
| 167 | C22×C3⋊D3 | C2×#67 | 1 | 1 | yes | characteristic |
| 168 | C22×C3×D3 | — | 12 | 1 | no | — |
| 169 | C2×C3×A4 | — | 4 | 1 | no | — |
| 170 | C2×C3×A4 | — | 8 | 1 | no | — |
| 171 | C2×D32 | — | 6 | 2 | no | — |
| 172 | C2×D32 | — | 12 | 1 | no | — |
| 173 | C2×D32 | — | 12 | 1 | no | — |
| 174 | C2×D32 | — | 12 | 1 | no | — |
| 175 | C2×D32 | — | 12 | 1 | no | — |
| 176 | C2×D32 | — | 12 | 1 | no | — |
| 177 | C2×D32 | — | 48 | 1 | no | — |
| 178 | C2×#157 | — | 2 | 1 | no | — |
| 179 | C2×#157 | — | 3 | 1 | no | — |
| 180 | C2×#157 | — | 3 | 1 | no | — |
| 181 | C2×#157 | — | 3 | 1 | no | — |
| 182 | C2×#157 | — | 3 | 1 | no | — |
| 183 | C2×#157 | — | 3 | 1 | no | — |
| 184 | C2×#157 | — | 3 | 1 | no | — |
| 185 | C2×#157 | — | 3 | 1 | no | — |
| 186 | C2×#157 | — | 6 | 2 | no | — |
| 187 | C2×#157 | — | 6 | 2 | no | — |
| 188 | C2×#157 | — | 6 | 1 | no | — |
| 189 | C2×#157 | — | 6 | 2 | no | — |
| 190 | C2×#157 | — | 6 | 1 | no | — |
| 191 | C2×#157 | — | 6 | 2 | no | — |
| 192 | C2×#157 | C2×S4 | 1 | 1 | yes | characteristic |
| 193 | D3×A4 | — | 12 | 1 | no | — |
| 194 | D3×A4 | — | 12 | 1 | no | — |
| 195 | C3⋊S4 | — | 4 | 2 | no | — |
| 196 | C3×S4 | — | 12 | 2 | no | — |
| 197 | C3×S4 | — | 24 | 2 | no | — |
| 198 | PSU(3,𝔽2) | — | 2 | 1 | no | — |
| 199 | PSU(3,𝔽2) | — | 3 | 4 | no | — |
| 200 | PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 201 | PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 202 | PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 203 | PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 204 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 205 | PSU(3,𝔽2) | C2×S4 | 1 | 2 | yes | complemented |
| 206 | GO+(4,𝔽2) | — | 6 | 2 | no | — |
| 207 | GO+(4,𝔽2) | — | 6 | 2 | no | — |
| 208 | GO+(4,𝔽2) | — | 12 | 1 | no | — |
| 209 | GO+(4,𝔽2) | — | 12 | 1 | no | — |
| 210 | AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 211 | AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 212 | C3×#67 | — | 12 | 2 | no | — |
| 213 | C3×#67 | — | 12 | 2 | no | — |
| 214 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 215 | #626 | — | 12 | 2 | no | — |
| 216 | #626 | — | 12 | 2 | no | — |
| 217 | #624 | — | 6 | 2 | no | — |
| 218 | #624 | — | 12 | 1 | no | — |
| 219 | C23×Q8 | — | 9 | 1 | no | — |
| 220 | C22×SD16 | — | 27 | 1 | no | — |
| 221 | C22×SD16 | — | 27 | 1 | no | — |
| 222 | C2×#121 | — | 27 | 1 | no | — |
| 223 | #448 | — | 27 | 4 | no | — |
| 224 | #448 | — | 27 | 4 | no | — |
| 225 | C2×#103 | — | 27 | 1 | no | — |
| 226 | C2×#103 | — | 27 | 1 | no | — |
| 227 | C2×C22⋊C8 | — | 27 | 1 | no | — |
| 228 | C2×C33 | — | 4 | 1 | no | — |
| 229 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 230 | C3×C3⋊D3 | — | 4 | 1 | no | — |
| 231 | C3×C3⋊D3 | — | 16 | 2 | no | — |
| 232 | C23×D3 | — | 12 | 1 | no | — |
| 233 | C23×D3 | — | 36 | 1 | no | — |
| 234 | C22×A4 | — | 9 | 1 | no | — |
| 235 | C2×S4 | — | 12 | 1 | no | — |
| 236 | C2×S4 | — | 18 | 2 | no | — |
| 237 | C2×S4 | — | 24 | 1 | no | — |
| 238 | C2×S4 | — | 36 | 1 | no | — |
| 239 | C2×C3×Q8 | — | 36 | 1 | no | — |
| 240 | C2×C3×D4 | — | 36 | 1 | no | — |
| 241 | C2×#67 | — | 12 | 1 | no | — |
| 242 | C2×#67 | — | 36 | 1 | no | — |
| 243 | D3×D4 | — | 36 | 2 | no | — |
| 244 | D3×D4 | — | 36 | 2 | no | — |
| 245 | D3×D4 | — | 36 | 2 | no | — |
| 246 | D3×D4 | — | 36 | 2 | no | — |
| 247 | C2×D12 | — | 36 | 1 | no | — |
| 248 | C2×D12 | — | 36 | 1 | no | — |
| 249 | C2×C4×D3 | — | 36 | 1 | no | — |
| 250 | C4×A4 | — | 9 | 1 | no | — |
| 251 | C4×A4 | — | 9 | 1 | no | — |
| 252 | C4×A4 | — | 18 | 2 | no | — |
| 253 | #215 | — | 36 | 4 | no | — |
| 254 | C2×C3⋊C8 | — | 36 | 1 | no | — |
| 255 | C22×C32 | — | 3 | 1 | no | — |
| 256 | C22×C32 | — | 3 | 1 | no | — |
| 257 | C22×C32 | C2×#215 | 1 | 1 | yes | characteristic, complemented |
| 258 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 259 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 260 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 261 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 262 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 263 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 264 | C2×C3⋊D3 | — | 3 | 1 | no | — |
| 265 | C2×C3⋊D3 | — | 6 | 1 | no | — |
| 266 | C2×C3⋊D3 | — | 16 | 1 | no | — |
| 267 | C2×C3⋊D3 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 268 | C2×C3×D3 | — | 12 | 2 | no | — |
| 269 | C2×C3×D3 | — | 24 | 1 | no | — |
| 270 | C2×C3×D3 | — | 24 | 1 | no | — |
| 271 | C2×C3×D3 | — | 48 | 1 | no | — |
| 272 | C2×C3×D3 | — | 48 | 1 | no | — |
| 273 | C2×C3×D3 | — | 96 | 1 | no | — |
| 274 | C3×A4 | — | 4 | 1 | no | — |
| 275 | C3×A4 | — | 8 | 1 | no | — |
| 276 | D32 | — | 12 | 2 | no | — |
| 277 | D32 | — | 12 | 2 | no | — |
| 278 | D32 | — | 24 | 1 | no | — |
| 279 | D32 | — | 24 | 1 | no | — |
| 280 | D32 | — | 48 | 2 | no | — |
| 281 | D32 | — | 48 | 2 | no | — |
| 282 | #157 | — | 2 | 2 | no | — |
| 283 | #157 | — | 3 | 1 | no | — |
| 284 | #157 | — | 3 | 1 | no | — |
| 285 | #157 | — | 6 | 2 | no | — |
| 286 | #157 | GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 287 | #157 | C22×S4 | 1 | 1 | yes | characteristic |
| 288 | C3×Dic3 | — | 12 | 2 | no | — |
| 289 | C22×Q8 | — | 9 | 2 | no | — |
| 290 | C22×Q8 | — | 18 | 1 | no | — |
| 291 | C22×Q8 | — | 27 | 1 | no | — |
| 292 | C22×Q8 | — | 27 | 1 | no | — |
| 293 | C22×Q8 | — | 27 | 2 | no | — |
| 294 | C22×Q8 | — | 54 | 1 | no | — |
| 295 | C22×Q8 | — | 54 | 1 | no | — |
| 296 | C22×D4 | — | 27 | 1 | no | — |
| 297 | C22×D4 | — | 54 | 1 | no | — |
| 298 | C23×C4 | — | 9 | 1 | no | — |
| 299 | C23×C4 | — | 18 | 1 | no | — |
| 300 | C2×SD16 | — | 27 | 4 | no | — |
| 301 | C2×SD16 | — | 27 | 4 | no | — |
| 302 | C2×SD16 | — | 54 | 1 | no | — |
| 303 | C2×SD16 | — | 54 | 1 | no | — |
| 304 | C2×SD16 | — | 54 | 2 | no | — |
| 305 | C2×SD16 | — | 54 | 2 | no | — |
| 306 | C2×SD16 | — | 54 | 2 | no | — |
| 307 | C22×C8 | — | 27 | 1 | no | — |
| 308 | C22×C8 | — | 27 | 1 | no | — |
| 309 | #121 | — | 27 | 2 | no | — |
| 310 | #121 | — | 27 | 2 | no | — |
| 311 | #121 | — | 54 | 1 | no | — |
| 312 | #121 | — | 54 | 1 | no | — |
| 313 | C2×C4⋊C4 | — | 27 | 1 | no | — |
| 314 | C2×C22⋊C4 | — | 54 | 1 | no | — |
| 315 | #103 | — | 27 | 4 | no | — |
| 316 | #103 | — | 27 | 4 | no | — |
| 317 | C22⋊C8 | — | 27 | 2 | no | — |
| 318 | C22⋊C8 | — | 27 | 2 | no | — |
| 319 | C33 | — | 4 | 1 | no | Sylow |
| 320 | C23×C3 | — | 4 | 1 | no | — |
| 321 | C23×C3 | — | 36 | 1 | no | — |
| 322 | C22×D3 | — | 12 | 1 | no | — |
| 323 | C22×D3 | — | 12 | 1 | no | — |
| 324 | C22×D3 | — | 12 | 1 | no | — |
| 325 | C22×D3 | — | 36 | 1 | no | — |
| 326 | C22×D3 | — | 36 | 1 | no | — |
| 327 | C22×D3 | — | 36 | 1 | no | — |
| 328 | C22×D3 | — | 36 | 1 | no | — |
| 329 | C22×D3 | — | 36 | 2 | no | — |
| 330 | C22×D3 | — | 36 | 2 | no | — |
| 331 | C22×D3 | — | 72 | 1 | no | — |
| 332 | C22×D3 | — | 72 | 1 | no | — |
| 333 | C22×D3 | — | 72 | 1 | no | — |
| 334 | C22×D3 | — | 72 | 1 | no | — |
| 335 | C22×D3 | — | 72 | 1 | no | — |
| 336 | C2×A4 | — | 8 | 1 | no | — |
| 337 | C2×A4 | — | 9 | 1 | no | — |
| 338 | C2×A4 | — | 9 | 1 | no | — |
| 339 | C2×A4 | AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 340 | S4 | — | 12 | 2 | no | — |
| 341 | S4 | — | 24 | 2 | no | — |
| 342 | C3×Q8 | — | 36 | 2 | no | — |
| 343 | C3×Q8 | — | 72 | 1 | no | — |
| 344 | C3×D4 | — | 36 | 2 | no | — |
| 345 | C3×D4 | — | 36 | 2 | no | — |
| 346 | C2×C3×C4 | — | 36 | 1 | no | — |
| 347 | C2×C3×C4 | — | 36 | 1 | no | — |
| 348 | C2×C3×C4 | — | 72 | 1 | no | — |
| 349 | #67 | — | 12 | 2 | no | — |
| 350 | #67 | — | 12 | 2 | no | — |
| 351 | #67 | — | 36 | 2 | no | — |
| 352 | #67 | — | 36 | 2 | no | — |
| 353 | C2×Dic3 | — | 12 | 1 | no | — |
| 354 | D12 | — | 36 | 2 | no | — |
| 355 | D12 | — | 36 | 2 | no | — |
| 356 | D12 | — | 36 | 2 | no | — |
| 357 | D12 | — | 72 | 1 | no | — |
| 358 | C4×D3 | — | 36 | 2 | no | — |
| 359 | C4×D3 | — | 36 | 2 | no | — |
| 360 | C3⋊C8 | — | 36 | 2 | no | — |
| 361 | C2×C32 | — | 3 | 1 | no | — |
| 362 | C2×C32 | — | 3 | 1 | no | — |
| 363 | C2×C32 | — | 16 | 1 | no | — |
| 364 | C2×C32 | — | 32 | 1 | no | — |
| 365 | C2×C32 | #5417 | 1 | 1 | yes | characteristic, complemented |
| 366 | C3⋊D3 | — | 3 | 1 | no | — |
| 367 | C3⋊D3 | — | 3 | 1 | no | — |
| 368 | C3⋊D3 | — | 16 | 2 | no | — |
| 369 | C3⋊D3 | #5417 | 1 | 1 | yes | characteristic, complemented |
| 370 | C3⋊D3 | C2×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 371 | C3×D3 | — | 24 | 2 | no | — |
| 372 | C3×D3 | — | 48 | 1 | no | — |
| 373 | C3×D3 | — | 48 | 1 | no | — |
| 374 | C3×D3 | — | 48 | 2 | no | — |
| 375 | C3×D3 | — | 96 | 2 | no | — |
| 376 | C24 | — | 9 | 1 | no | — |
| 377 | C24 | — | 54 | 1 | no | — |
| 378 | C2×Q8 | — | 9 | 1 | no | — |
| 379 | C2×Q8 | — | 27 | 1 | no | — |
| 380 | C2×Q8 | — | 27 | 2 | no | — |
| 381 | C2×Q8 | — | 27 | 2 | no | — |
| 382 | C2×Q8 | — | 27 | 2 | no | — |
| 383 | C2×Q8 | — | 27 | 2 | no | — |
| 384 | C2×Q8 | — | 27 | 2 | no | — |
| 385 | C2×Q8 | — | 54 | 1 | no | — |
| 386 | C2×Q8 | — | 54 | 1 | no | — |
| 387 | C2×Q8 | — | 54 | 1 | no | — |
| 388 | C2×Q8 | — | 54 | 2 | no | — |
| 389 | C2×Q8 | — | 54 | 1 | no | — |
| 390 | C2×Q8 | — | 54 | 1 | no | — |
| 391 | C2×Q8 | — | 54 | 2 | no | — |
| 392 | C2×Q8 | — | 54 | 4 | no | — |
| 393 | C2×D4 | — | 27 | 2 | no | — |
| 394 | C2×D4 | — | 36 | 1 | no | — |
| 395 | C2×D4 | — | 54 | 1 | no | — |
| 396 | C2×D4 | — | 54 | 1 | no | — |
| 397 | C2×D4 | — | 54 | 1 | no | — |
| 398 | C2×D4 | — | 54 | 1 | no | — |
| 399 | C2×D4 | — | 54 | 1 | no | — |
| 400 | C2×D4 | — | 54 | 2 | no | — |
| 401 | C2×D4 | — | 54 | 2 | no | — |
| 402 | C2×D4 | — | 108 | 1 | no | — |
| 403 | C2×D4 | — | 108 | 1 | no | — |
| 404 | C2×D4 | — | 108 | 1 | no | — |
| 405 | C22×C4 | — | 9 | 1 | no | — |
| 406 | C22×C4 | — | 9 | 1 | no | — |
| 407 | C22×C4 | — | 18 | 2 | no | — |
| 408 | C22×C4 | — | 27 | 1 | no | — |
| 409 | C22×C4 | — | 27 | 1 | no | — |
| 410 | C22×C4 | — | 27 | 1 | no | — |
| 411 | C22×C4 | — | 27 | 1 | no | — |
| 412 | C22×C4 | — | 54 | 1 | no | — |
| 413 | C22×C4 | — | 54 | 1 | no | — |
| 414 | C22×C4 | — | 54 | 2 | no | — |
| 415 | C22×C4 | — | 54 | 1 | no | — |
| 416 | SD16 | — | 54 | 4 | no | — |
| 417 | SD16 | — | 54 | 4 | no | — |
| 418 | SD16 | — | 54 | 8 | no | — |
| 419 | C2×C8 | — | 27 | 2 | no | — |
| 420 | C2×C8 | — | 27 | 2 | no | — |
| 421 | C2×C8 | — | 54 | 1 | no | — |
| 422 | C2×C8 | — | 54 | 1 | no | — |
| 423 | C2×C8 | — | 54 | 1 | no | — |
| 424 | C2×C8 | — | 54 | 1 | no | — |
| 425 | C4⋊C4 | — | 27 | 2 | no | — |
| 426 | C4⋊C4 | — | 54 | 1 | no | — |
| 427 | C22⋊C4 | — | 54 | 2 | no | — |
| 428 | C22⋊C4 | — | 54 | 2 | no | — |
| 429 | C22×C3 | — | 4 | 1 | no | — |
| 430 | C22×C3 | — | 12 | 1 | no | — |
| 431 | C22×C3 | — | 12 | 1 | no | — |
| 432 | C22×C3 | — | 36 | 1 | no | — |
| 433 | C22×C3 | — | 36 | 2 | no | — |
| 434 | C22×C3 | — | 72 | 1 | no | — |
| 435 | C22×C3 | — | 72 | 1 | no | — |
| 436 | C2×D3 | — | 12 | 1 | no | — |
| 437 | C2×D3 | — | 12 | 2 | no | — |
| 438 | C2×D3 | — | 24 | 1 | no | — |
| 439 | C2×D3 | — | 24 | 1 | no | — |
| 440 | C2×D3 | — | 36 | 1 | no | — |
| 441 | C2×D3 | — | 36 | 1 | no | — |
| 442 | C2×D3 | — | 36 | 1 | no | — |
| 443 | C2×D3 | — | 36 | 1 | no | — |
| 444 | C2×D3 | — | 36 | 1 | no | — |
| 445 | C2×D3 | — | 36 | 1 | no | — |
| 446 | C2×D3 | — | 36 | 1 | no | — |
| 447 | C2×D3 | — | 48 | 1 | no | — |
| 448 | C2×D3 | — | 72 | 1 | no | — |
| 449 | C2×D3 | — | 72 | 2 | no | — |
| 450 | C2×D3 | — | 72 | 2 | no | — |
| 451 | C2×D3 | — | 72 | 2 | no | — |
| 452 | C2×D3 | — | 72 | 2 | no | — |
| 453 | C2×D3 | — | 72 | 2 | no | — |
| 454 | C2×D3 | — | 96 | 1 | no | — |
| 455 | C2×D3 | — | 144 | 1 | no | — |
| 456 | A4 | — | 8 | 1 | no | — |
| 457 | A4 | C2×AΓL(1,𝔽9) | 1 | 1 | yes | characteristic, complemented |
| 458 | C3×C4 | — | 36 | 1 | no | — |
| 459 | C3×C4 | — | 36 | 1 | no | — |
| 460 | C3×C4 | — | 36 | 2 | no | — |
| 461 | C3×C4 | — | 72 | 2 | no | — |
| 462 | Dic3 | — | 12 | 2 | no | — |
| 463 | C32 | — | 16 | 1 | no | — |
| 464 | C32 | — | 32 | 1 | no | — |
| 465 | C32 | C2×#5417 | 1 | 1 | yes | characteristic, complemented |
| 466 | C23 | — | 9 | 1 | no | — |
| 467 | C23 | — | 9 | 1 | no | — |
| 468 | C23 | — | 27 | 1 | no | — |
| 469 | C23 | — | 27 | 1 | no | — |
| 470 | C23 | — | 27 | 1 | no | — |
| 471 | C23 | — | 27 | 1 | no | — |
| 472 | C23 | — | 36 | 1 | no | — |
| 473 | C23 | — | 54 | 2 | no | — |
| 474 | C23 | — | 108 | 1 | no | — |
| 475 | C23 | — | 108 | 1 | no | — |
| 476 | C23 | — | 108 | 1 | no | — |
| 477 | C23 | — | 108 | 1 | no | — |
| 478 | C23 | — | 108 | 1 | no | — |
| 479 | C23 | #89092 | 1 | 1 | yes | characteristic, complemented |
| 480 | Q8 | — | 9 | 2 | no | — |
| 481 | Q8 | — | 18 | 1 | no | — |
| 482 | Q8 | — | 27 | 2 | no | — |
| 483 | Q8 | — | 27 | 4 | no | — |
| 484 | Q8 | — | 54 | 1 | no | — |
| 485 | Q8 | — | 54 | 2 | no | — |
| 486 | Q8 | — | 54 | 2 | no | — |
| 487 | Q8 | — | 54 | 2 | no | — |
| 488 | D4 | — | 36 | 2 | no | — |
| 489 | D4 | — | 36 | 2 | no | — |
| 490 | D4 | — | 54 | 2 | no | — |
| 491 | D4 | — | 54 | 2 | no | — |
| 492 | D4 | — | 108 | 1 | no | — |
| 493 | D4 | — | 108 | 1 | no | — |
| 494 | D4 | — | 108 | 2 | no | — |
| 495 | D4 | — | 108 | 2 | no | — |
| 496 | C2×C4 | — | 9 | 1 | no | — |
| 497 | C2×C4 | — | 18 | 1 | no | — |
| 498 | C2×C4 | — | 27 | 1 | no | — |
| 499 | C2×C4 | — | 27 | 1 | no | — |
| 500 | C2×C4 | — | 27 | 1 | no | — |
| 501 | C2×C4 | — | 27 | 1 | no | — |
| 502 | C2×C4 | — | 27 | 1 | no | — |
| 503 | C2×C4 | — | 27 | 1 | no | — |
| 504 | C2×C4 | — | 27 | 1 | no | — |
| 505 | C2×C4 | — | 36 | 1 | no | — |
| 506 | C2×C4 | — | 54 | 2 | no | — |
| 507 | C2×C4 | — | 54 | 2 | no | — |
| 508 | C2×C4 | — | 54 | 1 | no | — |
| 509 | C2×C4 | — | 54 | 2 | no | — |
| 510 | C2×C4 | — | 54 | 1 | no | — |
| 511 | C2×C4 | — | 54 | 2 | no | — |
| 512 | C2×C4 | — | 54 | 2 | no | — |
| 513 | C2×C4 | — | 108 | 1 | no | — |
| 514 | C8 | — | 54 | 2 | no | — |
| 515 | C8 | — | 54 | 2 | no | — |
| 516 | C2×C3 | — | 4 | 1 | no | — |
| 517 | C2×C3 | — | 4 | 1 | no | — |
| 518 | C2×C3 | — | 12 | 1 | no | — |
| 519 | C2×C3 | — | 12 | 1 | no | — |
| 520 | C2×C3 | — | 32 | 1 | no | — |
| 521 | C2×C3 | — | 36 | 1 | no | — |
| 522 | C2×C3 | — | 36 | 1 | no | — |
| 523 | C2×C3 | — | 72 | 2 | no | — |
| 524 | D3 | — | 12 | 1 | no | — |
| 525 | D3 | — | 12 | 1 | no | — |
| 526 | D3 | — | 24 | 2 | no | — |
| 527 | D3 | — | 36 | 1 | no | — |
| 528 | D3 | — | 36 | 1 | no | — |
| 529 | D3 | — | 48 | 2 | no | — |
| 530 | D3 | — | 96 | 2 | no | — |
| 531 | C22 | — | 3 | 1 | no | — |
| 532 | C22 | — | 3 | 1 | no | — |
| 533 | C22 | — | 9 | 1 | no | — |
| 534 | C22 | — | 27 | 1 | no | — |
| 535 | C22 | — | 27 | 1 | no | — |
| 536 | C22 | — | 27 | 1 | no | — |
| 537 | C22 | — | 27 | 1 | no | — |
| 538 | C22 | — | 27 | 1 | no | — |
| 539 | C22 | — | 27 | 1 | no | — |
| 540 | C22 | — | 27 | 1 | no | — |
| 541 | C22 | — | 36 | 2 | no | — |
| 542 | C22 | — | 54 | 1 | no | — |
| 543 | C22 | — | 72 | 1 | no | — |
| 544 | C22 | — | 72 | 1 | no | — |
| 545 | C22 | — | 108 | 2 | no | — |
| 546 | C22 | — | 108 | 2 | no | — |
| 547 | C22 | — | 216 | 1 | no | — |
| 548 | C22 | — | 216 | 1 | no | — |
| 549 | C22 | C2×#89092 | 1 | 1 | yes | characteristic, complemented |
| 550 | C4 | — | 9 | 1 | no | — |
| 551 | C4 | — | 9 | 1 | no | — |
| 552 | C4 | — | 18 | 2 | no | — |
| 553 | C4 | — | 27 | 1 | no | — |
| 554 | C4 | — | 27 | 1 | no | — |
| 555 | C4 | — | 36 | 2 | no | — |
| 556 | C4 | — | 54 | 2 | no | — |
| 557 | C3 | — | 4 | 1 | no | — |
| 558 | C3 | — | 4 | 1 | no | — |
| 559 | C3 | — | 32 | 1 | no | — |
| 560 | C2 | — | 3 | 1 | no | — |
| 561 | C2 | — | 3 | 1 | no | — |
| 562 | C2 | — | 9 | 1 | no | — |
| 563 | C2 | — | 9 | 1 | no | — |
| 564 | C2 | — | 27 | 1 | no | — |
| 565 | C2 | — | 27 | 1 | no | — |
| 566 | C2 | — | 72 | 2 | no | — |
| 567 | C2 | #13181780 | 1 | 1 | yes | characteristic, direct product factor |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #13181780 |
| commutator, cosocle | A4×#157 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C32 | #215 |
| prime radical | C2×#157⋊S4 | C2 |
| hypocenter | C32×A4 | C2×SD16 |
| LCS | G ▷ A4×#157 ▷ A4×C3⋊D3 ▷ C32×A4 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×A4×PSU(3,𝔽2) | C2 | semidirect |
| 3. C2×A4⋊AGL(1,𝔽9) | C2 | semidirect |
| 4. #13181780 | C2 | direct (N × H) |
| 11. A4×PSU(3,𝔽2) | C22 | semidirect |
| 14. A4⋊AGL(1,𝔽9) | C22 | semidirect |
| 15. C23×PSU(3,𝔽2) | D3 | semidirect |
| 44. C22×PSU(3,𝔽2) | C2×D3 | semidirect |
| 67. C2×C32×A4 | SD16 | semidirect |
| 71. A4×C3⋊D3 | SD16 | semidirect |
| 113. C2×PSU(3,𝔽2) | S4 | semidirect |
| 145. C32×A4 | C2×SD16 | semidirect |
| 161. C23×C32 | #215 | semidirect |
| 166. C22×C3⋊D3 | #215 | semidirect |
| 205. PSU(3,𝔽2) | C2×S4 | semidirect |
| 257. C22×C32 | C2×#215 | semidirect |
| 339. C2×A4 | AΓL(1,𝔽9) | semidirect |
| 365. C2×C32 | #5417 | semidirect |
| 369. C3⋊D3 | #5417 | semidirect |
| 457. A4 | C2×AΓL(1,𝔽9) | semidirect |
| 465. C32 | C2×#5417 | semidirect |
| 479. C23 | #89092 | semidirect |
| 549. C22 | C2×#89092 | semidirect |
| 567. C2 | #13181780 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×A4×PSU(3,𝔽2) | 2 |
| C2×#157⋊S4 | 2 |
| C2×A4⋊AGL(1,𝔽9) | 2 |
| #13181780 | 2 |
| C2×#10596418 | 3 |
| C2×#89092 | 4 |
| C2×#5417 | 9 |