Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3651 conjugacy classes of subgroups.
The subgroup lattice has 565 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64313 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10596187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×D3×#127 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595309 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10595293 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #10595233 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | D4×#625 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10595144 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594008 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C4×#3798 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #10593897 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #86195 | — | 3 | 2 | no | maximal |
| 13 | C2×#3830 | C22 | 1 | 2 | yes | complemented |
| 14 | C2×C3×D3×D4 | C22 | 1 | 4 | yes | complemented |
| 15 | C2×C3×D3×D4 | C22 | 1 | 8 | yes | complemented |
| 16 | C2×D3×#67 | C22 | 1 | 8 | yes | complemented |
| 17 | C22×#625 | C22 | 1 | 4 | yes | complemented |
| 18 | C2×#3805 | C22 | 1 | 4 | yes | complemented |
| 19 | #64313 | — | 2 | 16 | no | — |
| 20 | C2×#3802 | C22 | 1 | 2 | yes | complemented |
| 21 | C2×#3802 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#3798 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#3795 | C22 | 1 | 4 | yes | complemented |
| 24 | C32×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #64147 | C22 | 1 | 4 | yes | complemented |
| 26 | #64145 | C22 | 1 | 2 | yes | complemented |
| 27 | D4×C3⋊Dic3 | C22 | 1 | 4 | yes | complemented |
| 28 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #64078 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C3×#940 | C22 | 1 | 8 | yes | complemented |
| 31 | C3×#940 | C22 | 1 | 4 | yes | complemented |
| 32 | C3×#874 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×C42×D3 | C22 | 1 | 2 | yes | complemented |
| 34 | #63983 | C22 | 1 | 8 | yes | complemented |
| 35 | #63980 | C22 | 1 | 8 | yes | complemented |
| 36 | #63976 | C22 | 1 | 16 | yes | complemented |
| 37 | #63970 | C22 | 1 | 16 | yes | complemented |
| 38 | C4×#627 | C22 | 1 | 2 | yes | complemented |
| 39 | #63914 | C22 | 1 | 4 | yes | complemented |
| 40 | #63914 | C22 | 1 | 2 | yes | complemented |
| 41 | #63908 | C22 | 1 | 8 | yes | complemented |
| 42 | C4×#626 | C22 | 1 | 4 | yes | complemented |
| 43 | C4×#625 | C22 | 1 | 2 | yes | complemented |
| 44 | Dic3×D12 | C22 | 1 | 8 | yes | complemented |
| 45 | #63874 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #63860 | C22 | 1 | 4 | yes | complemented |
| 47 | #63855 | C22 | 1 | 2 | yes | complemented |
| 48 | C2×#1004 | — | 3 | 4 | no | — |
| 49 | C2×C3×#127 | — | 3 | 2 | no | — |
| 50 | #5805 | — | 3 | 4 | no | — |
| 51 | D4×#67 | — | 3 | 8 | no | — |
| 52 | D4×#67 | — | 3 | 8 | no | — |
| 53 | #5718 | — | 3 | 8 | no | — |
| 54 | #5717 | — | 3 | 8 | no | — |
| 55 | #5716 | — | 3 | 2 | no | — |
| 56 | #5716 | — | 3 | 2 | no | — |
| 57 | #5716 | — | 6 | 1 | no | — |
| 58 | #5715 | — | 3 | 4 | no | — |
| 59 | #5715 | — | 3 | 4 | no | — |
| 60 | D3×#127 | — | 3 | 2 | no | — |
| 61 | D3×#127 | D3 | 1 | 2 | yes | complemented |
| 62 | #5477 | — | 3 | 2 | no | — |
| 63 | C4×#235 | — | 3 | 2 | no | — |
| 64 | C23×C3×D3 | C23 | 1 | 8 | yes | — |
| 65 | C22×D32 | C23 | 1 | 4 | yes | — |
| 66 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 67 | C2×C32×D4 | C23 | 1 | 4 | yes | — |
| 68 | C2×#638 | C23 | 1 | 4 | yes | — |
| 69 | C22×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 70 | #3830 | — | 2 | 8 | no | — |
| 71 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 72 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×#634 | C23 | 1 | 2 | yes | — |
| 74 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 75 | C2×C3×#67 | C23 | 1 | 16 | yes | — |
| 76 | C3×D3×D4 | — | 2 | 16 | no | — |
| 77 | C3×D3×D4 | — | 4 | 16 | no | — |
| 78 | C2×C3×D12 | C23 | 1 | 4 | yes | — |
| 79 | C2×C3×D12 | C23 | 1 | 8 | yes | — |
| 80 | C2×C3×C4×D3 | C23 | 1 | 4 | yes | — |
| 81 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 82 | D3×#67 | — | 2 | 32 | no | — |
| 83 | C2×#627 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×#626 | C23 | 1 | 2 | yes | — |
| 85 | C2×#625 | — | 2 | 16 | no | — |
| 86 | C2×#625 | C23 | 1 | 8 | yes | — |
| 87 | C2×#625 | C23 | 1 | 4 | yes | — |
| 88 | C2×#625 | C23 | 1 | 8 | yes | — |
| 89 | C2×#625 | C23 | 1 | 1 | yes | characteristic |
| 90 | #3805 | — | 2 | 16 | no | — |
| 91 | C2×D3×Dic3 | C23 | 1 | 8 | yes | — |
| 92 | #3802 | — | 2 | 8 | no | — |
| 93 | #3802 | — | 4 | 8 | no | — |
| 94 | #3798 | D4 | 1 | 8 | yes | complemented |
| 95 | #3795 | — | 2 | 16 | no | — |
| 96 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 97 | #3757 | C23 | 1 | 8 | yes | — |
| 98 | C4⋊(C3⋊Dic3) | C23 | 1 | 4 | yes | — |
| 99 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 100 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 101 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 102 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 103 | #3724 | C23 | 1 | 2 | yes | — |
| 104 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 105 | #3722 | C23 | 1 | 2 | yes | — |
| 106 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 107 | (C2×D3)⋊Dic3 | C23 | 1 | 16 | yes | — |
| 108 | #3498 | — | 9 | 1 | no | Sylow |
| 109 | C22×C3×D4 | — | 3 | 4 | no | — |
| 110 | C22×C3×D4 | — | 3 | 8 | no | — |
| 111 | C22×#67 | — | 3 | 8 | no | — |
| 112 | C22×#67 | — | 3 | 8 | no | — |
| 113 | #1004 | — | 6 | 32 | no | — |
| 114 | C2×#237 | — | 3 | 4 | no | — |
| 115 | C2×#237 | — | 3 | 8 | no | — |
| 116 | C2×#237 | — | 3 | 4 | no | — |
| 117 | C2×#237 | — | 6 | 2 | no | — |
| 118 | C2×D3×D4 | — | 3 | 8 | no | — |
| 119 | C2×D3×D4 | — | 3 | 4 | no | — |
| 120 | C2×D3×D4 | — | 3 | 8 | no | — |
| 121 | C2×D3×D4 | C2×D3 | 1 | 4 | yes | complemented |
| 122 | C2×D3×D4 | C2×D3 | 1 | 8 | yes | complemented |
| 123 | C2×#235 | — | 3 | 4 | no | — |
| 124 | C2×#235 | — | 3 | 2 | no | — |
| 125 | C3×#127 | — | 2 | 1 | no | — |
| 126 | C3×#127 | — | 3 | 4 | no | — |
| 127 | C3×#127 | — | 3 | 8 | no | — |
| 128 | C3×#127 | — | 3 | 2 | no | — |
| 129 | C3×#127 | C2×D3 | 1 | 2 | yes | complemented |
| 130 | C2×C3×C42 | — | 3 | 2 | no | — |
| 131 | #953 | — | 3 | 16 | no | — |
| 132 | #940 | — | 3 | 4 | no | — |
| 133 | #940 | — | 3 | 8 | no | — |
| 134 | #940 | C2×D3 | 1 | 4 | yes | complemented |
| 135 | #940 | C2×D3 | 1 | 8 | yes | complemented |
| 136 | #939 | — | 3 | 16 | no | — |
| 137 | #939 | — | 3 | 16 | no | — |
| 138 | #938 | — | 3 | 8 | no | — |
| 139 | #938 | — | 3 | 16 | no | — |
| 140 | #938 | — | 3 | 8 | no | — |
| 141 | #938 | — | 6 | 4 | no | — |
| 142 | #937 | — | 3 | 16 | no | — |
| 143 | #937 | — | 3 | 16 | no | — |
| 144 | #936 | — | 3 | 4 | no | — |
| 145 | #936 | — | 3 | 4 | no | — |
| 146 | #936 | — | 6 | 2 | no | — |
| 147 | D4×Dic3 | — | 3 | 8 | no | — |
| 148 | D4×Dic3 | — | 3 | 8 | no | — |
| 149 | D4×Dic3 | — | 6 | 4 | no | — |
| 150 | #930 | — | 3 | 8 | no | — |
| 151 | C4×#67 | — | 3 | 4 | no | — |
| 152 | C4×#67 | — | 3 | 4 | no | — |
| 153 | #926 | — | 3 | 2 | no | — |
| 154 | #875 | — | 3 | 4 | no | — |
| 155 | #874 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | C4×D12 | — | 3 | 8 | no | — |
| 157 | C4×D12 | — | 3 | 4 | no | — |
| 158 | #872 | — | 3 | 2 | no | — |
| 159 | #872 | — | 3 | 2 | no | — |
| 160 | C42×D3 | — | 3 | 2 | no | — |
| 161 | C42×D3 | — | 6 | 1 | no | — |
| 162 | C42×D3 | C2×D3 | 1 | 2 | yes | complemented |
| 163 | #869 | — | 3 | 2 | no | — |
| 164 | #869 | — | 6 | 1 | no | — |
| 165 | C4×Dic6 | — | 3 | 4 | no | — |
| 166 | C23×C32 | C24 | 1 | 4 | yes | — |
| 167 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 168 | C22×C3×D3 | — | 2 | 16 | no | — |
| 169 | C22×C3×D3 | — | 4 | 16 | no | — |
| 170 | C22×C3×D3 | C24 | 1 | 8 | yes | — |
| 171 | C22×C3×D3 | C24 | 1 | 2 | yes | — |
| 172 | C2×D32 | — | 2 | 8 | no | — |
| 173 | C2×D32 | — | 4 | 8 | no | — |
| 174 | C32×D4 | — | 2 | 4 | no | — |
| 175 | C32×D4 | — | 2 | 8 | no | — |
| 176 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 177 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 178 | #638 | — | 2 | 8 | no | — |
| 179 | C2×C3⋊Dic3 | — | 2 | 8 | no | — |
| 180 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 181 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 182 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 183 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 184 | C4×C3⋊D3 | C2×D4 | 1 | 4 | yes | complemented |
| 185 | #634 | — | 2 | 4 | no | — |
| 186 | C3×#67 | — | 2 | 16 | no | — |
| 187 | C3×#67 | — | 4 | 16 | no | — |
| 188 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 189 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 190 | C3×D12 | — | 2 | 8 | no | — |
| 191 | C3×D12 | — | 2 | 16 | no | — |
| 192 | C3×C4×D3 | — | 2 | 8 | no | — |
| 193 | C3×C4×D3 | C2×D4 | 1 | 8 | yes | complemented |
| 194 | #627 | C2×D4 | 1 | 4 | yes | complemented |
| 195 | #626 | C2×D4 | 1 | 8 | yes | complemented |
| 196 | #625 | — | 2 | 16 | no | — |
| 197 | #625 | — | 2 | 8 | no | — |
| 198 | #625 | — | 4 | 8 | no | — |
| 199 | #625 | C2×D4 | 1 | 4 | yes | complemented |
| 200 | D3×Dic3 | — | 2 | 16 | no | — |
| 201 | C2×H(5,𝔽2) | — | 9 | 2 | no | — |
| 202 | #550 | — | 9 | 4 | no | — |
| 203 | D42 | — | 9 | 8 | no | — |
| 204 | D42 | — | 9 | 4 | no | — |
| 205 | #535 | — | 9 | 2 | no | — |
| 206 | #535 | — | 9 | 4 | no | — |
| 207 | #532 | — | 9 | 2 | no | — |
| 208 | #532 | — | 9 | 1 | no | — |
| 209 | C2×#127 | — | 3 | 2 | no | — |
| 210 | C2×#127 | — | 9 | 1 | no | — |
| 211 | C4×#41 | — | 9 | 1 | no | — |
| 212 | C24×C3 | — | 3 | 8 | no | — |
| 213 | C23×D3 | — | 3 | 8 | no | — |
| 214 | C23×D3 | C22×D3 | 1 | 8 | yes | — |
| 215 | C2×C3×D4 | — | 2 | 4 | no | — |
| 216 | C2×C3×D4 | — | 2 | 2 | no | — |
| 217 | C2×C3×D4 | — | 3 | 8 | no | — |
| 218 | C2×C3×D4 | — | 3 | 16 | no | — |
| 219 | C2×C3×D4 | — | 3 | 8 | no | — |
| 220 | C2×C3×D4 | — | 3 | 4 | no | — |
| 221 | C2×C3×D4 | — | 6 | 16 | no | — |
| 222 | C2×C3×D4 | — | 12 | 16 | no | — |
| 223 | C2×C3×D4 | C22×D3 | 1 | 8 | yes | — |
| 224 | C2×C3×D4 | C22×D3 | 1 | 4 | yes | — |
| 225 | C22×C3×C4 | — | 3 | 2 | no | — |
| 226 | C22×C3×C4 | — | 3 | 4 | no | — |
| 227 | C2×#67 | — | 3 | 2 | no | — |
| 228 | C2×#67 | — | 3 | 8 | no | — |
| 229 | C2×#67 | — | 3 | 8 | no | — |
| 230 | C2×#67 | — | 3 | 8 | no | — |
| 231 | C2×#67 | — | 3 | 8 | no | — |
| 232 | C2×#67 | — | 3 | 16 | no | — |
| 233 | C2×#67 | — | 3 | 2 | no | — |
| 234 | C2×#67 | — | 6 | 4 | no | — |
| 235 | C2×#67 | — | 6 | 32 | no | — |
| 236 | C2×#67 | — | 6 | 32 | no | — |
| 237 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 238 | C2×#67 | C22×D3 | 1 | 16 | yes | — |
| 239 | C22×Dic3 | — | 3 | 8 | no | — |
| 240 | C22×Dic3 | — | 3 | 8 | no | — |
| 241 | C22×Dic3 | — | 6 | 4 | no | — |
| 242 | #237 | — | 6 | 32 | no | — |
| 243 | #237 | — | 6 | 16 | no | — |
| 244 | #237 | — | 6 | 16 | no | — |
| 245 | #237 | — | 12 | 8 | no | — |
| 246 | D3×D4 | — | 2 | 16 | no | — |
| 247 | D3×D4 | — | 4 | 16 | no | — |
| 248 | D3×D4 | — | 6 | 16 | no | — |
| 249 | D3×D4 | — | 6 | 32 | no | — |
| 250 | D3×D4 | — | 12 | 16 | no | — |
| 251 | #235 | — | 3 | 16 | no | — |
| 252 | #235 | — | 6 | 16 | no | — |
| 253 | C2×D12 | — | 3 | 2 | no | — |
| 254 | C2×D12 | C22×D3 | 1 | 8 | yes | — |
| 255 | C2×D12 | C22×D3 | 1 | 4 | yes | — |
| 256 | C2×C4×D3 | — | 3 | 2 | no | — |
| 257 | C2×C4×D3 | — | 3 | 8 | no | — |
| 258 | C2×C4×D3 | — | 3 | 4 | no | — |
| 259 | C2×C4×D3 | — | 6 | 1 | no | — |
| 260 | C2×C4×D3 | — | 6 | 2 | no | — |
| 261 | C2×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 262 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 263 | C2×Dic6 | — | 3 | 2 | no | — |
| 264 | C2×Dic6 | — | 3 | 4 | no | — |
| 265 | C2×Dic6 | — | 6 | 2 | no | — |
| 266 | C3×C42 | — | 2 | 1 | no | — |
| 267 | C3×C42 | — | 3 | 4 | no | — |
| 268 | C3×C42 | — | 3 | 2 | no | — |
| 269 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 270 | #217 | — | 3 | 16 | no | — |
| 271 | #217 | — | 3 | 4 | no | — |
| 272 | #217 | — | 3 | 16 | no | — |
| 273 | #217 | — | 6 | 8 | no | — |
| 274 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 275 | (C2×D3)⋊C4 | — | 3 | 16 | no | — |
| 276 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 277 | C4⋊Dic3 | — | 3 | 8 | no | — |
| 278 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 279 | C4⋊Dic3 | — | 6 | 4 | no | — |
| 280 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 281 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 282 | C4×Dic3 | — | 3 | 4 | no | — |
| 283 | C4×Dic3 | — | 3 | 2 | no | — |
| 284 | C4×Dic3 | — | 6 | 2 | no | — |
| 285 | C4×Dic3 | — | 6 | 1 | no | — |
| 286 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 287 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 288 | C22×C32 | — | 2 | 4 | no | — |
| 289 | C22×C32 | — | 2 | 8 | no | — |
| 290 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 291 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 292 | C2×C3⋊D3 | C22×D4 | 1 | 2 | yes | — |
| 293 | C2×C3×D3 | — | 2 | 4 | no | — |
| 294 | C2×C3×D3 | — | 2 | 8 | no | — |
| 295 | C2×C3×D3 | — | 2 | 16 | no | — |
| 296 | C2×C3×D3 | — | 8 | 16 | no | — |
| 297 | C2×C3×D3 | C22×D4 | 1 | 4 | yes | — |
| 298 | D32 | — | 8 | 8 | no | — |
| 299 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 300 | C32×C4 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 301 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 302 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 303 | C3⋊Dic3 | C22×D4 | 1 | 2 | yes | — |
| 304 | C3×Dic3 | — | 2 | 4 | no | — |
| 305 | C3×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 306 | H(5,𝔽2) | — | 18 | 16 | no | — |
| 307 | C2×#41 | — | 9 | 1 | no | — |
| 308 | C2×#41 | — | 9 | 4 | no | — |
| 309 | C2×#41 | — | 9 | 4 | no | — |
| 310 | C2×#41 | — | 9 | 2 | no | — |
| 311 | C22×D4 | — | 3 | 4 | no | — |
| 312 | C22×D4 | — | 3 | 8 | no | — |
| 313 | C22×D4 | — | 9 | 2 | no | — |
| 314 | C22×D4 | — | 9 | 4 | no | — |
| 315 | C22×D4 | — | 9 | 8 | no | — |
| 316 | C22×D4 | — | 9 | 4 | no | — |
| 317 | C4⋊Q8 | — | 9 | 1 | no | — |
| 318 | #127 | — | 3 | 4 | no | — |
| 319 | #127 | — | 3 | 8 | no | — |
| 320 | #127 | — | 3 | 2 | no | — |
| 321 | #127 | — | 9 | 2 | no | — |
| 322 | #127 | — | 9 | 4 | no | — |
| 323 | #127 | D32 | 1 | 1 | yes | characteristic, complemented |
| 324 | #124 | — | 9 | 4 | no | — |
| 325 | #124 | — | 9 | 2 | no | — |
| 326 | #121 | — | 9 | 8 | no | — |
| 327 | #121 | — | 9 | 16 | no | — |
| 328 | #121 | — | 9 | 8 | no | — |
| 329 | #121 | — | 9 | 4 | no | — |
| 330 | #120 | — | 9 | 8 | no | — |
| 331 | #120 | — | 9 | 16 | no | — |
| 332 | C4×Q8 | — | 9 | 2 | no | — |
| 333 | C4×D4 | — | 9 | 4 | no | — |
| 334 | C4×D4 | — | 9 | 8 | no | — |
| 335 | C4×D4 | — | 9 | 2 | no | — |
| 336 | C4×D4 | — | 9 | 4 | no | — |
| 337 | #117 | — | 9 | 1 | no | — |
| 338 | #117 | — | 9 | 2 | no | — |
| 339 | C2×C42 | — | 3 | 2 | no | — |
| 340 | C2×C42 | — | 9 | 1 | no | — |
| 341 | C23×C3 | — | 2 | 4 | no | — |
| 342 | C23×C3 | — | 3 | 2 | no | — |
| 343 | C23×C3 | — | 3 | 8 | no | — |
| 344 | C23×C3 | — | 6 | 16 | no | — |
| 345 | C23×C3 | — | 12 | 16 | no | — |
| 346 | C23×C3 | C23×D3 | 1 | 8 | yes | — |
| 347 | C22×D3 | — | 2 | 16 | no | — |
| 348 | C22×D3 | — | 3 | 2 | no | — |
| 349 | C22×D3 | — | 4 | 16 | no | — |
| 350 | C22×D3 | — | 6 | 1 | no | — |
| 351 | C22×D3 | — | 6 | 16 | no | — |
| 352 | C22×D3 | — | 12 | 16 | no | — |
| 353 | C22×D3 | C23×D3 | 1 | 8 | yes | — |
| 354 | C22×D3 | C23×D3 | 1 | 2 | yes | — |
| 355 | C3×D4 | — | 2 | 8 | no | — |
| 356 | C3×D4 | — | 2 | 16 | no | — |
| 357 | C3×D4 | — | 4 | 4 | no | — |
| 358 | C3×D4 | — | 4 | 8 | no | — |
| 359 | C3×D4 | — | 6 | 16 | no | — |
| 360 | C3×D4 | — | 6 | 8 | no | — |
| 361 | C3×D4 | — | 6 | 16 | no | — |
| 362 | C3×D4 | — | 12 | 16 | no | — |
| 363 | C2×C3×C4 | — | 2 | 2 | no | — |
| 364 | C2×C3×C4 | — | 2 | 1 | no | — |
| 365 | C2×C3×C4 | — | 3 | 2 | no | — |
| 366 | C2×C3×C4 | — | 3 | 8 | no | — |
| 367 | C2×C3×C4 | — | 3 | 4 | no | — |
| 368 | C2×C3×C4 | — | 6 | 8 | no | — |
| 369 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 370 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 371 | #67 | — | 2 | 16 | no | — |
| 372 | #67 | — | 3 | 8 | no | — |
| 373 | #67 | — | 3 | 8 | no | — |
| 374 | #67 | — | 4 | 16 | no | — |
| 375 | #67 | — | 6 | 16 | no | — |
| 376 | #67 | — | 6 | 16 | no | — |
| 377 | #67 | — | 6 | 16 | no | — |
| 378 | #67 | — | 6 | 16 | no | — |
| 379 | #67 | — | 12 | 8 | no | — |
| 380 | #67 | — | 12 | 16 | no | — |
| 381 | C2×Dic3 | — | 3 | 2 | no | — |
| 382 | C2×Dic3 | — | 3 | 4 | no | — |
| 383 | C2×Dic3 | — | 3 | 8 | no | — |
| 384 | C2×Dic3 | — | 6 | 1 | no | — |
| 385 | C2×Dic3 | — | 6 | 2 | no | — |
| 386 | C2×Dic3 | — | 6 | 4 | no | — |
| 387 | C2×Dic3 | — | 6 | 16 | no | — |
| 388 | C2×Dic3 | — | 6 | 16 | no | — |
| 389 | C2×Dic3 | — | 12 | 8 | no | — |
| 390 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 391 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 392 | D12 | — | 2 | 8 | no | — |
| 393 | D12 | — | 2 | 16 | no | — |
| 394 | D12 | — | 3 | 8 | no | — |
| 395 | C4×D3 | — | 2 | 8 | no | — |
| 396 | C4×D3 | — | 3 | 8 | no | — |
| 397 | C4×D3 | — | 6 | 4 | no | — |
| 398 | C4×D3 | — | 6 | 16 | no | — |
| 399 | C4×D3 | — | 6 | 8 | no | — |
| 400 | C4×D3 | — | 12 | 4 | no | — |
| 401 | C4×D3 | D3×D4 | 1 | 8 | yes | complemented |
| 402 | Dic6 | — | 3 | 8 | no | — |
| 403 | Dic6 | — | 6 | 8 | no | — |
| 404 | Dic6 | — | 12 | 4 | no | — |
| 405 | C2×C32 | — | 4 | 4 | no | — |
| 406 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 407 | C2×C32 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 408 | C3⋊D3 | — | 2 | 2 | no | — |
| 409 | C3×D3 | — | 2 | 4 | no | — |
| 410 | C3×D3 | — | 4 | 8 | no | — |
| 411 | C24 | — | 3 | 8 | no | — |
| 412 | C24 | — | 9 | 4 | no | — |
| 413 | #41 | — | 9 | 8 | no | — |
| 414 | #41 | — | 18 | 16 | no | — |
| 415 | #41 | — | 18 | 8 | no | — |
| 416 | #41 | — | 18 | 16 | no | — |
| 417 | C2×Q8 | — | 9 | 1 | no | — |
| 418 | C2×Q8 | — | 9 | 2 | no | — |
| 419 | C2×D4 | — | 3 | 8 | no | — |
| 420 | C2×D4 | — | 3 | 16 | no | — |
| 421 | C2×D4 | — | 3 | 8 | no | — |
| 422 | C2×D4 | — | 3 | 4 | no | — |
| 423 | C2×D4 | — | 6 | 16 | no | — |
| 424 | C2×D4 | — | 9 | 2 | no | — |
| 425 | C2×D4 | — | 9 | 1 | no | — |
| 426 | C2×D4 | — | 9 | 8 | no | — |
| 427 | C2×D4 | — | 9 | 4 | no | — |
| 428 | C2×D4 | — | 9 | 4 | no | — |
| 429 | C2×D4 | — | 9 | 8 | no | — |
| 430 | C2×D4 | — | 12 | 16 | no | — |
| 431 | C2×D4 | — | 18 | 8 | no | — |
| 432 | C2×D4 | — | 18 | 32 | no | — |
| 433 | C2×D4 | — | 18 | 16 | no | — |
| 434 | C2×D4 | — | 36 | 8 | no | — |
| 435 | C2×D4 | C2×D32 | 1 | 4 | yes | — |
| 436 | C2×D4 | C2×D32 | 1 | 2 | yes | — |
| 437 | C22×C4 | — | 3 | 2 | no | — |
| 438 | C22×C4 | — | 3 | 4 | no | — |
| 439 | C22×C4 | — | 9 | 8 | no | — |
| 440 | C22×C4 | — | 9 | 1 | no | — |
| 441 | C22×C4 | — | 9 | 4 | no | — |
| 442 | C22×C4 | — | 9 | 2 | no | — |
| 443 | C4⋊C4 | — | 9 | 2 | no | — |
| 444 | C4⋊C4 | — | 9 | 4 | no | — |
| 445 | C4⋊C4 | — | 9 | 4 | no | — |
| 446 | C22⋊C4 | — | 9 | 2 | no | — |
| 447 | C22⋊C4 | — | 9 | 4 | no | — |
| 448 | C22⋊C4 | — | 9 | 16 | no | — |
| 449 | C22⋊C4 | — | 9 | 8 | no | — |
| 450 | C42 | — | 3 | 2 | no | — |
| 451 | C42 | — | 3 | 4 | no | — |
| 452 | C42 | — | 9 | 1 | no | — |
| 453 | C42 | — | 9 | 2 | no | — |
| 454 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 455 | C22×C3 | — | 2 | 8 | no | — |
| 456 | C22×C3 | — | 2 | 16 | no | — |
| 457 | C22×C3 | — | 2 | 1 | no | — |
| 458 | C22×C3 | — | 3 | 4 | no | — |
| 459 | C22×C3 | — | 4 | 4 | no | — |
| 460 | C22×C3 | — | 4 | 8 | no | — |
| 461 | C22×C3 | — | 6 | 4 | no | — |
| 462 | C22×C3 | — | 6 | 8 | no | — |
| 463 | C22×C3 | — | 6 | 16 | no | — |
| 464 | C22×C3 | — | 24 | 16 | no | — |
| 465 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 466 | C2×D3 | — | 2 | 4 | no | — |
| 467 | C2×D3 | — | 2 | 8 | no | — |
| 468 | C2×D3 | — | 2 | 16 | no | — |
| 469 | C2×D3 | — | 3 | 4 | no | — |
| 470 | C2×D3 | — | 6 | 2 | no | — |
| 471 | C2×D3 | — | 6 | 4 | no | — |
| 472 | C2×D3 | — | 8 | 16 | no | — |
| 473 | C2×D3 | — | 12 | 2 | no | — |
| 474 | C2×D3 | — | 24 | 16 | no | — |
| 475 | C2×D3 | C2×D3×D4 | 1 | 4 | yes | — |
| 476 | C3×C4 | — | 2 | 2 | no | — |
| 477 | C3×C4 | — | 2 | 4 | no | — |
| 478 | C3×C4 | — | 3 | 4 | no | — |
| 479 | C3×C4 | — | 6 | 4 | no | — |
| 480 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 481 | C3×C4 | #1004 | 1 | 8 | yes | complemented |
| 482 | Dic3 | — | 2 | 4 | no | — |
| 483 | Dic3 | — | 3 | 4 | no | — |
| 484 | Dic3 | — | 6 | 2 | no | — |
| 485 | Dic3 | — | 6 | 8 | no | — |
| 486 | Dic3 | — | 6 | 4 | no | — |
| 487 | Dic3 | — | 12 | 4 | no | — |
| 488 | Dic3 | — | 12 | 2 | no | — |
| 489 | Dic3 | C2×D3×D4 | 1 | 4 | yes | — |
| 490 | C32 | #3498 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 491 | C23 | — | 3 | 2 | no | — |
| 492 | C23 | — | 3 | 8 | no | — |
| 493 | C23 | — | 6 | 16 | no | — |
| 494 | C23 | — | 9 | 1 | no | — |
| 495 | C23 | — | 12 | 16 | no | — |
| 496 | C23 | — | 18 | 8 | no | — |
| 497 | C23 | — | 36 | 8 | no | — |
| 498 | C23 | C22×D32 | 1 | 4 | yes | — |
| 499 | Q8 | — | 9 | 4 | no | — |
| 500 | Q8 | — | 18 | 4 | no | — |
| 501 | D4 | — | 2 | 4 | no | — |
| 502 | D4 | — | 2 | 8 | no | — |
| 503 | D4 | — | 6 | 16 | no | — |
| 504 | D4 | — | 6 | 8 | no | — |
| 505 | D4 | — | 6 | 16 | no | — |
| 506 | D4 | — | 9 | 8 | no | — |
| 507 | D4 | — | 9 | 4 | no | — |
| 508 | D4 | — | 12 | 16 | no | — |
| 509 | D4 | — | 18 | 8 | no | — |
| 510 | D4 | — | 18 | 8 | no | — |
| 511 | D4 | — | 18 | 16 | no | — |
| 512 | D4 | — | 36 | 8 | no | — |
| 513 | C2×C4 | — | 3 | 2 | no | — |
| 514 | C2×C4 | — | 3 | 8 | no | — |
| 515 | C2×C4 | — | 3 | 4 | no | — |
| 516 | C2×C4 | — | 6 | 8 | no | — |
| 517 | C2×C4 | — | 9 | 1 | no | — |
| 518 | C2×C4 | — | 9 | 4 | no | — |
| 519 | C2×C4 | — | 9 | 2 | no | — |
| 520 | C2×C4 | — | 9 | 4 | no | — |
| 521 | C2×C4 | — | 18 | 16 | no | — |
| 522 | C2×C4 | — | 18 | 8 | no | — |
| 523 | C2×C4 | — | 18 | 4 | no | — |
| 524 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 525 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 526 | C2×C3 | — | 2 | 1 | no | — |
| 527 | C2×C3 | — | 2 | 2 | no | — |
| 528 | C2×C3 | — | 4 | 8 | no | — |
| 529 | C2×C3 | — | 6 | 4 | no | — |
| 530 | C2×C3 | — | 8 | 4 | no | — |
| 531 | C2×C3 | — | 12 | 8 | no | — |
| 532 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 533 | C2×C3 | C2×#1004 | 1 | 4 | yes | — |
| 534 | D3 | — | 2 | 4 | no | — |
| 535 | D3 | — | 4 | 8 | no | — |
| 536 | D3 | — | 6 | 4 | no | — |
| 537 | D3 | — | 12 | 2 | no | — |
| 538 | C22 | — | 2 | 4 | no | — |
| 539 | C22 | — | 2 | 8 | no | — |
| 540 | C22 | — | 3 | 4 | no | — |
| 541 | C22 | — | 6 | 4 | no | — |
| 542 | C22 | — | 6 | 8 | no | — |
| 543 | C22 | — | 6 | 16 | no | — |
| 544 | C22 | — | 9 | 2 | no | — |
| 545 | C22 | — | 18 | 2 | no | — |
| 546 | C22 | — | 24 | 16 | no | — |
| 547 | C22 | — | 72 | 8 | no | — |
| 548 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 549 | C4 | — | 3 | 4 | no | — |
| 550 | C4 | — | 6 | 4 | no | — |
| 551 | C4 | — | 9 | 2 | no | — |
| 552 | C4 | — | 18 | 4 | no | — |
| 553 | C4 | — | 18 | 2 | no | — |
| 554 | C4 | D32×D4 | 1 | 2 | yes | — |
| 555 | C4 | #64313 | 1 | 4 | yes | complemented |
| 556 | C3 | — | 2 | 1 | no | — |
| 557 | C3 | #86195 | 1 | 2 | yes | complemented |
| 558 | C2 | — | 4 | 4 | no | — |
| 559 | C2 | — | 6 | 4 | no | — |
| 560 | C2 | — | 12 | 8 | no | — |
| 561 | C2 | — | 18 | 2 | no | — |
| 562 | C2 | C2×D32×D4 | 1 | 1 | yes | characteristic |
| 563 | C2 | C2×#64313 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#127 | C22 |
| hypercenter | #127 | D32 |
| hypocenter | C32 | #3498 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64313 | C2 | semidirect |
| 2. #10596187 | C2 | semidirect |
| 3. C3×D3×#127 | C2 | semidirect |
| 4. #10595309 | C2 | semidirect |
| 5. #10595293 | C2 | semidirect |
| 6. #10595233 | C2 | semidirect |
| 7. D4×#625 | C2 | semidirect |
| 8. #10595144 | C2 | semidirect |
| 9. #10594008 | C2 | semidirect |
| 10. C4×#3798 | C2 | semidirect |
| 11. #10593897 | C2 | semidirect |
| 13. C2×#3830 | C22 | semidirect |
| 14. C2×C3×D3×D4 | C22 | semidirect |
| 15. C2×C3×D3×D4 | C22 | semidirect |
| 16. C2×D3×#67 | C22 | semidirect |
| 17. C22×#625 | C22 | semidirect |
| 18. C2×#3805 | C22 | semidirect |
| 20. C2×#3802 | C22 | semidirect |
| 21. C2×#3802 | C22 | semidirect |
| 23. C2×#3795 | C22 | semidirect |
| 24. C32×#127 | C22 | semidirect |
| 25. #64147 | C22 | semidirect |
| 26. #64145 | C22 | semidirect |
| 27. D4×C3⋊Dic3 | C22 | semidirect |
| 28. C42×C3⋊D3 | C22 | semidirect |
| 29. #64078 | C22 | semidirect |
| 30. C3×#940 | C22 | semidirect |
| 31. C3×#940 | C22 | semidirect |
| 32. C3×#874 | C22 | semidirect |
| 33. C3×C42×D3 | C22 | semidirect |
| 34. #63983 | C22 | semidirect |
| 35. #63980 | C22 | semidirect |
| 36. #63976 | C22 | semidirect |
| 37. #63970 | C22 | semidirect |
| 38. C4×#627 | C22 | semidirect |
| 39. #63914 | C22 | semidirect |
| 40. #63914 | C22 | semidirect |
| 41. #63908 | C22 | semidirect |
| 42. C4×#626 | C22 | semidirect |
| 43. C4×#625 | C22 | semidirect |
| 44. Dic3×D12 | C22 | semidirect |
| 45. #63874 | C22 | semidirect |
| 46. #63860 | C22 | semidirect |
| 47. #63855 | C22 | semidirect |
| 61. D3×#127 | D3 | semidirect |
| 94. #3798 | D4 | semidirect |
| 121. C2×D3×D4 | C2×D3 | semidirect |
| 122. C2×D3×D4 | C2×D3 | semidirect |
| 129. C3×#127 | C2×D3 | semidirect |
| 134. #940 | C2×D3 | semidirect |
| 135. #940 | C2×D3 | semidirect |
| 155. #874 | C2×D3 | semidirect |
| 162. C42×D3 | C2×D3 | semidirect |
| 184. C4×C3⋊D3 | C2×D4 | semidirect |
| 193. C3×C4×D3 | C2×D4 | semidirect |
| 194. #627 | C2×D4 | semidirect |
| 195. #626 | C2×D4 | semidirect |
| 199. #625 | C2×D4 | semidirect |
| 300. C32×C4 | H(5,𝔽2) | semidirect |
| 323. #127 | D32 | semidirect |
| 401. C4×D3 | D3×D4 | semidirect |
| 481. C3×C4 | #1004 | semidirect |
| 490. C32 | #3498 | semidirect |
| 555. C4 | #64313 | semidirect |
| 557. C3 | #86195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64313 | 2 |
| #10596187 | 2 |
| C3×D3×#127 | 2 |
| #10595309 | 2 |
| #10595293 | 2 |
| #10595233 | 2 |
| D4×#625 | 2 |
| #10595144 | 2 |
| #10594008 | 2 |
| C4×#3798 | 2 |
| #10593897 | 2 |
| #86195 | 3 |