Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
583 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 583 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #33516 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22204 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #12734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11709 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #11025 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #7261 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #7183 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#135 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#508 | — | 2 | 1 | no | — |
| 10 | #3050 | C22 | 1 | 1 | yes | characteristic |
| 11 | #2929 | — | 2 | 1 | no | — |
| 12 | C22×#104 | — | 2 | 1 | no | — |
| 13 | C2×#408 | — | 2 | 1 | no | — |
| 14 | #2189 | — | 2 | 1 | no | — |
| 15 | #2188 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #2187 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #2186 | — | 2 | 1 | no | — |
| 18 | #2185 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #2184 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#359 | — | 2 | 1 | no | — |
| 21 | C2×#359 | — | 2 | 1 | no | — |
| 22 | #2138 | — | 2 | 1 | no | — |
| 23 | C2×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 25 | #1929 | — | 2 | 1 | no | — |
| 26 | #1922 | — | 2 | 1 | no | — |
| 27 | #1896 | — | 2 | 1 | no | — |
| 28 | #1876 | — | 2 | 1 | no | — |
| 29 | #1866 | — | 2 | 1 | no | — |
| 30 | #1810 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#341 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#336 | C22 | 1 | 1 | yes | characteristic |
| 33 | #1350 | — | 2 | 1 | no | — |
| 34 | #1349 | — | 2 | 1 | no | — |
| 35 | C22×#41 | — | 2 | 1 | no | — |
| 36 | C2×#135 | — | 2 | 1 | no | — |
| 37 | C2×#135 | — | 2 | 1 | no | — |
| 38 | C2×#135 | — | 2 | 1 | no | — |
| 39 | C2×#135 | — | 2 | 1 | no | — |
| 40 | C2×#135 | — | 4 | 2 | no | — |
| 41 | C2×#135 | — | 4 | 2 | no | — |
| 42 | C2×#135 | D4 | 1 | 1 | yes | characteristic |
| 43 | C22×Q16 | C2×C4 | 1 | 1 | yes | characteristic |
| 44 | C22×SD16 | — | 2 | 1 | no | — |
| 45 | C22×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C2×#131 | — | 2 | 1 | no | — |
| 47 | C22×M16 | — | 2 | 1 | no | — |
| 48 | C23×C8 | D4 | 1 | 1 | yes | characteristic |
| 49 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 50 | #525 | — | 2 | 1 | no | — |
| 51 | C22×C42 | D4 | 1 | 1 | yes | characteristic |
| 52 | #508 | — | 4 | 2 | no | — |
| 53 | #508 | — | 4 | 2 | no | — |
| 54 | C2×Q32 | — | 2 | 1 | no | — |
| 55 | C2×SD32 | — | 2 | 1 | no | — |
| 56 | C2×SD32 | — | 2 | 1 | no | — |
| 57 | C2×D16 | — | 2 | 1 | no | — |
| 58 | C22×C16 | — | 2 | 1 | no | — |
| 59 | C22×C16 | — | 2 | 1 | no | — |
| 60 | #467 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | #467 | D4 | 1 | 1 | yes | characteristic |
| 62 | #466 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | #466 | D4 | 1 | 1 | yes | characteristic |
| 64 | #465 | — | 2 | 1 | no | — |
| 65 | #465 | — | 2 | 1 | no | — |
| 66 | #435 | — | 4 | 1 | no | — |
| 67 | #435 | — | 4 | 1 | no | — |
| 68 | C8×D4 | — | 4 | 1 | no | — |
| 69 | C8×D4 | — | 4 | 1 | no | — |
| 70 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×#108 | D4 | 1 | 1 | yes | characteristic |
| 72 | #427 | D4 | 1 | 1 | yes | characteristic |
| 73 | #424 | — | 2 | 1 | no | — |
| 74 | C2×#104 | — | 2 | 1 | no | — |
| 75 | C2×#104 | — | 2 | 1 | no | — |
| 76 | C2×#104 | — | 4 | 2 | no | — |
| 77 | C2×#104 | — | 4 | 2 | no | — |
| 78 | C2×#104 | — | 4 | 2 | no | — |
| 79 | #416 | — | 2 | 1 | no | — |
| 80 | #408 | — | 2 | 1 | no | — |
| 81 | #408 | — | 4 | 2 | no | — |
| 82 | #408 | — | 4 | 2 | no | — |
| 83 | #407 | — | 2 | 1 | no | — |
| 84 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 85 | C2×C22⋊C8 | — | 4 | 1 | no | — |
| 86 | #405 | — | 2 | 1 | no | — |
| 87 | #359 | — | 4 | 2 | no | — |
| 88 | #359 | — | 4 | 2 | no | — |
| 89 | #358 | — | 2 | 1 | no | — |
| 90 | #358 | — | 2 | 1 | no | — |
| 91 | #357 | — | 2 | 1 | no | — |
| 92 | #357 | — | 2 | 1 | no | — |
| 93 | C22⋊C16 | — | 2 | 1 | no | — |
| 94 | C22⋊C16 | — | 2 | 1 | no | — |
| 95 | C22⋊C16 | — | 2 | 1 | no | — |
| 96 | C22⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 97 | C22⋊C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 98 | #341 | — | 2 | 1 | no | — |
| 99 | #341 | — | 2 | 1 | no | — |
| 100 | #341 | — | 2 | 1 | no | — |
| 101 | #339 | — | 2 | 1 | no | — |
| 102 | #339 | — | 2 | 1 | no | — |
| 103 | #336 | — | 2 | 1 | no | — |
| 104 | #336 | — | 2 | 1 | no | — |
| 105 | C2×#41 | — | 2 | 2 | no | — |
| 106 | C2×#41 | — | 2 | 2 | no | — |
| 107 | C2×#41 | — | 2 | 1 | no | — |
| 108 | C2×#41 | — | 4 | 1 | no | — |
| 109 | C2×#41 | — | 4 | 1 | no | — |
| 110 | C2×#41 | — | 4 | 1 | no | — |
| 111 | C2×#41 | — | 4 | 1 | no | — |
| 112 | C2×#41 | — | 4 | 1 | no | — |
| 113 | C2×#41 | — | 4 | 1 | no | — |
| 114 | C2×#41 | — | 4 | 1 | no | — |
| 115 | C2×#41 | — | 4 | 1 | no | — |
| 116 | C2×#41 | — | 4 | 1 | no | — |
| 117 | C2×#41 | — | 4 | 1 | no | — |
| 118 | C22×Q8 | — | 2 | 1 | no | — |
| 119 | C22×D4 | — | 2 | 1 | no | — |
| 120 | C22×D4 | — | 4 | 1 | no | — |
| 121 | C23×C4 | — | 2 | 1 | no | — |
| 122 | C23×C4 | — | 4 | 1 | no | — |
| 123 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | #135 | — | 2 | 2 | no | — |
| 125 | #135 | — | 2 | 2 | no | — |
| 126 | #135 | — | 2 | 2 | no | — |
| 127 | #135 | — | 2 | 2 | no | — |
| 128 | #135 | — | 4 | 1 | no | — |
| 129 | #135 | — | 4 | 1 | no | — |
| 130 | #135 | — | 4 | 1 | no | — |
| 131 | #135 | — | 4 | 1 | no | — |
| 132 | #135 | — | 4 | 1 | no | — |
| 133 | #135 | — | 4 | 1 | no | — |
| 134 | #135 | — | 4 | 2 | no | — |
| 135 | #135 | — | 4 | 2 | no | — |
| 136 | #135 | — | 4 | 2 | no | — |
| 137 | #135 | — | 4 | 2 | no | — |
| 138 | C2×Q16 | — | 2 | 1 | no | — |
| 139 | C2×Q16 | — | 2 | 1 | no | — |
| 140 | C2×Q16 | — | 4 | 2 | no | — |
| 141 | C2×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 142 | C2×SD16 | — | 2 | 1 | no | — |
| 143 | C2×SD16 | — | 4 | 2 | no | — |
| 144 | C2×SD16 | — | 4 | 2 | no | — |
| 145 | C2×SD16 | — | 4 | 1 | no | — |
| 146 | C2×SD16 | — | 4 | 1 | no | — |
| 147 | C2×D8 | — | 2 | 1 | no | — |
| 148 | C2×D8 | — | 2 | 1 | no | — |
| 149 | C2×D8 | — | 4 | 2 | no | — |
| 150 | C2×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 151 | #131 | — | 8 | 1 | no | — |
| 152 | #131 | — | 8 | 1 | no | — |
| 153 | C2×M16 | — | 2 | 2 | no | — |
| 154 | C2×M16 | — | 2 | 1 | no | — |
| 155 | C2×M16 | — | 2 | 1 | no | — |
| 156 | C2×M16 | — | 4 | 1 | no | — |
| 157 | C2×M16 | — | 4 | 1 | no | — |
| 158 | C2×M16 | — | 4 | 1 | no | — |
| 159 | C2×M16 | — | 4 | 1 | no | — |
| 160 | C2×M16 | — | 4 | 1 | no | — |
| 161 | C2×M16 | — | 4 | 1 | no | — |
| 162 | C22×C8 | — | 2 | 1 | no | — |
| 163 | C22×C8 | — | 2 | 1 | no | — |
| 164 | C22×C8 | — | 4 | 1 | no | — |
| 165 | C22×C8 | — | 4 | 1 | no | — |
| 166 | C22×C8 | — | 4 | 1 | no | — |
| 167 | C22×C8 | — | 4 | 1 | no | — |
| 168 | C22×C8 | — | 4 | 1 | no | — |
| 169 | C22×C8 | — | 4 | 1 | no | — |
| 170 | C22×C8 | D8 | 1 | 1 | yes | characteristic |
| 171 | C22×C8 | D8 | 1 | 1 | yes | characteristic |
| 172 | C22×C8 | C22×C4 | 1 | 1 | yes | characteristic |
| 173 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×C8 | #41 | 1 | 1 | yes | characteristic |
| 177 | C22×C8 | #41 | 1 | 1 | yes | characteristic |
| 178 | #123 | — | 4 | 1 | no | — |
| 179 | C22⋊Q8 | — | 2 | 1 | no | — |
| 180 | C22⋊Q8 | — | 2 | 1 | no | — |
| 181 | #121 | — | 2 | 1 | no | — |
| 182 | #121 | — | 2 | 1 | no | — |
| 183 | #120 | — | 4 | 1 | no | — |
| 184 | C4×D4 | — | 4 | 1 | no | — |
| 185 | C4×D4 | — | 4 | 1 | no | — |
| 186 | #117 | — | 2 | 1 | no | — |
| 187 | C2×C42 | — | 2 | 1 | no | — |
| 188 | C2×C42 | — | 2 | 1 | no | — |
| 189 | C2×C42 | — | 4 | 1 | no | — |
| 190 | C2×C42 | — | 4 | 1 | no | — |
| 191 | Q32 | — | 4 | 2 | no | — |
| 192 | SD32 | — | 4 | 2 | no | — |
| 193 | SD32 | — | 4 | 2 | no | — |
| 194 | D16 | — | 4 | 2 | no | — |
| 195 | C2×C16 | — | 2 | 1 | no | — |
| 196 | C2×C16 | — | 2 | 1 | no | — |
| 197 | C2×C16 | — | 4 | 1 | no | — |
| 198 | C2×C16 | — | 4 | 1 | no | — |
| 199 | C2×C16 | — | 4 | 1 | no | — |
| 200 | C2×C16 | — | 4 | 1 | no | — |
| 201 | C2×C16 | — | 4 | 1 | no | — |
| 202 | #108 | — | 4 | 1 | no | — |
| 203 | #108 | — | 4 | 1 | no | — |
| 204 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 205 | #107 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 206 | #106 | — | 2 | 1 | no | — |
| 207 | C4⋊C8 | — | 4 | 1 | no | — |
| 208 | C4⋊C8 | — | 4 | 1 | no | — |
| 209 | #104 | — | 4 | 8 | no | — |
| 210 | #104 | — | 8 | 1 | no | — |
| 211 | #104 | — | 8 | 1 | no | — |
| 212 | #103 | — | 2 | 1 | no | — |
| 213 | #103 | — | 2 | 1 | no | — |
| 214 | #102 | — | 2 | 1 | no | — |
| 215 | #102 | — | 2 | 1 | no | — |
| 216 | C22⋊C8 | — | 4 | 1 | no | — |
| 217 | C22⋊C8 | — | 4 | 1 | no | — |
| 218 | C22⋊C8 | — | 4 | 4 | no | — |
| 219 | C22⋊C8 | — | 4 | 4 | no | — |
| 220 | C22⋊C8 | — | 4 | 1 | no | — |
| 221 | C22⋊C8 | — | 4 | 1 | no | — |
| 222 | #97 | — | 4 | 1 | no | — |
| 223 | C4×C8 | — | 4 | 1 | no | — |
| 224 | C24 | — | 4 | 1 | no | — |
| 225 | C24 | #135 | 1 | 1 | yes | characteristic |
| 226 | #41 | — | 4 | 2 | no | — |
| 227 | #41 | — | 4 | 2 | no | — |
| 228 | #41 | — | 4 | 2 | no | — |
| 229 | #41 | — | 4 | 2 | no | — |
| 230 | #41 | — | 4 | 2 | no | — |
| 231 | #41 | — | 4 | 2 | no | — |
| 232 | #41 | — | 4 | 1 | no | — |
| 233 | #41 | — | 4 | 1 | no | — |
| 234 | #41 | — | 4 | 1 | no | — |
| 235 | #41 | — | 4 | 1 | no | — |
| 236 | #41 | — | 4 | 2 | no | — |
| 237 | #41 | — | 4 | 2 | no | — |
| 238 | #41 | — | 8 | 1 | no | — |
| 239 | #41 | — | 8 | 1 | no | — |
| 240 | #41 | — | 8 | 1 | no | — |
| 241 | #41 | — | 8 | 1 | no | — |
| 242 | #41 | — | 8 | 1 | no | — |
| 243 | #41 | — | 8 | 1 | no | — |
| 244 | #41 | — | 8 | 1 | no | — |
| 245 | #41 | — | 8 | 1 | no | — |
| 246 | C2×Q8 | — | 2 | 2 | no | — |
| 247 | C2×Q8 | — | 2 | 1 | no | — |
| 248 | C2×Q8 | — | 4 | 1 | no | — |
| 249 | C2×Q8 | — | 4 | 1 | no | — |
| 250 | C2×Q8 | — | 4 | 1 | no | — |
| 251 | C2×Q8 | — | 4 | 1 | no | — |
| 252 | C2×Q8 | — | 4 | 1 | no | — |
| 253 | C2×D4 | — | 2 | 2 | no | — |
| 254 | C2×D4 | — | 2 | 1 | no | — |
| 255 | C2×D4 | — | 4 | 1 | no | — |
| 256 | C2×D4 | — | 4 | 1 | no | — |
| 257 | C2×D4 | — | 4 | 1 | no | — |
| 258 | C2×D4 | — | 4 | 2 | no | — |
| 259 | C2×D4 | — | 4 | 2 | no | — |
| 260 | C2×D4 | — | 4 | 1 | no | — |
| 261 | C2×D4 | — | 4 | 1 | no | — |
| 262 | C2×D4 | — | 4 | 1 | no | — |
| 263 | C2×D4 | — | 4 | 1 | no | — |
| 264 | C2×D4 | — | 4 | 1 | no | — |
| 265 | C2×D4 | — | 8 | 1 | no | — |
| 266 | C2×D4 | — | 8 | 1 | no | — |
| 267 | C2×D4 | — | 8 | 1 | no | — |
| 268 | C2×D4 | — | 8 | 1 | no | — |
| 269 | C22×C4 | — | 2 | 1 | no | — |
| 270 | C22×C4 | — | 2 | 1 | no | — |
| 271 | C22×C4 | — | 2 | 1 | no | — |
| 272 | C22×C4 | — | 2 | 1 | no | — |
| 273 | C22×C4 | — | 2 | 2 | no | — |
| 274 | C22×C4 | — | 4 | 2 | no | — |
| 275 | C22×C4 | — | 4 | 2 | no | — |
| 276 | C22×C4 | — | 4 | 1 | no | — |
| 277 | C22×C4 | — | 4 | 1 | no | — |
| 278 | C22×C4 | — | 4 | 1 | no | — |
| 279 | C22×C4 | — | 4 | 1 | no | — |
| 280 | C22×C4 | — | 8 | 1 | no | — |
| 281 | C22×C4 | — | 8 | 1 | no | — |
| 282 | C22×C4 | — | 8 | 1 | no | — |
| 283 | C22×C4 | — | 8 | 1 | no | — |
| 284 | C22×C4 | — | 8 | 1 | no | — |
| 285 | C22×C4 | — | 8 | 1 | no | — |
| 286 | C22×C4 | C4×D4 | 1 | 1 | yes | characteristic |
| 287 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 288 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 289 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 290 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 291 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 292 | Q16 | — | 2 | 2 | no | — |
| 293 | Q16 | — | 2 | 2 | no | — |
| 294 | Q16 | — | 4 | 1 | no | — |
| 295 | Q16 | — | 4 | 1 | no | — |
| 296 | Q16 | — | 4 | 1 | no | — |
| 297 | SD16 | — | 4 | 2 | no | — |
| 298 | SD16 | — | 4 | 2 | no | — |
| 299 | SD16 | — | 4 | 2 | no | — |
| 300 | SD16 | — | 4 | 2 | no | — |
| 301 | SD16 | — | 8 | 1 | no | — |
| 302 | D8 | — | 2 | 2 | no | — |
| 303 | D8 | — | 2 | 2 | no | — |
| 304 | D8 | — | 4 | 1 | no | — |
| 305 | D8 | — | 4 | 1 | no | — |
| 306 | D8 | — | 4 | 1 | no | — |
| 307 | M16 | — | 4 | 2 | no | — |
| 308 | M16 | — | 4 | 2 | no | — |
| 309 | M16 | — | 4 | 1 | no | — |
| 310 | M16 | — | 4 | 1 | no | — |
| 311 | M16 | — | 4 | 1 | no | — |
| 312 | M16 | — | 4 | 1 | no | — |
| 313 | M16 | — | 8 | 2 | no | — |
| 314 | M16 | — | 8 | 1 | no | — |
| 315 | M16 | — | 8 | 1 | no | — |
| 316 | C2×C8 | — | 2 | 1 | no | — |
| 317 | C2×C8 | — | 2 | 1 | no | — |
| 318 | C2×C8 | — | 2 | 1 | no | — |
| 319 | C2×C8 | — | 2 | 1 | no | — |
| 320 | C2×C8 | — | 2 | 1 | no | — |
| 321 | C2×C8 | — | 2 | 1 | no | — |
| 322 | C2×C8 | — | 4 | 1 | no | — |
| 323 | C2×C8 | — | 4 | 1 | no | — |
| 324 | C2×C8 | — | 4 | 1 | no | — |
| 325 | C2×C8 | — | 4 | 1 | no | — |
| 326 | C2×C8 | — | 4 | 1 | no | — |
| 327 | C2×C8 | — | 4 | 1 | no | — |
| 328 | C2×C8 | — | 4 | 1 | no | — |
| 329 | C2×C8 | — | 4 | 1 | no | — |
| 330 | C2×C8 | — | 4 | 2 | no | — |
| 331 | C2×C8 | — | 4 | 1 | no | — |
| 332 | C2×C8 | — | 4 | 1 | no | — |
| 333 | C2×C8 | — | 8 | 1 | no | — |
| 334 | C2×C8 | — | 8 | 2 | no | — |
| 335 | C2×C8 | — | 8 | 1 | no | — |
| 336 | C2×C8 | — | 8 | 1 | no | — |
| 337 | C2×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 338 | C2×C8 | C4×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 340 | C2×C8 | #123 | 1 | 1 | yes | characteristic |
| 341 | C4⋊C4 | — | 2 | 1 | no | — |
| 342 | C4⋊C4 | — | 2 | 1 | no | — |
| 343 | C4⋊C4 | — | 4 | 1 | no | — |
| 344 | C4⋊C4 | — | 4 | 1 | no | — |
| 345 | C22⋊C4 | — | 4 | 1 | no | — |
| 346 | C22⋊C4 | — | 4 | 1 | no | — |
| 347 | C22⋊C4 | — | 4 | 1 | no | — |
| 348 | C22⋊C4 | — | 4 | 1 | no | — |
| 349 | C22⋊C4 | — | 4 | 1 | no | — |
| 350 | C42 | — | 4 | 2 | no | — |
| 351 | C42 | — | 4 | 1 | no | — |
| 352 | C42 | — | 4 | 1 | no | — |
| 353 | C42 | — | 4 | 1 | no | — |
| 354 | C16 | — | 4 | 1 | no | — |
| 355 | C16 | — | 4 | 1 | no | — |
| 356 | C16 | — | 8 | 1 | no | — |
| 357 | C23 | — | 2 | 1 | no | — |
| 358 | C23 | — | 2 | 1 | no | — |
| 359 | C23 | — | 2 | 1 | no | — |
| 360 | C23 | — | 2 | 1 | no | — |
| 361 | C23 | — | 4 | 1 | no | — |
| 362 | C23 | — | 4 | 2 | no | — |
| 363 | C23 | — | 4 | 1 | no | — |
| 364 | C23 | — | 8 | 1 | no | — |
| 365 | C23 | — | 8 | 1 | no | — |
| 366 | C23 | — | 8 | 1 | no | — |
| 367 | C23 | — | 8 | 1 | no | — |
| 368 | C23 | — | 8 | 1 | no | — |
| 369 | C23 | — | 8 | 1 | no | — |
| 370 | C23 | C4×D8 | 1 | 1 | yes | characteristic |
| 371 | C23 | #449 | 1 | 1 | yes | characteristic |
| 372 | C23 | #463 | 1 | 1 | yes | characteristic |
| 373 | Q8 | — | 4 | 2 | no | — |
| 374 | Q8 | — | 4 | 1 | no | — |
| 375 | Q8 | — | 4 | 2 | no | — |
| 376 | Q8 | — | 4 | 1 | no | — |
| 377 | Q8 | — | 8 | 1 | no | — |
| 378 | Q8 | — | 8 | 1 | no | — |
| 379 | D4 | — | 4 | 2 | no | — |
| 380 | D4 | — | 4 | 1 | no | — |
| 381 | D4 | — | 4 | 2 | no | — |
| 382 | D4 | — | 4 | 1 | no | — |
| 383 | D4 | — | 8 | 1 | no | — |
| 384 | D4 | — | 8 | 2 | no | — |
| 385 | D4 | — | 8 | 2 | no | — |
| 386 | D4 | — | 8 | 2 | no | — |
| 387 | D4 | — | 8 | 2 | no | — |
| 388 | D4 | — | 8 | 1 | no | — |
| 389 | D4 | — | 8 | 2 | no | — |
| 390 | D4 | — | 8 | 1 | no | — |
| 391 | D4 | — | 8 | 1 | no | — |
| 392 | D4 | — | 8 | 1 | no | — |
| 393 | D4 | — | 8 | 1 | no | — |
| 394 | C2×C4 | — | 2 | 1 | no | — |
| 395 | C2×C4 | — | 2 | 1 | no | — |
| 396 | C2×C4 | — | 2 | 1 | no | — |
| 397 | C2×C4 | — | 2 | 1 | no | — |
| 398 | C2×C4 | — | 2 | 1 | no | — |
| 399 | C2×C4 | — | 2 | 1 | no | — |
| 400 | C2×C4 | — | 2 | 1 | no | — |
| 401 | C2×C4 | — | 2 | 1 | no | — |
| 402 | C2×C4 | — | 2 | 1 | no | — |
| 403 | C2×C4 | — | 2 | 1 | no | — |
| 404 | C2×C4 | — | 4 | 2 | no | — |
| 405 | C2×C4 | — | 4 | 2 | no | — |
| 406 | C2×C4 | — | 4 | 1 | no | — |
| 407 | C2×C4 | — | 4 | 1 | no | — |
| 408 | C2×C4 | — | 4 | 1 | no | — |
| 409 | C2×C4 | — | 8 | 2 | no | — |
| 410 | C2×C4 | — | 8 | 2 | no | — |
| 411 | C2×C4 | — | 8 | 1 | no | — |
| 412 | C2×C4 | — | 8 | 1 | no | — |
| 413 | C2×C4 | — | 8 | 2 | no | — |
| 414 | C2×C4 | — | 8 | 1 | no | — |
| 415 | C2×C4 | — | 8 | 1 | no | — |
| 416 | C2×C4 | — | 8 | 1 | no | — |
| 417 | C2×C4 | — | 8 | 2 | no | — |
| 418 | C2×C4 | — | 8 | 2 | no | — |
| 419 | C2×C4 | — | 8 | 1 | no | — |
| 420 | C2×C4 | — | 8 | 2 | no | — |
| 421 | C2×C4 | #386 | 1 | 1 | yes | characteristic |
| 422 | C2×C4 | #442 | 1 | 1 | yes | characteristic |
| 423 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 424 | C2×C4 | #453 | 1 | 1 | yes | characteristic |
| 425 | C2×C4 | #454 | 1 | 1 | yes | characteristic |
| 426 | C2×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 428 | C2×C4 | #459 | 1 | 1 | yes | characteristic |
| 429 | C8 | — | 2 | 1 | no | — |
| 430 | C8 | — | 2 | 1 | no | — |
| 431 | C8 | — | 2 | 1 | no | — |
| 432 | C8 | — | 2 | 1 | no | — |
| 433 | C8 | — | 4 | 1 | no | — |
| 434 | C8 | — | 4 | 1 | no | — |
| 435 | C8 | — | 8 | 2 | no | — |
| 436 | C8 | — | 8 | 1 | no | — |
| 437 | C8 | — | 8 | 1 | no | — |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 2 | 1 | no | — |
| 440 | C22 | — | 2 | 1 | no | — |
| 441 | C22 | — | 2 | 1 | no | — |
| 442 | C22 | — | 2 | 1 | no | — |
| 443 | C22 | — | 2 | 1 | no | — |
| 444 | C22 | — | 2 | 1 | no | — |
| 445 | C22 | — | 4 | 1 | no | — |
| 446 | C22 | — | 4 | 1 | no | — |
| 447 | C22 | — | 4 | 1 | no | — |
| 448 | C22 | — | 4 | 1 | no | — |
| 449 | C22 | — | 8 | 2 | no | — |
| 450 | C22 | — | 8 | 2 | no | — |
| 451 | C22 | — | 8 | 2 | no | — |
| 452 | C22 | — | 8 | 1 | no | — |
| 453 | C22 | — | 8 | 1 | no | — |
| 454 | C22 | — | 8 | 1 | no | — |
| 455 | C22 | — | 16 | 1 | no | — |
| 456 | C22 | — | 16 | 1 | no | — |
| 457 | C22 | — | 16 | 1 | no | — |
| 458 | C22 | — | 16 | 1 | no | — |
| 459 | C22 | #1597 | 1 | 1 | yes | characteristic |
| 460 | C22 | #1600 | 1 | 1 | yes | characteristic |
| 461 | C22 | #1879 | 1 | 1 | yes | characteristic |
| 462 | C22 | #2178 | 1 | 1 | yes | characteristic |
| 463 | C22 | #2179 | 1 | 1 | yes | characteristic |
| 464 | C4 | — | 2 | 1 | no | — |
| 465 | C4 | — | 2 | 1 | no | — |
| 466 | C4 | — | 8 | 2 | no | — |
| 467 | C4 | — | 8 | 2 | no | — |
| 468 | C4 | — | 8 | 1 | no | — |
| 469 | C4 | — | 8 | 1 | no | — |
| 470 | C4 | — | 8 | 1 | no | — |
| 471 | C4 | #1595 | 1 | 1 | yes | characteristic |
| 472 | C4 | #1598 | 1 | 1 | yes | characteristic |
| 473 | C4 | #1883 | 1 | 1 | yes | characteristic |
| 474 | C4 | #1889 | 1 | 1 | yes | characteristic |
| 475 | C2 | — | 2 | 1 | no | — |
| 476 | C2 | — | 2 | 1 | no | — |
| 477 | C2 | — | 2 | 1 | no | — |
| 478 | C2 | — | 2 | 1 | no | — |
| 479 | C2 | — | 4 | 1 | no | — |
| 480 | C2 | — | 16 | 1 | no | — |
| 481 | C2 | — | 16 | 2 | no | — |
| 482 | C2 | #9041 | 1 | 1 | yes | characteristic |
| 483 | C2 | #13011 | 1 | 1 | yes | characteristic |
| 484 | C2 | #13024 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | #447 |
| commutator | C22×C8 | C22×C4 |
| Frattini, cosocle | C23×C8 | C23 |
| socle | C22 | #1879 |
| prime radical | #33516 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#336 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22204 | C2 | semidirect |
| 3. #12734 | C2 | semidirect |
| 4. #11709 | C2 | semidirect |
| 5. #11025 | C2 | semidirect |
| 6. #7261 | C2 | semidirect |
| 7. #7183 | C2 | semidirect |
| 15. #2188 | C4 | semidirect |
| 16. #2187 | C4 | semidirect |
| 18. #2185 | C4 | semidirect |
| 19. #2184 | C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33516 | 2 |
| #22204 | 2 |
| #12734 | 2 |
| #11709 | 2 |
| #11025 | 2 |
| #7261 | 2 |
| #7183 | 2 |