Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2103 conjugacy classes of subgroups.
The subgroup lattice has 695 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5689 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10594635 | C2 | 1 | 4 | yes | maximal |
| 4 | D3×#892 | C2 | 1 | 2 | yes | maximal |
| 5 | #10594502 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10594448 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10594400 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #10594388 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #10594387 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #10594344 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10593992 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #10593954 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #10593866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #86581 | — | 3 | 2 | no | maximal |
| 15 | C2×C4×D32 | C22 | 1 | 1 | yes | characteristic |
| 16 | C32×#125 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | #64105 | C22 | 1 | 4 | yes | — |
| 18 | #64101 | C22 | 1 | 2 | yes | — |
| 19 | #64097 | C22 | 1 | 2 | yes | complemented |
| 20 | #64096 | C22 | 1 | 4 | yes | complemented |
| 21 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64079 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C3×#897 | C22 | 1 | 4 | yes | — |
| 24 | C3×#896 | C22 | 1 | 4 | yes | — |
| 25 | C3×#892 | C22 | 1 | 2 | yes | — |
| 26 | C3×D3×C4⋊C4 | C22 | 1 | 2 | yes | — |
| 27 | C3×#890 | C22 | 1 | 2 | yes | complemented |
| 28 | C3×#889 | C22 | 1 | 4 | yes | complemented |
| 29 | C3×#888 | C22 | 1 | 4 | yes | complemented |
| 30 | C3×#888 | C22 | 1 | 2 | yes | complemented |
| 31 | C3×#872 | C22 | 1 | 2 | yes | — |
| 32 | C3×#869 | C22 | 1 | 2 | yes | complemented |
| 33 | #63921 | C22 | 1 | 2 | yes | — |
| 34 | D3×(C2×D3)⋊C4 | C22 | 1 | 4 | yes | — |
| 35 | #63918 | C22 | 1 | 2 | yes | complemented |
| 36 | #63899 | C22 | 1 | 4 | yes | — |
| 37 | #63896 | C22 | 1 | 4 | yes | — |
| 38 | #63895 | C22 | 1 | 4 | yes | — |
| 39 | D3×C4⋊Dic3 | C22 | 1 | 2 | yes | — |
| 40 | #63888 | C22 | 1 | 4 | yes | — |
| 41 | #63887 | C22 | 1 | 4 | yes | — |
| 42 | #63887 | C22 | 1 | 4 | yes | — |
| 43 | #63883 | C22 | 1 | 2 | yes | — |
| 44 | C4×#624 | C22 | 1 | 1 | yes | characteristic |
| 45 | #63878 | C22 | 1 | 4 | yes | — |
| 46 | #63878 | C22 | 1 | 2 | yes | — |
| 47 | #63878 | C22 | 1 | 2 | yes | — |
| 48 | C4×D3×Dic3 | C22 | 1 | 4 | yes | — |
| 49 | #63872 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #63872 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #63871 | C22 | 1 | 4 | yes | — |
| 52 | #63869 | C22 | 1 | 2 | yes | complemented |
| 53 | #63867 | C22 | 1 | 4 | yes | complemented |
| 54 | #63866 | C22 | 1 | 4 | yes | complemented |
| 55 | #63857 | C22 | 1 | 4 | yes | — |
| 56 | #63855 | C22 | 1 | 2 | yes | — |
| 57 | #63851 | C22 | 1 | 4 | yes | — |
| 58 | #63849 | C22 | 1 | 2 | yes | — |
| 59 | #63846 | C22 | 1 | 4 | yes | complemented |
| 60 | #63846 | C22 | 1 | 4 | yes | complemented |
| 61 | #63843 | C22 | 1 | 4 | yes | complemented |
| 62 | #63843 | C22 | 1 | 4 | yes | complemented |
| 63 | #63841 | C22 | 1 | 2 | yes | — |
| 64 | #63840 | C22 | 1 | 4 | yes | complemented |
| 65 | #63839 | C22 | 1 | 4 | yes | complemented |
| 66 | #63838 | C22 | 1 | 4 | yes | complemented |
| 67 | #63836 | C22 | 1 | 4 | yes | — |
| 68 | C3×#544 | — | 3 | 2 | no | — |
| 69 | #5729 | — | 3 | 2 | no | — |
| 70 | #5729 | — | 3 | 4 | no | — |
| 71 | #5729 | — | 3 | 2 | no | — |
| 72 | #5728 | — | 3 | 4 | no | — |
| 73 | #5728 | — | 3 | 2 | no | — |
| 74 | #5728 | — | 3 | 2 | no | — |
| 75 | #5689 | — | 3 | 2 | no | — |
| 76 | #5689 | — | 3 | 4 | no | — |
| 77 | #5689 | D3 | 1 | 2 | yes | complemented |
| 78 | #5688 | — | 3 | 2 | no | — |
| 79 | #5688 | — | 3 | 4 | no | — |
| 80 | #5688 | — | 3 | 2 | no | — |
| 81 | #5688 | — | 6 | 1 | no | — |
| 82 | #5634 | — | 3 | 4 | no | — |
| 83 | #5634 | — | 3 | 4 | no | — |
| 84 | #5622 | — | 3 | 4 | no | — |
| 85 | #5622 | — | 3 | 4 | no | — |
| 86 | D3×#117 | — | 3 | 2 | no | — |
| 87 | D3×#117 | — | 3 | 2 | no | — |
| 88 | #5519 | — | 3 | 2 | no | — |
| 89 | #5519 | — | 3 | 2 | no | — |
| 90 | C2×#892 | — | 3 | 2 | no | — |
| 91 | #5500 | — | 3 | 2 | no | — |
| 92 | C22×D32 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×C3⋊D3 | C23 | 1 | 2 | yes | — |
| 94 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×#634 | C23 | 1 | 4 | yes | — |
| 96 | C2×C3×C4×D3 | C23 | 1 | 4 | yes | — |
| 97 | C2×C3×C4×D3 | C23 | 1 | 2 | yes | — |
| 98 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 99 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 100 | C2×#627 | C23 | 1 | 4 | yes | — |
| 101 | C2×#624 | C23 | 1 | 2 | yes | — |
| 102 | C2×#624 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×D3×Dic3 | C23 | 1 | 4 | yes | — |
| 104 | C2×D3×Dic3 | C23 | 1 | 2 | yes | — |
| 105 | C4×D32 | Q8 | 1 | 8 | yes | complemented |
| 106 | C32×C4⋊C4 | C23 | 1 | 4 | yes | — |
| 107 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 108 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 109 | #3752 | C23 | 1 | 4 | yes | — |
| 110 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 111 | #3750 | C23 | 1 | 4 | yes | — |
| 112 | #3750 | C23 | 1 | 4 | yes | — |
| 113 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 114 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4×C3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 116 | C3×(C2×D3)⋊C4 | C23 | 1 | 4 | yes | — |
| 117 | C3×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 118 | C3×(C2×D3)⋊C4 | C23 | 1 | 2 | yes | — |
| 119 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 120 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 121 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 122 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 123 | C3×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 124 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 125 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 126 | C3×Dic3⋊C4 | C23 | 1 | 2 | yes | — |
| 127 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 128 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 129 | C3×C4×Dic3 | C23 | 1 | 2 | yes | — |
| 130 | #3724 | C23 | 1 | 4 | yes | — |
| 131 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 132 | Dic3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 133 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 134 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 135 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 136 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 137 | Dic3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 138 | #3722 | C23 | 1 | 4 | yes | — |
| 139 | (C2×D3)⋊Dic3 | C23 | 1 | 4 | yes | — |
| 140 | (C2×D3)⋊Dic3 | C23 | 1 | 2 | yes | — |
| 141 | (C2×D3)⋊Dic3 | C23 | 1 | 2 | yes | — |
| 142 | Dic32 | C23 | 1 | 4 | yes | — |
| 143 | Dic32 | C23 | 1 | 1 | yes | characteristic |
| 144 | Dic32 | C23 | 1 | 4 | yes | — |
| 145 | Dic32 | C23 | 1 | 1 | yes | characteristic |
| 146 | #3458 | — | 9 | 1 | no | Sylow |
| 147 | C22×C4×D3 | — | 3 | 2 | no | — |
| 148 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 149 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 150 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 151 | C3×#125 | — | 2 | 1 | no | — |
| 152 | C3×#125 | — | 3 | 4 | no | — |
| 153 | C3×#125 | — | 3 | 2 | no | — |
| 154 | C3×#125 | C2×D3 | 1 | 2 | yes | complemented |
| 155 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 156 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 157 | C3×#117 | — | 3 | 2 | no | — |
| 158 | C3×#117 | — | 3 | 2 | no | — |
| 159 | C2×C3×C4⋊C4 | — | 3 | 2 | no | — |
| 160 | #946 | — | 3 | 4 | no | — |
| 161 | #946 | — | 3 | 4 | no | — |
| 162 | #946 | — | 3 | 4 | no | — |
| 163 | #946 | — | 3 | 4 | no | — |
| 164 | Q8×Dic3 | — | 3 | 4 | no | — |
| 165 | Q8×Dic3 | — | 3 | 4 | no | — |
| 166 | #944 | — | 3 | 4 | no | — |
| 167 | #944 | — | 3 | 4 | no | — |
| 168 | C2×(C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 169 | #926 | — | 3 | 2 | no | — |
| 170 | #926 | — | 3 | 2 | no | — |
| 171 | C2×C4⋊Dic3 | — | 3 | 2 | no | — |
| 172 | #924 | — | 3 | 4 | no | — |
| 173 | #924 | — | 3 | 4 | no | — |
| 174 | C2×C4×Dic3 | — | 3 | 4 | no | — |
| 175 | #897 | — | 3 | 4 | no | — |
| 176 | #897 | — | 3 | 4 | no | — |
| 177 | #897 | — | 3 | 4 | no | — |
| 178 | #897 | C2×D3 | 1 | 4 | yes | — |
| 179 | #896 | — | 3 | 4 | no | — |
| 180 | #896 | — | 3 | 4 | no | — |
| 181 | #896 | — | 3 | 4 | no | — |
| 182 | #896 | — | 3 | 4 | no | — |
| 183 | #896 | — | 3 | 4 | no | — |
| 184 | #896 | — | 3 | 4 | no | — |
| 185 | #896 | — | 3 | 4 | no | — |
| 186 | #896 | — | 6 | 4 | no | — |
| 187 | #896 | C2×D3 | 1 | 4 | yes | — |
| 188 | #892 | — | 3 | 2 | no | — |
| 189 | #892 | — | 3 | 2 | no | — |
| 190 | #892 | — | 3 | 2 | no | — |
| 191 | #892 | — | 3 | 2 | no | — |
| 192 | #892 | — | 3 | 4 | no | — |
| 193 | #892 | — | 3 | 2 | no | — |
| 194 | #892 | — | 3 | 2 | no | — |
| 195 | #892 | — | 3 | 2 | no | — |
| 196 | #892 | — | 3 | 4 | no | — |
| 197 | #892 | — | 6 | 2 | no | — |
| 198 | #892 | C2×D3 | 1 | 2 | yes | — |
| 199 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 200 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 201 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 202 | D3×C4⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 203 | #890 | — | 3 | 4 | no | — |
| 204 | #890 | — | 3 | 2 | no | — |
| 205 | #890 | — | 3 | 4 | no | — |
| 206 | #890 | — | 3 | 2 | no | — |
| 207 | #890 | — | 3 | 2 | no | — |
| 208 | #890 | C2×D3 | 1 | 2 | yes | complemented |
| 209 | #889 | — | 3 | 4 | no | — |
| 210 | #889 | — | 3 | 4 | no | — |
| 211 | #889 | — | 3 | 4 | no | — |
| 212 | #889 | C2×D3 | 1 | 4 | yes | complemented |
| 213 | #888 | — | 3 | 4 | no | — |
| 214 | #888 | — | 3 | 2 | no | — |
| 215 | #888 | — | 3 | 2 | no | — |
| 216 | #888 | — | 3 | 4 | no | — |
| 217 | #888 | — | 3 | 4 | no | — |
| 218 | #888 | — | 3 | 2 | no | — |
| 219 | #888 | — | 6 | 2 | no | — |
| 220 | #888 | C2×D3 | 1 | 2 | yes | complemented |
| 221 | #888 | C2×D3 | 1 | 4 | yes | complemented |
| 222 | #887 | — | 3 | 4 | no | — |
| 223 | #887 | — | 3 | 4 | no | — |
| 224 | #887 | — | 3 | 4 | no | — |
| 225 | #887 | — | 3 | 4 | no | — |
| 226 | #887 | — | 3 | 4 | no | — |
| 227 | #887 | — | 3 | 4 | no | — |
| 228 | #887 | — | 6 | 4 | no | — |
| 229 | D3×C22⋊C4 | — | 3 | 4 | no | — |
| 230 | D3×C22⋊C4 | — | 3 | 2 | no | — |
| 231 | D3×C22⋊C4 | — | 3 | 2 | no | — |
| 232 | #878 | — | 3 | 4 | no | — |
| 233 | #878 | — | 3 | 4 | no | — |
| 234 | #878 | — | 3 | 4 | no | — |
| 235 | #878 | — | 3 | 4 | no | — |
| 236 | #877 | — | 3 | 4 | no | — |
| 237 | #877 | — | 3 | 2 | no | — |
| 238 | #877 | — | 3 | 2 | no | — |
| 239 | #872 | — | 3 | 2 | no | — |
| 240 | #872 | — | 3 | 4 | no | — |
| 241 | #872 | C2×D3 | 1 | 2 | yes | — |
| 242 | C42×D3 | — | 3 | 4 | no | — |
| 243 | C42×D3 | — | 3 | 2 | no | — |
| 244 | C42×D3 | — | 3 | 2 | no | — |
| 245 | C42×D3 | — | 6 | 1 | no | — |
| 246 | #870 | — | 3 | 2 | no | — |
| 247 | #870 | — | 3 | 2 | no | — |
| 248 | #870 | — | 3 | 4 | no | — |
| 249 | #870 | — | 6 | 1 | no | — |
| 250 | #869 | — | 3 | 4 | no | — |
| 251 | #869 | — | 3 | 2 | no | — |
| 252 | #869 | C2×D3 | 1 | 2 | yes | complemented |
| 253 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 254 | C22×C3×D3 | C24 | 1 | 2 | yes | — |
| 255 | C2×D32 | — | 4 | 2 | no | — |
| 256 | C2×D32 | C2×Q8 | 1 | 4 | yes | — |
| 257 | C2×C32×C4 | C24 | 1 | 4 | yes | — |
| 258 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 259 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 260 | C2×C3⋊Dic3 | C24 | 1 | 4 | yes | — |
| 261 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 262 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 263 | C4×C3⋊D3 | — | 4 | 2 | no | — |
| 264 | C4×C3⋊D3 | C2×Q8 | 1 | 4 | yes | — |
| 265 | #634 | — | 4 | 4 | no | — |
| 266 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 267 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 268 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 269 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 270 | C2×C3×Dic3 | C24 | 1 | 2 | yes | — |
| 271 | C3×C4×D3 | — | 4 | 4 | no | — |
| 272 | C3×C4×D3 | C2×Q8 | 1 | 8 | yes | — |
| 273 | C3×Dic6 | — | 4 | 4 | no | — |
| 274 | C3×Dic6 | — | 4 | 4 | no | — |
| 275 | #627 | — | 4 | 4 | no | — |
| 276 | #624 | — | 4 | 2 | no | — |
| 277 | #624 | C2×Q8 | 1 | 4 | yes | — |
| 278 | D3×Dic3 | — | 4 | 4 | no | — |
| 279 | D3×Dic3 | C2×Q8 | 1 | 8 | yes | — |
| 280 | #544 | — | 3 | 2 | no | — |
| 281 | #544 | — | 9 | 2 | no | — |
| 282 | #544 | — | 9 | 2 | no | — |
| 283 | #544 | — | 9 | 2 | no | — |
| 284 | #544 | — | 9 | 4 | no | — |
| 285 | #543 | — | 9 | 4 | no | — |
| 286 | #533 | — | 9 | 4 | no | — |
| 287 | #533 | — | 9 | 4 | no | — |
| 288 | #533 | — | 9 | 2 | no | — |
| 289 | #533 | — | 9 | 1 | no | — |
| 290 | #533 | — | 9 | 1 | no | — |
| 291 | C2×#117 | — | 9 | 2 | no | — |
| 292 | C2×#117 | — | 9 | 1 | no | — |
| 293 | C23×D3 | — | 3 | 2 | no | — |
| 294 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 295 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 296 | C22×C3×C4 | — | 3 | 2 | no | — |
| 297 | C22×C3×C4 | — | 3 | 4 | no | — |
| 298 | C22×Dic3 | — | 3 | 2 | no | — |
| 299 | C22×Dic3 | — | 3 | 4 | no | — |
| 300 | C2×C4×D3 | — | 3 | 2 | no | — |
| 301 | C2×C4×D3 | — | 3 | 2 | no | — |
| 302 | C2×C4×D3 | — | 3 | 2 | no | — |
| 303 | C2×C4×D3 | — | 3 | 16 | no | — |
| 304 | C2×C4×D3 | — | 3 | 4 | no | — |
| 305 | C2×C4×D3 | — | 3 | 2 | no | — |
| 306 | C2×C4×D3 | — | 3 | 2 | no | — |
| 307 | C2×C4×D3 | — | 3 | 2 | no | — |
| 308 | C2×C4×D3 | — | 3 | 2 | no | — |
| 309 | C2×C4×D3 | — | 6 | 1 | no | — |
| 310 | C2×C4×D3 | — | 6 | 2 | no | — |
| 311 | C2×C4×D3 | C22×D3 | 1 | 4 | yes | — |
| 312 | C2×C4×D3 | C22×D3 | 1 | 2 | yes | — |
| 313 | C2×Dic6 | — | 3 | 4 | no | — |
| 314 | C2×Dic6 | — | 3 | 4 | no | — |
| 315 | C2×Dic6 | — | 3 | 4 | no | — |
| 316 | C2×Dic6 | — | 3 | 4 | no | — |
| 317 | C2×Dic6 | — | 6 | 4 | no | — |
| 318 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 319 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 320 | C3×C4⋊C4 | — | 2 | 4 | no | — |
| 321 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 322 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 323 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 324 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 325 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 326 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 327 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 328 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 329 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 330 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 331 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 332 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 333 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 334 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 335 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 336 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 337 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 338 | C3×C42 | — | 2 | 1 | no | — |
| 339 | C3×C42 | — | 3 | 4 | no | — |
| 340 | C3×C42 | — | 3 | 2 | no | — |
| 341 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 342 | #217 | — | 3 | 4 | no | — |
| 343 | #217 | — | 3 | 2 | no | — |
| 344 | #217 | — | 3 | 2 | no | — |
| 345 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 346 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 347 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 348 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 349 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 350 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 351 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 352 | (C2×D3)⋊C4 | — | 6 | 4 | no | — |
| 353 | (C2×D3)⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 354 | (C2×D3)⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 355 | (C2×D3)⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 356 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 357 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 358 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 359 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 360 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 361 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 362 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 363 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 364 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 365 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 366 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 367 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 368 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 369 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 370 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 371 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 372 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 373 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 374 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 375 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 376 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 377 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 378 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 379 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 380 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 381 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 382 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 383 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 384 | Dic3⋊C4 | — | 6 | 4 | no | — |
| 385 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 386 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 387 | Dic3⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 388 | Dic3⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 389 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 390 | C4×Dic3 | — | 3 | 2 | no | — |
| 391 | C4×Dic3 | — | 3 | 2 | no | — |
| 392 | C4×Dic3 | — | 3 | 4 | no | — |
| 393 | C4×Dic3 | — | 3 | 2 | no | — |
| 394 | C4×Dic3 | — | 3 | 4 | no | — |
| 395 | C4×Dic3 | — | 3 | 4 | no | — |
| 396 | C4×Dic3 | — | 3 | 2 | no | — |
| 397 | C4×Dic3 | — | 3 | 4 | no | — |
| 398 | C4×Dic3 | — | 3 | 2 | no | — |
| 399 | C4×Dic3 | — | 3 | 4 | no | — |
| 400 | C4×Dic3 | — | 3 | 4 | no | — |
| 401 | C4×Dic3 | — | 6 | 2 | no | — |
| 402 | C4×Dic3 | — | 6 | 1 | no | — |
| 403 | C4×Dic3 | — | 6 | 4 | no | — |
| 404 | C4×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 405 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 406 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 407 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 408 | C2×C3⋊D3 | C22×Q8 | 1 | 2 | yes | — |
| 409 | C2×C3×D3 | — | 2 | 2 | no | — |
| 410 | C2×C3×D3 | — | 2 | 2 | no | — |
| 411 | C2×C3×D3 | C22×Q8 | 1 | 4 | yes | — |
| 412 | D32 | — | 4 | 4 | no | — |
| 413 | C32×C4 | — | 2 | 2 | no | — |
| 414 | C32×C4 | — | 2 | 4 | no | — |
| 415 | C32×C4 | C22×Q8 | 1 | 2 | yes | — |
| 416 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 417 | C3⋊Dic3 | — | 2 | 4 | no | — |
| 418 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 419 | C3×Dic3 | — | 2 | 4 | no | — |
| 420 | C3×Dic3 | — | 2 | 2 | no | — |
| 421 | C3×Dic3 | — | 2 | 2 | no | — |
| 422 | C3×Dic3 | — | 2 | 4 | no | — |
| 423 | C3×Dic3 | C22×Q8 | 1 | 4 | yes | — |
| 424 | C23×C4 | — | 9 | 1 | no | — |
| 425 | C4⋊Q8 | — | 3 | 4 | no | — |
| 426 | C4⋊Q8 | — | 3 | 2 | no | — |
| 427 | C4⋊Q8 | — | 3 | 2 | no | — |
| 428 | C4⋊Q8 | — | 9 | 2 | no | — |
| 429 | C4⋊Q8 | — | 9 | 4 | no | — |
| 430 | C4⋊Q8 | — | 9 | 4 | no | — |
| 431 | C4⋊Q8 | — | 9 | 4 | no | — |
| 432 | C4⋊Q8 | — | 9 | 2 | no | — |
| 433 | #125 | — | 3 | 4 | no | — |
| 434 | #125 | — | 3 | 2 | no | — |
| 435 | #125 | — | 9 | 4 | no | — |
| 436 | #125 | — | 9 | 2 | no | — |
| 437 | #125 | — | 9 | 4 | no | — |
| 438 | #125 | — | 9 | 4 | no | — |
| 439 | #125 | — | 9 | 1 | no | — |
| 440 | #125 | — | 9 | 1 | no | — |
| 441 | #125 | — | 9 | 1 | no | — |
| 442 | #125 | D32 | 1 | 1 | yes | characteristic, complemented |
| 443 | C22⋊Q8 | — | 3 | 4 | no | — |
| 444 | C22⋊Q8 | — | 3 | 4 | no | — |
| 445 | C22⋊Q8 | — | 9 | 4 | no | — |
| 446 | C22⋊Q8 | — | 9 | 4 | no | — |
| 447 | C22⋊Q8 | — | 9 | 4 | no | — |
| 448 | C22⋊Q8 | — | 9 | 4 | no | — |
| 449 | C22⋊Q8 | — | 9 | 4 | no | — |
| 450 | C22⋊Q8 | — | 9 | 4 | no | — |
| 451 | C22⋊Q8 | — | 9 | 4 | no | — |
| 452 | C22⋊Q8 | — | 9 | 4 | no | — |
| 453 | C22⋊Q8 | — | 9 | 4 | no | — |
| 454 | C22⋊Q8 | — | 9 | 4 | no | — |
| 455 | C4×Q8 | — | 9 | 4 | no | — |
| 456 | C4×Q8 | — | 9 | 4 | no | — |
| 457 | C4×Q8 | — | 9 | 4 | no | — |
| 458 | C4×Q8 | — | 9 | 4 | no | — |
| 459 | #117 | — | 3 | 2 | no | — |
| 460 | #117 | — | 3 | 2 | no | — |
| 461 | #117 | — | 9 | 4 | no | — |
| 462 | #117 | — | 9 | 2 | no | — |
| 463 | #117 | — | 9 | 4 | no | — |
| 464 | #117 | — | 9 | 2 | no | — |
| 465 | #117 | — | 9 | 2 | no | — |
| 466 | #117 | — | 9 | 2 | no | — |
| 467 | #117 | — | 9 | 2 | no | — |
| 468 | #117 | — | 9 | 2 | no | — |
| 469 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 470 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 471 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 472 | C2×C22⋊C4 | — | 9 | 2 | no | — |
| 473 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 474 | C2×C42 | — | 9 | 1 | no | — |
| 475 | C2×C42 | — | 9 | 4 | no | — |
| 476 | C2×C42 | — | 9 | 1 | no | — |
| 477 | C23×C3 | — | 3 | 2 | no | — |
| 478 | C22×D3 | — | 3 | 2 | no | — |
| 479 | C22×D3 | — | 3 | 8 | no | — |
| 480 | C22×D3 | — | 6 | 1 | no | — |
| 481 | C22×D3 | — | 12 | 2 | no | — |
| 482 | C22×D3 | — | 12 | 2 | no | — |
| 483 | C22×D3 | C23×D3 | 1 | 2 | yes | — |
| 484 | C3×Q8 | — | 12 | 4 | no | — |
| 485 | C3×Q8 | — | 12 | 4 | no | — |
| 486 | C2×C3×C4 | — | 2 | 1 | no | — |
| 487 | C2×C3×C4 | — | 2 | 2 | no | — |
| 488 | C2×C3×C4 | — | 2 | 4 | no | — |
| 489 | C2×C3×C4 | — | 3 | 2 | no | — |
| 490 | C2×C3×C4 | — | 3 | 8 | no | — |
| 491 | C2×C3×C4 | — | 3 | 4 | no | — |
| 492 | C2×C3×C4 | — | 3 | 2 | no | — |
| 493 | C2×C3×C4 | — | 3 | 4 | no | — |
| 494 | C2×C3×C4 | — | 3 | 2 | no | — |
| 495 | C2×C3×C4 | — | 12 | 4 | no | — |
| 496 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 497 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 498 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 499 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 500 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 501 | C2×Dic3 | — | 3 | 2 | no | — |
| 502 | C2×Dic3 | — | 3 | 8 | no | — |
| 503 | C2×Dic3 | — | 3 | 4 | no | — |
| 504 | C2×Dic3 | — | 3 | 2 | no | — |
| 505 | C2×Dic3 | — | 3 | 4 | no | — |
| 506 | C2×Dic3 | — | 3 | 2 | no | — |
| 507 | C2×Dic3 | — | 6 | 1 | no | — |
| 508 | C2×Dic3 | — | 6 | 2 | no | — |
| 509 | C2×Dic3 | — | 6 | 4 | no | — |
| 510 | C2×Dic3 | — | 12 | 4 | no | — |
| 511 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 512 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 513 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 514 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 515 | C2×Dic3 | C23×D3 | 1 | 2 | yes | — |
| 516 | C4×D3 | — | 3 | 8 | no | — |
| 517 | C4×D3 | — | 3 | 8 | no | — |
| 518 | C4×D3 | — | 3 | 8 | no | — |
| 519 | C4×D3 | — | 4 | 4 | no | — |
| 520 | C4×D3 | — | 6 | 4 | no | — |
| 521 | C4×D3 | — | 12 | 2 | no | — |
| 522 | C4×D3 | — | 12 | 2 | no | — |
| 523 | C4×D3 | — | 12 | 2 | no | — |
| 524 | C4×D3 | — | 12 | 2 | no | — |
| 525 | C4×D3 | — | 12 | 4 | no | — |
| 526 | C4×D3 | — | 12 | 4 | no | — |
| 527 | C4×D3 | D3×Q8 | 1 | 8 | yes | — |
| 528 | Dic6 | — | 4 | 4 | no | — |
| 529 | Dic6 | — | 4 | 4 | no | — |
| 530 | Dic6 | — | 12 | 4 | no | — |
| 531 | Dic6 | — | 12 | 4 | no | — |
| 532 | Dic6 | — | 12 | 4 | no | — |
| 533 | Dic6 | — | 12 | 4 | no | — |
| 534 | Dic6 | — | 12 | 8 | no | — |
| 535 | C2×C32 | C23×Q8 | 1 | 1 | yes | characteristic |
| 536 | C2×C32 | #585 | 1 | 2 | yes | — |
| 537 | C3⋊D3 | — | 2 | 2 | no | — |
| 538 | C3×D3 | — | 2 | 4 | no | — |
| 539 | C24 | — | 9 | 1 | no | — |
| 540 | C2×Q8 | — | 3 | 4 | no | — |
| 541 | C2×Q8 | — | 3 | 4 | no | — |
| 542 | C2×Q8 | — | 9 | 4 | no | — |
| 543 | C2×Q8 | — | 9 | 4 | no | — |
| 544 | C22×C4 | — | 3 | 2 | no | — |
| 545 | C22×C4 | — | 3 | 4 | no | — |
| 546 | C22×C4 | — | 9 | 1 | no | — |
| 547 | C22×C4 | — | 9 | 8 | no | — |
| 548 | C22×C4 | — | 9 | 2 | no | — |
| 549 | C22×C4 | — | 9 | 2 | no | — |
| 550 | C22×C4 | — | 9 | 4 | no | — |
| 551 | C22×C4 | — | 9 | 1 | no | — |
| 552 | C22×C4 | — | 9 | 2 | no | — |
| 553 | C4⋊C4 | — | 3 | 4 | no | — |
| 554 | C4⋊C4 | — | 3 | 2 | no | — |
| 555 | C4⋊C4 | — | 3 | 2 | no | — |
| 556 | C4⋊C4 | — | 3 | 2 | no | — |
| 557 | C4⋊C4 | — | 3 | 2 | no | — |
| 558 | C4⋊C4 | — | 3 | 4 | no | — |
| 559 | C4⋊C4 | — | 3 | 4 | no | — |
| 560 | C4⋊C4 | — | 3 | 4 | no | — |
| 561 | C4⋊C4 | — | 3 | 4 | no | — |
| 562 | C4⋊C4 | — | 9 | 2 | no | — |
| 563 | C4⋊C4 | — | 9 | 2 | no | — |
| 564 | C4⋊C4 | — | 9 | 4 | no | — |
| 565 | C4⋊C4 | — | 9 | 4 | no | — |
| 566 | C4⋊C4 | — | 9 | 4 | no | — |
| 567 | C4⋊C4 | — | 9 | 4 | no | — |
| 568 | C4⋊C4 | — | 9 | 4 | no | — |
| 569 | C4⋊C4 | — | 9 | 4 | no | — |
| 570 | C4⋊C4 | — | 9 | 2 | no | — |
| 571 | C4⋊C4 | — | 9 | 4 | no | — |
| 572 | C4⋊C4 | — | 9 | 4 | no | — |
| 573 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 574 | C4⋊C4 | C2×D32 | 1 | 4 | yes | — |
| 575 | C22⋊C4 | — | 3 | 2 | no | — |
| 576 | C22⋊C4 | — | 3 | 4 | no | — |
| 577 | C22⋊C4 | — | 3 | 2 | no | — |
| 578 | C22⋊C4 | — | 9 | 4 | no | — |
| 579 | C22⋊C4 | — | 9 | 2 | no | — |
| 580 | C22⋊C4 | — | 9 | 2 | no | — |
| 581 | C22⋊C4 | — | 9 | 4 | no | — |
| 582 | C22⋊C4 | — | 9 | 4 | no | — |
| 583 | C42 | — | 3 | 4 | no | — |
| 584 | C42 | — | 3 | 2 | no | — |
| 585 | C42 | — | 9 | 1 | no | — |
| 586 | C42 | — | 9 | 1 | no | — |
| 587 | C42 | — | 9 | 4 | no | — |
| 588 | C42 | — | 9 | 4 | no | — |
| 589 | C42 | — | 9 | 4 | no | — |
| 590 | C42 | — | 9 | 2 | no | — |
| 591 | C42 | — | 9 | 1 | no | — |
| 592 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 593 | C22×C3 | — | 2 | 1 | no | — |
| 594 | C22×C3 | — | 3 | 4 | no | — |
| 595 | C22×C3 | — | 6 | 2 | no | — |
| 596 | C22×C3 | — | 6 | 2 | no | — |
| 597 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 598 | C2×D3 | — | 2 | 2 | no | — |
| 599 | C2×D3 | — | 2 | 2 | no | — |
| 600 | C2×D3 | — | 3 | 4 | no | — |
| 601 | C2×D3 | — | 6 | 2 | no | — |
| 602 | C2×D3 | — | 6 | 2 | no | — |
| 603 | C2×D3 | — | 6 | 2 | no | — |
| 604 | C2×D3 | — | 12 | 2 | no | — |
| 605 | C2×D3 | — | 12 | 8 | no | — |
| 606 | C2×D3 | C2×D3×Q8 | 1 | 4 | yes | — |
| 607 | C3×C4 | — | 2 | 2 | no | — |
| 608 | C3×C4 | — | 2 | 4 | no | — |
| 609 | C3×C4 | — | 2 | 4 | no | — |
| 610 | C3×C4 | — | 2 | 2 | no | — |
| 611 | C3×C4 | — | 2 | 2 | no | — |
| 612 | C3×C4 | — | 3 | 4 | no | — |
| 613 | C3×C4 | — | 4 | 4 | no | — |
| 614 | C3×C4 | — | 4 | 2 | no | — |
| 615 | C3×C4 | — | 6 | 2 | no | — |
| 616 | C3×C4 | — | 6 | 4 | no | — |
| 617 | C3×C4 | — | 6 | 2 | no | — |
| 618 | C3×C4 | — | 6 | 4 | no | — |
| 619 | C3×C4 | C2×D3×Q8 | 1 | 4 | yes | — |
| 620 | Dic3 | — | 2 | 2 | no | — |
| 621 | Dic3 | — | 2 | 4 | no | — |
| 622 | Dic3 | — | 2 | 4 | no | — |
| 623 | Dic3 | — | 2 | 2 | no | — |
| 624 | Dic3 | — | 3 | 4 | no | — |
| 625 | Dic3 | — | 6 | 2 | no | — |
| 626 | Dic3 | — | 6 | 4 | no | — |
| 627 | Dic3 | — | 6 | 2 | no | — |
| 628 | Dic3 | — | 6 | 4 | no | — |
| 629 | Dic3 | — | 6 | 2 | no | — |
| 630 | Dic3 | — | 6 | 4 | no | — |
| 631 | Dic3 | — | 12 | 4 | no | — |
| 632 | Dic3 | C2×D3×Q8 | 1 | 4 | yes | — |
| 633 | C32 | #3458 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 634 | C23 | — | 3 | 2 | no | — |
| 635 | C23 | — | 9 | 4 | no | — |
| 636 | C23 | — | 9 | 1 | no | — |
| 637 | C23 | — | 36 | 2 | no | — |
| 638 | Q8 | — | 12 | 4 | no | — |
| 639 | Q8 | — | 12 | 4 | no | — |
| 640 | Q8 | — | 36 | 4 | no | — |
| 641 | Q8 | — | 36 | 4 | no | — |
| 642 | C2×C4 | — | 3 | 2 | no | — |
| 643 | C2×C4 | — | 3 | 8 | no | — |
| 644 | C2×C4 | — | 3 | 2 | no | — |
| 645 | C2×C4 | — | 3 | 4 | no | — |
| 646 | C2×C4 | — | 3 | 2 | no | — |
| 647 | C2×C4 | — | 3 | 4 | no | — |
| 648 | C2×C4 | — | 9 | 4 | no | — |
| 649 | C2×C4 | — | 9 | 8 | no | — |
| 650 | C2×C4 | — | 9 | 1 | no | — |
| 651 | C2×C4 | — | 9 | 4 | no | — |
| 652 | C2×C4 | — | 9 | 2 | no | — |
| 653 | C2×C4 | — | 9 | 4 | no | — |
| 654 | C2×C4 | — | 12 | 4 | no | — |
| 655 | C2×C4 | — | 36 | 2 | no | — |
| 656 | C2×C4 | — | 36 | 2 | no | — |
| 657 | C2×C4 | — | 36 | 4 | no | — |
| 658 | C2×C4 | C22×D32 | 1 | 4 | yes | — |
| 659 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 660 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 661 | C2×C3 | — | 2 | 1 | no | — |
| 662 | C2×C3 | — | 2 | 2 | no | — |
| 663 | C2×C3 | — | 6 | 4 | no | — |
| 664 | C2×C3 | C22×D3×Q8 | 1 | 2 | yes | — |
| 665 | C2×C3 | #5966 | 1 | 2 | yes | — |
| 666 | C2×C3 | #5968 | 1 | 2 | yes | — |
| 667 | D3 | — | 2 | 4 | no | — |
| 668 | D3 | — | 6 | 4 | no | — |
| 669 | D3 | — | 12 | 2 | no | — |
| 670 | C22 | — | 3 | 4 | no | — |
| 671 | C22 | — | 6 | 2 | no | — |
| 672 | C22 | — | 6 | 2 | no | — |
| 673 | C22 | — | 9 | 2 | no | — |
| 674 | C22 | — | 18 | 2 | no | — |
| 675 | C22 | — | 36 | 4 | no | — |
| 676 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 677 | C4 | — | 2 | 4 | no | — |
| 678 | C4 | — | 2 | 2 | no | — |
| 679 | C4 | — | 3 | 4 | no | — |
| 680 | C4 | — | 6 | 4 | no | — |
| 681 | C4 | — | 6 | 2 | no | — |
| 682 | C4 | — | 6 | 4 | no | — |
| 683 | C4 | — | 6 | 2 | no | — |
| 684 | C4 | — | 9 | 2 | no | — |
| 685 | C4 | — | 18 | 2 | no | — |
| 686 | C4 | — | 18 | 4 | no | — |
| 687 | C4 | D32×Q8 | 1 | 2 | yes | — |
| 688 | C3 | — | 2 | 1 | no | — |
| 689 | C3 | #86581 | 1 | 2 | yes | complemented |
| 690 | C2 | — | 6 | 4 | no | — |
| 691 | C2 | — | 18 | 2 | no | — |
| 692 | C2 | C2×D32×Q8 | 1 | 1 | yes | characteristic |
| 693 | C2 | #10596698 | 1 | 2 | yes | — |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×#125 | C22 |
| prime radical | C22×D32 | C23 |
| hypercenter | #125 | D32 |
| hypocenter | C32 | #3458 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596159 | C2 | semidirect |
| 2. C3×#5689 | C2 | semidirect |
| 5. #10594502 | C2 | semidirect |
| 6. #10594448 | C2 | semidirect |
| 7. #10594400 | C2 | semidirect |
| 8. #10594388 | C2 | semidirect |
| 9. #10594387 | C2 | semidirect |
| 10. #10594344 | C2 | semidirect |
| 12. #10593954 | C2 | semidirect |
| 13. #10593866 | C2 | semidirect |
| 16. C32×#125 | C22 | semidirect |
| 19. #64097 | C22 | semidirect |
| 20. #64096 | C22 | semidirect |
| 22. #64079 | C22 | semidirect |
| 27. C3×#890 | C22 | semidirect |
| 28. C3×#889 | C22 | semidirect |
| 29. C3×#888 | C22 | semidirect |
| 30. C3×#888 | C22 | semidirect |
| 32. C3×#869 | C22 | semidirect |
| 35. #63918 | C22 | semidirect |
| 49. #63872 | C22 | semidirect |
| 50. #63872 | C22 | semidirect |
| 52. #63869 | C22 | semidirect |
| 53. #63867 | C22 | semidirect |
| 54. #63866 | C22 | semidirect |
| 59. #63846 | C22 | semidirect |
| 60. #63846 | C22 | semidirect |
| 61. #63843 | C22 | semidirect |
| 62. #63843 | C22 | semidirect |
| 64. #63840 | C22 | semidirect |
| 65. #63839 | C22 | semidirect |
| 66. #63838 | C22 | semidirect |
| 77. #5689 | D3 | semidirect |
| 105. C4×D32 | Q8 | semidirect |
| 154. C3×#125 | C2×D3 | semidirect |
| 208. #890 | C2×D3 | semidirect |
| 212. #889 | C2×D3 | semidirect |
| 220. #888 | C2×D3 | semidirect |
| 221. #888 | C2×D3 | semidirect |
| 252. #869 | C2×D3 | semidirect |
| 442. #125 | D32 | semidirect |
| 633. C32 | #3458 | semidirect |
| 689. C3 | #86581 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596159 | 2 |
| C3×#5689 | 2 |
| #10594635 | 2 |
| D3×#892 | 2 |
| #10594502 | 2 |
| #10594448 | 2 |
| #10594400 | 2 |
| #10594388 | 2 |
| #10594387 | 2 |
| #10594344 | 2 |
| #10593992 | 2 |
| #10593954 | 2 |
| #10593866 | 2 |
| #86581 | 3 |