Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
790 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #28527 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #28231 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #25393 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C2×#1693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#1594 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10421 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10231 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #9836 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #9611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #9227 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #8210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#500 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#474 | C22 | 1 | 2 | yes | — |
| 14 | C2×#469 | — | 2 | 1 | no | — |
| 15 | C2×#468 | — | 2 | 2 | no | — |
| 16 | C2×#461 | C22 | 1 | 2 | yes | — |
| 17 | C2×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#436 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#436 | C22 | 1 | 2 | yes | — |
| 20 | #2542 | C22 | 1 | 2 | yes | — |
| 21 | #2537 | C22 | 1 | 2 | yes | — |
| 22 | #2093 | — | 2 | 2 | no | — |
| 23 | #2036 | — | 2 | 2 | no | — |
| 24 | #2034 | — | 2 | 2 | no | — |
| 25 | #2000 | — | 2 | 2 | no | — |
| 26 | #1990 | C22 | 1 | 2 | yes | — |
| 27 | #1970 | — | 2 | 1 | no | — |
| 28 | #1956 | C22 | 1 | 2 | yes | — |
| 29 | #1947 | C22 | 1 | 2 | yes | — |
| 30 | #1894 | — | 2 | 2 | no | — |
| 31 | #1845 | — | 2 | 1 | no | — |
| 32 | #1844 | C22 | 1 | 1 | yes | characteristic |
| 33 | #1809 | — | 2 | 1 | no | — |
| 34 | #1802 | C22 | 1 | 2 | yes | — |
| 35 | C8×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×#102 | C22 | 1 | 1 | yes | characteristic |
| 37 | #1693 | — | 2 | 4 | no | — |
| 38 | #1594 | — | 2 | 4 | no | — |
| 39 | C2×#334 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#332 | C22 | 1 | 2 | yes | — |
| 41 | C2×D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×D4⋊C8 | C22 | 1 | 2 | yes | — |
| 43 | C2×#322 | C22 | 1 | 1 | yes | characteristic |
| 44 | #1296 | C22 | 1 | 2 | yes | — |
| 45 | #1279 | C22 | 1 | 1 | yes | characteristic |
| 46 | #1277 | C22 | 1 | 1 | yes | characteristic |
| 47 | C22×SD16 | — | 2 | 2 | no | — |
| 48 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 49 | C22×M16 | — | 2 | 1 | no | — |
| 50 | C22×M16 | — | 2 | 2 | no | — |
| 51 | C2×C4⋊Q8 | C23 | 1 | 2 | yes | — |
| 52 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 53 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 54 | C2×#121 | — | 2 | 2 | no | — |
| 55 | C2×#121 | — | 2 | 2 | no | — |
| 56 | C2×C4×D4 | C23 | 1 | 2 | yes | — |
| 57 | C2×C4×D4 | C23 | 1 | 1 | yes | characteristic |
| 58 | #500 | — | 2 | 2 | no | — |
| 59 | #500 | — | 2 | 2 | no | — |
| 60 | #474 | — | 2 | 4 | no | — |
| 61 | #474 | — | 4 | 2 | no | — |
| 62 | #469 | — | 4 | 4 | no | — |
| 63 | #468 | — | 4 | 8 | no | — |
| 64 | #461 | — | 2 | 4 | no | — |
| 65 | #461 | — | 4 | 2 | no | — |
| 66 | C4×D8 | — | 2 | 2 | no | — |
| 67 | C4×D8 | — | 2 | 2 | no | — |
| 68 | #436 | — | 2 | 4 | no | — |
| 69 | #436 | — | 2 | 2 | no | — |
| 70 | #436 | — | 2 | 2 | no | — |
| 71 | #436 | — | 4 | 2 | no | — |
| 72 | C2×#107 | — | 2 | 1 | no | — |
| 73 | C2×#107 | — | 2 | 1 | no | — |
| 74 | C2×#107 | — | 2 | 2 | no | — |
| 75 | C2×#107 | — | 2 | 2 | no | — |
| 76 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×#106 | — | 2 | 1 | no | — |
| 78 | C2×#106 | — | 2 | 1 | no | — |
| 79 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×C4⋊C8 | C23 | 1 | 2 | yes | — |
| 81 | C2×C4⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×#103 | — | 2 | 2 | no | — |
| 83 | C2×#103 | — | 2 | 2 | no | — |
| 84 | C2×#103 | — | 2 | 2 | no | — |
| 85 | C2×#102 | — | 2 | 2 | no | — |
| 86 | C2×#102 | — | 2 | 2 | no | — |
| 87 | C2×#102 | D4 | 1 | 2 | yes | — |
| 88 | C2×#102 | D4 | 1 | 2 | yes | — |
| 89 | C2×C22⋊C8 | — | 2 | 2 | no | — |
| 90 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 91 | C2×C4×C8 | — | 2 | 1 | no | — |
| 92 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 95 | #399 | — | 4 | 2 | no | — |
| 96 | #394 | — | 4 | 2 | no | — |
| 97 | #390 | — | 2 | 2 | no | — |
| 98 | #384 | — | 2 | 2 | no | — |
| 99 | #384 | C23 | 1 | 2 | yes | — |
| 100 | #380 | — | 2 | 2 | no | — |
| 101 | #380 | — | 2 | 2 | no | — |
| 102 | C4×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 103 | #340 | — | 2 | 2 | no | — |
| 104 | #340 | — | 2 | 2 | no | — |
| 105 | #340 | — | 4 | 2 | no | — |
| 106 | #340 | D4 | 1 | 2 | yes | — |
| 107 | #336 | — | 2 | 1 | no | — |
| 108 | #334 | D4 | 1 | 4 | yes | complemented |
| 109 | #332 | — | 2 | 4 | no | — |
| 110 | D4⋊C8 | — | 2 | 4 | no | — |
| 111 | D4⋊C8 | — | 2 | 2 | no | — |
| 112 | #322 | — | 2 | 2 | no | — |
| 113 | C22×Q8 | — | 2 | 2 | no | — |
| 114 | C22×D4 | — | 4 | 2 | no | — |
| 115 | C22×D4 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | C22×D4 | C2×D4 | 1 | 2 | yes | — |
| 117 | C23×C4 | — | 2 | 1 | no | — |
| 118 | C23×C4 | — | 2 | 2 | no | — |
| 119 | C2×SD16 | — | 4 | 4 | no | — |
| 120 | C2×SD16 | — | 4 | 4 | no | — |
| 121 | C2×SD16 | — | 8 | 2 | no | — |
| 122 | C2×D8 | — | 2 | 2 | no | — |
| 123 | C2×D8 | — | 2 | 2 | no | — |
| 124 | C2×D8 | — | 2 | 2 | no | — |
| 125 | C2×M16 | — | 4 | 4 | no | — |
| 126 | C2×M16 | — | 4 | 4 | no | — |
| 127 | C2×M16 | — | 4 | 2 | no | — |
| 128 | C2×M16 | — | 4 | 2 | no | — |
| 129 | C2×M16 | — | 4 | 2 | no | — |
| 130 | C2×M16 | — | 8 | 2 | no | — |
| 131 | C22×C8 | — | 2 | 2 | no | — |
| 132 | C22×C8 | — | 2 | 1 | no | — |
| 133 | C22×C8 | — | 2 | 1 | no | — |
| 134 | C22×C8 | — | 2 | 1 | no | — |
| 135 | C22×C8 | C2×D4 | 1 | 2 | yes | — |
| 136 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C4⋊Q8 | — | 2 | 2 | no | — |
| 139 | C4⋊Q8 | — | 2 | 2 | no | — |
| 140 | C4⋊Q8 | — | 2 | 2 | no | — |
| 141 | C4⋊Q8 | — | 2 | 2 | no | — |
| 142 | C22⋊Q8 | — | 4 | 4 | no | — |
| 143 | C22⋊Q8 | — | 4 | 4 | no | — |
| 144 | C22⋊Q8 | — | 8 | 2 | no | — |
| 145 | C22⋊Q8 | — | 8 | 2 | no | — |
| 146 | #121 | — | 4 | 4 | no | — |
| 147 | #121 | — | 4 | 4 | no | — |
| 148 | #121 | — | 8 | 2 | no | — |
| 149 | #121 | — | 8 | 2 | no | — |
| 150 | C4×D4 | — | 2 | 2 | no | — |
| 151 | C4×D4 | — | 2 | 1 | no | — |
| 152 | C4×D4 | — | 2 | 1 | no | — |
| 153 | C4×D4 | — | 2 | 1 | no | — |
| 154 | C4×D4 | — | 2 | 2 | no | — |
| 155 | C4×D4 | — | 2 | 2 | no | — |
| 156 | C4×D4 | — | 2 | 2 | no | — |
| 157 | C4×D4 | — | 2 | 1 | no | — |
| 158 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 159 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 160 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 161 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 162 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 163 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 164 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 165 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×C4⋊C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C2×C4⋊C4 | C2×D4 | 1 | 2 | yes | — |
| 168 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 169 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 171 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 172 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 173 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 174 | C2×C42 | — | 2 | 1 | no | — |
| 175 | C2×C42 | C24 | 1 | 1 | yes | characteristic |
| 176 | #107 | — | 2 | 2 | no | — |
| 177 | #107 | — | 4 | 4 | no | — |
| 178 | #107 | — | 4 | 2 | no | — |
| 179 | #107 | — | 4 | 2 | no | — |
| 180 | #107 | — | 4 | 4 | no | — |
| 181 | #106 | — | 4 | 2 | no | — |
| 182 | #106 | — | 8 | 1 | no | — |
| 183 | C4⋊C8 | — | 2 | 1 | no | — |
| 184 | C4⋊C8 | — | 2 | 1 | no | — |
| 185 | C4⋊C8 | — | 2 | 2 | no | — |
| 186 | C4⋊C8 | — | 2 | 1 | no | — |
| 187 | C4⋊C8 | C2×D4 | 1 | 4 | yes | — |
| 188 | C4⋊C8 | #41 | 1 | 2 | yes | — |
| 189 | #103 | — | 4 | 4 | no | — |
| 190 | #103 | — | 4 | 4 | no | — |
| 191 | #103 | — | 8 | 2 | no | — |
| 192 | #102 | — | 2 | 4 | no | — |
| 193 | #102 | — | 2 | 4 | no | — |
| 194 | #102 | — | 4 | 4 | no | — |
| 195 | #102 | — | 4 | 4 | no | — |
| 196 | C22⋊C8 | — | 4 | 4 | no | — |
| 197 | C22⋊C8 | — | 4 | 2 | no | — |
| 198 | C4×C8 | — | 2 | 1 | no | — |
| 199 | C4×C8 | — | 2 | 1 | no | — |
| 200 | C4×C8 | — | 2 | 1 | no | — |
| 201 | C4×C8 | — | 2 | 1 | no | — |
| 202 | C4×C8 | — | 4 | 2 | no | — |
| 203 | C4×C8 | C2×D4 | 1 | 2 | yes | — |
| 204 | C4×C8 | #41 | 1 | 2 | yes | — |
| 205 | #95 | — | 2 | 1 | no | — |
| 206 | #95 | — | 4 | 2 | no | — |
| 207 | C24 | — | 2 | 2 | no | — |
| 208 | C24 | — | 2 | 1 | no | — |
| 209 | C2×Q8 | — | 4 | 2 | no | — |
| 210 | C2×Q8 | — | 4 | 2 | no | — |
| 211 | C2×Q8 | — | 4 | 2 | no | — |
| 212 | C2×Q8 | — | 4 | 2 | no | — |
| 213 | C2×Q8 | — | 4 | 2 | no | — |
| 214 | C2×Q8 | — | 4 | 2 | no | — |
| 215 | C2×D4 | — | 2 | 2 | no | — |
| 216 | C2×D4 | — | 2 | 1 | no | — |
| 217 | C2×D4 | — | 2 | 1 | no | — |
| 218 | C2×D4 | — | 2 | 2 | no | — |
| 219 | C2×D4 | — | 2 | 2 | no | — |
| 220 | C2×D4 | — | 2 | 2 | no | — |
| 221 | C2×D4 | — | 2 | 2 | no | — |
| 222 | C2×D4 | — | 2 | 2 | no | — |
| 223 | C2×D4 | — | 2 | 2 | no | — |
| 224 | C2×D4 | — | 2 | 2 | no | — |
| 225 | C2×D4 | — | 8 | 4 | no | — |
| 226 | C2×D4 | — | 8 | 4 | no | — |
| 227 | C2×D4 | — | 16 | 2 | no | — |
| 228 | C22×C4 | — | 2 | 2 | no | — |
| 229 | C22×C4 | — | 2 | 1 | no | — |
| 230 | C22×C4 | — | 2 | 2 | no | — |
| 231 | C22×C4 | — | 4 | 1 | no | — |
| 232 | C22×C4 | — | 4 | 2 | no | — |
| 233 | C22×C4 | — | 4 | 2 | no | — |
| 234 | C22×C4 | — | 4 | 1 | no | — |
| 235 | C22×C4 | — | 4 | 1 | no | — |
| 236 | C22×C4 | — | 4 | 2 | no | — |
| 237 | C22×C4 | — | 4 | 2 | no | — |
| 238 | C22×C4 | — | 4 | 1 | no | — |
| 239 | C22×C4 | — | 4 | 2 | no | — |
| 240 | C22×C4 | — | 4 | 2 | no | — |
| 241 | C22×C4 | — | 4 | 1 | no | — |
| 242 | C22×C4 | — | 4 | 1 | no | — |
| 243 | C22×C4 | — | 4 | 2 | no | — |
| 244 | C22×C4 | — | 4 | 2 | no | — |
| 245 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 246 | C22×C4 | C22×D4 | 1 | 1 | yes | characteristic |
| 247 | C22×C4 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 248 | SD16 | — | 8 | 8 | no | — |
| 249 | D8 | — | 4 | 4 | no | — |
| 250 | M16 | — | 8 | 8 | no | — |
| 251 | M16 | — | 8 | 4 | no | — |
| 252 | C2×C8 | — | 2 | 1 | no | — |
| 253 | C2×C8 | — | 2 | 1 | no | — |
| 254 | C2×C8 | — | 2 | 2 | no | — |
| 255 | C2×C8 | — | 2 | 4 | no | — |
| 256 | C2×C8 | — | 2 | 2 | no | — |
| 257 | C2×C8 | — | 2 | 2 | no | — |
| 258 | C2×C8 | — | 2 | 2 | no | — |
| 259 | C2×C8 | — | 4 | 1 | no | — |
| 260 | C2×C8 | — | 4 | 2 | no | — |
| 261 | C2×C8 | — | 4 | 2 | no | — |
| 262 | C2×C8 | — | 4 | 1 | no | — |
| 263 | C2×C8 | — | 4 | 2 | no | — |
| 264 | C2×C8 | — | 4 | 1 | no | — |
| 265 | C2×C8 | — | 4 | 1 | no | — |
| 266 | C2×C8 | — | 4 | 1 | no | — |
| 267 | C2×C8 | — | 4 | 1 | no | — |
| 268 | C2×C8 | #121 | 1 | 2 | yes | — |
| 269 | C2×C8 | #121 | 1 | 2 | yes | — |
| 270 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 271 | C2×C8 | #137 | 1 | 2 | yes | — |
| 272 | C4⋊C4 | — | 2 | 2 | no | — |
| 273 | C4⋊C4 | — | 2 | 2 | no | — |
| 274 | C4⋊C4 | — | 2 | 1 | no | — |
| 275 | C4⋊C4 | — | 2 | 1 | no | — |
| 276 | C4⋊C4 | — | 2 | 2 | no | — |
| 277 | C4⋊C4 | — | 4 | 2 | no | — |
| 278 | C4⋊C4 | — | 4 | 2 | no | — |
| 279 | C4⋊C4 | — | 4 | 2 | no | — |
| 280 | C4⋊C4 | — | 4 | 2 | no | — |
| 281 | C4⋊C4 | — | 4 | 2 | no | — |
| 282 | C4⋊C4 | — | 4 | 2 | no | — |
| 283 | C4⋊C4 | — | 4 | 2 | no | — |
| 284 | C4⋊C4 | — | 4 | 2 | no | — |
| 285 | C4⋊C4 | — | 8 | 4 | no | — |
| 286 | C4⋊C4 | — | 8 | 4 | no | — |
| 287 | C4⋊C4 | — | 8 | 2 | no | — |
| 288 | C4⋊C4 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 289 | C22⋊C4 | — | 4 | 1 | no | — |
| 290 | C22⋊C4 | — | 4 | 2 | no | — |
| 291 | C22⋊C4 | — | 4 | 1 | no | — |
| 292 | C22⋊C4 | — | 4 | 2 | no | — |
| 293 | C22⋊C4 | — | 8 | 4 | no | — |
| 294 | C22⋊C4 | — | 8 | 4 | no | — |
| 295 | C22⋊C4 | — | 8 | 4 | no | — |
| 296 | C22⋊C4 | — | 8 | 4 | no | — |
| 297 | C42 | — | 4 | 1 | no | — |
| 298 | C42 | — | 4 | 1 | no | — |
| 299 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 300 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 301 | C42 | C2×#41 | 1 | 1 | yes | characteristic |
| 302 | C42 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 303 | C23 | — | 4 | 1 | no | — |
| 304 | C23 | — | 4 | 2 | no | — |
| 305 | C23 | — | 4 | 2 | no | — |
| 306 | C23 | — | 4 | 2 | no | — |
| 307 | C23 | — | 4 | 2 | no | — |
| 308 | C23 | — | 4 | 2 | no | — |
| 309 | C23 | — | 4 | 1 | no | — |
| 310 | C23 | — | 4 | 1 | no | — |
| 311 | C23 | — | 4 | 2 | no | — |
| 312 | C23 | — | 4 | 2 | no | — |
| 313 | C23 | — | 4 | 2 | no | — |
| 314 | C23 | — | 4 | 2 | no | — |
| 315 | C23 | D42 | 1 | 1 | yes | characteristic |
| 316 | Q8 | — | 8 | 2 | no | — |
| 317 | Q8 | — | 8 | 2 | no | — |
| 318 | Q8 | — | 8 | 2 | no | — |
| 319 | Q8 | — | 8 | 2 | no | — |
| 320 | D4 | — | 4 | 2 | no | — |
| 321 | D4 | — | 4 | 2 | no | — |
| 322 | D4 | — | 4 | 1 | no | — |
| 323 | D4 | — | 4 | 1 | no | — |
| 324 | D4 | — | 4 | 2 | no | — |
| 325 | D4 | — | 4 | 2 | no | — |
| 326 | D4 | — | 4 | 2 | no | — |
| 327 | D4 | — | 16 | 8 | no | — |
| 328 | C2×C4 | — | 2 | 2 | no | — |
| 329 | C2×C4 | — | 2 | 4 | no | — |
| 330 | C2×C4 | — | 4 | 2 | no | — |
| 331 | C2×C4 | — | 4 | 2 | no | — |
| 332 | C2×C4 | — | 4 | 1 | no | — |
| 333 | C2×C4 | — | 4 | 2 | no | — |
| 334 | C2×C4 | — | 4 | 2 | no | — |
| 335 | C2×C4 | — | 4 | 2 | no | — |
| 336 | C2×C4 | — | 4 | 1 | no | — |
| 337 | C2×C4 | — | 4 | 1 | no | — |
| 338 | C2×C4 | — | 8 | 1 | no | — |
| 339 | C2×C4 | — | 8 | 1 | no | — |
| 340 | C2×C4 | — | 8 | 2 | no | — |
| 341 | C2×C4 | — | 8 | 2 | no | — |
| 342 | C2×C4 | — | 8 | 2 | no | — |
| 343 | C2×C4 | — | 8 | 2 | no | — |
| 344 | C2×C4 | — | 8 | 1 | no | — |
| 345 | C2×C4 | — | 8 | 1 | no | — |
| 346 | C2×C4 | — | 8 | 2 | no | — |
| 347 | C2×C4 | — | 8 | 2 | no | — |
| 348 | C2×C4 | — | 8 | 2 | no | — |
| 349 | C2×C4 | — | 8 | 2 | no | — |
| 350 | C2×C4 | — | 8 | 2 | no | — |
| 351 | C2×C4 | — | 8 | 2 | no | — |
| 352 | C2×C4 | C2×#121 | 1 | 1 | yes | characteristic |
| 353 | C2×C4 | #532 | 1 | 1 | yes | characteristic |
| 354 | C2×C4 | #540 | 1 | 1 | yes | characteristic |
| 355 | C2×C4 | D42 | 1 | 1 | yes | characteristic |
| 356 | C2×C4 | #546 | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | #550 | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 359 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 360 | C2×C4 | C2×#137 | 1 | 1 | yes | characteristic |
| 361 | C2×C4 | #576 | 1 | 2 | yes | — |
| 362 | C2×C4 | #577 | 1 | 1 | yes | characteristic |
| 363 | C2×C4 | #578 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 2 | 2 | no | — |
| 365 | C8 | — | 4 | 2 | no | — |
| 366 | C8 | — | 4 | 2 | no | — |
| 367 | C8 | — | 4 | 4 | no | — |
| 368 | C8 | — | 8 | 1 | no | — |
| 369 | C8 | — | 8 | 1 | no | — |
| 370 | C8 | #468 | 1 | 4 | yes | complemented |
| 371 | C22 | — | 8 | 1 | no | — |
| 372 | C22 | — | 8 | 2 | no | — |
| 373 | C22 | — | 8 | 2 | no | — |
| 374 | C22 | — | 8 | 1 | no | — |
| 375 | C22 | — | 8 | 1 | no | — |
| 376 | C22 | — | 8 | 2 | no | — |
| 377 | C22 | — | 8 | 2 | no | — |
| 378 | C22 | — | 8 | 2 | no | — |
| 379 | C22 | — | 8 | 2 | no | — |
| 380 | C22 | — | 8 | 2 | no | — |
| 381 | C22 | — | 8 | 2 | no | — |
| 382 | C22 | — | 8 | 2 | no | — |
| 383 | C22 | #2428 | 1 | 1 | yes | characteristic |
| 384 | C22 | #3264 | 1 | 2 | yes | — |
| 385 | C22 | #3272 | 1 | 1 | yes | characteristic |
| 386 | C22 | #3276 | 1 | 1 | yes | characteristic |
| 387 | C22 | #3289 | 1 | 2 | yes | — |
| 388 | C4 | — | 2 | 1 | no | — |
| 389 | C4 | — | 2 | 1 | no | — |
| 390 | C4 | — | 4 | 4 | no | — |
| 391 | C4 | — | 8 | 1 | no | — |
| 392 | C4 | — | 8 | 2 | no | — |
| 393 | C4 | — | 16 | 2 | no | — |
| 394 | C4 | — | 16 | 2 | no | — |
| 395 | C4 | C2×#468 | 1 | 1 | yes | characteristic |
| 396 | C4 | #3063 | 1 | 1 | yes | characteristic |
| 397 | C4 | #3176 | 1 | 1 | yes | characteristic |
| 398 | C4 | #3184 | 1 | 1 | yes | characteristic |
| 399 | C4 | #3274 | 1 | 2 | yes | — |
| 400 | C4 | #3329 | 1 | 1 | yes | characteristic |
| 401 | C4 | #3330 | 1 | 1 | yes | characteristic |
| 402 | C2 | — | 16 | 1 | no | — |
| 403 | C2 | — | 16 | 2 | no | — |
| 404 | C2 | #20163 | 1 | 2 | yes | — |
| 405 | C2 | #20167 | 1 | 2 | yes | — |
| 406 | C2 | #25393 | 1 | 1 | yes | characteristic |
| 407 | C2 | #25426 | 1 | 1 | yes | characteristic |
| 408 | C2 | #25445 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | D42 |
| commutator, Frattini, cosocle | C2×C42 | C24 |
| prime radical | #28231 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C42 ◁ G | |
| LECS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28527 | C2 | semidirect |
| 3. #25393 | C2 | semidirect |
| 4. C2×#1693 | C2 | semidirect |
| 5. C2×#1594 | C2 | semidirect |
| 6. #10421 | C2 | semidirect |
| 7. #10231 | C2 | semidirect |
| 8. #9836 | C2 | semidirect |
| 9. #9611 | C2 | semidirect |
| 10. #9227 | C2 | semidirect |
| 11. #8210 | C2 | semidirect |
| 108. #334 | D4 | semidirect |
| 370. C8 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28527 | 2 |
| #28231 | 2 |
| #25393 | 2 |
| C2×#1693 | 2 |
| C2×#1594 | 2 |
| #10421 | 2 |
| #10231 | 2 |
| #9836 | 2 |
| #9611 | 2 |
| #9227 | 2 |
| #8210 | 2 |