Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2600 conjugacy classes of subgroups.
The subgroup lattice has 820 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #87208 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | C3×#3291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #84013 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #81774 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #81762 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #80933 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #80931 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #80303 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | D3×#456 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #80281 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #80277 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #79895 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #79889 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #61111 | — | 3 | 1 | no | maximal, Sylow |
| 15 | D3×2−1+4 | C22 | 1 | 2 | yes | — |
| 16 | #5966 | C22 | 1 | 2 | yes | complemented |
| 17 | C3×#577 | C22 | 1 | 4 | yes | complemented |
| 18 | #5838 | C22 | 1 | 4 | yes | complemented |
| 19 | #5836 | C22 | 1 | 4 | yes | complemented |
| 20 | #5779 | — | 2 | 4 | no | — |
| 21 | #5779 | C22 | 1 | 4 | yes | complemented |
| 22 | D3×#137 | — | 2 | 4 | no | — |
| 23 | D3×#137 | C22 | 1 | 4 | yes | complemented |
| 24 | #5775 | — | 2 | 4 | no | — |
| 25 | #5775 | C22 | 1 | 4 | yes | complemented |
| 26 | #5773 | — | 2 | 4 | no | — |
| 27 | #5773 | C22 | 1 | 4 | yes | — |
| 28 | #5771 | — | 2 | 4 | no | — |
| 29 | #5771 | C22 | 1 | 4 | yes | complemented |
| 30 | #5768 | — | 2 | 4 | no | — |
| 31 | #5768 | C22 | 1 | 2 | yes | — |
| 32 | #5762 | — | 2 | 4 | no | — |
| 33 | #5762 | C22 | 1 | 4 | yes | complemented |
| 34 | C2×#915 | — | 2 | 4 | no | — |
| 35 | C2×#915 | C22 | 1 | 4 | yes | complemented |
| 36 | #5753 | C22 | 1 | 4 | yes | complemented |
| 37 | #5750 | C22 | 1 | 4 | yes | complemented |
| 38 | D3×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | #5716 | C22 | 1 | 1 | yes | characteristic |
| 40 | C3×#492 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C3×#471 | C22 | 1 | 4 | yes | complemented |
| 42 | C3×#456 | C22 | 1 | 2 | yes | complemented |
| 43 | C3×#453 | C22 | 1 | 2 | yes | complemented |
| 44 | C3×#443 | C22 | 1 | 2 | yes | complemented |
| 45 | #5246 | C22 | 1 | 2 | yes | complemented |
| 46 | #5242 | C22 | 1 | 2 | yes | complemented |
| 47 | #5205 | C22 | 1 | 4 | yes | complemented |
| 48 | #5204 | C22 | 1 | 4 | yes | complemented |
| 49 | #5201 | C22 | 1 | 4 | yes | complemented |
| 50 | #5200 | C22 | 1 | 4 | yes | complemented |
| 51 | #5197 | C22 | 1 | 2 | yes | complemented |
| 52 | #5177 | C22 | 1 | 4 | yes | complemented |
| 53 | #5167 | C22 | 1 | 4 | yes | complemented |
| 54 | #5145 | C22 | 1 | 4 | yes | complemented |
| 55 | #5143 | C22 | 1 | 4 | yes | complemented |
| 56 | #5095 | C22 | 1 | 2 | yes | complemented |
| 57 | #5092 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #5077 | C22 | 1 | 2 | yes | complemented |
| 59 | #5076 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #4896 | C22 | 1 | 4 | yes | complemented |
| 61 | #4894 | C22 | 1 | 2 | yes | complemented |
| 62 | #4893 | C22 | 1 | 2 | yes | complemented |
| 63 | #4826 | C22 | 1 | 4 | yes | complemented |
| 64 | #4826 | C22 | 1 | 4 | yes | complemented |
| 65 | #4824 | C22 | 1 | 4 | yes | complemented |
| 66 | D3×#104 | C22 | 1 | 4 | yes | complemented |
| 67 | #4755 | C22 | 1 | 4 | yes | complemented |
| 68 | #4752 | C22 | 1 | 2 | yes | complemented |
| 69 | D3×#101 | C22 | 1 | 2 | yes | complemented |
| 70 | #4748 | C22 | 1 | 4 | yes | complemented |
| 71 | #4746 | C22 | 1 | 2 | yes | complemented |
| 72 | #4745 | C22 | 1 | 2 | yes | complemented |
| 73 | #4700 | C22 | 1 | 2 | yes | complemented |
| 74 | #4699 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | C4×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic, complemented |
| 76 | #3586 | — | 3 | 4 | no | — |
| 77 | #3293 | — | 3 | 2 | no | — |
| 78 | #3293 | — | 3 | 2 | no | — |
| 79 | #3291 | — | 3 | 1 | no | — |
| 80 | #3291 | — | 3 | 2 | no | — |
| 81 | #3291 | D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | #3289 | — | 3 | 4 | no | — |
| 83 | #3289 | — | 3 | 4 | no | — |
| 84 | #3152 | — | 3 | 1 | no | — |
| 85 | #3069 | — | 3 | 4 | no | — |
| 86 | #3018 | — | 3 | 2 | no | — |
| 87 | C2×#456 | — | 3 | 2 | no | — |
| 88 | #2956 | — | 3 | 2 | no | — |
| 89 | C3×2−1+4 | C23 | 1 | 2 | yes | — |
| 90 | C3×H(5,𝔽2) | C23 | 1 | 2 | yes | — |
| 91 | #1010 | — | 2 | 4 | no | — |
| 92 | #1010 | — | 2 | 4 | no | — |
| 93 | #1010 | — | 4 | 2 | no | — |
| 94 | #1010 | C23 | 1 | 4 | yes | — |
| 95 | #1010 | C23 | 1 | 4 | yes | — |
| 96 | D3×#41 | — | 2 | 4 | no | — |
| 97 | D3×#41 | — | 2 | 4 | no | — |
| 98 | D3×#41 | — | 4 | 2 | no | — |
| 99 | D3×#41 | C23 | 1 | 4 | yes | — |
| 100 | #1007 | — | 2 | 4 | no | — |
| 101 | #1007 | C23 | 1 | 2 | yes | — |
| 102 | C2×D3×Q8 | — | 2 | 4 | no | — |
| 103 | C2×D3×Q8 | C23 | 1 | 2 | yes | — |
| 104 | #1004 | — | 2 | 4 | no | — |
| 105 | #1004 | — | 4 | 2 | no | — |
| 106 | #1004 | C23 | 1 | 2 | yes | — |
| 107 | C2×#237 | — | 2 | 4 | no | — |
| 108 | C2×#237 | — | 4 | 2 | no | — |
| 109 | C2×#237 | C23 | 1 | 2 | yes | — |
| 110 | C3×#137 | — | 2 | 4 | no | — |
| 111 | C3×#137 | C23 | 1 | 4 | yes | — |
| 112 | C3×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 113 | C3×AGL(1,ℤ/8) | C23 | 1 | 4 | yes | — |
| 114 | C3×#135 | — | 2 | 4 | no | — |
| 115 | C3×#135 | C23 | 1 | 2 | yes | — |
| 116 | C2×C3×SD16 | — | 2 | 4 | no | — |
| 117 | C2×C3×SD16 | C23 | 1 | 4 | yes | — |
| 118 | C3×#131 | C23 | 1 | 4 | yes | — |
| 119 | C3×C4⋊Q8 | C23 | 1 | 1 | yes | characteristic |
| 120 | C3×#127 | C23 | 1 | 1 | yes | characteristic |
| 121 | #951 | — | 2 | 4 | no | — |
| 122 | #951 | — | 2 | 4 | no | — |
| 123 | #951 | C23 | 1 | 4 | yes | — |
| 124 | #951 | C23 | 1 | 4 | yes | — |
| 125 | #950 | — | 2 | 4 | no | — |
| 126 | #950 | — | 2 | 4 | no | — |
| 127 | #950 | C23 | 1 | 4 | yes | — |
| 128 | #948 | C23 | 1 | 4 | yes | — |
| 129 | #944 | C23 | 1 | 2 | yes | — |
| 130 | C2×#216 | — | 2 | 4 | no | — |
| 131 | C2×#216 | C23 | 1 | 4 | yes | — |
| 132 | #942 | — | 2 | 4 | no | — |
| 133 | #942 | C23 | 1 | 4 | yes | — |
| 134 | #938 | — | 4 | 1 | no | — |
| 135 | #936 | C23 | 1 | 2 | yes | — |
| 136 | D4×Dic3 | — | 4 | 1 | no | — |
| 137 | C2×#214 | — | 2 | 4 | no | — |
| 138 | C2×#214 | C23 | 1 | 4 | yes | — |
| 139 | #932 | — | 2 | 4 | no | — |
| 140 | #932 | C23 | 1 | 4 | yes | — |
| 141 | #918 | — | 2 | 4 | no | — |
| 142 | #918 | — | 2 | 4 | no | — |
| 143 | #918 | D4 | 1 | 4 | yes | complemented |
| 144 | D3×Q16 | — | 2 | 4 | no | — |
| 145 | D3×Q16 | — | 2 | 4 | no | — |
| 146 | D3×Q16 | — | 2 | 4 | no | — |
| 147 | #916 | — | 2 | 4 | no | — |
| 148 | #916 | — | 2 | 4 | no | — |
| 149 | #916 | — | 2 | 4 | no | — |
| 150 | #915 | — | 2 | 4 | no | — |
| 151 | #915 | — | 2 | 4 | no | — |
| 152 | #915 | — | 2 | 4 | no | — |
| 153 | #915 | — | 2 | 4 | no | — |
| 154 | #915 | — | 2 | 4 | no | — |
| 155 | #915 | — | 2 | 4 | no | — |
| 156 | #915 | — | 2 | 4 | no | — |
| 157 | #915 | — | 2 | 4 | no | — |
| 158 | #915 | — | 2 | 4 | no | — |
| 159 | #915 | — | 2 | 4 | no | — |
| 160 | #915 | — | 2 | 4 | no | — |
| 161 | #915 | D4 | 1 | 4 | yes | complemented |
| 162 | #914 | — | 2 | 4 | no | — |
| 163 | #914 | D4 | 1 | 4 | yes | complemented |
| 164 | D3×SD16 | — | 2 | 4 | no | — |
| 165 | D3×SD16 | — | 2 | 4 | no | — |
| 166 | D3×SD16 | — | 2 | 4 | no | — |
| 167 | #912 | — | 2 | 4 | no | — |
| 168 | #912 | — | 2 | 4 | no | — |
| 169 | #912 | — | 2 | 4 | no | — |
| 170 | #911 | — | 2 | 4 | no | — |
| 171 | #911 | — | 2 | 4 | no | — |
| 172 | #911 | D4 | 1 | 4 | yes | complemented |
| 173 | #909 | — | 2 | 4 | no | — |
| 174 | #909 | — | 2 | 4 | no | — |
| 175 | #909 | C23 | 1 | 4 | yes | — |
| 176 | #909 | C23 | 1 | 4 | yes | — |
| 177 | #907 | — | 2 | 4 | no | — |
| 178 | #907 | C23 | 1 | 4 | yes | — |
| 179 | D3×M16 | — | 2 | 4 | no | — |
| 180 | D3×M16 | C23 | 1 | 4 | yes | — |
| 181 | C2×Dic12 | — | 2 | 4 | no | — |
| 182 | C2×Dic12 | C23 | 1 | 4 | yes | — |
| 183 | #904 | — | 2 | 4 | no | — |
| 184 | #904 | C23 | 1 | 2 | yes | — |
| 185 | #901 | — | 2 | 4 | no | — |
| 186 | #901 | C23 | 1 | 4 | yes | — |
| 187 | C2×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 188 | C2×ΓL(1,𝔽25) | C23 | 1 | 2 | yes | — |
| 189 | D3×C4⋊C4 | — | 4 | 1 | no | — |
| 190 | #888 | — | 4 | 1 | no | — |
| 191 | C42×D3 | C23 | 1 | 1 | yes | characteristic |
| 192 | #869 | C23 | 1 | 1 | yes | characteristic |
| 193 | #869 | C23 | 1 | 1 | yes | characteristic |
| 194 | C3×#108 | C23 | 1 | 2 | yes | — |
| 195 | C3×#104 | C23 | 1 | 4 | yes | — |
| 196 | C3×#101 | C23 | 1 | 2 | yes | — |
| 197 | C3×#100 | C23 | 1 | 2 | yes | — |
| 198 | C3×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 199 | #837 | C23 | 1 | 4 | yes | — |
| 200 | #836 | C23 | 1 | 2 | yes | — |
| 201 | #833 | C23 | 1 | 2 | yes | — |
| 202 | #825 | C23 | 1 | 4 | yes | — |
| 203 | #824 | C23 | 1 | 4 | yes | — |
| 204 | #824 | C23 | 1 | 4 | yes | — |
| 205 | #822 | C23 | 1 | 4 | yes | — |
| 206 | #819 | C23 | 1 | 2 | yes | — |
| 207 | #815 | C23 | 1 | 2 | yes | — |
| 208 | #805 | C23 | 1 | 4 | yes | — |
| 209 | C4×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 210 | #585 | — | 3 | 2 | no | — |
| 211 | C2×2−1+4 | — | 3 | 2 | no | — |
| 212 | #578 | — | 3 | 4 | no | — |
| 213 | #578 | — | 3 | 4 | no | — |
| 214 | #578 | — | 3 | 4 | no | — |
| 215 | #578 | — | 3 | 4 | no | — |
| 216 | #578 | — | 6 | 4 | no | — |
| 217 | #578 | — | 6 | 4 | no | — |
| 218 | #577 | — | 3 | 4 | no | — |
| 219 | #577 | — | 3 | 4 | no | — |
| 220 | #577 | — | 3 | 4 | no | — |
| 221 | #577 | — | 6 | 4 | no | — |
| 222 | #577 | — | 6 | 4 | no | — |
| 223 | #577 | C2×D3 | 1 | 4 | yes | complemented |
| 224 | #575 | — | 3 | 2 | no | — |
| 225 | #575 | — | 3 | 4 | no | — |
| 226 | #575 | — | 6 | 4 | no | — |
| 227 | #575 | — | 6 | 4 | no | — |
| 228 | C2×#137 | — | 3 | 4 | no | — |
| 229 | C2×#137 | — | 3 | 4 | no | — |
| 230 | C2×#137 | — | 6 | 4 | no | — |
| 231 | C2×#137 | — | 6 | 4 | no | — |
| 232 | #568 | — | 3 | 4 | no | — |
| 233 | #532 | — | 3 | 1 | no | — |
| 234 | C2×C4⋊Q8 | — | 3 | 1 | no | — |
| 235 | #497 | — | 3 | 4 | no | — |
| 236 | #494 | — | 3 | 1 | no | — |
| 237 | #494 | — | 3 | 1 | no | — |
| 238 | #492 | — | 3 | 1 | no | — |
| 239 | #492 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 240 | #473 | — | 3 | 4 | no | — |
| 241 | #473 | — | 3 | 4 | no | — |
| 242 | #473 | — | 3 | 4 | no | — |
| 243 | #473 | — | 3 | 4 | no | — |
| 244 | #471 | — | 3 | 4 | no | — |
| 245 | #471 | — | 3 | 4 | no | — |
| 246 | #471 | — | 3 | 4 | no | — |
| 247 | #471 | C2×D3 | 1 | 4 | yes | complemented |
| 248 | #456 | — | 3 | 2 | no | — |
| 249 | #456 | — | 3 | 4 | no | — |
| 250 | #456 | — | 3 | 2 | no | — |
| 251 | #456 | — | 3 | 4 | no | — |
| 252 | #456 | — | 3 | 4 | no | — |
| 253 | #456 | — | 3 | 2 | no | — |
| 254 | #456 | C2×D3 | 1 | 2 | yes | complemented |
| 255 | #455 | — | 3 | 2 | no | — |
| 256 | #455 | — | 3 | 2 | no | — |
| 257 | #454 | — | 3 | 4 | no | — |
| 258 | #453 | — | 3 | 2 | no | — |
| 259 | #453 | C2×D3 | 1 | 2 | yes | complemented |
| 260 | #444 | — | 3 | 2 | no | — |
| 261 | #444 | — | 3 | 4 | no | — |
| 262 | #444 | — | 3 | 2 | no | — |
| 263 | #443 | — | 3 | 4 | no | — |
| 264 | #443 | — | 3 | 2 | no | — |
| 265 | #443 | C2×D3 | 1 | 2 | yes | complemented |
| 266 | #430 | — | 3 | 2 | no | — |
| 267 | C2×#104 | — | 3 | 4 | no | — |
| 268 | #413 | — | 3 | 2 | no | — |
| 269 | C2×#101 | — | 3 | 2 | no | — |
| 270 | C4×M16 | — | 3 | 1 | no | — |
| 271 | C3×#41 | — | 2 | 4 | no | — |
| 272 | C3×#41 | — | 2 | 4 | no | — |
| 273 | C3×#41 | — | 4 | 2 | no | — |
| 274 | C3×#41 | C24 | 1 | 4 | yes | — |
| 275 | C2×C3×Q8 | — | 2 | 4 | no | — |
| 276 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 277 | C2×C3×D4 | — | 2 | 4 | no | — |
| 278 | C2×C3×D4 | — | 4 | 1 | no | — |
| 279 | C2×C3×D4 | — | 4 | 2 | no | — |
| 280 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 281 | C2×#67 | — | 2 | 2 | no | — |
| 282 | C2×#67 | — | 4 | 2 | no | — |
| 283 | C2×#67 | — | 4 | 2 | no | — |
| 284 | C2×#67 | — | 4 | 4 | no | — |
| 285 | C22×Dic3 | — | 2 | 2 | no | — |
| 286 | C22×Dic3 | — | 4 | 2 | no | — |
| 287 | #239 | — | 2 | 4 | no | — |
| 288 | #239 | — | 4 | 2 | no | — |
| 289 | #239 | C2×D4 | 1 | 4 | yes | — |
| 290 | D3×Q8 | — | 2 | 4 | no | — |
| 291 | D3×Q8 | — | 2 | 4 | no | — |
| 292 | D3×Q8 | — | 2 | 4 | no | — |
| 293 | D3×Q8 | — | 2 | 4 | no | — |
| 294 | D3×Q8 | — | 2 | 4 | no | — |
| 295 | D3×Q8 | — | 4 | 4 | no | — |
| 296 | D3×Q8 | — | 4 | 2 | no | — |
| 297 | D3×Q8 | C2×D4 | 1 | 4 | yes | — |
| 298 | #237 | — | 2 | 4 | no | — |
| 299 | #237 | — | 2 | 4 | no | — |
| 300 | #237 | — | 2 | 4 | no | — |
| 301 | #237 | — | 2 | 4 | no | — |
| 302 | #237 | — | 2 | 4 | no | — |
| 303 | #237 | — | 2 | 4 | no | — |
| 304 | #237 | — | 4 | 4 | no | — |
| 305 | #237 | — | 4 | 4 | no | — |
| 306 | #237 | — | 4 | 4 | no | — |
| 307 | #237 | — | 4 | 4 | no | — |
| 308 | #237 | — | 4 | 4 | no | — |
| 309 | #237 | — | 4 | 4 | no | — |
| 310 | #237 | — | 4 | 2 | no | — |
| 311 | #237 | C2×D4 | 1 | 4 | yes | — |
| 312 | D3×D4 | — | 2 | 4 | no | — |
| 313 | D3×D4 | — | 2 | 4 | no | — |
| 314 | D3×D4 | — | 4 | 4 | no | — |
| 315 | D3×D4 | — | 4 | 2 | no | — |
| 316 | D3×D4 | C2×D4 | 1 | 4 | yes | — |
| 317 | #235 | — | 2 | 4 | no | — |
| 318 | #235 | — | 2 | 4 | no | — |
| 319 | #235 | — | 2 | 4 | no | — |
| 320 | #235 | — | 4 | 4 | no | — |
| 321 | #235 | — | 4 | 4 | no | — |
| 322 | #235 | — | 4 | 4 | no | — |
| 323 | #235 | — | 4 | 2 | no | — |
| 324 | #235 | C24 | 1 | 4 | yes | — |
| 325 | C2×C4×D3 | — | 2 | 4 | no | — |
| 326 | C2×C4×D3 | — | 2 | 1 | no | — |
| 327 | C2×C4×D3 | — | 2 | 2 | no | — |
| 328 | C2×C4×D3 | — | 4 | 2 | no | — |
| 329 | C2×C4×D3 | — | 4 | 4 | no | — |
| 330 | C2×C4×D3 | C24 | 1 | 1 | yes | characteristic |
| 331 | C2×Dic6 | — | 2 | 4 | no | — |
| 332 | C2×Dic6 | — | 2 | 4 | no | — |
| 333 | C2×Dic6 | — | 2 | 2 | no | — |
| 334 | C2×Dic6 | — | 4 | 2 | no | — |
| 335 | C2×Dic6 | — | 4 | 4 | no | — |
| 336 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 337 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 338 | C3×Q16 | — | 2 | 4 | no | — |
| 339 | C3×Q16 | C2×D4 | 1 | 2 | yes | — |
| 340 | C3×SD16 | — | 2 | 4 | no | — |
| 341 | C3×SD16 | — | 2 | 4 | no | — |
| 342 | C3×SD16 | — | 2 | 4 | no | — |
| 343 | C3×SD16 | — | 2 | 4 | no | — |
| 344 | C3×SD16 | C2×D4 | 1 | 4 | yes | — |
| 345 | C3×D8 | — | 2 | 4 | no | — |
| 346 | C3×D8 | C2×D4 | 1 | 2 | yes | — |
| 347 | C3×M16 | — | 2 | 4 | no | — |
| 348 | C3×M16 | C24 | 1 | 4 | yes | — |
| 349 | C2×C3×C8 | — | 2 | 4 | no | — |
| 350 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 351 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 352 | C3×C42 | C24 | 1 | 1 | yes | characteristic |
| 353 | #217 | — | 4 | 2 | no | — |
| 354 | #216 | — | 2 | 4 | no | — |
| 355 | #216 | — | 2 | 4 | no | — |
| 356 | #216 | — | 2 | 4 | no | — |
| 357 | #216 | — | 2 | 4 | no | — |
| 358 | #216 | — | 2 | 4 | no | — |
| 359 | #216 | C2×D4 | 1 | 4 | yes | — |
| 360 | #215 | — | 2 | 4 | no | — |
| 361 | #215 | C2×D4 | 1 | 4 | yes | — |
| 362 | #214 | — | 2 | 4 | no | — |
| 363 | #214 | — | 2 | 4 | no | — |
| 364 | #214 | — | 2 | 4 | no | — |
| 365 | #214 | — | 2 | 4 | no | — |
| 366 | #214 | — | 2 | 4 | no | — |
| 367 | #214 | C2×D4 | 1 | 4 | yes | — |
| 368 | #213 | — | 2 | 4 | no | — |
| 369 | #213 | C2×D4 | 1 | 4 | yes | — |
| 370 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 371 | C4⋊Dic3 | — | 4 | 1 | no | — |
| 372 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 373 | C4×Dic3 | — | 2 | 1 | no | — |
| 374 | C4×Dic3 | C24 | 1 | 1 | yes | characteristic |
| 375 | #208 | — | 2 | 4 | no | — |
| 376 | #208 | C24 | 1 | 4 | yes | — |
| 377 | C2×C3⋊C8 | — | 2 | 4 | no | — |
| 378 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 379 | Dic12 | — | 2 | 4 | no | — |
| 380 | Dic12 | — | 2 | 4 | no | — |
| 381 | Dic12 | — | 2 | 4 | no | — |
| 382 | Dic12 | — | 2 | 4 | no | — |
| 383 | Dic12 | C2×D4 | 1 | 2 | yes | — |
| 384 | D24 | C2×D4 | 1 | 2 | yes | — |
| 385 | #204 | — | 2 | 4 | no | — |
| 386 | #204 | — | 2 | 4 | no | — |
| 387 | #204 | C2×D4 | 1 | 4 | yes | — |
| 388 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 389 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 390 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 391 | ΓL(1,𝔽25) | C2×D4 | 1 | 4 | yes | — |
| 392 | ΓL(1,𝔽25) | C2×D4 | 1 | 4 | yes | — |
| 393 | D3×C8 | — | 2 | 4 | no | — |
| 394 | D3×C8 | — | 2 | 4 | no | — |
| 395 | D3×C8 | — | 2 | 4 | no | — |
| 396 | 2−1+4 | — | 3 | 4 | no | — |
| 397 | 2−1+4 | — | 3 | 4 | no | — |
| 398 | 2−1+4 | — | 3 | 2 | no | — |
| 399 | 2−1+4 | — | 6 | 4 | no | — |
| 400 | 2−1+4 | — | 6 | 4 | no | — |
| 401 | 2−1+4 | — | 6 | 4 | no | — |
| 402 | 2−1+4 | — | 12 | 2 | no | — |
| 403 | 2−1+4 | C22×D3 | 1 | 2 | yes | — |
| 404 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 405 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 406 | H(5,𝔽2) | — | 12 | 2 | no | — |
| 407 | H(5,𝔽2) | C22×D3 | 1 | 2 | yes | — |
| 408 | C2×#41 | — | 3 | 4 | no | — |
| 409 | C2×#41 | — | 3 | 2 | no | — |
| 410 | C2×#41 | — | 6 | 4 | no | — |
| 411 | C2×#41 | — | 6 | 4 | no | — |
| 412 | C2×#41 | — | 6 | 4 | no | — |
| 413 | C2×#41 | — | 12 | 2 | no | — |
| 414 | C2×#41 | — | 12 | 2 | no | — |
| 415 | C22×Q8 | — | 3 | 2 | no | — |
| 416 | C22×Q8 | — | 6 | 4 | no | — |
| 417 | #137 | — | 2 | 4 | no | — |
| 418 | #137 | — | 3 | 4 | no | — |
| 419 | #137 | — | 3 | 4 | no | — |
| 420 | #137 | — | 3 | 4 | no | — |
| 421 | #137 | — | 3 | 4 | no | — |
| 422 | #137 | — | 3 | 4 | no | — |
| 423 | #137 | — | 3 | 4 | no | — |
| 424 | #137 | — | 3 | 4 | no | — |
| 425 | #137 | — | 6 | 4 | no | — |
| 426 | #137 | — | 6 | 4 | no | — |
| 427 | #137 | — | 6 | 4 | no | — |
| 428 | #137 | — | 6 | 4 | no | — |
| 429 | #137 | — | 6 | 4 | no | — |
| 430 | #137 | — | 6 | 4 | no | — |
| 431 | #137 | — | 6 | 4 | no | — |
| 432 | #137 | — | 6 | 4 | no | — |
| 433 | #137 | — | 6 | 4 | no | — |
| 434 | #137 | — | 6 | 4 | no | — |
| 435 | #137 | — | 6 | 4 | no | — |
| 436 | #137 | — | 6 | 4 | no | — |
| 437 | #137 | — | 6 | 4 | no | — |
| 438 | #137 | — | 6 | 4 | no | — |
| 439 | #137 | — | 6 | 4 | no | — |
| 440 | #137 | — | 6 | 4 | no | — |
| 441 | #137 | — | 6 | 4 | no | — |
| 442 | #137 | — | 6 | 4 | no | — |
| 443 | #137 | C22×D3 | 1 | 4 | yes | — |
| 444 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 445 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 446 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 447 | AGL(1,ℤ/8) | — | 3 | 4 | no | — |
| 448 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 449 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 450 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 451 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 452 | AGL(1,ℤ/8) | C22×D3 | 1 | 4 | yes | — |
| 453 | #135 | — | 2 | 4 | no | — |
| 454 | #135 | — | 3 | 4 | no | — |
| 455 | #135 | — | 3 | 2 | no | — |
| 456 | #135 | — | 6 | 4 | no | — |
| 457 | #135 | — | 6 | 4 | no | — |
| 458 | #135 | — | 6 | 4 | no | — |
| 459 | #135 | — | 6 | 4 | no | — |
| 460 | #135 | — | 6 | 4 | no | — |
| 461 | #135 | — | 6 | 4 | no | — |
| 462 | #135 | — | 6 | 4 | no | — |
| 463 | #135 | — | 6 | 4 | no | — |
| 464 | #135 | — | 6 | 4 | no | — |
| 465 | #135 | C22×D3 | 1 | 2 | yes | — |
| 466 | C2×Q16 | — | 3 | 4 | no | — |
| 467 | C2×Q16 | — | 3 | 4 | no | — |
| 468 | C2×Q16 | — | 6 | 4 | no | — |
| 469 | C2×Q16 | — | 6 | 4 | no | — |
| 470 | C2×Q16 | — | 6 | 4 | no | — |
| 471 | C2×Q16 | — | 6 | 4 | no | — |
| 472 | C2×Q16 | — | 6 | 4 | no | — |
| 473 | C2×SD16 | — | 2 | 4 | no | — |
| 474 | C2×SD16 | — | 3 | 4 | no | — |
| 475 | C2×SD16 | — | 6 | 4 | no | — |
| 476 | C2×SD16 | — | 6 | 4 | no | — |
| 477 | C2×SD16 | — | 6 | 4 | no | — |
| 478 | C2×SD16 | — | 6 | 4 | no | — |
| 479 | C2×SD16 | C22×D3 | 1 | 4 | yes | — |
| 480 | #131 | — | 3 | 4 | no | — |
| 481 | #131 | — | 3 | 4 | no | — |
| 482 | #131 | — | 3 | 4 | no | — |
| 483 | #131 | — | 6 | 4 | no | — |
| 484 | #131 | — | 6 | 4 | no | — |
| 485 | #131 | C22×D3 | 1 | 4 | yes | — |
| 486 | C2×M16 | — | 3 | 2 | no | — |
| 487 | C2×M16 | — | 3 | 4 | no | — |
| 488 | C2×M16 | — | 6 | 4 | no | — |
| 489 | C2×M16 | — | 6 | 4 | no | — |
| 490 | C4⋊Q8 | — | 3 | 2 | no | — |
| 491 | C4⋊Q8 | — | 3 | 1 | no | — |
| 492 | C4⋊Q8 | — | 3 | 1 | no | — |
| 493 | C4⋊Q8 | — | 12 | 1 | no | — |
| 494 | C4⋊Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 495 | #127 | C22×D3 | 1 | 1 | yes | characteristic |
| 496 | #124 | — | 3 | 2 | no | — |
| 497 | #121 | — | 12 | 1 | no | — |
| 498 | C4×D4 | — | 12 | 1 | no | — |
| 499 | C2×C4⋊C4 | — | 12 | 1 | no | — |
| 500 | C2×C42 | — | 3 | 1 | no | — |
| 501 | #108 | — | 3 | 4 | no | — |
| 502 | #108 | — | 3 | 2 | no | — |
| 503 | #108 | C22×D3 | 1 | 2 | yes | — |
| 504 | #104 | — | 3 | 4 | no | — |
| 505 | #104 | — | 3 | 4 | no | — |
| 506 | #104 | — | 3 | 4 | no | — |
| 507 | #104 | C22×D3 | 1 | 4 | yes | — |
| 508 | #101 | — | 3 | 2 | no | — |
| 509 | #101 | — | 3 | 4 | no | — |
| 510 | #101 | — | 3 | 4 | no | — |
| 511 | #101 | C22×D3 | 1 | 2 | yes | — |
| 512 | #100 | — | 3 | 2 | no | — |
| 513 | #100 | C22×D3 | 1 | 2 | yes | — |
| 514 | #97 | — | 3 | 2 | no | — |
| 515 | C4×C8 | — | 3 | 1 | no | — |
| 516 | C4×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 517 | C23×C3 | — | 2 | 2 | no | — |
| 518 | C23×C3 | — | 4 | 2 | no | — |
| 519 | C22×D3 | — | 2 | 4 | no | — |
| 520 | C22×D3 | — | 4 | 2 | no | — |
| 521 | C22×D3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 522 | C3×Q8 | — | 2 | 4 | no | — |
| 523 | C3×Q8 | — | 4 | 2 | no | — |
| 524 | C3×Q8 | C22×D4 | 1 | 4 | yes | — |
| 525 | C3×D4 | — | 2 | 4 | no | — |
| 526 | C3×D4 | — | 2 | 4 | no | — |
| 527 | C3×D4 | — | 4 | 4 | no | — |
| 528 | C3×D4 | — | 4 | 2 | no | — |
| 529 | C3×D4 | — | 8 | 2 | no | — |
| 530 | C3×D4 | C22×D4 | 1 | 4 | yes | — |
| 531 | C2×C3×C4 | — | 2 | 1 | no | — |
| 532 | C2×C3×C4 | — | 2 | 4 | no | — |
| 533 | C2×C3×C4 | — | 2 | 2 | no | — |
| 534 | C2×C3×C4 | — | 4 | 2 | no | — |
| 535 | C2×C3×C4 | — | 4 | 4 | no | — |
| 536 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 537 | #67 | — | 2 | 4 | no | — |
| 538 | #67 | — | 2 | 4 | no | — |
| 539 | #67 | — | 2 | 4 | no | — |
| 540 | #67 | — | 4 | 4 | no | — |
| 541 | #67 | — | 4 | 4 | no | — |
| 542 | #67 | — | 4 | 4 | no | — |
| 543 | #67 | — | 4 | 4 | no | — |
| 544 | C2×Dic3 | — | 2 | 4 | no | — |
| 545 | C2×Dic3 | — | 2 | 1 | no | — |
| 546 | C2×Dic3 | — | 2 | 2 | no | — |
| 547 | C2×Dic3 | — | 2 | 2 | no | — |
| 548 | C2×Dic3 | — | 4 | 2 | no | — |
| 549 | C2×Dic3 | — | 4 | 4 | no | — |
| 550 | C2×Dic3 | — | 4 | 4 | no | — |
| 551 | C2×Dic3 | — | 4 | 2 | no | — |
| 552 | C2×Dic3 | — | 4 | 2 | no | — |
| 553 | C2×Dic3 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 554 | D12 | — | 2 | 4 | no | — |
| 555 | D12 | — | 4 | 2 | no | — |
| 556 | D12 | C22×D4 | 1 | 4 | yes | — |
| 557 | C4×D3 | — | 2 | 4 | no | — |
| 558 | C4×D3 | — | 2 | 4 | no | — |
| 559 | C4×D3 | — | 2 | 4 | no | — |
| 560 | C4×D3 | — | 4 | 4 | no | — |
| 561 | C4×D3 | — | 4 | 4 | no | — |
| 562 | C4×D3 | — | 4 | 4 | no | — |
| 563 | C4×D3 | — | 4 | 2 | no | — |
| 564 | C4×D3 | — | 4 | 2 | no | — |
| 565 | C4×D3 | — | 4 | 2 | no | — |
| 566 | C4×D3 | C22×D4 | 1 | 4 | yes | — |
| 567 | Dic6 | — | 2 | 4 | no | — |
| 568 | Dic6 | — | 2 | 4 | no | — |
| 569 | Dic6 | — | 2 | 4 | no | — |
| 570 | Dic6 | — | 4 | 2 | no | — |
| 571 | Dic6 | — | 4 | 4 | no | — |
| 572 | Dic6 | — | 4 | 4 | no | — |
| 573 | Dic6 | — | 4 | 4 | no | — |
| 574 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 575 | C3×C8 | — | 2 | 4 | no | — |
| 576 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 577 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 578 | C3⋊C8 | — | 2 | 4 | no | — |
| 579 | C3⋊C8 | C22×D4 | 1 | 4 | yes | — |
| 580 | #41 | — | 2 | 4 | no | — |
| 581 | #41 | — | 2 | 4 | no | — |
| 582 | #41 | — | 3 | 4 | no | — |
| 583 | #41 | — | 3 | 4 | no | — |
| 584 | #41 | — | 3 | 4 | no | — |
| 585 | #41 | — | 4 | 2 | no | — |
| 586 | #41 | — | 6 | 4 | no | — |
| 587 | #41 | — | 6 | 4 | no | — |
| 588 | #41 | — | 6 | 4 | no | — |
| 589 | #41 | — | 6 | 4 | no | — |
| 590 | #41 | — | 6 | 4 | no | — |
| 591 | #41 | — | 6 | 4 | no | — |
| 592 | #41 | — | 6 | 4 | no | — |
| 593 | #41 | — | 6 | 4 | no | — |
| 594 | #41 | — | 6 | 4 | no | — |
| 595 | #41 | — | 6 | 4 | no | — |
| 596 | #41 | — | 12 | 2 | no | — |
| 597 | #41 | — | 12 | 4 | no | — |
| 598 | #41 | — | 12 | 4 | no | — |
| 599 | #41 | — | 12 | 4 | no | — |
| 600 | #41 | — | 12 | 4 | no | — |
| 601 | #41 | — | 12 | 4 | no | — |
| 602 | #41 | — | 12 | 4 | no | — |
| 603 | #41 | — | 12 | 4 | no | — |
| 604 | #41 | — | 12 | 4 | no | — |
| 605 | #41 | — | 12 | 2 | no | — |
| 606 | #41 | — | 12 | 4 | no | — |
| 607 | #41 | — | 12 | 2 | no | — |
| 608 | #41 | C23×D3 | 1 | 4 | yes | — |
| 609 | C2×Q8 | — | 2 | 4 | no | — |
| 610 | C2×Q8 | — | 3 | 4 | no | — |
| 611 | C2×Q8 | — | 3 | 2 | no | — |
| 612 | C2×Q8 | — | 3 | 2 | no | — |
| 613 | C2×Q8 | — | 6 | 2 | no | — |
| 614 | C2×Q8 | — | 6 | 4 | no | — |
| 615 | C2×Q8 | — | 6 | 4 | no | — |
| 616 | C2×Q8 | — | 6 | 4 | no | — |
| 617 | C2×Q8 | — | 6 | 4 | no | — |
| 618 | C2×Q8 | — | 6 | 4 | no | — |
| 619 | C2×Q8 | — | 6 | 4 | no | — |
| 620 | C2×Q8 | — | 6 | 4 | no | — |
| 621 | C2×Q8 | — | 12 | 4 | no | — |
| 622 | C2×Q8 | — | 12 | 2 | no | — |
| 623 | C2×Q8 | — | 12 | 2 | no | — |
| 624 | C2×Q8 | — | 12 | 4 | no | — |
| 625 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 626 | C2×D4 | — | 2 | 4 | no | — |
| 627 | C2×D4 | — | 3 | 4 | no | — |
| 628 | C2×D4 | — | 4 | 1 | no | — |
| 629 | C2×D4 | — | 4 | 2 | no | — |
| 630 | C2×D4 | — | 6 | 4 | no | — |
| 631 | C2×D4 | — | 6 | 4 | no | — |
| 632 | C2×D4 | — | 6 | 2 | no | — |
| 633 | C2×D4 | — | 12 | 4 | no | — |
| 634 | C2×D4 | — | 12 | 2 | no | — |
| 635 | C2×D4 | — | 12 | 2 | no | — |
| 636 | C2×D4 | — | 12 | 2 | no | — |
| 637 | C2×D4 | — | 12 | 4 | no | — |
| 638 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 639 | C22×C4 | — | 3 | 1 | no | — |
| 640 | C22×C4 | — | 6 | 4 | no | — |
| 641 | C22×C4 | — | 6 | 1 | no | — |
| 642 | C22×C4 | — | 6 | 2 | no | — |
| 643 | C22×C4 | — | 6 | 2 | no | — |
| 644 | C22×C4 | — | 12 | 2 | no | — |
| 645 | C22×C4 | — | 12 | 4 | no | — |
| 646 | C22×C4 | — | 12 | 2 | no | — |
| 647 | Q16 | — | 2 | 4 | no | — |
| 648 | Q16 | — | 3 | 4 | no | — |
| 649 | Q16 | — | 3 | 2 | no | — |
| 650 | Q16 | — | 6 | 4 | no | — |
| 651 | Q16 | — | 6 | 4 | no | — |
| 652 | Q16 | — | 6 | 4 | no | — |
| 653 | Q16 | — | 6 | 4 | no | — |
| 654 | Q16 | — | 6 | 4 | no | — |
| 655 | Q16 | — | 6 | 4 | no | — |
| 656 | Q16 | — | 6 | 4 | no | — |
| 657 | Q16 | — | 6 | 4 | no | — |
| 658 | Q16 | — | 6 | 4 | no | — |
| 659 | Q16 | D3×D4 | 1 | 2 | yes | — |
| 660 | SD16 | — | 2 | 4 | no | — |
| 661 | SD16 | — | 2 | 4 | no | — |
| 662 | SD16 | — | 2 | 4 | no | — |
| 663 | SD16 | — | 2 | 4 | no | — |
| 664 | SD16 | — | 3 | 4 | no | — |
| 665 | SD16 | — | 3 | 4 | no | — |
| 666 | SD16 | — | 3 | 4 | no | — |
| 667 | SD16 | — | 6 | 4 | no | — |
| 668 | SD16 | — | 6 | 4 | no | — |
| 669 | SD16 | — | 6 | 4 | no | — |
| 670 | SD16 | — | 6 | 4 | no | — |
| 671 | SD16 | — | 6 | 4 | no | — |
| 672 | SD16 | — | 6 | 4 | no | — |
| 673 | SD16 | — | 6 | 4 | no | — |
| 674 | SD16 | — | 6 | 4 | no | — |
| 675 | SD16 | D3×D4 | 1 | 4 | yes | — |
| 676 | D8 | — | 2 | 4 | no | — |
| 677 | D8 | — | 3 | 4 | no | — |
| 678 | D8 | — | 3 | 2 | no | — |
| 679 | D8 | — | 6 | 4 | no | — |
| 680 | D8 | D3×D4 | 1 | 2 | yes | — |
| 681 | M16 | — | 2 | 4 | no | — |
| 682 | M16 | — | 3 | 4 | no | — |
| 683 | M16 | — | 3 | 4 | no | — |
| 684 | M16 | — | 3 | 4 | no | — |
| 685 | M16 | — | 6 | 4 | no | — |
| 686 | M16 | — | 6 | 4 | no | — |
| 687 | M16 | — | 6 | 4 | no | — |
| 688 | M16 | — | 6 | 4 | no | — |
| 689 | M16 | C23×D3 | 1 | 4 | yes | — |
| 690 | C2×C8 | — | 2 | 4 | no | — |
| 691 | C2×C8 | — | 3 | 2 | no | — |
| 692 | C2×C8 | — | 6 | 4 | no | — |
| 693 | C2×C8 | — | 6 | 4 | no | — |
| 694 | C2×C8 | — | 6 | 4 | no | — |
| 695 | C2×C8 | — | 6 | 4 | no | — |
| 696 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 697 | C4⋊C4 | — | 4 | 1 | no | — |
| 698 | C4⋊C4 | — | 12 | 2 | no | — |
| 699 | C4⋊C4 | — | 12 | 1 | no | — |
| 700 | C4⋊C4 | — | 12 | 1 | no | — |
| 701 | C22⋊C4 | — | 12 | 2 | no | — |
| 702 | C42 | — | 3 | 1 | no | — |
| 703 | C42 | — | 6 | 1 | no | — |
| 704 | C42 | C23×D3 | 1 | 1 | yes | characteristic |
| 705 | C22×C3 | — | 2 | 4 | no | — |
| 706 | C22×C3 | — | 4 | 2 | no | — |
| 707 | C22×C3 | — | 8 | 2 | no | — |
| 708 | C22×C3 | — | 16 | 2 | no | — |
| 709 | C22×C3 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 710 | C2×D3 | — | 2 | 4 | no | — |
| 711 | C2×D3 | — | 4 | 1 | no | — |
| 712 | C2×D3 | — | 8 | 4 | no | — |
| 713 | C2×D3 | — | 16 | 2 | no | — |
| 714 | C2×D3 | D42 | 1 | 2 | yes | — |
| 715 | C3×C4 | — | 2 | 2 | no | — |
| 716 | C3×C4 | — | 2 | 4 | no | — |
| 717 | C3×C4 | — | 4 | 2 | no | — |
| 718 | C3×C4 | C23×D4 | 1 | 2 | yes | — |
| 719 | Dic3 | — | 2 | 4 | no | — |
| 720 | Dic3 | — | 4 | 1 | no | — |
| 721 | Dic3 | — | 4 | 2 | no | — |
| 722 | Dic3 | — | 4 | 2 | no | — |
| 723 | Dic3 | D42 | 1 | 2 | yes | — |
| 724 | C23 | — | 2 | 2 | no | — |
| 725 | C23 | — | 3 | 1 | no | — |
| 726 | C23 | — | 4 | 2 | no | — |
| 727 | C23 | — | 6 | 4 | no | — |
| 728 | C23 | — | 12 | 2 | no | — |
| 729 | Q8 | — | 2 | 4 | no | — |
| 730 | Q8 | — | 3 | 4 | no | — |
| 731 | Q8 | — | 4 | 2 | no | — |
| 732 | Q8 | — | 6 | 4 | no | — |
| 733 | Q8 | — | 6 | 4 | no | — |
| 734 | Q8 | — | 6 | 4 | no | — |
| 735 | Q8 | — | 12 | 4 | no | — |
| 736 | Q8 | — | 12 | 4 | no | — |
| 737 | Q8 | — | 12 | 4 | no | — |
| 738 | Q8 | — | 12 | 2 | no | — |
| 739 | Q8 | C2×D3×D4 | 1 | 4 | yes | — |
| 740 | D4 | — | 2 | 4 | no | — |
| 741 | D4 | — | 2 | 4 | no | — |
| 742 | D4 | — | 3 | 4 | no | — |
| 743 | D4 | — | 4 | 4 | no | — |
| 744 | D4 | — | 4 | 2 | no | — |
| 745 | D4 | — | 6 | 4 | no | — |
| 746 | D4 | — | 6 | 4 | no | — |
| 747 | D4 | — | 6 | 4 | no | — |
| 748 | D4 | — | 6 | 4 | no | — |
| 749 | D4 | — | 8 | 2 | no | — |
| 750 | D4 | — | 12 | 2 | no | — |
| 751 | D4 | — | 12 | 4 | no | — |
| 752 | D4 | — | 12 | 4 | no | — |
| 753 | D4 | — | 12 | 4 | no | — |
| 754 | D4 | — | 12 | 4 | no | — |
| 755 | D4 | C2×D3×D4 | 1 | 4 | yes | — |
| 756 | C2×C4 | — | 2 | 1 | no | — |
| 757 | C2×C4 | — | 2 | 4 | no | — |
| 758 | C2×C4 | — | 2 | 2 | no | — |
| 759 | C2×C4 | — | 3 | 1 | no | — |
| 760 | C2×C4 | — | 3 | 4 | no | — |
| 761 | C2×C4 | — | 4 | 2 | no | — |
| 762 | C2×C4 | — | 4 | 4 | no | — |
| 763 | C2×C4 | — | 6 | 4 | no | — |
| 764 | C2×C4 | — | 6 | 4 | no | — |
| 765 | C2×C4 | — | 6 | 4 | no | — |
| 766 | C2×C4 | — | 6 | 4 | no | — |
| 767 | C2×C4 | — | 6 | 1 | no | — |
| 768 | C2×C4 | — | 6 | 2 | no | — |
| 769 | C2×C4 | — | 6 | 2 | no | — |
| 770 | C2×C4 | — | 12 | 4 | no | — |
| 771 | C2×C4 | — | 12 | 4 | no | — |
| 772 | C2×C4 | — | 12 | 2 | no | — |
| 773 | C2×C4 | — | 12 | 2 | no | — |
| 774 | C2×C4 | — | 12 | 2 | no | — |
| 775 | C2×C4 | — | 12 | 4 | no | — |
| 776 | C2×C4 | — | 12 | 2 | no | — |
| 777 | C2×C4 | — | 12 | 2 | no | — |
| 778 | C2×C4 | — | 12 | 2 | no | — |
| 779 | C2×C4 | — | 12 | 4 | no | — |
| 780 | C2×C4 | — | 12 | 4 | no | — |
| 781 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 782 | C8 | — | 2 | 4 | no | — |
| 783 | C8 | — | 3 | 4 | no | — |
| 784 | C8 | — | 6 | 4 | no | — |
| 785 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 786 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 787 | C2×C3 | — | 2 | 1 | no | — |
| 788 | C2×C3 | — | 4 | 4 | no | — |
| 789 | C2×C3 | — | 8 | 2 | no | — |
| 790 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 791 | D3 | — | 2 | 2 | no | — |
| 792 | D3 | — | 4 | 4 | no | — |
| 793 | C22 | — | 2 | 4 | no | — |
| 794 | C22 | — | 3 | 2 | no | — |
| 795 | C22 | — | 4 | 2 | no | — |
| 796 | C22 | — | 6 | 4 | no | — |
| 797 | C22 | — | 8 | 2 | no | — |
| 798 | C22 | — | 12 | 1 | no | — |
| 799 | C22 | — | 16 | 2 | no | — |
| 800 | C22 | — | 24 | 4 | no | — |
| 801 | C22 | — | 48 | 2 | no | — |
| 802 | C22 | D3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 803 | C4 | — | 2 | 2 | no | — |
| 804 | C4 | — | 2 | 4 | no | — |
| 805 | C4 | — | 3 | 2 | no | — |
| 806 | C4 | — | 4 | 2 | no | — |
| 807 | C4 | — | 6 | 4 | no | — |
| 808 | C4 | — | 12 | 1 | no | — |
| 809 | C4 | — | 12 | 2 | no | — |
| 810 | C4 | — | 12 | 2 | no | — |
| 811 | C4 | C22×D3×D4 | 1 | 2 | yes | — |
| 812 | C3 | #61111 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 813 | C2 | — | 2 | 1 | no | — |
| 814 | C2 | — | 4 | 4 | no | — |
| 815 | C2 | — | 6 | 2 | no | — |
| 816 | C2 | — | 8 | 2 | no | — |
| 817 | C2 | — | 12 | 4 | no | — |
| 818 | C2 | D3×D42 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×D42 |
| commutator, cosocle | C2×C3×C4 | C25 |
| Frattini | C2×C4 | C24×D3 |
| Fitting | C3×#3291 | C2 |
| socle | C2×C3 | C2×D42 |
| hypercenter | #3291 | D3 |
| hypocenter | C3 | #61111 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #3291 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87208 | C2 | semidirect |
| 2. C3×#3291 | C2 | semidirect |
| 3. #84013 | C2 | semidirect |
| 4. #81774 | C2 | semidirect |
| 5. #81762 | C2 | semidirect |
| 6. #80933 | C2 | semidirect |
| 7. #80931 | C2 | semidirect |
| 8. #80303 | C2 | semidirect |
| 9. D3×#456 | C2 | semidirect |
| 10. #80281 | C2 | semidirect |
| 11. #80277 | C2 | semidirect |
| 12. #79895 | C2 | semidirect |
| 13. #79889 | C2 | semidirect |
| 16. #5966 | C22 | semidirect |
| 17. C3×#577 | C22 | semidirect |
| 18. #5838 | C22 | semidirect |
| 19. #5836 | C22 | semidirect |
| 21. #5779 | C22 | semidirect |
| 23. D3×#137 | C22 | semidirect |
| 25. #5775 | C22 | semidirect |
| 29. #5771 | C22 | semidirect |
| 33. #5762 | C22 | semidirect |
| 35. C2×#915 | C22 | semidirect |
| 36. #5753 | C22 | semidirect |
| 37. #5750 | C22 | semidirect |
| 38. D3×C4⋊Q8 | C22 | semidirect |
| 40. C3×#492 | C22 | semidirect |
| 41. C3×#471 | C22 | semidirect |
| 42. C3×#456 | C22 | semidirect |
| 43. C3×#453 | C22 | semidirect |
| 44. C3×#443 | C22 | semidirect |
| 45. #5246 | C22 | semidirect |
| 46. #5242 | C22 | semidirect |
| 47. #5205 | C22 | semidirect |
| 48. #5204 | C22 | semidirect |
| 49. #5201 | C22 | semidirect |
| 50. #5200 | C22 | semidirect |
| 51. #5197 | C22 | semidirect |
| 52. #5177 | C22 | semidirect |
| 53. #5167 | C22 | semidirect |
| 54. #5145 | C22 | semidirect |
| 55. #5143 | C22 | semidirect |
| 56. #5095 | C22 | semidirect |
| 57. #5092 | C22 | semidirect |
| 58. #5077 | C22 | semidirect |
| 59. #5076 | C22 | semidirect |
| 60. #4896 | C22 | semidirect |
| 61. #4894 | C22 | semidirect |
| 62. #4893 | C22 | semidirect |
| 63. #4826 | C22 | semidirect |
| 64. #4826 | C22 | semidirect |
| 65. #4824 | C22 | semidirect |
| 66. D3×#104 | C22 | semidirect |
| 67. #4755 | C22 | semidirect |
| 68. #4752 | C22 | semidirect |
| 69. D3×#101 | C22 | semidirect |
| 70. #4748 | C22 | semidirect |
| 71. #4746 | C22 | semidirect |
| 72. #4745 | C22 | semidirect |
| 73. #4700 | C22 | semidirect |
| 74. #4699 | C22 | semidirect |
| 75. C4×ΓL(1,𝔽25) | C22 | semidirect |
| 81. #3291 | D3 | semidirect |
| 143. #918 | D4 | semidirect |
| 161. #915 | D4 | semidirect |
| 163. #914 | D4 | semidirect |
| 172. #911 | D4 | semidirect |
| 223. #577 | C2×D3 | semidirect |
| 239. #492 | C2×D3 | semidirect |
| 247. #471 | C2×D3 | semidirect |
| 254. #456 | C2×D3 | semidirect |
| 259. #453 | C2×D3 | semidirect |
| 265. #443 | C2×D3 | semidirect |
| 812. C3 | #61111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87208 | 2 |
| C3×#3291 | 2 |
| #84013 | 2 |
| #81774 | 2 |
| #81762 | 2 |
| #80933 | 2 |
| #80931 | 2 |
| #80303 | 2 |
| D3×#456 | 2 |
| #80281 | 2 |
| #80277 | 2 |
| #79895 | 2 |
| #79889 | 2 |
| #61111 | 3 |