Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
3745 conjugacy classes of subgroups.
The subgroup lattice has 736 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#64314 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C3⋊D3×#127 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3×#5715 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595292 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #10595289 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | D3×#940 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10595269 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10595168 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10595153 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10594001 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10593971 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #10593966 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #86316 | — | 3 | 2 | no | maximal |
| 14 | C2×D4×C3⋊D3 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×D4×C3⋊D3 | C22 | 1 | 4 | yes | complemented |
| 16 | C2×C3×#237 | C22 | 1 | 2 | yes | complemented |
| 17 | C2×C3×D3×D4 | C22 | 1 | 2 | yes | complemented |
| 18 | C2×#3811 | C22 | 1 | 4 | yes | complemented |
| 19 | C2×D3×#67 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×D3×#67 | C22 | 1 | 8 | yes | complemented |
| 21 | C22×#626 | C22 | 1 | 4 | yes | complemented |
| 22 | C2×#3804 | C22 | 1 | 4 | yes | complemented |
| 23 | #64314 | — | 2 | 16 | no | — |
| 24 | C2×D3×D12 | C22 | 1 | 2 | yes | complemented |
| 25 | C2×#3799 | C22 | 1 | 2 | yes | complemented |
| 26 | C2×#3798 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#3796 | C22 | 1 | 2 | yes | complemented |
| 28 | C32×#127 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | #64149 | C22 | 1 | 2 | yes | complemented |
| 30 | #64149 | C22 | 1 | 4 | yes | complemented |
| 31 | #64083 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | C3×#940 | C22 | 1 | 2 | yes | complemented |
| 34 | C3×#939 | C22 | 1 | 8 | yes | complemented |
| 35 | C3×#937 | C22 | 1 | 8 | yes | complemented |
| 36 | C3×#936 | C22 | 1 | 2 | yes | complemented |
| 37 | C3×#875 | C22 | 1 | 2 | yes | complemented |
| 38 | C3×#872 | C22 | 1 | 2 | yes | complemented |
| 39 | #63981 | C22 | 1 | 8 | yes | complemented |
| 40 | #63979 | C22 | 1 | 8 | yes | complemented |
| 41 | #63971 | C22 | 1 | 8 | yes | complemented |
| 42 | #63971 | C22 | 1 | 8 | yes | complemented |
| 43 | #63952 | C22 | 1 | 8 | yes | complemented |
| 44 | #63923 | C22 | 1 | 8 | yes | complemented |
| 45 | #63914 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #63912 | C22 | 1 | 4 | yes | complemented |
| 47 | #63911 | C22 | 1 | 2 | yes | complemented |
| 48 | #63910 | C22 | 1 | 8 | yes | complemented |
| 49 | #63902 | C22 | 1 | 2 | yes | complemented |
| 50 | #63902 | C22 | 1 | 4 | yes | complemented |
| 51 | #63881 | C22 | 1 | 4 | yes | complemented |
| 52 | C4×D3×Dic3 | C22 | 1 | 2 | yes | complemented |
| 53 | #63874 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #63873 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #63864 | C22 | 1 | 2 | yes | complemented |
| 56 | #63838 | C22 | 1 | 2 | yes | complemented |
| 57 | C2×#1009 | — | 3 | 2 | no | — |
| 58 | C2×#1004 | — | 3 | 2 | no | — |
| 59 | C3×#535 | — | 3 | 2 | no | — |
| 60 | #5832 | — | 3 | 2 | no | — |
| 61 | C2×#940 | — | 3 | 2 | no | — |
| 62 | #5715 | — | 3 | 2 | no | — |
| 63 | #5715 | D3 | 1 | 2 | yes | complemented |
| 64 | D3×#127 | — | 3 | 2 | no | — |
| 65 | D3×#127 | — | 3 | 2 | no | — |
| 66 | D3×#127 | — | 6 | 1 | no | — |
| 67 | #5674 | — | 3 | 2 | no | — |
| 68 | #5674 | — | 3 | 2 | no | — |
| 69 | #5668 | — | 3 | 2 | no | — |
| 70 | #5668 | — | 3 | 2 | no | — |
| 71 | #5609 | — | 3 | 8 | no | — |
| 72 | #5599 | — | 3 | 8 | no | — |
| 73 | #5590 | — | 3 | 8 | no | — |
| 74 | #5590 | — | 3 | 8 | no | — |
| 75 | #5525 | — | 3 | 2 | no | — |
| 76 | #5522 | — | 3 | 2 | no | — |
| 77 | C23×C3⋊D3 | C23 | 1 | 4 | yes | — |
| 78 | C23×C3×D3 | C23 | 1 | 4 | yes | — |
| 79 | C22×D32 | C23 | 1 | 4 | yes | — |
| 80 | C2×C32×D4 | C23 | 1 | 2 | yes | — |
| 81 | C2×C32×D4 | C23 | 1 | 4 | yes | — |
| 82 | C2×#638 | C23 | 1 | 4 | yes | — |
| 83 | C2×#638 | C23 | 1 | 8 | yes | — |
| 84 | D4×C3⋊D3 | — | 2 | 8 | no | — |
| 85 | D4×C3⋊D3 | — | 4 | 8 | no | — |
| 86 | C2×C4⋊(C3⋊D3) | C23 | 1 | 2 | yes | — |
| 87 | C2×C4⋊(C3⋊D3) | C23 | 1 | 4 | yes | — |
| 88 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 89 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×C3×#67 | C23 | 1 | 4 | yes | — |
| 91 | C2×C3×#67 | C23 | 1 | 4 | yes | — |
| 92 | C2×C3×#67 | C23 | 1 | 8 | yes | — |
| 93 | C22×C3×Dic3 | C23 | 1 | 4 | yes | — |
| 94 | C3×#237 | — | 2 | 8 | no | — |
| 95 | C3×D3×D4 | — | 2 | 8 | no | — |
| 96 | C2×C3×D12 | C23 | 1 | 2 | yes | — |
| 97 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 98 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 99 | #3811 | — | 2 | 16 | no | — |
| 100 | D3×#67 | — | 2 | 16 | no | — |
| 101 | D3×#67 | — | 4 | 16 | no | — |
| 102 | C2×#627 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×#626 | — | 2 | 16 | no | — |
| 104 | C2×#626 | C23 | 1 | 4 | yes | — |
| 105 | C2×#626 | C23 | 1 | 4 | yes | — |
| 106 | C2×#626 | C23 | 1 | 4 | yes | — |
| 107 | C2×#626 | C23 | 1 | 8 | yes | — |
| 108 | C2×#626 | C23 | 1 | 2 | yes | — |
| 109 | C2×#625 | C23 | 1 | 4 | yes | — |
| 110 | C2×#625 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×#624 | C23 | 1 | 4 | yes | — |
| 112 | #3804 | — | 2 | 16 | no | — |
| 113 | C2×D3×Dic3 | C23 | 1 | 4 | yes | — |
| 114 | C2×D3×Dic3 | C23 | 1 | 4 | yes | — |
| 115 | D3×D12 | — | 2 | 8 | no | — |
| 116 | #3799 | — | 2 | 8 | no | — |
| 117 | #3798 | D4 | 1 | 8 | yes | complemented |
| 118 | #3796 | — | 2 | 8 | no | — |
| 119 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 120 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 121 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 122 | C3×#217 | C23 | 1 | 8 | yes | — |
| 123 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 124 | C3×(C2×D3)⋊C4 | C23 | 1 | 8 | yes | — |
| 125 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 126 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 127 | #3724 | C23 | 1 | 2 | yes | — |
| 128 | #3724 | C23 | 1 | 4 | yes | — |
| 129 | #3722 | C23 | 1 | 8 | yes | — |
| 130 | #3722 | C23 | 1 | 2 | yes | — |
| 131 | Dic32 | C23 | 1 | 4 | yes | — |
| 132 | #3498 | — | 9 | 1 | no | Sylow |
| 133 | C2×C3×#41 | — | 3 | 2 | no | — |
| 134 | C22×C3×D4 | — | 3 | 2 | no | — |
| 135 | C22×#67 | — | 3 | 4 | no | — |
| 136 | C22×#67 | — | 3 | 8 | no | — |
| 137 | C22×#67 | — | 3 | 4 | no | — |
| 138 | #1009 | — | 6 | 16 | no | — |
| 139 | C2×#239 | — | 3 | 2 | no | — |
| 140 | C2×#239 | — | 3 | 2 | no | — |
| 141 | #1004 | — | 6 | 16 | no | — |
| 142 | C2×#237 | — | 3 | 4 | no | — |
| 143 | C2×#237 | — | 3 | 2 | no | — |
| 144 | C2×#237 | C2×D3 | 1 | 2 | yes | complemented |
| 145 | C2×D3×D4 | — | 3 | 4 | no | — |
| 146 | C2×D3×D4 | — | 3 | 2 | no | — |
| 147 | C2×D3×D4 | — | 3 | 2 | no | — |
| 148 | C2×D3×D4 | — | 3 | 4 | no | — |
| 149 | C2×D3×D4 | — | 3 | 4 | no | — |
| 150 | C2×D3×D4 | — | 3 | 8 | no | — |
| 151 | C2×D3×D4 | — | 3 | 8 | no | — |
| 152 | C2×D3×D4 | — | 3 | 2 | no | — |
| 153 | C2×D3×D4 | — | 6 | 2 | no | — |
| 154 | C2×D3×D4 | — | 6 | 4 | no | — |
| 155 | C2×D3×D4 | C2×D3 | 1 | 2 | yes | complemented |
| 156 | C2×#235 | — | 3 | 4 | no | — |
| 157 | C2×#235 | — | 3 | 2 | no | — |
| 158 | C2×#235 | — | 3 | 2 | no | — |
| 159 | C22×D12 | — | 3 | 4 | no | — |
| 160 | C22×D12 | — | 3 | 2 | no | — |
| 161 | C3×#127 | — | 2 | 1 | no | — |
| 162 | C3×#127 | — | 3 | 2 | no | — |
| 163 | C3×#127 | C2×D3 | 1 | 2 | yes | complemented |
| 164 | C3×#124 | — | 3 | 2 | no | — |
| 165 | C3×#124 | — | 3 | 2 | no | — |
| 166 | C3×#121 | — | 3 | 8 | no | — |
| 167 | C3×#120 | — | 3 | 8 | no | — |
| 168 | C3×#117 | — | 3 | 2 | no | — |
| 169 | #947 | — | 3 | 2 | no | — |
| 170 | #944 | — | 3 | 2 | no | — |
| 171 | #940 | — | 3 | 2 | no | — |
| 172 | #940 | — | 3 | 2 | no | — |
| 173 | #940 | — | 3 | 8 | no | — |
| 174 | #940 | — | 3 | 8 | no | — |
| 175 | #940 | — | 3 | 8 | no | — |
| 176 | #940 | — | 3 | 2 | no | — |
| 177 | #940 | — | 3 | 2 | no | — |
| 178 | #940 | — | 6 | 2 | no | — |
| 179 | #940 | — | 6 | 4 | no | — |
| 180 | #940 | C2×D3 | 1 | 2 | yes | complemented |
| 181 | #939 | — | 3 | 8 | no | — |
| 182 | #939 | — | 3 | 8 | no | — |
| 183 | #939 | C2×D3 | 1 | 8 | yes | complemented |
| 184 | #937 | — | 3 | 8 | no | — |
| 185 | #937 | C2×D3 | 1 | 8 | yes | complemented |
| 186 | #936 | C2×D3 | 1 | 2 | yes | complemented |
| 187 | C4×#67 | — | 3 | 8 | no | — |
| 188 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 189 | #895 | — | 3 | 8 | no | — |
| 190 | #893 | — | 3 | 4 | no | — |
| 191 | #887 | — | 3 | 4 | no | — |
| 192 | #884 | — | 3 | 8 | no | — |
| 193 | #884 | — | 3 | 8 | no | — |
| 194 | #884 | — | 3 | 8 | no | — |
| 195 | #884 | — | 3 | 8 | no | — |
| 196 | #882 | — | 3 | 8 | no | — |
| 197 | #882 | — | 3 | 8 | no | — |
| 198 | #882 | — | 3 | 8 | no | — |
| 199 | #67⋊C4 | — | 3 | 8 | no | — |
| 200 | #67⋊C4 | — | 3 | 8 | no | — |
| 201 | #67⋊C4 | — | 3 | 4 | no | — |
| 202 | #67⋊C4 | — | 3 | 4 | no | — |
| 203 | #875 | — | 3 | 2 | no | — |
| 204 | #875 | C2×D3 | 1 | 2 | yes | complemented |
| 205 | #874 | — | 3 | 2 | no | — |
| 206 | #874 | — | 3 | 2 | no | — |
| 207 | #874 | — | 6 | 1 | no | — |
| 208 | #872 | — | 3 | 2 | no | — |
| 209 | #872 | C2×D3 | 1 | 2 | yes | complemented |
| 210 | C42×D3 | — | 3 | 2 | no | — |
| 211 | C42×D3 | — | 3 | 2 | no | — |
| 212 | C42×D3 | — | 6 | 1 | no | — |
| 213 | C23×C32 | C24 | 1 | 4 | yes | — |
| 214 | C22×C3⋊D3 | — | 2 | 8 | no | — |
| 215 | C22×C3⋊D3 | — | 4 | 8 | no | — |
| 216 | C22×C3⋊D3 | C24 | 1 | 4 | yes | — |
| 217 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 218 | C22×C3×D3 | — | 2 | 8 | no | — |
| 219 | C22×C3×D3 | — | 4 | 8 | no | — |
| 220 | C22×C3×D3 | C24 | 1 | 4 | yes | — |
| 221 | C22×C3×D3 | C24 | 1 | 2 | yes | — |
| 222 | C2×D32 | — | 2 | 8 | no | — |
| 223 | C2×D32 | — | 4 | 8 | no | — |
| 224 | C32×D4 | — | 2 | 4 | no | — |
| 225 | C32×D4 | — | 4 | 4 | no | — |
| 226 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 227 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 228 | #638 | — | 2 | 8 | no | — |
| 229 | #638 | — | 2 | 16 | no | — |
| 230 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 231 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 232 | C4⋊(C3⋊D3) | — | 2 | 4 | no | — |
| 233 | C4⋊(C3⋊D3) | — | 4 | 4 | no | — |
| 234 | C4×C3⋊D3 | — | 2 | 4 | no | — |
| 235 | C4×C3⋊D3 | C2×D4 | 1 | 4 | yes | complemented |
| 236 | C3×#67 | — | 2 | 8 | no | — |
| 237 | C3×#67 | — | 2 | 8 | no | — |
| 238 | C3×#67 | — | 4 | 8 | no | — |
| 239 | C2×C3×Dic3 | — | 2 | 8 | no | — |
| 240 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 241 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 242 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 243 | C3×D12 | — | 2 | 4 | no | — |
| 244 | C3×C4×D3 | C2×D4 | 1 | 8 | yes | complemented |
| 245 | C3×Dic6 | — | 2 | 4 | no | — |
| 246 | #627 | C2×D4 | 1 | 4 | yes | complemented |
| 247 | #626 | — | 2 | 8 | no | — |
| 248 | #626 | — | 2 | 8 | no | — |
| 249 | #626 | — | 2 | 8 | no | — |
| 250 | #626 | — | 4 | 8 | no | — |
| 251 | #626 | C2×D4 | 1 | 8 | yes | complemented |
| 252 | #625 | — | 2 | 8 | no | — |
| 253 | #625 | C2×D4 | 1 | 4 | yes | complemented |
| 254 | #624 | — | 2 | 8 | no | — |
| 255 | D3×Dic3 | — | 2 | 8 | no | — |
| 256 | D3×Dic3 | — | 2 | 8 | no | — |
| 257 | C2×H(5,𝔽2) | — | 9 | 2 | no | — |
| 258 | #550 | — | 9 | 4 | no | — |
| 259 | D42 | — | 9 | 4 | no | — |
| 260 | D42 | — | 9 | 8 | no | — |
| 261 | #535 | — | 3 | 2 | no | — |
| 262 | #535 | — | 9 | 2 | no | — |
| 263 | #535 | — | 9 | 2 | no | — |
| 264 | #532 | — | 9 | 1 | no | — |
| 265 | #532 | — | 9 | 2 | no | — |
| 266 | C2×#127 | — | 9 | 2 | no | — |
| 267 | C2×#127 | — | 9 | 1 | no | — |
| 268 | C4×#41 | — | 9 | 1 | no | — |
| 269 | C24×C3 | — | 3 | 4 | no | — |
| 270 | C23×D3 | — | 3 | 4 | no | — |
| 271 | C23×D3 | — | 3 | 4 | no | — |
| 272 | C23×D3 | — | 3 | 4 | no | — |
| 273 | C23×D3 | — | 3 | 4 | no | — |
| 274 | C23×D3 | — | 6 | 4 | no | — |
| 275 | C23×D3 | C22×D3 | 1 | 4 | yes | — |
| 276 | C3×#41 | — | 6 | 8 | no | — |
| 277 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 278 | C2×C3×D4 | — | 2 | 2 | no | — |
| 279 | C2×C3×D4 | — | 2 | 4 | no | — |
| 280 | C2×C3×D4 | — | 3 | 4 | no | — |
| 281 | C2×C3×D4 | — | 3 | 4 | no | — |
| 282 | C2×C3×D4 | — | 3 | 8 | no | — |
| 283 | C2×C3×D4 | — | 3 | 2 | no | — |
| 284 | C2×C3×D4 | — | 6 | 8 | no | — |
| 285 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 286 | C2×C3×D4 | C22×D3 | 1 | 2 | yes | — |
| 287 | C2×C3×D4 | C22×D3 | 1 | 8 | yes | — |
| 288 | C22×C3×C4 | — | 3 | 2 | no | — |
| 289 | C22×C3×C4 | — | 3 | 4 | no | — |
| 290 | C2×#67 | — | 3 | 2 | no | — |
| 291 | C2×#67 | — | 3 | 8 | no | — |
| 292 | C2×#67 | — | 3 | 4 | no | — |
| 293 | C2×#67 | — | 3 | 8 | no | — |
| 294 | C2×#67 | — | 3 | 4 | no | — |
| 295 | C2×#67 | — | 3 | 8 | no | — |
| 296 | C2×#67 | — | 3 | 2 | no | — |
| 297 | C2×#67 | — | 3 | 4 | no | — |
| 298 | C2×#67 | — | 3 | 4 | no | — |
| 299 | C2×#67 | — | 3 | 4 | no | — |
| 300 | C2×#67 | — | 3 | 8 | no | — |
| 301 | C2×#67 | — | 6 | 8 | no | — |
| 302 | C2×#67 | — | 6 | 4 | no | — |
| 303 | C2×#67 | — | 6 | 16 | no | — |
| 304 | C2×#67 | — | 6 | 16 | no | — |
| 305 | C2×#67 | — | 12 | 16 | no | — |
| 306 | C2×#67 | C22×D3 | 1 | 4 | yes | — |
| 307 | C2×#67 | C22×D3 | 1 | 4 | yes | — |
| 308 | C2×#67 | C22×D3 | 1 | 8 | yes | — |
| 309 | C22×Dic3 | — | 3 | 4 | no | — |
| 310 | C22×Dic3 | — | 3 | 4 | no | — |
| 311 | C22×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 312 | #239 | — | 6 | 8 | no | — |
| 313 | #239 | — | 6 | 8 | no | — |
| 314 | #237 | — | 2 | 8 | no | — |
| 315 | #237 | — | 6 | 8 | no | — |
| 316 | #237 | — | 6 | 16 | no | — |
| 317 | D3×D4 | — | 2 | 8 | no | — |
| 318 | D3×D4 | — | 6 | 8 | no | — |
| 319 | D3×D4 | — | 6 | 8 | no | — |
| 320 | D3×D4 | — | 6 | 16 | no | — |
| 321 | D3×D4 | — | 6 | 16 | no | — |
| 322 | D3×D4 | — | 6 | 16 | no | — |
| 323 | D3×D4 | — | 6 | 8 | no | — |
| 324 | D3×D4 | — | 12 | 8 | no | — |
| 325 | D3×D4 | — | 12 | 16 | no | — |
| 326 | D3×D4 | — | 12 | 16 | no | — |
| 327 | D3×D4 | — | 12 | 16 | no | — |
| 328 | #235 | — | 3 | 16 | no | — |
| 329 | #235 | — | 6 | 8 | no | — |
| 330 | #235 | — | 6 | 16 | no | — |
| 331 | C2×D12 | — | 3 | 2 | no | — |
| 332 | C2×D12 | — | 3 | 4 | no | — |
| 333 | C2×D12 | — | 3 | 4 | no | — |
| 334 | C2×D12 | — | 3 | 4 | no | — |
| 335 | C2×D12 | — | 3 | 2 | no | — |
| 336 | C2×D12 | — | 3 | 2 | no | — |
| 337 | C2×D12 | — | 3 | 8 | no | — |
| 338 | C2×D12 | — | 3 | 8 | no | — |
| 339 | C2×D12 | — | 6 | 2 | no | — |
| 340 | C2×D12 | — | 6 | 4 | no | — |
| 341 | C2×D12 | — | 6 | 8 | no | — |
| 342 | C2×D12 | — | 6 | 16 | no | — |
| 343 | C2×D12 | C22×D3 | 1 | 2 | yes | — |
| 344 | C2×C4×D3 | — | 3 | 2 | no | — |
| 345 | C2×C4×D3 | — | 3 | 4 | no | — |
| 346 | C2×C4×D3 | — | 3 | 4 | no | — |
| 347 | C2×C4×D3 | — | 3 | 4 | no | — |
| 348 | C2×C4×D3 | — | 3 | 4 | no | — |
| 349 | C2×C4×D3 | — | 3 | 4 | no | — |
| 350 | C2×C4×D3 | — | 6 | 1 | no | — |
| 351 | C2×C4×D3 | — | 6 | 2 | no | — |
| 352 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 353 | C2×Dic6 | — | 3 | 2 | no | — |
| 354 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 355 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 356 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 357 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 358 | C3×C22⋊C4 | — | 3 | 8 | no | — |
| 359 | C3×C42 | — | 2 | 1 | no | — |
| 360 | C3×C42 | — | 3 | 2 | no | — |
| 361 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 362 | #217 | C22×D3 | 1 | 8 | yes | — |
| 363 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 364 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 365 | (C2×D3)⋊C4 | — | 3 | 8 | no | — |
| 366 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 367 | (C2×D3)⋊C4 | C22×D3 | 1 | 8 | yes | — |
| 368 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 369 | Dic3⋊C4 | — | 3 | 8 | no | — |
| 370 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 371 | C4×Dic3 | — | 3 | 2 | no | — |
| 372 | C4×Dic3 | — | 3 | 4 | no | — |
| 373 | C4×Dic3 | — | 3 | 4 | no | — |
| 374 | C4×Dic3 | — | 3 | 4 | no | — |
| 375 | C4×Dic3 | — | 6 | 1 | no | — |
| 376 | C4×Dic3 | — | 6 | 2 | no | — |
| 377 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 378 | C22×C32 | — | 2 | 4 | no | — |
| 379 | C22×C32 | — | 2 | 8 | no | — |
| 380 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 381 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 382 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 383 | C2×C3⋊D3 | — | 2 | 8 | no | — |
| 384 | C2×C3⋊D3 | — | 8 | 8 | no | — |
| 385 | C2×C3⋊D3 | C22×D4 | 1 | 2 | yes | — |
| 386 | C2×C3×D3 | — | 2 | 4 | no | — |
| 387 | C2×C3×D3 | — | 2 | 4 | no | — |
| 388 | C2×C3×D3 | — | 2 | 8 | no | — |
| 389 | C2×C3×D3 | — | 8 | 8 | no | — |
| 390 | C2×C3×D3 | C22×D4 | 1 | 4 | yes | — |
| 391 | D32 | — | 8 | 8 | no | — |
| 392 | C32×C4 | — | 2 | 2 | no | — |
| 393 | C32×C4 | C22×D4 | 1 | 2 | yes | — |
| 394 | C3⋊Dic3 | C22×D4 | 1 | 2 | yes | — |
| 395 | C3⋊Dic3 | H(5,𝔽2) | 1 | 4 | yes | complemented |
| 396 | C3×Dic3 | — | 2 | 4 | no | — |
| 397 | C3×Dic3 | — | 2 | 4 | no | — |
| 398 | C3×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 399 | H(5,𝔽2) | — | 18 | 16 | no | — |
| 400 | C2×#41 | — | 3 | 2 | no | — |
| 401 | C2×#41 | — | 9 | 1 | no | — |
| 402 | C2×#41 | — | 9 | 4 | no | — |
| 403 | C2×#41 | — | 9 | 2 | no | — |
| 404 | C2×#41 | — | 9 | 2 | no | — |
| 405 | C22×D4 | — | 3 | 2 | no | — |
| 406 | C22×D4 | — | 9 | 2 | no | — |
| 407 | C22×D4 | — | 9 | 4 | no | — |
| 408 | C22×D4 | — | 9 | 4 | no | — |
| 409 | C22×D4 | — | 9 | 4 | no | — |
| 410 | C22×D4 | — | 9 | 8 | no | — |
| 411 | C22×D4 | — | 9 | 2 | no | — |
| 412 | C22×D4 | — | 9 | 4 | no | — |
| 413 | C4⋊Q8 | — | 9 | 1 | no | — |
| 414 | #127 | — | 3 | 2 | no | — |
| 415 | #127 | — | 9 | 2 | no | — |
| 416 | #127 | — | 9 | 1 | no | — |
| 417 | #127 | — | 9 | 8 | no | — |
| 418 | #127 | — | 9 | 2 | no | — |
| 419 | #127 | — | 9 | 4 | no | — |
| 420 | #127 | — | 9 | 1 | no | — |
| 421 | #127 | D32 | 1 | 1 | yes | characteristic, complemented |
| 422 | #124 | — | 3 | 2 | no | — |
| 423 | #124 | — | 3 | 2 | no | — |
| 424 | #124 | — | 9 | 2 | no | — |
| 425 | #121 | — | 3 | 8 | no | — |
| 426 | #121 | — | 9 | 4 | no | — |
| 427 | #121 | — | 9 | 8 | no | — |
| 428 | #121 | — | 9 | 8 | no | — |
| 429 | #121 | — | 9 | 8 | no | — |
| 430 | #120 | — | 3 | 8 | no | — |
| 431 | #120 | — | 9 | 8 | no | — |
| 432 | #120 | — | 9 | 8 | no | — |
| 433 | C4×Q8 | — | 9 | 2 | no | — |
| 434 | C4×D4 | — | 9 | 2 | no | — |
| 435 | C4×D4 | — | 9 | 4 | no | — |
| 436 | C4×D4 | — | 9 | 4 | no | — |
| 437 | C4×D4 | — | 9 | 8 | no | — |
| 438 | #117 | — | 3 | 2 | no | — |
| 439 | #117 | — | 9 | 1 | no | — |
| 440 | C2×C42 | — | 9 | 2 | no | — |
| 441 | C2×C42 | — | 9 | 1 | no | — |
| 442 | C23×C3 | — | 2 | 4 | no | — |
| 443 | C23×C3 | — | 3 | 2 | no | — |
| 444 | C23×C3 | — | 3 | 4 | no | — |
| 445 | C23×C3 | — | 6 | 8 | no | — |
| 446 | C23×C3 | — | 12 | 8 | no | — |
| 447 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 448 | C23×C3 | C23×D3 | 1 | 4 | yes | — |
| 449 | C22×D3 | — | 2 | 8 | no | — |
| 450 | C22×D3 | — | 3 | 2 | no | — |
| 451 | C22×D3 | — | 3 | 4 | no | — |
| 452 | C22×D3 | — | 3 | 4 | no | — |
| 453 | C22×D3 | — | 4 | 8 | no | — |
| 454 | C22×D3 | — | 6 | 1 | no | — |
| 455 | C22×D3 | — | 6 | 4 | no | — |
| 456 | C22×D3 | — | 6 | 8 | no | — |
| 457 | C22×D3 | — | 6 | 8 | no | — |
| 458 | C22×D3 | — | 6 | 8 | no | — |
| 459 | C22×D3 | — | 6 | 8 | no | — |
| 460 | C22×D3 | — | 12 | 8 | no | — |
| 461 | C22×D3 | — | 12 | 8 | no | — |
| 462 | C22×D3 | — | 12 | 8 | no | — |
| 463 | C22×D3 | — | 12 | 8 | no | — |
| 464 | C22×D3 | — | 12 | 8 | no | — |
| 465 | C22×D3 | — | 12 | 16 | no | — |
| 466 | C22×D3 | C23×D3 | 1 | 4 | yes | — |
| 467 | C22×D3 | C23×D3 | 1 | 2 | yes | — |
| 468 | C3×Q8 | — | 6 | 4 | no | — |
| 469 | C3×D4 | — | 2 | 4 | no | — |
| 470 | C3×D4 | — | 2 | 4 | no | — |
| 471 | C3×D4 | — | 4 | 4 | no | — |
| 472 | C3×D4 | — | 4 | 8 | no | — |
| 473 | C3×D4 | — | 4 | 8 | no | — |
| 474 | C3×D4 | — | 6 | 8 | no | — |
| 475 | C3×D4 | — | 6 | 8 | no | — |
| 476 | C3×D4 | — | 6 | 4 | no | — |
| 477 | C3×D4 | — | 12 | 8 | no | — |
| 478 | C2×C3×C4 | — | 2 | 2 | no | — |
| 479 | C2×C3×C4 | — | 2 | 1 | no | — |
| 480 | C2×C3×C4 | — | 3 | 2 | no | — |
| 481 | C2×C3×C4 | — | 3 | 8 | no | — |
| 482 | C2×C3×C4 | — | 3 | 4 | no | — |
| 483 | C2×C3×C4 | — | 3 | 4 | no | — |
| 484 | C2×C3×C4 | — | 6 | 8 | no | — |
| 485 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 486 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 487 | #67 | — | 2 | 8 | no | — |
| 488 | #67 | — | 2 | 8 | no | — |
| 489 | #67 | — | 3 | 8 | no | — |
| 490 | #67 | — | 3 | 8 | no | — |
| 491 | #67 | — | 4 | 8 | no | — |
| 492 | #67 | — | 6 | 8 | no | — |
| 493 | #67 | — | 6 | 8 | no | — |
| 494 | #67 | — | 6 | 16 | no | — |
| 495 | #67 | — | 6 | 8 | no | — |
| 496 | #67 | — | 6 | 8 | no | — |
| 497 | #67 | — | 6 | 16 | no | — |
| 498 | #67 | — | 6 | 16 | no | — |
| 499 | #67 | — | 6 | 8 | no | — |
| 500 | #67 | — | 12 | 8 | no | — |
| 501 | #67 | — | 12 | 16 | no | — |
| 502 | #67 | — | 12 | 8 | no | — |
| 503 | C2×Dic3 | — | 2 | 8 | no | — |
| 504 | C2×Dic3 | — | 3 | 4 | no | — |
| 505 | C2×Dic3 | — | 3 | 2 | no | — |
| 506 | C2×Dic3 | — | 6 | 2 | no | — |
| 507 | C2×Dic3 | — | 6 | 1 | no | — |
| 508 | C2×Dic3 | — | 6 | 8 | no | — |
| 509 | C2×Dic3 | — | 6 | 8 | no | — |
| 510 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 511 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 512 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 513 | D12 | — | 2 | 4 | no | — |
| 514 | D12 | — | 3 | 8 | no | — |
| 515 | D12 | — | 6 | 8 | no | — |
| 516 | D12 | — | 6 | 8 | no | — |
| 517 | D12 | — | 6 | 8 | no | — |
| 518 | D12 | — | 6 | 4 | no | — |
| 519 | D12 | — | 6 | 4 | no | — |
| 520 | D12 | — | 12 | 4 | no | — |
| 521 | D12 | — | 12 | 8 | no | — |
| 522 | D12 | — | 12 | 8 | no | — |
| 523 | D12 | — | 12 | 8 | no | — |
| 524 | C4×D3 | — | 3 | 8 | no | — |
| 525 | C4×D3 | — | 6 | 4 | no | — |
| 526 | C4×D3 | — | 6 | 8 | no | — |
| 527 | C4×D3 | — | 6 | 8 | no | — |
| 528 | C4×D3 | — | 6 | 8 | no | — |
| 529 | C4×D3 | — | 6 | 8 | no | — |
| 530 | C4×D3 | — | 6 | 8 | no | — |
| 531 | C4×D3 | — | 6 | 8 | no | — |
| 532 | C4×D3 | D3×D4 | 1 | 8 | yes | complemented |
| 533 | Dic6 | — | 2 | 4 | no | — |
| 534 | Dic6 | — | 3 | 8 | no | — |
| 535 | C2×C32 | — | 4 | 4 | no | — |
| 536 | C2×C32 | C23×D4 | 1 | 1 | yes | characteristic |
| 537 | C2×C32 | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 538 | C3⋊D3 | — | 2 | 2 | no | — |
| 539 | C3⋊D3 | — | 4 | 4 | no | — |
| 540 | C3×D3 | — | 2 | 4 | no | — |
| 541 | C3×D3 | — | 4 | 4 | no | — |
| 542 | C24 | — | 3 | 4 | no | — |
| 543 | C24 | — | 9 | 4 | no | — |
| 544 | C24 | — | 9 | 4 | no | — |
| 545 | #41 | — | 6 | 8 | no | — |
| 546 | #41 | — | 9 | 8 | no | — |
| 547 | #41 | — | 18 | 8 | no | — |
| 548 | #41 | — | 18 | 16 | no | — |
| 549 | #41 | — | 18 | 8 | no | — |
| 550 | C2×Q8 | — | 3 | 2 | no | — |
| 551 | C2×Q8 | — | 9 | 1 | no | — |
| 552 | C2×D4 | — | 3 | 4 | no | — |
| 553 | C2×D4 | — | 3 | 4 | no | — |
| 554 | C2×D4 | — | 3 | 8 | no | — |
| 555 | C2×D4 | — | 3 | 2 | no | — |
| 556 | C2×D4 | — | 6 | 8 | no | — |
| 557 | C2×D4 | — | 9 | 2 | no | — |
| 558 | C2×D4 | — | 9 | 4 | no | — |
| 559 | C2×D4 | — | 9 | 4 | no | — |
| 560 | C2×D4 | — | 9 | 4 | no | — |
| 561 | C2×D4 | — | 9 | 8 | no | — |
| 562 | C2×D4 | — | 9 | 1 | no | — |
| 563 | C2×D4 | — | 9 | 4 | no | — |
| 564 | C2×D4 | — | 9 | 8 | no | — |
| 565 | C2×D4 | — | 9 | 4 | no | — |
| 566 | C2×D4 | — | 9 | 2 | no | — |
| 567 | C2×D4 | — | 9 | 4 | no | — |
| 568 | C2×D4 | — | 18 | 8 | no | — |
| 569 | C2×D4 | — | 18 | 16 | no | — |
| 570 | C2×D4 | — | 18 | 8 | no | — |
| 571 | C2×D4 | — | 18 | 16 | no | — |
| 572 | C2×D4 | — | 18 | 16 | no | — |
| 573 | C2×D4 | — | 36 | 8 | no | — |
| 574 | C2×D4 | — | 36 | 16 | no | — |
| 575 | C2×D4 | C2×D32 | 1 | 2 | yes | — |
| 576 | C2×D4 | C2×D32 | 1 | 4 | yes | — |
| 577 | C22×C4 | — | 3 | 2 | no | — |
| 578 | C22×C4 | — | 3 | 4 | no | — |
| 579 | C22×C4 | — | 9 | 4 | no | — |
| 580 | C22×C4 | — | 9 | 4 | no | — |
| 581 | C22×C4 | — | 9 | 4 | no | — |
| 582 | C22×C4 | — | 9 | 1 | no | — |
| 583 | C22×C4 | — | 9 | 2 | no | — |
| 584 | C4⋊C4 | — | 3 | 4 | no | — |
| 585 | C4⋊C4 | — | 9 | 2 | no | — |
| 586 | C4⋊C4 | — | 9 | 4 | no | — |
| 587 | C22⋊C4 | — | 3 | 8 | no | — |
| 588 | C22⋊C4 | — | 3 | 4 | no | — |
| 589 | C22⋊C4 | — | 3 | 8 | no | — |
| 590 | C22⋊C4 | — | 9 | 2 | no | — |
| 591 | C22⋊C4 | — | 9 | 8 | no | — |
| 592 | C42 | — | 3 | 2 | no | — |
| 593 | C42 | — | 9 | 4 | no | — |
| 594 | C42 | — | 9 | 1 | no | — |
| 595 | C42 | — | 9 | 2 | no | — |
| 596 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 597 | C22×C3 | — | 2 | 4 | no | — |
| 598 | C22×C3 | — | 2 | 4 | no | — |
| 599 | C22×C3 | — | 2 | 8 | no | — |
| 600 | C22×C3 | — | 2 | 8 | no | — |
| 601 | C22×C3 | — | 2 | 1 | no | — |
| 602 | C22×C3 | — | 3 | 4 | no | — |
| 603 | C22×C3 | — | 4 | 4 | no | — |
| 604 | C22×C3 | — | 4 | 8 | no | — |
| 605 | C22×C3 | — | 6 | 4 | no | — |
| 606 | C22×C3 | — | 6 | 4 | no | — |
| 607 | C22×C3 | — | 6 | 8 | no | — |
| 608 | C22×C3 | — | 24 | 8 | no | — |
| 609 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 610 | C2×D3 | — | 2 | 4 | no | — |
| 611 | C2×D3 | — | 2 | 4 | no | — |
| 612 | C2×D3 | — | 2 | 8 | no | — |
| 613 | C2×D3 | — | 3 | 4 | no | — |
| 614 | C2×D3 | — | 6 | 2 | no | — |
| 615 | C2×D3 | — | 6 | 4 | no | — |
| 616 | C2×D3 | — | 6 | 4 | no | — |
| 617 | C2×D3 | — | 6 | 4 | no | — |
| 618 | C2×D3 | — | 6 | 4 | no | — |
| 619 | C2×D3 | — | 6 | 8 | no | — |
| 620 | C2×D3 | — | 6 | 8 | no | — |
| 621 | C2×D3 | — | 8 | 8 | no | — |
| 622 | C2×D3 | — | 12 | 4 | no | — |
| 623 | C2×D3 | — | 12 | 8 | no | — |
| 624 | C2×D3 | — | 24 | 8 | no | — |
| 625 | C2×D3 | — | 24 | 8 | no | — |
| 626 | C2×D3 | — | 24 | 8 | no | — |
| 627 | C2×D3 | — | 24 | 8 | no | — |
| 628 | C2×D3 | — | 24 | 16 | no | — |
| 629 | C2×D3 | C2×D3×D4 | 1 | 4 | yes | — |
| 630 | C3×C4 | — | 2 | 4 | no | — |
| 631 | C3×C4 | — | 2 | 4 | no | — |
| 632 | C3×C4 | — | 2 | 2 | no | — |
| 633 | C3×C4 | — | 3 | 4 | no | — |
| 634 | C3×C4 | — | 6 | 4 | no | — |
| 635 | C3×C4 | — | 6 | 4 | no | — |
| 636 | C3×C4 | C2×D3×D4 | 1 | 4 | yes | — |
| 637 | Dic3 | — | 2 | 4 | no | — |
| 638 | Dic3 | — | 2 | 4 | no | — |
| 639 | Dic3 | — | 3 | 4 | no | — |
| 640 | Dic3 | — | 3 | 8 | no | — |
| 641 | Dic3 | — | 6 | 2 | no | — |
| 642 | Dic3 | — | 6 | 4 | no | — |
| 643 | Dic3 | C2×D3×D4 | 1 | 4 | yes | — |
| 644 | C32 | #3498 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 645 | C23 | — | 3 | 2 | no | — |
| 646 | C23 | — | 3 | 4 | no | — |
| 647 | C23 | — | 6 | 8 | no | — |
| 648 | C23 | — | 9 | 1 | no | — |
| 649 | C23 | — | 9 | 4 | no | — |
| 650 | C23 | — | 12 | 8 | no | — |
| 651 | C23 | — | 18 | 8 | no | — |
| 652 | C23 | — | 18 | 8 | no | — |
| 653 | C23 | — | 36 | 8 | no | — |
| 654 | C23 | — | 36 | 8 | no | — |
| 655 | C23 | C22×D32 | 1 | 4 | yes | — |
| 656 | Q8 | — | 6 | 4 | no | — |
| 657 | Q8 | — | 9 | 4 | no | — |
| 658 | D4 | — | 2 | 4 | no | — |
| 659 | D4 | — | 4 | 4 | no | — |
| 660 | D4 | — | 6 | 8 | no | — |
| 661 | D4 | — | 6 | 8 | no | — |
| 662 | D4 | — | 6 | 4 | no | — |
| 663 | D4 | — | 9 | 8 | no | — |
| 664 | D4 | — | 9 | 4 | no | — |
| 665 | D4 | — | 12 | 8 | no | — |
| 666 | D4 | — | 18 | 8 | no | — |
| 667 | D4 | — | 18 | 8 | no | — |
| 668 | D4 | — | 18 | 8 | no | — |
| 669 | D4 | — | 18 | 8 | no | — |
| 670 | D4 | — | 18 | 16 | no | — |
| 671 | D4 | — | 18 | 8 | no | — |
| 672 | D4 | — | 18 | 4 | no | — |
| 673 | D4 | — | 36 | 4 | no | — |
| 674 | D4 | — | 36 | 8 | no | — |
| 675 | C2×C4 | — | 3 | 2 | no | — |
| 676 | C2×C4 | — | 3 | 8 | no | — |
| 677 | C2×C4 | — | 3 | 4 | no | — |
| 678 | C2×C4 | — | 3 | 4 | no | — |
| 679 | C2×C4 | — | 6 | 8 | no | — |
| 680 | C2×C4 | — | 9 | 2 | no | — |
| 681 | C2×C4 | — | 9 | 1 | no | — |
| 682 | C2×C4 | — | 9 | 4 | no | — |
| 683 | C2×C4 | — | 18 | 4 | no | — |
| 684 | C2×C4 | — | 18 | 8 | no | — |
| 685 | C2×C4 | — | 18 | 8 | no | — |
| 686 | C2×C4 | — | 18 | 8 | no | — |
| 687 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 688 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 689 | C2×C3 | — | 2 | 1 | no | — |
| 690 | C2×C3 | — | 2 | 2 | no | — |
| 691 | C2×C3 | — | 4 | 4 | no | — |
| 692 | C2×C3 | — | 4 | 4 | no | — |
| 693 | C2×C3 | — | 6 | 4 | no | — |
| 694 | C2×C3 | — | 8 | 4 | no | — |
| 695 | C2×C3 | — | 12 | 4 | no | — |
| 696 | C2×C3 | C22×D3×D4 | 1 | 2 | yes | — |
| 697 | C2×C3 | D3×H(5,𝔽2) | 1 | 4 | yes | — |
| 698 | D3 | — | 2 | 4 | no | — |
| 699 | D3 | — | 4 | 4 | no | — |
| 700 | D3 | — | 6 | 4 | no | — |
| 701 | D3 | — | 6 | 4 | no | — |
| 702 | D3 | — | 12 | 4 | no | — |
| 703 | D3 | — | 12 | 4 | no | — |
| 704 | D3 | — | 24 | 4 | no | — |
| 705 | C22 | — | 2 | 4 | no | — |
| 706 | C22 | — | 2 | 8 | no | — |
| 707 | C22 | — | 3 | 4 | no | — |
| 708 | C22 | — | 6 | 4 | no | — |
| 709 | C22 | — | 6 | 4 | no | — |
| 710 | C22 | — | 6 | 8 | no | — |
| 711 | C22 | — | 9 | 2 | no | — |
| 712 | C22 | — | 18 | 2 | no | — |
| 713 | C22 | — | 18 | 4 | no | — |
| 714 | C22 | — | 18 | 8 | no | — |
| 715 | C22 | — | 24 | 8 | no | — |
| 716 | C22 | — | 72 | 8 | no | — |
| 717 | C22 | — | 72 | 8 | no | — |
| 718 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 719 | C4 | — | 2 | 2 | no | — |
| 720 | C4 | — | 3 | 4 | no | — |
| 721 | C4 | — | 6 | 4 | no | — |
| 722 | C4 | — | 6 | 4 | no | — |
| 723 | C4 | — | 9 | 2 | no | — |
| 724 | C4 | — | 9 | 4 | no | — |
| 725 | C4 | D32×D4 | 1 | 2 | yes | — |
| 726 | C3 | — | 2 | 1 | no | — |
| 727 | C3 | #86316 | 1 | 2 | yes | complemented |
| 728 | C2 | — | 4 | 4 | no | — |
| 729 | C2 | — | 6 | 4 | no | — |
| 730 | C2 | — | 12 | 4 | no | — |
| 731 | C2 | — | 18 | 2 | no | — |
| 732 | C2 | — | 36 | 4 | no | — |
| 733 | C2 | C2×D32×D4 | 1 | 1 | yes | characteristic |
| 734 | C2 | #10596675 | 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×#64314 | C2 | semidirect |
| 2. C3⋊D3×#127 | C2 | semidirect |
| 3. C3×#5715 | C2 | semidirect |
| 4. #10595292 | C2 | semidirect |
| 5. #10595289 | C2 | semidirect |
| 6. D3×#940 | C2 | semidirect |
| 7. #10595269 | C2 | semidirect |
| 8. #10595168 | C2 | semidirect |
| 9. #10595153 | C2 | semidirect |
| 10. #10594001 | C2 | semidirect |
| 11. #10593971 | C2 | semidirect |
| 12. #10593966 | C2 | semidirect |
| 14. C2×D4×C3⋊D3 | C22 | semidirect |
| 15. C2×D4×C3⋊D3 | C22 | semidirect |
| 16. C2×C3×#237 | C22 | semidirect |
| 17. C2×C3×D3×D4 | C22 | semidirect |
| 18. C2×#3811 | C22 | semidirect |
| 19. C2×D3×#67 | C22 | semidirect |
| 20. C2×D3×#67 | C22 | semidirect |
| 21. C22×#626 | C22 | semidirect |
| 22. C2×#3804 | C22 | semidirect |
| 24. C2×D3×D12 | C22 | semidirect |
| 25. C2×#3799 | C22 | semidirect |
| 27. C2×#3796 | C22 | semidirect |
| 28. C32×#127 | C22 | semidirect |
| 29. #64149 | C22 | semidirect |
| 30. #64149 | C22 | semidirect |
| 31. #64083 | C22 | semidirect |
| 32. C42×C3⋊D3 | C22 | semidirect |
| 33. C3×#940 | C22 | semidirect |
| 34. C3×#939 | C22 | semidirect |
| 35. C3×#937 | C22 | semidirect |
| 36. C3×#936 | C22 | semidirect |
| 37. C3×#875 | C22 | semidirect |
| 38. C3×#872 | C22 | semidirect |
| 39. #63981 | C22 | semidirect |
| 40. #63979 | C22 | semidirect |
| 41. #63971 | C22 | semidirect |
| 42. #63971 | C22 | semidirect |
| 43. #63952 | C22 | semidirect |
| 44. #63923 | C22 | semidirect |
| 45. #63914 | C22 | semidirect |
| 46. #63912 | C22 | semidirect |
| 47. #63911 | C22 | semidirect |
| 48. #63910 | C22 | semidirect |
| 49. #63902 | C22 | semidirect |
| 50. #63902 | C22 | semidirect |
| 51. #63881 | C22 | semidirect |
| 52. C4×D3×Dic3 | C22 | semidirect |
| 53. #63874 | C22 | semidirect |
| 54. #63873 | C22 | semidirect |
| 55. #63864 | C22 | semidirect |
| 56. #63838 | C22 | semidirect |
| 63. #5715 | D3 | semidirect |
| 117. #3798 | D4 | semidirect |
| 144. C2×#237 | C2×D3 | semidirect |
| 155. C2×D3×D4 | C2×D3 | semidirect |
| 163. C3×#127 | C2×D3 | semidirect |
| 180. #940 | C2×D3 | semidirect |
| 183. #939 | C2×D3 | semidirect |
| 185. #937 | C2×D3 | semidirect |
| 186. #936 | C2×D3 | semidirect |
| 204. #875 | C2×D3 | semidirect |
| 209. #872 | C2×D3 | semidirect |
| 235. C4×C3⋊D3 | C2×D4 | semidirect |
| 244. C3×C4×D3 | C2×D4 | semidirect |
| 246. #627 | C2×D4 | semidirect |
| 251. #626 | C2×D4 | semidirect |
| 253. #625 | C2×D4 | semidirect |
| 395. C3⋊Dic3 | H(5,𝔽2) | semidirect |
| 421. #127 | D32 | semidirect |
| 532. C4×D3 | D3×D4 | semidirect |
| 644. C32 | #3498 | semidirect |
| 727. C3 | #86316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64314 | 2 |
| C3⋊D3×#127 | 2 |
| C3×#5715 | 2 |
| #10595292 | 2 |
| #10595289 | 2 |
| D3×#940 | 2 |
| #10595269 | 2 |
| #10595168 | 2 |
| #10595153 | 2 |
| #10594001 | 2 |
| #10593971 | 2 |
| #10593966 | 2 |
| #86316 | 3 |