Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
927 conjugacy classes of subgroups.
The subgroup lattice has 409 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3417 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #33470 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22460 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22457 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13248 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #13020 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #13016 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #12832 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #12744 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #12742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #12617 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#578 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#578 | C22 | 1 | 1 | yes | characteristic |
| 14 | #3417 | — | 2 | 8 | no | — |
| 15 | C2×#510 | C4 | 1 | 2 | yes | complemented |
| 16 | C2×#510 | C4 | 1 | 2 | yes | complemented |
| 17 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#510 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#508 | C4 | 1 | 2 | yes | complemented |
| 20 | C2×#508 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×Q32 | C4 | 1 | 2 | yes | complemented |
| 22 | C22×Q32 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 24 | #2957 | C22 | 1 | 2 | yes | — |
| 25 | #2950 | C22 | 1 | 2 | yes | — |
| 26 | #2889 | — | 2 | 1 | no | — |
| 27 | #2884 | — | 2 | 1 | no | — |
| 28 | #2180 | — | 2 | 8 | no | — |
| 29 | #2155 | C22 | 1 | 2 | yes | — |
| 30 | C2×#362 | C22 | 1 | 2 | yes | — |
| 31 | #2145 | C22 | 1 | 2 | yes | — |
| 32 | #2143 | C22 | 1 | 2 | yes | — |
| 33 | #2141 | C22 | 1 | 2 | yes | — |
| 34 | #2115 | C22 | 1 | 1 | yes | characteristic |
| 35 | #2110 | C22 | 1 | 2 | yes | — |
| 36 | #1979 | C22 | 1 | 2 | yes | — |
| 37 | #1976 | C22 | 1 | 2 | yes | — |
| 38 | #1905 | — | 2 | 2 | no | — |
| 39 | #1902 | — | 2 | 2 | no | — |
| 40 | #1813 | C22 | 1 | 1 | yes | characteristic |
| 41 | #1812 | C22 | 1 | 1 | yes | characteristic |
| 42 | #1796 | — | 2 | 1 | no | — |
| 43 | #1796 | — | 2 | 1 | no | — |
| 44 | #1757 | C22 | 1 | 1 | yes | characteristic |
| 45 | #1382 | C22 | 1 | 2 | yes | — |
| 46 | #1379 | C22 | 1 | 2 | yes | — |
| 47 | C2×2−1+4 | — | 2 | 1 | no | — |
| 48 | C2×2−1+4 | — | 2 | 1 | no | — |
| 49 | #578 | — | 2 | 4 | no | — |
| 50 | #578 | — | 2 | 4 | no | — |
| 51 | #578 | — | 4 | 2 | no | — |
| 52 | #578 | — | 4 | 2 | no | — |
| 53 | C2×#137 | — | 2 | 1 | no | — |
| 54 | C2×#137 | — | 2 | 1 | no | — |
| 55 | C2×#137 | — | 2 | 2 | no | — |
| 56 | C2×#137 | — | 2 | 2 | no | — |
| 57 | C2×#135 | C2×C4 | 1 | 2 | yes | — |
| 58 | C2×#135 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×#135 | C23 | 1 | 1 | yes | characteristic |
| 61 | C22×Q16 | C2×C4 | 1 | 2 | yes | — |
| 62 | C22×Q16 | C2×C4 | 1 | 2 | yes | — |
| 63 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 64 | C22×Q16 | C23 | 1 | 1 | yes | characteristic |
| 65 | #568 | — | 2 | 2 | no | — |
| 66 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 67 | #519 | — | 2 | 2 | no | — |
| 68 | #510 | — | 2 | 8 | no | — |
| 69 | #510 | — | 2 | 8 | no | — |
| 70 | #510 | — | 2 | 4 | no | — |
| 71 | #510 | D4 | 1 | 8 | yes | — |
| 72 | #508 | — | 2 | 4 | no | — |
| 73 | #508 | — | 2 | 8 | no | — |
| 74 | C2×Q32 | — | 2 | 4 | no | — |
| 75 | C2×Q32 | — | 2 | 8 | no | — |
| 76 | C2×Q32 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C2×Q32 | C2×C4 | 1 | 2 | yes | — |
| 78 | C2×Q32 | C2×C4 | 1 | 2 | yes | — |
| 79 | C2×Q32 | C2×C4 | 1 | 2 | yes | — |
| 80 | C2×Q32 | C2×C4 | 1 | 2 | yes | — |
| 81 | C2×SD32 | C2×C4 | 1 | 2 | yes | — |
| 82 | C2×SD32 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C2×SD32 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×SD32 | C2×C4 | 1 | 2 | yes | — |
| 85 | C2×D16 | C2×C4 | 1 | 1 | yes | characteristic |
| 86 | #504 | — | 2 | 4 | no | — |
| 87 | C2×M32 | C2×C4 | 1 | 2 | yes | — |
| 88 | C2×M32 | C23 | 1 | 2 | yes | — |
| 89 | C2×M32 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C16 | C2×C4 | 1 | 2 | yes | — |
| 91 | C22×C16 | C23 | 1 | 1 | yes | characteristic |
| 92 | #444 | — | 2 | 4 | no | — |
| 93 | #443 | — | 4 | 2 | no | — |
| 94 | #441 | — | 2 | 4 | no | — |
| 95 | C4×Q16 | — | 4 | 2 | no | — |
| 96 | C2×#108 | C23 | 1 | 2 | yes | — |
| 97 | #427 | C23 | 1 | 2 | yes | — |
| 98 | #421 | — | 2 | 2 | no | — |
| 99 | #421 | — | 2 | 2 | no | — |
| 100 | #419 | — | 2 | 2 | no | — |
| 101 | #419 | — | 2 | 2 | no | — |
| 102 | #413 | — | 2 | 1 | no | — |
| 103 | #413 | — | 4 | 2 | no | — |
| 104 | #413 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#101 | — | 2 | 2 | no | — |
| 106 | C2×#101 | — | 4 | 2 | no | — |
| 107 | #410 | — | 2 | 1 | no | — |
| 108 | #410 | — | 2 | 2 | no | — |
| 109 | #410 | — | 4 | 4 | no | — |
| 110 | #410 | D4 | 1 | 1 | yes | characteristic |
| 111 | #405 | C23 | 1 | 2 | yes | — |
| 112 | #365 | — | 2 | 4 | no | — |
| 113 | #362 | — | 2 | 4 | no | — |
| 114 | #360 | — | 2 | 4 | no | — |
| 115 | #359 | — | 4 | 2 | no | — |
| 116 | #358 | — | 4 | 2 | no | — |
| 117 | #349 | — | 2 | 2 | no | — |
| 118 | #347 | — | 2 | 4 | no | — |
| 119 | #344 | D4 | 1 | 2 | yes | — |
| 120 | #338 | — | 2 | 1 | no | — |
| 121 | H(3,ℤ/4) | — | 2 | 1 | no | — |
| 122 | 2−1+4 | — | 4 | 4 | no | — |
| 123 | 2−1+4 | — | 4 | 4 | no | — |
| 124 | 2−1+4 | — | 8 | 2 | no | — |
| 125 | 2−1+4 | — | 8 | 2 | no | — |
| 126 | C2×#41 | — | 2 | 2 | no | — |
| 127 | C2×#41 | — | 2 | 2 | no | — |
| 128 | C2×#41 | — | 2 | 1 | no | — |
| 129 | C2×#41 | — | 2 | 1 | no | — |
| 130 | C2×#41 | — | 4 | 2 | no | — |
| 131 | C2×#41 | — | 4 | 1 | no | — |
| 132 | C2×#41 | — | 4 | 2 | no | — |
| 133 | C2×#41 | — | 4 | 1 | no | — |
| 134 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C22×Q8 | — | 2 | 2 | no | — |
| 136 | C22×Q8 | — | 2 | 2 | no | — |
| 137 | C22×Q8 | — | 2 | 1 | no | — |
| 138 | C22×Q8 | — | 2 | 1 | no | — |
| 139 | C22×Q8 | — | 4 | 1 | no | — |
| 140 | C22×Q8 | — | 4 | 1 | no | — |
| 141 | #137 | — | 4 | 8 | no | — |
| 142 | #137 | — | 4 | 8 | no | — |
| 143 | #137 | — | 4 | 4 | no | — |
| 144 | #137 | — | 4 | 4 | no | — |
| 145 | #135 | — | 2 | 4 | no | — |
| 146 | #135 | — | 2 | 4 | no | — |
| 147 | #135 | — | 2 | 2 | no | — |
| 148 | #135 | — | 2 | 2 | no | — |
| 149 | #135 | — | 2 | 2 | no | — |
| 150 | #135 | — | 4 | 2 | no | — |
| 151 | #135 | — | 4 | 2 | no | — |
| 152 | #135 | C2×D4 | 1 | 4 | yes | — |
| 153 | C2×Q16 | — | 2 | 4 | no | — |
| 154 | C2×Q16 | — | 2 | 4 | no | — |
| 155 | C2×Q16 | — | 2 | 2 | no | — |
| 156 | C2×Q16 | — | 2 | 2 | no | — |
| 157 | C2×Q16 | — | 2 | 2 | no | — |
| 158 | C2×Q16 | — | 2 | 1 | no | — |
| 159 | C2×Q16 | — | 2 | 1 | no | — |
| 160 | C2×Q16 | — | 2 | 2 | no | — |
| 161 | C2×Q16 | — | 2 | 2 | no | — |
| 162 | C2×Q16 | — | 4 | 2 | no | — |
| 163 | C2×Q16 | — | 4 | 2 | no | — |
| 164 | C2×Q16 | C22×C4 | 1 | 1 | yes | characteristic |
| 165 | C2×Q16 | C22×C4 | 1 | 2 | yes | — |
| 166 | C2×Q16 | C22×C4 | 1 | 1 | yes | characteristic |
| 167 | C2×Q16 | C22×C4 | 1 | 2 | yes | — |
| 168 | C2×Q16 | C2×D4 | 1 | 4 | yes | — |
| 169 | C2×SD16 | — | 2 | 2 | no | — |
| 170 | C2×SD16 | — | 2 | 2 | no | — |
| 171 | C2×SD16 | — | 2 | 1 | no | — |
| 172 | C2×SD16 | — | 2 | 1 | no | — |
| 173 | C2×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 174 | C2×D8 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | #131 | — | 2 | 2 | no | — |
| 176 | #131 | — | 2 | 2 | no | — |
| 177 | #131 | — | 4 | 4 | no | — |
| 178 | #131 | — | 8 | 2 | no | — |
| 179 | C2×M16 | — | 2 | 2 | no | — |
| 180 | C2×M16 | — | 4 | 4 | no | — |
| 181 | C2×M16 | C2×D4 | 1 | 2 | yes | — |
| 182 | C2×M16 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C2×M16 | #41 | 1 | 2 | yes | — |
| 184 | C22×C8 | C22×C4 | 1 | 2 | yes | — |
| 185 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 186 | C4×Q8 | — | 4 | 4 | no | — |
| 187 | C4×Q8 | — | 8 | 2 | no | — |
| 188 | #117 | — | 2 | 2 | no | — |
| 189 | #117 | — | 4 | 4 | no | — |
| 190 | #117 | C2×D4 | 1 | 2 | yes | — |
| 191 | Q32 | — | 2 | 2 | no | — |
| 192 | Q32 | — | 2 | 4 | no | — |
| 193 | Q32 | — | 2 | 4 | no | — |
| 194 | Q32 | — | 2 | 4 | no | — |
| 195 | Q32 | C22⋊C4 | 1 | 8 | yes | — |
| 196 | SD32 | — | 2 | 2 | no | — |
| 197 | SD32 | — | 2 | 2 | no | — |
| 198 | SD32 | — | 2 | 4 | no | — |
| 199 | SD32 | C22⋊C4 | 1 | 8 | yes | — |
| 200 | D16 | — | 2 | 2 | no | — |
| 201 | M32 | — | 2 | 4 | no | — |
| 202 | M32 | — | 2 | 2 | no | — |
| 203 | M32 | — | 2 | 2 | no | — |
| 204 | M32 | C2×D4 | 1 | 4 | yes | — |
| 205 | C2×C16 | — | 2 | 2 | no | — |
| 206 | C2×C16 | — | 2 | 4 | no | — |
| 207 | C2×C16 | — | 2 | 2 | no | — |
| 208 | C2×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 209 | C2×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 210 | C2×C16 | C22×C4 | 1 | 2 | yes | — |
| 211 | #108 | — | 2 | 2 | no | — |
| 212 | #108 | — | 2 | 2 | no | — |
| 213 | #107 | — | 2 | 2 | no | — |
| 214 | #106 | — | 2 | 2 | no | — |
| 215 | #104 | — | 4 | 4 | no | — |
| 216 | #104 | — | 8 | 2 | no | — |
| 217 | #103 | — | 4 | 4 | no | — |
| 218 | #103 | — | 8 | 2 | no | — |
| 219 | #101 | — | 2 | 1 | no | — |
| 220 | #101 | — | 4 | 4 | no | — |
| 221 | #101 | — | 4 | 1 | no | — |
| 222 | #100 | — | 2 | 1 | no | — |
| 223 | #100 | — | 4 | 1 | no | — |
| 224 | #99 | — | 2 | 2 | no | — |
| 225 | #99 | — | 4 | 4 | no | — |
| 226 | #99 | — | 4 | 2 | no | — |
| 227 | #97 | — | 2 | 2 | no | — |
| 228 | C4×C8 | — | 2 | 2 | no | — |
| 229 | #41 | — | 2 | 2 | no | — |
| 230 | #41 | — | 2 | 2 | no | — |
| 231 | #41 | — | 2 | 4 | no | — |
| 232 | #41 | — | 4 | 4 | no | — |
| 233 | #41 | — | 4 | 4 | no | — |
| 234 | #41 | — | 4 | 2 | no | — |
| 235 | #41 | — | 4 | 2 | no | — |
| 236 | #41 | — | 4 | 2 | no | — |
| 237 | #41 | — | 8 | 2 | no | — |
| 238 | #41 | — | 8 | 2 | no | — |
| 239 | #41 | — | 8 | 8 | no | — |
| 240 | #41 | — | 8 | 4 | no | — |
| 241 | #41 | — | 8 | 8 | no | — |
| 242 | #41 | — | 8 | 4 | no | — |
| 243 | C2×Q8 | — | 2 | 1 | no | — |
| 244 | C2×Q8 | — | 2 | 2 | no | — |
| 245 | C2×Q8 | — | 2 | 2 | no | — |
| 246 | C2×Q8 | — | 2 | 1 | no | — |
| 247 | C2×Q8 | — | 2 | 4 | no | — |
| 248 | C2×Q8 | — | 4 | 4 | no | — |
| 249 | C2×Q8 | — | 4 | 4 | no | — |
| 250 | C2×Q8 | — | 4 | 1 | no | — |
| 251 | C2×Q8 | — | 4 | 1 | no | — |
| 252 | C2×Q8 | — | 4 | 2 | no | — |
| 253 | C2×Q8 | — | 4 | 2 | no | — |
| 254 | C2×Q8 | — | 4 | 2 | no | — |
| 255 | C2×Q8 | — | 4 | 2 | no | — |
| 256 | C2×Q8 | — | 4 | 2 | no | — |
| 257 | C2×Q8 | — | 8 | 2 | no | — |
| 258 | C2×Q8 | — | 8 | 2 | no | — |
| 259 | C2×Q8 | — | 8 | 4 | no | — |
| 260 | C2×Q8 | — | 8 | 4 | no | — |
| 261 | C2×Q8 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 262 | C2×D4 | — | 2 | 1 | no | — |
| 263 | C2×D4 | — | 2 | 1 | no | — |
| 264 | C2×D4 | — | 4 | 1 | no | — |
| 265 | C2×D4 | — | 4 | 1 | no | — |
| 266 | C2×D4 | — | 4 | 2 | no | — |
| 267 | C2×D4 | — | 4 | 2 | no | — |
| 268 | C2×D4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 269 | C2×D4 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 270 | C22×C4 | — | 4 | 1 | no | — |
| 271 | C22×C4 | — | 4 | 1 | no | — |
| 272 | C22×C4 | — | 4 | 1 | no | — |
| 273 | C22×C4 | — | 4 | 2 | no | — |
| 274 | C22×C4 | — | 4 | 2 | no | — |
| 275 | C22×C4 | — | 4 | 1 | no | — |
| 276 | C22×C4 | — | 4 | 2 | no | — |
| 277 | C22×C4 | — | 4 | 2 | no | — |
| 278 | C22×C4 | C4×D4 | 1 | 2 | yes | — |
| 279 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 280 | Q16 | — | 2 | 1 | no | — |
| 281 | Q16 | — | 2 | 2 | no | — |
| 282 | Q16 | — | 2 | 2 | no | — |
| 283 | Q16 | — | 2 | 1 | no | — |
| 284 | Q16 | — | 2 | 2 | no | — |
| 285 | Q16 | — | 2 | 1 | no | — |
| 286 | Q16 | — | 2 | 4 | no | — |
| 287 | Q16 | — | 4 | 4 | no | — |
| 288 | Q16 | — | 4 | 4 | no | — |
| 289 | Q16 | — | 4 | 2 | no | — |
| 290 | Q16 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 291 | Q16 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 292 | SD16 | — | 2 | 4 | no | — |
| 293 | SD16 | — | 4 | 4 | no | — |
| 294 | SD16 | — | 4 | 4 | no | — |
| 295 | SD16 | — | 4 | 2 | no | — |
| 296 | D8 | — | 2 | 1 | no | — |
| 297 | D8 | — | 2 | 1 | no | — |
| 298 | D8 | — | 2 | 1 | no | — |
| 299 | D8 | C2×C22⋊C4 | 1 | 2 | yes | — |
| 300 | M16 | — | 2 | 2 | no | — |
| 301 | M16 | — | 2 | 4 | no | — |
| 302 | M16 | — | 2 | 2 | no | — |
| 303 | M16 | — | 2 | 2 | no | — |
| 304 | M16 | — | 4 | 2 | no | — |
| 305 | M16 | — | 4 | 2 | no | — |
| 306 | M16 | — | 8 | 4 | no | — |
| 307 | C2×C8 | — | 2 | 2 | no | — |
| 308 | C2×C8 | — | 2 | 2 | no | — |
| 309 | C2×C8 | — | 2 | 2 | no | — |
| 310 | C2×C8 | — | 4 | 2 | no | — |
| 311 | C2×C8 | — | 8 | 4 | no | — |
| 312 | C2×C8 | C4×D4 | 1 | 2 | yes | — |
| 313 | C2×C8 | C23×C4 | 1 | 1 | yes | characteristic |
| 314 | C2×C8 | C22×D4 | 1 | 2 | yes | — |
| 315 | C2×C8 | C2×#41 | 1 | 1 | yes | characteristic |
| 316 | C2×C8 | H(5,𝔽2) | 1 | 2 | yes | — |
| 317 | C4⋊C4 | — | 2 | 2 | no | — |
| 318 | C4⋊C4 | — | 4 | 2 | no | — |
| 319 | C4⋊C4 | — | 8 | 4 | no | — |
| 320 | C22⋊C4 | — | 2 | 2 | no | — |
| 321 | C22⋊C4 | — | 4 | 2 | no | — |
| 322 | C42 | — | 2 | 2 | no | — |
| 323 | C42 | — | 4 | 2 | no | — |
| 324 | C42 | — | 8 | 4 | no | — |
| 325 | C16 | — | 2 | 1 | no | — |
| 326 | C16 | — | 2 | 1 | no | — |
| 327 | C16 | — | 4 | 2 | no | — |
| 328 | C16 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 329 | C23 | — | 4 | 1 | no | — |
| 330 | C23 | — | 4 | 1 | no | — |
| 331 | C23 | #442 | 1 | 2 | yes | — |
| 332 | C23 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 333 | Q8 | — | 2 | 2 | no | — |
| 334 | Q8 | — | 2 | 2 | no | — |
| 335 | Q8 | — | 2 | 4 | no | — |
| 336 | Q8 | — | 4 | 2 | no | — |
| 337 | Q8 | — | 4 | 1 | no | — |
| 338 | Q8 | — | 4 | 4 | no | — |
| 339 | Q8 | — | 4 | 2 | no | — |
| 340 | Q8 | — | 4 | 1 | no | — |
| 341 | Q8 | — | 4 | 2 | no | — |
| 342 | Q8 | — | 4 | 1 | no | — |
| 343 | Q8 | — | 8 | 4 | no | — |
| 344 | Q8 | — | 8 | 4 | no | — |
| 345 | Q8 | — | 8 | 2 | no | — |
| 346 | D4 | — | 2 | 4 | no | — |
| 347 | D4 | — | 2 | 2 | no | — |
| 348 | D4 | — | 2 | 2 | no | — |
| 349 | D4 | — | 4 | 4 | no | — |
| 350 | D4 | — | 4 | 1 | no | — |
| 351 | D4 | — | 4 | 1 | no | — |
| 352 | D4 | — | 4 | 1 | no | — |
| 353 | D4 | — | 8 | 4 | no | — |
| 354 | D4 | — | 8 | 4 | no | — |
| 355 | D4 | — | 8 | 2 | no | — |
| 356 | C2×C4 | — | 2 | 2 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 4 | 1 | no | — |
| 359 | C2×C4 | — | 4 | 2 | no | — |
| 360 | C2×C4 | — | 4 | 4 | no | — |
| 361 | C2×C4 | — | 4 | 4 | no | — |
| 362 | C2×C4 | — | 4 | 2 | no | — |
| 363 | C2×C4 | — | 4 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 2 | no | — |
| 365 | C2×C4 | — | 8 | 4 | no | — |
| 366 | C2×C4 | — | 8 | 4 | no | — |
| 367 | C2×C4 | — | 8 | 4 | no | — |
| 368 | C2×C4 | — | 8 | 4 | no | — |
| 369 | C2×C4 | — | 8 | 2 | no | — |
| 370 | C2×C4 | — | 8 | 2 | no | — |
| 371 | C2×C4 | — | 8 | 2 | no | — |
| 372 | C2×C4 | #442 | 1 | 2 | yes | — |
| 373 | C2×C4 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 374 | C2×C4 | D42 | 1 | 2 | yes | — |
| 375 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | #576 | 1 | 2 | yes | — |
| 377 | C8 | — | 2 | 2 | no | — |
| 378 | C8 | — | 4 | 2 | no | — |
| 379 | C8 | — | 8 | 2 | no | — |
| 380 | C8 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 381 | C8 | #518 | 1 | 1 | yes | characteristic |
| 382 | C8 | #546 | 1 | 2 | yes | — |
| 383 | C22 | — | 2 | 2 | no | — |
| 384 | C22 | — | 4 | 1 | no | — |
| 385 | C22 | — | 4 | 2 | no | — |
| 386 | C22 | — | 4 | 2 | no | — |
| 387 | C22 | — | 8 | 1 | no | — |
| 388 | C22 | — | 16 | 1 | no | — |
| 389 | C22 | — | 16 | 1 | no | — |
| 390 | C22 | C2×#442 | 1 | 1 | yes | characteristic |
| 391 | C22 | #3264 | 1 | 2 | yes | — |
| 392 | C4 | — | 2 | 2 | no | — |
| 393 | C4 | — | 4 | 2 | no | — |
| 394 | C4 | — | 4 | 4 | no | — |
| 395 | C4 | — | 8 | 2 | no | — |
| 396 | C4 | — | 8 | 2 | no | — |
| 397 | C4 | — | 8 | 1 | no | — |
| 398 | C4 | — | 16 | 2 | no | — |
| 399 | C4 | D4×C22⋊C4 | 1 | 1 | yes | characteristic |
| 400 | C4 | #2948 | 1 | 1 | yes | characteristic |
| 401 | C4 | #3264 | 1 | 2 | yes | — |
| 402 | C2 | — | 2 | 2 | no | — |
| 403 | C2 | — | 2 | 1 | no | — |
| 404 | C2 | — | 4 | 2 | no | — |
| 405 | C2 | — | 8 | 2 | no | — |
| 406 | C2 | — | 16 | 1 | no | — |
| 407 | C2 | #22436 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #22436 |
| commutator | C2×C8 | C23×C4 |
| Frattini, cosocle | C22×C8 | C24 |
| prime radical | C2×#3417 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ #1757 ◁ G | |
| LECS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #33470 | C2 | semidirect |
| 3. #22460 | C2 | semidirect |
| 4. #22457 | C2 | semidirect |
| 5. #13248 | C2 | semidirect |
| 6. #13020 | C2 | semidirect |
| 7. #13016 | C2 | semidirect |
| 8. #12832 | C2 | semidirect |
| 9. #12744 | C2 | semidirect |
| 10. #12742 | C2 | semidirect |
| 11. #12617 | C2 | semidirect |
| 15. C2×#510 | C4 | semidirect |
| 16. C2×#510 | C4 | semidirect |
| 19. C2×#508 | C4 | semidirect |
| 21. C22×Q32 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3417 | 2 |
| #33470 | 2 |
| #22460 | 2 |
| #22457 | 2 |
| #13248 | 2 |
| #13020 | 2 |
| #13016 | 2 |
| #12832 | 2 |
| #12744 | 2 |
| #12742 | 2 |
| #12617 | 2 |