Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1805 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1805 conjugacy classes of subgroups — too many to draw. Only its 143 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 | C22×2−1+4⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×#985 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #85538 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 4 | C2×#5426 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#5421 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#5419 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#3013 | — | 3 | 1 | no | maximal, Sylow |
| 8 | C2×2−1+4⋊C3 | — | 2 | 4 | no | — |
| 9 | C2×2−1+4⋊C3 | C22 | 1 | 4 | yes | complemented |
| 10 | C22×#41⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 11 | C23×SL(2,𝔽3) | C22 | 1 | 2 | yes | — |
| 12 | C2×#985 | — | 2 | 4 | no | — |
| 13 | C2×#985 | C22 | 1 | 4 | yes | complemented |
| 14 | C22×GL(2,𝔽3) | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#226 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#938 | — | 4 | 1 | no | maximal |
| 17 | #5426 | C22 | 1 | 4 | yes | complemented |
| 18 | #5421 | C22 | 1 | 8 | yes | complemented |
| 19 | #5419 | C22 | 1 | 8 | yes | complemented |
| 20 | C2×#859 | C22 | 1 | 2 | yes | — |
| 21 | C22×2−1+4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×#137 | — | 3 | 1 | no | — |
| 23 | C22×#135 | — | 3 | 1 | no | — |
| 24 | C2×#537 | — | 3 | 1 | no | — |
| 25 | #3013 | — | 3 | 8 | no | — |
| 26 | #3013 | — | 3 | 8 | no | — |
| 27 | C2×#452 | — | 3 | 2 | no | — |
| 28 | C2×#449 | — | 3 | 2 | no | — |
| 29 | C2×#451 | — | 3 | 2 | no | — |
| 30 | C2×#448 | — | 3 | 2 | no | — |
| 31 | C2×#417 | — | 3 | 1 | no | — |
| 32 | C22×#103 | — | 3 | 1 | no | — |
| 33 | C2×#408 | — | 3 | 1 | no | — |
| 34 | C22×C3×D4 | — | 4 | 1 | no | — |
| 35 | C22×#67 | — | 4 | 2 | no | — |
| 36 | C22×C4×D3 | — | 4 | 1 | no | — |
| 37 | 2−1+4⋊C3 | — | 2 | 8 | no | — |
| 38 | C2×#41⋊C3 | D4 | 1 | 4 | yes | complemented |
| 39 | C2×#41⋊C3 | C23 | 1 | 2 | yes | — |
| 40 | C22×SL(2,𝔽3) | — | 2 | 4 | no | — |
| 41 | C22×SL(2,𝔽3) | C23 | 1 | 4 | yes | — |
| 42 | C22×SL(2,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 43 | #985 | — | 2 | 8 | no | — |
| 44 | C2×GL(2,𝔽3) | — | 2 | 2 | no | — |
| 45 | C2×GL(2,𝔽3) | C23 | 1 | 2 | yes | — |
| 46 | C2×#226 | — | 2 | 2 | no | — |
| 47 | C2×#226 | C23 | 1 | 2 | yes | — |
| 48 | C2×#217 | — | 4 | 2 | no | — |
| 49 | #938 | — | 4 | 8 | no | — |
| 50 | C2×C4⋊Dic3 | — | 4 | 1 | no | — |
| 51 | #859 | C23 | 1 | 4 | yes | — |
| 52 | C2×2−1+4 | — | 2 | 4 | no | — |
| 53 | C2×2−1+4 | — | 3 | 4 | no | — |
| 54 | C2×2−1+4 | — | 6 | 4 | no | — |
| 55 | C2×2−1+4 | C2×D3 | 1 | 4 | yes | complemented |
| 56 | C22×#41 | — | 3 | 1 | no | — |
| 57 | C22×#41 | — | 3 | 2 | no | — |
| 58 | C22×#41 | — | 3 | 1 | no | — |
| 59 | C22×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | C23×Q8 | — | 3 | 1 | no | — |
| 61 | C23×Q8 | C2×D3 | 1 | 2 | yes | — |
| 62 | C2×#137 | — | 3 | 8 | no | — |
| 63 | C2×#137 | — | 6 | 8 | no | — |
| 64 | C2×#135 | — | 3 | 4 | no | — |
| 65 | C2×#135 | — | 3 | 4 | no | — |
| 66 | C2×#135 | — | 6 | 4 | no | — |
| 67 | C2×#135 | — | 6 | 4 | no | — |
| 68 | C22×Q16 | — | 3 | 2 | no | — |
| 69 | C22×Q16 | — | 3 | 1 | no | — |
| 70 | C22×SD16 | — | 3 | 2 | no | — |
| 71 | C22×SD16 | — | 3 | 1 | no | — |
| 72 | C22×SD16 | — | 3 | 1 | no | — |
| 73 | C22×D8 | — | 3 | 1 | no | — |
| 74 | C22×M16 | — | 3 | 1 | no | — |
| 75 | C23×C8 | — | 3 | 1 | no | — |
| 76 | #537 | — | 3 | 8 | no | — |
| 77 | #537 | — | 6 | 4 | no | — |
| 78 | C2×C22⋊Q8 | — | 3 | 2 | no | — |
| 79 | C2×C22⋊Q8 | — | 6 | 1 | no | — |
| 80 | C2×#121 | — | 3 | 2 | no | — |
| 81 | C2×#121 | — | 6 | 2 | no | — |
| 82 | C2×#121 | — | 6 | 1 | no | — |
| 83 | C22×C4⋊C4 | — | 3 | 1 | no | — |
| 84 | #452 | — | 3 | 16 | no | — |
| 85 | #451 | — | 3 | 8 | no | — |
| 86 | #451 | — | 3 | 8 | no | — |
| 87 | #449 | — | 3 | 16 | no | — |
| 88 | #448 | — | 3 | 8 | no | — |
| 89 | #448 | — | 3 | 8 | no | — |
| 90 | #417 | — | 3 | 4 | no | — |
| 91 | #417 | — | 3 | 4 | no | — |
| 92 | C2×#103 | — | 3 | 2 | no | — |
| 93 | C2×#103 | — | 3 | 2 | no | — |
| 94 | C2×#103 | — | 3 | 8 | no | — |
| 95 | C2×#103 | — | 3 | 2 | no | — |
| 96 | C2×#102 | — | 3 | 2 | no | — |
| 97 | #408 | — | 3 | 8 | no | — |
| 98 | C2×C22⋊C8 | — | 3 | 2 | no | — |
| 99 | C2×C22⋊C8 | — | 3 | 2 | no | — |
| 100 | C24×C3 | — | 4 | 2 | no | — |
| 101 | C23×D3 | — | 4 | 1 | no | — |
| 102 | C2×C3×D4 | — | 4 | 4 | no | — |
| 103 | C2×C3×D4 | — | 8 | 4 | no | — |
| 104 | C22×C3×C4 | — | 4 | 1 | no | — |
| 105 | C2×#67 | — | 4 | 8 | no | — |
| 106 | C2×#67 | — | 8 | 8 | no | — |
| 107 | C22×Dic3 | — | 4 | 1 | no | — |
| 108 | C22×Dic3 | — | 4 | 2 | no | — |
| 109 | C2×C4×D3 | — | 4 | 4 | no | — |
| 110 | C2×C4×D3 | — | 8 | 4 | no | — |
| 111 | #41⋊C3 | C2×D4 | 1 | 4 | yes | complemented |
| 112 | C2×SL(2,𝔽3) | — | 2 | 4 | no | — |
| 113 | C2×SL(2,𝔽3) | C2×D4 | 1 | 2 | yes | — |
| 114 | C2×SL(2,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 115 | GL(2,𝔽3) | — | 2 | 2 | no | — |
| 116 | #226 | — | 2 | 2 | no | — |
| 117 | #217 | — | 4 | 8 | no | — |
| 118 | C4⋊Dic3 | — | 4 | 4 | no | — |
| 119 | 2−1+4 | — | 2 | 8 | no | — |
| 120 | 2−1+4 | — | 6 | 8 | no | — |
| 121 | 2−1+4 | — | 6 | 16 | no | — |
| 122 | 2−1+4 | — | 6 | 16 | no | — |
| 123 | C2×#41 | — | 3 | 4 | no | — |
| 124 | C2×#41 | — | 3 | 4 | no | — |
| 125 | C2×#41 | — | 3 | 2 | no | — |
| 126 | C2×#41 | — | 3 | 4 | no | — |
| 127 | C2×#41 | — | 3 | 8 | no | — |
| 128 | C2×#41 | — | 3 | 4 | no | — |
| 129 | C2×#41 | — | 6 | 4 | no | — |
| 130 | C2×#41 | — | 6 | 4 | no | — |
| 131 | C2×#41 | — | 6 | 4 | no | — |
| 132 | C2×#41 | — | 6 | 2 | no | — |
| 133 | C2×#41 | — | 6 | 4 | no | — |
| 134 | C2×#41 | — | 6 | 4 | no | — |
| 135 | C2×#41 | — | 6 | 8 | no | — |
| 136 | C2×#41 | — | 6 | 8 | no | — |
| 137 | C2×#41 | #67 | 1 | 4 | yes | complemented |
| 138 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 139 | C22×Q8 | — | 2 | 4 | no | — |
| 140 | C22×Q8 | — | 3 | 1 | no | — |
| 141 | C22×Q8 | — | 3 | 2 | no | — |
| 142 | C22×Q8 | — | 3 | 4 | no | — |
| 143 | C22×Q8 | — | 3 | 4 | no | — |
| 144 | C22×Q8 | — | 3 | 8 | no | — |
| 145 | C22×Q8 | — | 3 | 1 | no | — |
| 146 | C22×Q8 | — | 6 | 2 | no | — |
| 147 | C22×Q8 | — | 6 | 4 | no | — |
| 148 | C22×Q8 | — | 6 | 4 | no | — |
| 149 | C22×Q8 | C22×D3 | 1 | 4 | yes | — |
| 150 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 151 | C22×D4 | — | 3 | 1 | no | — |
| 152 | C22×D4 | — | 3 | 2 | no | — |
| 153 | C22×D4 | — | 3 | 1 | no | — |
| 154 | C22×D4 | — | 6 | 1 | no | — |
| 155 | C22×D4 | — | 6 | 2 | no | — |
| 156 | C22×D4 | S4 | 1 | 1 | yes | characteristic |
| 157 | C23×C4 | — | 3 | 1 | no | — |
| 158 | C23×C4 | — | 3 | 2 | no | — |
| 159 | C23×C4 | — | 6 | 1 | no | — |
| 160 | C23×C4 | — | 6 | 1 | no | — |
| 161 | C23×C4 | — | 6 | 1 | no | — |
| 162 | #137 | — | 6 | 32 | no | — |
| 163 | #135 | — | 6 | 16 | no | — |
| 164 | #135 | — | 6 | 8 | no | — |
| 165 | #135 | — | 6 | 8 | no | — |
| 166 | C2×Q16 | — | 3 | 2 | no | — |
| 167 | C2×Q16 | — | 3 | 8 | no | — |
| 168 | C2×Q16 | — | 3 | 2 | no | — |
| 169 | C2×Q16 | — | 6 | 2 | no | — |
| 170 | C2×Q16 | — | 6 | 8 | no | — |
| 171 | C2×Q16 | — | 6 | 2 | no | — |
| 172 | C2×SD16 | — | 3 | 2 | no | — |
| 173 | C2×SD16 | — | 3 | 4 | no | — |
| 174 | C2×SD16 | — | 3 | 8 | no | — |
| 175 | C2×SD16 | — | 3 | 2 | no | — |
| 176 | C2×SD16 | — | 6 | 4 | no | — |
| 177 | C2×SD16 | — | 6 | 2 | no | — |
| 178 | C2×SD16 | — | 6 | 8 | no | — |
| 179 | C2×SD16 | — | 6 | 2 | no | — |
| 180 | C2×D8 | — | 3 | 4 | no | — |
| 181 | C2×D8 | — | 6 | 4 | no | — |
| 182 | C2×M16 | — | 3 | 4 | no | — |
| 183 | C2×M16 | — | 6 | 4 | no | — |
| 184 | C22×C8 | — | 3 | 1 | no | — |
| 185 | C22×C8 | — | 3 | 1 | no | — |
| 186 | C22×C8 | — | 3 | 4 | no | — |
| 187 | C22×C8 | — | 3 | 2 | no | — |
| 188 | C22×C8 | — | 6 | 4 | no | — |
| 189 | C22⋊Q8 | — | 3 | 8 | no | — |
| 190 | C22⋊Q8 | — | 6 | 4 | no | — |
| 191 | C22⋊Q8 | — | 6 | 8 | no | — |
| 192 | #121 | — | 3 | 8 | no | — |
| 193 | #121 | — | 6 | 4 | no | — |
| 194 | #121 | — | 6 | 16 | no | — |
| 195 | #121 | — | 6 | 8 | no | — |
| 196 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 197 | C2×C4⋊C4 | — | 3 | 4 | no | — |
| 198 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 199 | C2×C4⋊C4 | — | 6 | 2 | no | — |
| 200 | C2×C4⋊C4 | — | 6 | 1 | no | — |
| 201 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 202 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 203 | #103 | — | 3 | 8 | no | — |
| 204 | #103 | — | 3 | 8 | no | — |
| 205 | #103 | — | 3 | 4 | no | — |
| 206 | #103 | — | 3 | 4 | no | — |
| 207 | #102 | — | 3 | 8 | no | — |
| 208 | C22⋊C8 | — | 3 | 8 | no | — |
| 209 | C22⋊C8 | — | 3 | 8 | no | — |
| 210 | C23×C3 | — | 4 | 4 | no | — |
| 211 | C23×C3 | — | 4 | 1 | no | — |
| 212 | C23×C3 | — | 8 | 4 | no | — |
| 213 | C23×C3 | — | 8 | 4 | no | — |
| 214 | C23×C3 | — | 8 | 4 | no | — |
| 215 | C22×D3 | — | 4 | 2 | no | — |
| 216 | C22×D3 | — | 4 | 4 | no | — |
| 217 | C22×D3 | — | 8 | 2 | no | — |
| 218 | C22×D3 | — | 8 | 2 | no | — |
| 219 | C3×D4 | — | 8 | 8 | no | — |
| 220 | C2×C3×C4 | — | 4 | 4 | no | — |
| 221 | C2×C3×C4 | — | 4 | 2 | no | — |
| 222 | #67 | — | 8 | 16 | no | — |
| 223 | C2×Dic3 | — | 4 | 4 | no | — |
| 224 | C2×Dic3 | — | 4 | 2 | no | — |
| 225 | C2×Dic3 | — | 8 | 2 | no | — |
| 226 | C2×Dic3 | — | 8 | 4 | no | — |
| 227 | C4×D3 | — | 8 | 8 | no | — |
| 228 | SL(2,𝔽3) | C22×D4 | 1 | 1 | yes | characteristic |
| 229 | C24 | — | 3 | 1 | no | — |
| 230 | C24 | — | 6 | 1 | no | — |
| 231 | C24 | C2×S4 | 1 | 2 | yes | — |
| 232 | #41 | — | 3 | 8 | no | — |
| 233 | #41 | — | 3 | 4 | no | — |
| 234 | #41 | — | 6 | 4 | no | — |
| 235 | #41 | — | 6 | 8 | no | — |
| 236 | #41 | — | 6 | 8 | no | — |
| 237 | #41 | — | 6 | 16 | no | — |
| 238 | #41 | — | 6 | 8 | no | — |
| 239 | #41 | — | 6 | 8 | no | — |
| 240 | #41 | — | 6 | 16 | no | — |
| 241 | #41 | — | 6 | 16 | no | — |
| 242 | #41 | — | 6 | 32 | no | — |
| 243 | #41 | — | 12 | 8 | no | — |
| 244 | #41 | C2×#67 | 1 | 4 | yes | complemented |
| 245 | C2×Q8 | — | 2 | 4 | no | — |
| 246 | C2×Q8 | — | 3 | 4 | no | — |
| 247 | C2×Q8 | — | 3 | 1 | no | — |
| 248 | C2×Q8 | — | 3 | 4 | no | — |
| 249 | C2×Q8 | — | 3 | 2 | no | — |
| 250 | C2×Q8 | — | 3 | 8 | no | — |
| 251 | C2×Q8 | — | 3 | 16 | no | — |
| 252 | C2×Q8 | — | 3 | 2 | no | — |
| 253 | C2×Q8 | — | 6 | 2 | no | — |
| 254 | C2×Q8 | — | 6 | 8 | no | — |
| 255 | C2×Q8 | — | 6 | 16 | no | — |
| 256 | C2×Q8 | — | 6 | 1 | no | — |
| 257 | C2×Q8 | — | 6 | 4 | no | — |
| 258 | C2×Q8 | — | 6 | 2 | no | — |
| 259 | C2×Q8 | — | 6 | 2 | no | — |
| 260 | C2×Q8 | — | 6 | 8 | no | — |
| 261 | C2×Q8 | — | 6 | 4 | no | — |
| 262 | C2×Q8 | — | 6 | 4 | no | — |
| 263 | C2×Q8 | — | 6 | 8 | no | — |
| 264 | C2×Q8 | C2×#67 | 1 | 2 | yes | — |
| 265 | C2×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 266 | C2×D4 | — | 2 | 4 | no | — |
| 267 | C2×D4 | — | 3 | 2 | no | — |
| 268 | C2×D4 | — | 3 | 4 | no | — |
| 269 | C2×D4 | — | 3 | 8 | no | — |
| 270 | C2×D4 | — | 3 | 2 | no | — |
| 271 | C2×D4 | — | 6 | 2 | no | — |
| 272 | C2×D4 | — | 6 | 1 | no | — |
| 273 | C2×D4 | — | 6 | 2 | no | — |
| 274 | C2×D4 | — | 6 | 2 | no | — |
| 275 | C2×D4 | — | 6 | 1 | no | — |
| 276 | C2×D4 | — | 6 | 8 | no | — |
| 277 | C2×D4 | — | 6 | 4 | no | — |
| 278 | C2×D4 | — | 6 | 8 | no | — |
| 279 | C2×D4 | — | 12 | 4 | no | — |
| 280 | C2×D4 | — | 24 | 4 | no | — |
| 281 | C2×D4 | C2×S4 | 1 | 4 | yes | — |
| 282 | C22×C4 | — | 3 | 1 | no | — |
| 283 | C22×C4 | — | 3 | 4 | no | — |
| 284 | C22×C4 | — | 3 | 4 | no | — |
| 285 | C22×C4 | — | 3 | 2 | no | — |
| 286 | C22×C4 | — | 3 | 2 | no | — |
| 287 | C22×C4 | — | 3 | 4 | no | — |
| 288 | C22×C4 | — | 3 | 4 | no | — |
| 289 | C22×C4 | — | 3 | 2 | no | — |
| 290 | C22×C4 | — | 6 | 4 | no | — |
| 291 | C22×C4 | — | 6 | 4 | no | — |
| 292 | C22×C4 | — | 6 | 4 | no | — |
| 293 | C22×C4 | — | 6 | 8 | no | — |
| 294 | C22×C4 | — | 6 | 2 | no | — |
| 295 | C22×C4 | — | 6 | 1 | no | — |
| 296 | C22×C4 | — | 6 | 4 | no | — |
| 297 | C22×C4 | — | 6 | 4 | no | — |
| 298 | C22×C4 | — | 12 | 4 | no | — |
| 299 | C22×C4 | — | 24 | 2 | no | — |
| 300 | C22×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 301 | Q16 | — | 6 | 4 | no | — |
| 302 | Q16 | — | 6 | 2 | no | — |
| 303 | Q16 | — | 6 | 16 | no | — |
| 304 | Q16 | — | 6 | 2 | no | — |
| 305 | SD16 | — | 6 | 8 | no | — |
| 306 | SD16 | — | 6 | 4 | no | — |
| 307 | SD16 | — | 6 | 2 | no | — |
| 308 | SD16 | — | 6 | 16 | no | — |
| 309 | SD16 | — | 6 | 2 | no | — |
| 310 | D8 | — | 6 | 8 | no | — |
| 311 | M16 | — | 6 | 8 | no | — |
| 312 | C2×C8 | — | 3 | 4 | no | — |
| 313 | C2×C8 | — | 3 | 2 | no | — |
| 314 | C2×C8 | — | 3 | 2 | no | — |
| 315 | C2×C8 | — | 6 | 2 | no | — |
| 316 | C2×C8 | — | 6 | 2 | no | — |
| 317 | C2×C8 | — | 6 | 8 | no | — |
| 318 | C2×C8 | — | 6 | 4 | no | — |
| 319 | C4⋊C4 | — | 3 | 4 | no | — |
| 320 | C4⋊C4 | — | 6 | 2 | no | — |
| 321 | C4⋊C4 | — | 6 | 8 | no | — |
| 322 | C4⋊C4 | — | 6 | 4 | no | — |
| 323 | C22⋊C4 | — | 6 | 8 | no | — |
| 324 | C22⋊C4 | — | 6 | 8 | no | — |
| 325 | C22×C3 | — | 4 | 2 | no | — |
| 326 | C22×C3 | — | 4 | 2 | no | — |
| 327 | C22×C3 | — | 4 | 2 | no | — |
| 328 | C22×C3 | — | 4 | 1 | no | — |
| 329 | C22×C3 | — | 8 | 4 | no | — |
| 330 | C22×C3 | — | 8 | 4 | no | — |
| 331 | C22×C3 | — | 8 | 4 | no | — |
| 332 | C22×C3 | — | 16 | 8 | no | — |
| 333 | C2×D3 | — | 4 | 4 | no | — |
| 334 | C2×D3 | — | 8 | 2 | no | — |
| 335 | C2×D3 | — | 8 | 2 | no | — |
| 336 | C2×D3 | — | 8 | 8 | no | — |
| 337 | C3×C4 | — | 4 | 4 | no | — |
| 338 | Dic3 | — | 8 | 2 | no | — |
| 339 | Dic3 | — | 8 | 4 | no | — |
| 340 | C23 | — | 2 | 4 | no | — |
| 341 | C23 | — | 2 | 4 | no | — |
| 342 | C23 | — | 2 | 4 | no | — |
| 343 | C23 | — | 3 | 4 | no | — |
| 344 | C23 | — | 3 | 2 | no | — |
| 345 | C23 | — | 6 | 2 | no | — |
| 346 | C23 | — | 6 | 2 | no | — |
| 347 | C23 | — | 6 | 2 | no | — |
| 348 | C23 | — | 12 | 2 | no | — |
| 349 | C23 | — | 12 | 2 | no | — |
| 350 | C23 | — | 12 | 2 | no | — |
| 351 | C23 | C22×S4 | 1 | 4 | yes | — |
| 352 | C23 | C22×S4 | 1 | 1 | yes | characteristic |
| 353 | Q8 | — | 3 | 2 | no | — |
| 354 | Q8 | — | 3 | 1 | no | — |
| 355 | Q8 | — | 3 | 8 | no | — |
| 356 | Q8 | — | 6 | 1 | no | — |
| 357 | Q8 | — | 6 | 4 | no | — |
| 358 | Q8 | — | 6 | 8 | no | — |
| 359 | Q8 | — | 6 | 2 | no | — |
| 360 | Q8 | — | 6 | 2 | no | — |
| 361 | Q8 | — | 6 | 8 | no | — |
| 362 | Q8 | — | 12 | 2 | no | — |
| 363 | Q8 | C22×#67 | 1 | 1 | yes | characteristic |
| 364 | D4 | — | 2 | 8 | no | — |
| 365 | D4 | — | 3 | 4 | no | — |
| 366 | D4 | — | 6 | 2 | no | — |
| 367 | D4 | — | 6 | 4 | no | — |
| 368 | D4 | — | 6 | 2 | no | — |
| 369 | D4 | — | 6 | 2 | no | — |
| 370 | D4 | — | 6 | 16 | no | — |
| 371 | D4 | — | 12 | 2 | no | — |
| 372 | D4 | — | 12 | 8 | no | — |
| 373 | D4 | — | 24 | 8 | no | — |
| 374 | C2×C4 | — | 3 | 2 | no | — |
| 375 | C2×C4 | — | 3 | 2 | no | — |
| 376 | C2×C4 | — | 3 | 1 | no | — |
| 377 | C2×C4 | — | 3 | 1 | no | — |
| 378 | C2×C4 | — | 3 | 4 | no | — |
| 379 | C2×C4 | — | 3 | 4 | no | — |
| 380 | C2×C4 | — | 3 | 8 | no | — |
| 381 | C2×C4 | — | 3 | 4 | no | — |
| 382 | C2×C4 | — | 6 | 4 | no | — |
| 383 | C2×C4 | — | 6 | 4 | no | — |
| 384 | C2×C4 | — | 6 | 8 | no | — |
| 385 | C2×C4 | — | 6 | 16 | no | — |
| 386 | C2×C4 | — | 6 | 4 | no | — |
| 387 | C2×C4 | — | 6 | 4 | no | — |
| 388 | C2×C4 | — | 6 | 2 | no | — |
| 389 | C2×C4 | — | 12 | 4 | no | — |
| 390 | C2×C4 | — | 12 | 2 | no | — |
| 391 | C2×C4 | — | 12 | 8 | no | — |
| 392 | C2×C4 | — | 24 | 4 | no | — |
| 393 | C2×C4 | GL(2,ℤ/4) | 1 | 4 | yes | — |
| 394 | C2×C4 | C22×S4 | 1 | 2 | yes | — |
| 395 | C8 | — | 6 | 2 | no | — |
| 396 | C8 | — | 6 | 2 | no | — |
| 397 | C8 | — | 6 | 4 | no | — |
| 398 | C2×C3 | — | 4 | 4 | no | — |
| 399 | C2×C3 | — | 4 | 1 | no | — |
| 400 | C2×C3 | — | 4 | 1 | no | — |
| 401 | C2×C3 | — | 4 | 1 | no | — |
| 402 | C2×C3 | — | 16 | 4 | no | — |
| 403 | D3 | — | 8 | 4 | no | — |
| 404 | C22 | — | 2 | 4 | no | — |
| 405 | C22 | — | 2 | 4 | no | — |
| 406 | C22 | — | 2 | 4 | no | — |
| 407 | C22 | — | 3 | 4 | no | — |
| 408 | C22 | — | 4 | 8 | no | — |
| 409 | C22 | — | 6 | 8 | no | — |
| 410 | C22 | — | 6 | 2 | no | — |
| 411 | C22 | — | 6 | 2 | no | — |
| 412 | C22 | — | 12 | 2 | no | — |
| 413 | C22 | — | 12 | 2 | no | — |
| 414 | C22 | — | 12 | 2 | no | — |
| 415 | C22 | — | 24 | 4 | no | — |
| 416 | C22 | #5926 | 1 | 2 | yes | — |
| 417 | C22 | #5927 | 1 | 2 | yes | — |
| 418 | C22 | C2×GL(2,ℤ/4) | 1 | 2 | yes | — |
| 419 | C22 | C23×S4 | 1 | 1 | yes | characteristic |
| 420 | C4 | — | 3 | 1 | no | — |
| 421 | C4 | — | 3 | 1 | no | — |
| 422 | C4 | — | 3 | 2 | no | — |
| 423 | C4 | — | 6 | 4 | no | — |
| 424 | C4 | — | 12 | 4 | no | — |
| 425 | C4 | — | 12 | 2 | no | — |
| 426 | C4 | C2×GL(2,ℤ/4) | 1 | 4 | yes | — |
| 427 | C3 | — | 4 | 1 | no | Sylow |
| 428 | C2 | — | 4 | 4 | no | — |
| 429 | C2 | — | 6 | 4 | no | — |
| 430 | C2 | — | 24 | 2 | no | — |
| 431 | C2 | #85538 | 1 | 4 | yes | direct product factor |
| 432 | C2 | C2×#5926 | 1 | 1 | yes | characteristic |
| 433 | C2 | C2×#5927 | 1 | 1 | yes | characteristic |
| 434 | C2 | C22×GL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C22×S4 |
| commutator, cosocle | C2×SL(2,𝔽3) | C24 |
| Frattini | C22 | C23×S4 |
| Fitting | C22×2−1+4 | D3 |
| hypercenter | C22×D4 | S4 |
| hypocenter | SL(2,𝔽3) | C22×D4 |
| LCS | G ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3) | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×2−1+4⋊C3 | C2 | semidirect |
| 2. C22×#985 | C2 | semidirect |
| 3. #85538 | C2 | direct (N × H) |
| 4. C2×#5426 | C2 | semidirect |
| 5. C2×#5421 | C2 | semidirect |
| 6. C2×#5419 | C2 | semidirect |
| 9. C2×2−1+4⋊C3 | C22 | semidirect |
| 13. C2×#985 | C22 | semidirect |
| 17. #5426 | C22 | semidirect |
| 18. #5421 | C22 | semidirect |
| 19. #5419 | C22 | semidirect |
| 21. C22×2−1+4 | D3 | semidirect |
| 38. C2×#41⋊C3 | D4 | semidirect |
| 55. C2×2−1+4 | C2×D3 | semidirect |
| 111. #41⋊C3 | C2×D4 | semidirect |
| 137. C2×#41 | #67 | semidirect |
| 244. #41 | C2×#67 | semidirect |
| 431. C2 | #85538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×2−1+4⋊C3 | 2 |
| C22×#985 | 2 |
| #85538 | 2 |
| C2×#5426 | 2 |
| C2×#5421 | 2 |
| C2×#5419 | 2 |
| C2×#3013 | 3 |
| C2×#938 | 4 |