Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3409 conjugacy classes of subgroups.
The subgroup lattice has 499 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×#634 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#64298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5791 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595501 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10594921 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594918 | C2 | 1 | 8 | yes | maximal, complemented |
| 7 | #10594915 | C2 | 1 | 8 | yes | maximal, complemented |
| 8 | #10594856 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594828 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #86022 | — | 3 | 2 | no | maximal |
| 11 | C23×C32×C4 | C22 | 1 | 1 | yes | characteristic |
| 12 | C23×C3⋊Dic3 | C22 | 1 | 2 | yes | — |
| 13 | C22×#634 | — | 2 | 8 | no | — |
| 14 | C22×#634 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×#634 | C22 | 1 | 8 | yes | — |
| 16 | C22×#634 | C22 | 1 | 2 | yes | — |
| 17 | C22×#634 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C3×#235 | C22 | 1 | 2 | yes | — |
| 19 | C2×#3805 | C22 | 1 | 4 | yes | — |
| 20 | #64298 | — | 2 | 8 | no | — |
| 21 | C2×#3795 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×D3×Dic6 | C22 | 1 | 4 | yes | complemented |
| 23 | C3×#953 | C22 | 1 | 4 | yes | — |
| 24 | C3×#930 | C22 | 1 | 4 | yes | — |
| 25 | C3×#929 | C22 | 1 | 4 | yes | — |
| 26 | C3×C4×#67 | C22 | 1 | 8 | yes | — |
| 27 | C3×#926 | C22 | 1 | 2 | yes | — |
| 28 | C3×#924 | C22 | 1 | 4 | yes | — |
| 29 | #63982 | C22 | 1 | 8 | yes | — |
| 30 | #63980 | C22 | 1 | 8 | yes | — |
| 31 | #67⋊Dic3 | C22 | 1 | 16 | yes | — |
| 32 | #63962 | C22 | 1 | 8 | yes | — |
| 33 | #63957 | C22 | 1 | 4 | yes | — |
| 34 | #63913 | C22 | 1 | 8 | yes | complemented |
| 35 | #63896 | C22 | 1 | 16 | yes | complemented |
| 36 | #63866 | C22 | 1 | 4 | yes | complemented |
| 37 | #63860 | C22 | 1 | 4 | yes | complemented |
| 38 | #63857 | C22 | 1 | 8 | yes | complemented |
| 39 | #63844 | C22 | 1 | 8 | yes | complemented |
| 40 | #63840 | C22 | 1 | 8 | yes | complemented |
| 41 | C2×#1010 | — | 3 | 2 | no | — |
| 42 | C23×Dic6 | — | 3 | 2 | no | — |
| 43 | C23×Dic6 | — | 6 | 1 | no | — |
| 44 | C3×#525 | — | 3 | 2 | no | — |
| 45 | #5825 | — | 3 | 2 | no | — |
| 46 | #5791 | D3 | 1 | 2 | yes | complemented |
| 47 | #5648 | — | 3 | 8 | no | — |
| 48 | #5632 | — | 3 | 8 | no | — |
| 49 | #5598 | — | 3 | 8 | no | — |
| 50 | #5586 | — | 3 | 8 | no | — |
| 51 | #5552 | — | 3 | 8 | no | — |
| 52 | D4×Dic6 | — | 3 | 8 | no | — |
| 53 | #5526 | — | 3 | 2 | no | — |
| 54 | #5516 | — | 3 | 2 | no | — |
| 55 | C24×C32 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×C32×C4 | — | 2 | 4 | no | — |
| 57 | C22×C32×C4 | C23 | 1 | 4 | yes | — |
| 58 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 59 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 60 | C22×C3⋊Dic3 | — | 2 | 8 | no | — |
| 61 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 62 | C22×C3⋊Dic3 | C23 | 1 | 8 | yes | — |
| 63 | C22×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 64 | C2×#634 | — | 2 | 4 | no | — |
| 65 | C2×#634 | — | 2 | 8 | no | — |
| 66 | C2×#634 | — | 2 | 32 | no | — |
| 67 | C2×#634 | D4 | 1 | 8 | yes | complemented |
| 68 | C2×#634 | C23 | 1 | 8 | yes | — |
| 69 | C2×#634 | C23 | 1 | 4 | yes | — |
| 70 | C2×#634 | C23 | 1 | 4 | yes | — |
| 71 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 72 | C2×C3×#67 | C23 | 1 | 4 | yes | — |
| 73 | C3×#235 | — | 2 | 8 | no | — |
| 74 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 75 | C2×C3×C4×D3 | C23 | 1 | 4 | yes | — |
| 76 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 77 | C2×#627 | C23 | 1 | 4 | yes | — |
| 78 | C2×#625 | C23 | 1 | 4 | yes | — |
| 79 | #3805 | — | 2 | 16 | no | — |
| 80 | C2×D3×Dic3 | C23 | 1 | 8 | yes | — |
| 81 | #3795 | — | 2 | 16 | no | — |
| 82 | D3×Dic6 | — | 2 | 16 | no | — |
| 83 | C3×#217 | C23 | 1 | 8 | yes | — |
| 84 | C3×#217 | C23 | 1 | 4 | yes | — |
| 85 | C3×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 86 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 87 | C3×Dic3⋊C4 | C23 | 1 | 8 | yes | — |
| 88 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 89 | #3724 | C23 | 1 | 8 | yes | — |
| 90 | Dic3⋊Dic3 | C23 | 1 | 16 | yes | — |
| 91 | (C2×D3)⋊Dic3 | C23 | 1 | 16 | yes | — |
| 92 | Dic32 | C23 | 1 | 8 | yes | — |
| 93 | #3486 | — | 9 | 1 | no | Sylow |
| 94 | C2×C3×#41 | — | 3 | 2 | no | — |
| 95 | C23×C3×C4 | — | 2 | 1 | no | — |
| 96 | C23×C3×C4 | C2×D3 | 1 | 2 | yes | — |
| 97 | C23×Dic3 | — | 3 | 4 | no | — |
| 98 | C23×Dic3 | — | 6 | 2 | no | — |
| 99 | #1010 | — | 6 | 16 | no | — |
| 100 | C2×D3×Q8 | — | 3 | 4 | no | — |
| 101 | C2×#237 | — | 3 | 8 | no | — |
| 102 | C2×#237 | — | 3 | 4 | no | — |
| 103 | C2×#235 | — | 3 | 4 | no | — |
| 104 | C2×#235 | C2×D3 | 1 | 2 | yes | — |
| 105 | C22×Dic6 | — | 3 | 2 | no | — |
| 106 | C22×Dic6 | — | 3 | 8 | no | — |
| 107 | C22×Dic6 | — | 3 | 4 | no | — |
| 108 | C22×Dic6 | — | 3 | 2 | no | — |
| 109 | C22×Dic6 | — | 3 | 8 | no | — |
| 110 | C22×Dic6 | — | 3 | 4 | no | — |
| 111 | C22×Dic6 | — | 6 | 1 | no | — |
| 112 | C22×Dic6 | — | 6 | 1 | no | — |
| 113 | C22×Dic6 | — | 6 | 2 | no | — |
| 114 | C22×Dic6 | — | 6 | 8 | no | — |
| 115 | C22×Dic6 | — | 6 | 16 | no | — |
| 116 | C22×Dic6 | — | 6 | 16 | no | — |
| 117 | C3×#123 | — | 3 | 4 | no | — |
| 118 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 119 | C3×#121 | — | 3 | 4 | no | — |
| 120 | C3×#120 | — | 3 | 4 | no | — |
| 121 | C3×C4×D4 | — | 3 | 8 | no | — |
| 122 | C3×#117 | — | 3 | 2 | no | — |
| 123 | #953 | C2×D3 | 1 | 4 | yes | — |
| 124 | #944 | — | 3 | 4 | no | — |
| 125 | #939 | — | 3 | 16 | no | — |
| 126 | #936 | — | 3 | 4 | no | — |
| 127 | #935 | — | 3 | 8 | no | — |
| 128 | D4×Dic3 | — | 3 | 16 | no | — |
| 129 | #930 | C2×D3 | 1 | 4 | yes | — |
| 130 | #929 | C2×D3 | 1 | 4 | yes | — |
| 131 | C4×#67 | C2×D3 | 1 | 8 | yes | — |
| 132 | #926 | C2×D3 | 1 | 2 | yes | — |
| 133 | #924 | — | 3 | 8 | no | — |
| 134 | #924 | C2×D3 | 1 | 4 | yes | — |
| 135 | #897 | — | 3 | 8 | no | — |
| 136 | #896 | — | 3 | 16 | no | — |
| 137 | #888 | — | 3 | 16 | no | — |
| 138 | #887 | — | 3 | 8 | no | — |
| 139 | #886 | — | 3 | 8 | no | — |
| 140 | #885 | — | 3 | 16 | no | — |
| 141 | #67⋊C4 | — | 3 | 16 | no | — |
| 142 | #878 | — | 3 | 16 | no | — |
| 143 | #878 | — | 3 | 16 | no | — |
| 144 | #877 | — | 3 | 8 | no | — |
| 145 | #875 | — | 3 | 4 | no | — |
| 146 | #869 | — | 3 | 4 | no | — |
| 147 | C4×Dic6 | — | 3 | 8 | no | — |
| 148 | C23×C32 | — | 2 | 2 | no | — |
| 149 | C23×C32 | — | 2 | 4 | no | — |
| 150 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 151 | C23×C32 | C24 | 1 | 2 | yes | — |
| 152 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 153 | C2×C32×C4 | — | 2 | 2 | no | — |
| 154 | C2×C32×C4 | — | 2 | 8 | no | — |
| 155 | C2×C32×C4 | C2×D4 | 1 | 4 | yes | — |
| 156 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 157 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 158 | C2×C3⋊Dic3 | — | 2 | 4 | no | — |
| 159 | C2×C3⋊Dic3 | — | 2 | 16 | no | — |
| 160 | C2×C3⋊Dic3 | C2×D4 | 1 | 8 | yes | — |
| 161 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 162 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 163 | #634 | — | 2 | 8 | no | — |
| 164 | #634 | — | 2 | 16 | no | — |
| 165 | #634 | C2×D4 | 1 | 16 | yes | — |
| 166 | C3×#67 | — | 2 | 8 | no | — |
| 167 | C3×#67 | — | 2 | 16 | no | — |
| 168 | C2×C3×Dic3 | C24 | 1 | 8 | yes | — |
| 169 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 170 | C3×D12 | — | 2 | 4 | no | — |
| 171 | C3×C4×D3 | — | 2 | 8 | no | — |
| 172 | C3×Dic6 | — | 2 | 4 | no | — |
| 173 | #627 | — | 2 | 8 | no | — |
| 174 | #625 | — | 2 | 8 | no | — |
| 175 | D3×Dic3 | — | 2 | 16 | no | — |
| 176 | C2×2−1+4 | — | 9 | 1 | no | — |
| 177 | C23×Q8 | — | 9 | 1 | no | — |
| 178 | D4×Q8 | — | 9 | 8 | no | — |
| 179 | #548 | — | 9 | 8 | no | — |
| 180 | #536 | — | 9 | 2 | no | — |
| 181 | #536 | — | 9 | 4 | no | — |
| 182 | #525 | — | 3 | 2 | no | — |
| 183 | #525 | — | 9 | 4 | no | — |
| 184 | #519 | — | 9 | 1 | no | — |
| 185 | C24×C3 | — | 2 | 1 | no | — |
| 186 | C24×C3 | C22×D3 | 1 | 2 | yes | — |
| 187 | C3×#41 | — | 6 | 8 | no | — |
| 188 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 189 | C2×C3×D4 | — | 3 | 8 | no | — |
| 190 | C2×C3×D4 | — | 3 | 4 | no | — |
| 191 | C2×C3×D4 | — | 3 | 2 | no | — |
| 192 | C22×C3×C4 | — | 2 | 8 | no | — |
| 193 | C22×C3×C4 | — | 2 | 8 | no | — |
| 194 | C22×C3×C4 | — | 2 | 4 | no | — |
| 195 | C22×C3×C4 | — | 2 | 1 | no | — |
| 196 | C22×C3×C4 | — | 2 | 1 | no | — |
| 197 | C22×C3×C4 | — | 3 | 4 | no | — |
| 198 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 199 | C22×C3×C4 | C22×D3 | 1 | 4 | yes | — |
| 200 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 201 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 202 | C2×#67 | — | 3 | 8 | no | — |
| 203 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 204 | C2×#67 | C22×D3 | 1 | 4 | yes | — |
| 205 | C22×Dic3 | — | 3 | 4 | no | — |
| 206 | C22×Dic3 | — | 3 | 16 | no | — |
| 207 | C22×Dic3 | — | 3 | 4 | no | — |
| 208 | C22×Dic3 | — | 3 | 8 | no | — |
| 209 | C22×Dic3 | — | 6 | 2 | no | — |
| 210 | C22×Dic3 | — | 6 | 8 | no | — |
| 211 | C22×Dic3 | — | 6 | 2 | no | — |
| 212 | C22×Dic3 | — | 6 | 16 | no | — |
| 213 | C22×Dic3 | — | 6 | 16 | no | — |
| 214 | D3×Q8 | — | 6 | 16 | no | — |
| 215 | #237 | — | 6 | 16 | no | — |
| 216 | #237 | — | 6 | 32 | no | — |
| 217 | #235 | — | 2 | 8 | no | — |
| 218 | #235 | — | 6 | 16 | no | — |
| 219 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 220 | C2×C4×D3 | — | 3 | 8 | no | — |
| 221 | C2×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 222 | C2×Dic6 | — | 3 | 16 | no | — |
| 223 | C2×Dic6 | — | 3 | 4 | no | — |
| 224 | C2×Dic6 | — | 3 | 4 | no | — |
| 225 | C2×Dic6 | — | 3 | 4 | no | — |
| 226 | C2×Dic6 | — | 3 | 16 | no | — |
| 227 | C2×Dic6 | — | 3 | 4 | no | — |
| 228 | C2×Dic6 | — | 3 | 8 | no | — |
| 229 | C2×Dic6 | — | 6 | 8 | no | — |
| 230 | C2×Dic6 | — | 6 | 4 | no | — |
| 231 | C2×Dic6 | — | 6 | 8 | no | — |
| 232 | C2×Dic6 | — | 6 | 4 | no | — |
| 233 | C2×Dic6 | — | 6 | 16 | no | — |
| 234 | C2×Dic6 | — | 6 | 32 | no | — |
| 235 | C2×Dic6 | — | 6 | 32 | no | — |
| 236 | C2×Dic6 | — | 6 | 16 | no | — |
| 237 | C2×Dic6 | — | 6 | 16 | no | — |
| 238 | C2×Dic6 | — | 6 | 64 | no | — |
| 239 | C2×Dic6 | — | 6 | 8 | no | — |
| 240 | C2×Dic6 | — | 6 | 8 | no | — |
| 241 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 242 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 243 | C3×C4⋊C4 | — | 3 | 8 | no | — |
| 244 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 245 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 246 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 247 | C3×C42 | — | 3 | 4 | no | — |
| 248 | #217 | — | 3 | 16 | no | — |
| 249 | #217 | C22×D3 | 1 | 4 | yes | — |
| 250 | #217 | C22×D3 | 1 | 8 | yes | — |
| 251 | (C2×D3)⋊C4 | — | 3 | 16 | no | — |
| 252 | (C2×D3)⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 253 | C4⋊Dic3 | — | 3 | 16 | no | — |
| 254 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 255 | Dic3⋊C4 | — | 3 | 16 | no | — |
| 256 | Dic3⋊C4 | — | 3 | 16 | no | — |
| 257 | Dic3⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 258 | C4×Dic3 | — | 3 | 16 | no | — |
| 259 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 260 | C22×C32 | — | 2 | 8 | no | — |
| 261 | C22×C32 | — | 2 | 2 | no | — |
| 262 | C22×C32 | — | 2 | 2 | no | — |
| 263 | C22×C32 | — | 2 | 2 | no | — |
| 264 | C22×C32 | C22×D4 | 1 | 2 | yes | — |
| 265 | C22×C32 | 2−1+4 | 1 | 4 | yes | complemented |
| 266 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 267 | C2×C3×D3 | — | 2 | 4 | no | — |
| 268 | C2×C3×D3 | — | 2 | 8 | no | — |
| 269 | C32×C4 | — | 2 | 2 | no | — |
| 270 | C32×C4 | C22×D4 | 1 | 4 | yes | — |
| 271 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 272 | C3⋊Dic3 | C22×D4 | 1 | 8 | yes | — |
| 273 | C3×Dic3 | — | 2 | 4 | no | — |
| 274 | C3×Dic3 | — | 2 | 8 | no | — |
| 275 | 2−1+4 | — | 18 | 8 | no | — |
| 276 | C2×#41 | — | 3 | 2 | no | — |
| 277 | C2×#41 | — | 9 | 4 | no | — |
| 278 | C2×#41 | — | 9 | 4 | no | — |
| 279 | C22×Q8 | — | 9 | 4 | no | — |
| 280 | C22×Q8 | — | 9 | 1 | no | — |
| 281 | C22×Q8 | — | 9 | 2 | no | — |
| 282 | C22×Q8 | — | 9 | 1 | no | — |
| 283 | C22×Q8 | — | 9 | 8 | no | — |
| 284 | C22×Q8 | — | 18 | 8 | no | — |
| 285 | C23×C4 | — | 9 | 2 | no | — |
| 286 | C23×C4 | D32 | 1 | 1 | yes | characteristic |
| 287 | C4⋊Q8 | — | 9 | 4 | no | — |
| 288 | C4⋊Q8 | — | 9 | 8 | no | — |
| 289 | #124 | — | 9 | 4 | no | — |
| 290 | #124 | — | 9 | 8 | no | — |
| 291 | #123 | — | 3 | 4 | no | — |
| 292 | #123 | — | 9 | 8 | no | — |
| 293 | C22⋊Q8 | — | 3 | 4 | no | — |
| 294 | C22⋊Q8 | — | 9 | 8 | no | — |
| 295 | C22⋊Q8 | — | 9 | 16 | no | — |
| 296 | C22⋊Q8 | — | 9 | 8 | no | — |
| 297 | #121 | — | 3 | 4 | no | — |
| 298 | #121 | — | 9 | 8 | no | — |
| 299 | #120 | — | 3 | 4 | no | — |
| 300 | C4×Q8 | — | 9 | 8 | no | — |
| 301 | C4×D4 | — | 3 | 8 | no | — |
| 302 | C4×D4 | — | 9 | 16 | no | — |
| 303 | #117 | — | 3 | 2 | no | — |
| 304 | #117 | — | 9 | 4 | no | — |
| 305 | C23×C3 | — | 2 | 4 | no | — |
| 306 | C23×C3 | — | 2 | 8 | no | — |
| 307 | C23×C3 | — | 2 | 4 | no | — |
| 308 | C23×C3 | — | 2 | 8 | no | — |
| 309 | C23×C3 | — | 2 | 2 | no | — |
| 310 | C23×C3 | — | 2 | 1 | no | — |
| 311 | C23×C3 | — | 3 | 4 | no | — |
| 312 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 313 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 314 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 315 | C3×Q8 | — | 6 | 4 | no | — |
| 316 | C3×D4 | — | 6 | 8 | no | — |
| 317 | C3×D4 | — | 6 | 16 | no | — |
| 318 | C3×D4 | — | 6 | 4 | no | — |
| 319 | C2×C3×C4 | — | 2 | 4 | no | — |
| 320 | C2×C3×C4 | — | 2 | 16 | no | — |
| 321 | C2×C3×C4 | — | 2 | 4 | no | — |
| 322 | C2×C3×C4 | — | 2 | 8 | no | — |
| 323 | C2×C3×C4 | — | 2 | 8 | no | — |
| 324 | C2×C3×C4 | — | 2 | 2 | no | — |
| 325 | C2×C3×C4 | — | 2 | 2 | no | — |
| 326 | C2×C3×C4 | — | 2 | 4 | no | — |
| 327 | C2×C3×C4 | — | 3 | 8 | no | — |
| 328 | C2×C3×C4 | — | 3 | 4 | no | — |
| 329 | C2×C3×C4 | — | 6 | 8 | no | — |
| 330 | C2×C3×C4 | D3×D4 | 1 | 8 | yes | — |
| 331 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 332 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 333 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 334 | #67 | — | 2 | 8 | no | — |
| 335 | #67 | — | 2 | 16 | no | — |
| 336 | #67 | — | 6 | 16 | no | — |
| 337 | C2×Dic3 | — | 3 | 16 | no | — |
| 338 | C2×Dic3 | — | 3 | 8 | no | — |
| 339 | C2×Dic3 | — | 3 | 8 | no | — |
| 340 | C2×Dic3 | — | 6 | 8 | no | — |
| 341 | C2×Dic3 | — | 6 | 4 | no | — |
| 342 | C2×Dic3 | — | 6 | 4 | no | — |
| 343 | C2×Dic3 | — | 6 | 16 | no | — |
| 344 | C2×Dic3 | — | 6 | 32 | no | — |
| 345 | C2×Dic3 | — | 6 | 32 | no | — |
| 346 | C2×Dic3 | — | 6 | 8 | no | — |
| 347 | C2×Dic3 | — | 6 | 8 | no | — |
| 348 | C2×Dic3 | C23×D3 | 1 | 8 | yes | — |
| 349 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 350 | D12 | — | 2 | 4 | no | — |
| 351 | C4×D3 | — | 2 | 8 | no | — |
| 352 | C4×D3 | — | 6 | 16 | no | — |
| 353 | Dic6 | — | 2 | 4 | no | — |
| 354 | Dic6 | — | 3 | 16 | no | — |
| 355 | Dic6 | — | 3 | 16 | no | — |
| 356 | Dic6 | — | 6 | 16 | no | — |
| 357 | Dic6 | — | 6 | 16 | no | — |
| 358 | Dic6 | — | 6 | 32 | no | — |
| 359 | Dic6 | — | 6 | 32 | no | — |
| 360 | Dic6 | — | 6 | 16 | no | — |
| 361 | Dic6 | — | 6 | 8 | no | — |
| 362 | Dic6 | — | 6 | 8 | no | — |
| 363 | C2×C32 | — | 2 | 2 | no | — |
| 364 | C2×C32 | — | 2 | 4 | no | — |
| 365 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 366 | C2×C32 | C2×2−1+4 | 1 | 2 | yes | — |
| 367 | C3×D3 | — | 4 | 4 | no | — |
| 368 | C24 | C2×D32 | 1 | 1 | yes | characteristic |
| 369 | #41 | — | 6 | 8 | no | — |
| 370 | #41 | — | 18 | 16 | no | — |
| 371 | #41 | — | 18 | 16 | no | — |
| 372 | C2×Q8 | — | 3 | 2 | no | — |
| 373 | C2×Q8 | — | 9 | 4 | no | — |
| 374 | C2×Q8 | — | 9 | 4 | no | — |
| 375 | C2×Q8 | — | 9 | 8 | no | — |
| 376 | C2×Q8 | — | 9 | 4 | no | — |
| 377 | C2×Q8 | — | 9 | 8 | no | — |
| 378 | C2×Q8 | — | 18 | 8 | no | — |
| 379 | C2×Q8 | — | 18 | 32 | no | — |
| 380 | C2×Q8 | — | 18 | 16 | no | — |
| 381 | C2×Q8 | — | 18 | 4 | no | — |
| 382 | C2×D4 | — | 3 | 8 | no | — |
| 383 | C2×D4 | — | 3 | 4 | no | — |
| 384 | C2×D4 | — | 3 | 2 | no | — |
| 385 | C2×D4 | — | 9 | 4 | no | — |
| 386 | C22×C4 | — | 2 | 4 | no | — |
| 387 | C22×C4 | — | 3 | 4 | no | — |
| 388 | C22×C4 | — | 9 | 8 | no | — |
| 389 | C22×C4 | — | 9 | 2 | no | — |
| 390 | C22×C4 | — | 9 | 8 | no | — |
| 391 | C22×C4 | — | 9 | 2 | no | — |
| 392 | C22×C4 | — | 18 | 8 | no | — |
| 393 | C22×C4 | C2×D32 | 1 | 4 | yes | — |
| 394 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 395 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 396 | C4⋊C4 | — | 3 | 4 | no | — |
| 397 | C4⋊C4 | — | 3 | 8 | no | — |
| 398 | C4⋊C4 | — | 9 | 8 | no | — |
| 399 | C4⋊C4 | — | 9 | 16 | no | — |
| 400 | C22⋊C4 | — | 3 | 4 | no | — |
| 401 | C22⋊C4 | — | 3 | 8 | no | — |
| 402 | C22⋊C4 | — | 3 | 8 | no | — |
| 403 | C22⋊C4 | — | 9 | 16 | no | — |
| 404 | C42 | — | 3 | 4 | no | — |
| 405 | C42 | — | 9 | 8 | no | — |
| 406 | C22×C3 | — | 2 | 4 | no | — |
| 407 | C22×C3 | — | 2 | 16 | no | — |
| 408 | C22×C3 | — | 2 | 16 | no | — |
| 409 | C22×C3 | — | 2 | 4 | no | — |
| 410 | C22×C3 | — | 2 | 4 | no | — |
| 411 | C22×C3 | — | 2 | 4 | no | — |
| 412 | C22×C3 | — | 2 | 4 | no | — |
| 413 | C22×C3 | — | 2 | 4 | no | — |
| 414 | C22×C3 | — | 2 | 4 | no | — |
| 415 | C22×C3 | — | 2 | 2 | no | — |
| 416 | C22×C3 | — | 2 | 1 | no | — |
| 417 | C22×C3 | — | 6 | 4 | no | — |
| 418 | C22×C3 | — | 6 | 8 | no | — |
| 419 | C22×C3 | C2×D3×D4 | 1 | 4 | yes | — |
| 420 | C22×C3 | #1010 | 1 | 8 | yes | complemented |
| 421 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 422 | C2×D3 | — | 2 | 4 | no | — |
| 423 | C2×D3 | — | 2 | 8 | no | — |
| 424 | C3×C4 | — | 2 | 4 | no | — |
| 425 | C3×C4 | — | 2 | 4 | no | — |
| 426 | C3×C4 | — | 2 | 4 | no | — |
| 427 | C3×C4 | — | 6 | 4 | no | — |
| 428 | C3×C4 | — | 6 | 8 | no | — |
| 429 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 430 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 431 | Dic3 | — | 2 | 4 | no | — |
| 432 | Dic3 | — | 2 | 8 | no | — |
| 433 | Dic3 | — | 3 | 16 | no | — |
| 434 | Dic3 | — | 6 | 8 | no | — |
| 435 | Dic3 | — | 6 | 8 | no | — |
| 436 | Dic3 | — | 6 | 8 | no | — |
| 437 | C32 | #3486 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 438 | C23 | — | 2 | 4 | no | — |
| 439 | C23 | — | 2 | 2 | no | — |
| 440 | C23 | — | 3 | 4 | no | — |
| 441 | C23 | C22×D32 | 1 | 2 | yes | — |
| 442 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 443 | Q8 | — | 6 | 4 | no | — |
| 444 | Q8 | — | 9 | 16 | no | — |
| 445 | Q8 | — | 18 | 16 | no | — |
| 446 | Q8 | — | 18 | 8 | no | — |
| 447 | Q8 | — | 18 | 8 | no | — |
| 448 | D4 | — | 6 | 16 | no | — |
| 449 | D4 | — | 6 | 8 | no | — |
| 450 | D4 | — | 6 | 4 | no | — |
| 451 | D4 | — | 18 | 8 | no | — |
| 452 | C2×C4 | — | 2 | 2 | no | — |
| 453 | C2×C4 | — | 2 | 8 | no | — |
| 454 | C2×C4 | — | 3 | 8 | no | — |
| 455 | C2×C4 | — | 3 | 4 | no | — |
| 456 | C2×C4 | — | 6 | 8 | no | — |
| 457 | C2×C4 | — | 9 | 8 | no | — |
| 458 | C2×C4 | — | 9 | 4 | no | — |
| 459 | C2×C4 | — | 9 | 4 | no | — |
| 460 | C2×C4 | — | 18 | 16 | no | — |
| 461 | C2×C4 | — | 18 | 16 | no | — |
| 462 | C2×C4 | — | 18 | 4 | no | — |
| 463 | C2×C4 | #3811 | 1 | 4 | yes | — |
| 464 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 465 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 466 | C2×C3 | — | 2 | 8 | no | — |
| 467 | C2×C3 | — | 2 | 4 | no | — |
| 468 | C2×C3 | — | 2 | 4 | no | — |
| 469 | C2×C3 | — | 2 | 8 | no | — |
| 470 | C2×C3 | — | 2 | 2 | no | — |
| 471 | C2×C3 | — | 2 | 1 | no | — |
| 472 | C2×C3 | — | 12 | 4 | no | — |
| 473 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 474 | C2×C3 | C2×#1010 | 1 | 4 | yes | — |
| 475 | D3 | — | 4 | 4 | no | — |
| 476 | C22 | — | 2 | 8 | no | — |
| 477 | C22 | — | 2 | 2 | no | — |
| 478 | C22 | — | 2 | 2 | no | — |
| 479 | C22 | — | 2 | 2 | no | — |
| 480 | C22 | — | 6 | 8 | no | — |
| 481 | C22 | — | 6 | 4 | no | — |
| 482 | C22 | #64298 | 1 | 4 | yes | complemented |
| 483 | C22 | C2×#3811 | 1 | 2 | yes | — |
| 484 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 485 | C4 | — | 2 | 2 | no | — |
| 486 | C4 | — | 6 | 8 | no | — |
| 487 | C4 | — | 6 | 4 | no | — |
| 488 | C4 | — | 9 | 8 | no | — |
| 489 | C4 | — | 18 | 4 | no | — |
| 490 | C4 | C2×#3811 | 1 | 4 | yes | — |
| 491 | C3 | — | 2 | 1 | no | — |
| 492 | C3 | #86022 | 1 | 2 | yes | complemented |
| 493 | C2 | — | 2 | 4 | no | — |
| 494 | C2 | — | 2 | 2 | no | — |
| 495 | C2 | — | 12 | 4 | no | — |
| 496 | C2 | C2×#64298 | 1 | 2 | yes | — |
| 497 | C2 | C22×#3811 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C23×C32×C4 | C22 |
| hypercenter | C23×C4 | D32 |
| hypocenter | C32 | #3486 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#634 | C2 | semidirect |
| 2. C2×#64298 | C2 | semidirect |
| 3. C3×#5791 | C2 | semidirect |
| 4. #10595501 | C2 | semidirect |
| 5. #10594921 | C2 | semidirect |
| 6. #10594918 | C2 | semidirect |
| 7. #10594915 | C2 | semidirect |
| 8. #10594856 | C2 | semidirect |
| 9. #10594828 | C2 | semidirect |
| 21. C2×#3795 | C22 | semidirect |
| 22. C2×D3×Dic6 | C22 | semidirect |
| 34. #63913 | C22 | semidirect |
| 35. #63896 | C22 | semidirect |
| 36. #63866 | C22 | semidirect |
| 37. #63860 | C22 | semidirect |
| 38. #63857 | C22 | semidirect |
| 39. #63844 | C22 | semidirect |
| 40. #63840 | C22 | semidirect |
| 46. #5791 | D3 | semidirect |
| 67. C2×#634 | D4 | semidirect |
| 265. C22×C32 | 2−1+4 | semidirect |
| 420. C22×C3 | #1010 | semidirect |
| 437. C32 | #3486 | semidirect |
| 482. C22 | #64298 | semidirect |
| 492. C3 | #86022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#634 | 2 |
| C2×#64298 | 2 |
| C3×#5791 | 2 |
| #10595501 | 2 |
| #10594921 | 2 |
| #10594918 | 2 |
| #10594915 | 2 |
| #10594856 | 2 |
| #10594828 | 2 |
| #86022 | 3 |