Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1485 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1485 conjugacy classes of subgroups — too many to draw. Only its 135 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×#5923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#986 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3428⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #85368 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #85355 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #85347 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #85346 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #60426 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C22×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 10 | #5923 | — | 2 | 4 | no | — |
| 11 | C2×#986 | — | 2 | 4 | no | — |
| 12 | C2×#986 | C22 | 1 | 2 | yes | — |
| 13 | C2×#986 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×#986 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#985 | C22 | 1 | 2 | yes | complemented |
| 16 | C2×#984 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C2×#983 | C22 | 1 | 2 | yes | complemented |
| 18 | C22×GL(2,𝔽3) | C22 | 1 | 2 | yes | complemented |
| 19 | #5525 | — | 4 | 1 | no | maximal |
| 20 | #520⋊C3 | C22 | 1 | 2 | yes | complemented |
| 21 | #519⋊C3 | C22 | 1 | 2 | yes | complemented |
| 22 | C4×#41⋊C3 | C22 | 1 | 2 | yes | complemented |
| 23 | #5395 | C22 | 1 | 8 | yes | complemented |
| 24 | C4⋊GL(2,𝔽3) | C22 | 1 | 8 | yes | complemented |
| 25 | C2×#575 | — | 3 | 1 | no | — |
| 26 | C22×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 27 | C2×#535 | — | 3 | 1 | no | — |
| 28 | #3428 | D3 | 1 | 1 | yes | characteristic, complemented |
| 29 | #3045 | — | 3 | 4 | no | — |
| 30 | #3045 | — | 3 | 4 | no | — |
| 31 | #3043 | — | 3 | 4 | no | — |
| 32 | #3041 | — | 3 | 4 | no | — |
| 33 | #3040 | — | 3 | 2 | no | — |
| 34 | #3040 | — | 3 | 2 | no | — |
| 35 | #3038 | — | 3 | 2 | no | — |
| 36 | #3038 | — | 3 | 2 | no | — |
| 37 | #2905 | — | 3 | 1 | no | — |
| 38 | #2896 | — | 3 | 1 | no | — |
| 39 | C2×#418 | — | 3 | 1 | no | — |
| 40 | C2×#235 | — | 4 | 1 | no | — |
| 41 | C22×D12 | — | 4 | 1 | no | — |
| 42 | C2×#41⋊C3 | D4 | 1 | 4 | yes | complemented |
| 43 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 45 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 46 | #986 | — | 2 | 4 | no | — |
| 47 | #986 | — | 2 | 2 | no | — |
| 48 | #986 | — | 2 | 4 | no | — |
| 49 | #985 | — | 2 | 4 | no | — |
| 50 | #984 | — | 2 | 2 | no | — |
| 51 | #983 | — | 2 | 4 | no | — |
| 52 | C2×GL(2,𝔽3) | — | 2 | 4 | no | — |
| 53 | C2×GL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 54 | C2×GL(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 55 | C2×#226 | C23 | 1 | 2 | yes | complemented |
| 56 | C3×#117 | — | 4 | 1 | no | — |
| 57 | #895 | — | 4 | 4 | no | — |
| 58 | #882 | — | 4 | 4 | no | — |
| 59 | #875 | — | 4 | 2 | no | — |
| 60 | #874 | — | 4 | 2 | no | — |
| 61 | C4×SL(2,𝔽3) | C23 | 1 | 4 | yes | complemented |
| 62 | C22×#41 | — | 3 | 1 | no | — |
| 63 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 64 | C23×D4 | — | 3 | 1 | no | — |
| 65 | #575 | — | 6 | 4 | no | — |
| 66 | #575 | — | 6 | 4 | no | — |
| 67 | C2×#137 | — | 3 | 1 | no | — |
| 68 | C2×#137 | — | 3 | 1 | no | — |
| 69 | C2×#137 | — | 3 | 2 | no | — |
| 70 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 71 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 72 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 73 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 74 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 75 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 76 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 77 | C2×AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 78 | C2×AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 79 | C2×#135 | — | 3 | 2 | no | — |
| 80 | C2×#135 | — | 3 | 2 | no | — |
| 81 | C22×SD16 | — | 3 | 2 | no | — |
| 82 | C22×D8 | — | 3 | 2 | no | — |
| 83 | C22×M16 | — | 3 | 1 | no | — |
| 84 | C22×M16 | — | 3 | 1 | no | — |
| 85 | #535 | — | 3 | 4 | no | — |
| 86 | #535 | — | 3 | 4 | no | — |
| 87 | #535 | — | 6 | 1 | no | — |
| 88 | #535 | — | 6 | 2 | no | — |
| 89 | #535 | — | 6 | 1 | no | — |
| 90 | C2×#127 | — | 3 | 2 | no | — |
| 91 | C2×#124 | — | 3 | 2 | no | — |
| 92 | C2×#121 | — | 6 | 2 | no | — |
| 93 | C2×#120 | — | 6 | 2 | no | — |
| 94 | #520 | — | 3 | 2 | no | — |
| 95 | #520 | C2×D3 | 1 | 2 | yes | complemented |
| 96 | #519 | C2×D3 | 1 | 2 | yes | — |
| 97 | #518 | — | 3 | 2 | no | — |
| 98 | C4×#41 | — | 3 | 2 | no | — |
| 99 | C4×#41 | C2×D3 | 1 | 2 | yes | complemented |
| 100 | C2×#117 | — | 3 | 1 | no | — |
| 101 | C2×#117 | — | 3 | 1 | no | — |
| 102 | #464 | — | 3 | 8 | no | — |
| 103 | #464 | — | 3 | 8 | no | — |
| 104 | #463 | — | 3 | 8 | no | — |
| 105 | #463 | — | 3 | 8 | no | — |
| 106 | #460 | — | 3 | 8 | no | — |
| 107 | #460 | — | 3 | 8 | no | — |
| 108 | #459 | — | 3 | 8 | no | — |
| 109 | #459 | — | 3 | 8 | no | — |
| 110 | #424 | — | 3 | 4 | no | — |
| 111 | #424 | — | 3 | 4 | no | — |
| 112 | #423 | — | 3 | 2 | no | — |
| 113 | #423 | — | 3 | 2 | no | — |
| 114 | #419 | — | 3 | 2 | no | — |
| 115 | #418 | — | 3 | 2 | no | — |
| 116 | #418 | — | 3 | 2 | no | — |
| 117 | #418 | — | 3 | 4 | no | — |
| 118 | #418 | — | 3 | 2 | no | — |
| 119 | #417 | — | 3 | 4 | no | — |
| 120 | #416 | — | 3 | 4 | no | — |
| 121 | C2×#102 | — | 3 | 4 | no | — |
| 122 | C23×D3 | — | 4 | 2 | no | — |
| 123 | C22×C3×C4 | — | 4 | 1 | no | — |
| 124 | C2×#67 | — | 4 | 2 | no | — |
| 125 | #235 | — | 8 | 4 | no | — |
| 126 | C2×D12 | — | 4 | 2 | no | — |
| 127 | C2×D12 | — | 4 | 1 | no | — |
| 128 | C2×D12 | — | 4 | 2 | no | — |
| 129 | C2×D12 | — | 4 | 8 | no | — |
| 130 | C2×D12 | — | 8 | 4 | no | — |
| 131 | C2×C4×D3 | — | 4 | 2 | no | — |
| 132 | C2×Dic6 | — | 4 | 1 | no | — |
| 133 | #41⋊C3 | C2×D4 | 1 | 2 | yes | — |
| 134 | #41⋊C3 | C2×D4 | 1 | 2 | yes | complemented |
| 135 | C2×SL(2,𝔽3) | C2×D4 | 1 | 2 | yes | complemented |
| 136 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 137 | GL(2,𝔽3) | — | 2 | 4 | no | — |
| 138 | GL(2,𝔽3) | — | 2 | 2 | no | — |
| 139 | #226 | — | 2 | 2 | no | — |
| 140 | C3×C4⋊C4 | — | 4 | 2 | no | — |
| 141 | C3×C22⋊C4 | — | 4 | 2 | no | — |
| 142 | C3×C42 | — | 4 | 2 | no | — |
| 143 | (C2×D3)⋊C4 | — | 4 | 8 | no | — |
| 144 | C25 | — | 6 | 1 | no | — |
| 145 | C2×#41 | — | 3 | 1 | no | — |
| 146 | C2×#41 | — | 3 | 1 | no | — |
| 147 | C2×#41 | — | 3 | 4 | no | — |
| 148 | C2×#41 | — | 3 | 2 | no | — |
| 149 | C2×#41 | — | 3 | 2 | no | — |
| 150 | C2×#41 | — | 6 | 1 | no | — |
| 151 | C2×#41 | — | 6 | 4 | no | — |
| 152 | C2×#41 | — | 6 | 4 | no | — |
| 153 | C2×#41 | — | 6 | 1 | no | — |
| 154 | C2×#41 | D12 | 1 | 4 | yes | complemented |
| 155 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 156 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 157 | C22×Q8 | — | 3 | 1 | no | — |
| 158 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 159 | C22×D4 | — | 3 | 1 | no | — |
| 160 | C22×D4 | — | 3 | 2 | no | — |
| 161 | C22×D4 | — | 3 | 1 | no | — |
| 162 | C22×D4 | — | 3 | 2 | no | — |
| 163 | C22×D4 | — | 3 | 2 | no | — |
| 164 | C22×D4 | — | 6 | 4 | no | — |
| 165 | C22×D4 | — | 6 | 4 | no | — |
| 166 | C22×D4 | — | 6 | 1 | no | — |
| 167 | C22×D4 | — | 6 | 1 | no | — |
| 168 | C22×D4 | — | 6 | 4 | no | — |
| 169 | C22×D4 | — | 6 | 1 | no | — |
| 170 | C22×D4 | — | 6 | 1 | no | — |
| 171 | C23×C4 | — | 3 | 1 | no | — |
| 172 | C23×C4 | — | 6 | 1 | no | — |
| 173 | #137 | — | 6 | 4 | no | — |
| 174 | #137 | — | 6 | 4 | no | — |
| 175 | #137 | — | 6 | 2 | no | — |
| 176 | #137 | — | 6 | 2 | no | — |
| 177 | #137 | — | 6 | 4 | no | — |
| 178 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 179 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 180 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 181 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 182 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 183 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 184 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 185 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 186 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 187 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 188 | #135 | — | 6 | 8 | no | — |
| 189 | #135 | — | 6 | 4 | no | — |
| 190 | #135 | — | 6 | 4 | no | — |
| 191 | C2×Q16 | — | 3 | 2 | no | — |
| 192 | C2×Q16 | — | 3 | 2 | no | — |
| 193 | C2×SD16 | — | 3 | 4 | no | — |
| 194 | C2×SD16 | — | 3 | 2 | no | — |
| 195 | C2×SD16 | — | 3 | 2 | no | — |
| 196 | C2×SD16 | — | 3 | 2 | no | — |
| 197 | C2×SD16 | — | 3 | 4 | no | — |
| 198 | C2×SD16 | — | 3 | 2 | no | — |
| 199 | C2×SD16 | — | 6 | 4 | no | — |
| 200 | C2×SD16 | — | 6 | 4 | no | — |
| 201 | C2×D8 | — | 3 | 4 | no | — |
| 202 | C2×D8 | — | 3 | 4 | no | — |
| 203 | C2×D8 | — | 3 | 2 | no | — |
| 204 | C2×D8 | — | 3 | 2 | no | — |
| 205 | C2×D8 | — | 6 | 8 | no | — |
| 206 | C2×M16 | — | 3 | 2 | no | — |
| 207 | C2×M16 | — | 3 | 2 | no | — |
| 208 | C2×M16 | — | 3 | 1 | no | — |
| 209 | C2×M16 | — | 3 | 1 | no | — |
| 210 | C2×M16 | — | 3 | 2 | no | — |
| 211 | C2×M16 | — | 6 | 4 | no | — |
| 212 | C2×M16 | — | 6 | 4 | no | — |
| 213 | C22×C8 | — | 3 | 2 | no | — |
| 214 | C22×C8 | — | 3 | 2 | no | — |
| 215 | #127 | — | 3 | 8 | no | — |
| 216 | #127 | — | 6 | 2 | no | — |
| 217 | #127 | — | 6 | 2 | no | — |
| 218 | #124 | — | 3 | 8 | no | — |
| 219 | #124 | — | 6 | 2 | no | — |
| 220 | #124 | — | 6 | 2 | no | — |
| 221 | #121 | — | 6 | 4 | no | — |
| 222 | #121 | — | 6 | 8 | no | — |
| 223 | #121 | — | 6 | 4 | no | — |
| 224 | #120 | — | 6 | 4 | no | — |
| 225 | #120 | — | 6 | 8 | no | — |
| 226 | #120 | — | 6 | 4 | no | — |
| 227 | C4×Q8 | — | 3 | 4 | no | — |
| 228 | C4×Q8 | C22×D3 | 1 | 4 | yes | — |
| 229 | C4×D4 | — | 3 | 4 | no | — |
| 230 | C4×D4 | — | 3 | 4 | no | — |
| 231 | C4×D4 | — | 6 | 4 | no | — |
| 232 | #117 | — | 3 | 1 | no | — |
| 233 | #117 | — | 3 | 2 | no | — |
| 234 | #117 | — | 3 | 2 | no | — |
| 235 | #117 | — | 3 | 2 | no | — |
| 236 | #117 | — | 3 | 2 | no | — |
| 237 | #117 | — | 3 | 2 | no | — |
| 238 | #117 | — | 6 | 1 | no | — |
| 239 | #117 | S4 | 1 | 1 | yes | characteristic |
| 240 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 241 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 242 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 243 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 244 | C2×C22⋊C4 | — | 6 | 4 | no | — |
| 245 | C2×C42 | — | 3 | 2 | no | — |
| 246 | C2×C42 | — | 6 | 1 | no | — |
| 247 | C4⋊C8 | — | 3 | 8 | no | — |
| 248 | C4⋊C8 | — | 3 | 8 | no | — |
| 249 | #103 | — | 3 | 8 | no | — |
| 250 | #102 | — | 3 | 8 | no | — |
| 251 | #102 | — | 3 | 8 | no | — |
| 252 | #102 | — | 3 | 8 | no | — |
| 253 | C23×C3 | — | 4 | 1 | no | — |
| 254 | C22×D3 | — | 4 | 4 | no | — |
| 255 | C22×D3 | — | 4 | 2 | no | — |
| 256 | C22×D3 | — | 8 | 4 | no | — |
| 257 | C22×D3 | — | 16 | 4 | no | — |
| 258 | C2×C3×C4 | — | 4 | 4 | no | — |
| 259 | C2×C3×C4 | — | 4 | 1 | no | — |
| 260 | C2×C3×C4 | — | 4 | 1 | no | — |
| 261 | C2×C3×C4 | — | 4 | 4 | no | — |
| 262 | #67 | — | 8 | 4 | no | — |
| 263 | C2×Dic3 | — | 4 | 2 | no | — |
| 264 | D12 | — | 8 | 4 | no | — |
| 265 | D12 | — | 8 | 4 | no | — |
| 266 | D12 | — | 8 | 2 | no | — |
| 267 | D12 | — | 16 | 8 | no | — |
| 268 | C4×D3 | — | 8 | 4 | no | — |
| 269 | Dic6 | — | 8 | 2 | no | — |
| 270 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 271 | C24 | — | 3 | 1 | no | — |
| 272 | C24 | — | 6 | 2 | no | — |
| 273 | C24 | — | 6 | 1 | no | — |
| 274 | C24 | — | 6 | 2 | no | — |
| 275 | C24 | — | 6 | 2 | no | — |
| 276 | C24 | — | 12 | 4 | no | — |
| 277 | C24 | — | 24 | 4 | no | — |
| 278 | #41 | — | 3 | 4 | no | — |
| 279 | #41 | — | 3 | 2 | no | — |
| 280 | #41 | — | 3 | 4 | no | — |
| 281 | #41 | — | 3 | 2 | no | — |
| 282 | #41 | — | 6 | 2 | no | — |
| 283 | #41 | — | 6 | 2 | no | — |
| 284 | #41 | — | 6 | 4 | no | — |
| 285 | #41 | — | 6 | 4 | no | — |
| 286 | #41 | — | 6 | 4 | no | — |
| 287 | #41 | — | 6 | 4 | no | — |
| 288 | #41 | — | 12 | 4 | no | — |
| 289 | #41 | — | 12 | 4 | no | — |
| 290 | #41 | C2×D12 | 1 | 2 | yes | — |
| 291 | #41 | C2×D12 | 1 | 2 | yes | — |
| 292 | C2×Q8 | — | 3 | 1 | no | — |
| 293 | C2×Q8 | — | 3 | 2 | no | — |
| 294 | C2×Q8 | — | 3 | 2 | no | — |
| 295 | C2×Q8 | — | 6 | 2 | no | — |
| 296 | C2×Q8 | — | 6 | 2 | no | — |
| 297 | C2×Q8 | — | 6 | 1 | no | — |
| 298 | C2×Q8 | C2×D12 | 1 | 2 | yes | — |
| 299 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 300 | C2×D4 | — | 3 | 1 | no | — |
| 301 | C2×D4 | — | 3 | 1 | no | — |
| 302 | C2×D4 | — | 3 | 4 | no | — |
| 303 | C2×D4 | — | 3 | 4 | no | — |
| 304 | C2×D4 | — | 3 | 2 | no | — |
| 305 | C2×D4 | — | 6 | 1 | no | — |
| 306 | C2×D4 | — | 6 | 2 | no | — |
| 307 | C2×D4 | — | 6 | 4 | no | — |
| 308 | C2×D4 | — | 6 | 4 | no | — |
| 309 | C2×D4 | — | 6 | 4 | no | — |
| 310 | C2×D4 | — | 6 | 2 | no | — |
| 311 | C2×D4 | — | 6 | 4 | no | — |
| 312 | C2×D4 | — | 6 | 4 | no | — |
| 313 | C2×D4 | — | 6 | 4 | no | — |
| 314 | C2×D4 | — | 6 | 2 | no | — |
| 315 | C2×D4 | — | 6 | 2 | no | — |
| 316 | C2×D4 | — | 6 | 8 | no | — |
| 317 | C2×D4 | — | 6 | 2 | no | — |
| 318 | C2×D4 | — | 6 | 2 | no | — |
| 319 | C2×D4 | — | 6 | 2 | no | — |
| 320 | C2×D4 | — | 6 | 2 | no | — |
| 321 | C2×D4 | — | 6 | 1 | no | — |
| 322 | C2×D4 | — | 6 | 8 | no | — |
| 323 | C2×D4 | — | 12 | 4 | no | — |
| 324 | C2×D4 | — | 12 | 4 | no | — |
| 325 | C2×D4 | — | 12 | 4 | no | — |
| 326 | C2×D4 | — | 12 | 4 | no | — |
| 327 | C2×D4 | — | 24 | 8 | no | — |
| 328 | C22×C4 | — | 3 | 1 | no | — |
| 329 | C22×C4 | — | 3 | 4 | no | — |
| 330 | C22×C4 | — | 3 | 4 | no | — |
| 331 | C22×C4 | — | 3 | 1 | no | — |
| 332 | C22×C4 | — | 3 | 1 | no | — |
| 333 | C22×C4 | — | 3 | 1 | no | — |
| 334 | C22×C4 | — | 3 | 1 | no | — |
| 335 | C22×C4 | — | 3 | 4 | no | — |
| 336 | C22×C4 | — | 6 | 2 | no | — |
| 337 | C22×C4 | — | 6 | 2 | no | — |
| 338 | C22×C4 | — | 6 | 1 | no | — |
| 339 | C22×C4 | — | 6 | 2 | no | — |
| 340 | C22×C4 | — | 12 | 4 | no | — |
| 341 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 342 | Q16 | — | 6 | 4 | no | — |
| 343 | Q16 | — | 6 | 2 | no | — |
| 344 | Q16 | — | 6 | 2 | no | — |
| 345 | SD16 | — | 6 | 4 | no | — |
| 346 | SD16 | — | 6 | 4 | no | — |
| 347 | SD16 | — | 6 | 8 | no | — |
| 348 | SD16 | — | 6 | 4 | no | — |
| 349 | SD16 | — | 6 | 4 | no | — |
| 350 | SD16 | — | 6 | 2 | no | — |
| 351 | SD16 | — | 6 | 4 | no | — |
| 352 | SD16 | — | 6 | 2 | no | — |
| 353 | D8 | — | 6 | 8 | no | — |
| 354 | D8 | — | 6 | 8 | no | — |
| 355 | D8 | — | 6 | 4 | no | — |
| 356 | D8 | — | 6 | 4 | no | — |
| 357 | M16 | — | 6 | 4 | no | — |
| 358 | M16 | — | 6 | 4 | no | — |
| 359 | M16 | — | 6 | 4 | no | — |
| 360 | M16 | — | 6 | 2 | no | — |
| 361 | M16 | — | 6 | 2 | no | — |
| 362 | C2×C8 | — | 3 | 2 | no | — |
| 363 | C2×C8 | — | 3 | 2 | no | — |
| 364 | C2×C8 | — | 3 | 4 | no | — |
| 365 | C2×C8 | — | 6 | 4 | no | — |
| 366 | C2×C8 | — | 6 | 4 | no | — |
| 367 | C4⋊C4 | — | 3 | 4 | no | — |
| 368 | C4⋊C4 | — | 3 | 2 | no | — |
| 369 | C4⋊C4 | — | 3 | 4 | no | — |
| 370 | C4⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 371 | C22⋊C4 | — | 3 | 2 | no | — |
| 372 | C22⋊C4 | — | 3 | 4 | no | — |
| 373 | C22⋊C4 | — | 6 | 2 | no | — |
| 374 | C22⋊C4 | — | 6 | 8 | no | — |
| 375 | C22⋊C4 | — | 6 | 8 | no | — |
| 376 | C22⋊C4 | C2×S4 | 1 | 2 | yes | — |
| 377 | C42 | — | 3 | 4 | no | — |
| 378 | C42 | — | 3 | 2 | no | — |
| 379 | C42 | — | 6 | 2 | no | — |
| 380 | C42 | C2×S4 | 1 | 2 | yes | — |
| 381 | C22×C3 | — | 4 | 2 | no | — |
| 382 | C22×C3 | — | 4 | 1 | no | — |
| 383 | C22×C3 | — | 8 | 2 | no | — |
| 384 | C2×D3 | — | 8 | 2 | no | — |
| 385 | C2×D3 | — | 8 | 4 | no | — |
| 386 | C2×D3 | — | 8 | 4 | no | — |
| 387 | C2×D3 | — | 8 | 8 | no | — |
| 388 | C2×D3 | — | 16 | 8 | no | — |
| 389 | C3×C4 | — | 4 | 2 | no | — |
| 390 | C3×C4 | — | 4 | 2 | no | — |
| 391 | C3×C4 | — | 8 | 4 | no | — |
| 392 | Dic3 | — | 8 | 2 | no | — |
| 393 | C23 | — | 3 | 1 | no | — |
| 394 | C23 | — | 3 | 1 | no | — |
| 395 | C23 | — | 3 | 4 | no | — |
| 396 | C23 | — | 6 | 4 | no | — |
| 397 | C23 | — | 6 | 2 | no | — |
| 398 | C23 | — | 12 | 2 | no | — |
| 399 | C23 | — | 12 | 2 | no | — |
| 400 | C23 | — | 12 | 4 | no | — |
| 401 | C23 | — | 12 | 4 | no | — |
| 402 | C23 | — | 12 | 4 | no | — |
| 403 | C23 | — | 12 | 8 | no | — |
| 404 | C23 | — | 12 | 4 | no | — |
| 405 | C23 | — | 24 | 4 | no | — |
| 406 | C23 | — | 24 | 4 | no | — |
| 407 | C23 | — | 24 | 16 | no | — |
| 408 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 409 | Q8 | — | 3 | 2 | no | — |
| 410 | Q8 | — | 3 | 1 | no | — |
| 411 | Q8 | — | 6 | 1 | no | — |
| 412 | Q8 | — | 6 | 2 | no | — |
| 413 | Q8 | — | 6 | 2 | no | — |
| 414 | Q8 | — | 12 | 2 | no | — |
| 415 | Q8 | C22×D12 | 1 | 1 | yes | characteristic |
| 416 | D4 | — | 3 | 2 | no | — |
| 417 | D4 | — | 3 | 2 | no | — |
| 418 | D4 | — | 6 | 4 | no | — |
| 419 | D4 | — | 6 | 1 | no | — |
| 420 | D4 | — | 6 | 1 | no | — |
| 421 | D4 | — | 6 | 4 | no | — |
| 422 | D4 | — | 6 | 2 | no | — |
| 423 | D4 | — | 6 | 4 | no | — |
| 424 | D4 | — | 6 | 2 | no | — |
| 425 | D4 | — | 12 | 4 | no | — |
| 426 | D4 | — | 12 | 4 | no | — |
| 427 | D4 | — | 12 | 4 | no | — |
| 428 | D4 | — | 12 | 4 | no | — |
| 429 | D4 | — | 12 | 4 | no | — |
| 430 | D4 | — | 12 | 2 | no | — |
| 431 | D4 | — | 24 | 8 | no | — |
| 432 | D4 | — | 24 | 8 | no | — |
| 433 | C2×C4 | — | 3 | 2 | no | — |
| 434 | C2×C4 | — | 3 | 2 | no | — |
| 435 | C2×C4 | — | 3 | 1 | no | — |
| 436 | C2×C4 | — | 3 | 1 | no | — |
| 437 | C2×C4 | — | 3 | 2 | no | — |
| 438 | C2×C4 | — | 3 | 2 | no | — |
| 439 | C2×C4 | — | 3 | 4 | no | — |
| 440 | C2×C4 | — | 3 | 2 | no | — |
| 441 | C2×C4 | — | 3 | 2 | no | — |
| 442 | C2×C4 | — | 3 | 4 | no | — |
| 443 | C2×C4 | — | 3 | 4 | no | — |
| 444 | C2×C4 | — | 6 | 2 | no | — |
| 445 | C2×C4 | — | 12 | 4 | no | — |
| 446 | C2×C4 | — | 12 | 4 | no | — |
| 447 | C2×C4 | — | 12 | 2 | no | — |
| 448 | C2×C4 | — | 12 | 4 | no | — |
| 449 | C2×C4 | — | 24 | 2 | no | — |
| 450 | C2×C4 | C4⋊S4 | 1 | 4 | yes | — |
| 451 | C2×C4 | C22×S4 | 1 | 4 | yes | — |
| 452 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 453 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 454 | C8 | — | 6 | 4 | no | — |
| 455 | C8 | — | 6 | 2 | no | — |
| 456 | C8 | — | 6 | 2 | no | — |
| 457 | C2×C3 | — | 4 | 1 | no | — |
| 458 | C2×C3 | — | 4 | 2 | no | — |
| 459 | C2×C3 | — | 8 | 2 | no | — |
| 460 | D3 | — | 16 | 2 | no | — |
| 461 | D3 | — | 16 | 4 | no | — |
| 462 | C22 | — | 2 | 2 | no | — |
| 463 | C22 | — | 3 | 2 | no | — |
| 464 | C22 | — | 3 | 2 | no | — |
| 465 | C22 | — | 6 | 2 | no | — |
| 466 | C22 | — | 6 | 2 | no | — |
| 467 | C22 | — | 12 | 4 | no | — |
| 468 | C22 | — | 12 | 2 | no | — |
| 469 | C22 | — | 12 | 4 | no | — |
| 470 | C22 | — | 12 | 4 | no | — |
| 471 | C22 | — | 12 | 8 | no | — |
| 472 | C22 | — | 24 | 8 | no | — |
| 473 | C22 | — | 24 | 4 | no | — |
| 474 | C22 | — | 24 | 8 | no | — |
| 475 | C22 | — | 24 | 8 | no | — |
| 476 | C22 | C2×C4⋊S4 | 1 | 2 | yes | — |
| 477 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 478 | C4 | — | 2 | 4 | no | — |
| 479 | C4 | — | 3 | 1 | no | — |
| 480 | C4 | — | 3 | 2 | no | — |
| 481 | C4 | — | 3 | 1 | no | — |
| 482 | C4 | — | 6 | 4 | no | — |
| 483 | C4 | — | 12 | 2 | no | — |
| 484 | C4 | C2×C4⋊S4 | 1 | 2 | yes | — |
| 485 | C4 | C2×C4⋊S4 | 1 | 2 | yes | — |
| 486 | C3 | — | 4 | 1 | no | Sylow |
| 487 | C2 | — | 2 | 2 | no | — |
| 488 | C2 | — | 6 | 2 | no | — |
| 489 | C2 | — | 6 | 2 | no | — |
| 490 | C2 | — | 24 | 4 | no | — |
| 491 | C2 | — | 24 | 2 | no | — |
| 492 | C2 | C22×C4⋊S4 | 1 | 1 | yes | characteristic |
| 493 | C2 | #87498 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle | C22 | C23×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Fitting | #3428 | D3 |
| hypercenter | #117 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5923 | C2 | semidirect |
| 2. C22×#986 | C2 | semidirect |
| 3. #3428⋊C3 | C2 | semidirect |
| 4. #85368 | C2 | semidirect |
| 5. #85355 | C2 | semidirect |
| 6. #85347 | C2 | semidirect |
| 7. #85346 | C2 | semidirect |
| 13. C2×#986 | C22 | semidirect |
| 14. C2×#986 | C22 | semidirect |
| 15. C2×#985 | C22 | semidirect |
| 16. C2×#984 | C22 | semidirect |
| 17. C2×#983 | C22 | semidirect |
| 18. C22×GL(2,𝔽3) | C22 | semidirect |
| 20. #520⋊C3 | C22 | semidirect |
| 21. #519⋊C3 | C22 | semidirect |
| 22. C4×#41⋊C3 | C22 | semidirect |
| 23. #5395 | C22 | semidirect |
| 24. C4⋊GL(2,𝔽3) | C22 | semidirect |
| 28. #3428 | D3 | semidirect |
| 42. C2×#41⋊C3 | D4 | semidirect |
| 54. C2×GL(2,𝔽3) | C23 | semidirect |
| 55. C2×#226 | C23 | semidirect |
| 61. C4×SL(2,𝔽3) | C23 | semidirect |
| 95. #520 | C2×D3 | semidirect |
| 99. C4×#41 | C2×D3 | semidirect |
| 134. #41⋊C3 | C2×D4 | semidirect |
| 135. C2×SL(2,𝔽3) | C2×D4 | semidirect |
| 154. C2×#41 | D12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5923 | 2 |
| C22×#986 | 2 |
| #3428⋊C3 | 2 |
| #85368 | 2 |
| #85355 | 2 |
| #85347 | 2 |
| #85346 | 2 |
| #60426 | 3 |
| #5525 | 4 |