Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2674 conjugacy classes of subgroups.
The subgroup lattice has 1028 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C22×#915 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#5753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #86355 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #86315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#3057 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #83854 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #83795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #83411 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #83390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #80844 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | #80843 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #80688 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #80687 | C2 | 1 | 4 | yes | maximal, complemented |
| 14 | #79181 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #79169 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #78977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 17 | #78958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 18 | #78945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 19 | #78927 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 20 | #61061 | — | 3 | 1 | no | maximal, Sylow |
| 21 | C2×#1010 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#1010 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×D3×Q8 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×#237 | C22 | 1 | 1 | yes | characteristic |
| 25 | C22×C3×SD16 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×C3×#131 | C22 | 1 | 1 | yes | characteristic |
| 27 | C3×#536 | C22 | 1 | 1 | yes | characteristic |
| 28 | C3×#535 | C22 | 1 | 1 | yes | characteristic |
| 29 | #5828 | C22 | 1 | 1 | yes | characteristic |
| 30 | #5816 | C22 | 1 | 1 | yes | characteristic |
| 31 | C22×#216 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#942 | C22 | 1 | 1 | yes | characteristic |
| 33 | #5805 | C22 | 1 | 1 | yes | characteristic |
| 34 | C22×#214 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#932 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#915 | — | 2 | 8 | no | — |
| 37 | C2×#915 | C22 | 1 | 4 | yes | — |
| 38 | C2×#915 | C22 | 1 | 4 | yes | — |
| 39 | #5753 | — | 2 | 8 | no | — |
| 40 | C2×#909 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#909 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 43 | C2×#909 | C22 | 1 | 2 | yes | complemented |
| 44 | C22×Dic12 | C22 | 1 | 1 | yes | characteristic |
| 45 | C22×Dic12 | C22 | 1 | 2 | yes | complemented |
| 46 | C2×#904 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#904 | C22 | 1 | 2 | yes | complemented |
| 48 | C22×ΓL(1,𝔽25) | C22 | 1 | 1 | yes | characteristic |
| 49 | #5727 | — | 2 | 2 | no | — |
| 50 | #5718 | — | 2 | 2 | no | — |
| 51 | #5677 | — | 2 | 2 | no | — |
| 52 | #5677 | — | 2 | 2 | no | — |
| 53 | #5656 | — | 2 | 2 | no | — |
| 54 | #5648 | — | 2 | 2 | no | — |
| 55 | #5633 | C22 | 1 | 4 | yes | complemented |
| 56 | #5632 | C22 | 1 | 4 | yes | complemented |
| 57 | #5599 | C22 | 1 | 4 | yes | — |
| 58 | #5598 | C22 | 1 | 4 | yes | — |
| 59 | #5592 | — | 2 | 2 | no | — |
| 60 | #5586 | — | 2 | 2 | no | — |
| 61 | #5524 | C22 | 1 | 1 | yes | characteristic |
| 62 | #5524 | C22 | 1 | 1 | yes | characteristic |
| 63 | #5516 | C22 | 1 | 1 | yes | characteristic |
| 64 | #5516 | C22 | 1 | 1 | yes | characteristic |
| 65 | C3×#468 | C22 | 1 | 4 | yes | complemented |
| 66 | C3×#465 | C22 | 1 | 4 | yes | complemented |
| 67 | C3×#427 | C22 | 1 | 1 | yes | characteristic |
| 68 | C3×#419 | C22 | 1 | 1 | yes | characteristic |
| 69 | C3×#418 | C22 | 1 | 1 | yes | characteristic |
| 70 | #5234 | C22 | 1 | 1 | yes | characteristic |
| 71 | #5176 | C22 | 1 | 2 | yes | complemented |
| 72 | #5175 | C22 | 1 | 2 | yes | complemented |
| 73 | #5168 | C22 | 1 | 2 | yes | complemented |
| 74 | #5167 | C22 | 1 | 2 | yes | complemented |
| 75 | #5128 | C22 | 1 | 4 | yes | complemented |
| 76 | #5126 | C22 | 1 | 1 | yes | characteristic |
| 77 | #5119 | C22 | 1 | 1 | yes | characteristic |
| 78 | #5111 | C22 | 1 | 4 | yes | complemented |
| 79 | #5101 | C22 | 1 | 1 | yes | characteristic |
| 80 | #5050 | C22 | 1 | 4 | yes | complemented |
| 81 | #5047 | C22 | 1 | 4 | yes | complemented |
| 82 | #5040 | C22 | 1 | 4 | yes | complemented |
| 83 | #5037 | C22 | 1 | 4 | yes | complemented |
| 84 | #5004 | C22 | 1 | 1 | yes | characteristic |
| 85 | #5004 | C22 | 1 | 1 | yes | characteristic |
| 86 | #5002 | C22 | 1 | 1 | yes | characteristic |
| 87 | #5002 | C22 | 1 | 1 | yes | characteristic |
| 88 | #4886 | C22 | 1 | 2 | yes | complemented |
| 89 | #4886 | C22 | 1 | 2 | yes | complemented |
| 90 | #4873 | C22 | 1 | 4 | yes | complemented |
| 91 | #4867 | C22 | 1 | 2 | yes | complemented |
| 92 | #4865 | C22 | 1 | 2 | yes | complemented |
| 93 | #4853 | C22 | 1 | 4 | yes | complemented |
| 94 | #4809 | C22 | 1 | 4 | yes | complemented |
| 95 | #4806 | C22 | 1 | 4 | yes | complemented |
| 96 | #4798 | C22 | 1 | 4 | yes | complemented |
| 97 | #4795 | C22 | 1 | 4 | yes | complemented |
| 98 | #4783 | C22 | 1 | 4 | yes | — |
| 99 | #4781 | C22 | 1 | 4 | yes | — |
| 100 | #4767 | C22 | 1 | 4 | yes | complemented |
| 101 | #4762 | C22 | 1 | 4 | yes | complemented |
| 102 | C2×#578 | — | 3 | 1 | no | — |
| 103 | C22×#137 | — | 3 | 1 | no | — |
| 104 | #3487 | — | 3 | 1 | no | — |
| 105 | #3486 | — | 3 | 1 | no | — |
| 106 | #3278 | — | 3 | 4 | no | — |
| 107 | #3277 | — | 3 | 4 | no | — |
| 108 | #3271 | — | 3 | 4 | no | — |
| 109 | #3270 | — | 3 | 4 | no | — |
| 110 | #3154 | — | 3 | 1 | no | — |
| 111 | #3057 | D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | #3054 | — | 3 | 1 | no | — |
| 113 | #3044 | — | 3 | 1 | no | — |
| 114 | #3043 | — | 3 | 1 | no | — |
| 115 | #3011 | — | 3 | 1 | no | — |
| 116 | #3010 | — | 3 | 1 | no | — |
| 117 | #3005 | — | 3 | 1 | no | — |
| 118 | #3004 | — | 3 | 1 | no | — |
| 119 | #2950 | — | 3 | 1 | no | — |
| 120 | #2930 | — | 3 | 1 | no | — |
| 121 | C2×C3×#41 | C23 | 1 | 1 | yes | characteristic |
| 122 | C22×C3×Q8 | C23 | 1 | 1 | yes | characteristic |
| 123 | C22×C3×D4 | C23 | 1 | 1 | yes | characteristic |
| 124 | C22×#67 | — | 2 | 1 | no | — |
| 125 | C23×Dic3 | — | 2 | 1 | no | — |
| 126 | #1010 | — | 2 | 4 | no | — |
| 127 | #1010 | — | 2 | 4 | no | — |
| 128 | #1010 | — | 4 | 2 | no | — |
| 129 | #1010 | — | 4 | 2 | no | — |
| 130 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 131 | C2×D3×Q8 | — | 2 | 1 | no | — |
| 132 | C2×D3×Q8 | — | 2 | 2 | no | — |
| 133 | C2×D3×Q8 | — | 2 | 4 | no | — |
| 134 | C2×D3×Q8 | — | 4 | 2 | no | — |
| 135 | C2×D3×Q8 | C23 | 1 | 4 | yes | — |
| 136 | C2×#237 | — | 2 | 2 | no | — |
| 137 | C2×#237 | — | 2 | 1 | no | — |
| 138 | C2×#237 | — | 2 | 1 | no | — |
| 139 | C2×#237 | — | 2 | 2 | no | — |
| 140 | C2×#237 | — | 2 | 2 | no | — |
| 141 | C2×#237 | — | 2 | 4 | no | — |
| 142 | C2×#237 | — | 4 | 2 | no | — |
| 143 | C2×#237 | C23 | 1 | 4 | yes | — |
| 144 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 145 | C2×#235 | C23 | 1 | 1 | yes | characteristic |
| 146 | C2×#235 | C23 | 1 | 2 | yes | — |
| 147 | C2×#235 | C23 | 1 | 2 | yes | — |
| 148 | C22×C4×D3 | — | 2 | 1 | no | — |
| 149 | C22×C4×D3 | C23 | 1 | 1 | yes | characteristic |
| 150 | C22×Dic6 | — | 2 | 1 | no | — |
| 151 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 152 | C22×Dic6 | C23 | 1 | 2 | yes | — |
| 153 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 154 | C22×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 155 | C2×C3×SD16 | — | 2 | 4 | no | — |
| 156 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 157 | C2×C3×SD16 | C23 | 1 | 2 | yes | — |
| 158 | C3×#131 | — | 2 | 4 | no | — |
| 159 | C2×C3×M16 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×C3×M16 | C23 | 1 | 2 | yes | — |
| 161 | C22×C3×C8 | C23 | 1 | 2 | yes | — |
| 162 | C22×C3×C8 | C23 | 1 | 1 | yes | characteristic |
| 163 | C3×C4⋊Q8 | — | 2 | 1 | no | — |
| 164 | C3×#127 | — | 2 | 1 | no | — |
| 165 | C3×#124 | — | 2 | 1 | no | — |
| 166 | C3×#124 | — | 2 | 1 | no | — |
| 167 | C3×#123 | — | 2 | 2 | no | — |
| 168 | C3×C22⋊Q8 | C23 | 1 | 4 | yes | — |
| 169 | C3×#121 | C23 | 1 | 4 | yes | — |
| 170 | C3×#120 | — | 2 | 2 | no | — |
| 171 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 172 | C3×#117 | C23 | 1 | 1 | yes | characteristic |
| 173 | #953 | — | 2 | 2 | no | — |
| 174 | #947 | C23 | 1 | 2 | yes | — |
| 175 | #946 | — | 2 | 2 | no | — |
| 176 | #946 | D4 | 1 | 2 | yes | — |
| 177 | #944 | C23 | 1 | 2 | yes | — |
| 178 | C2×#216 | — | 2 | 4 | no | — |
| 179 | C2×#216 | C23 | 1 | 4 | yes | — |
| 180 | C2×#216 | C23 | 1 | 2 | yes | — |
| 181 | #942 | — | 4 | 2 | no | — |
| 182 | C2×#215 | C23 | 1 | 2 | yes | — |
| 183 | #940 | — | 2 | 4 | no | — |
| 184 | #940 | C23 | 1 | 2 | yes | — |
| 185 | #939 | — | 2 | 4 | no | — |
| 186 | #939 | — | 2 | 4 | no | — |
| 187 | #938 | — | 2 | 2 | no | — |
| 188 | #938 | D4 | 1 | 2 | yes | — |
| 189 | #937 | D4 | 1 | 2 | yes | — |
| 190 | #936 | C23 | 1 | 2 | yes | — |
| 191 | #935 | D4 | 1 | 2 | yes | — |
| 192 | D4×Dic3 | — | 2 | 4 | no | — |
| 193 | C2×#214 | — | 2 | 4 | no | — |
| 194 | C2×#214 | C23 | 1 | 4 | yes | — |
| 195 | C2×#214 | C23 | 1 | 2 | yes | — |
| 196 | #932 | — | 4 | 2 | no | — |
| 197 | C2×#213 | C23 | 1 | 2 | yes | — |
| 198 | #929 | — | 2 | 2 | no | — |
| 199 | C4×#67 | C23 | 1 | 4 | yes | — |
| 200 | #926 | C23 | 1 | 1 | yes | characteristic |
| 201 | C2×#208 | C23 | 1 | 1 | yes | characteristic |
| 202 | C22×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 203 | #915 | — | 2 | 16 | no | — |
| 204 | #915 | — | 2 | 16 | no | — |
| 205 | #909 | — | 2 | 4 | no | — |
| 206 | #909 | — | 2 | 4 | no | — |
| 207 | #909 | — | 2 | 8 | no | — |
| 208 | #909 | — | 2 | 8 | no | — |
| 209 | C2×Dic12 | — | 2 | 8 | no | — |
| 210 | C2×Dic12 | D4 | 1 | 8 | yes | complemented |
| 211 | C2×Dic12 | C23 | 1 | 1 | yes | characteristic |
| 212 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 213 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 214 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 215 | C2×Dic12 | C23 | 1 | 2 | yes | — |
| 216 | #904 | — | 2 | 4 | no | — |
| 217 | #904 | — | 2 | 8 | no | — |
| 218 | C2×D24 | C23 | 1 | 1 | yes | characteristic |
| 219 | C2×#204 | C23 | 1 | 1 | yes | characteristic |
| 220 | C2×#204 | C23 | 1 | 1 | yes | characteristic |
| 221 | C2×#204 | C23 | 1 | 2 | yes | — |
| 222 | C2×#204 | C23 | 1 | 2 | yes | — |
| 223 | C2×ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 224 | C2×ΓL(1,𝔽25) | C23 | 1 | 2 | yes | — |
| 225 | C2×ΓL(1,𝔽25) | C23 | 1 | 2 | yes | — |
| 226 | #897 | C23 | 1 | 2 | yes | — |
| 227 | #897 | C23 | 1 | 2 | yes | — |
| 228 | #896 | — | 2 | 4 | no | — |
| 229 | #896 | — | 2 | 4 | no | — |
| 230 | #895 | C23 | 1 | 2 | yes | — |
| 231 | #895 | C23 | 1 | 2 | yes | — |
| 232 | #893 | — | 2 | 4 | no | — |
| 233 | #888 | — | 2 | 4 | no | — |
| 234 | #887 | C23 | 1 | 4 | yes | — |
| 235 | #887 | C23 | 1 | 4 | yes | — |
| 236 | #886 | — | 2 | 1 | no | — |
| 237 | #886 | — | 2 | 1 | no | — |
| 238 | #885 | — | 2 | 4 | no | — |
| 239 | #885 | — | 2 | 4 | no | — |
| 240 | #884 | — | 2 | 4 | no | — |
| 241 | #884 | — | 2 | 4 | no | — |
| 242 | #882 | — | 2 | 1 | no | — |
| 243 | #882 | — | 2 | 1 | no | — |
| 244 | #67⋊C4 | — | 2 | 4 | no | — |
| 245 | #67⋊C4 | — | 2 | 4 | no | — |
| 246 | #878 | — | 2 | 4 | no | — |
| 247 | #878 | — | 2 | 4 | no | — |
| 248 | #877 | — | 2 | 2 | no | — |
| 249 | #877 | — | 2 | 2 | no | — |
| 250 | C4×D12 | — | 2 | 2 | no | — |
| 251 | C4×D12 | — | 2 | 2 | no | — |
| 252 | C4×Dic6 | — | 2 | 2 | no | — |
| 253 | C4×Dic6 | — | 2 | 2 | no | — |
| 254 | C3×#107 | C23 | 1 | 2 | yes | — |
| 255 | C3×#106 | C23 | 1 | 2 | yes | — |
| 256 | C3×#103 | C23 | 1 | 4 | yes | — |
| 257 | C3×#102 | C23 | 1 | 4 | yes | — |
| 258 | #830 | C23 | 1 | 4 | yes | — |
| 259 | (C2×D3)⋊C8 | C23 | 1 | 4 | yes | — |
| 260 | #815 | C23 | 1 | 2 | yes | — |
| 261 | Dic3⋊C8 | C23 | 1 | 4 | yes | — |
| 262 | C8×Dic3 | C23 | 1 | 2 | yes | — |
| 263 | #810 | C23 | 1 | 2 | yes | — |
| 264 | #810 | C23 | 1 | 2 | yes | — |
| 265 | #810 | C23 | 1 | 4 | yes | — |
| 266 | #810 | C23 | 1 | 4 | yes | — |
| 267 | #809 | C23 | 1 | 2 | yes | — |
| 268 | #809 | C23 | 1 | 2 | yes | — |
| 269 | C2×2−1+4 | — | 3 | 1 | no | — |
| 270 | C2×2−1+4 | — | 3 | 1 | no | — |
| 271 | C22×#41 | — | 3 | 1 | no | — |
| 272 | C23×Q8 | — | 3 | 1 | no | — |
| 273 | #578 | — | 6 | 8 | no | — |
| 274 | C2×#137 | — | 3 | 1 | no | — |
| 275 | C2×#137 | — | 3 | 4 | no | — |
| 276 | C2×#137 | — | 3 | 4 | no | — |
| 277 | C2×#137 | — | 3 | 1 | no | — |
| 278 | C2×#137 | — | 3 | 1 | no | — |
| 279 | C2×#137 | — | 3 | 2 | no | — |
| 280 | C2×#137 | — | 3 | 2 | no | — |
| 281 | C2×#137 | — | 6 | 8 | no | — |
| 282 | C2×AGL(1,ℤ/8) | — | 3 | 1 | no | — |
| 283 | C2×#135 | — | 3 | 1 | no | — |
| 284 | C2×#135 | — | 3 | 2 | no | — |
| 285 | C22×Q16 | — | 3 | 1 | no | — |
| 286 | C22×Q16 | — | 3 | 1 | no | — |
| 287 | C22×Q16 | — | 3 | 2 | no | — |
| 288 | C22×SD16 | — | 3 | 1 | no | — |
| 289 | C22×SD16 | C2×D3 | 1 | 1 | yes | characteristic |
| 290 | C2×#131 | C2×D3 | 1 | 1 | yes | characteristic |
| 291 | C22×M16 | — | 3 | 1 | no | — |
| 292 | #550 | — | 3 | 4 | no | — |
| 293 | #550 | — | 6 | 2 | no | — |
| 294 | D4×Q8 | — | 3 | 4 | no | — |
| 295 | D4×Q8 | — | 6 | 2 | no | — |
| 296 | #548 | — | 3 | 4 | no | — |
| 297 | #548 | — | 3 | 4 | no | — |
| 298 | #548 | — | 6 | 2 | no | — |
| 299 | #548 | — | 6 | 2 | no | — |
| 300 | #536 | — | 3 | 1 | no | — |
| 301 | #536 | — | 6 | 2 | no | — |
| 302 | #536 | C2×D3 | 1 | 1 | yes | characteristic |
| 303 | #535 | — | 3 | 1 | no | — |
| 304 | #535 | — | 6 | 2 | no | — |
| 305 | #535 | C2×D3 | 1 | 1 | yes | characteristic |
| 306 | #525 | — | 3 | 1 | no | — |
| 307 | #525 | — | 3 | 1 | no | — |
| 308 | #525 | — | 3 | 1 | no | — |
| 309 | #525 | — | 6 | 2 | no | — |
| 310 | #525 | — | 6 | 2 | no | — |
| 311 | #519 | — | 3 | 1 | no | — |
| 312 | #519 | — | 3 | 1 | no | — |
| 313 | #497 | — | 3 | 2 | no | — |
| 314 | #496 | — | 3 | 2 | no | — |
| 315 | #495 | — | 3 | 2 | no | — |
| 316 | #492 | — | 3 | 2 | no | — |
| 317 | #470 | — | 3 | 2 | no | — |
| 318 | #469 | — | 3 | 2 | no | — |
| 319 | #468 | — | 3 | 2 | no | — |
| 320 | #468 | — | 3 | 2 | no | — |
| 321 | #468 | C2×D3 | 1 | 4 | yes | complemented |
| 322 | #465 | C2×D3 | 1 | 4 | yes | complemented |
| 323 | #464 | — | 3 | 4 | no | — |
| 324 | #464 | — | 3 | 4 | no | — |
| 325 | #462 | — | 3 | 4 | no | — |
| 326 | #460 | — | 3 | 4 | no | — |
| 327 | #452 | — | 3 | 4 | no | — |
| 328 | #452 | — | 3 | 4 | no | — |
| 329 | #451 | — | 3 | 4 | no | — |
| 330 | #451 | — | 3 | 4 | no | — |
| 331 | #449 | — | 3 | 4 | no | — |
| 332 | #449 | — | 3 | 4 | no | — |
| 333 | #448 | — | 3 | 4 | no | — |
| 334 | #448 | — | 3 | 4 | no | — |
| 335 | #441 | — | 3 | 4 | no | — |
| 336 | C4×Q16 | — | 3 | 4 | no | — |
| 337 | #436 | — | 3 | 4 | no | — |
| 338 | #435 | — | 3 | 4 | no | — |
| 339 | #427 | C2×D3 | 1 | 1 | yes | characteristic |
| 340 | #424 | — | 3 | 1 | no | — |
| 341 | #419 | — | 3 | 1 | no | — |
| 342 | #419 | — | 3 | 1 | no | — |
| 343 | #419 | C2×D3 | 1 | 1 | yes | characteristic |
| 344 | #418 | C2×D3 | 1 | 1 | yes | characteristic |
| 345 | #416 | — | 3 | 1 | no | — |
| 346 | #416 | — | 3 | 1 | no | — |
| 347 | #408 | — | 3 | 1 | no | — |
| 348 | #407 | — | 3 | 1 | no | — |
| 349 | #405 | — | 3 | 1 | no | — |
| 350 | C24×C3 | — | 2 | 1 | no | — |
| 351 | C23×D3 | C2×D4 | 1 | 1 | yes | characteristic |
| 352 | C3×#41 | — | 2 | 2 | no | — |
| 353 | C3×#41 | — | 2 | 2 | no | — |
| 354 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 355 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 356 | C2×C3×Q8 | — | 2 | 2 | no | — |
| 357 | C2×C3×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 358 | C2×C3×Q8 | C24 | 1 | 2 | yes | — |
| 359 | C2×C3×D4 | — | 2 | 4 | no | — |
| 360 | C2×C3×D4 | — | 2 | 2 | no | — |
| 361 | C2×C3×D4 | — | 2 | 1 | no | — |
| 362 | C2×C3×D4 | — | 2 | 2 | no | — |
| 363 | C2×C3×D4 | C2×D4 | 1 | 2 | yes | — |
| 364 | C2×C3×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 365 | C2×C3×D4 | C24 | 1 | 2 | yes | — |
| 366 | C22×C3×C4 | — | 2 | 1 | no | — |
| 367 | C22×C3×C4 | C24 | 1 | 2 | yes | — |
| 368 | C22×C3×C4 | C24 | 1 | 1 | yes | characteristic |
| 369 | C2×#67 | — | 2 | 1 | no | — |
| 370 | C2×#67 | — | 2 | 1 | no | — |
| 371 | C2×#67 | — | 2 | 2 | no | — |
| 372 | C2×#67 | — | 2 | 2 | no | — |
| 373 | C2×#67 | — | 2 | 4 | no | — |
| 374 | C2×#67 | — | 2 | 4 | no | — |
| 375 | C2×#67 | — | 4 | 4 | no | — |
| 376 | C2×#67 | C2×D4 | 1 | 4 | yes | — |
| 377 | C22×Dic3 | — | 2 | 1 | no | — |
| 378 | C22×Dic3 | — | 2 | 1 | no | — |
| 379 | C22×Dic3 | — | 2 | 2 | no | — |
| 380 | C22×Dic3 | — | 2 | 2 | no | — |
| 381 | C22×Dic3 | — | 2 | 4 | no | — |
| 382 | C22×Dic3 | — | 4 | 4 | no | — |
| 383 | C22×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 384 | D3×Q8 | — | 2 | 8 | no | — |
| 385 | D3×Q8 | — | 4 | 4 | no | — |
| 386 | D3×Q8 | — | 4 | 8 | no | — |
| 387 | D3×Q8 | — | 4 | 4 | no | — |
| 388 | D3×Q8 | — | 4 | 4 | no | — |
| 389 | #237 | — | 2 | 8 | no | — |
| 390 | #237 | — | 4 | 4 | no | — |
| 391 | #237 | — | 4 | 8 | no | — |
| 392 | #237 | — | 4 | 4 | no | — |
| 393 | #237 | — | 4 | 4 | no | — |
| 394 | #237 | — | 4 | 8 | no | — |
| 395 | #237 | — | 4 | 8 | no | — |
| 396 | #235 | — | 2 | 2 | no | — |
| 397 | #235 | — | 2 | 2 | no | — |
| 398 | #235 | — | 2 | 2 | no | — |
| 399 | #235 | — | 2 | 2 | no | — |
| 400 | #235 | — | 2 | 4 | no | — |
| 401 | #235 | — | 2 | 4 | no | — |
| 402 | #235 | — | 4 | 2 | no | — |
| 403 | #235 | — | 4 | 2 | no | — |
| 404 | C2×D12 | — | 2 | 2 | no | — |
| 405 | C2×D12 | — | 2 | 2 | no | — |
| 406 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 407 | C2×D12 | C24 | 1 | 1 | yes | characteristic |
| 408 | C2×C4×D3 | — | 2 | 2 | no | — |
| 409 | C2×C4×D3 | — | 2 | 2 | no | — |
| 410 | C2×C4×D3 | — | 2 | 4 | no | — |
| 411 | C2×C4×D3 | — | 2 | 1 | no | — |
| 412 | C2×C4×D3 | — | 2 | 1 | no | — |
| 413 | C2×C4×D3 | — | 2 | 2 | no | — |
| 414 | C2×C4×D3 | — | 2 | 2 | no | — |
| 415 | C2×C4×D3 | — | 4 | 4 | no | — |
| 416 | C2×C4×D3 | C2×D4 | 1 | 2 | yes | — |
| 417 | C2×C4×D3 | C24 | 1 | 2 | yes | — |
| 418 | C2×Dic6 | — | 2 | 1 | no | — |
| 419 | C2×Dic6 | — | 2 | 1 | no | — |
| 420 | C2×Dic6 | — | 2 | 2 | no | — |
| 421 | C2×Dic6 | — | 2 | 2 | no | — |
| 422 | C2×Dic6 | — | 2 | 4 | no | — |
| 423 | C2×Dic6 | — | 2 | 4 | no | — |
| 424 | C2×Dic6 | — | 2 | 2 | no | — |
| 425 | C2×Dic6 | — | 2 | 2 | no | — |
| 426 | C2×Dic6 | — | 2 | 4 | no | — |
| 427 | C2×Dic6 | — | 4 | 2 | no | — |
| 428 | C2×Dic6 | — | 4 | 2 | no | — |
| 429 | C2×Dic6 | — | 4 | 4 | no | — |
| 430 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 431 | C2×Dic6 | C2×D4 | 1 | 4 | yes | — |
| 432 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 433 | C2×Dic6 | C24 | 1 | 1 | yes | characteristic |
| 434 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 435 | C2×Dic6 | C24 | 1 | 2 | yes | — |
| 436 | C3×SD16 | — | 2 | 4 | no | — |
| 437 | C3×SD16 | — | 2 | 4 | no | — |
| 438 | C3×M16 | — | 2 | 2 | no | — |
| 439 | C3×M16 | — | 2 | 4 | no | — |
| 440 | C2×C3×C8 | — | 2 | 4 | no | — |
| 441 | C2×C3×C8 | C2×D4 | 1 | 4 | yes | — |
| 442 | C2×C3×C8 | C24 | 1 | 2 | yes | — |
| 443 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 444 | C2×C3×C8 | C24 | 1 | 1 | yes | characteristic |
| 445 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 446 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 447 | C3×C4⋊C4 | C24 | 1 | 2 | yes | — |
| 448 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 449 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 450 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 451 | C3×C22⋊C4 | — | 2 | 4 | no | — |
| 452 | C3×C42 | — | 2 | 1 | no | — |
| 453 | C3×C42 | — | 2 | 1 | no | — |
| 454 | #217 | — | 2 | 4 | no | — |
| 455 | #217 | C2×D4 | 1 | 2 | yes | — |
| 456 | #217 | C2×D4 | 1 | 4 | yes | — |
| 457 | #216 | — | 2 | 8 | no | — |
| 458 | #216 | — | 4 | 2 | no | — |
| 459 | #215 | — | 4 | 2 | no | — |
| 460 | #214 | — | 2 | 8 | no | — |
| 461 | #214 | — | 4 | 2 | no | — |
| 462 | #213 | — | 4 | 2 | no | — |
| 463 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 464 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 465 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 466 | (C2×D3)⋊C4 | — | 2 | 2 | no | — |
| 467 | (C2×D3)⋊C4 | — | 2 | 4 | no | — |
| 468 | (C2×D3)⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 469 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 470 | C4⋊Dic3 | — | 2 | 2 | no | — |
| 471 | C4⋊Dic3 | C2×D4 | 1 | 2 | yes | — |
| 472 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 473 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 474 | Dic3⋊C4 | — | 2 | 4 | no | — |
| 475 | Dic3⋊C4 | C2×D4 | 1 | 4 | yes | — |
| 476 | C4×Dic3 | — | 2 | 4 | no | — |
| 477 | C4×Dic3 | — | 2 | 4 | no | — |
| 478 | C4×Dic3 | C24 | 1 | 2 | yes | — |
| 479 | #208 | — | 2 | 2 | no | — |
| 480 | C2×C3⋊C8 | — | 2 | 2 | no | — |
| 481 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 482 | C2×C3⋊C8 | C24 | 1 | 2 | yes | — |
| 483 | Dic12 | — | 2 | 4 | no | — |
| 484 | Dic12 | — | 2 | 4 | no | — |
| 485 | Dic12 | — | 2 | 2 | no | — |
| 486 | Dic12 | C2×D4 | 1 | 8 | yes | — |
| 487 | Dic12 | C2×D4 | 1 | 8 | yes | — |
| 488 | D24 | — | 2 | 2 | no | — |
| 489 | #204 | — | 2 | 4 | no | — |
| 490 | #204 | — | 2 | 4 | no | — |
| 491 | #204 | — | 2 | 2 | no | — |
| 492 | #204 | — | 2 | 2 | no | — |
| 493 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 494 | ΓL(1,𝔽25) | — | 2 | 4 | no | — |
| 495 | 2−1+4 | — | 6 | 4 | no | — |
| 496 | 2−1+4 | — | 6 | 4 | no | — |
| 497 | 2−1+4 | — | 12 | 2 | no | — |
| 498 | 2−1+4 | — | 12 | 2 | no | — |
| 499 | C2×#41 | — | 3 | 4 | no | — |
| 500 | C2×#41 | — | 3 | 1 | no | — |
| 501 | C2×#41 | — | 3 | 1 | no | — |
| 502 | C2×#41 | — | 3 | 2 | no | — |
| 503 | C2×#41 | — | 3 | 2 | no | — |
| 504 | C2×#41 | — | 6 | 2 | no | — |
| 505 | C2×#41 | — | 6 | 2 | no | — |
| 506 | C2×#41 | — | 6 | 2 | no | — |
| 507 | C2×#41 | — | 6 | 1 | no | — |
| 508 | C2×#41 | — | 6 | 1 | no | — |
| 509 | C2×#41 | — | 6 | 4 | no | — |
| 510 | C2×#41 | — | 12 | 2 | no | — |
| 511 | C2×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 512 | C22×Q8 | — | 3 | 4 | no | — |
| 513 | C22×Q8 | — | 3 | 1 | no | — |
| 514 | C22×Q8 | — | 3 | 1 | no | — |
| 515 | C22×Q8 | — | 3 | 2 | no | — |
| 516 | C22×Q8 | — | 3 | 2 | no | — |
| 517 | C22×Q8 | — | 6 | 1 | no | — |
| 518 | C22×Q8 | — | 6 | 2 | no | — |
| 519 | C22×Q8 | — | 6 | 1 | no | — |
| 520 | C22×Q8 | — | 6 | 1 | no | — |
| 521 | C22×Q8 | — | 6 | 4 | no | — |
| 522 | C22×Q8 | — | 12 | 2 | no | — |
| 523 | C22×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 524 | C22×D4 | — | 6 | 1 | no | — |
| 525 | C22×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 526 | C23×C4 | — | 3 | 1 | no | — |
| 527 | C23×C4 | — | 6 | 1 | no | — |
| 528 | C23×C4 | — | 6 | 1 | no | — |
| 529 | #137 | — | 6 | 8 | no | — |
| 530 | #137 | — | 6 | 8 | no | — |
| 531 | #137 | — | 6 | 4 | no | — |
| 532 | #137 | — | 6 | 4 | no | — |
| 533 | #137 | — | 6 | 16 | no | — |
| 534 | #137 | — | 6 | 16 | no | — |
| 535 | #137 | — | 12 | 2 | no | — |
| 536 | AGL(1,ℤ/8) | — | 12 | 2 | no | — |
| 537 | #135 | — | 6 | 8 | no | — |
| 538 | #135 | — | 6 | 4 | no | — |
| 539 | C2×Q16 | — | 3 | 4 | no | — |
| 540 | C2×Q16 | — | 3 | 2 | no | — |
| 541 | C2×Q16 | — | 3 | 8 | no | — |
| 542 | C2×Q16 | — | 3 | 2 | no | — |
| 543 | C2×Q16 | — | 3 | 2 | no | — |
| 544 | C2×Q16 | — | 3 | 1 | no | — |
| 545 | C2×Q16 | — | 3 | 2 | no | — |
| 546 | C2×Q16 | — | 3 | 2 | no | — |
| 547 | C2×Q16 | — | 6 | 8 | no | — |
| 548 | C2×Q16 | — | 6 | 4 | no | — |
| 549 | C2×SD16 | — | 2 | 4 | no | — |
| 550 | C2×SD16 | — | 3 | 4 | no | — |
| 551 | C2×SD16 | — | 3 | 2 | no | — |
| 552 | C2×SD16 | — | 3 | 2 | no | — |
| 553 | C2×SD16 | — | 3 | 2 | no | — |
| 554 | C2×SD16 | — | 3 | 2 | no | — |
| 555 | C2×SD16 | — | 3 | 1 | no | — |
| 556 | C2×SD16 | — | 3 | 1 | no | — |
| 557 | C2×SD16 | — | 6 | 4 | no | — |
| 558 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 559 | C2×SD16 | C22×D3 | 1 | 2 | yes | — |
| 560 | C2×D8 | — | 3 | 2 | no | — |
| 561 | C2×D8 | — | 3 | 1 | no | — |
| 562 | #131 | — | 2 | 4 | no | — |
| 563 | C2×M16 | — | 3 | 1 | no | — |
| 564 | C2×M16 | — | 3 | 2 | no | — |
| 565 | C2×M16 | — | 3 | 2 | no | — |
| 566 | C2×M16 | — | 6 | 4 | no | — |
| 567 | C2×M16 | C22×D3 | 1 | 1 | yes | characteristic |
| 568 | C2×M16 | C22×D3 | 1 | 2 | yes | — |
| 569 | C22×C8 | — | 3 | 1 | no | — |
| 570 | C22×C8 | C22×D3 | 1 | 2 | yes | — |
| 571 | C22×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 572 | C4⋊Q8 | — | 2 | 1 | no | — |
| 573 | C4⋊Q8 | — | 3 | 2 | no | — |
| 574 | C4⋊Q8 | — | 6 | 4 | no | — |
| 575 | #127 | — | 2 | 1 | no | — |
| 576 | #127 | — | 3 | 2 | no | — |
| 577 | #127 | — | 6 | 4 | no | — |
| 578 | #124 | — | 2 | 1 | no | — |
| 579 | #124 | — | 2 | 1 | no | — |
| 580 | #124 | — | 3 | 2 | no | — |
| 581 | #124 | — | 3 | 2 | no | — |
| 582 | #124 | — | 6 | 4 | no | — |
| 583 | #124 | — | 6 | 4 | no | — |
| 584 | #123 | — | 2 | 2 | no | — |
| 585 | #123 | — | 3 | 2 | no | — |
| 586 | #123 | — | 6 | 1 | no | — |
| 587 | #123 | — | 6 | 1 | no | — |
| 588 | #123 | — | 6 | 2 | no | — |
| 589 | C22⋊Q8 | — | 3 | 2 | no | — |
| 590 | C22⋊Q8 | — | 3 | 2 | no | — |
| 591 | C22⋊Q8 | — | 3 | 2 | no | — |
| 592 | C22⋊Q8 | — | 6 | 4 | no | — |
| 593 | C22⋊Q8 | — | 6 | 4 | no | — |
| 594 | C22⋊Q8 | — | 6 | 4 | no | — |
| 595 | C22⋊Q8 | — | 6 | 4 | no | — |
| 596 | C22⋊Q8 | — | 6 | 2 | no | — |
| 597 | C22⋊Q8 | C22×D3 | 1 | 4 | yes | — |
| 598 | #121 | — | 3 | 2 | no | — |
| 599 | #121 | — | 3 | 2 | no | — |
| 600 | #121 | — | 3 | 2 | no | — |
| 601 | #121 | — | 6 | 4 | no | — |
| 602 | #121 | — | 6 | 4 | no | — |
| 603 | #121 | — | 6 | 4 | no | — |
| 604 | #121 | — | 6 | 2 | no | — |
| 605 | #121 | — | 6 | 4 | no | — |
| 606 | #121 | C22×D3 | 1 | 4 | yes | — |
| 607 | #120 | — | 2 | 2 | no | — |
| 608 | #120 | — | 3 | 2 | no | — |
| 609 | #120 | — | 6 | 1 | no | — |
| 610 | #120 | — | 6 | 1 | no | — |
| 611 | #120 | — | 6 | 2 | no | — |
| 612 | C4×Q8 | — | 3 | 4 | no | — |
| 613 | C4×Q8 | — | 3 | 4 | no | — |
| 614 | C4×Q8 | — | 6 | 2 | no | — |
| 615 | C4×Q8 | — | 6 | 2 | no | — |
| 616 | C4×D4 | — | 3 | 4 | no | — |
| 617 | C4×D4 | — | 6 | 2 | no | — |
| 618 | C4×D4 | — | 6 | 2 | no | — |
| 619 | C4×D4 | — | 6 | 4 | no | — |
| 620 | C4×D4 | — | 6 | 4 | no | — |
| 621 | C4×D4 | — | 6 | 4 | no | — |
| 622 | C4×D4 | — | 6 | 4 | no | — |
| 623 | #117 | — | 3 | 1 | no | — |
| 624 | #117 | — | 6 | 2 | no | — |
| 625 | #117 | — | 6 | 2 | no | — |
| 626 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 627 | #117 | C22×D3 | 1 | 1 | yes | characteristic |
| 628 | #107 | C22×D3 | 1 | 2 | yes | — |
| 629 | #106 | C22×D3 | 1 | 2 | yes | — |
| 630 | C4⋊C8 | — | 3 | 4 | no | — |
| 631 | #103 | — | 3 | 2 | no | — |
| 632 | #103 | — | 3 | 2 | no | — |
| 633 | #103 | — | 3 | 4 | no | — |
| 634 | #103 | — | 3 | 4 | no | — |
| 635 | #103 | C22×D3 | 1 | 4 | yes | — |
| 636 | #102 | — | 3 | 2 | no | — |
| 637 | #102 | — | 3 | 2 | no | — |
| 638 | #102 | C22×D3 | 1 | 4 | yes | — |
| 639 | C22⋊C8 | — | 3 | 4 | no | — |
| 640 | C22⋊C8 | — | 3 | 4 | no | — |
| 641 | #97 | — | 3 | 2 | no | — |
| 642 | C4×C8 | — | 3 | 2 | no | — |
| 643 | C23×C3 | — | 2 | 2 | no | — |
| 644 | C23×C3 | — | 4 | 2 | no | — |
| 645 | C23×C3 | — | 8 | 2 | no | — |
| 646 | C23×C3 | C22×D4 | 1 | 2 | yes | — |
| 647 | C23×C3 | C22×D4 | 1 | 1 | yes | characteristic |
| 648 | C22×D3 | — | 2 | 2 | no | — |
| 649 | C22×D3 | — | 2 | 1 | no | — |
| 650 | C22×D3 | — | 2 | 1 | no | — |
| 651 | C22×D3 | — | 4 | 2 | no | — |
| 652 | C22×D3 | C22×D4 | 1 | 2 | yes | — |
| 653 | C3×Q8 | — | 2 | 2 | no | — |
| 654 | C3×Q8 | — | 2 | 2 | no | — |
| 655 | C3×Q8 | — | 2 | 2 | no | — |
| 656 | C3×Q8 | — | 4 | 2 | no | — |
| 657 | C3×D4 | — | 2 | 4 | no | — |
| 658 | C3×D4 | — | 2 | 2 | no | — |
| 659 | C3×D4 | — | 2 | 2 | no | — |
| 660 | C3×D4 | — | 2 | 2 | no | — |
| 661 | C3×D4 | — | 4 | 2 | no | — |
| 662 | C3×D4 | — | 8 | 4 | no | — |
| 663 | C2×C3×C4 | — | 2 | 2 | no | — |
| 664 | C2×C3×C4 | — | 2 | 2 | no | — |
| 665 | C2×C3×C4 | — | 2 | 2 | no | — |
| 666 | C2×C3×C4 | — | 2 | 2 | no | — |
| 667 | C2×C3×C4 | — | 2 | 2 | no | — |
| 668 | C2×C3×C4 | — | 4 | 2 | no | — |
| 669 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 670 | C2×C3×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 671 | C2×C3×C4 | C22×D4 | 1 | 2 | yes | — |
| 672 | C2×C3×C4 | H(5,𝔽2) | 1 | 2 | yes | — |
| 673 | C2×C3×C4 | C25 | 1 | 1 | yes | characteristic |
| 674 | #67 | — | 4 | 4 | no | — |
| 675 | #67 | — | 4 | 8 | no | — |
| 676 | #67 | — | 4 | 4 | no | — |
| 677 | #67 | — | 4 | 4 | no | — |
| 678 | #67 | — | 4 | 2 | no | — |
| 679 | #67 | — | 4 | 2 | no | — |
| 680 | #67 | — | 8 | 4 | no | — |
| 681 | C2×Dic3 | — | 2 | 4 | no | — |
| 682 | C2×Dic3 | — | 2 | 4 | no | — |
| 683 | C2×Dic3 | — | 2 | 2 | no | — |
| 684 | C2×Dic3 | — | 2 | 2 | no | — |
| 685 | C2×Dic3 | — | 2 | 2 | no | — |
| 686 | C2×Dic3 | — | 2 | 1 | no | — |
| 687 | C2×Dic3 | — | 2 | 1 | no | — |
| 688 | C2×Dic3 | — | 4 | 8 | no | — |
| 689 | C2×Dic3 | — | 4 | 4 | no | — |
| 690 | C2×Dic3 | — | 4 | 4 | no | — |
| 691 | C2×Dic3 | C22×D4 | 1 | 4 | yes | — |
| 692 | C2×Dic3 | C22×D4 | 1 | 2 | yes | — |
| 693 | D12 | — | 2 | 1 | no | — |
| 694 | D12 | — | 2 | 1 | no | — |
| 695 | D12 | — | 2 | 1 | no | — |
| 696 | D12 | — | 2 | 1 | no | — |
| 697 | D12 | — | 4 | 4 | no | — |
| 698 | D12 | — | 8 | 2 | no | — |
| 699 | C4×D3 | — | 2 | 4 | no | — |
| 700 | C4×D3 | — | 2 | 2 | no | — |
| 701 | C4×D3 | — | 2 | 2 | no | — |
| 702 | C4×D3 | — | 4 | 4 | no | — |
| 703 | C4×D3 | — | 4 | 4 | no | — |
| 704 | C4×D3 | — | 4 | 8 | no | — |
| 705 | C4×D3 | — | 4 | 2 | no | — |
| 706 | C4×D3 | — | 4 | 2 | no | — |
| 707 | Dic6 | — | 2 | 4 | no | — |
| 708 | Dic6 | — | 2 | 4 | no | — |
| 709 | Dic6 | — | 2 | 2 | no | — |
| 710 | Dic6 | — | 2 | 2 | no | — |
| 711 | Dic6 | — | 2 | 1 | no | — |
| 712 | Dic6 | — | 2 | 1 | no | — |
| 713 | Dic6 | — | 2 | 1 | no | — |
| 714 | Dic6 | — | 2 | 1 | no | — |
| 715 | Dic6 | — | 4 | 8 | no | — |
| 716 | Dic6 | — | 4 | 4 | no | — |
| 717 | Dic6 | — | 4 | 4 | no | — |
| 718 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 719 | Dic6 | C22×D4 | 1 | 4 | yes | — |
| 720 | C3×C8 | — | 2 | 2 | no | — |
| 721 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 722 | C3×C8 | C22×D4 | 1 | 2 | yes | — |
| 723 | C3⋊C8 | — | 2 | 2 | no | — |
| 724 | C3⋊C8 | — | 2 | 2 | no | — |
| 725 | C24 | — | 2 | 1 | no | — |
| 726 | C24 | — | 3 | 1 | no | — |
| 727 | #41 | — | 2 | 2 | no | — |
| 728 | #41 | — | 2 | 2 | no | — |
| 729 | #41 | — | 6 | 4 | no | — |
| 730 | #41 | — | 6 | 4 | no | — |
| 731 | #41 | — | 6 | 8 | no | — |
| 732 | #41 | — | 6 | 2 | no | — |
| 733 | #41 | — | 6 | 2 | no | — |
| 734 | #41 | — | 6 | 2 | no | — |
| 735 | #41 | — | 6 | 2 | no | — |
| 736 | #41 | — | 12 | 2 | no | — |
| 737 | #41 | — | 12 | 2 | no | — |
| 738 | #41 | — | 12 | 4 | no | — |
| 739 | #41 | — | 12 | 8 | no | — |
| 740 | #41 | — | 12 | 8 | no | — |
| 741 | #41 | — | 12 | 8 | no | — |
| 742 | #41 | — | 12 | 4 | no | — |
| 743 | #41 | — | 12 | 4 | no | — |
| 744 | C2×Q8 | — | 2 | 1 | no | — |
| 745 | C2×Q8 | — | 2 | 2 | no | — |
| 746 | C2×Q8 | — | 2 | 2 | no | — |
| 747 | C2×Q8 | — | 3 | 4 | no | — |
| 748 | C2×Q8 | — | 3 | 4 | no | — |
| 749 | C2×Q8 | — | 3 | 2 | no | — |
| 750 | C2×Q8 | — | 3 | 2 | no | — |
| 751 | C2×Q8 | — | 3 | 1 | no | — |
| 752 | C2×Q8 | — | 3 | 1 | no | — |
| 753 | C2×Q8 | — | 6 | 4 | no | — |
| 754 | C2×Q8 | — | 6 | 4 | no | — |
| 755 | C2×Q8 | — | 6 | 4 | no | — |
| 756 | C2×Q8 | — | 6 | 1 | no | — |
| 757 | C2×Q8 | — | 6 | 1 | no | — |
| 758 | C2×Q8 | — | 6 | 2 | no | — |
| 759 | C2×Q8 | — | 6 | 2 | no | — |
| 760 | C2×Q8 | — | 6 | 2 | no | — |
| 761 | C2×Q8 | — | 6 | 2 | no | — |
| 762 | C2×Q8 | — | 6 | 8 | no | — |
| 763 | C2×Q8 | — | 12 | 2 | no | — |
| 764 | C2×Q8 | — | 12 | 2 | no | — |
| 765 | C2×Q8 | — | 12 | 4 | no | — |
| 766 | C2×Q8 | — | 12 | 4 | no | — |
| 767 | C2×Q8 | — | 12 | 8 | no | — |
| 768 | C2×Q8 | — | 12 | 4 | no | — |
| 769 | C2×Q8 | — | 12 | 4 | no | — |
| 770 | C2×Q8 | D3×D4 | 1 | 1 | yes | characteristic |
| 771 | C2×Q8 | C23×D3 | 1 | 2 | yes | — |
| 772 | C2×D4 | — | 2 | 4 | no | — |
| 773 | C2×D4 | — | 2 | 2 | no | — |
| 774 | C2×D4 | — | 2 | 1 | no | — |
| 775 | C2×D4 | — | 2 | 2 | no | — |
| 776 | C2×D4 | — | 3 | 4 | no | — |
| 777 | C2×D4 | — | 3 | 1 | no | — |
| 778 | C2×D4 | — | 3 | 1 | no | — |
| 779 | C2×D4 | — | 6 | 2 | no | — |
| 780 | C2×D4 | — | 6 | 2 | no | — |
| 781 | C2×D4 | — | 6 | 4 | no | — |
| 782 | C2×D4 | — | 6 | 4 | no | — |
| 783 | C2×D4 | — | 6 | 1 | no | — |
| 784 | C2×D4 | — | 6 | 1 | no | — |
| 785 | C2×D4 | — | 6 | 2 | no | — |
| 786 | C2×D4 | — | 6 | 2 | no | — |
| 787 | C2×D4 | — | 12 | 4 | no | — |
| 788 | C2×D4 | D3×D4 | 1 | 2 | yes | — |
| 789 | C2×D4 | D3×D4 | 1 | 1 | yes | characteristic |
| 790 | C2×D4 | C23×D3 | 1 | 2 | yes | — |
| 791 | C22×C4 | — | 2 | 1 | no | — |
| 792 | C22×C4 | — | 3 | 1 | no | — |
| 793 | C22×C4 | — | 3 | 2 | no | — |
| 794 | C22×C4 | — | 3 | 2 | no | — |
| 795 | C22×C4 | — | 6 | 4 | no | — |
| 796 | C22×C4 | — | 6 | 4 | no | — |
| 797 | C22×C4 | — | 6 | 1 | no | — |
| 798 | C22×C4 | — | 6 | 1 | no | — |
| 799 | C22×C4 | — | 6 | 2 | no | — |
| 800 | C22×C4 | — | 6 | 2 | no | — |
| 801 | C22×C4 | — | 6 | 2 | no | — |
| 802 | C22×C4 | — | 6 | 2 | no | — |
| 803 | C22×C4 | — | 6 | 2 | no | — |
| 804 | C22×C4 | — | 6 | 1 | no | — |
| 805 | C22×C4 | — | 6 | 2 | no | — |
| 806 | C22×C4 | — | 6 | 1 | no | — |
| 807 | C22×C4 | — | 12 | 4 | no | — |
| 808 | C22×C4 | — | 12 | 4 | no | — |
| 809 | C22×C4 | C23×D3 | 1 | 2 | yes | — |
| 810 | C22×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 811 | Q16 | — | 3 | 8 | no | — |
| 812 | Q16 | — | 3 | 8 | no | — |
| 813 | Q16 | — | 6 | 4 | no | — |
| 814 | Q16 | — | 6 | 4 | no | — |
| 815 | Q16 | — | 6 | 8 | no | — |
| 816 | Q16 | — | 6 | 2 | no | — |
| 817 | Q16 | — | 12 | 2 | no | — |
| 818 | SD16 | — | 2 | 4 | no | — |
| 819 | SD16 | — | 2 | 4 | no | — |
| 820 | SD16 | — | 6 | 4 | no | — |
| 821 | SD16 | — | 6 | 4 | no | — |
| 822 | SD16 | — | 6 | 8 | no | — |
| 823 | SD16 | — | 6 | 2 | no | — |
| 824 | SD16 | — | 6 | 2 | no | — |
| 825 | SD16 | — | 12 | 2 | no | — |
| 826 | SD16 | — | 12 | 2 | no | — |
| 827 | D8 | — | 6 | 2 | no | — |
| 828 | D8 | — | 12 | 2 | no | — |
| 829 | M16 | — | 2 | 2 | no | — |
| 830 | M16 | — | 2 | 4 | no | — |
| 831 | M16 | — | 6 | 2 | no | — |
| 832 | M16 | — | 6 | 4 | no | — |
| 833 | M16 | — | 6 | 4 | no | — |
| 834 | C2×C8 | — | 2 | 4 | no | — |
| 835 | C2×C8 | — | 3 | 2 | no | — |
| 836 | C2×C8 | — | 3 | 2 | no | — |
| 837 | C2×C8 | — | 6 | 2 | no | — |
| 838 | C2×C8 | D3×D4 | 1 | 4 | yes | — |
| 839 | C2×C8 | C23×D3 | 1 | 2 | yes | — |
| 840 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 841 | C2×C8 | C23×D3 | 1 | 1 | yes | characteristic |
| 842 | C4⋊C4 | — | 2 | 4 | no | — |
| 843 | C4⋊C4 | — | 3 | 2 | no | — |
| 844 | C4⋊C4 | — | 3 | 4 | no | — |
| 845 | C4⋊C4 | — | 6 | 4 | no | — |
| 846 | C4⋊C4 | — | 6 | 4 | no | — |
| 847 | C4⋊C4 | — | 6 | 2 | no | — |
| 848 | C4⋊C4 | — | 6 | 2 | no | — |
| 849 | C4⋊C4 | — | 6 | 4 | no | — |
| 850 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 851 | C4⋊C4 | C23×D3 | 1 | 2 | yes | — |
| 852 | C22⋊C4 | — | 2 | 1 | no | — |
| 853 | C22⋊C4 | — | 2 | 1 | no | — |
| 854 | C22⋊C4 | — | 2 | 4 | no | — |
| 855 | C22⋊C4 | — | 2 | 4 | no | — |
| 856 | C22⋊C4 | — | 3 | 2 | no | — |
| 857 | C22⋊C4 | — | 3 | 4 | no | — |
| 858 | C22⋊C4 | — | 3 | 4 | no | — |
| 859 | C22⋊C4 | — | 6 | 2 | no | — |
| 860 | C22⋊C4 | — | 6 | 2 | no | — |
| 861 | C22⋊C4 | — | 6 | 4 | no | — |
| 862 | C22⋊C4 | — | 6 | 2 | no | — |
| 863 | C22⋊C4 | — | 6 | 2 | no | — |
| 864 | C22⋊C4 | — | 6 | 4 | no | — |
| 865 | C42 | — | 2 | 1 | no | — |
| 866 | C42 | — | 2 | 1 | no | — |
| 867 | C42 | — | 3 | 2 | no | — |
| 868 | C42 | — | 6 | 4 | no | — |
| 869 | C42 | — | 6 | 4 | no | — |
| 870 | C22×C3 | — | 2 | 2 | no | — |
| 871 | C22×C3 | — | 2 | 4 | no | — |
| 872 | C22×C3 | — | 2 | 2 | no | — |
| 873 | C22×C3 | — | 4 | 4 | no | — |
| 874 | C22×C3 | — | 4 | 2 | no | — |
| 875 | C22×C3 | — | 8 | 4 | no | — |
| 876 | C22×C3 | D42 | 1 | 2 | yes | — |
| 877 | C22×C3 | C23×D4 | 1 | 1 | yes | characteristic |
| 878 | C2×D3 | — | 2 | 2 | no | — |
| 879 | C2×D3 | — | 2 | 2 | no | — |
| 880 | C2×D3 | — | 2 | 2 | no | — |
| 881 | C2×D3 | — | 4 | 4 | no | — |
| 882 | C2×D3 | — | 4 | 2 | no | — |
| 883 | C2×D3 | — | 4 | 2 | no | — |
| 884 | C2×D3 | — | 4 | 1 | no | — |
| 885 | C2×D3 | — | 4 | 1 | no | — |
| 886 | C3×C4 | — | 2 | 2 | no | — |
| 887 | C3×C4 | — | 4 | 2 | no | — |
| 888 | C3×C4 | — | 4 | 2 | no | — |
| 889 | C3×C4 | — | 4 | 2 | no | — |
| 890 | C3×C4 | D42 | 1 | 2 | yes | — |
| 891 | C3×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 892 | C3×C4 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 893 | Dic3 | — | 2 | 4 | no | — |
| 894 | Dic3 | — | 2 | 4 | no | — |
| 895 | Dic3 | — | 2 | 4 | no | — |
| 896 | Dic3 | — | 2 | 2 | no | — |
| 897 | Dic3 | — | 4 | 1 | no | — |
| 898 | Dic3 | — | 4 | 1 | no | — |
| 899 | C23 | — | 2 | 2 | no | — |
| 900 | C23 | — | 3 | 2 | no | — |
| 901 | C23 | — | 4 | 2 | no | — |
| 902 | C23 | — | 6 | 2 | no | — |
| 903 | C23 | — | 6 | 1 | no | — |
| 904 | C23 | — | 6 | 1 | no | — |
| 905 | C23 | — | 8 | 2 | no | — |
| 906 | C23 | — | 12 | 2 | no | — |
| 907 | C23 | C2×D3×D4 | 1 | 2 | yes | — |
| 908 | C23 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 909 | Q8 | — | 2 | 2 | no | — |
| 910 | Q8 | — | 2 | 2 | no | — |
| 911 | Q8 | — | 2 | 2 | no | — |
| 912 | Q8 | — | 3 | 4 | no | — |
| 913 | Q8 | — | 3 | 4 | no | — |
| 914 | Q8 | — | 4 | 2 | no | — |
| 915 | Q8 | — | 6 | 2 | no | — |
| 916 | Q8 | — | 6 | 2 | no | — |
| 917 | Q8 | — | 6 | 4 | no | — |
| 918 | Q8 | — | 6 | 4 | no | — |
| 919 | Q8 | — | 6 | 1 | no | — |
| 920 | Q8 | — | 6 | 1 | no | — |
| 921 | Q8 | — | 6 | 1 | no | — |
| 922 | Q8 | — | 6 | 1 | no | — |
| 923 | Q8 | — | 12 | 4 | no | — |
| 924 | Q8 | — | 12 | 4 | no | — |
| 925 | Q8 | — | 12 | 8 | no | — |
| 926 | D4 | — | 2 | 4 | no | — |
| 927 | D4 | — | 2 | 2 | no | — |
| 928 | D4 | — | 2 | 2 | no | — |
| 929 | D4 | — | 2 | 2 | no | — |
| 930 | D4 | — | 4 | 2 | no | — |
| 931 | D4 | — | 6 | 1 | no | — |
| 932 | D4 | — | 6 | 1 | no | — |
| 933 | D4 | — | 6 | 1 | no | — |
| 934 | D4 | — | 6 | 1 | no | — |
| 935 | D4 | — | 8 | 4 | no | — |
| 936 | D4 | — | 12 | 4 | no | — |
| 937 | D4 | — | 12 | 4 | no | — |
| 938 | D4 | — | 12 | 4 | no | — |
| 939 | D4 | — | 12 | 4 | no | — |
| 940 | D4 | — | 12 | 8 | no | — |
| 941 | D4 | — | 12 | 2 | no | — |
| 942 | D4 | — | 12 | 2 | no | — |
| 943 | D4 | — | 24 | 2 | no | — |
| 944 | D4 | — | 24 | 4 | no | — |
| 945 | C2×C4 | — | 2 | 2 | no | — |
| 946 | C2×C4 | — | 2 | 2 | no | — |
| 947 | C2×C4 | — | 2 | 2 | no | — |
| 948 | C2×C4 | — | 2 | 2 | no | — |
| 949 | C2×C4 | — | 2 | 2 | no | — |
| 950 | C2×C4 | — | 3 | 4 | no | — |
| 951 | C2×C4 | — | 3 | 2 | no | — |
| 952 | C2×C4 | — | 4 | 2 | no | — |
| 953 | C2×C4 | — | 6 | 2 | no | — |
| 954 | C2×C4 | — | 6 | 2 | no | — |
| 955 | C2×C4 | — | 6 | 2 | no | — |
| 956 | C2×C4 | — | 6 | 4 | no | — |
| 957 | C2×C4 | — | 6 | 4 | no | — |
| 958 | C2×C4 | — | 6 | 2 | no | — |
| 959 | C2×C4 | — | 6 | 2 | no | — |
| 960 | C2×C4 | — | 6 | 4 | no | — |
| 961 | C2×C4 | — | 6 | 1 | no | — |
| 962 | C2×C4 | — | 6 | 1 | no | — |
| 963 | C2×C4 | — | 12 | 4 | no | — |
| 964 | C2×C4 | — | 12 | 4 | no | — |
| 965 | C2×C4 | — | 12 | 8 | no | — |
| 966 | C2×C4 | — | 12 | 8 | no | — |
| 967 | C2×C4 | — | 12 | 4 | no | — |
| 968 | C2×C4 | — | 12 | 4 | no | — |
| 969 | C2×C4 | — | 12 | 2 | no | — |
| 970 | C2×C4 | — | 12 | 2 | no | — |
| 971 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 972 | C2×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 973 | C2×C4 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 974 | C2×C4 | #1009 | 1 | 2 | yes | — |
| 975 | C2×C4 | C24×D3 | 1 | 1 | yes | characteristic |
| 976 | C8 | — | 2 | 2 | no | — |
| 977 | C8 | — | 6 | 2 | no | — |
| 978 | C8 | — | 6 | 2 | no | — |
| 979 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 980 | C8 | C2×D3×D4 | 1 | 2 | yes | — |
| 981 | C2×C3 | — | 2 | 2 | no | — |
| 982 | C2×C3 | — | 4 | 2 | no | — |
| 983 | C2×C3 | — | 8 | 2 | no | — |
| 984 | C2×C3 | C2×D42 | 1 | 1 | yes | characteristic |
| 985 | C2×C3 | #3586 | 1 | 2 | yes | — |
| 986 | D3 | — | 4 | 2 | no | — |
| 987 | D3 | — | 8 | 1 | no | — |
| 988 | D3 | — | 8 | 1 | no | — |
| 989 | C22 | — | 2 | 2 | no | — |
| 990 | C22 | — | 2 | 4 | no | — |
| 991 | C22 | — | 2 | 2 | no | — |
| 992 | C22 | — | 4 | 4 | no | — |
| 993 | C22 | — | 4 | 2 | no | — |
| 994 | C22 | — | 6 | 2 | no | — |
| 995 | C22 | — | 6 | 2 | no | — |
| 996 | C22 | — | 6 | 2 | no | — |
| 997 | C22 | — | 8 | 4 | no | — |
| 998 | C22 | — | 12 | 4 | no | — |
| 999 | C22 | — | 12 | 2 | no | — |
| 1000 | C22 | — | 12 | 2 | no | — |
| 1001 | C22 | — | 12 | 1 | no | — |
| 1002 | C22 | — | 12 | 1 | no | — |
| 1003 | C22 | #5609 | 1 | 2 | yes | — |
| 1004 | C22 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 1005 | C4 | — | 2 | 2 | no | — |
| 1006 | C4 | — | 4 | 2 | no | — |
| 1007 | C4 | — | 4 | 2 | no | — |
| 1008 | C4 | — | 4 | 2 | no | — |
| 1009 | C4 | — | 6 | 4 | no | — |
| 1010 | C4 | — | 6 | 2 | no | — |
| 1011 | C4 | — | 6 | 4 | no | — |
| 1012 | C4 | — | 6 | 4 | no | — |
| 1013 | C4 | — | 12 | 1 | no | — |
| 1014 | C4 | — | 12 | 1 | no | — |
| 1015 | C4 | #5609 | 1 | 2 | yes | — |
| 1016 | C4 | C22×D3×D4 | 1 | 1 | yes | characteristic |
| 1017 | C4 | C2×#1009 | 1 | 1 | yes | characteristic |
| 1018 | C3 | #61061 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 1019 | C2 | — | 2 | 2 | no | — |
| 1020 | C2 | — | 4 | 2 | no | — |
| 1021 | C2 | — | 8 | 2 | no | — |
| 1022 | C2 | — | 12 | 2 | no | — |
| 1023 | C2 | — | 24 | 1 | no | — |
| 1024 | C2 | — | 24 | 1 | no | — |
| 1025 | C2 | C2×#5609 | 1 | 1 | yes | characteristic |
| 1026 | C2 | #87208 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#915 | C2 | semidirect |
| 2. C2×#5753 | C2 | semidirect |
| 3. #86355 | C2 | semidirect |
| 4. #86315 | C2 | semidirect |
| 5. C3×#3057 | C2 | semidirect |
| 6. #83854 | C2 | semidirect |
| 7. #83795 | C2 | semidirect |
| 8. #83411 | C2 | semidirect |
| 9. #83390 | C2 | semidirect |
| 10. #80844 | C2 | semidirect |
| 11. #80843 | C2 | semidirect |
| 12. #80688 | C2 | semidirect |
| 13. #80687 | C2 | semidirect |
| 14. #79181 | C2 | semidirect |
| 15. #79169 | C2 | semidirect |
| 16. #78977 | C2 | semidirect |
| 17. #78958 | C2 | semidirect |
| 18. #78945 | C2 | semidirect |
| 19. #78927 | C2 | semidirect |
| 42. C2×#909 | C22 | semidirect |
| 43. C2×#909 | C22 | semidirect |
| 45. C22×Dic12 | C22 | semidirect |
| 47. C2×#904 | C22 | semidirect |
| 55. #5633 | C22 | semidirect |
| 56. #5632 | C22 | semidirect |
| 65. C3×#468 | C22 | semidirect |
| 66. C3×#465 | C22 | semidirect |
| 71. #5176 | C22 | semidirect |
| 72. #5175 | C22 | semidirect |
| 73. #5168 | C22 | semidirect |
| 74. #5167 | C22 | semidirect |
| 75. #5128 | C22 | semidirect |
| 78. #5111 | C22 | semidirect |
| 80. #5050 | C22 | semidirect |
| 81. #5047 | C22 | semidirect |
| 82. #5040 | C22 | semidirect |
| 83. #5037 | C22 | semidirect |
| 88. #4886 | C22 | semidirect |
| 89. #4886 | C22 | semidirect |
| 90. #4873 | C22 | semidirect |
| 91. #4867 | C22 | semidirect |
| 92. #4865 | C22 | semidirect |
| 93. #4853 | C22 | semidirect |
| 94. #4809 | C22 | semidirect |
| 95. #4806 | C22 | semidirect |
| 96. #4798 | C22 | semidirect |
| 97. #4795 | C22 | semidirect |
| 100. #4767 | C22 | semidirect |
| 101. #4762 | C22 | semidirect |
| 111. #3057 | D3 | semidirect |
| 210. C2×Dic12 | D4 | semidirect |
| 321. #468 | C2×D3 | semidirect |
| 322. #465 | C2×D3 | semidirect |
| 1018. C3 | #61061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#915 | 2 |
| C2×#5753 | 2 |
| #86355 | 2 |
| #86315 | 2 |
| C3×#3057 | 2 |
| #83854 | 2 |
| #83795 | 2 |
| #83411 | 2 |
| #83390 | 2 |
| #80844 | 2 |
| #80843 | 2 |
| #80688 | 2 |
| #80687 | 2 |
| #79181 | 2 |
| #79169 | 2 |
| #78977 | 2 |
| #78958 | 2 |
| #78945 | 2 |
| #78927 | 2 |
| #61061 | 3 |