Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1399 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 1399 conjugacy classes of subgroups — too many to draw. Only its 119 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×#5926 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#578⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#5431 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #85473 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 5 | C2×#5407 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#5404 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#3290 | — | 3 | 1 | no | maximal, Sylow |
| 8 | C2×2−1+4⋊C3 | C22 | 1 | 2 | yes | complemented |
| 9 | #5926 | — | 2 | 4 | no | — |
| 10 | #5926 | C22 | 1 | 8 | yes | complemented |
| 11 | C2×#986 | C22 | 1 | 2 | yes | complemented |
| 12 | C2×#985 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#983 | — | 2 | 2 | no | — |
| 14 | C22×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 15 | C2×D3×D8 | — | 4 | 1 | no | maximal |
| 16 | #578⋊C3 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×#131⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 18 | #5431 | C22 | 1 | 8 | yes | complemented |
| 19 | C2×GU(2,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #5407 | C22 | 1 | 4 | yes | complemented |
| 21 | #5404 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#578 | D3 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×#577 | — | 3 | 2 | no | — |
| 24 | C2×#576 | — | 3 | 1 | no | — |
| 25 | #3290 | — | 3 | 8 | no | — |
| 26 | #3290 | — | 3 | 8 | no | — |
| 27 | C2×#495 | — | 3 | 1 | no | — |
| 28 | C2×#473 | — | 3 | 1 | no | — |
| 29 | C2×#472 | — | 3 | 1 | no | — |
| 30 | C2×#471 | — | 3 | 2 | no | — |
| 31 | C2×#454 | — | 3 | 2 | no | — |
| 32 | C2×#455 | — | 3 | 2 | no | — |
| 33 | C2×#443 | — | 3 | 1 | no | — |
| 34 | C2×#443 | — | 3 | 1 | no | — |
| 35 | C2×D3×D4 | — | 4 | 2 | no | — |
| 36 | 2−1+4⋊C3 | — | 2 | 2 | no | — |
| 37 | 2−1+4⋊C3 | C23 | 1 | 4 | yes | complemented |
| 38 | C2×#41⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 39 | C22×SL(2,𝔽3) | — | 2 | 2 | no | — |
| 40 | #986 | — | 2 | 2 | no | — |
| 41 | #986 | C23 | 1 | 4 | yes | complemented |
| 42 | #985 | D4 | 1 | 2 | yes | — |
| 43 | #985 | C23 | 1 | 2 | yes | — |
| 44 | #983 | — | 2 | 8 | no | — |
| 45 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 46 | C2×GL(2,𝔽3) | — | 2 | 8 | no | — |
| 47 | C2×GL(2,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 48 | C2×#226 | D4 | 1 | 1 | yes | characteristic |
| 49 | C2×C3×D8 | — | 4 | 1 | no | — |
| 50 | C2×#213 | — | 4 | 2 | no | — |
| 51 | D3×D8 | — | 4 | 8 | no | — |
| 52 | C2×D24 | — | 4 | 1 | no | — |
| 53 | C2×D3×C8 | — | 4 | 1 | no | — |
| 54 | #131⋊C3 | C23 | 1 | 2 | yes | complemented |
| 55 | GU(2,𝔽3) | C23 | 1 | 2 | yes | complemented |
| 56 | C2×2−1+4 | C2×D3 | 1 | 2 | yes | complemented |
| 57 | C2×H(5,𝔽2) | — | 3 | 2 | no | — |
| 58 | #578 | — | 3 | 4 | no | — |
| 59 | #578 | C2×D3 | 1 | 4 | yes | complemented |
| 60 | #577 | — | 3 | 8 | no | — |
| 61 | #577 | — | 3 | 8 | no | — |
| 62 | #577 | — | 6 | 4 | no | — |
| 63 | #577 | — | 6 | 4 | no | — |
| 64 | #576 | — | 3 | 8 | no | — |
| 65 | #576 | — | 6 | 4 | no | — |
| 66 | C2×#137 | — | 3 | 2 | no | — |
| 67 | C2×#137 | — | 3 | 2 | no | — |
| 68 | C2×#137 | — | 6 | 2 | no | — |
| 69 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 70 | C2×AGL(1,ℤ/8) | — | 3 | 2 | no | — |
| 71 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 72 | C2×AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 73 | C2×#135 | — | 3 | 1 | no | — |
| 74 | C2×#135 | — | 3 | 1 | no | — |
| 75 | C2×#135 | — | 6 | 2 | no | — |
| 76 | C2×#135 | — | 6 | 1 | no | — |
| 77 | C22×Q16 | — | 3 | 1 | no | — |
| 78 | C22×SD16 | — | 3 | 2 | no | — |
| 79 | C22×SD16 | — | 6 | 2 | no | — |
| 80 | C22×D8 | — | 3 | 1 | no | — |
| 81 | C22×D8 | — | 6 | 1 | no | — |
| 82 | C2×#131 | — | 3 | 2 | no | — |
| 83 | C2×#131 | — | 3 | 1 | no | — |
| 84 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 85 | C2×#124 | — | 3 | 2 | no | — |
| 86 | #495 | — | 3 | 8 | no | — |
| 87 | #473 | — | 3 | 8 | no | — |
| 88 | #472 | — | 3 | 4 | no | — |
| 89 | #472 | — | 3 | 4 | no | — |
| 90 | #471 | — | 3 | 16 | no | — |
| 91 | #455 | — | 3 | 16 | no | — |
| 92 | #454 | — | 3 | 8 | no | — |
| 93 | #454 | — | 3 | 8 | no | — |
| 94 | #443 | — | 3 | 4 | no | — |
| 95 | #443 | — | 3 | 8 | no | — |
| 96 | #443 | — | 3 | 4 | no | — |
| 97 | C2×#108 | — | 3 | 1 | no | — |
| 98 | C2×#108 | — | 3 | 1 | no | — |
| 99 | C2×#104 | — | 3 | 1 | no | — |
| 100 | C2×#104 | — | 3 | 2 | no | — |
| 101 | C2×#104 | — | 3 | 1 | no | — |
| 102 | C2×#101 | — | 3 | 2 | no | — |
| 103 | C2×#100 | — | 3 | 2 | no | — |
| 104 | C2×C4×C8 | — | 3 | 1 | no | — |
| 105 | C23×D3 | — | 8 | 2 | no | — |
| 106 | C2×C3×D4 | — | 4 | 2 | no | — |
| 107 | C2×#67 | — | 8 | 2 | no | — |
| 108 | D3×D4 | — | 4 | 8 | no | — |
| 109 | D3×D4 | — | 8 | 4 | no | — |
| 110 | C2×D12 | — | 4 | 2 | no | — |
| 111 | C2×C4×D3 | — | 4 | 1 | no | — |
| 112 | #41⋊C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 113 | #41⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 114 | C2×SL(2,𝔽3) | — | 2 | 4 | no | — |
| 115 | C2×SL(2,𝔽3) | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | GL(2,𝔽3) | — | 2 | 4 | no | — |
| 117 | GL(2,𝔽3) | C2×D4 | 1 | 2 | yes | — |
| 118 | #226 | C2×D4 | 1 | 2 | yes | — |
| 119 | C3×D8 | — | 4 | 4 | no | — |
| 120 | C2×C3×C8 | — | 4 | 1 | no | — |
| 121 | #213 | — | 4 | 8 | no | — |
| 122 | C2×C3⋊C8 | — | 4 | 1 | no | — |
| 123 | D24 | — | 4 | 4 | no | — |
| 124 | D3×C8 | — | 4 | 4 | no | — |
| 125 | 2−1+4 | — | 2 | 2 | no | — |
| 126 | 2−1+4 | — | 3 | 4 | no | — |
| 127 | 2−1+4 | — | 6 | 2 | no | — |
| 128 | 2−1+4 | C22×D3 | 1 | 4 | yes | complemented |
| 129 | H(5,𝔽2) | — | 3 | 8 | no | — |
| 130 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 131 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 132 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 133 | C2×#41 | — | 3 | 1 | no | — |
| 134 | C2×#41 | — | 3 | 2 | no | — |
| 135 | C2×#41 | — | 6 | 2 | no | — |
| 136 | C2×#41 | — | 6 | 2 | no | — |
| 137 | C2×#41 | — | 6 | 2 | no | — |
| 138 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 139 | C22×Q8 | — | 2 | 2 | no | — |
| 140 | C22×Q8 | — | 3 | 2 | no | — |
| 141 | C22×D4 | — | 3 | 2 | no | — |
| 142 | C22×D4 | — | 6 | 2 | no | — |
| 143 | C22×D4 | — | 6 | 2 | no | — |
| 144 | C22×D4 | — | 12 | 2 | no | — |
| 145 | #137 | — | 3 | 8 | no | — |
| 146 | #137 | — | 3 | 8 | no | — |
| 147 | #137 | — | 6 | 4 | no | — |
| 148 | #137 | — | 6 | 8 | no | — |
| 149 | #137 | — | 6 | 8 | no | — |
| 150 | #137 | — | 6 | 4 | no | — |
| 151 | AGL(1,ℤ/8) | — | 3 | 8 | no | — |
| 152 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 153 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 154 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 155 | AGL(1,ℤ/8) | — | 6 | 8 | no | — |
| 156 | AGL(1,ℤ/8) | — | 6 | 16 | no | — |
| 157 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 158 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 159 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 160 | #135 | — | 3 | 2 | no | — |
| 161 | #135 | — | 3 | 2 | no | — |
| 162 | #135 | — | 3 | 2 | no | — |
| 163 | #135 | — | 3 | 2 | no | — |
| 164 | #135 | — | 3 | 4 | no | — |
| 165 | #135 | — | 3 | 4 | no | — |
| 166 | #135 | — | 6 | 8 | no | — |
| 167 | #135 | — | 6 | 8 | no | — |
| 168 | #135 | — | 6 | 8 | no | — |
| 169 | C2×Q16 | — | 3 | 1 | no | — |
| 170 | C2×Q16 | — | 3 | 4 | no | — |
| 171 | C2×Q16 | — | 3 | 1 | no | — |
| 172 | C2×Q16 | — | 6 | 2 | no | — |
| 173 | C2×Q16 | — | 6 | 1 | no | — |
| 174 | C2×Q16 | — | 6 | 2 | no | — |
| 175 | C2×SD16 | — | 3 | 1 | no | — |
| 176 | C2×SD16 | — | 3 | 1 | no | — |
| 177 | C2×SD16 | — | 3 | 2 | no | — |
| 178 | C2×SD16 | — | 3 | 8 | no | — |
| 179 | C2×SD16 | — | 6 | 2 | no | — |
| 180 | C2×SD16 | — | 6 | 2 | no | — |
| 181 | C2×SD16 | — | 6 | 4 | no | — |
| 182 | C2×SD16 | — | 6 | 8 | no | — |
| 183 | C2×SD16 | — | 6 | 8 | no | — |
| 184 | C2×SD16 | — | 6 | 2 | no | — |
| 185 | C2×SD16 | — | 6 | 2 | no | — |
| 186 | C2×SD16 | — | 6 | 2 | no | — |
| 187 | C2×D8 | — | 3 | 1 | no | — |
| 188 | C2×D8 | — | 3 | 4 | no | — |
| 189 | C2×D8 | — | 6 | 1 | no | — |
| 190 | C2×D8 | — | 6 | 2 | no | — |
| 191 | C2×D8 | — | 6 | 2 | no | — |
| 192 | C2×D8 | — | 6 | 2 | no | — |
| 193 | C2×D8 | — | 6 | 8 | no | — |
| 194 | C2×D8 | — | 6 | 1 | no | — |
| 195 | C2×D8 | S4 | 1 | 1 | yes | characteristic |
| 196 | #131 | — | 3 | 2 | no | — |
| 197 | #131 | — | 3 | 4 | no | — |
| 198 | #131 | — | 3 | 8 | no | — |
| 199 | #131 | — | 6 | 2 | no | — |
| 200 | #131 | — | 6 | 4 | no | — |
| 201 | #131 | C22×D3 | 1 | 2 | yes | complemented |
| 202 | C2×M16 | — | 3 | 1 | no | — |
| 203 | C2×M16 | — | 3 | 1 | no | — |
| 204 | C2×M16 | — | 3 | 2 | no | — |
| 205 | C2×M16 | — | 6 | 1 | no | — |
| 206 | C2×M16 | — | 6 | 2 | no | — |
| 207 | C22×C8 | — | 3 | 1 | no | — |
| 208 | C22×C8 | — | 3 | 1 | no | — |
| 209 | C22×C8 | — | 6 | 2 | no | — |
| 210 | C22×C8 | — | 6 | 1 | no | — |
| 211 | #124 | — | 3 | 8 | no | — |
| 212 | #124 | — | 12 | 2 | no | — |
| 213 | C2×C22⋊C4 | — | 12 | 2 | no | — |
| 214 | C2×C42 | — | 3 | 1 | no | — |
| 215 | #108 | — | 3 | 4 | no | — |
| 216 | #108 | — | 3 | 4 | no | — |
| 217 | #104 | — | 3 | 2 | no | — |
| 218 | #104 | — | 3 | 8 | no | — |
| 219 | #104 | — | 3 | 4 | no | — |
| 220 | #104 | — | 3 | 2 | no | — |
| 221 | #101 | — | 3 | 8 | no | — |
| 222 | #100 | — | 3 | 8 | no | — |
| 223 | C4×C8 | — | 3 | 4 | no | — |
| 224 | C23×C3 | — | 8 | 2 | no | — |
| 225 | C22×D3 | — | 4 | 1 | no | — |
| 226 | C22×D3 | — | 8 | 8 | no | — |
| 227 | C22×D3 | — | 8 | 2 | no | — |
| 228 | C22×D3 | — | 16 | 8 | no | — |
| 229 | C3×D4 | — | 4 | 4 | no | — |
| 230 | C3×D4 | — | 8 | 2 | no | — |
| 231 | C2×C3×C4 | — | 4 | 1 | no | — |
| 232 | #67 | — | 8 | 8 | no | — |
| 233 | C2×Dic3 | — | 4 | 1 | no | — |
| 234 | D12 | — | 4 | 4 | no | — |
| 235 | D12 | — | 8 | 2 | no | — |
| 236 | C4×D3 | — | 4 | 2 | no | — |
| 237 | C4×D3 | — | 4 | 2 | no | — |
| 238 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 239 | C3×C8 | — | 4 | 2 | no | — |
| 240 | C3⋊C8 | — | 4 | 2 | no | — |
| 241 | C24 | — | 6 | 2 | no | — |
| 242 | C24 | — | 12 | 2 | no | — |
| 243 | #41 | — | 3 | 1 | no | — |
| 244 | #41 | — | 3 | 1 | no | — |
| 245 | #41 | — | 3 | 2 | no | — |
| 246 | #41 | — | 3 | 2 | no | — |
| 247 | #41 | — | 3 | 4 | no | — |
| 248 | #41 | — | 3 | 4 | no | — |
| 249 | #41 | — | 6 | 2 | no | — |
| 250 | #41 | — | 6 | 2 | no | — |
| 251 | #41 | — | 6 | 1 | no | — |
| 252 | #41 | — | 6 | 1 | no | — |
| 253 | #41 | — | 6 | 4 | no | — |
| 254 | #41 | — | 6 | 4 | no | — |
| 255 | #41 | — | 6 | 8 | no | — |
| 256 | #41 | — | 6 | 8 | no | — |
| 257 | #41 | — | 12 | 4 | no | — |
| 258 | #41 | — | 12 | 4 | no | — |
| 259 | #41 | — | 12 | 4 | no | — |
| 260 | #41 | D3×D4 | 1 | 1 | yes | characteristic |
| 261 | #41 | C23×D3 | 1 | 1 | yes | characteristic |
| 262 | C2×Q8 | — | 2 | 4 | no | — |
| 263 | C2×Q8 | — | 3 | 1 | no | — |
| 264 | C2×Q8 | — | 3 | 4 | no | — |
| 265 | C2×Q8 | — | 3 | 2 | no | — |
| 266 | C2×Q8 | — | 6 | 2 | no | — |
| 267 | C2×Q8 | — | 6 | 2 | no | — |
| 268 | C2×Q8 | — | 6 | 2 | no | — |
| 269 | C2×Q8 | — | 6 | 2 | no | — |
| 270 | C2×Q8 | — | 6 | 4 | no | — |
| 271 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×D4 | — | 3 | 1 | no | — |
| 273 | C2×D4 | — | 3 | 1 | no | — |
| 274 | C2×D4 | — | 3 | 4 | no | — |
| 275 | C2×D4 | — | 6 | 2 | no | — |
| 276 | C2×D4 | — | 6 | 2 | no | — |
| 277 | C2×D4 | — | 6 | 2 | no | — |
| 278 | C2×D4 | — | 6 | 2 | no | — |
| 279 | C2×D4 | — | 6 | 8 | no | — |
| 280 | C2×D4 | — | 6 | 2 | no | — |
| 281 | C2×D4 | — | 6 | 1 | no | — |
| 282 | C2×D4 | — | 6 | 8 | no | — |
| 283 | C2×D4 | — | 6 | 2 | no | — |
| 284 | C2×D4 | — | 12 | 4 | no | — |
| 285 | C2×D4 | — | 12 | 4 | no | — |
| 286 | C2×D4 | — | 12 | 2 | no | — |
| 287 | C2×D4 | — | 12 | 2 | no | — |
| 288 | C2×D4 | — | 12 | 8 | no | — |
| 289 | C2×D4 | — | 12 | 8 | no | — |
| 290 | C2×D4 | C2×S4 | 1 | 2 | yes | — |
| 291 | C22×C4 | — | 3 | 1 | no | — |
| 292 | C22×C4 | — | 6 | 2 | no | — |
| 293 | C22×C4 | — | 6 | 1 | no | — |
| 294 | C22×C4 | — | 6 | 2 | no | — |
| 295 | C22×C4 | — | 6 | 1 | no | — |
| 296 | C22×C4 | — | 12 | 2 | no | — |
| 297 | Q16 | — | 3 | 2 | no | — |
| 298 | Q16 | — | 3 | 2 | no | — |
| 299 | Q16 | — | 3 | 4 | no | — |
| 300 | Q16 | — | 6 | 4 | no | — |
| 301 | Q16 | — | 6 | 8 | no | — |
| 302 | SD16 | — | 3 | 2 | no | — |
| 303 | SD16 | — | 3 | 2 | no | — |
| 304 | SD16 | — | 3 | 2 | no | — |
| 305 | SD16 | — | 3 | 2 | no | — |
| 306 | SD16 | — | 3 | 8 | no | — |
| 307 | SD16 | — | 6 | 8 | no | — |
| 308 | SD16 | — | 6 | 8 | no | — |
| 309 | SD16 | — | 6 | 8 | no | — |
| 310 | SD16 | — | 6 | 4 | no | — |
| 311 | SD16 | — | 6 | 8 | no | — |
| 312 | SD16 | — | 6 | 4 | no | — |
| 313 | D8 | — | 3 | 2 | no | — |
| 314 | D8 | — | 3 | 2 | no | — |
| 315 | D8 | — | 6 | 4 | no | — |
| 316 | D8 | — | 6 | 4 | no | — |
| 317 | D8 | — | 6 | 4 | no | — |
| 318 | D8 | — | 6 | 8 | no | — |
| 319 | D8 | — | 6 | 4 | no | — |
| 320 | D8 | C2×S4 | 1 | 4 | yes | — |
| 321 | M16 | — | 3 | 2 | no | — |
| 322 | M16 | — | 3 | 4 | no | — |
| 323 | M16 | — | 3 | 2 | no | — |
| 324 | M16 | — | 6 | 1 | no | — |
| 325 | M16 | — | 6 | 4 | no | — |
| 326 | M16 | — | 6 | 8 | no | — |
| 327 | M16 | — | 6 | 1 | no | — |
| 328 | M16 | — | 6 | 2 | no | — |
| 329 | C2×C8 | — | 3 | 2 | no | — |
| 330 | C2×C8 | — | 3 | 1 | no | — |
| 331 | C2×C8 | — | 3 | 1 | no | — |
| 332 | C2×C8 | — | 3 | 2 | no | — |
| 333 | C2×C8 | — | 3 | 1 | no | — |
| 334 | C2×C8 | — | 3 | 2 | no | — |
| 335 | C2×C8 | — | 3 | 2 | no | — |
| 336 | C2×C8 | — | 6 | 8 | no | — |
| 337 | C2×C8 | — | 6 | 2 | no | — |
| 338 | C2×C8 | — | 6 | 1 | no | — |
| 339 | C2×C8 | — | 6 | 4 | no | — |
| 340 | C2×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 341 | C22⋊C4 | — | 12 | 8 | no | — |
| 342 | C42 | — | 3 | 2 | no | — |
| 343 | C42 | — | 6 | 1 | no | — |
| 344 | C22×C3 | — | 4 | 1 | no | — |
| 345 | C22×C3 | — | 8 | 4 | no | — |
| 346 | C22×C3 | — | 16 | 4 | no | — |
| 347 | C2×D3 | — | 4 | 2 | no | — |
| 348 | C2×D3 | — | 4 | 4 | no | — |
| 349 | C2×D3 | — | 8 | 4 | no | — |
| 350 | C2×D3 | — | 16 | 4 | no | — |
| 351 | C2×D3 | — | 16 | 16 | no | — |
| 352 | C3×C4 | — | 4 | 1 | no | — |
| 353 | C3×C4 | — | 4 | 1 | no | — |
| 354 | Dic3 | — | 4 | 2 | no | — |
| 355 | C23 | — | 2 | 2 | no | — |
| 356 | C23 | — | 3 | 1 | no | — |
| 357 | C23 | — | 6 | 4 | no | — |
| 358 | C23 | — | 6 | 1 | no | — |
| 359 | C23 | — | 12 | 8 | no | — |
| 360 | C23 | — | 12 | 2 | no | — |
| 361 | C23 | — | 12 | 2 | no | — |
| 362 | C23 | — | 24 | 4 | no | — |
| 363 | C23 | — | 48 | 4 | no | — |
| 364 | Q8 | — | 3 | 1 | no | — |
| 365 | Q8 | — | 3 | 2 | no | — |
| 366 | Q8 | — | 3 | 4 | no | — |
| 367 | Q8 | — | 6 | 4 | no | — |
| 368 | Q8 | — | 6 | 1 | no | — |
| 369 | Q8 | — | 6 | 2 | no | — |
| 370 | Q8 | — | 12 | 2 | no | — |
| 371 | Q8 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 372 | D4 | — | 2 | 2 | no | — |
| 373 | D4 | — | 3 | 1 | no | — |
| 374 | D4 | — | 3 | 1 | no | — |
| 375 | D4 | — | 3 | 2 | no | — |
| 376 | D4 | — | 6 | 1 | no | — |
| 377 | D4 | — | 6 | 1 | no | — |
| 378 | D4 | — | 6 | 4 | no | — |
| 379 | D4 | — | 6 | 4 | no | — |
| 380 | D4 | — | 6 | 4 | no | — |
| 381 | D4 | — | 6 | 2 | no | — |
| 382 | D4 | — | 6 | 2 | no | — |
| 383 | D4 | — | 6 | 4 | no | — |
| 384 | D4 | — | 12 | 2 | no | — |
| 385 | D4 | — | 12 | 8 | no | — |
| 386 | D4 | — | 12 | 8 | no | — |
| 387 | D4 | — | 12 | 2 | no | — |
| 388 | D4 | C22×S4 | 1 | 4 | yes | — |
| 389 | C2×C4 | — | 3 | 1 | no | — |
| 390 | C2×C4 | — | 3 | 1 | no | — |
| 391 | C2×C4 | — | 3 | 1 | no | — |
| 392 | C2×C4 | — | 3 | 1 | no | — |
| 393 | C2×C4 | — | 3 | 1 | no | — |
| 394 | C2×C4 | — | 6 | 4 | no | — |
| 395 | C2×C4 | — | 6 | 4 | no | — |
| 396 | C2×C4 | — | 6 | 2 | no | — |
| 397 | C2×C4 | — | 6 | 1 | no | — |
| 398 | C2×C4 | — | 6 | 2 | no | — |
| 399 | C2×C4 | — | 6 | 2 | no | — |
| 400 | C2×C4 | — | 6 | 4 | no | — |
| 401 | C2×C4 | — | 6 | 2 | no | — |
| 402 | C2×C4 | — | 12 | 2 | no | — |
| 403 | C2×C4 | — | 12 | 8 | no | — |
| 404 | C2×C4 | — | 12 | 2 | no | — |
| 405 | C2×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 406 | C8 | — | 3 | 2 | no | — |
| 407 | C8 | — | 3 | 2 | no | — |
| 408 | C8 | — | 3 | 2 | no | — |
| 409 | C8 | — | 6 | 4 | no | — |
| 410 | C8 | — | 6 | 2 | no | — |
| 411 | C8 | C22×S4 | 1 | 2 | yes | — |
| 412 | C2×C3 | — | 4 | 1 | no | — |
| 413 | C2×C3 | — | 4 | 2 | no | — |
| 414 | C2×C3 | — | 16 | 4 | no | — |
| 415 | D3 | — | 4 | 4 | no | — |
| 416 | D3 | — | 16 | 4 | no | — |
| 417 | C22 | — | 2 | 4 | no | — |
| 418 | C22 | — | 3 | 1 | no | — |
| 419 | C22 | — | 3 | 1 | no | — |
| 420 | C22 | — | 4 | 4 | no | — |
| 421 | C22 | — | 6 | 2 | no | — |
| 422 | C22 | — | 6 | 2 | no | — |
| 423 | C22 | — | 12 | 2 | no | — |
| 424 | C22 | — | 12 | 4 | no | — |
| 425 | C22 | — | 24 | 4 | no | — |
| 426 | C22 | — | 24 | 4 | no | — |
| 427 | C22 | — | 48 | 8 | no | — |
| 428 | C22 | — | 48 | 2 | no | — |
| 429 | C22 | D4×S4 | 1 | 1 | yes | characteristic |
| 430 | C4 | — | 3 | 1 | no | — |
| 431 | C4 | — | 3 | 1 | no | — |
| 432 | C4 | — | 6 | 4 | no | — |
| 433 | C4 | — | 6 | 2 | no | — |
| 434 | C4 | — | 12 | 2 | no | — |
| 435 | C4 | D4×S4 | 1 | 1 | yes | characteristic |
| 436 | C4 | C23×S4 | 1 | 1 | yes | characteristic |
| 437 | C3 | — | 4 | 1 | no | Sylow |
| 438 | C2 | — | 4 | 4 | no | — |
| 439 | C2 | — | 6 | 1 | no | — |
| 440 | C2 | — | 6 | 1 | no | — |
| 441 | C2 | — | 12 | 2 | no | — |
| 442 | C2 | — | 24 | 4 | no | — |
| 443 | C2 | #85473 | 1 | 2 | yes | direct product factor |
| 444 | C2 | C2×D4×S4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | D4×S4 |
| commutator, cosocle | #41⋊C3 | C24 |
| Frattini | C4 | C23×S4 |
| Fitting | C2×#578 | D3 |
| hypercenter | C2×D8 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ #41⋊C3 ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×D8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#5926 | C2 | semidirect |
| 2. C2×#578⋊C3 | C2 | semidirect |
| 3. C2×#5431 | C2 | semidirect |
| 4. #85473 | C2 | direct (N × H) |
| 5. C2×#5407 | C2 | semidirect |
| 6. C2×#5404 | C2 | semidirect |
| 8. C2×2−1+4⋊C3 | C22 | semidirect |
| 10. #5926 | C22 | semidirect |
| 11. C2×#986 | C22 | semidirect |
| 16. #578⋊C3 | C22 | semidirect |
| 17. C2×#131⋊C3 | C22 | semidirect |
| 18. #5431 | C22 | semidirect |
| 19. C2×GU(2,𝔽3) | C22 | semidirect |
| 20. #5407 | C22 | semidirect |
| 21. #5404 | C22 | semidirect |
| 22. C2×#578 | D3 | semidirect |
| 37. 2−1+4⋊C3 | C23 | semidirect |
| 41. #986 | C23 | semidirect |
| 54. #131⋊C3 | C23 | semidirect |
| 55. GU(2,𝔽3) | C23 | semidirect |
| 56. C2×2−1+4 | C2×D3 | semidirect |
| 59. #578 | C2×D3 | semidirect |
| 84. C2×#131 | C2×D3 | semidirect |
| 128. 2−1+4 | C22×D3 | semidirect |
| 201. #131 | C22×D3 | semidirect |
| 443. C2 | #85473 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5926 | 2 |
| C2×#578⋊C3 | 2 |
| C2×#5431 | 2 |
| #85473 | 2 |
| C2×#5407 | 2 |
| C2×#5404 | 2 |
| C2×#3290 | 3 |
| C2×D3×D8 | 4 |