Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1616 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 1616 conjugacy classes of subgroups — too many to draw. Only its 161 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 | #86572 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #73824 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×#2029 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #71897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #69500 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #68965 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #68959 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #29684 | — | 3 | 1 | no | maximal, Sylow |
| 9 | C23×#67 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#543 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#953 | C22 | 1 | 3 | yes | — |
| 12 | #5645 | — | 2 | 3 | no | — |
| 13 | #5644 | — | 2 | 3 | no | — |
| 14 | #5627 | — | 2 | 3 | no | — |
| 15 | #5624 | — | 2 | 3 | no | — |
| 16 | #5493 | C22 | 1 | 3 | yes | — |
| 17 | C2×#884 | — | 2 | 3 | no | — |
| 18 | C2×#882 | C22 | 1 | 3 | yes | — |
| 19 | C2×#67⋊C4 | C22 | 1 | 3 | yes | — |
| 20 | C3×#379 | C22 | 1 | 3 | yes | — |
| 21 | #4960 | — | 2 | 3 | no | — |
| 22 | #4959 | — | 2 | 3 | no | — |
| 23 | #4957 | — | 2 | 3 | no | — |
| 24 | #4955 | C22 | 1 | 3 | yes | — |
| 25 | C2×#806 | C22 | 1 | 6 | yes | — |
| 26 | #4942 | C22 | 1 | 3 | yes | — |
| 27 | C3×#342 | C22 | 1 | 3 | yes | — |
| 28 | #4526 | C22 | 1 | 3 | yes | — |
| 29 | #3459 | — | 3 | 1 | no | — |
| 30 | #2408 | — | 3 | 3 | no | — |
| 31 | #2029 | — | 3 | 1 | no | — |
| 32 | #2029 | D3 | 1 | 1 | yes | characteristic, complemented |
| 33 | #2021 | — | 3 | 3 | no | — |
| 34 | #2021 | — | 3 | 3 | no | — |
| 35 | #1799 | — | 3 | 3 | no | — |
| 36 | C25×C3 | C23 | 1 | 1 | yes | characteristic |
| 37 | C24×D3 | C23 | 1 | 1 | yes | characteristic |
| 38 | C22×#67 | — | 2 | 3 | no | — |
| 39 | C22×#67 | — | 2 | 3 | no | — |
| 40 | C22×#67 | — | 2 | 3 | no | — |
| 41 | C22×#67 | — | 4 | 4 | no | — |
| 42 | C22×#67 | C23 | 1 | 3 | yes | — |
| 43 | C23×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×#239 | — | 2 | 1 | no | — |
| 45 | C22×D12 | — | 2 | 3 | no | — |
| 46 | C22×C4×D3 | D4 | 1 | 3 | yes | complemented |
| 47 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 48 | C3×C22⋊Q8 | — | 2 | 3 | no | — |
| 49 | C2×C3×C22⋊C4 | — | 2 | 3 | no | — |
| 50 | C2×C3×C22⋊C4 | — | 2 | 3 | no | — |
| 51 | C2×C3×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 52 | C2×C3×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 53 | #953 | — | 4 | 6 | no | — |
| 54 | C2×#217 | — | 2 | 3 | no | — |
| 55 | C2×#217 | C23 | 1 | 3 | yes | — |
| 56 | #947 | — | 2 | 3 | no | — |
| 57 | #946 | — | 2 | 3 | no | — |
| 58 | Q8×Dic3 | — | 2 | 1 | no | — |
| 59 | #930 | — | 2 | 3 | no | — |
| 60 | #930 | — | 2 | 3 | no | — |
| 61 | C2×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 62 | C2×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 63 | C2×(C2×D3)⋊C4 | — | 2 | 3 | no | — |
| 64 | C2×(C2×D3)⋊C4 | D4 | 1 | 3 | yes | complemented |
| 65 | C2×Dic3⋊C4 | — | 2 | 3 | no | — |
| 66 | C2×Dic3⋊C4 | D4 | 1 | 3 | yes | complemented |
| 67 | C2×C4×Dic3 | D4 | 1 | 3 | yes | complemented |
| 68 | #898 | — | 2 | 6 | no | — |
| 69 | #895 | — | 2 | 3 | no | — |
| 70 | #894 | — | 2 | 6 | no | — |
| 71 | #893 | — | 2 | 3 | no | — |
| 72 | #892 | — | 2 | 3 | no | — |
| 73 | #890 | — | 2 | 3 | no | — |
| 74 | #886 | — | 2 | 6 | no | — |
| 75 | #884 | — | 4 | 12 | no | — |
| 76 | #882 | — | 2 | 6 | no | — |
| 77 | #882 | — | 4 | 6 | no | — |
| 78 | #67⋊C4 | — | 2 | 6 | no | — |
| 79 | #67⋊C4 | — | 2 | 6 | no | — |
| 80 | C3⋊#95 | — | 2 | 3 | no | — |
| 81 | #806 | — | 4 | 6 | no | — |
| 82 | C23×D4 | — | 3 | 1 | no | — |
| 83 | #543 | C2×D3 | 1 | 1 | yes | characteristic |
| 84 | #539 | — | 6 | 3 | no | — |
| 85 | #538 | — | 6 | 3 | no | — |
| 86 | #534 | — | 3 | 3 | no | — |
| 87 | #529 | — | 6 | 3 | no | — |
| 88 | #525 | — | 6 | 3 | no | — |
| 89 | C2×#121 | — | 6 | 3 | no | — |
| 90 | C2×#120 | — | 3 | 3 | no | — |
| 91 | C2×#120 | — | 3 | 3 | no | — |
| 92 | C2×C4×D4 | — | 3 | 3 | no | — |
| 93 | C2×#99 | — | 3 | 6 | no | — |
| 94 | #394 | — | 6 | 3 | no | — |
| 95 | #392 | — | 6 | 3 | no | — |
| 96 | #390 | — | 6 | 3 | no | — |
| 97 | #380 | — | 3 | 3 | no | — |
| 98 | #379 | — | 3 | 3 | no | — |
| 99 | #379 | C2×D3 | 1 | 3 | yes | — |
| 100 | #342 | — | 3 | 3 | no | — |
| 101 | #342 | C2×D3 | 1 | 3 | yes | — |
| 102 | C24×C3 | — | 2 | 3 | no | — |
| 103 | C24×C3 | — | 2 | 3 | no | — |
| 104 | C24×C3 | — | 2 | 1 | no | — |
| 105 | C24×C3 | — | 4 | 2 | no | — |
| 106 | C24×C3 | — | 8 | 1 | no | — |
| 107 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 108 | C23×D3 | — | 2 | 3 | no | — |
| 109 | C23×D3 | — | 2 | 3 | no | — |
| 110 | C23×D3 | — | 2 | 1 | no | — |
| 111 | C23×D3 | — | 4 | 2 | no | — |
| 112 | C23×D3 | — | 8 | 1 | no | — |
| 113 | C23×D3 | C2×D4 | 1 | 3 | yes | — |
| 114 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 115 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 116 | C22×C3×C4 | — | 2 | 3 | no | — |
| 117 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 118 | C22×C3×C4 | C2×D4 | 1 | 3 | yes | — |
| 119 | C2×#67 | — | 2 | 12 | no | — |
| 120 | C2×#67 | — | 2 | 6 | no | — |
| 121 | C2×#67 | — | 2 | 3 | no | — |
| 122 | C2×#67 | — | 2 | 6 | no | — |
| 123 | C2×#67 | — | 2 | 3 | no | — |
| 124 | C2×#67 | — | 4 | 6 | no | — |
| 125 | C2×#67 | — | 4 | 6 | no | — |
| 126 | C2×#67 | — | 4 | 6 | no | — |
| 127 | C2×#67 | — | 4 | 6 | no | — |
| 128 | C2×#67 | — | 4 | 6 | no | — |
| 129 | C2×#67 | — | 4 | 3 | no | — |
| 130 | C2×#67 | — | 4 | 1 | no | — |
| 131 | C2×#67 | — | 8 | 3 | no | — |
| 132 | C22×Dic3 | — | 2 | 3 | no | — |
| 133 | C22×Dic3 | — | 4 | 2 | no | — |
| 134 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 135 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 136 | C22×Dic3 | C2×D4 | 1 | 3 | yes | — |
| 137 | #239 | — | 8 | 2 | no | — |
| 138 | C2×D12 | — | 2 | 3 | no | — |
| 139 | C2×D12 | — | 2 | 3 | no | — |
| 140 | C2×D12 | — | 4 | 6 | no | — |
| 141 | C2×D12 | — | 4 | 6 | no | — |
| 142 | C2×D12 | — | 8 | 3 | no | — |
| 143 | C2×C4×D3 | — | 2 | 3 | no | — |
| 144 | C2×C4×D3 | — | 2 | 3 | no | — |
| 145 | C2×C4×D3 | — | 4 | 6 | no | — |
| 146 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 147 | C3×C4⋊C4 | — | 2 | 3 | no | — |
| 148 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 149 | C3×C22⋊C4 | — | 2 | 6 | no | — |
| 150 | C3×C22⋊C4 | — | 4 | 6 | no | — |
| 151 | C3×C22⋊C4 | — | 8 | 3 | no | — |
| 152 | #217 | — | 2 | 6 | no | — |
| 153 | #217 | — | 4 | 6 | no | — |
| 154 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 155 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 156 | (C2×D3)⋊C4 | — | 2 | 6 | no | — |
| 157 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 158 | (C2×D3)⋊C4 | — | 4 | 6 | no | — |
| 159 | (C2×D3)⋊C4 | — | 8 | 3 | no | — |
| 160 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 161 | C4⋊Dic3 | — | 2 | 3 | no | — |
| 162 | Dic3⋊C4 | — | 2 | 6 | no | — |
| 163 | Dic3⋊C4 | — | 4 | 6 | no | — |
| 164 | C4×Dic3 | — | 2 | 3 | no | — |
| 165 | C4×Dic3 | — | 2 | 3 | no | — |
| 166 | C25 | — | 3 | 1 | no | — |
| 167 | C25 | C22×D3 | 1 | 1 | yes | characteristic |
| 168 | C2×#41 | — | 6 | 1 | no | — |
| 169 | C22×D4 | — | 3 | 3 | no | — |
| 170 | C22×D4 | — | 6 | 3 | no | — |
| 171 | C22×D4 | — | 6 | 3 | no | — |
| 172 | C22×D4 | — | 6 | 3 | no | — |
| 173 | C22×D4 | — | 6 | 3 | no | — |
| 174 | C22×D4 | — | 12 | 4 | no | — |
| 175 | C23×C4 | — | 3 | 1 | no | — |
| 176 | C23×C4 | — | 3 | 3 | no | — |
| 177 | #126 | — | 6 | 6 | no | — |
| 178 | #125 | — | 6 | 3 | no | — |
| 179 | #124 | — | 6 | 3 | no | — |
| 180 | #123 | — | 6 | 6 | no | — |
| 181 | #123 | — | 6 | 6 | no | — |
| 182 | C22⋊Q8 | — | 2 | 3 | no | — |
| 183 | C22⋊Q8 | — | 2 | 3 | no | — |
| 184 | C22⋊Q8 | — | 6 | 3 | no | — |
| 185 | #121 | — | 6 | 3 | no | — |
| 186 | #121 | — | 6 | 3 | no | — |
| 187 | #121 | — | 6 | 3 | no | — |
| 188 | #121 | — | 12 | 12 | no | — |
| 189 | #120 | — | 6 | 6 | no | — |
| 190 | #120 | — | 12 | 6 | no | — |
| 191 | #120 | — | 12 | 6 | no | — |
| 192 | C4×Q8 | — | 6 | 1 | no | — |
| 193 | C4×D4 | — | 6 | 6 | no | — |
| 194 | C4×D4 | — | 6 | 6 | no | — |
| 195 | C4×D4 | — | 6 | 3 | no | — |
| 196 | #117 | — | 6 | 3 | no | — |
| 197 | C2×C4⋊C4 | — | 3 | 3 | no | — |
| 198 | C2×C4⋊C4 | — | 6 | 3 | no | — |
| 199 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 200 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 201 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 202 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 203 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 204 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 205 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 206 | C2×C22⋊C4 | — | 6 | 3 | no | — |
| 207 | C2×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 208 | C2×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 209 | C2×C42 | — | 3 | 3 | no | — |
| 210 | #99 | — | 12 | 6 | no | — |
| 211 | #95 | — | 6 | 3 | no | — |
| 212 | C23×C3 | — | 2 | 6 | no | — |
| 213 | C23×C3 | — | 4 | 1 | no | — |
| 214 | C23×C3 | — | 4 | 1 | no | — |
| 215 | C23×C3 | — | 4 | 3 | no | — |
| 216 | C23×C3 | — | 4 | 3 | no | — |
| 217 | C23×C3 | — | 4 | 3 | no | — |
| 218 | C23×C3 | — | 4 | 1 | no | — |
| 219 | C23×C3 | — | 4 | 3 | no | — |
| 220 | C23×C3 | — | 4 | 3 | no | — |
| 221 | C23×C3 | — | 8 | 6 | no | — |
| 222 | C23×C3 | — | 8 | 2 | no | — |
| 223 | C23×C3 | C22×D4 | 1 | 3 | yes | — |
| 224 | C23×C3 | H(5,𝔽2) | 1 | 3 | yes | — |
| 225 | C23×C3 | 2−1+4 | 1 | 1 | yes | characteristic |
| 226 | C22×D3 | — | 2 | 6 | no | — |
| 227 | C22×D3 | — | 2 | 3 | no | — |
| 228 | C22×D3 | — | 2 | 3 | no | — |
| 229 | C22×D3 | — | 2 | 3 | no | — |
| 230 | C22×D3 | — | 4 | 3 | no | — |
| 231 | C22×D3 | — | 4 | 3 | no | — |
| 232 | C22×D3 | — | 4 | 3 | no | — |
| 233 | C22×D3 | — | 4 | 3 | no | — |
| 234 | C22×D3 | — | 4 | 3 | no | — |
| 235 | C22×D3 | — | 4 | 1 | no | — |
| 236 | C22×D3 | — | 4 | 3 | no | — |
| 237 | C22×D3 | — | 4 | 3 | no | — |
| 238 | C22×D3 | — | 8 | 6 | no | — |
| 239 | C22×D3 | — | 8 | 2 | no | — |
| 240 | C3×Q8 | — | 8 | 1 | no | — |
| 241 | C3×Q8 | — | 8 | 1 | no | — |
| 242 | C2×C3×C4 | — | 2 | 3 | no | — |
| 243 | C2×C3×C4 | — | 2 | 3 | no | — |
| 244 | C2×C3×C4 | — | 4 | 3 | no | — |
| 245 | C2×C3×C4 | — | 4 | 3 | no | — |
| 246 | C2×C3×C4 | — | 4 | 3 | no | — |
| 247 | C2×C3×C4 | — | 4 | 3 | no | — |
| 248 | C2×C3×C4 | — | 4 | 3 | no | — |
| 249 | #67 | — | 4 | 12 | no | — |
| 250 | #67 | — | 4 | 6 | no | — |
| 251 | #67 | — | 4 | 6 | no | — |
| 252 | #67 | — | 4 | 4 | no | — |
| 253 | #67 | — | 8 | 12 | no | — |
| 254 | C2×Dic3 | — | 2 | 6 | no | — |
| 255 | C2×Dic3 | — | 2 | 3 | no | — |
| 256 | C2×Dic3 | — | 2 | 3 | no | — |
| 257 | C2×Dic3 | — | 2 | 3 | no | — |
| 258 | C2×Dic3 | — | 4 | 3 | no | — |
| 259 | C2×Dic3 | — | 4 | 3 | no | — |
| 260 | C2×Dic3 | — | 4 | 3 | no | — |
| 261 | C2×Dic3 | — | 4 | 3 | no | — |
| 262 | C2×Dic3 | #120 | 1 | 3 | yes | — |
| 263 | C2×Dic3 | #120 | 1 | 1 | yes | characteristic |
| 264 | D12 | — | 8 | 3 | no | — |
| 265 | D12 | — | 8 | 3 | no | — |
| 266 | D12 | — | 8 | 12 | no | — |
| 267 | C4×D3 | — | 4 | 6 | no | — |
| 268 | C4×D3 | — | 8 | 3 | no | — |
| 269 | C24 | — | 2 | 3 | no | — |
| 270 | C24 | — | 2 | 1 | no | — |
| 271 | C24 | — | 2 | 3 | no | — |
| 272 | C24 | — | 3 | 3 | no | — |
| 273 | C24 | — | 4 | 2 | no | — |
| 274 | C24 | — | 6 | 3 | no | — |
| 275 | C24 | — | 6 | 1 | no | — |
| 276 | C24 | — | 6 | 3 | no | — |
| 277 | C24 | — | 8 | 1 | no | — |
| 278 | C24 | — | 12 | 2 | no | — |
| 279 | C24 | — | 24 | 1 | no | — |
| 280 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 281 | #41 | — | 24 | 2 | no | — |
| 282 | C2×Q8 | — | 2 | 1 | no | — |
| 283 | C2×Q8 | — | 2 | 1 | no | — |
| 284 | C2×D4 | — | 6 | 3 | no | — |
| 285 | C2×D4 | — | 6 | 3 | no | — |
| 286 | C2×D4 | — | 6 | 12 | no | — |
| 287 | C2×D4 | — | 6 | 6 | no | — |
| 288 | C2×D4 | — | 6 | 3 | no | — |
| 289 | C2×D4 | — | 6 | 3 | no | — |
| 290 | C2×D4 | — | 6 | 6 | no | — |
| 291 | C2×D4 | — | 12 | 1 | no | — |
| 292 | C2×D4 | — | 12 | 3 | no | — |
| 293 | C2×D4 | — | 12 | 6 | no | — |
| 294 | C2×D4 | — | 12 | 6 | no | — |
| 295 | C2×D4 | — | 12 | 6 | no | — |
| 296 | C2×D4 | — | 12 | 6 | no | — |
| 297 | C2×D4 | — | 12 | 6 | no | — |
| 298 | C2×D4 | — | 12 | 6 | no | — |
| 299 | C2×D4 | — | 12 | 6 | no | — |
| 300 | C2×D4 | — | 24 | 3 | no | — |
| 301 | C2×D4 | — | 24 | 3 | no | — |
| 302 | C22×C4 | — | 2 | 3 | no | — |
| 303 | C22×C4 | — | 3 | 3 | no | — |
| 304 | C22×C4 | — | 3 | 3 | no | — |
| 305 | C22×C4 | — | 3 | 3 | no | — |
| 306 | C22×C4 | — | 6 | 3 | no | — |
| 307 | C22×C4 | — | 6 | 3 | no | — |
| 308 | C22×C4 | — | 6 | 3 | no | — |
| 309 | C22×C4 | — | 12 | 6 | no | — |
| 310 | C22×C4 | — | 12 | 2 | no | — |
| 311 | C22×C4 | D3×D4 | 1 | 3 | yes | — |
| 312 | C22×C4 | D3×D4 | 1 | 3 | yes | — |
| 313 | C4⋊C4 | — | 2 | 3 | no | — |
| 314 | C4⋊C4 | — | 2 | 3 | no | — |
| 315 | C4⋊C4 | — | 6 | 6 | no | — |
| 316 | C4⋊C4 | — | 6 | 3 | no | — |
| 317 | C4⋊C4 | — | 6 | 3 | no | — |
| 318 | C4⋊C4 | — | 12 | 6 | no | — |
| 319 | C22⋊C4 | — | 2 | 6 | no | — |
| 320 | C22⋊C4 | — | 2 | 6 | no | — |
| 321 | C22⋊C4 | — | 4 | 6 | no | — |
| 322 | C22⋊C4 | — | 6 | 6 | no | — |
| 323 | C22⋊C4 | — | 6 | 6 | no | — |
| 324 | C22⋊C4 | — | 6 | 6 | no | — |
| 325 | C22⋊C4 | — | 6 | 6 | no | — |
| 326 | C22⋊C4 | — | 8 | 3 | no | — |
| 327 | C22⋊C4 | — | 12 | 6 | no | — |
| 328 | C22⋊C4 | — | 12 | 6 | no | — |
| 329 | C22⋊C4 | — | 12 | 6 | no | — |
| 330 | C22⋊C4 | — | 24 | 3 | no | — |
| 331 | C42 | — | 6 | 3 | no | — |
| 332 | C42 | — | 6 | 3 | no | — |
| 333 | C22×C3 | — | 2 | 3 | no | — |
| 334 | C22×C3 | — | 2 | 3 | no | — |
| 335 | C22×C3 | — | 4 | 3 | no | — |
| 336 | C22×C3 | — | 4 | 1 | no | — |
| 337 | C22×C3 | — | 4 | 6 | no | — |
| 338 | C22×C3 | — | 4 | 6 | no | — |
| 339 | C22×C3 | — | 4 | 2 | no | — |
| 340 | C22×C3 | — | 8 | 3 | no | — |
| 341 | C22×C3 | — | 8 | 3 | no | — |
| 342 | C22×C3 | — | 8 | 1 | no | — |
| 343 | C22×C3 | — | 8 | 1 | no | — |
| 344 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 345 | C22×C3 | #535 | 1 | 3 | yes | — |
| 346 | C22×C3 | #537 | 1 | 3 | yes | — |
| 347 | C2×D3 | — | 4 | 6 | no | — |
| 348 | C2×D3 | — | 4 | 6 | no | — |
| 349 | C2×D3 | — | 4 | 6 | no | — |
| 350 | C2×D3 | — | 4 | 3 | no | — |
| 351 | C2×D3 | — | 4 | 3 | no | — |
| 352 | C2×D3 | — | 4 | 2 | no | — |
| 353 | C2×D3 | — | 4 | 3 | no | — |
| 354 | C2×D3 | — | 8 | 3 | no | — |
| 355 | C2×D3 | — | 8 | 3 | no | — |
| 356 | C2×D3 | — | 8 | 1 | no | — |
| 357 | C2×D3 | — | 8 | 1 | no | — |
| 358 | C2×D3 | — | 8 | 3 | no | — |
| 359 | C3×C4 | — | 4 | 3 | no | — |
| 360 | C3×C4 | — | 4 | 3 | no | — |
| 361 | C3×C4 | — | 8 | 3 | no | — |
| 362 | Dic3 | — | 2 | 3 | no | — |
| 363 | Dic3 | — | 4 | 3 | no | — |
| 364 | Dic3 | — | 8 | 3 | no | — |
| 365 | Dic3 | B(4,𝔽2) | 1 | 2 | yes | — |
| 366 | C23 | — | 2 | 6 | no | — |
| 367 | C23 | — | 4 | 1 | no | — |
| 368 | C23 | — | 4 | 1 | no | — |
| 369 | C23 | — | 4 | 3 | no | — |
| 370 | C23 | — | 4 | 3 | no | — |
| 371 | C23 | — | 4 | 3 | no | — |
| 372 | C23 | — | 4 | 3 | no | — |
| 373 | C23 | — | 4 | 1 | no | — |
| 374 | C23 | — | 4 | 3 | no | — |
| 375 | C23 | — | 6 | 6 | no | — |
| 376 | C23 | — | 6 | 3 | no | — |
| 377 | C23 | — | 6 | 3 | no | — |
| 378 | C23 | — | 6 | 3 | no | — |
| 379 | C23 | — | 8 | 2 | no | — |
| 380 | C23 | — | 8 | 6 | no | — |
| 381 | C23 | — | 12 | 3 | no | — |
| 382 | C23 | — | 12 | 3 | no | — |
| 383 | C23 | — | 12 | 3 | no | — |
| 384 | C23 | — | 12 | 3 | no | — |
| 385 | C23 | — | 12 | 3 | no | — |
| 386 | C23 | — | 12 | 3 | no | — |
| 387 | C23 | — | 12 | 1 | no | — |
| 388 | C23 | — | 12 | 3 | no | — |
| 389 | C23 | — | 24 | 2 | no | — |
| 390 | C23 | — | 24 | 6 | no | — |
| 391 | C23 | C2×D3×D4 | 1 | 3 | yes | — |
| 392 | C23 | #1007 | 1 | 1 | yes | characteristic |
| 393 | C23 | #1009 | 1 | 3 | yes | — |
| 394 | Q8 | — | 8 | 1 | no | — |
| 395 | Q8 | — | 8 | 1 | no | — |
| 396 | D4 | — | 12 | 4 | no | — |
| 397 | D4 | — | 12 | 12 | no | — |
| 398 | D4 | — | 12 | 6 | no | — |
| 399 | D4 | — | 12 | 6 | no | — |
| 400 | D4 | — | 24 | 3 | no | — |
| 401 | D4 | — | 24 | 3 | no | — |
| 402 | D4 | — | 24 | 12 | no | — |
| 403 | D4 | — | 24 | 12 | no | — |
| 404 | C2×C4 | — | 2 | 3 | no | — |
| 405 | C2×C4 | — | 2 | 3 | no | — |
| 406 | C2×C4 | — | 3 | 1 | no | — |
| 407 | C2×C4 | — | 3 | 3 | no | — |
| 408 | C2×C4 | — | 4 | 3 | no | — |
| 409 | C2×C4 | — | 4 | 3 | no | — |
| 410 | C2×C4 | — | 4 | 3 | no | — |
| 411 | C2×C4 | — | 4 | 3 | no | — |
| 412 | C2×C4 | — | 4 | 3 | no | — |
| 413 | C2×C4 | — | 6 | 6 | no | — |
| 414 | C2×C4 | — | 6 | 3 | no | — |
| 415 | C2×C4 | — | 6 | 3 | no | — |
| 416 | C2×C4 | — | 6 | 3 | no | — |
| 417 | C2×C4 | — | 12 | 6 | no | — |
| 418 | C2×C4 | — | 12 | 3 | no | — |
| 419 | C2×C4 | — | 12 | 3 | no | — |
| 420 | C2×C4 | — | 12 | 3 | no | — |
| 421 | C2×C4 | — | 12 | 3 | no | — |
| 422 | C2×C4 | — | 24 | 3 | no | — |
| 423 | C2×C3 | — | 2 | 3 | no | — |
| 424 | C2×C3 | — | 2 | 3 | no | — |
| 425 | C2×C3 | — | 8 | 2 | no | — |
| 426 | C2×C3 | #2615 | 1 | 1 | yes | characteristic |
| 427 | C2×C3 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 428 | C2×C3 | #3027 | 1 | 1 | yes | characteristic |
| 429 | D3 | — | 8 | 2 | no | — |
| 430 | D3 | — | 8 | 3 | no | — |
| 431 | C22 | — | 2 | 3 | no | — |
| 432 | C22 | — | 2 | 3 | no | — |
| 433 | C22 | — | 4 | 1 | no | — |
| 434 | C22 | — | 4 | 3 | no | — |
| 435 | C22 | — | 4 | 6 | no | — |
| 436 | C22 | — | 4 | 6 | no | — |
| 437 | C22 | — | 4 | 2 | no | — |
| 438 | C22 | — | 8 | 3 | no | — |
| 439 | C22 | — | 8 | 3 | no | — |
| 440 | C22 | — | 8 | 1 | no | — |
| 441 | C22 | — | 8 | 1 | no | — |
| 442 | C22 | — | 12 | 6 | no | — |
| 443 | C22 | — | 12 | 6 | no | — |
| 444 | C22 | — | 12 | 6 | no | — |
| 445 | C22 | — | 12 | 3 | no | — |
| 446 | C22 | — | 12 | 3 | no | — |
| 447 | C22 | — | 12 | 3 | no | — |
| 448 | C22 | — | 12 | 2 | no | — |
| 449 | C22 | — | 24 | 3 | no | — |
| 450 | C22 | — | 24 | 3 | no | — |
| 451 | C22 | — | 24 | 3 | no | — |
| 452 | C22 | — | 24 | 1 | no | — |
| 453 | C22 | — | 24 | 1 | no | — |
| 454 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 455 | C22 | #5629 | 1 | 3 | yes | — |
| 456 | C22 | #5674 | 1 | 3 | yes | — |
| 457 | C4 | — | 3 | 2 | no | — |
| 458 | C4 | — | 4 | 3 | no | — |
| 459 | C4 | — | 4 | 3 | no | — |
| 460 | C4 | — | 6 | 3 | no | — |
| 461 | C4 | — | 8 | 3 | no | — |
| 462 | C4 | — | 12 | 3 | no | — |
| 463 | C4 | — | 24 | 3 | no | — |
| 464 | C3 | #29684 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 465 | C2 | — | 2 | 3 | no | — |
| 466 | C2 | — | 2 | 3 | no | — |
| 467 | C2 | — | 8 | 2 | no | — |
| 468 | C2 | — | 24 | 2 | no | — |
| 469 | C2 | — | 24 | 3 | no | — |
| 470 | C2 | #76809 | 1 | 1 | yes | characteristic |
| 471 | C2 | #80305 | 1 | 1 | yes | characteristic |
| 472 | C2 | D3×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D3×#120 |
| commutator, cosocle | C24×C3 | C24 |
| Frattini | C24 | C23×D3 |
| Fitting | C3×#2029 | C2 |
| socle | C22×C3 | C2×#120 |
| hypercenter | #2029 | D3 |
| hypocenter | C3 | #29684 |
| LCS | G ▷ C24×C3 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ #2029 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #86572 | C2 | semidirect |
| 2. #73824 | C2 | semidirect |
| 3. C3×#2029 | C2 | semidirect |
| 4. #71897 | C2 | semidirect |
| 5. #69500 | C2 | semidirect |
| 6. #68965 | C2 | semidirect |
| 7. #68959 | C2 | semidirect |
| 32. #2029 | D3 | semidirect |
| 46. C22×C4×D3 | D4 | semidirect |
| 64. C2×(C2×D3)⋊C4 | D4 | semidirect |
| 66. C2×Dic3⋊C4 | D4 | semidirect |
| 67. C2×C4×Dic3 | D4 | semidirect |
| 464. C3 | #29684 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #86572 | 2 |
| #73824 | 2 |
| C3×#2029 | 2 |
| #71897 | 2 |
| #69500 | 2 |
| #68965 | 2 |
| #68959 | 2 |
| #29684 | 3 |