Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
753 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 753 conjugacy classes of subgroups — too many to draw. Only its 72 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 | #33521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #29749 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23390 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #12734 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#1348 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11422 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #7264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#135 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#537 | — | 2 | 1 | no | — |
| 10 | C2×#510 | — | 2 | 1 | no | — |
| 11 | C2×#467 | C22 | 1 | 1 | yes | characteristic |
| 12 | #3007 | — | 2 | 1 | no | — |
| 13 | C2×#417 | — | 2 | 1 | no | — |
| 14 | C2×#408 | C22 | 1 | 1 | yes | characteristic |
| 15 | #2189 | — | 2 | 2 | no | — |
| 16 | #2188 | — | 2 | 1 | no | — |
| 17 | #2187 | — | 2 | 1 | no | — |
| 18 | C2×#359 | — | 2 | 2 | no | — |
| 19 | #2139 | — | 2 | 1 | no | — |
| 20 | #2112 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 22 | #2078 | — | 2 | 1 | no | — |
| 23 | #2052 | — | 2 | 2 | no | — |
| 24 | #2020 | — | 2 | 1 | no | — |
| 25 | #2001 | — | 2 | 1 | no | — |
| 26 | #2000 | — | 2 | 2 | no | — |
| 27 | #1999 | — | 2 | 1 | no | — |
| 28 | #1901 | — | 2 | 1 | no | — |
| 29 | #1810 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#340 | C22 | 1 | 1 | yes | characteristic |
| 31 | #1348 | — | 2 | 2 | no | — |
| 32 | #1315 | — | 2 | 2 | no | — |
| 33 | C22×#41 | — | 2 | 1 | no | — |
| 34 | C22×#41 | D4 | 1 | 1 | yes | characteristic |
| 35 | C2×#137 | — | 2 | 2 | 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 | 4 | no | — |
| 41 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 42 | C22×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 43 | C22×SD16 | — | 2 | 1 | no | — |
| 44 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 45 | C22×M16 | D4 | 1 | 1 | yes | characteristic |
| 46 | C23×C8 | C23 | 1 | 1 | yes | characteristic |
| 47 | #537 | — | 4 | 4 | no | — |
| 48 | #537 | — | 4 | 4 | no | — |
| 49 | C2×C22⋊Q8 | — | 2 | 2 | no | — |
| 50 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 51 | C2×C22⋊Q8 | — | 4 | 1 | no | — |
| 52 | C2×#121 | — | 2 | 2 | no | — |
| 53 | C2×#121 | — | 4 | 2 | no | — |
| 54 | C2×#121 | — | 4 | 1 | no | — |
| 55 | C22×C4⋊C4 | — | 2 | 1 | no | — |
| 56 | #510 | — | 4 | 4 | no | — |
| 57 | C2×Q32 | — | 2 | 2 | no | — |
| 58 | C2×SD32 | — | 2 | 2 | no | — |
| 59 | C2×M32 | — | 2 | 1 | no | — |
| 60 | C22×C16 | — | 2 | 1 | no | — |
| 61 | #467 | — | 2 | 1 | no | — |
| 62 | #467 | — | 2 | 1 | no | — |
| 63 | #467 | — | 2 | 1 | no | — |
| 64 | #467 | — | 2 | 1 | no | — |
| 65 | #452 | — | 4 | 2 | no | — |
| 66 | #451 | — | 4 | 1 | no | — |
| 67 | #450 | — | 4 | 1 | no | — |
| 68 | C2×#108 | D4 | 1 | 2 | yes | complemented |
| 69 | C2×#107 | D4 | 1 | 1 | yes | characteristic, complemented |
| 70 | #417 | — | 2 | 2 | no | — |
| 71 | #417 | — | 4 | 4 | no | — |
| 72 | C2×#103 | — | 2 | 2 | no | — |
| 73 | C2×#103 | — | 2 | 1 | no | — |
| 74 | C2×#102 | — | 2 | 2 | no | — |
| 75 | C2×#101 | — | 2 | 2 | no | — |
| 76 | #408 | — | 2 | 1 | no | — |
| 77 | #408 | — | 2 | 1 | no | — |
| 78 | #408 | — | 2 | 1 | no | — |
| 79 | #408 | — | 2 | 1 | no | — |
| 80 | #407 | — | 2 | 1 | no | — |
| 81 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 82 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 83 | #359 | — | 4 | 4 | no | — |
| 84 | #358 | — | 2 | 2 | no | — |
| 85 | #357 | — | 2 | 2 | no | — |
| 86 | C22⋊C16 | — | 2 | 1 | no | — |
| 87 | C22⋊C16 | — | 2 | 1 | no | — |
| 88 | C22⋊C16 | — | 2 | 1 | no | — |
| 89 | C22⋊C16 | D4 | 1 | 2 | yes | complemented |
| 90 | #343 | — | 2 | 2 | no | — |
| 91 | #341 | — | 2 | 1 | no | — |
| 92 | #340 | — | 2 | 1 | no | — |
| 93 | #340 | D4 | 1 | 2 | yes | — |
| 94 | C2×#41 | — | 2 | 4 | no | — |
| 95 | C2×#41 | — | 2 | 1 | no | — |
| 96 | C2×#41 | — | 2 | 1 | no | — |
| 97 | C2×#41 | — | 2 | 1 | no | — |
| 98 | C2×#41 | — | 2 | 1 | no | — |
| 99 | C2×#41 | — | 4 | 2 | no | — |
| 100 | C2×#41 | — | 4 | 2 | no | — |
| 101 | C2×#41 | — | 4 | 2 | no | — |
| 102 | C2×#41 | — | 4 | 2 | no | — |
| 103 | C2×#41 | — | 4 | 2 | no | — |
| 104 | C2×#41 | — | 4 | 1 | no | — |
| 105 | C2×#41 | — | 4 | 1 | no | — |
| 106 | C2×#41 | — | 4 | 1 | no | — |
| 107 | C2×#41 | — | 4 | 1 | no | — |
| 108 | C22×Q8 | — | 2 | 1 | no | — |
| 109 | C22×Q8 | — | 2 | 1 | no | — |
| 110 | C22×Q8 | D8 | 1 | 1 | yes | characteristic |
| 111 | C22×D4 | — | 2 | 1 | no | — |
| 112 | C22×D4 | — | 2 | 1 | no | — |
| 113 | C22×D4 | — | 4 | 1 | no | — |
| 114 | C22×D4 | — | 4 | 2 | no | — |
| 115 | C22×D4 | D8 | 1 | 1 | yes | characteristic |
| 116 | C23×C4 | — | 2 | 1 | no | — |
| 117 | C23×C4 | — | 4 | 1 | no | — |
| 118 | C23×C4 | — | 4 | 1 | no | — |
| 119 | C23×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 120 | #137 | — | 8 | 2 | no | — |
| 121 | #137 | — | 8 | 2 | no | — |
| 122 | #135 | — | 2 | 4 | no | — |
| 123 | #135 | — | 2 | 4 | no | — |
| 124 | #135 | — | 4 | 2 | no | — |
| 125 | #135 | — | 4 | 2 | no | — |
| 126 | #135 | — | 4 | 2 | no | — |
| 127 | #135 | — | 4 | 2 | no | — |
| 128 | #135 | — | 4 | 2 | no | — |
| 129 | #135 | — | 4 | 2 | no | — |
| 130 | C2×Q16 | — | 2 | 1 | no | — |
| 131 | C2×Q16 | — | 2 | 1 | no | — |
| 132 | C2×Q16 | — | 2 | 1 | no | — |
| 133 | C2×Q16 | — | 2 | 1 | no | — |
| 134 | C2×Q16 | — | 4 | 2 | no | — |
| 135 | C2×Q16 | — | 4 | 2 | no | — |
| 136 | C2×Q16 | — | 4 | 2 | no | — |
| 137 | C2×SD16 | — | 4 | 2 | no | — |
| 138 | C2×SD16 | — | 4 | 2 | no | — |
| 139 | C2×SD16 | — | 4 | 2 | no | — |
| 140 | C2×SD16 | — | 4 | 1 | no | — |
| 141 | C2×SD16 | — | 4 | 1 | no | — |
| 142 | C2×D8 | — | 2 | 1 | no | — |
| 143 | C2×D8 | — | 2 | 1 | no | — |
| 144 | C2×D8 | — | 4 | 2 | no | — |
| 145 | C2×M16 | — | 2 | 1 | no | — |
| 146 | C2×M16 | — | 2 | 2 | no | — |
| 147 | C2×M16 | — | 2 | 1 | no | — |
| 148 | C2×M16 | — | 4 | 2 | no | — |
| 149 | C22×C8 | — | 2 | 1 | no | — |
| 150 | C22×C8 | — | 4 | 2 | no | — |
| 151 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 155 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×C8 | #41 | 1 | 1 | yes | characteristic |
| 157 | C22⋊Q8 | — | 4 | 4 | no | — |
| 158 | C22⋊Q8 | — | 4 | 4 | no | — |
| 159 | C22⋊Q8 | — | 4 | 8 | no | — |
| 160 | C22⋊Q8 | — | 4 | 1 | no | — |
| 161 | C22⋊Q8 | — | 4 | 1 | no | — |
| 162 | C22⋊Q8 | — | 4 | 1 | no | — |
| 163 | C22⋊Q8 | — | 4 | 1 | no | — |
| 164 | #121 | — | 4 | 4 | no | — |
| 165 | #121 | — | 4 | 4 | no | — |
| 166 | #121 | — | 4 | 8 | no | — |
| 167 | #121 | — | 4 | 16 | no | — |
| 168 | C2×C4⋊C4 | — | 2 | 4 | no | — |
| 169 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 170 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 171 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 172 | C2×C4⋊C4 | — | 4 | 2 | no | — |
| 173 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 174 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 175 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 176 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 177 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 178 | Q32 | — | 4 | 4 | no | — |
| 179 | SD32 | — | 4 | 4 | no | — |
| 180 | M32 | — | 4 | 2 | no | — |
| 181 | C2×C16 | — | 2 | 2 | no | — |
| 182 | C2×C16 | — | 4 | 2 | no | — |
| 183 | C2×C16 | — | 4 | 1 | no | — |
| 184 | #108 | — | 4 | 2 | no | — |
| 185 | #107 | — | 2 | 1 | no | — |
| 186 | #107 | — | 2 | 1 | no | — |
| 187 | #103 | — | 4 | 4 | no | — |
| 188 | #103 | — | 4 | 2 | no | — |
| 189 | #103 | — | 4 | 1 | no | — |
| 190 | #103 | — | 4 | 1 | no | — |
| 191 | #102 | — | 4 | 4 | no | — |
| 192 | #102 | — | 4 | 2 | no | — |
| 193 | #101 | — | 8 | 2 | no | — |
| 194 | C22⋊C8 | — | 4 | 1 | no | — |
| 195 | C22⋊C8 | — | 4 | 1 | no | — |
| 196 | C22⋊C8 | — | 4 | 1 | no | — |
| 197 | C22⋊C8 | — | 4 | 1 | no | — |
| 198 | C22⋊C8 | — | 4 | 1 | no | — |
| 199 | C22⋊C8 | — | 4 | 1 | no | — |
| 200 | C24 | — | 2 | 1 | no | — |
| 201 | C24 | — | 4 | 1 | no | — |
| 202 | C24 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 203 | #41 | — | 4 | 4 | no | — |
| 204 | #41 | — | 4 | 4 | no | — |
| 205 | #41 | — | 4 | 4 | no | — |
| 206 | #41 | — | 4 | 2 | no | — |
| 207 | #41 | — | 4 | 4 | no | — |
| 208 | #41 | — | 4 | 2 | no | — |
| 209 | #41 | — | 8 | 2 | no | — |
| 210 | #41 | — | 8 | 2 | no | — |
| 211 | #41 | — | 8 | 2 | no | — |
| 212 | #41 | — | 8 | 2 | no | — |
| 213 | #41 | — | 8 | 2 | no | — |
| 214 | #41 | — | 8 | 1 | no | — |
| 215 | #41 | — | 8 | 1 | no | — |
| 216 | #41 | — | 8 | 2 | no | — |
| 217 | C2×Q8 | — | 2 | 2 | no | — |
| 218 | C2×Q8 | — | 2 | 1 | no | — |
| 219 | C2×Q8 | — | 2 | 1 | no | — |
| 220 | C2×Q8 | — | 4 | 2 | no | — |
| 221 | C2×Q8 | — | 4 | 1 | no | — |
| 222 | C2×Q8 | — | 4 | 1 | no | — |
| 223 | C2×Q8 | — | 4 | 1 | no | — |
| 224 | C2×Q8 | — | 4 | 1 | no | — |
| 225 | C2×Q8 | — | 4 | 1 | no | — |
| 226 | C2×Q8 | — | 4 | 1 | no | — |
| 227 | C2×Q8 | — | 4 | 1 | no | — |
| 228 | C2×Q8 | — | 4 | 2 | no | — |
| 229 | C2×Q8 | — | 4 | 2 | no | — |
| 230 | C2×D4 | — | 2 | 2 | no | — |
| 231 | C2×D4 | — | 2 | 1 | no | — |
| 232 | C2×D4 | — | 2 | 1 | no | — |
| 233 | C2×D4 | — | 4 | 1 | no | — |
| 234 | C2×D4 | — | 4 | 1 | no | — |
| 235 | C2×D4 | — | 4 | 2 | no | — |
| 236 | C2×D4 | — | 4 | 1 | no | — |
| 237 | C2×D4 | — | 4 | 4 | no | — |
| 238 | C2×D4 | — | 4 | 4 | no | — |
| 239 | C2×D4 | — | 4 | 1 | no | — |
| 240 | C2×D4 | — | 4 | 1 | no | — |
| 241 | C2×D4 | — | 4 | 8 | no | — |
| 242 | C2×D4 | — | 4 | 1 | no | — |
| 243 | C2×D4 | — | 4 | 1 | no | — |
| 244 | C2×D4 | — | 8 | 2 | no | — |
| 245 | C2×D4 | — | 8 | 1 | no | — |
| 246 | C2×D4 | — | 8 | 1 | no | — |
| 247 | C2×D4 | — | 16 | 2 | no | — |
| 248 | C2×D4 | — | 16 | 2 | no | — |
| 249 | C22×C4 | — | 2 | 2 | no | — |
| 250 | C22×C4 | — | 2 | 2 | no | — |
| 251 | C22×C4 | — | 2 | 1 | no | — |
| 252 | C22×C4 | — | 4 | 2 | no | — |
| 253 | C22×C4 | — | 4 | 2 | no | — |
| 254 | C22×C4 | — | 4 | 4 | no | — |
| 255 | C22×C4 | — | 4 | 2 | no | — |
| 256 | C22×C4 | — | 4 | 1 | no | — |
| 257 | C22×C4 | — | 4 | 4 | no | — |
| 258 | C22×C4 | — | 4 | 1 | no | — |
| 259 | C22×C4 | — | 4 | 1 | no | — |
| 260 | C22×C4 | — | 4 | 1 | no | — |
| 261 | C22×C4 | — | 4 | 1 | no | — |
| 262 | C22×C4 | — | 8 | 2 | no | — |
| 263 | C22×C4 | — | 8 | 1 | no | — |
| 264 | C22×C4 | — | 8 | 1 | no | — |
| 265 | C22×C4 | — | 16 | 1 | no | — |
| 266 | C22×C4 | — | 16 | 1 | no | — |
| 267 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 268 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 269 | C22×C4 | #121 | 1 | 1 | yes | characteristic |
| 270 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 271 | C22×C4 | #135 | 1 | 1 | yes | characteristic |
| 272 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 273 | Q16 | — | 2 | 2 | no | — |
| 274 | Q16 | — | 2 | 2 | no | — |
| 275 | Q16 | — | 4 | 1 | no | — |
| 276 | Q16 | — | 4 | 1 | no | — |
| 277 | Q16 | — | 4 | 2 | no | — |
| 278 | Q16 | — | 8 | 1 | no | — |
| 279 | Q16 | — | 8 | 4 | no | — |
| 280 | SD16 | — | 4 | 4 | no | — |
| 281 | SD16 | — | 4 | 4 | no | — |
| 282 | SD16 | — | 8 | 4 | no | — |
| 283 | D8 | — | 2 | 2 | no | — |
| 284 | D8 | — | 2 | 2 | no | — |
| 285 | D8 | — | 4 | 1 | no | — |
| 286 | D8 | — | 4 | 1 | no | — |
| 287 | M16 | — | 4 | 2 | no | — |
| 288 | M16 | — | 4 | 2 | no | — |
| 289 | M16 | — | 4 | 2 | no | — |
| 290 | M16 | — | 8 | 1 | no | — |
| 291 | C2×C8 | — | 2 | 2 | no | — |
| 292 | C2×C8 | — | 2 | 2 | no | — |
| 293 | C2×C8 | — | 4 | 1 | no | — |
| 294 | C2×C8 | — | 4 | 1 | no | — |
| 295 | C2×C8 | — | 4 | 1 | no | — |
| 296 | C2×C8 | — | 4 | 1 | no | — |
| 297 | C2×C8 | — | 4 | 2 | no | — |
| 298 | C2×C8 | — | 4 | 1 | no | — |
| 299 | C2×C8 | — | 4 | 2 | no | — |
| 300 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 301 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 302 | C2×C8 | #121 | 1 | 1 | yes | characteristic |
| 303 | C2×C8 | #127 | 1 | 1 | yes | characteristic |
| 304 | C4⋊C4 | — | 2 | 4 | no | — |
| 305 | C4⋊C4 | — | 4 | 4 | no | — |
| 306 | C4⋊C4 | — | 4 | 2 | no | — |
| 307 | C4⋊C4 | — | 4 | 8 | no | — |
| 308 | C4⋊C4 | — | 4 | 1 | no | — |
| 309 | C4⋊C4 | — | 4 | 1 | no | — |
| 310 | C4⋊C4 | — | 8 | 1 | no | — |
| 311 | C4⋊C4 | — | 8 | 1 | no | — |
| 312 | C22⋊C4 | — | 4 | 8 | no | — |
| 313 | C22⋊C4 | — | 4 | 8 | no | — |
| 314 | C22⋊C4 | — | 8 | 1 | no | — |
| 315 | C22⋊C4 | — | 8 | 1 | no | — |
| 316 | C16 | — | 4 | 2 | no | — |
| 317 | C16 | — | 8 | 1 | no | — |
| 318 | C23 | — | 2 | 2 | no | — |
| 319 | C23 | — | 2 | 1 | no | — |
| 320 | C23 | — | 2 | 1 | no | — |
| 321 | C23 | — | 4 | 1 | no | — |
| 322 | C23 | — | 4 | 2 | no | — |
| 323 | C23 | — | 4 | 2 | no | — |
| 324 | C23 | — | 4 | 2 | no | — |
| 325 | C23 | — | 4 | 1 | no | — |
| 326 | C23 | — | 4 | 1 | no | — |
| 327 | C23 | — | 4 | 1 | no | — |
| 328 | C23 | — | 8 | 1 | no | — |
| 329 | C23 | — | 8 | 1 | no | — |
| 330 | C23 | — | 8 | 1 | no | — |
| 331 | C23 | — | 8 | 1 | no | — |
| 332 | C23 | — | 8 | 1 | no | — |
| 333 | C23 | — | 8 | 1 | no | — |
| 334 | C23 | #447 | 1 | 1 | yes | characteristic |
| 335 | C23 | #449 | 1 | 1 | yes | characteristic |
| 336 | C23 | #469 | 1 | 1 | yes | characteristic |
| 337 | Q8 | — | 4 | 2 | no | — |
| 338 | Q8 | — | 4 | 2 | no | — |
| 339 | Q8 | — | 4 | 2 | no | — |
| 340 | Q8 | — | 8 | 1 | no | — |
| 341 | Q8 | — | 8 | 1 | no | — |
| 342 | Q8 | — | 8 | 1 | no | — |
| 343 | Q8 | — | 8 | 2 | no | — |
| 344 | Q8 | — | 8 | 1 | no | — |
| 345 | Q8 | — | 8 | 1 | no | — |
| 346 | D4 | — | 4 | 2 | no | — |
| 347 | D4 | — | 4 | 2 | no | — |
| 348 | D4 | — | 4 | 2 | no | — |
| 349 | D4 | — | 8 | 1 | no | — |
| 350 | D4 | — | 8 | 1 | no | — |
| 351 | D4 | — | 8 | 2 | no | — |
| 352 | D4 | — | 8 | 4 | no | — |
| 353 | D4 | — | 8 | 2 | no | — |
| 354 | D4 | — | 8 | 4 | no | — |
| 355 | D4 | — | 8 | 1 | no | — |
| 356 | D4 | — | 16 | 8 | no | — |
| 357 | C2×C4 | — | 2 | 2 | no | — |
| 358 | C2×C4 | — | 2 | 2 | no | — |
| 359 | C2×C4 | — | 2 | 2 | no | — |
| 360 | C2×C4 | — | 2 | 1 | no | — |
| 361 | C2×C4 | — | 2 | 1 | no | — |
| 362 | C2×C4 | — | 2 | 1 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 4 | 4 | no | — |
| 365 | C2×C4 | — | 4 | 2 | no | — |
| 366 | C2×C4 | — | 4 | 2 | no | — |
| 367 | C2×C4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 8 | 2 | no | — |
| 369 | C2×C4 | — | 8 | 4 | no | — |
| 370 | C2×C4 | — | 8 | 1 | no | — |
| 371 | C2×C4 | — | 8 | 2 | no | — |
| 372 | C2×C4 | — | 8 | 2 | no | — |
| 373 | C2×C4 | — | 8 | 1 | no | — |
| 374 | C2×C4 | — | 8 | 4 | no | — |
| 375 | C2×C4 | — | 8 | 1 | no | — |
| 376 | C2×C4 | — | 8 | 1 | no | — |
| 377 | C2×C4 | — | 8 | 2 | no | — |
| 378 | C2×C4 | — | 8 | 1 | no | — |
| 379 | C2×C4 | — | 8 | 1 | no | — |
| 380 | C2×C4 | — | 16 | 4 | no | — |
| 381 | C2×C4 | — | 16 | 1 | no | — |
| 382 | C2×C4 | #392 | 1 | 1 | yes | characteristic |
| 383 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 384 | C2×C4 | #449 | 1 | 1 | yes | characteristic |
| 385 | C2×C4 | #453 | 1 | 2 | yes | — |
| 386 | C2×C4 | B(4,𝔽2) | 1 | 2 | yes | — |
| 387 | C2×C4 | #466 | 1 | 1 | yes | characteristic |
| 388 | C8 | — | 2 | 1 | no | — |
| 389 | C8 | — | 2 | 1 | no | — |
| 390 | C8 | — | 2 | 1 | no | — |
| 391 | C8 | — | 2 | 1 | no | — |
| 392 | C8 | — | 8 | 2 | no | — |
| 393 | C8 | — | 8 | 1 | no | — |
| 394 | C22 | — | 2 | 1 | no | — |
| 395 | C22 | — | 2 | 1 | no | — |
| 396 | C22 | — | 2 | 1 | no | — |
| 397 | C22 | — | 2 | 1 | no | — |
| 398 | C22 | — | 2 | 1 | no | — |
| 399 | C22 | — | 2 | 1 | no | — |
| 400 | C22 | — | 2 | 1 | no | — |
| 401 | C22 | — | 4 | 2 | no | — |
| 402 | C22 | — | 4 | 2 | no | — |
| 403 | C22 | — | 8 | 2 | no | — |
| 404 | C22 | — | 8 | 2 | no | — |
| 405 | C22 | — | 8 | 2 | no | — |
| 406 | C22 | — | 8 | 2 | no | — |
| 407 | C22 | — | 8 | 1 | no | — |
| 408 | C22 | — | 8 | 2 | no | — |
| 409 | C22 | — | 8 | 1 | no | — |
| 410 | C22 | — | 8 | 1 | no | — |
| 411 | C22 | — | 16 | 1 | no | — |
| 412 | C22 | — | 16 | 1 | no | — |
| 413 | C22 | — | 16 | 1 | no | — |
| 414 | C22 | — | 16 | 1 | no | — |
| 415 | C22 | #1600 | 1 | 2 | yes | — |
| 416 | C22 | #1999 | 1 | 1 | yes | characteristic |
| 417 | C22 | #2194 | 1 | 1 | yes | characteristic |
| 418 | C22 | #2195 | 1 | 1 | yes | characteristic |
| 419 | C4 | — | 2 | 1 | no | — |
| 420 | C4 | — | 2 | 1 | no | — |
| 421 | C4 | — | 8 | 4 | no | — |
| 422 | C4 | — | 8 | 1 | no | — |
| 423 | C4 | — | 8 | 2 | no | — |
| 424 | C4 | — | 16 | 1 | no | — |
| 425 | C4 | — | 16 | 1 | no | — |
| 426 | C4 | #1595 | 1 | 2 | yes | — |
| 427 | C4 | #2002 | 1 | 1 | yes | characteristic |
| 428 | C4 | #2021 | 1 | 1 | yes | characteristic |
| 429 | C2 | — | 2 | 1 | no | — |
| 430 | C2 | — | 2 | 1 | no | — |
| 431 | C2 | — | 2 | 2 | no | — |
| 432 | C2 | — | 4 | 1 | no | — |
| 433 | C2 | — | 16 | 1 | no | — |
| 434 | C2 | — | 16 | 2 | no | — |
| 435 | C2 | #9914 | 1 | 1 | yes | characteristic |
| 436 | C2 | #13308 | 1 | 1 | yes | characteristic |
| 437 | C2 | #13318 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #1999 |
| commutator, Frattini, cosocle | C23×C8 | C23 |
| prime radical | #23390 | C2 |
| LCS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C23×C4 ◁ C2×#408 ◁ G | |
| LECS | G ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #33521 | C2 | semidirect |
| 2. #29749 | C2 | semidirect |
| 4. #12734 | C2 | semidirect |
| 5. C2×#1348 | C2 | semidirect |
| 6. #11422 | C2 | semidirect |
| 7. #7264 | C2 | semidirect |
| 42. C22×Q16 | D4 | semidirect |
| 68. C2×#108 | D4 | semidirect |
| 69. C2×#107 | D4 | semidirect |
| 89. C22⋊C16 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #33521 | 2 |
| #29749 | 2 |
| #23390 | 2 |
| #12734 | 2 |
| C2×#1348 | 2 |
| #11422 | 2 |
| #7264 | 2 |