Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1396 conjugacy classes of subgroups.
The subgroup lattice has 1040 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #85868 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #78688 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#4741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#1913 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #71851 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #71656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70037 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #70036 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #70034 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #70025 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #68970 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #68967 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #68962 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #68960 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #23996 | — | 3 | 1 | no | maximal, Sylow |
| 17 | C2×#1004 | C22 | 1 | 1 | yes | characteristic |
| 18 | C3×#534 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#518 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #5804 | C22 | 1 | 1 | yes | characteristic |
| 21 | #5804 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#937 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#937 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #5560 | — | 2 | 2 | no | — |
| 25 | #5556 | — | 2 | 2 | no | — |
| 26 | #5550 | — | 2 | 2 | no | — |
| 27 | #5547 | — | 2 | 2 | no | — |
| 28 | #5527 | — | 2 | 2 | no | — |
| 29 | #5490 | — | 2 | 2 | no | — |
| 30 | C2×#882 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#882 | C22 | 1 | 1 | yes | characteristic |
| 32 | #5486 | C22 | 1 | 1 | yes | characteristic |
| 33 | #5486 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×D3×C22⋊C4 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #5483 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×C3×#99 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C3×#99 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×C3×#99 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#834 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#834 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#834 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #5053 | — | 2 | 2 | no | — |
| 43 | #5032 | — | 2 | 2 | no | — |
| 44 | #4955 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #4955 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 49 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 50 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#806 | C22 | 1 | 1 | yes | characteristic |
| 52 | D3×#99 | — | 2 | 2 | no | — |
| 53 | #4741 | — | 2 | 2 | no | — |
| 54 | #4741 | — | 2 | 2 | no | — |
| 55 | #4740 | — | 2 | 2 | no | — |
| 56 | C3×#342 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C3×#342 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #4527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #4527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #4527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #4527 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #4526 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #4526 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #3490 | — | 3 | 1 | no | — |
| 65 | #3026 | — | 3 | 1 | no | — |
| 66 | C2×B(4,𝔽2) | — | 3 | 1 | no | — |
| 67 | #2883 | — | 3 | 1 | no | — |
| 68 | #2032 | — | 3 | 1 | no | — |
| 69 | #2032 | — | 3 | 1 | no | — |
| 70 | #2021 | — | 3 | 1 | no | — |
| 71 | #2021 | — | 3 | 1 | no | — |
| 72 | #1913 | — | 3 | 1 | no | — |
| 73 | #1913 | — | 3 | 1 | no | — |
| 74 | #1913 | D3 | 1 | 1 | yes | characteristic, complemented |
| 75 | #1898 | — | 3 | 1 | no | — |
| 76 | #1898 | — | 3 | 1 | no | — |
| 77 | #1889 | — | 3 | 1 | no | — |
| 78 | #1828 | — | 3 | 1 | no | — |
| 79 | C24×D3 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 82 | C22×#67 | — | 2 | 1 | no | — |
| 83 | C22×#67 | — | 2 | 1 | no | — |
| 84 | C22×#67 | — | 2 | 1 | no | — |
| 85 | C22×#67 | C23 | 1 | 1 | yes | characteristic |
| 86 | C22×#67 | C23 | 1 | 1 | yes | characteristic |
| 87 | #1004 | — | 2 | 2 | no | — |
| 88 | #1004 | — | 2 | 2 | no | — |
| 89 | #1004 | — | 4 | 1 | no | — |
| 90 | #1004 | — | 4 | 1 | no | — |
| 91 | C2×#237 | — | 2 | 1 | no | — |
| 92 | C2×#237 | — | 2 | 1 | no | — |
| 93 | C2×D3×D4 | — | 2 | 1 | no | — |
| 94 | C2×D3×D4 | — | 2 | 1 | no | — |
| 95 | C2×#235 | — | 2 | 1 | no | — |
| 96 | C2×#235 | — | 2 | 2 | no | — |
| 97 | C22×D12 | — | 2 | 1 | no | — |
| 98 | C22×D12 | — | 2 | 1 | no | — |
| 99 | C22×C4×D3 | — | 2 | 1 | no | — |
| 100 | C3×#123 | — | 2 | 1 | no | — |
| 101 | C3×#123 | — | 2 | 1 | no | — |
| 102 | C3×#121 | — | 4 | 1 | no | — |
| 103 | C3×#120 | — | 2 | 1 | no | — |
| 104 | C3×#120 | — | 2 | 1 | no | — |
| 105 | C3×C4×D4 | — | 2 | 2 | no | — |
| 106 | C3×C4×D4 | — | 2 | 2 | no | — |
| 107 | C3×#117 | — | 2 | 1 | no | — |
| 108 | C2×C3×C22⋊C4 | — | 2 | 1 | no | — |
| 109 | C2×C3×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C3×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×C3×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×C3×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C3×C22⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 114 | #953 | — | 2 | 1 | no | — |
| 115 | #953 | D4 | 1 | 2 | yes | complemented |
| 116 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 117 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 118 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 120 | C2×#217 | C23 | 1 | 1 | yes | characteristic |
| 121 | #939 | — | 2 | 2 | no | — |
| 122 | #939 | — | 4 | 1 | no | — |
| 123 | #937 | — | 2 | 1 | no | — |
| 124 | #937 | — | 2 | 1 | no | — |
| 125 | #937 | — | 2 | 1 | no | — |
| 126 | #937 | — | 2 | 2 | no | — |
| 127 | #937 | — | 2 | 1 | no | — |
| 128 | #937 | — | 2 | 1 | no | — |
| 129 | #937 | — | 2 | 1 | no | — |
| 130 | #937 | — | 4 | 1 | no | — |
| 131 | #935 | — | 2 | 1 | no | — |
| 132 | #935 | — | 2 | 1 | no | — |
| 133 | #930 | — | 2 | 2 | no | — |
| 134 | #929 | — | 2 | 2 | no | — |
| 135 | #929 | — | 2 | 1 | no | — |
| 136 | #929 | D4 | 1 | 2 | yes | complemented |
| 137 | C4×#67 | — | 2 | 2 | no | — |
| 138 | C4×#67 | — | 2 | 2 | no | — |
| 139 | C4×#67 | — | 4 | 1 | no | — |
| 140 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 141 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 142 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 143 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 144 | C2×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 145 | C2×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 146 | C2×(C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 147 | #924 | — | 2 | 2 | no | — |
| 148 | #898 | — | 2 | 2 | no | — |
| 149 | #896 | — | 2 | 2 | no | — |
| 150 | #894 | — | 2 | 2 | no | — |
| 151 | #894 | — | 2 | 2 | no | — |
| 152 | #885 | — | 2 | 2 | no | — |
| 153 | #884 | — | 2 | 2 | no | — |
| 154 | #884 | — | 2 | 2 | no | — |
| 155 | #883 | — | 2 | 2 | no | — |
| 156 | #882 | — | 2 | 2 | no | — |
| 157 | #882 | — | 2 | 1 | no | — |
| 158 | #882 | — | 2 | 1 | no | — |
| 159 | #882 | — | 4 | 1 | no | — |
| 160 | #882 | D4 | 1 | 2 | yes | complemented |
| 161 | #882 | D4 | 1 | 2 | yes | complemented |
| 162 | #67⋊C4 | — | 2 | 2 | no | — |
| 163 | #67⋊C4 | — | 4 | 1 | no | — |
| 164 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 165 | D3×C22⋊C4 | — | 2 | 2 | no | — |
| 166 | D3×C22⋊C4 | — | 2 | 1 | no | — |
| 167 | D3×C22⋊C4 | D4 | 1 | 2 | yes | complemented |
| 168 | #878 | — | 2 | 2 | no | — |
| 169 | #878 | — | 2 | 2 | no | — |
| 170 | #877 | — | 2 | 1 | no | — |
| 171 | #877 | D4 | 1 | 2 | yes | complemented |
| 172 | #876 | — | 2 | 2 | no | — |
| 173 | #875 | — | 2 | 2 | no | — |
| 174 | C4×D12 | — | 2 | 2 | no | — |
| 175 | #872 | — | 2 | 2 | no | — |
| 176 | C3×#99 | — | 2 | 2 | no | — |
| 177 | C3×#99 | — | 2 | 2 | no | — |
| 178 | C3×#99 | — | 4 | 1 | no | — |
| 179 | #834 | — | 2 | 2 | no | — |
| 180 | #834 | — | 2 | 2 | no | — |
| 181 | #834 | — | 4 | 1 | no | — |
| 182 | #806 | — | 2 | 2 | no | — |
| 183 | #806 | — | 2 | 2 | no | — |
| 184 | #806 | — | 2 | 2 | no | — |
| 185 | #806 | — | 2 | 2 | no | — |
| 186 | #806 | — | 2 | 2 | no | — |
| 187 | #806 | — | 2 | 2 | no | — |
| 188 | C2×H(5,𝔽2) | — | 3 | 1 | no | — |
| 189 | #551 | — | 6 | 2 | no | — |
| 190 | #551 | — | 6 | 2 | no | — |
| 191 | #546 | — | 6 | 2 | no | — |
| 192 | #546 | — | 6 | 2 | no | — |
| 193 | #543 | — | 3 | 1 | no | — |
| 194 | #538 | — | 6 | 2 | no | — |
| 195 | #534 | — | 3 | 1 | no | — |
| 196 | #534 | — | 3 | 1 | no | — |
| 197 | #534 | C2×D3 | 1 | 1 | yes | characteristic |
| 198 | #525 | — | 6 | 2 | no | — |
| 199 | C2×#120 | — | 3 | 1 | no | — |
| 200 | C2×#120 | — | 3 | 1 | no | — |
| 201 | C2×#120 | — | 3 | 1 | no | — |
| 202 | C2×#120 | — | 3 | 1 | no | — |
| 203 | #518 | — | 3 | 1 | no | — |
| 204 | #518 | — | 3 | 1 | no | — |
| 205 | #518 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 206 | C22×C22⋊C4 | — | 3 | 1 | no | — |
| 207 | #458 | — | 6 | 2 | no | — |
| 208 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 209 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 210 | B(4,𝔽2) | — | 6 | 2 | no | — |
| 211 | #410 | — | 6 | 2 | no | — |
| 212 | C2×#99 | — | 3 | 1 | no | — |
| 213 | C2×#99 | — | 3 | 1 | no | — |
| 214 | C2×#99 | — | 3 | 1 | no | — |
| 215 | C2×#99 | — | 3 | 1 | no | — |
| 216 | C2×#99 | — | 3 | 1 | no | — |
| 217 | C2×#99 | — | 3 | 1 | no | — |
| 218 | C2×#99 | — | 3 | 1 | no | — |
| 219 | C2×#99 | — | 3 | 1 | no | — |
| 220 | C2×#99 | — | 3 | 1 | no | — |
| 221 | C2×#99 | — | 6 | 2 | no | — |
| 222 | C2×#99 | C2×D3 | 1 | 1 | yes | characteristic |
| 223 | C2×#99 | C2×D3 | 1 | 1 | yes | characteristic |
| 224 | C2×#99 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 225 | #379 | — | 3 | 1 | no | — |
| 226 | #379 | — | 3 | 1 | no | — |
| 227 | #342 | — | 3 | 1 | no | — |
| 228 | #342 | — | 3 | 1 | no | — |
| 229 | #342 | — | 3 | 1 | no | — |
| 230 | #342 | — | 3 | 1 | no | — |
| 231 | #342 | — | 3 | 1 | no | — |
| 232 | #342 | — | 3 | 1 | no | — |
| 233 | #342 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 234 | #342 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 235 | C24×C3 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C24×C3 | #41 | 1 | 1 | yes | characteristic, complemented |
| 237 | C24×C3 | C24 | 1 | 1 | yes | characteristic |
| 238 | C23×D3 | — | 2 | 1 | no | — |
| 239 | C23×D3 | — | 2 | 1 | no | — |
| 240 | C23×D3 | — | 2 | 1 | no | — |
| 241 | C23×D3 | — | 2 | 1 | no | — |
| 242 | C23×D3 | — | 2 | 1 | no | — |
| 243 | C23×D3 | — | 2 | 1 | no | — |
| 244 | C23×D3 | — | 2 | 1 | no | — |
| 245 | C23×D3 | — | 8 | 2 | no | — |
| 246 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 247 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C23×D3 | #41 | 1 | 1 | yes | characteristic, complemented |
| 250 | C2×C3×D4 | — | 2 | 1 | no | — |
| 251 | C2×C3×D4 | — | 2 | 1 | no | — |
| 252 | C2×C3×D4 | — | 2 | 1 | no | — |
| 253 | C2×C3×D4 | — | 2 | 1 | no | — |
| 254 | C2×C3×D4 | — | 2 | 1 | no | — |
| 255 | C2×C3×D4 | — | 2 | 1 | no | — |
| 256 | C2×C3×D4 | — | 2 | 1 | no | — |
| 257 | C2×C3×D4 | — | 2 | 1 | no | — |
| 258 | C2×C3×D4 | — | 2 | 1 | no | — |
| 259 | C2×C3×D4 | — | 2 | 1 | no | — |
| 260 | C2×C3×D4 | — | 2 | 1 | no | — |
| 261 | C2×C3×D4 | — | 2 | 1 | no | — |
| 262 | C2×C3×D4 | — | 4 | 1 | no | — |
| 263 | C22×C3×C4 | — | 2 | 2 | no | — |
| 264 | C22×C3×C4 | — | 2 | 1 | no | — |
| 265 | C22×C3×C4 | — | 2 | 1 | no | — |
| 266 | C22×C3×C4 | — | 2 | 1 | no | — |
| 267 | C22×C3×C4 | — | 2 | 1 | no | — |
| 268 | C22×C3×C4 | — | 2 | 1 | no | — |
| 269 | C22×C3×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C22×C3×C4 | #41 | 1 | 1 | yes | characteristic, complemented |
| 271 | C2×#67 | — | 2 | 1 | no | — |
| 272 | C2×#67 | — | 2 | 1 | no | — |
| 273 | C2×#67 | — | 2 | 1 | no | — |
| 274 | C2×#67 | — | 2 | 1 | no | — |
| 275 | C2×#67 | — | 2 | 2 | no | — |
| 276 | C2×#67 | — | 2 | 1 | no | — |
| 277 | C2×#67 | — | 2 | 1 | no | — |
| 278 | C2×#67 | — | 2 | 1 | no | — |
| 279 | C2×#67 | — | 2 | 1 | no | — |
| 280 | C2×#67 | — | 2 | 1 | no | — |
| 281 | C2×#67 | — | 2 | 1 | no | — |
| 282 | C2×#67 | — | 2 | 1 | no | — |
| 283 | C2×#67 | — | 2 | 1 | no | — |
| 284 | C2×#67 | — | 2 | 2 | no | — |
| 285 | C2×#67 | — | 2 | 2 | no | — |
| 286 | C2×#67 | — | 4 | 2 | no | — |
| 287 | C2×#67 | — | 4 | 2 | no | — |
| 288 | C2×#67 | — | 4 | 1 | no | — |
| 289 | C2×#67 | — | 4 | 1 | no | — |
| 290 | C2×#67 | — | 4 | 1 | no | — |
| 291 | C2×#67 | — | 8 | 2 | no | — |
| 292 | C2×#67 | — | 8 | 2 | no | — |
| 293 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 294 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 295 | C22×Dic3 | — | 2 | 1 | no | — |
| 296 | C22×Dic3 | — | 2 | 1 | no | — |
| 297 | C22×Dic3 | — | 2 | 1 | no | — |
| 298 | C22×Dic3 | — | 2 | 1 | no | — |
| 299 | C22×Dic3 | — | 2 | 1 | no | — |
| 300 | C22×Dic3 | — | 2 | 1 | no | — |
| 301 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 302 | C22×Dic3 | #41 | 1 | 1 | yes | characteristic, complemented |
| 303 | #237 | — | 4 | 2 | no | — |
| 304 | #237 | — | 4 | 2 | no | — |
| 305 | #237 | — | 4 | 2 | no | — |
| 306 | #237 | — | 4 | 2 | no | — |
| 307 | D3×D4 | — | 4 | 2 | no | — |
| 308 | D3×D4 | — | 4 | 2 | no | — |
| 309 | D3×D4 | — | 4 | 2 | no | — |
| 310 | D3×D4 | — | 4 | 2 | no | — |
| 311 | #235 | — | 4 | 2 | no | — |
| 312 | #235 | — | 4 | 2 | no | — |
| 313 | #235 | — | 8 | 4 | no | — |
| 314 | C2×D12 | — | 2 | 1 | no | — |
| 315 | C2×D12 | — | 2 | 2 | no | — |
| 316 | C2×D12 | — | 2 | 2 | no | — |
| 317 | C2×D12 | — | 4 | 1 | no | — |
| 318 | C2×D12 | — | 4 | 1 | no | — |
| 319 | C2×D12 | — | 8 | 2 | no | — |
| 320 | C2×D12 | — | 8 | 2 | no | — |
| 321 | C2×C4×D3 | — | 2 | 2 | no | — |
| 322 | C2×C4×D3 | — | 2 | 1 | no | — |
| 323 | C2×C4×D3 | — | 2 | 1 | no | — |
| 324 | C2×C4×D3 | — | 2 | 2 | no | — |
| 325 | C2×C4×D3 | — | 2 | 2 | no | — |
| 326 | C2×C4×D3 | — | 4 | 1 | no | — |
| 327 | C2×C4×D3 | — | 8 | 2 | no | — |
| 328 | C2×Dic6 | — | 2 | 1 | no | — |
| 329 | C2×Dic6 | — | 2 | 2 | no | — |
| 330 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 331 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 332 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 333 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 334 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 335 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 336 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 337 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 338 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 339 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 340 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 341 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 342 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 343 | C3×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 344 | C3×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 345 | C3×C42 | — | 2 | 2 | no | — |
| 346 | #217 | — | 2 | 1 | no | — |
| 347 | #217 | — | 2 | 1 | no | — |
| 348 | #217 | — | 2 | 2 | no | — |
| 349 | #217 | — | 2 | 1 | no | — |
| 350 | #217 | — | 2 | 1 | no | — |
| 351 | #217 | — | 2 | 1 | no | — |
| 352 | #217 | — | 2 | 1 | no | — |
| 353 | #217 | — | 2 | 1 | no | — |
| 354 | #217 | — | 2 | 1 | no | — |
| 355 | #217 | — | 4 | 1 | no | — |
| 356 | #217 | C2×D4 | 1 | 2 | yes | — |
| 357 | #217 | C2×D4 | 1 | 2 | yes | — |
| 358 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 359 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 360 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 361 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 362 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 363 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 364 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 365 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 366 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 367 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 368 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 369 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 370 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 371 | (C2×D3)⋊C4 | — | 4 | 1 | no | — |
| 372 | (C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 373 | (C2×D3)⋊C4 | — | 8 | 2 | no | — |
| 374 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 375 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 376 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 377 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 378 | Dic3⋊C4 | — | 2 | 2 | no | — |
| 379 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 380 | Dic3⋊C4 | — | 4 | 1 | no | — |
| 381 | C4×Dic3 | — | 2 | 2 | no | — |
| 382 | C4×Dic3 | — | 4 | 1 | no | — |
| 383 | C25 | — | 3 | 1 | no | — |
| 384 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 385 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 386 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 387 | H(5,𝔽2) | — | 12 | 1 | no | — |
| 388 | C2×#41 | — | 6 | 2 | no | — |
| 389 | C2×#41 | — | 6 | 1 | no | — |
| 390 | C2×#41 | — | 6 | 1 | no | — |
| 391 | C2×#41 | — | 6 | 1 | no | — |
| 392 | C22×D4 | — | 3 | 1 | no | — |
| 393 | C22×D4 | — | 3 | 1 | no | — |
| 394 | C22×D4 | — | 6 | 1 | no | — |
| 395 | C22×D4 | — | 6 | 1 | no | — |
| 396 | C22×D4 | — | 6 | 1 | no | — |
| 397 | C22×D4 | — | 6 | 1 | no | — |
| 398 | C22×D4 | — | 6 | 1 | no | — |
| 399 | C22×D4 | — | 6 | 1 | no | — |
| 400 | C22×D4 | — | 6 | 1 | no | — |
| 401 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 402 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 403 | C23×C4 | — | 6 | 1 | no | — |
| 404 | #126 | — | 6 | 2 | no | — |
| 405 | #126 | — | 6 | 2 | no | — |
| 406 | #124 | — | 6 | 2 | no | — |
| 407 | #124 | — | 6 | 2 | no | — |
| 408 | #123 | — | 2 | 1 | no | — |
| 409 | #123 | — | 2 | 1 | no | — |
| 410 | #123 | — | 3 | 2 | no | — |
| 411 | #123 | — | 6 | 2 | no | — |
| 412 | #123 | — | 6 | 2 | no | — |
| 413 | #123 | — | 6 | 2 | no | — |
| 414 | #123 | — | 6 | 2 | no | — |
| 415 | #123 | — | 6 | 1 | no | — |
| 416 | #123 | — | 6 | 1 | no | — |
| 417 | #123 | — | 6 | 1 | no | — |
| 418 | C22⋊Q8 | — | 6 | 2 | no | — |
| 419 | C22⋊Q8 | — | 6 | 2 | no | — |
| 420 | C22⋊Q8 | — | 6 | 2 | no | — |
| 421 | C22⋊Q8 | — | 6 | 2 | no | — |
| 422 | #121 | — | 4 | 1 | no | — |
| 423 | #121 | — | 6 | 2 | no | — |
| 424 | #121 | — | 6 | 2 | no | — |
| 425 | #121 | — | 6 | 2 | no | — |
| 426 | #121 | — | 6 | 2 | no | — |
| 427 | #121 | — | 12 | 1 | no | — |
| 428 | #120 | — | 2 | 1 | no | — |
| 429 | #120 | — | 2 | 1 | no | — |
| 430 | #120 | — | 3 | 2 | no | — |
| 431 | #120 | — | 3 | 2 | no | — |
| 432 | #120 | — | 3 | 2 | no | — |
| 433 | #120 | — | 6 | 2 | no | — |
| 434 | #120 | — | 6 | 1 | no | — |
| 435 | #120 | — | 6 | 1 | no | — |
| 436 | #120 | — | 6 | 2 | no | — |
| 437 | #120 | — | 6 | 1 | no | — |
| 438 | #120 | — | 6 | 1 | no | — |
| 439 | #120 | — | 6 | 1 | no | — |
| 440 | #120 | — | 6 | 1 | no | — |
| 441 | #120 | — | 6 | 1 | no | — |
| 442 | #120 | — | 6 | 1 | no | — |
| 443 | #120 | — | 6 | 1 | no | — |
| 444 | #120 | — | 12 | 1 | no | — |
| 445 | #120 | — | 12 | 1 | no | — |
| 446 | C4×D4 | — | 2 | 2 | no | — |
| 447 | C4×D4 | — | 2 | 2 | no | — |
| 448 | C4×D4 | — | 6 | 2 | no | — |
| 449 | C4×D4 | — | 6 | 2 | no | — |
| 450 | C4×D4 | — | 6 | 2 | no | — |
| 451 | C4×D4 | — | 6 | 2 | no | — |
| 452 | C4×D4 | — | 12 | 1 | no | — |
| 453 | C4×D4 | — | 12 | 1 | no | — |
| 454 | #117 | — | 2 | 1 | no | — |
| 455 | #117 | — | 3 | 2 | no | — |
| 456 | #117 | — | 6 | 2 | no | — |
| 457 | #117 | — | 6 | 1 | no | — |
| 458 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 459 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 460 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 461 | C2×C22⋊C4 | — | 3 | 2 | no | — |
| 462 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 463 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 464 | C2×C22⋊C4 | — | 3 | 1 | no | — |
| 465 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 466 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 467 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 468 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 469 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 470 | C2×C22⋊C4 | — | 6 | 2 | no | — |
| 471 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 472 | C2×C22⋊C4 | — | 6 | 1 | no | — |
| 473 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 474 | C2×C22⋊C4 | — | 12 | 1 | no | — |
| 475 | C2×C22⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 476 | C2×C22⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 477 | C2×C22⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 478 | C2×C22⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 479 | C2×C22⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 480 | #99 | — | 2 | 2 | no | — |
| 481 | #99 | — | 2 | 2 | no | — |
| 482 | #99 | — | 4 | 1 | no | — |
| 483 | #99 | — | 6 | 2 | no | — |
| 484 | #99 | — | 6 | 2 | no | — |
| 485 | #99 | — | 6 | 2 | no | — |
| 486 | #99 | — | 6 | 2 | no | — |
| 487 | #99 | — | 6 | 2 | no | — |
| 488 | #99 | — | 6 | 2 | no | — |
| 489 | #99 | — | 6 | 2 | no | — |
| 490 | #99 | — | 6 | 2 | no | — |
| 491 | #99 | — | 12 | 1 | no | — |
| 492 | C23×C3 | — | 2 | 1 | no | — |
| 493 | C23×C3 | — | 2 | 1 | no | — |
| 494 | C23×C3 | — | 2 | 1 | no | — |
| 495 | C23×C3 | — | 2 | 1 | no | — |
| 496 | C23×C3 | — | 2 | 1 | no | — |
| 497 | C23×C3 | — | 2 | 1 | no | — |
| 498 | C23×C3 | — | 8 | 1 | no | — |
| 499 | C23×C3 | — | 8 | 1 | no | — |
| 500 | C23×C3 | — | 8 | 1 | no | — |
| 501 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 502 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 503 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 504 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 505 | C23×C3 | C2×#41 | 1 | 1 | yes | characteristic |
| 506 | C23×C3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 507 | C23×C3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 508 | C22×D3 | — | 2 | 1 | no | — |
| 509 | C22×D3 | — | 2 | 1 | no | — |
| 510 | C22×D3 | — | 2 | 1 | no | — |
| 511 | C22×D3 | — | 2 | 1 | no | — |
| 512 | C22×D3 | — | 2 | 1 | no | — |
| 513 | C22×D3 | — | 2 | 1 | no | — |
| 514 | C22×D3 | — | 2 | 1 | no | — |
| 515 | C22×D3 | — | 2 | 1 | no | — |
| 516 | C22×D3 | — | 2 | 1 | no | — |
| 517 | C22×D3 | — | 2 | 1 | no | — |
| 518 | C22×D3 | — | 2 | 1 | no | — |
| 519 | C22×D3 | — | 4 | 2 | no | — |
| 520 | C22×D3 | — | 4 | 2 | no | — |
| 521 | C22×D3 | — | 4 | 2 | no | — |
| 522 | C22×D3 | — | 4 | 2 | no | — |
| 523 | C22×D3 | — | 4 | 2 | no | — |
| 524 | C22×D3 | — | 4 | 2 | no | — |
| 525 | C22×D3 | — | 4 | 2 | no | — |
| 526 | C22×D3 | — | 4 | 2 | no | — |
| 527 | C22×D3 | — | 4 | 1 | no | — |
| 528 | C22×D3 | — | 4 | 1 | no | — |
| 529 | C22×D3 | — | 4 | 1 | no | — |
| 530 | C22×D3 | — | 4 | 1 | no | — |
| 531 | C22×D3 | — | 8 | 1 | no | — |
| 532 | C22×D3 | — | 8 | 1 | no | — |
| 533 | C22×D3 | — | 8 | 1 | no | — |
| 534 | C22×D3 | — | 8 | 1 | no | — |
| 535 | C22×D3 | — | 8 | 1 | no | — |
| 536 | C22×D3 | — | 8 | 1 | no | — |
| 537 | C22×D3 | — | 8 | 1 | no | — |
| 538 | C22×D3 | — | 8 | 1 | no | — |
| 539 | C22×D3 | — | 8 | 1 | no | — |
| 540 | C22×D3 | — | 16 | 1 | no | — |
| 541 | C22×D3 | #120 | 1 | 2 | yes | — |
| 542 | C3×D4 | — | 4 | 1 | no | — |
| 543 | C3×D4 | — | 4 | 1 | no | — |
| 544 | C3×D4 | — | 4 | 1 | no | — |
| 545 | C3×D4 | — | 4 | 1 | no | — |
| 546 | C3×D4 | — | 4 | 1 | no | — |
| 547 | C3×D4 | — | 4 | 1 | no | — |
| 548 | C3×D4 | — | 4 | 1 | no | — |
| 549 | C3×D4 | — | 4 | 1 | no | — |
| 550 | C3×D4 | — | 16 | 1 | no | — |
| 551 | C2×C3×C4 | — | 2 | 2 | no | — |
| 552 | C2×C3×C4 | — | 2 | 2 | no | — |
| 553 | C2×C3×C4 | — | 2 | 1 | no | — |
| 554 | C2×C3×C4 | — | 2 | 1 | no | — |
| 555 | C2×C3×C4 | — | 2 | 1 | no | — |
| 556 | C2×C3×C4 | — | 2 | 1 | no | — |
| 557 | C2×C3×C4 | — | 2 | 1 | no | — |
| 558 | C2×C3×C4 | — | 2 | 1 | no | — |
| 559 | C2×C3×C4 | — | 4 | 1 | no | — |
| 560 | C2×C3×C4 | — | 4 | 1 | no | — |
| 561 | C2×C3×C4 | — | 4 | 1 | no | — |
| 562 | C2×C3×C4 | — | 8 | 1 | no | — |
| 563 | C2×C3×C4 | — | 8 | 1 | no | — |
| 564 | C2×C3×C4 | — | 8 | 2 | no | — |
| 565 | C2×C3×C4 | — | 8 | 1 | no | — |
| 566 | C2×C3×C4 | — | 8 | 1 | no | — |
| 567 | C2×C3×C4 | — | 8 | 1 | no | — |
| 568 | #67 | — | 2 | 2 | no | — |
| 569 | #67 | — | 2 | 2 | no | — |
| 570 | #67 | — | 2 | 2 | no | — |
| 571 | #67 | — | 2 | 2 | no | — |
| 572 | #67 | — | 4 | 2 | no | — |
| 573 | #67 | — | 4 | 4 | no | — |
| 574 | #67 | — | 4 | 2 | no | — |
| 575 | #67 | — | 4 | 1 | no | — |
| 576 | #67 | — | 4 | 1 | no | — |
| 577 | #67 | — | 4 | 1 | no | — |
| 578 | #67 | — | 4 | 1 | no | — |
| 579 | #67 | — | 8 | 2 | no | — |
| 580 | #67 | — | 8 | 2 | no | — |
| 581 | #67 | — | 8 | 2 | no | — |
| 582 | #67 | — | 8 | 2 | no | — |
| 583 | #67 | — | 16 | 1 | no | — |
| 584 | C2×Dic3 | — | 2 | 1 | no | — |
| 585 | C2×Dic3 | — | 2 | 1 | no | — |
| 586 | C2×Dic3 | — | 2 | 2 | no | — |
| 587 | C2×Dic3 | — | 2 | 2 | no | — |
| 588 | C2×Dic3 | — | 2 | 1 | no | — |
| 589 | C2×Dic3 | — | 2 | 1 | no | — |
| 590 | C2×Dic3 | — | 2 | 1 | no | — |
| 591 | C2×Dic3 | — | 4 | 2 | no | — |
| 592 | C2×Dic3 | — | 4 | 1 | no | — |
| 593 | C2×Dic3 | — | 4 | 1 | no | — |
| 594 | C2×Dic3 | — | 4 | 1 | no | — |
| 595 | C2×Dic3 | — | 8 | 1 | no | — |
| 596 | C2×Dic3 | — | 8 | 1 | no | — |
| 597 | C2×Dic3 | — | 8 | 1 | no | — |
| 598 | C2×Dic3 | — | 8 | 1 | no | — |
| 599 | C2×Dic3 | — | 8 | 1 | no | — |
| 600 | C2×Dic3 | #120 | 1 | 2 | yes | — |
| 601 | D12 | — | 4 | 4 | no | — |
| 602 | D12 | — | 4 | 2 | no | — |
| 603 | D12 | — | 8 | 2 | no | — |
| 604 | D12 | — | 8 | 2 | no | — |
| 605 | D12 | — | 8 | 2 | no | — |
| 606 | C4×D3 | — | 4 | 2 | no | — |
| 607 | C4×D3 | — | 4 | 4 | no | — |
| 608 | C4×D3 | — | 4 | 2 | no | — |
| 609 | C4×D3 | — | 8 | 2 | no | — |
| 610 | C4×D3 | — | 8 | 2 | no | — |
| 611 | C4×D3 | — | 16 | 1 | no | — |
| 612 | Dic6 | — | 4 | 2 | no | — |
| 613 | Dic6 | — | 8 | 2 | no | — |
| 614 | C24 | — | 3 | 1 | no | — |
| 615 | C24 | — | 3 | 1 | no | — |
| 616 | C24 | — | 3 | 1 | no | — |
| 617 | C24 | — | 3 | 1 | no | — |
| 618 | C24 | — | 6 | 1 | no | — |
| 619 | C24 | — | 6 | 1 | no | — |
| 620 | C24 | — | 6 | 1 | no | — |
| 621 | C24 | — | 6 | 1 | no | — |
| 622 | C24 | — | 6 | 1 | no | — |
| 623 | C24 | — | 6 | 1 | no | — |
| 624 | C24 | — | 6 | 1 | no | — |
| 625 | C24 | — | 24 | 2 | no | — |
| 626 | C24 | #235 | 1 | 1 | yes | characteristic, complemented |
| 627 | C24 | D3×D4 | 1 | 1 | yes | characteristic |
| 628 | C24 | C23×D3 | 1 | 1 | yes | characteristic |
| 629 | #41 | — | 12 | 2 | no | — |
| 630 | #41 | — | 12 | 2 | no | — |
| 631 | #41 | — | 12 | 2 | no | — |
| 632 | #41 | — | 12 | 2 | no | — |
| 633 | #41 | — | 12 | 2 | no | — |
| 634 | #41 | — | 12 | 2 | no | — |
| 635 | #41 | — | 24 | 4 | no | — |
| 636 | C2×Q8 | — | 6 | 1 | no | — |
| 637 | C2×Q8 | — | 6 | 2 | no | — |
| 638 | C2×D4 | — | 2 | 1 | no | — |
| 639 | C2×D4 | — | 2 | 1 | no | — |
| 640 | C2×D4 | — | 2 | 1 | no | — |
| 641 | C2×D4 | — | 2 | 1 | no | — |
| 642 | C2×D4 | — | 2 | 1 | no | — |
| 643 | C2×D4 | — | 2 | 1 | no | — |
| 644 | C2×D4 | — | 2 | 1 | no | — |
| 645 | C2×D4 | — | 2 | 1 | no | — |
| 646 | C2×D4 | — | 2 | 1 | no | — |
| 647 | C2×D4 | — | 2 | 1 | no | — |
| 648 | C2×D4 | — | 2 | 1 | no | — |
| 649 | C2×D4 | — | 2 | 1 | no | — |
| 650 | C2×D4 | — | 3 | 2 | no | — |
| 651 | C2×D4 | — | 3 | 2 | no | — |
| 652 | C2×D4 | — | 4 | 1 | no | — |
| 653 | C2×D4 | — | 6 | 2 | no | — |
| 654 | C2×D4 | — | 6 | 1 | no | — |
| 655 | C2×D4 | — | 6 | 2 | no | — |
| 656 | C2×D4 | — | 6 | 1 | no | — |
| 657 | C2×D4 | — | 6 | 1 | no | — |
| 658 | C2×D4 | — | 6 | 1 | no | — |
| 659 | C2×D4 | — | 6 | 1 | no | — |
| 660 | C2×D4 | — | 6 | 2 | no | — |
| 661 | C2×D4 | — | 6 | 1 | no | — |
| 662 | C2×D4 | — | 6 | 1 | no | — |
| 663 | C2×D4 | — | 6 | 1 | no | — |
| 664 | C2×D4 | — | 6 | 1 | no | — |
| 665 | C2×D4 | — | 6 | 1 | no | — |
| 666 | C2×D4 | — | 6 | 1 | no | — |
| 667 | C2×D4 | — | 6 | 1 | no | — |
| 668 | C2×D4 | — | 6 | 1 | no | — |
| 669 | C2×D4 | — | 6 | 2 | no | — |
| 670 | C2×D4 | — | 6 | 2 | no | — |
| 671 | C2×D4 | — | 12 | 1 | no | — |
| 672 | C2×D4 | — | 12 | 1 | no | — |
| 673 | C2×D4 | — | 12 | 2 | no | — |
| 674 | C2×D4 | — | 12 | 2 | no | — |
| 675 | C2×D4 | — | 12 | 2 | no | — |
| 676 | C2×D4 | — | 12 | 2 | no | — |
| 677 | C2×D4 | — | 12 | 2 | no | — |
| 678 | C2×D4 | — | 12 | 2 | no | — |
| 679 | C2×D4 | — | 12 | 1 | no | — |
| 680 | C2×D4 | — | 12 | 1 | no | — |
| 681 | C2×D4 | — | 12 | 1 | no | — |
| 682 | C2×D4 | — | 24 | 2 | no | — |
| 683 | C2×D4 | — | 24 | 2 | no | — |
| 684 | C2×D4 | — | 24 | 2 | no | — |
| 685 | C2×D4 | — | 24 | 2 | no | — |
| 686 | C22×C4 | — | 2 | 2 | no | — |
| 687 | C22×C4 | — | 2 | 1 | no | — |
| 688 | C22×C4 | — | 2 | 1 | no | — |
| 689 | C22×C4 | — | 2 | 1 | no | — |
| 690 | C22×C4 | — | 2 | 1 | no | — |
| 691 | C22×C4 | — | 2 | 1 | no | — |
| 692 | C22×C4 | — | 3 | 1 | no | — |
| 693 | C22×C4 | — | 3 | 1 | no | — |
| 694 | C22×C4 | — | 6 | 2 | no | — |
| 695 | C22×C4 | — | 6 | 1 | no | — |
| 696 | C22×C4 | — | 6 | 1 | no | — |
| 697 | C22×C4 | — | 6 | 2 | no | — |
| 698 | C22×C4 | — | 6 | 2 | no | — |
| 699 | C22×C4 | — | 6 | 1 | no | — |
| 700 | C22×C4 | — | 6 | 1 | no | — |
| 701 | C22×C4 | — | 6 | 1 | no | — |
| 702 | C22×C4 | — | 6 | 1 | no | — |
| 703 | C22×C4 | — | 6 | 1 | no | — |
| 704 | C22×C4 | — | 6 | 1 | no | — |
| 705 | C22×C4 | — | 12 | 1 | no | — |
| 706 | C22×C4 | — | 24 | 2 | no | — |
| 707 | C22×C4 | #235 | 1 | 1 | yes | characteristic, complemented |
| 708 | C22×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 709 | C4⋊C4 | — | 2 | 2 | no | — |
| 710 | C4⋊C4 | — | 4 | 1 | no | — |
| 711 | C4⋊C4 | — | 6 | 2 | no | — |
| 712 | C4⋊C4 | — | 6 | 2 | no | — |
| 713 | C4⋊C4 | — | 6 | 2 | no | — |
| 714 | C4⋊C4 | — | 6 | 2 | no | — |
| 715 | C4⋊C4 | — | 6 | 2 | no | — |
| 716 | C4⋊C4 | — | 12 | 1 | no | — |
| 717 | C4⋊C4 | — | 12 | 1 | no | — |
| 718 | C22⋊C4 | — | 2 | 2 | no | — |
| 719 | C22⋊C4 | — | 2 | 1 | no | — |
| 720 | C22⋊C4 | — | 2 | 1 | no | — |
| 721 | C22⋊C4 | — | 2 | 1 | no | — |
| 722 | C22⋊C4 | — | 2 | 1 | no | — |
| 723 | C22⋊C4 | — | 2 | 1 | no | — |
| 724 | C22⋊C4 | — | 2 | 1 | no | — |
| 725 | C22⋊C4 | — | 2 | 1 | no | — |
| 726 | C22⋊C4 | — | 2 | 1 | no | — |
| 727 | C22⋊C4 | — | 3 | 2 | no | — |
| 728 | C22⋊C4 | — | 3 | 2 | no | — |
| 729 | C22⋊C4 | — | 4 | 1 | no | — |
| 730 | C22⋊C4 | — | 4 | 1 | no | — |
| 731 | C22⋊C4 | — | 6 | 2 | no | — |
| 732 | C22⋊C4 | — | 6 | 2 | no | — |
| 733 | C22⋊C4 | — | 6 | 2 | no | — |
| 734 | C22⋊C4 | — | 6 | 2 | no | — |
| 735 | C22⋊C4 | — | 6 | 2 | no | — |
| 736 | C22⋊C4 | — | 6 | 2 | no | — |
| 737 | C22⋊C4 | — | 6 | 2 | no | — |
| 738 | C22⋊C4 | — | 6 | 2 | no | — |
| 739 | C22⋊C4 | — | 6 | 2 | no | — |
| 740 | C22⋊C4 | — | 6 | 1 | no | — |
| 741 | C22⋊C4 | — | 6 | 1 | no | — |
| 742 | C22⋊C4 | — | 6 | 1 | no | — |
| 743 | C22⋊C4 | — | 6 | 1 | no | — |
| 744 | C22⋊C4 | — | 6 | 1 | no | — |
| 745 | C22⋊C4 | — | 6 | 1 | no | — |
| 746 | C22⋊C4 | — | 6 | 1 | no | — |
| 747 | C22⋊C4 | — | 6 | 1 | no | — |
| 748 | C22⋊C4 | — | 12 | 1 | no | — |
| 749 | C22⋊C4 | — | 12 | 1 | no | — |
| 750 | C22⋊C4 | — | 12 | 1 | no | — |
| 751 | C22⋊C4 | — | 12 | 1 | no | — |
| 752 | C22⋊C4 | — | 12 | 1 | no | — |
| 753 | C22⋊C4 | — | 12 | 1 | no | — |
| 754 | C22⋊C4 | — | 12 | 1 | no | — |
| 755 | C22⋊C4 | — | 24 | 2 | no | — |
| 756 | C22⋊C4 | — | 24 | 2 | no | — |
| 757 | C22⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 758 | C22⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 759 | C42 | — | 2 | 2 | no | — |
| 760 | C42 | — | 6 | 2 | no | — |
| 761 | C42 | — | 12 | 1 | no | — |
| 762 | C22×C3 | — | 4 | 1 | no | — |
| 763 | C22×C3 | — | 4 | 1 | no | — |
| 764 | C22×C3 | — | 4 | 1 | no | — |
| 765 | C22×C3 | — | 4 | 1 | no | — |
| 766 | C22×C3 | — | 4 | 1 | no | — |
| 767 | C22×C3 | — | 4 | 1 | no | — |
| 768 | C22×C3 | — | 4 | 1 | no | — |
| 769 | C22×C3 | — | 4 | 2 | no | — |
| 770 | C22×C3 | — | 4 | 1 | no | — |
| 771 | C22×C3 | — | 4 | 1 | no | — |
| 772 | C22×C3 | — | 8 | 1 | no | — |
| 773 | C22×C3 | — | 8 | 1 | no | — |
| 774 | C22×C3 | — | 8 | 1 | no | — |
| 775 | C22×C3 | — | 8 | 1 | no | — |
| 776 | C22×C3 | — | 8 | 1 | no | — |
| 777 | C22×C3 | C2×#120 | 1 | 1 | yes | characteristic |
| 778 | C22×C3 | #525 | 1 | 1 | yes | characteristic |
| 779 | C22×C3 | #535 | 1 | 1 | yes | characteristic |
| 780 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 781 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 782 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 783 | C22×C3 | #546 | 1 | 1 | yes | characteristic |
| 784 | C2×D3 | — | 2 | 2 | no | — |
| 785 | C2×D3 | — | 2 | 2 | no | — |
| 786 | C2×D3 | — | 2 | 2 | no | — |
| 787 | C2×D3 | — | 2 | 2 | no | — |
| 788 | C2×D3 | — | 4 | 1 | no | — |
| 789 | C2×D3 | — | 4 | 1 | no | — |
| 790 | C2×D3 | — | 4 | 1 | no | — |
| 791 | C2×D3 | — | 4 | 1 | no | — |
| 792 | C2×D3 | — | 4 | 2 | no | — |
| 793 | C2×D3 | — | 4 | 1 | no | — |
| 794 | C2×D3 | — | 4 | 1 | no | — |
| 795 | C2×D3 | — | 4 | 1 | no | — |
| 796 | C2×D3 | — | 4 | 1 | no | — |
| 797 | C2×D3 | — | 4 | 1 | no | — |
| 798 | C2×D3 | — | 4 | 1 | no | — |
| 799 | C2×D3 | — | 4 | 1 | no | — |
| 800 | C2×D3 | — | 4 | 1 | no | — |
| 801 | C2×D3 | — | 8 | 1 | no | — |
| 802 | C2×D3 | — | 8 | 1 | no | — |
| 803 | C2×D3 | — | 8 | 2 | no | — |
| 804 | C2×D3 | — | 8 | 2 | no | — |
| 805 | C2×D3 | — | 8 | 2 | no | — |
| 806 | C2×D3 | — | 8 | 2 | no | — |
| 807 | C2×D3 | — | 8 | 1 | no | — |
| 808 | C2×D3 | — | 8 | 1 | no | — |
| 809 | C2×D3 | — | 8 | 1 | no | — |
| 810 | C2×D3 | — | 16 | 2 | no | — |
| 811 | C3×C4 | — | 4 | 2 | no | — |
| 812 | C3×C4 | — | 4 | 2 | no | — |
| 813 | C3×C4 | — | 4 | 1 | no | — |
| 814 | C3×C4 | — | 4 | 1 | no | — |
| 815 | C3×C4 | — | 8 | 1 | no | — |
| 816 | C3×C4 | — | 8 | 1 | no | — |
| 817 | C3×C4 | — | 8 | 1 | no | — |
| 818 | Dic3 | — | 2 | 2 | no | — |
| 819 | Dic3 | — | 4 | 2 | no | — |
| 820 | Dic3 | — | 4 | 2 | no | — |
| 821 | Dic3 | — | 4 | 1 | no | — |
| 822 | Dic3 | — | 8 | 1 | no | — |
| 823 | Dic3 | — | 8 | 1 | no | — |
| 824 | Dic3 | — | 8 | 1 | no | — |
| 825 | C23 | — | 2 | 1 | no | — |
| 826 | C23 | — | 2 | 1 | no | — |
| 827 | C23 | — | 2 | 1 | no | — |
| 828 | C23 | — | 2 | 1 | no | — |
| 829 | C23 | — | 2 | 1 | no | — |
| 830 | C23 | — | 2 | 1 | no | — |
| 831 | C23 | — | 3 | 2 | no | — |
| 832 | C23 | — | 6 | 1 | no | — |
| 833 | C23 | — | 6 | 1 | no | — |
| 834 | C23 | — | 6 | 1 | no | — |
| 835 | C23 | — | 6 | 1 | no | — |
| 836 | C23 | — | 6 | 1 | no | — |
| 837 | C23 | — | 6 | 1 | no | — |
| 838 | C23 | — | 6 | 1 | no | — |
| 839 | C23 | — | 6 | 1 | no | — |
| 840 | C23 | — | 6 | 1 | no | — |
| 841 | C23 | — | 6 | 1 | no | — |
| 842 | C23 | — | 6 | 1 | no | — |
| 843 | C23 | — | 8 | 1 | no | — |
| 844 | C23 | — | 8 | 1 | no | — |
| 845 | C23 | — | 8 | 1 | no | — |
| 846 | C23 | — | 12 | 2 | no | — |
| 847 | C23 | — | 12 | 2 | no | — |
| 848 | C23 | — | 12 | 2 | no | — |
| 849 | C23 | — | 12 | 2 | no | — |
| 850 | C23 | — | 12 | 2 | no | — |
| 851 | C23 | — | 12 | 2 | no | — |
| 852 | C23 | — | 12 | 2 | no | — |
| 853 | C23 | — | 12 | 2 | no | — |
| 854 | C23 | — | 12 | 1 | no | — |
| 855 | C23 | — | 12 | 1 | no | — |
| 856 | C23 | — | 12 | 1 | no | — |
| 857 | C23 | — | 12 | 1 | no | — |
| 858 | C23 | — | 24 | 1 | no | — |
| 859 | C23 | — | 24 | 1 | no | — |
| 860 | C23 | — | 24 | 1 | no | — |
| 861 | C23 | — | 24 | 1 | no | — |
| 862 | C23 | — | 24 | 1 | no | — |
| 863 | C23 | — | 24 | 1 | no | — |
| 864 | C23 | — | 24 | 1 | no | — |
| 865 | C23 | — | 24 | 1 | no | — |
| 866 | C23 | — | 24 | 1 | no | — |
| 867 | C23 | — | 48 | 1 | no | — |
| 868 | C23 | C2×#235 | 1 | 1 | yes | characteristic |
| 869 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 870 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 871 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 872 | C23 | #1004 | 1 | 1 | yes | characteristic |
| 873 | C23 | D3×#41 | 1 | 1 | yes | characteristic |
| 874 | C23 | #1009 | 1 | 1 | yes | characteristic |
| 875 | Q8 | — | 12 | 2 | no | — |
| 876 | Q8 | — | 24 | 2 | no | — |
| 877 | D4 | — | 4 | 1 | no | — |
| 878 | D4 | — | 4 | 1 | no | — |
| 879 | D4 | — | 4 | 1 | no | — |
| 880 | D4 | — | 4 | 1 | no | — |
| 881 | D4 | — | 4 | 1 | no | — |
| 882 | D4 | — | 4 | 1 | no | — |
| 883 | D4 | — | 4 | 1 | no | — |
| 884 | D4 | — | 4 | 1 | no | — |
| 885 | D4 | — | 6 | 2 | no | — |
| 886 | D4 | — | 6 | 2 | no | — |
| 887 | D4 | — | 6 | 2 | no | — |
| 888 | D4 | — | 6 | 2 | no | — |
| 889 | D4 | — | 12 | 2 | no | — |
| 890 | D4 | — | 12 | 4 | no | — |
| 891 | D4 | — | 12 | 2 | no | — |
| 892 | D4 | — | 12 | 2 | no | — |
| 893 | D4 | — | 12 | 4 | no | — |
| 894 | D4 | — | 12 | 1 | no | — |
| 895 | D4 | — | 12 | 1 | no | — |
| 896 | D4 | — | 12 | 1 | no | — |
| 897 | D4 | — | 12 | 1 | no | — |
| 898 | D4 | — | 16 | 1 | no | — |
| 899 | D4 | — | 24 | 2 | no | — |
| 900 | D4 | — | 24 | 2 | no | — |
| 901 | D4 | — | 24 | 2 | no | — |
| 902 | D4 | — | 24 | 2 | no | — |
| 903 | D4 | — | 24 | 2 | no | — |
| 904 | D4 | — | 24 | 2 | no | — |
| 905 | D4 | — | 24 | 2 | no | — |
| 906 | D4 | — | 48 | 1 | no | — |
| 907 | C2×C4 | — | 2 | 1 | no | — |
| 908 | C2×C4 | — | 2 | 1 | no | — |
| 909 | C2×C4 | — | 2 | 1 | no | — |
| 910 | C2×C4 | — | 2 | 1 | no | — |
| 911 | C2×C4 | — | 2 | 1 | no | — |
| 912 | C2×C4 | — | 2 | 1 | no | — |
| 913 | C2×C4 | — | 2 | 2 | no | — |
| 914 | C2×C4 | — | 2 | 2 | no | — |
| 915 | C2×C4 | — | 3 | 2 | no | — |
| 916 | C2×C4 | — | 4 | 1 | no | — |
| 917 | C2×C4 | — | 4 | 1 | no | — |
| 918 | C2×C4 | — | 4 | 1 | no | — |
| 919 | C2×C4 | — | 6 | 1 | no | — |
| 920 | C2×C4 | — | 6 | 1 | no | — |
| 921 | C2×C4 | — | 6 | 1 | no | — |
| 922 | C2×C4 | — | 6 | 1 | no | — |
| 923 | C2×C4 | — | 6 | 2 | no | — |
| 924 | C2×C4 | — | 6 | 2 | no | — |
| 925 | C2×C4 | — | 6 | 1 | no | — |
| 926 | C2×C4 | — | 8 | 1 | no | — |
| 927 | C2×C4 | — | 8 | 1 | no | — |
| 928 | C2×C4 | — | 8 | 2 | no | — |
| 929 | C2×C4 | — | 8 | 1 | no | — |
| 930 | C2×C4 | — | 8 | 1 | no | — |
| 931 | C2×C4 | — | 8 | 1 | no | — |
| 932 | C2×C4 | — | 12 | 2 | no | — |
| 933 | C2×C4 | — | 12 | 4 | no | — |
| 934 | C2×C4 | — | 12 | 2 | no | — |
| 935 | C2×C4 | — | 12 | 2 | no | — |
| 936 | C2×C4 | — | 12 | 1 | no | — |
| 937 | C2×C4 | — | 12 | 1 | no | — |
| 938 | C2×C4 | — | 12 | 1 | no | — |
| 939 | C2×C4 | — | 24 | 2 | no | — |
| 940 | C2×C4 | — | 24 | 2 | no | — |
| 941 | C2×C4 | — | 24 | 1 | no | — |
| 942 | C2×C4 | — | 24 | 1 | no | — |
| 943 | C2×C4 | — | 24 | 1 | no | — |
| 944 | C2×C4 | — | 24 | 1 | no | — |
| 945 | C2×C4 | — | 24 | 1 | no | — |
| 946 | C2×C4 | — | 48 | 1 | no | — |
| 947 | C2×C3 | — | 2 | 1 | no | — |
| 948 | C2×C3 | — | 2 | 1 | no | — |
| 949 | C2×C3 | — | 2 | 1 | no | — |
| 950 | C2×C3 | — | 2 | 1 | no | — |
| 951 | C2×C3 | — | 2 | 1 | no | — |
| 952 | C2×C3 | — | 2 | 1 | no | — |
| 953 | C2×C3 | — | 2 | 1 | no | — |
| 954 | C2×C3 | — | 8 | 1 | no | — |
| 955 | C2×C3 | — | 8 | 1 | no | — |
| 956 | C2×C3 | #2404 | 1 | 1 | yes | characteristic |
| 957 | D3 | — | 4 | 2 | no | — |
| 958 | D3 | — | 4 | 2 | no | — |
| 959 | D3 | — | 8 | 1 | no | — |
| 960 | D3 | — | 8 | 1 | no | — |
| 961 | C22 | — | 4 | 1 | no | — |
| 962 | C22 | — | 4 | 1 | no | — |
| 963 | C22 | — | 4 | 1 | no | — |
| 964 | C22 | — | 4 | 1 | no | — |
| 965 | C22 | — | 4 | 1 | no | — |
| 966 | C22 | — | 4 | 1 | no | — |
| 967 | C22 | — | 4 | 1 | no | — |
| 968 | C22 | — | 4 | 2 | no | — |
| 969 | C22 | — | 4 | 1 | no | — |
| 970 | C22 | — | 4 | 1 | no | — |
| 971 | C22 | — | 6 | 2 | no | — |
| 972 | C22 | — | 6 | 2 | no | — |
| 973 | C22 | — | 6 | 2 | no | — |
| 974 | C22 | — | 6 | 2 | no | — |
| 975 | C22 | — | 8 | 1 | no | — |
| 976 | C22 | — | 8 | 1 | no | — |
| 977 | C22 | — | 8 | 1 | no | — |
| 978 | C22 | — | 8 | 1 | no | — |
| 979 | C22 | — | 8 | 1 | no | — |
| 980 | C22 | — | 12 | 2 | no | — |
| 981 | C22 | — | 12 | 1 | no | — |
| 982 | C22 | — | 12 | 1 | no | — |
| 983 | C22 | — | 12 | 1 | no | — |
| 984 | C22 | — | 12 | 1 | no | — |
| 985 | C22 | — | 12 | 1 | no | — |
| 986 | C22 | — | 12 | 1 | no | — |
| 987 | C22 | — | 12 | 1 | no | — |
| 988 | C22 | — | 12 | 1 | no | — |
| 989 | C22 | — | 12 | 1 | no | — |
| 990 | C22 | — | 12 | 1 | no | — |
| 991 | C22 | — | 12 | 1 | no | — |
| 992 | C22 | — | 12 | 1 | no | — |
| 993 | C22 | — | 24 | 1 | no | — |
| 994 | C22 | — | 24 | 1 | no | — |
| 995 | C22 | — | 24 | 2 | no | — |
| 996 | C22 | — | 24 | 2 | no | — |
| 997 | C22 | — | 24 | 2 | no | — |
| 998 | C22 | — | 24 | 2 | no | — |
| 999 | C22 | — | 24 | 1 | no | — |
| 1000 | C22 | — | 24 | 1 | no | — |
| 1001 | C22 | — | 24 | 1 | no | — |
| 1002 | C22 | — | 48 | 2 | no | — |
| 1003 | C22 | #5490 | 1 | 1 | yes | characteristic |
| 1004 | C22 | #5547 | 1 | 1 | yes | characteristic |
| 1005 | C22 | #5550 | 1 | 1 | yes | characteristic |
| 1006 | C22 | D3×#120 | 1 | 1 | yes | characteristic |
| 1007 | C22 | #5607 | 1 | 1 | yes | characteristic |
| 1008 | C22 | #5612 | 1 | 1 | yes | characteristic |
| 1009 | C22 | #5654 | 1 | 1 | yes | characteristic |
| 1010 | C4 | — | 4 | 2 | no | — |
| 1011 | C4 | — | 4 | 2 | no | — |
| 1012 | C4 | — | 4 | 1 | no | — |
| 1013 | C4 | — | 4 | 1 | no | — |
| 1014 | C4 | — | 6 | 2 | no | — |
| 1015 | C4 | — | 8 | 1 | no | — |
| 1016 | C4 | — | 8 | 1 | no | — |
| 1017 | C4 | — | 8 | 1 | no | — |
| 1018 | C4 | — | 12 | 2 | no | — |
| 1019 | C4 | — | 12 | 2 | no | — |
| 1020 | C4 | — | 12 | 1 | no | — |
| 1021 | C4 | — | 24 | 1 | no | — |
| 1022 | C4 | — | 24 | 1 | no | — |
| 1023 | C4 | — | 24 | 1 | no | — |
| 1024 | C3 | #23996 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 1025 | C2 | — | 2 | 1 | no | — |
| 1026 | C2 | — | 2 | 1 | no | — |
| 1027 | C2 | — | 2 | 1 | no | — |
| 1028 | C2 | — | 2 | 1 | no | — |
| 1029 | C2 | — | 2 | 1 | no | — |
| 1030 | C2 | — | 2 | 1 | no | — |
| 1031 | C2 | — | 2 | 1 | no | — |
| 1032 | C2 | — | 8 | 1 | no | — |
| 1033 | C2 | — | 8 | 1 | no | — |
| 1034 | C2 | — | 12 | 2 | no | — |
| 1035 | C2 | — | 12 | 2 | no | — |
| 1036 | C2 | — | 24 | 1 | no | — |
| 1037 | C2 | — | 24 | 1 | no | — |
| 1038 | C2 | #74886 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #74886 |
| commutator, cosocle | C24×C3 | C24 |
| Frattini | C24 | C23×D3 |
| Fitting | C3×#1913 | C2 |
| socle | C2×C3 | #2404 |
| hypercenter | #1913 | D3 |
| hypocenter | C3 | #23996 |
| LCS | G ▷ C24×C3 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C24 ◁ #1913 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #85868 | C2 | semidirect |
| 2. #83375 | C2 | semidirect |
| 3. #78688 | C2 | semidirect |
| 4. C2×#4741 | C2 | semidirect |
| 5. C3×#1913 | C2 | semidirect |
| 6. #71851 | C2 | semidirect |
| 7. #71656 | C2 | semidirect |
| 8. #70037 | C2 | semidirect |
| 9. #70036 | C2 | semidirect |
| 10. #70034 | C2 | semidirect |
| 11. #70025 | C2 | semidirect |
| 12. #68970 | C2 | semidirect |
| 13. #68967 | C2 | semidirect |
| 14. #68962 | C2 | semidirect |
| 15. #68960 | C2 | semidirect |
| 19. C3×#518 | C22 | semidirect |
| 23. C2×#937 | C22 | semidirect |
| 34. C2×D3×C22⋊C4 | C22 | semidirect |
| 35. #5483 | C22 | semidirect |
| 38. C2×C3×#99 | C22 | semidirect |
| 41. C2×#834 | C22 | semidirect |
| 44. #4955 | C22 | semidirect |
| 45. #4955 | C22 | semidirect |
| 56. C3×#342 | C22 | semidirect |
| 57. C3×#342 | C22 | semidirect |
| 58. #4527 | C22 | semidirect |
| 59. #4527 | C22 | semidirect |
| 60. #4527 | C22 | semidirect |
| 61. #4527 | C22 | semidirect |
| 62. #4526 | C22 | semidirect |
| 63. #4526 | C22 | semidirect |
| 74. #1913 | D3 | semidirect |
| 115. #953 | D4 | semidirect |
| 136. #929 | D4 | semidirect |
| 160. #882 | D4 | semidirect |
| 161. #882 | D4 | semidirect |
| 167. D3×C22⋊C4 | D4 | semidirect |
| 171. #877 | D4 | semidirect |
| 205. #518 | C2×D3 | semidirect |
| 224. C2×#99 | C2×D3 | semidirect |
| 233. #342 | C2×D3 | semidirect |
| 234. #342 | C2×D3 | semidirect |
| 236. C24×C3 | #41 | semidirect |
| 249. C23×D3 | #41 | semidirect |
| 270. C22×C3×C4 | #41 | semidirect |
| 302. C22×Dic3 | #41 | semidirect |
| 626. C24 | #235 | semidirect |
| 707. C22×C4 | #235 | semidirect |
| 1024. C3 | #23996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #85868 | 2 |
| #83375 | 2 |
| #78688 | 2 |
| C2×#4741 | 2 |
| C3×#1913 | 2 |
| #71851 | 2 |
| #71656 | 2 |
| #70037 | 2 |
| #70036 | 2 |
| #70034 | 2 |
| #70025 | 2 |
| #68970 | 2 |
| #68967 | 2 |
| #68962 | 2 |
| #68960 | 2 |
| #23996 | 3 |