Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2039 conjugacy classes of subgroups.
The subgroup lattice has 705 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596093 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#5623 | C2 | 1 | 2 | yes | maximal |
| 3 | #10595421 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #10595338 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10594812 | C2 | 1 | 2 | yes | maximal |
| 6 | #10594810 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C2×#63838 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10594597 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #10594597 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10594315 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #10594314 | C2 | 1 | 4 | yes | maximal, complemented |
| 12 | #10594313 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | #10594245 | C2 | 1 | 2 | yes | maximal |
| 14 | #10594033 | C2 | 1 | 2 | yes | maximal |
| 15 | #10594029 | C2 | 1 | 4 | yes | maximal |
| 16 | #86585 | — | 3 | 2 | no | maximal |
| 17 | C22×#627 | C22 | 1 | 1 | yes | characteristic |
| 18 | C32×C22⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 19 | Q8×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 20 | #64153 | C22 | 1 | 1 | yes | characteristic |
| 21 | #64133 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×C3⋊Dic3 | C22 | 1 | 1 | yes | characteristic |
| 23 | #64098 | C22 | 1 | 2 | yes | — |
| 24 | #64097 | C22 | 1 | 1 | yes | characteristic |
| 25 | #64096 | C22 | 1 | 2 | yes | — |
| 26 | #64096 | C22 | 1 | 1 | yes | characteristic |
| 27 | #64087 | C22 | 1 | 2 | yes | — |
| 28 | #64086 | C22 | 1 | 2 | yes | — |
| 29 | C3×#944 | C22 | 1 | 4 | yes | — |
| 30 | C3×#924 | C22 | 1 | 2 | yes | — |
| 31 | C2×C3×Dic3⋊C4 | C22 | 1 | 2 | yes | — |
| 32 | C3×#889 | C22 | 1 | 4 | yes | — |
| 33 | C3×#889 | C22 | 1 | 4 | yes | — |
| 34 | C3×#888 | C22 | 1 | 4 | yes | — |
| 35 | C3×#878 | C22 | 1 | 4 | yes | — |
| 36 | C3×#877 | C22 | 1 | 4 | yes | — |
| 37 | #63982 | C22 | 1 | 2 | yes | — |
| 38 | C2×#3724 | C22 | 1 | 1 | yes | characteristic |
| 39 | #63964 | C22 | 1 | 4 | yes | — |
| 40 | #63957 | C22 | 1 | 2 | yes | — |
| 41 | #63955 | C22 | 1 | 4 | yes | — |
| 42 | C2×Dic32 | C22 | 1 | 2 | yes | — |
| 43 | #63919 | C22 | 1 | 2 | yes | — |
| 44 | #63919 | C22 | 1 | 1 | yes | characteristic |
| 45 | C4×#627 | C22 | 1 | 2 | yes | — |
| 46 | C4×#627 | C22 | 1 | 2 | yes | — |
| 47 | #63873 | C22 | 1 | 1 | yes | characteristic |
| 48 | #63873 | C22 | 1 | 2 | yes | — |
| 49 | #63870 | C22 | 1 | 2 | yes | — |
| 50 | #63870 | C22 | 1 | 2 | yes | — |
| 51 | #63870 | C22 | 1 | 2 | yes | — |
| 52 | #63847 | C22 | 1 | 4 | yes | — |
| 53 | #63846 | C22 | 1 | 4 | yes | — |
| 54 | #63846 | C22 | 1 | 4 | yes | — |
| 55 | #63845 | C22 | 1 | 4 | yes | — |
| 56 | #63845 | C22 | 1 | 4 | yes | — |
| 57 | #63844 | C22 | 1 | 4 | yes | — |
| 58 | #63843 | C22 | 1 | 2 | yes | — |
| 59 | Dic3×Dic6 | C22 | 1 | 4 | yes | — |
| 60 | #63840 | C22 | 1 | 4 | yes | — |
| 61 | #63840 | C22 | 1 | 4 | yes | — |
| 62 | #63839 | C22 | 1 | 4 | yes | — |
| 63 | #63839 | C22 | 1 | 4 | yes | — |
| 64 | #63839 | C22 | 1 | 4 | yes | — |
| 65 | #63838 | C22 | 1 | 2 | yes | — |
| 66 | #63838 | C22 | 1 | 2 | yes | — |
| 67 | #63838 | C22 | 1 | 2 | yes | — |
| 68 | #63838 | C22 | 1 | 2 | yes | — |
| 69 | #63838 | C22 | 1 | 2 | yes | — |
| 70 | #63838 | C22 | 1 | 2 | yes | — |
| 71 | #63838 | C22 | 1 | 2 | yes | — |
| 72 | #63837 | C22 | 1 | 4 | yes | — |
| 73 | #63837 | C22 | 1 | 4 | yes | — |
| 74 | #63837 | C22 | 1 | 4 | yes | — |
| 75 | #63837 | C22 | 1 | 4 | yes | — |
| 76 | C3×#544 | — | 3 | 2 | no | — |
| 77 | #5722 | — | 3 | 4 | no | — |
| 78 | #5722 | — | 3 | 4 | no | — |
| 79 | #5721 | — | 3 | 4 | no | — |
| 80 | #5721 | — | 3 | 4 | no | — |
| 81 | #5685 | — | 3 | 4 | no | — |
| 82 | #5685 | — | 3 | 4 | no | — |
| 83 | #5685 | — | 3 | 4 | no | — |
| 84 | #5685 | — | 3 | 4 | no | — |
| 85 | #5623 | — | 3 | 2 | no | — |
| 86 | #5623 | — | 3 | 4 | no | — |
| 87 | #5623 | D3 | 1 | 2 | yes | — |
| 88 | #5622 | — | 3 | 2 | no | — |
| 89 | #5622 | — | 3 | 2 | no | — |
| 90 | #5622 | — | 3 | 4 | no | — |
| 91 | #5622 | — | 6 | 1 | no | — |
| 92 | #5517 | — | 3 | 4 | no | — |
| 93 | #5516 | — | 3 | 4 | no | — |
| 94 | #5500 | — | 3 | 2 | no | — |
| 95 | C2×#887 | — | 3 | 2 | no | — |
| 96 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 97 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 98 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 99 | C22×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×#634 | C23 | 1 | 2 | yes | — |
| 101 | C2×#634 | C23 | 1 | 1 | yes | characteristic |
| 102 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 103 | C22×C3×Dic3 | C23 | 1 | 2 | yes | — |
| 104 | C2×C3×Dic6 | C23 | 1 | 4 | yes | — |
| 105 | C2×C3×Dic6 | C23 | 1 | 2 | yes | — |
| 106 | C2×#627 | Q8 | 1 | 8 | yes | complemented |
| 107 | C2×#627 | C23 | 1 | 2 | yes | — |
| 108 | C2×#627 | C23 | 1 | 4 | yes | — |
| 109 | C2×#627 | C23 | 1 | 2 | yes | — |
| 110 | C2×#627 | C23 | 1 | 2 | yes | — |
| 111 | C32×C4⋊C4 | C23 | 1 | 2 | yes | — |
| 112 | C32×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 113 | C32×C22⋊C4 | C23 | 1 | 2 | yes | — |
| 114 | #3757 | C23 | 1 | 2 | yes | — |
| 115 | C4⋊(C3⋊Dic3) | C23 | 1 | 2 | yes | — |
| 116 | C4⋊(C3⋊Dic3) | C23 | 1 | 1 | yes | characteristic |
| 117 | #3750 | C23 | 1 | 2 | yes | — |
| 118 | #3750 | C23 | 1 | 2 | yes | — |
| 119 | #3750 | C23 | 1 | 2 | yes | — |
| 120 | #3750 | C23 | 1 | 2 | yes | — |
| 121 | #3750 | C23 | 1 | 2 | yes | — |
| 122 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 123 | C4×C3⋊Dic3 | C23 | 1 | 2 | yes | — |
| 124 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 125 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 126 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 127 | C4×C3⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 128 | C3×#217 | C23 | 1 | 4 | yes | — |
| 129 | C3×C4⋊Dic3 | C23 | 1 | 4 | yes | — |
| 130 | C3×C4⋊Dic3 | C23 | 1 | 2 | yes | — |
| 131 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 132 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 133 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 134 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 135 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 136 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 137 | C3×Dic3⋊C4 | C23 | 1 | 4 | yes | — |
| 138 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 139 | C3×C4×Dic3 | C23 | 1 | 4 | yes | — |
| 140 | #3724 | C23 | 1 | 2 | yes | — |
| 141 | #3724 | C23 | 1 | 2 | yes | — |
| 142 | #3724 | C23 | 1 | 2 | yes | — |
| 143 | #3724 | C23 | 1 | 2 | yes | — |
| 144 | #3724 | C23 | 1 | 2 | yes | — |
| 145 | #3724 | C23 | 1 | 4 | yes | — |
| 146 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 147 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 148 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 149 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 150 | Dic3⋊Dic3 | C23 | 1 | 4 | yes | — |
| 151 | Dic32 | C23 | 1 | 4 | yes | — |
| 152 | Dic32 | C23 | 1 | 4 | yes | — |
| 153 | Dic32 | C23 | 1 | 4 | yes | — |
| 154 | Dic32 | C23 | 1 | 4 | yes | — |
| 155 | Dic32 | C23 | 1 | 4 | yes | — |
| 156 | #3502 | — | 9 | 1 | no | Sylow |
| 157 | C22×Dic6 | — | 3 | 2 | no | — |
| 158 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 159 | C3×C4⋊Q8 | — | 3 | 4 | no | — |
| 160 | C3×#125 | — | 3 | 4 | no | — |
| 161 | C3×#125 | — | 3 | 4 | no | — |
| 162 | C3×C22⋊Q8 | — | 2 | 1 | no | — |
| 163 | C3×C22⋊Q8 | — | 3 | 2 | no | — |
| 164 | C3×C22⋊Q8 | — | 3 | 4 | no | — |
| 165 | C3×C22⋊Q8 | C2×D3 | 1 | 2 | yes | — |
| 166 | C3×#117 | — | 3 | 4 | no | — |
| 167 | C2×C3×C4⋊C4 | — | 3 | 2 | no | — |
| 168 | Q8×Dic3 | — | 3 | 2 | no | — |
| 169 | Q8×Dic3 | — | 3 | 2 | no | — |
| 170 | Q8×Dic3 | — | 3 | 4 | no | — |
| 171 | Q8×Dic3 | — | 6 | 1 | no | — |
| 172 | #944 | — | 3 | 2 | no | — |
| 173 | #944 | — | 3 | 4 | no | — |
| 174 | #944 | — | 3 | 2 | no | — |
| 175 | #944 | — | 3 | 4 | no | — |
| 176 | #944 | — | 3 | 4 | no | — |
| 177 | #944 | — | 3 | 4 | no | — |
| 178 | #944 | — | 6 | 1 | no | — |
| 179 | #944 | C2×D3 | 1 | 4 | yes | — |
| 180 | #926 | — | 3 | 4 | no | — |
| 181 | #924 | — | 3 | 2 | no | — |
| 182 | #924 | — | 3 | 4 | no | — |
| 183 | #924 | — | 6 | 1 | no | — |
| 184 | #924 | C2×D3 | 1 | 2 | yes | — |
| 185 | C2×Dic3⋊C4 | — | 3 | 2 | no | — |
| 186 | C2×Dic3⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 187 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 188 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 189 | C2×C4×Dic3 | — | 3 | 2 | no | — |
| 190 | C2×C4×Dic3 | — | 6 | 1 | no | — |
| 191 | #890 | — | 3 | 4 | no | — |
| 192 | #890 | — | 3 | 4 | no | — |
| 193 | #890 | — | 3 | 4 | no | — |
| 194 | #890 | — | 3 | 4 | no | — |
| 195 | #889 | — | 3 | 4 | no | — |
| 196 | #889 | — | 3 | 4 | no | — |
| 197 | #889 | — | 3 | 4 | no | — |
| 198 | #889 | — | 3 | 4 | no | — |
| 199 | #889 | — | 3 | 4 | no | — |
| 200 | #889 | — | 3 | 4 | no | — |
| 201 | #889 | — | 3 | 4 | no | — |
| 202 | #889 | — | 3 | 4 | no | — |
| 203 | #889 | — | 3 | 4 | no | — |
| 204 | #889 | — | 3 | 4 | no | — |
| 205 | #889 | — | 6 | 2 | no | — |
| 206 | #889 | C2×D3 | 1 | 4 | yes | — |
| 207 | #889 | C2×D3 | 1 | 4 | yes | — |
| 208 | #888 | — | 3 | 4 | no | — |
| 209 | #888 | — | 3 | 4 | no | — |
| 210 | #888 | — | 3 | 4 | no | — |
| 211 | #888 | — | 3 | 2 | no | — |
| 212 | #888 | — | 3 | 2 | no | — |
| 213 | #888 | — | 3 | 4 | no | — |
| 214 | #888 | — | 3 | 4 | no | — |
| 215 | #888 | — | 3 | 4 | no | — |
| 216 | #888 | — | 3 | 4 | no | — |
| 217 | #888 | — | 3 | 4 | no | — |
| 218 | #888 | — | 6 | 1 | no | — |
| 219 | #888 | C2×D3 | 1 | 4 | yes | — |
| 220 | #887 | — | 3 | 2 | no | — |
| 221 | #887 | — | 3 | 2 | no | — |
| 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 | — | 3 | 4 | no | — |
| 229 | #887 | — | 3 | 4 | no | — |
| 230 | #887 | — | 3 | 4 | no | — |
| 231 | #887 | — | 3 | 4 | no | — |
| 232 | #887 | — | 3 | 4 | no | — |
| 233 | #887 | — | 3 | 4 | no | — |
| 234 | #887 | — | 3 | 4 | no | — |
| 235 | #887 | — | 6 | 1 | no | — |
| 236 | #887 | — | 6 | 2 | no | — |
| 237 | #878 | — | 3 | 4 | no | — |
| 238 | #878 | — | 3 | 4 | no | — |
| 239 | #878 | — | 3 | 4 | no | — |
| 240 | #878 | — | 6 | 2 | no | — |
| 241 | #878 | C2×D3 | 1 | 4 | yes | — |
| 242 | #877 | — | 3 | 4 | no | — |
| 243 | #877 | — | 3 | 4 | no | — |
| 244 | #877 | — | 3 | 4 | no | — |
| 245 | #877 | — | 6 | 2 | no | — |
| 246 | #877 | C2×D3 | 1 | 4 | yes | — |
| 247 | C4×Dic6 | — | 3 | 4 | no | — |
| 248 | C4×Dic6 | — | 3 | 4 | no | — |
| 249 | C4×Dic6 | — | 3 | 4 | no | — |
| 250 | C4×Dic6 | — | 3 | 4 | no | — |
| 251 | C4×Dic6 | — | 3 | 4 | no | — |
| 252 | C4×Dic6 | — | 3 | 4 | no | — |
| 253 | C4×Dic6 | — | 3 | 4 | no | — |
| 254 | C4×Dic6 | — | 3 | 4 | no | — |
| 255 | C23×C32 | C24 | 1 | 1 | yes | characteristic |
| 256 | C32×Q8 | — | 4 | 1 | no | — |
| 257 | C2×C32×C4 | — | 4 | 1 | no | — |
| 258 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 259 | C2×C32×C4 | C24 | 1 | 2 | yes | — |
| 260 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 261 | C2×C32×C4 | C24 | 1 | 1 | yes | characteristic |
| 262 | C2×C3⋊Dic3 | — | 2 | 2 | no | — |
| 263 | C2×C3⋊Dic3 | C2×Q8 | 1 | 4 | yes | — |
| 264 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 265 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 266 | C2×C3⋊Dic3 | C24 | 1 | 2 | yes | — |
| 267 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 268 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 269 | C2×C3⋊Dic3 | C24 | 1 | 1 | yes | characteristic |
| 270 | #634 | — | 2 | 4 | no | — |
| 271 | #634 | — | 4 | 1 | no | — |
| 272 | C2×C3×Dic3 | — | 4 | 2 | no | — |
| 273 | C2×C3×Dic3 | C2×Q8 | 1 | 8 | yes | — |
| 274 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 275 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 276 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 277 | C2×C3×Dic3 | C24 | 1 | 4 | yes | — |
| 278 | C3×Dic6 | — | 4 | 2 | no | — |
| 279 | C3×Dic6 | — | 4 | 4 | no | — |
| 280 | #627 | — | 2 | 4 | no | — |
| 281 | #627 | — | 4 | 4 | no | — |
| 282 | #627 | C2×Q8 | 1 | 8 | yes | — |
| 283 | #627 | C2×Q8 | 1 | 8 | yes | — |
| 284 | Q82 | — | 9 | 2 | no | — |
| 285 | Q82 | — | 9 | 2 | no | — |
| 286 | #557 | — | 9 | 2 | no | — |
| 287 | #557 | — | 9 | 2 | no | — |
| 288 | #557 | — | 9 | 2 | no | — |
| 289 | #557 | — | 9 | 4 | no | — |
| 290 | #557 | — | 9 | 2 | no | — |
| 291 | #544 | — | 3 | 2 | no | — |
| 292 | #544 | — | 9 | 2 | no | — |
| 293 | #544 | — | 9 | 2 | no | — |
| 294 | #533 | — | 9 | 4 | no | — |
| 295 | #533 | — | 9 | 1 | no | — |
| 296 | #533 | — | 9 | 1 | no | — |
| 297 | #519 | — | 9 | 2 | no | — |
| 298 | C2×C4×Q8 | — | 9 | 1 | no | — |
| 299 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 300 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 301 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 302 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 303 | C22×C3×C4 | — | 2 | 1 | no | — |
| 304 | C22×C3×C4 | — | 3 | 2 | no | — |
| 305 | C22×C3×C4 | — | 3 | 2 | no | — |
| 306 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 307 | C22×Dic3 | — | 3 | 2 | no | — |
| 308 | C22×Dic3 | — | 3 | 2 | no | — |
| 309 | C22×Dic3 | — | 6 | 1 | no | — |
| 310 | C22×Dic3 | — | 6 | 1 | no | — |
| 311 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 312 | C22×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 313 | C2×Dic6 | — | 3 | 16 | no | — |
| 314 | C2×Dic6 | — | 3 | 4 | no | — |
| 315 | C2×Dic6 | — | 3 | 4 | no | — |
| 316 | C2×Dic6 | — | 3 | 4 | no | — |
| 317 | C2×Dic6 | — | 3 | 4 | no | — |
| 318 | C2×Dic6 | — | 3 | 2 | no | — |
| 319 | C2×Dic6 | — | 3 | 4 | no | — |
| 320 | C2×Dic6 | — | 3 | 4 | no | — |
| 321 | C2×Dic6 | — | 6 | 2 | no | — |
| 322 | C2×Dic6 | — | 6 | 1 | no | — |
| 323 | C2×Dic6 | C22×D3 | 1 | 4 | yes | — |
| 324 | C2×Dic6 | C22×D3 | 1 | 2 | yes | — |
| 325 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 326 | C3×C4⋊C4 | — | 2 | 2 | no | — |
| 327 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 328 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 329 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 330 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 331 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 332 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 333 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 334 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 335 | C3×C4⋊C4 | — | 3 | 4 | no | — |
| 336 | C3×C4⋊C4 | C22×D3 | 1 | 2 | yes | — |
| 337 | C3×C4⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 338 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 339 | C3×C22⋊C4 | — | 3 | 4 | no | — |
| 340 | C3×C22⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 341 | C3×C42 | — | 3 | 4 | no | — |
| 342 | C3×C42 | — | 3 | 4 | no | — |
| 343 | #217 | — | 3 | 4 | no | — |
| 344 | #217 | — | 6 | 2 | no | — |
| 345 | #217 | C22×D3 | 1 | 4 | yes | — |
| 346 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 347 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 348 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 349 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 350 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 351 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 352 | C4⋊Dic3 | — | 3 | 4 | no | — |
| 353 | C4⋊Dic3 | — | 6 | 2 | no | — |
| 354 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 355 | C4⋊Dic3 | C22×D3 | 1 | 4 | yes | — |
| 356 | C4⋊Dic3 | C22×D3 | 1 | 2 | yes | — |
| 357 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 358 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 359 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 360 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 361 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 362 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 363 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 364 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 365 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 366 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 367 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 368 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 369 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 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 | — | 6 | 2 | no | — |
| 375 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 376 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 377 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 378 | Dic3⋊C4 | — | 6 | 2 | no | — |
| 379 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 380 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 381 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 382 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 383 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 384 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 385 | Dic3⋊C4 | C22×D3 | 1 | 4 | yes | — |
| 386 | C4×Dic3 | — | 3 | 4 | no | — |
| 387 | C4×Dic3 | — | 3 | 4 | no | — |
| 388 | C4×Dic3 | — | 3 | 2 | no | — |
| 389 | C4×Dic3 | — | 3 | 2 | no | — |
| 390 | C4×Dic3 | — | 3 | 2 | no | — |
| 391 | C4×Dic3 | — | 3 | 2 | no | — |
| 392 | C4×Dic3 | — | 3 | 4 | no | — |
| 393 | C4×Dic3 | — | 3 | 4 | no | — |
| 394 | C4×Dic3 | — | 3 | 4 | no | — |
| 395 | C4×Dic3 | — | 3 | 4 | no | — |
| 396 | C4×Dic3 | — | 3 | 4 | no | — |
| 397 | C4×Dic3 | — | 3 | 4 | no | — |
| 398 | C4×Dic3 | — | 3 | 4 | no | — |
| 399 | C4×Dic3 | — | 3 | 4 | no | — |
| 400 | C4×Dic3 | — | 3 | 4 | no | — |
| 401 | C4×Dic3 | — | 3 | 4 | no | — |
| 402 | C4×Dic3 | — | 6 | 2 | no | — |
| 403 | C4×Dic3 | — | 6 | 2 | no | — |
| 404 | C4×Dic3 | — | 6 | 1 | no | — |
| 405 | C4×Dic3 | — | 6 | 1 | no | — |
| 406 | C4×Dic3 | — | 6 | 1 | no | — |
| 407 | C4×Dic3 | — | 6 | 1 | no | — |
| 408 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 409 | C4×Dic3 | C22×D3 | 1 | 4 | yes | — |
| 410 | C22×C32 | — | 2 | 1 | no | — |
| 411 | C22×C32 | — | 2 | 1 | no | — |
| 412 | C22×C32 | C22×Q8 | 1 | 2 | yes | — |
| 413 | C22×C32 | C25 | 1 | 1 | yes | characteristic |
| 414 | C32×C4 | — | 2 | 1 | no | — |
| 415 | C32×C4 | — | 2 | 2 | no | — |
| 416 | C32×C4 | — | 2 | 1 | no | — |
| 417 | C32×C4 | — | 2 | 2 | no | — |
| 418 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 419 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 420 | C3⋊Dic3 | — | 2 | 2 | no | — |
| 421 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 422 | C3⋊Dic3 | C22×Q8 | 1 | 2 | yes | — |
| 423 | C3⋊Dic3 | 2−1+4 | 1 | 2 | yes | — |
| 424 | C3×Dic3 | — | 2 | 4 | no | — |
| 425 | C3×Dic3 | — | 2 | 4 | no | — |
| 426 | C3×Dic3 | — | 2 | 4 | no | — |
| 427 | C3×Dic3 | C22×Q8 | 1 | 8 | yes | — |
| 428 | C22×Q8 | — | 9 | 1 | no | — |
| 429 | C4⋊Q8 | — | 3 | 4 | no | — |
| 430 | C4⋊Q8 | — | 3 | 4 | no | — |
| 431 | C4⋊Q8 | — | 9 | 4 | no | — |
| 432 | C4⋊Q8 | — | 9 | 1 | no | — |
| 433 | C4⋊Q8 | — | 9 | 4 | no | — |
| 434 | C4⋊Q8 | — | 9 | 2 | no | — |
| 435 | C4⋊Q8 | — | 9 | 4 | no | — |
| 436 | C4⋊Q8 | — | 9 | 4 | no | — |
| 437 | C4⋊Q8 | — | 9 | 4 | no | — |
| 438 | C4⋊Q8 | — | 9 | 1 | no | — |
| 439 | C4⋊Q8 | — | 9 | 2 | no | — |
| 440 | C4⋊Q8 | — | 9 | 1 | no | — |
| 441 | C4⋊Q8 | — | 9 | 1 | no | — |
| 442 | #125 | — | 3 | 4 | no | — |
| 443 | #125 | — | 3 | 4 | no | — |
| 444 | #125 | — | 9 | 2 | no | — |
| 445 | #125 | — | 9 | 4 | no | — |
| 446 | #125 | — | 9 | 4 | no | — |
| 447 | #125 | — | 9 | 4 | no | — |
| 448 | #125 | — | 9 | 2 | no | — |
| 449 | #125 | — | 9 | 2 | no | — |
| 450 | #125 | — | 9 | 4 | no | — |
| 451 | #125 | — | 9 | 4 | no | — |
| 452 | #125 | — | 9 | 2 | no | — |
| 453 | C22⋊Q8 | — | 3 | 2 | no | — |
| 454 | C22⋊Q8 | — | 3 | 4 | no | — |
| 455 | C22⋊Q8 | — | 9 | 2 | no | — |
| 456 | C22⋊Q8 | — | 9 | 4 | no | — |
| 457 | C22⋊Q8 | — | 9 | 1 | no | — |
| 458 | C22⋊Q8 | — | 9 | 2 | no | — |
| 459 | C22⋊Q8 | D32 | 1 | 1 | yes | characteristic |
| 460 | C4×Q8 | — | 9 | 2 | no | — |
| 461 | C4×Q8 | — | 9 | 2 | no | — |
| 462 | C4×Q8 | — | 9 | 4 | no | — |
| 463 | C4×Q8 | — | 9 | 4 | no | — |
| 464 | C4×Q8 | — | 9 | 4 | no | — |
| 465 | C4×Q8 | — | 9 | 4 | no | — |
| 466 | C4×Q8 | — | 9 | 4 | no | — |
| 467 | C4×Q8 | — | 9 | 4 | no | — |
| 468 | C4×Q8 | — | 9 | 2 | no | — |
| 469 | C4×Q8 | — | 9 | 2 | no | — |
| 470 | C4×Q8 | — | 9 | 2 | no | — |
| 471 | C4×Q8 | — | 9 | 2 | no | — |
| 472 | C4×Q8 | — | 9 | 2 | no | — |
| 473 | C4×Q8 | — | 9 | 2 | no | — |
| 474 | C4×Q8 | — | 9 | 2 | no | — |
| 475 | C4×Q8 | — | 9 | 2 | no | — |
| 476 | C4×Q8 | — | 9 | 1 | no | — |
| 477 | C4×Q8 | — | 9 | 1 | no | — |
| 478 | C4×Q8 | — | 9 | 2 | no | — |
| 479 | #117 | — | 3 | 4 | no | — |
| 480 | #117 | — | 9 | 2 | no | — |
| 481 | #117 | — | 9 | 4 | no | — |
| 482 | #117 | — | 9 | 2 | no | — |
| 483 | C2×C4⋊C4 | — | 3 | 2 | no | — |
| 484 | C2×C4⋊C4 | — | 9 | 1 | no | — |
| 485 | C2×C42 | — | 9 | 2 | no | — |
| 486 | C2×C42 | — | 9 | 1 | no | — |
| 487 | C23×C3 | — | 2 | 1 | no | — |
| 488 | C23×C3 | C23×D3 | 1 | 2 | yes | — |
| 489 | C3×Q8 | — | 4 | 2 | no | — |
| 490 | C3×Q8 | — | 4 | 2 | no | — |
| 491 | C3×Q8 | — | 12 | 2 | no | — |
| 492 | C3×Q8 | — | 12 | 4 | no | — |
| 493 | C2×C3×C4 | — | 2 | 1 | no | — |
| 494 | C2×C3×C4 | — | 2 | 1 | no | — |
| 495 | C2×C3×C4 | — | 2 | 2 | no | — |
| 496 | C2×C3×C4 | — | 2 | 2 | no | — |
| 497 | C2×C3×C4 | — | 3 | 8 | no | — |
| 498 | C2×C3×C4 | — | 3 | 4 | no | — |
| 499 | C2×C3×C4 | — | 3 | 4 | no | — |
| 500 | C2×C3×C4 | — | 3 | 4 | no | — |
| 501 | C2×C3×C4 | — | 3 | 4 | no | — |
| 502 | C2×C3×C4 | — | 4 | 2 | no | — |
| 503 | C2×C3×C4 | — | 4 | 2 | no | — |
| 504 | C2×C3×C4 | — | 12 | 2 | no | — |
| 505 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 506 | C2×C3×C4 | C23×D3 | 1 | 2 | yes | — |
| 507 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 508 | C2×C3×C4 | C23×D3 | 1 | 4 | yes | — |
| 509 | C2×Dic3 | — | 3 | 8 | no | — |
| 510 | C2×Dic3 | — | 3 | 2 | no | — |
| 511 | C2×Dic3 | — | 3 | 2 | no | — |
| 512 | C2×Dic3 | — | 3 | 2 | no | — |
| 513 | C2×Dic3 | — | 3 | 2 | no | — |
| 514 | C2×Dic3 | — | 3 | 4 | no | — |
| 515 | C2×Dic3 | — | 3 | 4 | no | — |
| 516 | C2×Dic3 | — | 4 | 2 | no | — |
| 517 | C2×Dic3 | — | 6 | 4 | no | — |
| 518 | C2×Dic3 | — | 6 | 1 | no | — |
| 519 | C2×Dic3 | — | 6 | 1 | no | — |
| 520 | C2×Dic3 | — | 6 | 1 | no | — |
| 521 | C2×Dic3 | — | 6 | 1 | no | — |
| 522 | C2×Dic3 | — | 6 | 2 | no | — |
| 523 | C2×Dic3 | — | 6 | 2 | no | — |
| 524 | C2×Dic3 | — | 6 | 4 | no | — |
| 525 | C2×Dic3 | — | 12 | 2 | no | — |
| 526 | C2×Dic3 | D3×Q8 | 1 | 8 | yes | — |
| 527 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 528 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 529 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 530 | C2×Dic3 | C23×D3 | 1 | 4 | yes | — |
| 531 | Dic6 | — | 3 | 16 | no | — |
| 532 | Dic6 | — | 3 | 16 | no | — |
| 533 | Dic6 | — | 4 | 2 | no | — |
| 534 | Dic6 | — | 4 | 4 | no | — |
| 535 | Dic6 | — | 6 | 8 | no | — |
| 536 | Dic6 | — | 6 | 8 | no | — |
| 537 | Dic6 | — | 12 | 4 | no | — |
| 538 | Dic6 | — | 12 | 4 | no | — |
| 539 | Dic6 | — | 12 | 4 | no | — |
| 540 | Dic6 | — | 12 | 2 | no | — |
| 541 | Dic6 | — | 12 | 2 | no | — |
| 542 | C2×C32 | — | 2 | 2 | no | — |
| 543 | C2×C32 | C23×Q8 | 1 | 1 | yes | characteristic |
| 544 | C2×C32 | C2×2−1+4 | 1 | 1 | yes | characteristic |
| 545 | C2×C32 | #585 | 1 | 1 | yes | characteristic |
| 546 | C2×Q8 | — | 3 | 2 | no | — |
| 547 | C2×Q8 | — | 3 | 4 | no | — |
| 548 | C2×Q8 | — | 9 | 2 | no | — |
| 549 | C2×Q8 | — | 9 | 2 | no | — |
| 550 | C2×Q8 | — | 9 | 8 | no | — |
| 551 | C2×Q8 | — | 9 | 2 | no | — |
| 552 | C2×Q8 | — | 9 | 4 | no | — |
| 553 | C2×Q8 | — | 9 | 2 | no | — |
| 554 | C2×Q8 | — | 9 | 1 | no | — |
| 555 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 556 | C22×C4 | — | 3 | 2 | no | — |
| 557 | C22×C4 | — | 3 | 2 | no | — |
| 558 | C22×C4 | — | 9 | 1 | no | — |
| 559 | C22×C4 | — | 9 | 1 | no | — |
| 560 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 561 | C4⋊C4 | — | 3 | 4 | no | — |
| 562 | C4⋊C4 | — | 3 | 4 | no | — |
| 563 | C4⋊C4 | — | 3 | 4 | no | — |
| 564 | C4⋊C4 | — | 3 | 4 | no | — |
| 565 | C4⋊C4 | — | 3 | 4 | no | — |
| 566 | C4⋊C4 | — | 3 | 2 | no | — |
| 567 | C4⋊C4 | — | 3 | 4 | no | — |
| 568 | C4⋊C4 | — | 3 | 4 | no | — |
| 569 | C4⋊C4 | — | 3 | 4 | no | — |
| 570 | C4⋊C4 | — | 9 | 2 | no | — |
| 571 | C4⋊C4 | — | 9 | 2 | no | — |
| 572 | C4⋊C4 | — | 9 | 2 | no | — |
| 573 | C4⋊C4 | — | 9 | 4 | no | — |
| 574 | C4⋊C4 | — | 9 | 2 | no | — |
| 575 | C4⋊C4 | — | 9 | 4 | no | — |
| 576 | C4⋊C4 | — | 9 | 4 | no | — |
| 577 | C4⋊C4 | — | 9 | 2 | no | — |
| 578 | C4⋊C4 | — | 9 | 4 | no | — |
| 579 | C4⋊C4 | — | 9 | 4 | no | — |
| 580 | C4⋊C4 | — | 9 | 4 | no | — |
| 581 | C4⋊C4 | — | 9 | 2 | no | — |
| 582 | C4⋊C4 | — | 9 | 2 | no | — |
| 583 | C4⋊C4 | — | 9 | 2 | no | — |
| 584 | C4⋊C4 | — | 9 | 2 | no | — |
| 585 | C4⋊C4 | — | 9 | 2 | no | — |
| 586 | C4⋊C4 | — | 9 | 1 | no | — |
| 587 | C4⋊C4 | — | 9 | 2 | no | — |
| 588 | C4⋊C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 589 | C4⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 590 | C22⋊C4 | — | 3 | 4 | no | — |
| 591 | C22⋊C4 | — | 9 | 2 | no | — |
| 592 | C22⋊C4 | C2×D32 | 1 | 2 | yes | — |
| 593 | C42 | — | 3 | 4 | no | — |
| 594 | C42 | — | 3 | 4 | no | — |
| 595 | C42 | — | 9 | 4 | no | — |
| 596 | C42 | — | 9 | 4 | no | — |
| 597 | C42 | — | 9 | 4 | no | — |
| 598 | C42 | — | 9 | 4 | no | — |
| 599 | C42 | — | 9 | 4 | no | — |
| 600 | C42 | — | 9 | 1 | no | — |
| 601 | C42 | — | 9 | 1 | no | — |
| 602 | C42 | — | 9 | 1 | no | — |
| 603 | C42 | — | 9 | 1 | no | — |
| 604 | C42 | — | 9 | 2 | no | — |
| 605 | C42 | — | 9 | 2 | no | — |
| 606 | C22×C3 | — | 2 | 2 | no | — |
| 607 | C22×C3 | — | 2 | 2 | no | — |
| 608 | C22×C3 | — | 2 | 2 | no | — |
| 609 | C22×C3 | — | 2 | 1 | no | — |
| 610 | C22×C3 | — | 4 | 1 | no | — |
| 611 | C22×C3 | — | 4 | 1 | no | — |
| 612 | C22×C3 | C2×D3×Q8 | 1 | 4 | yes | — |
| 613 | C22×C3 | C24×D3 | 1 | 2 | yes | — |
| 614 | C3×C4 | — | 2 | 2 | no | — |
| 615 | C3×C4 | — | 2 | 2 | no | — |
| 616 | C3×C4 | — | 2 | 4 | no | — |
| 617 | C3×C4 | — | 2 | 2 | no | — |
| 618 | C3×C4 | — | 2 | 4 | no | — |
| 619 | C3×C4 | — | 3 | 8 | no | — |
| 620 | C3×C4 | — | 4 | 2 | no | — |
| 621 | C3×C4 | — | 4 | 1 | no | — |
| 622 | C3×C4 | — | 4 | 2 | no | — |
| 623 | C3×C4 | — | 6 | 4 | no | — |
| 624 | C3×C4 | — | 6 | 4 | no | — |
| 625 | C3×C4 | — | 6 | 4 | no | — |
| 626 | Dic3 | — | 2 | 4 | no | — |
| 627 | Dic3 | — | 2 | 4 | no | — |
| 628 | Dic3 | — | 2 | 4 | no | — |
| 629 | Dic3 | — | 3 | 4 | no | — |
| 630 | Dic3 | — | 3 | 4 | no | — |
| 631 | Dic3 | — | 3 | 4 | no | — |
| 632 | Dic3 | — | 6 | 2 | no | — |
| 633 | Dic3 | — | 6 | 2 | no | — |
| 634 | Dic3 | — | 6 | 2 | no | — |
| 635 | Dic3 | — | 6 | 4 | no | — |
| 636 | Dic3 | — | 6 | 4 | no | — |
| 637 | Dic3 | — | 6 | 2 | no | — |
| 638 | Dic3 | — | 12 | 2 | no | — |
| 639 | Dic3 | — | 12 | 2 | no | — |
| 640 | Dic3 | — | 12 | 1 | no | — |
| 641 | Dic3 | C2×D3×Q8 | 1 | 8 | yes | — |
| 642 | C32 | #3502 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 643 | C23 | C22×D32 | 1 | 1 | yes | characteristic |
| 644 | Q8 | — | 4 | 1 | no | — |
| 645 | Q8 | — | 9 | 8 | no | — |
| 646 | Q8 | — | 9 | 8 | no | — |
| 647 | Q8 | — | 12 | 2 | no | — |
| 648 | Q8 | — | 12 | 4 | no | — |
| 649 | Q8 | — | 18 | 4 | no | — |
| 650 | Q8 | — | 18 | 4 | no | — |
| 651 | Q8 | — | 36 | 1 | no | — |
| 652 | Q8 | — | 36 | 4 | no | — |
| 653 | C2×C4 | — | 3 | 8 | no | — |
| 654 | C2×C4 | — | 3 | 4 | no | — |
| 655 | C2×C4 | — | 3 | 4 | no | — |
| 656 | C2×C4 | — | 3 | 4 | no | — |
| 657 | C2×C4 | — | 3 | 4 | no | — |
| 658 | C2×C4 | — | 4 | 1 | no | — |
| 659 | C2×C4 | — | 9 | 4 | no | — |
| 660 | C2×C4 | — | 9 | 1 | no | — |
| 661 | C2×C4 | — | 9 | 1 | no | — |
| 662 | C2×C4 | — | 9 | 1 | no | — |
| 663 | C2×C4 | — | 9 | 1 | no | — |
| 664 | C2×C4 | — | 9 | 2 | no | — |
| 665 | C2×C4 | — | 9 | 2 | no | — |
| 666 | C2×C4 | — | 12 | 2 | no | — |
| 667 | C2×C4 | — | 18 | 2 | no | — |
| 668 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 669 | C2×C4 | C22×D32 | 1 | 2 | yes | — |
| 670 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 671 | C2×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 672 | C2×C3 | — | 2 | 4 | no | — |
| 673 | C2×C3 | — | 2 | 1 | no | — |
| 674 | C2×C3 | — | 2 | 1 | no | — |
| 675 | C2×C3 | — | 2 | 1 | no | — |
| 676 | C2×C3 | — | 4 | 2 | no | — |
| 677 | C2×C3 | C22×D3×Q8 | 1 | 2 | yes | — |
| 678 | C2×C3 | #5966 | 1 | 2 | yes | — |
| 679 | C2×C3 | D3×2−1+4 | 1 | 2 | yes | — |
| 680 | C22 | — | 2 | 1 | no | — |
| 681 | C22 | — | 2 | 1 | no | — |
| 682 | C22 | D32×Q8 | 1 | 2 | yes | — |
| 683 | C22 | C23×D32 | 1 | 1 | yes | characteristic |
| 684 | C4 | — | 2 | 1 | no | — |
| 685 | C4 | — | 2 | 1 | no | — |
| 686 | C4 | — | 2 | 2 | no | — |
| 687 | C4 | — | 2 | 2 | no | — |
| 688 | C4 | — | 3 | 8 | no | — |
| 689 | C4 | — | 6 | 4 | no | — |
| 690 | C4 | — | 6 | 4 | no | — |
| 691 | C4 | — | 6 | 4 | no | — |
| 692 | C4 | — | 9 | 2 | no | — |
| 693 | C4 | — | 9 | 2 | no | — |
| 694 | C4 | — | 9 | 2 | no | — |
| 695 | C4 | — | 18 | 2 | no | — |
| 696 | C4 | — | 18 | 1 | no | — |
| 697 | C4 | — | 18 | 2 | no | — |
| 698 | C3 | — | 2 | 1 | no | — |
| 699 | C3 | #86585 | 1 | 2 | yes | complemented |
| 700 | C2 | — | 2 | 2 | no | — |
| 701 | C2 | #10596679 | 1 | 1 | yes | characteristic |
| 702 | C2 | C2×D32×Q8 | 1 | 1 | yes | characteristic |
| 703 | C2 | #10596694 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D32 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×C22⋊Q8 | C22 |
| prime radical | C23×C32 | C24 |
| hypercenter | C22⋊Q8 | D32 |
| hypocenter | C32 | #3502 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10595421 | C2 | semidirect |
| 4. #10595338 | C2 | semidirect |
| 8. #10594597 | C2 | semidirect |
| 9. #10594597 | C2 | semidirect |
| 10. #10594315 | C2 | semidirect |
| 11. #10594314 | C2 | semidirect |
| 12. #10594313 | C2 | semidirect |
| 106. C2×#627 | Q8 | semidirect |
| 642. C32 | #3502 | semidirect |
| 699. C3 | #86585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596093 | 2 |
| C3×#5623 | 2 |
| #10595421 | 2 |
| #10595338 | 2 |
| #10594812 | 2 |
| #10594810 | 2 |
| C2×#63838 | 2 |
| #10594597 | 2 |
| #10594315 | 2 |
| #10594314 | 2 |
| #10594313 | 2 |
| #10594245 | 2 |
| #10594033 | 2 |
| #10594029 | 2 |
| #86585 | 3 |