Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2039 conjugacy classes of subgroups.
The subgroup lattice has 740 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596049 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5567 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #10595421 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595375 | C2 | 1 | 2 | yes | maximal |
| 5 | #10594596 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #10594401 | C2 | 1 | 2 | yes | maximal |
| 7 | #10594398 | C2 | 1 | 4 | yes | maximal |
| 8 | #10594315 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4×#3797 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #10593856 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10593855 | C2 | 1 | 2 | yes | maximal |
| 12 | #10593854 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #10593853 | C2 | 1 | 2 | yes | maximal, complemented |
| 14 | #10593853 | C2 | 1 | 2 | yes | maximal, complemented |
| 15 | #10593848 | C2 | 1 | 2 | yes | maximal |
| 16 | #87032 | — | 3 | 2 | no | maximal |
| 17 | C2×#3797 | C22 | 1 | 1 | yes | characteristic |
| 18 | C32×C4×Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | #64155 | C22 | 1 | 1 | yes | characteristic |
| 20 | #64153 | C22 | 1 | 1 | yes | characteristic |
| 21 | #64106 | C22 | 1 | 1 | yes | characteristic |
| 22 | #64105 | C22 | 1 | 2 | yes | — |
| 23 | #64098 | C22 | 1 | 2 | yes | — |
| 24 | #64097 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64081 | C22 | 1 | 2 | yes | — |
| 26 | C42×C3⋊D3 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×#634 | C22 | 1 | 1 | yes | characteristic |
| 28 | C4×#634 | C22 | 1 | 2 | yes | — |
| 29 | C3×#944 | C22 | 1 | 4 | yes | — |
| 30 | C3×#889 | C22 | 1 | 4 | yes | — |
| 31 | C3×#889 | C22 | 1 | 4 | yes | — |
| 32 | C3×#887 | C22 | 1 | 4 | yes | — |
| 33 | C3×#870 | C22 | 1 | 2 | yes | — |
| 34 | C3×#870 | C22 | 1 | 2 | yes | — |
| 35 | C3×#869 | C22 | 1 | 2 | yes | — |
| 36 | C3×C4×Dic6 | C22 | 1 | 2 | yes | — |
| 37 | C3×C4×Dic6 | C22 | 1 | 2 | yes | — |
| 38 | C3×C4×Dic6 | C22 | 1 | 2 | yes | — |
| 39 | #63919 | C22 | 1 | 1 | yes | characteristic |
| 40 | #63919 | C22 | 1 | 2 | yes | — |
| 41 | #63919 | C22 | 1 | 1 | yes | characteristic |
| 42 | #63918 | C22 | 1 | 4 | yes | — |
| 43 | C4×#627 | C22 | 1 | 2 | yes | — |
| 44 | #63900 | C22 | 1 | 1 | yes | characteristic |
| 45 | #63895 | C22 | 1 | 4 | yes | — |
| 46 | #63888 | C22 | 1 | 4 | yes | — |
| 47 | #63883 | C22 | 1 | 2 | yes | — |
| 48 | C4×#624 | C22 | 1 | 2 | yes | — |
| 49 | #63872 | C22 | 1 | 2 | yes | — |
| 50 | #63867 | C22 | 1 | 4 | yes | — |
| 51 | #63867 | C22 | 1 | 4 | yes | — |
| 52 | #63865 | C22 | 1 | 2 | yes | — |
| 53 | #63865 | C22 | 1 | 2 | yes | — |
| 54 | #63849 | C22 | 1 | 2 | yes | — |
| 55 | #63847 | C22 | 1 | 4 | yes | — |
| 56 | #63845 | C22 | 1 | 4 | yes | — |
| 57 | #63845 | C22 | 1 | 4 | yes | — |
| 58 | #63844 | C22 | 1 | 4 | yes | — |
| 59 | #63843 | C22 | 1 | 2 | yes | — |
| 60 | #63843 | C22 | 1 | 2 | yes | — |
| 61 | #63843 | C22 | 1 | 2 | yes | — |
| 62 | #63840 | C22 | 1 | 4 | yes | — |
| 63 | #63840 | C22 | 1 | 4 | yes | — |
| 64 | #63839 | C22 | 1 | 4 | yes | — |
| 65 | #63839 | C22 | 1 | 4 | yes | — |
| 66 | #63839 | C22 | 1 | 4 | yes | — |
| 67 | #63838 | C22 | 1 | 2 | yes | — |
| 68 | #63838 | C22 | 1 | 2 | yes | — |
| 69 | #63838 | C22 | 1 | 2 | yes | — |
| 70 | #63837 | C22 | 1 | 4 | yes | — |
| 71 | #63837 | C22 | 1 | 4 | yes | — |
| 72 | #63837 | C22 | 1 | 4 | yes | — |
| 73 | #63837 | C22 | 1 | 4 | yes | — |
| 74 | #63836 | C22 | 1 | 4 | yes | — |
| 75 | #63836 | C22 | 1 | 4 | yes | — |
| 76 | C3×#557 | — | 3 | 2 | no | — |
| 77 | #5729 | — | 3 | 4 | no | — |
| 78 | #5729 | — | 3 | 2 | no | — |
| 79 | #5722 | — | 3 | 4 | no | — |
| 80 | #5722 | — | 3 | 2 | no | — |
| 81 | #5689 | — | 3 | 4 | no | — |
| 82 | #5689 | — | 3 | 2 | no | — |
| 83 | #5688 | — | 3 | 4 | no | — |
| 84 | #5688 | — | 3 | 2 | no | — |
| 85 | #5685 | — | 3 | 4 | no | — |
| 86 | #5685 | — | 3 | 4 | no | — |
| 87 | #5685 | — | 3 | 2 | no | — |
| 88 | #5685 | — | 3 | 2 | no | — |
| 89 | #5578 | — | 3 | 2 | no | — |
| 90 | #5578 | — | 3 | 4 | no | — |
| 91 | #5578 | — | 6 | 1 | no | — |
| 92 | #5572 | — | 3 | 2 | no | — |
| 93 | #5572 | — | 3 | 2 | no | — |
| 94 | C4×D3×Q8 | — | 3 | 2 | no | — |
| 95 | #5569 | — | 3 | 2 | no | — |
| 96 | #5569 | — | 3 | 2 | no | — |
| 97 | #5567 | — | 3 | 4 | no | — |
| 98 | #5567 | D3 | 1 | 2 | yes | complemented |
| 99 | Q8×Dic6 | — | 3 | 2 | no | — |
| 100 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 102 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×C4×C3⋊D3 | C23 | 1 | 1 | yes | characteristic |
| 104 | C2×#634 | C23 | 1 | 2 | yes | — |
| 105 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 106 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 107 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 108 | C2×#627 | C23 | 1 | 2 | yes | — |
| 109 | C2×#627 | C23 | 1 | 4 | yes | — |
| 110 | C2×#627 | C23 | 1 | 2 | yes | — |
| 111 | C2×#627 | C23 | 1 | 2 | yes | — |
| 112 | C2×#624 | C23 | 1 | 2 | yes | — |
| 113 | C2×#624 | C23 | 1 | 2 | yes | — |
| 114 | #3797 | Q8 | 1 | 8 | yes | complemented |
| 115 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 116 | C32×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 117 | C32×C42 | C23 | 1 | 1 | yes | characteristic |
| 118 | C32×C42 | C23 | 1 | 2 | yes | — |
| 119 | #3752 | C23 | 1 | 2 | yes | — |
| 120 | #3752 | C23 | 1 | 2 | yes | — |
| 121 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 122 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 123 | #3750 | C23 | 1 | 2 | yes | — |
| 124 | #3750 | C23 | 1 | 2 | yes | — |
| 125 | #3750 | C23 | 1 | 2 | yes | — |
| 126 | #3750 | C23 | 1 | 2 | yes | — |
| 127 | #3750 | C23 | 1 | 2 | yes | — |
| 128 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 129 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 130 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 132 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 133 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 134 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 135 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 136 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 137 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 138 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 139 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 140 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 141 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 142 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 143 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 144 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 145 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 146 | #3724 | C23 | 1 | 2 | yes | — |
| 147 | #3724 | C23 | 1 | 2 | yes | — |
| 148 | #3724 | C23 | 1 | 2 | yes | — |
| 149 | #3724 | C23 | 1 | 4 | yes | — |
| 150 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 151 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 152 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 153 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 154 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 155 | #3722 | C23 | 1 | 4 | yes | — |
| 156 | Dic32 | C23 | 1 | 4 | yes | — |
| 157 | Dic32 | C23 | 1 | 4 | yes | — |
| 158 | Dic32 | C23 | 1 | 4 | yes | — |
| 159 | Dic32 | C23 | 1 | 4 | yes | — |
| 160 | #3502 | — | 9 | 1 | no | Sylow |
| 161 | C2×D3×Q8 | — | 3 | 2 | no | — |
| 162 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 163 | C3×C4⋊Q8 | — | 3 | 2 | no | — |
| 164 | C3×#125 | — | 3 | 4 | no | — |
| 165 | C3×#125 | — | 3 | 4 | no | — |
| 166 | C3×#125 | — | 3 | 2 | no | — |
| 167 | C3×#125 | — | 3 | 2 | no | — |
| 168 | C3×C4×Q8 | — | 2 | 1 | no | — |
| 169 | C3×C4×Q8 | — | 3 | 4 | no | — |
| 170 | C3×C4×Q8 | — | 3 | 2 | no | — |
| 171 | C3×C4×Q8 | — | 3 | 2 | no | — |
| 172 | C3×C4×Q8 | — | 3 | 2 | no | — |
| 173 | C3×C4×Q8 | C2×D3 | 1 | 2 | yes | — |
| 174 | #946 | — | 3 | 2 | no | — |
| 175 | #946 | — | 3 | 4 | no | — |
| 176 | #946 | — | 6 | 1 | no | — |
| 177 | Q8×Dic3 | — | 3 | 2 | no | — |
| 178 | Q8×Dic3 | — | 3 | 2 | no | — |
| 179 | Q8×Dic3 | — | 3 | 2 | no | — |
| 180 | #944 | — | 3 | 2 | no | — |
| 181 | #944 | — | 3 | 4 | no | — |
| 182 | #944 | — | 3 | 4 | no | — |
| 183 | #944 | — | 3 | 4 | no | — |
| 184 | #944 | — | 6 | 1 | no | — |
| 185 | #944 | C2×D3 | 1 | 4 | yes | — |
| 186 | #897 | — | 3 | 2 | no | — |
| 187 | #897 | — | 3 | 4 | no | — |
| 188 | #897 | — | 6 | 1 | no | — |
| 189 | #896 | — | 3 | 4 | no | — |
| 190 | #896 | — | 3 | 2 | no | — |
| 191 | #896 | — | 3 | 2 | no | — |
| 192 | #896 | — | 3 | 4 | no | — |
| 193 | #896 | — | 3 | 4 | no | — |
| 194 | #896 | — | 3 | 4 | no | — |
| 195 | #896 | — | 6 | 2 | no | — |
| 196 | #892 | — | 3 | 2 | no | — |
| 197 | #892 | — | 3 | 2 | no | — |
| 198 | #892 | — | 3 | 4 | no | — |
| 199 | #892 | — | 3 | 4 | no | — |
| 200 | D3×C4⋊C4 | — | 3 | 2 | no | — |
| 201 | D3×C4⋊C4 | — | 3 | 4 | no | — |
| 202 | #890 | — | 3 | 2 | no | — |
| 203 | #890 | — | 3 | 2 | no | — |
| 204 | #890 | — | 3 | 4 | no | — |
| 205 | #890 | — | 3 | 4 | no | — |
| 206 | #889 | — | 3 | 2 | no | — |
| 207 | #889 | — | 3 | 2 | no | — |
| 208 | #889 | — | 3 | 4 | no | — |
| 209 | #889 | — | 3 | 4 | no | — |
| 210 | #889 | — | 3 | 4 | no | — |
| 211 | #889 | — | 3 | 4 | no | — |
| 212 | #889 | — | 3 | 4 | no | — |
| 213 | #889 | — | 3 | 4 | no | — |
| 214 | #889 | — | 6 | 2 | no | — |
| 215 | #889 | C2×D3 | 1 | 4 | yes | — |
| 216 | #889 | C2×D3 | 1 | 4 | yes | — |
| 217 | #888 | — | 3 | 4 | no | — |
| 218 | #888 | — | 3 | 4 | no | — |
| 219 | #888 | — | 3 | 4 | no | — |
| 220 | #888 | — | 3 | 2 | no | — |
| 221 | #888 | — | 3 | 2 | no | — |
| 222 | #888 | — | 3 | 2 | no | — |
| 223 | #888 | — | 3 | 2 | no | — |
| 224 | #888 | — | 3 | 2 | no | — |
| 225 | #888 | — | 3 | 4 | no | — |
| 226 | #888 | — | 3 | 4 | no | — |
| 227 | #888 | — | 3 | 4 | no | — |
| 228 | #888 | — | 3 | 4 | no | — |
| 229 | #888 | — | 3 | 4 | no | — |
| 230 | #888 | — | 6 | 1 | no | — |
| 231 | #887 | — | 3 | 2 | no | — |
| 232 | #887 | — | 3 | 2 | no | — |
| 233 | #887 | — | 3 | 2 | no | — |
| 234 | #887 | — | 3 | 4 | no | — |
| 235 | #887 | — | 3 | 4 | no | — |
| 236 | #887 | — | 3 | 4 | no | — |
| 237 | #887 | — | 3 | 4 | no | — |
| 238 | #887 | — | 3 | 4 | no | — |
| 239 | #887 | — | 3 | 4 | no | — |
| 240 | #887 | — | 3 | 4 | no | — |
| 241 | #887 | — | 3 | 4 | no | — |
| 242 | #887 | C2×D3 | 1 | 4 | yes | — |
| 243 | #872 | — | 3 | 2 | no | — |
| 244 | #872 | — | 3 | 2 | no | — |
| 245 | #872 | — | 3 | 4 | no | — |
| 246 | #872 | — | 3 | 4 | no | — |
| 247 | #872 | — | 6 | 2 | no | — |
| 248 | C42×D3 | — | 3 | 2 | no | — |
| 249 | C42×D3 | — | 3 | 4 | no | — |
| 250 | C42×D3 | — | 6 | 1 | no | — |
| 251 | #870 | — | 3 | 4 | no | — |
| 252 | #870 | — | 3 | 4 | no | — |
| 253 | #870 | C2×D3 | 1 | 2 | yes | — |
| 254 | #870 | C2×D3 | 1 | 2 | yes | — |
| 255 | #869 | — | 3 | 4 | no | — |
| 256 | #869 | C2×D3 | 1 | 2 | yes | — |
| 257 | C4×Dic6 | — | 3 | 2 | no | — |
| 258 | C4×Dic6 | — | 3 | 2 | no | — |
| 259 | C4×Dic6 | — | 3 | 2 | no | — |
| 260 | C4×Dic6 | — | 3 | 4 | no | — |
| 261 | C4×Dic6 | — | 3 | 4 | no | — |
| 262 | C4×Dic6 | — | 3 | 4 | no | — |
| 263 | C4×Dic6 | — | 3 | 4 | no | — |
| 264 | C4×Dic6 | — | 3 | 4 | no | — |
| 265 | C4×Dic6 | — | 3 | 4 | no | — |
| 266 | C4×Dic6 | — | 6 | 1 | no | — |
| 267 | C4×Dic6 | — | 6 | 2 | no | — |
| 268 | C4×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 269 | C4×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 270 | C4×Dic6 | C2×D3 | 1 | 2 | yes | — |
| 271 | C22×C3⋊D3 | C24 | 1 | 1 | yes | characteristic |
| 272 | C32×Q8 | — | 4 | 1 | no | — |
| 273 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 274 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 275 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 276 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 277 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 278 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 279 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 280 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 281 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 282 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 283 | C4×C3⋊D3 | — | 2 | 2 | no | — |
| 284 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 285 | C4×C3⋊D3 | C2×Q8 | 1 | 4 | yes | — |
| 286 | #634 | — | 2 | 4 | no | — |
| 287 | #634 | — | 4 | 1 | no | — |
| 288 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 289 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 290 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 291 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 292 | C3×Dic6 | — | 4 | 4 | no | — |
| 293 | C3×Dic6 | C2×Q8 | 1 | 8 | yes | — |
| 294 | #627 | — | 2 | 4 | no | — |
| 295 | #627 | — | 4 | 4 | no | — |
| 296 | #627 | — | 4 | 2 | no | — |
| 297 | #627 | C2×Q8 | 1 | 8 | yes | — |
| 298 | #624 | — | 4 | 2 | no | — |
| 299 | #624 | C2×Q8 | 1 | 8 | yes | — |
| 300 | Q82 | — | 9 | 2 | no | — |
| 301 | Q82 | — | 9 | 2 | no | — |
| 302 | #557 | — | 3 | 2 | no | — |
| 303 | #557 | — | 9 | 4 | no | — |
| 304 | #557 | — | 9 | 2 | no | — |
| 305 | #557 | — | 9 | 2 | no | — |
| 306 | #557 | — | 9 | 2 | no | — |
| 307 | #544 | — | 9 | 2 | no | — |
| 308 | #544 | — | 9 | 2 | no | — |
| 309 | #544 | — | 9 | 2 | no | — |
| 310 | #533 | — | 9 | 4 | no | — |
| 311 | #533 | — | 9 | 1 | no | — |
| 312 | #533 | — | 9 | 1 | no | — |
| 313 | #519 | — | 9 | 2 | no | — |
| 314 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 315 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 316 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 317 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 318 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 319 | D3×Q8 | — | 3 | 16 | no | — |
| 320 | C2×C4×D3 | — | 3 | 2 | no | — |
| 321 | C2×C4×D3 | — | 3 | 4 | no | — |
| 322 | C2×C4×D3 | — | 3 | 2 | no | — |
| 323 | C2×C4×D3 | — | 3 | 2 | no | — |
| 324 | C2×C4×D3 | — | 3 | 4 | no | — |
| 325 | C2×C4×D3 | — | 6 | 1 | no | — |
| 326 | C2×C4×D3 | — | 6 | 1 | no | — |
| 327 | C2×C4×D3 | — | 6 | 1 | no | — |
| 328 | C2×Dic6 | — | 3 | 4 | no | — |
| 329 | C2×Dic6 | — | 3 | 2 | no | — |
| 330 | C2×Dic6 | — | 3 | 2 | no | — |
| 331 | C2×Dic6 | — | 3 | 4 | no | — |
| 332 | C2×Dic6 | — | 3 | 2 | no | — |
| 333 | C2×Dic6 | — | 3 | 4 | no | — |
| 334 | C2×Dic6 | — | 3 | 4 | no | — |
| 335 | C2×Dic6 | — | 3 | 4 | no | — |
| 336 | C2×Dic6 | — | 6 | 2 | no | — |
| 337 | C2×Dic6 | — | 6 | 1 | no | — |
| 338 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 339 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 340 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 341 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 342 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 343 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 344 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 345 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 346 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 347 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 348 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 349 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 350 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 351 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 352 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 353 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 354 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 355 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 356 | C3×C42 | — | 2 | 1 | no | — |
| 357 | C3×C42 | — | 2 | 2 | no | — |
| 358 | C3×C42 | — | 3 | 4 | no | — |
| 359 | C3×C42 | — | 3 | 4 | no | — |
| 360 | C3×C42 | — | 3 | 4 | no | — |
| 361 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 362 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 363 | C3×C42 | C22×D3 | 1 | 2 | yes | — |
| 364 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 365 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 366 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 367 | (C2×D3)⋊C4 | — | 3 | 2 | no | — |
| 368 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 369 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 370 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 371 | (C2×D3)⋊C4 | — | 6 | 2 | no | — |
| 372 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 373 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 374 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 375 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 376 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 377 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 378 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 379 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 380 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 381 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 382 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 383 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 384 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 385 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 386 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 387 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 388 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 389 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 390 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 391 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 392 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 393 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 394 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 395 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 396 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 397 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 398 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 399 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 400 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 401 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 402 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 403 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 404 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 405 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 406 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 407 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 408 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 409 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 410 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 411 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 412 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 413 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 414 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 415 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 416 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 417 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 418 | C4×Dic3 | — | 3 | 2 | no | — |
| 419 | C4×Dic3 | — | 3 | 2 | no | — |
| 420 | C4×Dic3 | — | 3 | 2 | no | — |
| 421 | C4×Dic3 | — | 3 | 2 | no | — |
| 422 | C4×Dic3 | — | 3 | 2 | no | — |
| 423 | C4×Dic3 | — | 3 | 4 | no | — |
| 424 | C4×Dic3 | — | 3 | 4 | no | — |
| 425 | C4×Dic3 | — | 3 | 4 | no | — |
| 426 | C4×Dic3 | — | 3 | 4 | no | — |
| 427 | C4×Dic3 | — | 3 | 4 | no | — |
| 428 | C4×Dic3 | — | 3 | 4 | no | — |
| 429 | C4×Dic3 | — | 3 | 4 | no | — |
| 430 | C4×Dic3 | — | 3 | 4 | no | — |
| 431 | C4×Dic3 | — | 6 | 1 | no | — |
| 432 | C4×Dic3 | — | 6 | 2 | no | — |
| 433 | C4×Dic3 | — | 6 | 1 | no | — |
| 434 | C4×Dic3 | — | 6 | 1 | no | — |
| 435 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 436 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 437 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 438 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 439 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 440 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 441 | C2×C3⋊D3 | C22×Q8 | 1 | 2 | yes | — |
| 442 | C32×C4 | — | 2 | 1 | no | — |
| 443 | C32×C4 | — | 2 | 2 | no | — |
| 444 | C32×C4 | — | 2 | 1 | no | — |
| 445 | C32×C4 | — | 2 | 2 | no | — |
| 446 | C32×C4 | C22×Q8 | 1 | 2 | yes | — |
| 447 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 448 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 449 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 450 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 451 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | — |
| 452 | C3×Dic3 | — | 2 | 4 | no | — |
| 453 | C3×Dic3 | — | 2 | 4 | no | — |
| 454 | C3×Dic3 | — | 2 | 4 | no | — |
| 455 | C3×Dic3 | C22×Q8 | 1 | 8 | yes | — |
| 456 | C22×Q8 | — | 9 | 1 | no | — |
| 457 | C4⋊Q8 | — | 3 | 4 | no | — |
| 458 | C4⋊Q8 | — | 3 | 2 | no | — |
| 459 | C4⋊Q8 | — | 9 | 4 | no | — |
| 460 | C4⋊Q8 | — | 9 | 4 | no | — |
| 461 | C4⋊Q8 | — | 9 | 1 | no | — |
| 462 | C4⋊Q8 | — | 9 | 1 | no | — |
| 463 | C4⋊Q8 | — | 9 | 4 | no | — |
| 464 | C4⋊Q8 | — | 9 | 2 | no | — |
| 465 | C4⋊Q8 | — | 9 | 4 | no | — |
| 466 | C4⋊Q8 | — | 9 | 4 | no | — |
| 467 | C4⋊Q8 | — | 9 | 4 | no | — |
| 468 | C4⋊Q8 | — | 9 | 1 | no | — |
| 469 | C4⋊Q8 | — | 9 | 1 | no | — |
| 470 | #125 | — | 3 | 4 | no | — |
| 471 | #125 | — | 3 | 4 | no | — |
| 472 | #125 | — | 3 | 2 | no | — |
| 473 | #125 | — | 3 | 2 | no | — |
| 474 | #125 | — | 9 | 4 | no | — |
| 475 | #125 | — | 9 | 4 | no | — |
| 476 | #125 | — | 9 | 4 | no | — |
| 477 | #125 | — | 9 | 4 | no | — |
| 478 | #125 | — | 9 | 4 | no | — |
| 479 | #125 | — | 9 | 2 | no | — |
| 480 | #125 | — | 9 | 2 | no | — |
| 481 | C22⋊Q8 | — | 9 | 2 | no | — |
| 482 | C22⋊Q8 | — | 9 | 2 | no | — |
| 483 | C22⋊Q8 | — | 9 | 4 | no | — |
| 484 | C22⋊Q8 | — | 9 | 4 | no | — |
| 485 | C22⋊Q8 | — | 9 | 1 | no | — |
| 486 | C22⋊Q8 | — | 9 | 2 | no | — |
| 487 | C22⋊Q8 | — | 9 | 1 | no | — |
| 488 | C4×Q8 | — | 3 | 4 | no | — |
| 489 | C4×Q8 | — | 3 | 2 | no | — |
| 490 | C4×Q8 | — | 3 | 2 | no | — |
| 491 | C4×Q8 | — | 3 | 2 | no | — |
| 492 | C4×Q8 | — | 9 | 2 | no | — |
| 493 | C4×Q8 | — | 9 | 4 | no | — |
| 494 | C4×Q8 | — | 9 | 4 | no | — |
| 495 | C4×Q8 | — | 9 | 4 | no | — |
| 496 | C4×Q8 | — | 9 | 4 | no | — |
| 497 | C4×Q8 | — | 9 | 4 | no | — |
| 498 | C4×Q8 | — | 9 | 2 | no | — |
| 499 | C4×Q8 | — | 9 | 2 | no | — |
| 500 | C4×Q8 | — | 9 | 2 | no | — |
| 501 | C4×Q8 | — | 9 | 2 | no | — |
| 502 | C4×Q8 | — | 9 | 2 | no | — |
| 503 | C4×Q8 | — | 9 | 2 | no | — |
| 504 | C4×Q8 | — | 9 | 1 | no | — |
| 505 | C4×Q8 | — | 9 | 2 | no | — |
| 506 | C4×Q8 | D32 | 1 | 1 | yes | characteristic |
| 507 | #117 | — | 9 | 4 | no | — |
| 508 | #117 | — | 9 | 4 | no | — |
| 509 | #117 | — | 9 | 2 | no | — |
| 510 | #117 | — | 9 | 2 | no | — |
| 511 | C2×C4⋊C4 | — | 9 | 2 | no | — |
| 512 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 513 | C2×C42 | — | 9 | 2 | no | — |
| 514 | C2×C42 | — | 9 | 1 | no | — |
| 515 | C22×D3 | — | 3 | 2 | no | — |
| 516 | C22×D3 | — | 6 | 1 | no | — |
| 517 | C3×Q8 | — | 3 | 8 | no | — |
| 518 | C3×Q8 | — | 4 | 2 | no | — |
| 519 | C3×Q8 | — | 4 | 2 | no | — |
| 520 | C3×Q8 | — | 12 | 4 | no | — |
| 521 | C2×C3×C4 | — | 2 | 1 | no | — |
| 522 | C2×C3×C4 | — | 2 | 1 | no | — |
| 523 | C2×C3×C4 | — | 2 | 1 | no | — |
| 524 | C2×C3×C4 | — | 2 | 2 | no | — |
| 525 | C2×C3×C4 | — | 2 | 2 | no | — |
| 526 | C2×C3×C4 | — | 3 | 4 | no | — |
| 527 | C2×C3×C4 | — | 3 | 4 | no | — |
| 528 | C2×C3×C4 | — | 3 | 4 | no | — |
| 529 | C2×C3×C4 | — | 3 | 4 | no | — |
| 530 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 531 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 532 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 533 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 534 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 535 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 536 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 537 | C2×Dic3 | — | 3 | 2 | no | — |
| 538 | C2×Dic3 | — | 3 | 2 | no | — |
| 539 | C2×Dic3 | — | 3 | 2 | no | — |
| 540 | C2×Dic3 | — | 3 | 2 | no | — |
| 541 | C2×Dic3 | — | 3 | 2 | no | — |
| 542 | C2×Dic3 | — | 3 | 2 | no | — |
| 543 | C2×Dic3 | — | 3 | 2 | no | — |
| 544 | C2×Dic3 | — | 6 | 1 | no | — |
| 545 | C2×Dic3 | — | 6 | 1 | no | — |
| 546 | C2×Dic3 | — | 6 | 1 | no | — |
| 547 | C2×Dic3 | — | 6 | 2 | no | — |
| 548 | C2×Dic3 | — | 6 | 2 | no | — |
| 549 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 550 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 551 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 552 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 553 | C4×D3 | — | 3 | 8 | no | — |
| 554 | C4×D3 | — | 3 | 16 | no | — |
| 555 | C4×D3 | — | 6 | 4 | no | — |
| 556 | C4×D3 | — | 6 | 4 | no | — |
| 557 | C4×D3 | — | 12 | 2 | no | — |
| 558 | C4×D3 | — | 12 | 4 | no | — |
| 559 | C4×D3 | — | 12 | 2 | no | — |
| 560 | C4×D3 | — | 12 | 2 | no | — |
| 561 | Dic6 | — | 3 | 16 | no | — |
| 562 | Dic6 | — | 4 | 4 | no | — |
| 563 | Dic6 | — | 6 | 8 | no | — |
| 564 | Dic6 | — | 6 | 4 | no | — |
| 565 | Dic6 | — | 6 | 4 | no | — |
| 566 | Dic6 | — | 12 | 4 | no | — |
| 567 | Dic6 | — | 12 | 4 | no | — |
| 568 | Dic6 | — | 12 | 4 | no | — |
| 569 | Dic6 | — | 12 | 4 | no | — |
| 570 | Dic6 | — | 12 | 2 | no | — |
| 571 | Dic6 | — | 12 | 2 | no | — |
| 572 | Dic6 | D3×Q8 | 1 | 8 | yes | — |
| 573 | C2×C32 | C23×Q8 | 1 | 1 | yes | characteristic |
| 574 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 575 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 576 | C3⋊D3 | — | 2 | 2 | no | — |
| 577 | C2×Q8 | — | 3 | 2 | no | — |
| 578 | C2×Q8 | — | 3 | 4 | no | — |
| 579 | C2×Q8 | — | 9 | 2 | no | — |
| 580 | C2×Q8 | — | 9 | 2 | no | — |
| 581 | C2×Q8 | — | 9 | 2 | no | — |
| 582 | C2×Q8 | — | 9 | 4 | no | — |
| 583 | C2×Q8 | — | 9 | 8 | no | — |
| 584 | C2×Q8 | — | 9 | 2 | no | — |
| 585 | C2×Q8 | — | 9 | 1 | no | — |
| 586 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 587 | C22×C4 | — | 9 | 2 | no | — |
| 588 | C22×C4 | — | 9 | 2 | no | — |
| 589 | C22×C4 | — | 9 | 1 | no | — |
| 590 | C22×C4 | — | 9 | 1 | no | — |
| 591 | C22×C4 | — | 9 | 1 | no | — |
| 592 | C4⋊C4 | — | 3 | 4 | no | — |
| 593 | C4⋊C4 | — | 3 | 2 | no | — |
| 594 | C4⋊C4 | — | 3 | 4 | no | — |
| 595 | C4⋊C4 | — | 3 | 2 | no | — |
| 596 | C4⋊C4 | — | 3 | 4 | no | — |
| 597 | C4⋊C4 | — | 3 | 2 | no | — |
| 598 | C4⋊C4 | — | 3 | 4 | no | — |
| 599 | C4⋊C4 | — | 3 | 4 | no | — |
| 600 | C4⋊C4 | — | 3 | 4 | no | — |
| 601 | C4⋊C4 | — | 3 | 4 | no | — |
| 602 | C4⋊C4 | — | 3 | 4 | no | — |
| 603 | C4⋊C4 | — | 9 | 2 | no | — |
| 604 | C4⋊C4 | — | 9 | 4 | no | — |
| 605 | C4⋊C4 | — | 9 | 4 | no | — |
| 606 | C4⋊C4 | — | 9 | 4 | no | — |
| 607 | C4⋊C4 | — | 9 | 2 | no | — |
| 608 | C4⋊C4 | — | 9 | 2 | no | — |
| 609 | C4⋊C4 | — | 9 | 4 | no | — |
| 610 | C4⋊C4 | — | 9 | 4 | no | — |
| 611 | C4⋊C4 | — | 9 | 4 | no | — |
| 612 | C4⋊C4 | — | 9 | 2 | no | — |
| 613 | C4⋊C4 | — | 9 | 2 | no | — |
| 614 | C4⋊C4 | — | 9 | 2 | no | — |
| 615 | C4⋊C4 | — | 9 | 2 | no | — |
| 616 | C4⋊C4 | — | 9 | 1 | no | — |
| 617 | C4⋊C4 | — | 9 | 2 | no | — |
| 618 | C4⋊C4 | — | 9 | 2 | no | — |
| 619 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 620 | C4⋊C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 621 | C22⋊C4 | — | 9 | 4 | no | — |
| 622 | C22⋊C4 | — | 9 | 2 | no | — |
| 623 | C22⋊C4 | — | 9 | 2 | no | — |
| 624 | C42 | — | 3 | 4 | no | — |
| 625 | C42 | — | 3 | 4 | no | — |
| 626 | C42 | — | 3 | 4 | no | — |
| 627 | C42 | — | 9 | 4 | no | — |
| 628 | C42 | — | 9 | 4 | no | — |
| 629 | C42 | — | 9 | 4 | no | — |
| 630 | C42 | — | 9 | 4 | no | — |
| 631 | C42 | — | 9 | 1 | no | — |
| 632 | C42 | — | 9 | 1 | no | — |
| 633 | C42 | — | 9 | 1 | no | — |
| 634 | C42 | — | 9 | 2 | no | — |
| 635 | C42 | C2×D32 | 1 | 1 | yes | characteristic |
| 636 | C42 | C2×D32 | 1 | 2 | yes | — |
| 637 | C22×C3 | — | 2 | 1 | no | — |
| 638 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 639 | C2×D3 | — | 3 | 4 | no | — |
| 640 | C2×D3 | — | 6 | 2 | no | — |
| 641 | C2×D3 | — | 6 | 2 | no | — |
| 642 | C2×D3 | — | 6 | 2 | no | — |
| 643 | C2×D3 | — | 12 | 1 | no | — |
| 644 | C2×D3 | — | 12 | 1 | no | — |
| 645 | C3×C4 | — | 2 | 2 | no | — |
| 646 | C3×C4 | — | 2 | 2 | no | — |
| 647 | C3×C4 | — | 2 | 2 | no | — |
| 648 | C3×C4 | — | 2 | 2 | no | — |
| 649 | C3×C4 | — | 2 | 2 | no | — |
| 650 | C3×C4 | — | 2 | 2 | no | — |
| 651 | C3×C4 | — | 2 | 2 | no | — |
| 652 | C3×C4 | — | 2 | 2 | no | — |
| 653 | C3×C4 | — | 3 | 8 | no | — |
| 654 | C3×C4 | — | 4 | 2 | no | — |
| 655 | C3×C4 | — | 4 | 1 | no | — |
| 656 | C3×C4 | — | 4 | 2 | no | — |
| 657 | C3×C4 | — | 6 | 4 | no | — |
| 658 | C3×C4 | — | 6 | 4 | no | — |
| 659 | C3×C4 | — | 6 | 4 | no | — |
| 660 | C3×C4 | C2×D3×Q8 | 1 | 4 | yes | — |
| 661 | Dic3 | — | 2 | 4 | no | — |
| 662 | Dic3 | — | 2 | 4 | no | — |
| 663 | Dic3 | — | 2 | 4 | no | — |
| 664 | Dic3 | — | 3 | 4 | no | — |
| 665 | Dic3 | — | 3 | 4 | no | — |
| 666 | Dic3 | — | 6 | 2 | no | — |
| 667 | Dic3 | — | 6 | 2 | no | — |
| 668 | Dic3 | — | 6 | 2 | no | — |
| 669 | Dic3 | — | 6 | 2 | no | — |
| 670 | Dic3 | — | 6 | 2 | no | — |
| 671 | Dic3 | — | 6 | 2 | no | — |
| 672 | Dic3 | — | 6 | 2 | no | — |
| 673 | Dic3 | — | 12 | 2 | no | — |
| 674 | Dic3 | — | 12 | 2 | no | — |
| 675 | Dic3 | — | 12 | 1 | no | — |
| 676 | Dic3 | C2×D3×Q8 | 1 | 8 | yes | — |
| 677 | C32 | #3502 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 678 | C23 | — | 9 | 1 | no | — |
| 679 | Q8 | — | 3 | 8 | no | — |
| 680 | Q8 | — | 4 | 1 | no | — |
| 681 | Q8 | — | 9 | 8 | no | — |
| 682 | Q8 | — | 12 | 4 | no | — |
| 683 | Q8 | — | 18 | 4 | no | — |
| 684 | Q8 | — | 18 | 4 | no | — |
| 685 | Q8 | — | 36 | 1 | no | — |
| 686 | Q8 | — | 36 | 4 | no | — |
| 687 | Q8 | — | 36 | 2 | no | — |
| 688 | C2×C4 | — | 3 | 4 | no | — |
| 689 | C2×C4 | — | 3 | 4 | no | — |
| 690 | C2×C4 | — | 3 | 4 | no | — |
| 691 | C2×C4 | — | 3 | 4 | no | — |
| 692 | C2×C4 | — | 9 | 8 | no | — |
| 693 | C2×C4 | — | 9 | 1 | no | — |
| 694 | C2×C4 | — | 9 | 1 | no | — |
| 695 | C2×C4 | — | 9 | 4 | no | — |
| 696 | C2×C4 | — | 9 | 2 | no | — |
| 697 | C2×C4 | — | 9 | 2 | no | — |
| 698 | C2×C4 | — | 9 | 1 | no | — |
| 699 | C2×C4 | — | 18 | 2 | no | — |
| 700 | C2×C4 | — | 36 | 1 | no | — |
| 701 | C2×C4 | — | 36 | 2 | no | — |
| 702 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 703 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 704 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 705 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 706 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 707 | C2×C3 | — | 2 | 1 | no | — |
| 708 | C2×C3 | — | 2 | 1 | no | — |
| 709 | C2×C3 | — | 2 | 1 | no | — |
| 710 | C2×C3 | C22×D3×Q8 | 1 | 2 | yes | — |
| 711 | C2×C3 | #5964 | 1 | 2 | yes | — |
| 712 | C2×C3 | D3×2−1+4 | 1 | 2 | yes | — |
| 713 | D3 | — | 6 | 4 | no | — |
| 714 | D3 | — | 12 | 2 | no | — |
| 715 | C22 | — | 9 | 2 | no | — |
| 716 | C22 | — | 18 | 1 | no | — |
| 717 | C22 | — | 18 | 1 | no | — |
| 718 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 719 | C4 | — | 2 | 1 | no | — |
| 720 | C4 | — | 2 | 2 | no | — |
| 721 | C4 | — | 2 | 1 | no | — |
| 722 | C4 | — | 2 | 2 | no | — |
| 723 | C4 | — | 3 | 8 | no | — |
| 724 | C4 | — | 6 | 4 | no | — |
| 725 | C4 | — | 6 | 4 | no | — |
| 726 | C4 | — | 6 | 4 | no | — |
| 727 | C4 | — | 9 | 2 | no | — |
| 728 | C4 | — | 9 | 2 | no | — |
| 729 | C4 | — | 18 | 1 | no | — |
| 730 | C4 | — | 18 | 2 | no | — |
| 731 | C4 | — | 18 | 2 | no | — |
| 732 | C4 | D32×Q8 | 1 | 2 | yes | — |
| 733 | C3 | — | 2 | 1 | no | — |
| 734 | C3 | #87032 | 1 | 2 | yes | complemented |
| 735 | C2 | — | 18 | 2 | no | — |
| 736 | C2 | #10596669 | 1 | 1 | yes | characteristic |
| 737 | C2 | C2×D32×Q8 | 1 | 1 | yes | characteristic |
| 738 | C2 | #10596694 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C4×Q8 | C22 |
| prime radical | C22×C3⋊D3 | C24 |
| hypercenter | C4×Q8 | D32 |
| hypocenter | C32 | #3502 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5567 | C2 | semidirect |
| 3. #10595421 | C2 | semidirect |
| 5. #10594596 | C2 | semidirect |
| 8. #10594315 | C2 | semidirect |
| 10. #10593856 | C2 | semidirect |
| 13. #10593853 | C2 | semidirect |
| 14. #10593853 | C2 | semidirect |
| 98. #5567 | D3 | semidirect |
| 114. #3797 | Q8 | semidirect |
| 677. C32 | #3502 | semidirect |
| 734. C3 | #87032 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596049 | 2 |
| C3×#5567 | 2 |
| #10595421 | 2 |
| #10595375 | 2 |
| #10594596 | 2 |
| #10594401 | 2 |
| #10594398 | 2 |
| #10594315 | 2 |
| C4×#3797 | 2 |
| #10593856 | 2 |
| #10593855 | 2 |
| #10593854 | 2 |
| #10593853 | 2 |
| #10593848 | 2 |
| #87032 | 3 |