Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1336 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 | #87187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #83914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #79180 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #78690 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #78553 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#1976 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #70664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70413 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #70406 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #70043 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #69897 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #24285 | — | 3 | 1 | no | maximal, Sylow |
| 13 | #5964 | C22 | 1 | 2 | yes | — |
| 14 | C2×C3×#135 | C22 | 1 | 1 | yes | characteristic |
| 15 | #5828 | C22 | 1 | 2 | yes | complemented |
| 16 | #5822 | C22 | 1 | 2 | yes | — |
| 17 | #5771 | — | 2 | 1 | no | — |
| 18 | #5770 | — | 2 | 2 | no | — |
| 19 | #5769 | — | 2 | 1 | no | — |
| 20 | #5768 | — | 2 | 2 | no | — |
| 21 | D3×#135 | — | 2 | 2 | no | — |
| 22 | #5766 | — | 2 | 1 | no | — |
| 23 | #5762 | — | 2 | 2 | no | — |
| 24 | #5757 | — | 2 | 1 | no | — |
| 25 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#901 | C22 | 1 | 1 | yes | characteristic |
| 27 | C22×D3×C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #5524 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5524 | C22 | 1 | 2 | yes | complemented |
| 30 | C3×#427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C3×#421 | C22 | 1 | 2 | yes | complemented |
| 32 | C3×#410 | C22 | 1 | 2 | yes | complemented |
| 33 | C3×#405 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #5233 | C22 | 1 | 2 | yes | complemented |
| 35 | #5188 | — | 2 | 1 | no | — |
| 36 | #5171 | — | 2 | 2 | no | — |
| 37 | #5157 | — | 2 | 1 | no | — |
| 38 | #5139 | C22 | 1 | 2 | yes | complemented |
| 39 | #5129 | C22 | 1 | 1 | yes | characteristic |
| 40 | #5126 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5106 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #5006 | C22 | 1 | 2 | yes | — |
| 43 | #5006 | C22 | 1 | 2 | yes | complemented |
| 44 | #5002 | C22 | 1 | 2 | yes | complemented |
| 45 | #4999 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #4887 | — | 2 | 1 | no | — |
| 47 | #4883 | — | 2 | 1 | no | — |
| 48 | #4864 | — | 2 | 2 | no | — |
| 49 | #4742 | — | 2 | 4 | no | — |
| 50 | #4741 | — | 2 | 4 | no | — |
| 51 | #4706 | — | 2 | 2 | no | — |
| 52 | C8×D12 | — | 2 | 2 | no | — |
| 53 | #4531 | C22 | 1 | 2 | yes | complemented |
| 54 | #3584 | — | 3 | 1 | no | — |
| 55 | #3050 | — | 3 | 1 | no | — |
| 56 | #3050 | — | 3 | 1 | no | — |
| 57 | #3025 | — | 3 | 2 | no | — |
| 58 | #2929 | — | 3 | 1 | no | — |
| 59 | #2053 | — | 3 | 2 | no | — |
| 60 | #2010 | — | 3 | 2 | no | — |
| 61 | #1976 | — | 3 | 1 | no | — |
| 62 | #1976 | D3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #1812 | — | 3 | 1 | no | — |
| 64 | #1794 | — | 3 | 2 | no | — |
| 65 | C2×C3×#41 | C23 | 1 | 2 | yes | — |
| 66 | #1010 | — | 2 | 2 | no | — |
| 67 | #1010 | — | 2 | 2 | no | — |
| 68 | #1009 | — | 2 | 2 | no | — |
| 69 | #1009 | — | 2 | 2 | no | — |
| 70 | D3×#41 | — | 2 | 4 | no | — |
| 71 | D3×#41 | — | 4 | 2 | no | — |
| 72 | #1007 | — | 2 | 2 | no | — |
| 73 | #1004 | — | 2 | 2 | no | — |
| 74 | #1004 | — | 2 | 4 | no | — |
| 75 | C2×#235 | — | 4 | 2 | no | — |
| 76 | C2×#235 | C23 | 1 | 2 | yes | — |
| 77 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 78 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 79 | C3×#135 | — | 2 | 1 | no | — |
| 80 | C3×#135 | — | 2 | 1 | no | — |
| 81 | C3×#135 | — | 2 | 1 | no | — |
| 82 | C3×#135 | — | 2 | 1 | no | — |
| 83 | C2×C3×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2×C3×SD16 | D4 | 1 | 2 | yes | complemented |
| 85 | C2×C3×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 87 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 88 | C3×#117 | C23 | 1 | 2 | yes | — |
| 89 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 90 | #951 | — | 2 | 2 | no | — |
| 91 | #950 | — | 2 | 4 | no | — |
| 92 | #949 | — | 2 | 2 | no | — |
| 93 | #946 | — | 2 | 2 | no | — |
| 94 | #942 | — | 2 | 2 | no | — |
| 95 | #938 | — | 2 | 2 | no | — |
| 96 | #937 | — | 2 | 2 | no | — |
| 97 | #935 | — | 2 | 2 | no | — |
| 98 | #932 | — | 2 | 2 | no | — |
| 99 | C4×#67 | — | 4 | 2 | no | — |
| 100 | #926 | C23 | 1 | 2 | yes | — |
| 101 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 103 | #919 | — | 2 | 2 | no | — |
| 104 | #918 | — | 2 | 4 | no | — |
| 105 | D3×Q16 | — | 2 | 2 | no | — |
| 106 | #916 | — | 2 | 4 | no | — |
| 107 | #915 | — | 2 | 4 | no | — |
| 108 | #914 | — | 2 | 4 | no | — |
| 109 | D3×SD16 | — | 2 | 4 | no | — |
| 110 | #912 | — | 2 | 2 | no | — |
| 111 | #911 | — | 2 | 4 | no | — |
| 112 | D3×D8 | — | 2 | 2 | no | — |
| 113 | C2×Dic12 | D4 | 1 | 1 | yes | characteristic, complemented |
| 114 | #904 | — | 2 | 1 | no | — |
| 115 | #904 | — | 2 | 1 | no | — |
| 116 | #904 | — | 2 | 1 | no | — |
| 117 | #904 | — | 2 | 1 | no | — |
| 118 | C2×D24 | D4 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×#204 | D4 | 1 | 2 | yes | complemented |
| 120 | #901 | — | 2 | 1 | no | — |
| 121 | #901 | — | 2 | 1 | no | — |
| 122 | #901 | — | 2 | 1 | no | — |
| 123 | #901 | — | 2 | 1 | no | — |
| 124 | C2×ΓL(1,𝔽25) | D4 | 1 | 2 | yes | complemented |
| 125 | C2×D3×C8 | — | 2 | 1 | no | — |
| 126 | C2×D3×C8 | — | 2 | 1 | no | — |
| 127 | C2×D3×C8 | — | 2 | 1 | no | — |
| 128 | C2×D3×C8 | — | 2 | 1 | no | — |
| 129 | C2×D3×C8 | — | 2 | 1 | no | — |
| 130 | C2×D3×C8 | — | 2 | 1 | no | — |
| 131 | C2×D3×C8 | D4 | 1 | 2 | yes | complemented |
| 132 | #897 | — | 2 | 1 | no | — |
| 133 | #897 | — | 2 | 2 | no | — |
| 134 | #895 | — | 2 | 1 | no | — |
| 135 | #895 | — | 2 | 2 | no | — |
| 136 | #886 | — | 2 | 2 | no | — |
| 137 | #886 | D4 | 1 | 2 | yes | — |
| 138 | #882 | — | 2 | 2 | no | — |
| 139 | #882 | D4 | 1 | 2 | yes | — |
| 140 | C4×D12 | — | 2 | 2 | no | — |
| 141 | C4×D12 | — | 4 | 2 | no | — |
| 142 | C3×#107 | — | 2 | 1 | no | — |
| 143 | C3×#106 | — | 2 | 1 | no | — |
| 144 | C3×#104 | — | 4 | 2 | no | — |
| 145 | C3×#99 | — | 2 | 4 | no | — |
| 146 | C3×#97 | — | 2 | 1 | no | — |
| 147 | C3×C4×C8 | — | 2 | 1 | no | — |
| 148 | #835 | — | 2 | 2 | no | — |
| 149 | #832 | — | 2 | 2 | no | — |
| 150 | #825 | — | 4 | 2 | no | — |
| 151 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 152 | (C2×D3)⋊C8 | — | 2 | 2 | no | — |
| 153 | #818 | — | 2 | 1 | no | — |
| 154 | #817 | — | 2 | 1 | no | — |
| 155 | #810 | — | 2 | 2 | no | — |
| 156 | #809 | — | 2 | 2 | no | — |
| 157 | #806 | — | 2 | 4 | no | — |
| 158 | #806 | — | 2 | 4 | no | — |
| 159 | C4⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 160 | #585 | — | 3 | 2 | no | — |
| 161 | #578 | — | 6 | 1 | no | — |
| 162 | #578 | — | 6 | 1 | no | — |
| 163 | #577 | — | 6 | 2 | no | — |
| 164 | #577 | — | 6 | 2 | no | — |
| 165 | #576 | — | 6 | 1 | no | — |
| 166 | #576 | — | 6 | 1 | no | — |
| 167 | #575 | — | 3 | 2 | no | — |
| 168 | #575 | — | 6 | 2 | no | — |
| 169 | C2×#135 | — | 3 | 1 | no | — |
| 170 | C2×#135 | — | 6 | 2 | no | — |
| 171 | C2×#135 | C2×D3 | 1 | 1 | yes | characteristic |
| 172 | C2×#131 | — | 3 | 1 | no | — |
| 173 | C23×C8 | — | 3 | 1 | no | — |
| 174 | #525 | — | 3 | 2 | no | — |
| 175 | #525 | — | 3 | 1 | no | — |
| 176 | #525 | — | 3 | 2 | no | — |
| 177 | #467 | — | 6 | 1 | no | — |
| 178 | #467 | — | 6 | 1 | no | — |
| 179 | #466 | — | 6 | 1 | no | — |
| 180 | #466 | — | 6 | 1 | no | — |
| 181 | #465 | — | 6 | 2 | no | — |
| 182 | #465 | — | 6 | 2 | no | — |
| 183 | #458 | — | 6 | 4 | no | — |
| 184 | B(4,𝔽2) | — | 6 | 4 | no | — |
| 185 | #435 | — | 6 | 2 | no | — |
| 186 | C8×D4 | — | 6 | 2 | no | — |
| 187 | #427 | — | 3 | 1 | no | — |
| 188 | #427 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 189 | #424 | — | 3 | 1 | no | — |
| 190 | #421 | — | 3 | 2 | no | — |
| 191 | #421 | C2×D3 | 1 | 2 | yes | complemented |
| 192 | #416 | — | 3 | 2 | no | — |
| 193 | #416 | — | 3 | 2 | no | — |
| 194 | #410 | — | 3 | 2 | no | — |
| 195 | #410 | — | 3 | 2 | no | — |
| 196 | #410 | C2×D3 | 1 | 2 | yes | complemented |
| 197 | #408 | — | 3 | 1 | no | — |
| 198 | #407 | — | 3 | 1 | no | — |
| 199 | #405 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 200 | H(3,ℤ/4) | — | 3 | 2 | no | — |
| 201 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C3×#41 | — | 2 | 2 | no | — |
| 203 | C3×#41 | — | 2 | 2 | no | — |
| 204 | C3×#41 | — | 2 | 2 | no | — |
| 205 | C3×#41 | — | 2 | 2 | no | — |
| 206 | C2×C3×Q8 | C2×D4 | 1 | 2 | yes | — |
| 207 | C2×C3×D4 | — | 2 | 2 | no | — |
| 208 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 209 | C22×C3×C4 | — | 2 | 2 | no | — |
| 210 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 211 | C2×#67 | — | 2 | 2 | no | — |
| 212 | C2×#67 | — | 4 | 4 | no | — |
| 213 | C2×#67 | — | 4 | 2 | no | — |
| 214 | C2×#67 | C2×D4 | 1 | 2 | yes | — |
| 215 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | #239 | — | 2 | 4 | no | — |
| 217 | #239 | — | 4 | 2 | no | — |
| 218 | D3×Q8 | — | 2 | 4 | no | — |
| 219 | D3×Q8 | — | 4 | 2 | no | — |
| 220 | #237 | — | 2 | 4 | no | — |
| 221 | #237 | — | 4 | 2 | no | — |
| 222 | #237 | — | 4 | 4 | no | — |
| 223 | #237 | — | 4 | 4 | no | — |
| 224 | D3×D4 | — | 2 | 4 | no | — |
| 225 | D3×D4 | — | 4 | 2 | no | — |
| 226 | D3×D4 | — | 4 | 4 | no | — |
| 227 | D3×D4 | — | 4 | 4 | no | — |
| 228 | #235 | — | 2 | 1 | no | — |
| 229 | #235 | — | 2 | 1 | no | — |
| 230 | #235 | — | 2 | 1 | no | — |
| 231 | #235 | — | 2 | 1 | no | — |
| 232 | #235 | — | 2 | 2 | no | — |
| 233 | #235 | — | 2 | 2 | no | — |
| 234 | #235 | — | 2 | 2 | no | — |
| 235 | #235 | — | 2 | 2 | no | — |
| 236 | #235 | — | 4 | 2 | no | — |
| 237 | #235 | — | 4 | 2 | no | — |
| 238 | #235 | — | 4 | 4 | no | — |
| 239 | #235 | — | 4 | 4 | no | — |
| 240 | C2×D12 | — | 2 | 2 | no | — |
| 241 | C2×D12 | — | 4 | 2 | no | — |
| 242 | C2×D12 | — | 4 | 2 | no | — |
| 243 | C2×D12 | C2×D4 | 1 | 2 | yes | — |
| 244 | C2×D12 | #41 | 1 | 1 | yes | characteristic |
| 245 | C2×C4×D3 | — | 2 | 1 | no | — |
| 246 | C2×C4×D3 | — | 2 | 1 | no | — |
| 247 | C2×C4×D3 | — | 2 | 1 | no | — |
| 248 | C2×C4×D3 | — | 2 | 1 | no | — |
| 249 | C2×C4×D3 | — | 2 | 1 | no | — |
| 250 | C2×C4×D3 | — | 2 | 2 | no | — |
| 251 | C2×C4×D3 | — | 2 | 1 | no | — |
| 252 | C2×C4×D3 | — | 4 | 4 | no | — |
| 253 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 254 | C2×Dic6 | — | 4 | 2 | no | — |
| 255 | C2×Dic6 | C2×D4 | 1 | 2 | yes | — |
| 256 | C2×Dic6 | #41 | 1 | 1 | yes | characteristic |
| 257 | C3×Q16 | — | 2 | 1 | no | — |
| 258 | C3×Q16 | — | 2 | 1 | no | — |
| 259 | C3×SD16 | — | 2 | 2 | no | — |
| 260 | C3×SD16 | — | 2 | 2 | no | — |
| 261 | C3×D8 | — | 2 | 1 | no | — |
| 262 | C3×D8 | — | 2 | 1 | no | — |
| 263 | C3×M16 | — | 2 | 1 | no | — |
| 264 | C3×M16 | — | 2 | 1 | no | — |
| 265 | C2×C3×C8 | — | 2 | 1 | no | — |
| 266 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C3×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 273 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 274 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 275 | C3×C22⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 276 | C3×C42 | — | 2 | 1 | no | — |
| 277 | C3×C42 | — | 2 | 2 | no | — |
| 278 | #217 | — | 2 | 2 | no | — |
| 279 | #217 | — | 4 | 2 | no | — |
| 280 | #216 | — | 2 | 4 | no | — |
| 281 | #215 | — | 2 | 4 | no | — |
| 282 | #214 | — | 2 | 4 | no | — |
| 283 | #213 | — | 2 | 4 | no | — |
| 284 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 285 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 286 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 287 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 288 | (C2×D3)⋊C4 | — | 4 | 2 | no | — |
| 289 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 290 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 291 | C4⋊Dic3 | — | 4 | 2 | no | — |
| 292 | Dic3⋊C4 | — | 4 | 2 | no | — |
| 293 | C4×Dic3 | — | 2 | 2 | no | — |
| 294 | #208 | — | 2 | 1 | no | — |
| 295 | #208 | — | 2 | 1 | no | — |
| 296 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 297 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 298 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 299 | C2×C3⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 300 | Dic12 | — | 2 | 1 | no | — |
| 301 | Dic12 | — | 2 | 1 | no | — |
| 302 | D24 | — | 2 | 1 | no | — |
| 303 | D24 | — | 2 | 1 | no | — |
| 304 | #204 | — | 2 | 2 | no | — |
| 305 | #204 | — | 2 | 2 | no | — |
| 306 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 307 | ΓL(1,𝔽25) | — | 2 | 2 | no | — |
| 308 | D3×C8 | — | 2 | 2 | no | — |
| 309 | D3×C8 | — | 2 | 2 | no | — |
| 310 | D3×C8 | — | 4 | 1 | no | — |
| 311 | D3×C8 | — | 4 | 1 | no | — |
| 312 | D3×C8 | — | 4 | 1 | no | — |
| 313 | D3×C8 | — | 4 | 1 | no | — |
| 314 | 2−1+4 | — | 6 | 2 | no | — |
| 315 | 2−1+4 | — | 6 | 2 | no | — |
| 316 | 2−1+4 | — | 6 | 2 | no | — |
| 317 | H(5,𝔽2) | — | 6 | 4 | no | — |
| 318 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 319 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 320 | H(5,𝔽2) | — | 6 | 2 | no | — |
| 321 | C2×#41 | — | 3 | 1 | no | — |
| 322 | C2×#41 | — | 3 | 2 | no | — |
| 323 | C2×#41 | — | 6 | 4 | no | — |
| 324 | C2×#41 | — | 12 | 2 | no | — |
| 325 | C2×#41 | — | 12 | 2 | no | — |
| 326 | C2×#41 | C22×D3 | 1 | 2 | yes | — |
| 327 | C23×C4 | — | 3 | 1 | no | — |
| 328 | #137 | — | 6 | 4 | no | — |
| 329 | #137 | — | 6 | 4 | no | — |
| 330 | #137 | — | 6 | 2 | no | — |
| 331 | #137 | — | 6 | 2 | no | — |
| 332 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 333 | AGL(1,ℤ/8) | — | 6 | 4 | no | — |
| 334 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 335 | AGL(1,ℤ/8) | — | 6 | 2 | no | — |
| 336 | #135 | — | 2 | 1 | no | — |
| 337 | #135 | — | 2 | 1 | no | — |
| 338 | #135 | — | 2 | 1 | no | — |
| 339 | #135 | — | 2 | 1 | no | — |
| 340 | #135 | — | 6 | 4 | no | — |
| 341 | #135 | — | 6 | 2 | no | — |
| 342 | #135 | — | 6 | 4 | no | — |
| 343 | #135 | — | 6 | 2 | no | — |
| 344 | #135 | — | 6 | 1 | no | — |
| 345 | #135 | — | 6 | 1 | no | — |
| 346 | #135 | — | 6 | 1 | no | — |
| 347 | #135 | — | 6 | 1 | no | — |
| 348 | C2×Q16 | — | 3 | 1 | no | — |
| 349 | C2×Q16 | — | 6 | 2 | no | — |
| 350 | C2×Q16 | D12 | 1 | 1 | yes | characteristic, complemented |
| 351 | C2×SD16 | — | 3 | 2 | no | — |
| 352 | C2×SD16 | — | 6 | 4 | no | — |
| 353 | C2×SD16 | D12 | 1 | 2 | yes | complemented |
| 354 | C2×D8 | — | 3 | 1 | no | — |
| 355 | C2×D8 | — | 6 | 2 | no | — |
| 356 | C2×D8 | D12 | 1 | 1 | yes | characteristic, complemented |
| 357 | #131 | — | 6 | 1 | no | — |
| 358 | #131 | — | 6 | 1 | no | — |
| 359 | #131 | — | 6 | 1 | no | — |
| 360 | #131 | — | 6 | 1 | no | — |
| 361 | C2×M16 | — | 3 | 1 | no | — |
| 362 | C2×M16 | — | 3 | 2 | no | — |
| 363 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 364 | C22×C8 | — | 3 | 2 | no | — |
| 365 | C22×C8 | — | 3 | 1 | no | — |
| 366 | C22×C8 | — | 6 | 1 | no | — |
| 367 | C22×C8 | — | 6 | 1 | no | — |
| 368 | C22×C8 | — | 6 | 1 | no | — |
| 369 | C22×C8 | — | 6 | 1 | no | — |
| 370 | C22×C8 | — | 6 | 1 | no | — |
| 371 | C22×C8 | — | 6 | 1 | no | — |
| 372 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 373 | #123 | — | 3 | 2 | no | — |
| 374 | #123 | — | 6 | 2 | no | — |
| 375 | #123 | — | 6 | 2 | no | — |
| 376 | C22⋊Q8 | — | 6 | 1 | no | — |
| 377 | C22⋊Q8 | — | 6 | 2 | no | — |
| 378 | C22⋊Q8 | — | 6 | 2 | no | — |
| 379 | #121 | — | 6 | 1 | no | — |
| 380 | #121 | — | 6 | 2 | no | — |
| 381 | #121 | — | 6 | 2 | no | — |
| 382 | #120 | — | 3 | 2 | no | — |
| 383 | #120 | — | 6 | 2 | no | — |
| 384 | #120 | — | 6 | 2 | no | — |
| 385 | C4×D4 | — | 6 | 2 | no | — |
| 386 | C4×D4 | — | 12 | 2 | no | — |
| 387 | C4×D4 | — | 12 | 2 | no | — |
| 388 | #117 | — | 3 | 2 | no | — |
| 389 | #117 | C22×D3 | 1 | 2 | yes | — |
| 390 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 391 | #107 | — | 2 | 1 | no | — |
| 392 | #107 | — | 6 | 1 | no | — |
| 393 | #106 | — | 2 | 1 | no | — |
| 394 | #106 | — | 6 | 1 | no | — |
| 395 | C4⋊C8 | — | 6 | 2 | no | — |
| 396 | #104 | — | 4 | 2 | no | — |
| 397 | #104 | — | 12 | 2 | no | — |
| 398 | #103 | — | 6 | 2 | no | — |
| 399 | #103 | — | 6 | 2 | no | — |
| 400 | #102 | — | 6 | 2 | no | — |
| 401 | #102 | — | 6 | 2 | no | — |
| 402 | #99 | — | 2 | 4 | no | — |
| 403 | #99 | — | 6 | 4 | no | — |
| 404 | #99 | — | 6 | 4 | no | — |
| 405 | C22⋊C8 | — | 6 | 2 | no | — |
| 406 | C22⋊C8 | — | 6 | 2 | no | — |
| 407 | #97 | — | 2 | 1 | no | — |
| 408 | C4×C8 | — | 2 | 1 | no | — |
| 409 | C23×C3 | — | 2 | 2 | no | — |
| 410 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 411 | C22×D3 | — | 2 | 1 | no | — |
| 412 | C22×D3 | — | 2 | 1 | no | — |
| 413 | C22×D3 | — | 2 | 1 | no | — |
| 414 | C22×D3 | — | 2 | 2 | no | — |
| 415 | C22×D3 | — | 4 | 2 | no | — |
| 416 | C22×D3 | — | 4 | 4 | no | — |
| 417 | C22×D3 | #121 | 1 | 2 | yes | — |
| 418 | C3×Q8 | — | 2 | 2 | no | — |
| 419 | C3×Q8 | — | 2 | 2 | no | — |
| 420 | C3×D4 | — | 2 | 2 | no | — |
| 421 | C3×D4 | — | 2 | 2 | no | — |
| 422 | C3×D4 | — | 4 | 2 | no | — |
| 423 | C3×D4 | — | 4 | 2 | no | — |
| 424 | C2×C3×C4 | — | 2 | 2 | no | — |
| 425 | C2×C3×C4 | — | 2 | 2 | no | — |
| 426 | C2×C3×C4 | — | 4 | 2 | no | — |
| 427 | C2×C3×C4 | — | 4 | 2 | no | — |
| 428 | C2×C3×C4 | — | 4 | 2 | no | — |
| 429 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 431 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 432 | C2×C3×C4 | C2×#41 | 1 | 1 | yes | characteristic |
| 433 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 434 | C2×C3×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 435 | #67 | — | 2 | 2 | no | — |
| 436 | #67 | — | 2 | 2 | no | — |
| 437 | #67 | — | 4 | 4 | no | — |
| 438 | #67 | — | 4 | 4 | no | — |
| 439 | #67 | — | 4 | 2 | no | — |
| 440 | #67 | — | 4 | 2 | no | — |
| 441 | #67 | — | 8 | 4 | no | — |
| 442 | C2×Dic3 | — | 2 | 1 | no | — |
| 443 | C2×Dic3 | — | 2 | 1 | no | — |
| 444 | C2×Dic3 | — | 2 | 1 | no | — |
| 445 | C2×Dic3 | — | 2 | 2 | no | — |
| 446 | C2×Dic3 | — | 4 | 4 | no | — |
| 447 | C2×Dic3 | — | 4 | 2 | no | — |
| 448 | C2×Dic3 | #121 | 1 | 2 | yes | — |
| 449 | D12 | — | 2 | 2 | no | — |
| 450 | D12 | — | 2 | 1 | no | — |
| 451 | D12 | — | 2 | 1 | no | — |
| 452 | D12 | — | 2 | 2 | no | — |
| 453 | D12 | — | 4 | 4 | no | — |
| 454 | D12 | — | 4 | 4 | no | — |
| 455 | D12 | — | 8 | 4 | no | — |
| 456 | C4×D3 | — | 2 | 2 | no | — |
| 457 | C4×D3 | — | 2 | 2 | no | — |
| 458 | C4×D3 | — | 4 | 4 | no | — |
| 459 | C4×D3 | — | 4 | 4 | no | — |
| 460 | C4×D3 | — | 4 | 1 | no | — |
| 461 | C4×D3 | — | 4 | 1 | no | — |
| 462 | C4×D3 | — | 4 | 2 | no | — |
| 463 | C4×D3 | — | 4 | 1 | no | — |
| 464 | C4×D3 | — | 4 | 1 | no | — |
| 465 | C4×D3 | — | 4 | 2 | no | — |
| 466 | Dic6 | — | 2 | 1 | no | — |
| 467 | Dic6 | — | 2 | 1 | no | — |
| 468 | Dic6 | — | 2 | 2 | no | — |
| 469 | Dic6 | — | 2 | 2 | no | — |
| 470 | Dic6 | — | 4 | 4 | no | — |
| 471 | C3×C8 | — | 4 | 1 | no | — |
| 472 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 473 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 474 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 475 | C3×C8 | #120 | 1 | 1 | yes | characteristic |
| 476 | C3⋊C8 | — | 2 | 2 | no | — |
| 477 | C3⋊C8 | — | 4 | 1 | no | — |
| 478 | C24 | — | 3 | 1 | no | — |
| 479 | #41 | — | 2 | 2 | no | — |
| 480 | #41 | — | 2 | 2 | no | — |
| 481 | #41 | — | 2 | 2 | no | — |
| 482 | #41 | — | 2 | 2 | no | — |
| 483 | #41 | — | 6 | 1 | no | — |
| 484 | #41 | — | 6 | 1 | no | — |
| 485 | #41 | — | 6 | 1 | no | — |
| 486 | #41 | — | 6 | 1 | no | — |
| 487 | #41 | — | 6 | 4 | no | — |
| 488 | #41 | — | 6 | 4 | no | — |
| 489 | #41 | — | 6 | 2 | no | — |
| 490 | #41 | — | 6 | 2 | no | — |
| 491 | #41 | — | 6 | 2 | no | — |
| 492 | #41 | — | 6 | 2 | no | — |
| 493 | #41 | — | 12 | 4 | no | — |
| 494 | #41 | — | 12 | 4 | no | — |
| 495 | #41 | — | 12 | 4 | no | — |
| 496 | #41 | — | 12 | 2 | no | — |
| 497 | #41 | — | 12 | 2 | no | — |
| 498 | #41 | — | 12 | 4 | no | — |
| 499 | #41 | — | 12 | 2 | no | — |
| 500 | #41 | — | 12 | 2 | no | — |
| 501 | C2×Q8 | — | 3 | 1 | no | — |
| 502 | C2×Q8 | — | 3 | 2 | no | — |
| 503 | C2×Q8 | — | 6 | 4 | no | — |
| 504 | C2×Q8 | — | 12 | 2 | no | — |
| 505 | C2×Q8 | — | 12 | 2 | no | — |
| 506 | C2×Q8 | C2×D12 | 1 | 2 | yes | — |
| 507 | C2×D4 | — | 2 | 2 | no | — |
| 508 | C2×D4 | — | 3 | 2 | no | — |
| 509 | C2×D4 | — | 3 | 2 | no | — |
| 510 | C2×D4 | — | 3 | 1 | no | — |
| 511 | C2×D4 | — | 6 | 2 | no | — |
| 512 | C2×D4 | — | 6 | 4 | no | — |
| 513 | C2×D4 | — | 6 | 2 | no | — |
| 514 | C2×D4 | — | 12 | 2 | no | — |
| 515 | C2×D4 | — | 12 | 2 | no | — |
| 516 | C2×D4 | — | 12 | 2 | no | — |
| 517 | C2×D4 | — | 12 | 4 | no | — |
| 518 | C2×D4 | — | 12 | 4 | no | — |
| 519 | C2×D4 | — | 12 | 4 | no | — |
| 520 | C2×D4 | — | 12 | 2 | no | — |
| 521 | C2×D4 | C2×D12 | 1 | 2 | yes | — |
| 522 | C22×C4 | — | 2 | 2 | no | — |
| 523 | C22×C4 | — | 3 | 2 | no | — |
| 524 | C22×C4 | — | 3 | 1 | no | — |
| 525 | C22×C4 | — | 6 | 1 | no | — |
| 526 | C22×C4 | — | 6 | 1 | no | — |
| 527 | C22×C4 | — | 6 | 1 | no | — |
| 528 | C22×C4 | — | 6 | 1 | no | — |
| 529 | C22×C4 | — | 6 | 2 | no | — |
| 530 | C22×C4 | — | 6 | 1 | no | — |
| 531 | C22×C4 | — | 6 | 1 | no | — |
| 532 | C22×C4 | — | 12 | 4 | no | — |
| 533 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 534 | Q16 | — | 2 | 1 | no | — |
| 535 | Q16 | — | 2 | 1 | no | — |
| 536 | Q16 | — | 6 | 4 | no | — |
| 537 | Q16 | — | 6 | 1 | no | — |
| 538 | Q16 | — | 6 | 1 | no | — |
| 539 | SD16 | — | 2 | 2 | no | — |
| 540 | SD16 | — | 2 | 2 | no | — |
| 541 | SD16 | — | 6 | 4 | no | — |
| 542 | SD16 | — | 6 | 4 | no | — |
| 543 | SD16 | — | 6 | 2 | no | — |
| 544 | SD16 | — | 6 | 2 | no | — |
| 545 | D8 | — | 2 | 1 | no | — |
| 546 | D8 | — | 2 | 1 | no | — |
| 547 | D8 | — | 6 | 4 | no | — |
| 548 | D8 | — | 6 | 1 | no | — |
| 549 | D8 | — | 6 | 1 | no | — |
| 550 | M16 | — | 2 | 1 | no | — |
| 551 | M16 | — | 2 | 1 | no | — |
| 552 | M16 | — | 6 | 1 | no | — |
| 553 | M16 | — | 6 | 1 | no | — |
| 554 | M16 | — | 6 | 2 | no | — |
| 555 | M16 | — | 6 | 2 | no | — |
| 556 | C2×C8 | — | 2 | 1 | no | — |
| 557 | C2×C8 | — | 3 | 2 | no | — |
| 558 | C2×C8 | — | 6 | 2 | no | — |
| 559 | C2×C8 | — | 6 | 2 | no | — |
| 560 | C2×C8 | — | 6 | 1 | no | — |
| 561 | C2×C8 | — | 6 | 1 | no | — |
| 562 | C2×C8 | — | 6 | 1 | no | — |
| 563 | C2×C8 | — | 12 | 1 | no | — |
| 564 | C2×C8 | — | 12 | 1 | no | — |
| 565 | C2×C8 | — | 12 | 1 | no | — |
| 566 | C2×C8 | — | 12 | 1 | no | — |
| 567 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 568 | C2×C8 | C2×D12 | 1 | 1 | yes | characteristic |
| 569 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 570 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 571 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 572 | C2×C8 | D3×D4 | 1 | 1 | yes | characteristic |
| 573 | C4⋊C4 | — | 2 | 1 | no | — |
| 574 | C4⋊C4 | — | 2 | 2 | no | — |
| 575 | C4⋊C4 | — | 6 | 2 | no | — |
| 576 | C4⋊C4 | — | 6 | 2 | no | — |
| 577 | C4⋊C4 | — | 12 | 2 | no | — |
| 578 | C4⋊C4 | — | 12 | 2 | no | — |
| 579 | C22⋊C4 | — | 2 | 2 | no | — |
| 580 | C22⋊C4 | — | 6 | 2 | no | — |
| 581 | C22⋊C4 | — | 6 | 2 | no | — |
| 582 | C22⋊C4 | — | 6 | 2 | no | — |
| 583 | C22⋊C4 | — | 12 | 2 | no | — |
| 584 | C22⋊C4 | — | 12 | 2 | no | — |
| 585 | C22⋊C4 | — | 12 | 2 | no | — |
| 586 | C22⋊C4 | — | 12 | 2 | no | — |
| 587 | C22⋊C4 | D3×D4 | 1 | 2 | yes | — |
| 588 | C42 | — | 2 | 1 | no | — |
| 589 | C42 | — | 2 | 2 | no | — |
| 590 | C42 | — | 6 | 2 | no | — |
| 591 | C22×C3 | — | 4 | 1 | no | — |
| 592 | C22×C3 | — | 4 | 2 | no | — |
| 593 | C22×C3 | — | 8 | 2 | no | — |
| 594 | C22×C3 | C2×#121 | 1 | 1 | yes | characteristic |
| 595 | C22×C3 | D42 | 1 | 1 | yes | characteristic |
| 596 | C22×C3 | D42 | 1 | 1 | yes | characteristic |
| 597 | C2×D3 | — | 2 | 2 | no | — |
| 598 | C2×D3 | — | 2 | 2 | no | — |
| 599 | C2×D3 | — | 2 | 2 | no | — |
| 600 | C2×D3 | — | 2 | 2 | no | — |
| 601 | C2×D3 | — | 4 | 1 | no | — |
| 602 | C2×D3 | — | 4 | 1 | no | — |
| 603 | C2×D3 | — | 4 | 1 | no | — |
| 604 | C2×D3 | — | 4 | 1 | no | — |
| 605 | C2×D3 | — | 4 | 2 | no | — |
| 606 | C2×D3 | — | 4 | 2 | no | — |
| 607 | C2×D3 | — | 8 | 2 | no | — |
| 608 | C2×D3 | — | 16 | 4 | no | — |
| 609 | C3×C4 | — | 4 | 2 | no | — |
| 610 | C3×C4 | — | 4 | 2 | no | — |
| 611 | C3×C4 | — | 8 | 2 | no | — |
| 612 | C3×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 613 | C3×C4 | #535 | 1 | 1 | yes | characteristic |
| 614 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 615 | C3×C4 | #546 | 1 | 1 | yes | characteristic |
| 616 | Dic3 | — | 2 | 2 | no | — |
| 617 | Dic3 | — | 4 | 2 | no | — |
| 618 | Dic3 | — | 4 | 1 | no | — |
| 619 | Dic3 | — | 8 | 2 | no | — |
| 620 | C23 | — | 2 | 2 | no | — |
| 621 | C23 | — | 3 | 2 | no | — |
| 622 | C23 | — | 6 | 1 | no | — |
| 623 | C23 | — | 6 | 1 | no | — |
| 624 | C23 | — | 6 | 1 | no | — |
| 625 | C23 | — | 6 | 2 | no | — |
| 626 | C23 | — | 12 | 2 | no | — |
| 627 | C23 | — | 12 | 4 | no | — |
| 628 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 629 | Q8 | — | 2 | 2 | no | — |
| 630 | Q8 | — | 2 | 2 | no | — |
| 631 | Q8 | — | 6 | 1 | no | — |
| 632 | Q8 | — | 6 | 1 | no | — |
| 633 | Q8 | — | 6 | 2 | no | — |
| 634 | Q8 | — | 6 | 2 | no | — |
| 635 | Q8 | — | 12 | 4 | no | — |
| 636 | D4 | — | 2 | 2 | no | — |
| 637 | D4 | — | 2 | 2 | no | — |
| 638 | D4 | — | 4 | 2 | no | — |
| 639 | D4 | — | 4 | 2 | no | — |
| 640 | D4 | — | 6 | 2 | no | — |
| 641 | D4 | — | 6 | 2 | no | — |
| 642 | D4 | — | 6 | 1 | no | — |
| 643 | D4 | — | 6 | 2 | no | — |
| 644 | D4 | — | 6 | 2 | no | — |
| 645 | D4 | — | 6 | 1 | no | — |
| 646 | D4 | — | 12 | 4 | no | — |
| 647 | D4 | — | 12 | 4 | no | — |
| 648 | D4 | — | 12 | 4 | no | — |
| 649 | D4 | — | 12 | 4 | no | — |
| 650 | D4 | — | 12 | 2 | no | — |
| 651 | D4 | — | 12 | 2 | no | — |
| 652 | D4 | — | 24 | 4 | no | — |
| 653 | D4 | — | 24 | 4 | no | — |
| 654 | C2×C4 | — | 2 | 2 | no | — |
| 655 | C2×C4 | — | 2 | 2 | no | — |
| 656 | C2×C4 | — | 3 | 2 | no | — |
| 657 | C2×C4 | — | 4 | 2 | no | — |
| 658 | C2×C4 | — | 4 | 2 | no | — |
| 659 | C2×C4 | — | 4 | 2 | no | — |
| 660 | C2×C4 | — | 6 | 2 | no | — |
| 661 | C2×C4 | — | 6 | 2 | no | — |
| 662 | C2×C4 | — | 6 | 1 | no | — |
| 663 | C2×C4 | — | 6 | 2 | no | — |
| 664 | C2×C4 | — | 6 | 1 | no | — |
| 665 | C2×C4 | — | 6 | 1 | no | — |
| 666 | C2×C4 | — | 12 | 4 | no | — |
| 667 | C2×C4 | — | 12 | 4 | no | — |
| 668 | C2×C4 | — | 12 | 4 | no | — |
| 669 | C2×C4 | — | 12 | 1 | no | — |
| 670 | C2×C4 | — | 12 | 1 | no | — |
| 671 | C2×C4 | — | 12 | 1 | no | — |
| 672 | C2×C4 | — | 12 | 2 | no | — |
| 673 | C2×C4 | — | 12 | 1 | no | — |
| 674 | C2×C4 | — | 12 | 2 | no | — |
| 675 | C2×C4 | — | 12 | 2 | no | — |
| 676 | C2×C4 | C22×D12 | 1 | 1 | yes | characteristic |
| 677 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 678 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 679 | C2×C4 | #1004 | 1 | 1 | yes | characteristic |
| 680 | C2×C4 | D3×#41 | 1 | 1 | yes | characteristic |
| 681 | C2×C4 | #1009 | 1 | 1 | yes | characteristic |
| 682 | C8 | — | 4 | 1 | no | — |
| 683 | C8 | — | 6 | 2 | no | — |
| 684 | C8 | — | 12 | 1 | no | — |
| 685 | C8 | #882 | 1 | 1 | yes | characteristic |
| 686 | C8 | #882 | 1 | 1 | yes | characteristic |
| 687 | C8 | #882 | 1 | 1 | yes | characteristic |
| 688 | C8 | #882 | 1 | 1 | yes | characteristic |
| 689 | C2×C3 | — | 2 | 1 | no | — |
| 690 | C2×C3 | — | 2 | 1 | no | — |
| 691 | C2×C3 | — | 2 | 1 | no | — |
| 692 | C2×C3 | — | 8 | 2 | no | — |
| 693 | C2×C3 | #2408 | 1 | 1 | yes | characteristic |
| 694 | D3 | — | 4 | 2 | no | — |
| 695 | D3 | — | 4 | 2 | no | — |
| 696 | D3 | — | 8 | 2 | no | — |
| 697 | C22 | — | 4 | 1 | no | — |
| 698 | C22 | — | 4 | 2 | no | — |
| 699 | C22 | — | 6 | 2 | no | — |
| 700 | C22 | — | 6 | 2 | no | — |
| 701 | C22 | — | 6 | 2 | no | — |
| 702 | C22 | — | 6 | 2 | no | — |
| 703 | C22 | — | 8 | 2 | no | — |
| 704 | C22 | — | 12 | 2 | no | — |
| 705 | C22 | — | 12 | 1 | no | — |
| 706 | C22 | — | 12 | 1 | no | — |
| 707 | C22 | — | 12 | 1 | no | — |
| 708 | C22 | — | 12 | 1 | no | — |
| 709 | C22 | — | 12 | 2 | no | — |
| 710 | C22 | — | 24 | 2 | no | — |
| 711 | C22 | — | 48 | 4 | no | — |
| 712 | C22 | D4×D12 | 1 | 1 | yes | characteristic |
| 713 | C22 | D3×#121 | 1 | 1 | yes | characteristic |
| 714 | C22 | #5717 | 1 | 1 | yes | characteristic |
| 715 | C4 | — | 4 | 2 | no | — |
| 716 | C4 | — | 4 | 2 | no | — |
| 717 | C4 | — | 6 | 2 | no | — |
| 718 | C4 | — | 8 | 2 | no | — |
| 719 | C4 | — | 12 | 1 | no | — |
| 720 | C4 | — | 12 | 2 | no | — |
| 721 | C4 | — | 24 | 2 | no | — |
| 722 | C4 | C2×#882 | 1 | 1 | yes | characteristic |
| 723 | C4 | #5554 | 1 | 1 | yes | characteristic |
| 724 | C4 | #5607 | 1 | 1 | yes | characteristic |
| 725 | C4 | #5676 | 1 | 1 | yes | characteristic |
| 726 | C3 | #24285 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 727 | C2 | — | 2 | 1 | no | — |
| 728 | C2 | — | 2 | 1 | no | — |
| 729 | C2 | — | 2 | 1 | no | — |
| 730 | C2 | — | 8 | 2 | no | — |
| 731 | C2 | — | 12 | 2 | no | — |
| 732 | C2 | — | 12 | 2 | no | — |
| 733 | C2 | — | 24 | 2 | no | — |
| 734 | C2 | #76436 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | #5607 |
| commutator, cosocle | C22×C3×C4 | C24 |
| Frattini | C22×C4 | C23×D3 |
| Fitting | C3×#1976 | C2 |
| socle | C2×C3 | #2408 |
| hypercenter | #1976 | D3 |
| hypocenter | C3 | #24285 |
| LCS | G ▷ C22×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #1976 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #87187 | C2 | semidirect |
| 2. #83914 | C2 | semidirect |
| 3. #79180 | C2 | semidirect |
| 4. #78690 | C2 | semidirect |
| 5. #78553 | C2 | semidirect |
| 6. C3×#1976 | C2 | semidirect |
| 7. #70664 | C2 | semidirect |
| 8. #70413 | C2 | semidirect |
| 9. #70406 | C2 | semidirect |
| 10. #70043 | C2 | semidirect |
| 11. #69897 | C2 | semidirect |
| 15. #5828 | C22 | semidirect |
| 27. C22×D3×C8 | C22 | semidirect |
| 29. #5524 | C22 | semidirect |
| 30. C3×#427 | C22 | semidirect |
| 31. C3×#421 | C22 | semidirect |
| 32. C3×#410 | C22 | semidirect |
| 33. C3×#405 | C22 | semidirect |
| 34. #5233 | C22 | semidirect |
| 38. #5139 | C22 | semidirect |
| 40. #5126 | C22 | semidirect |
| 41. #5106 | C22 | semidirect |
| 43. #5006 | C22 | semidirect |
| 44. #5002 | C22 | semidirect |
| 45. #4999 | C22 | semidirect |
| 53. #4531 | C22 | semidirect |
| 62. #1976 | D3 | semidirect |
| 83. C2×C3×Q16 | D4 | semidirect |
| 84. C2×C3×SD16 | D4 | semidirect |
| 85. C2×C3×D8 | D4 | semidirect |
| 113. C2×Dic12 | D4 | semidirect |
| 118. C2×D24 | D4 | semidirect |
| 119. C2×#204 | D4 | semidirect |
| 124. C2×ΓL(1,𝔽25) | D4 | semidirect |
| 131. C2×D3×C8 | D4 | semidirect |
| 188. #427 | C2×D3 | semidirect |
| 191. #421 | C2×D3 | semidirect |
| 196. #410 | C2×D3 | semidirect |
| 199. #405 | C2×D3 | semidirect |
| 350. C2×Q16 | D12 | semidirect |
| 353. C2×SD16 | D12 | semidirect |
| 356. C2×D8 | D12 | semidirect |
| 726. C3 | #24285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #87187 | 2 |
| #83914 | 2 |
| #79180 | 2 |
| #78690 | 2 |
| #78553 | 2 |
| C3×#1976 | 2 |
| #70664 | 2 |
| #70413 | 2 |
| #70406 | 2 |
| #70043 | 2 |
| #69897 | 2 |
| #24285 | 3 |