Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1013 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 1013 conjugacy classes of subgroups — too many to draw. Only its 162 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 | C2×#3273 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#2243 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#2226 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#1693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #12378 | C2 | 1 | 8 | yes | maximal, direct product factor |
| 6 | C2×#1360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×#1333 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#1330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C22×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 10 | C2×#546 | — | 2 | 1 | no | — |
| 11 | #3273 | — | 2 | 2 | no | — |
| 12 | #3273 | — | 2 | 2 | no | — |
| 13 | #3273 | — | 2 | 2 | no | — |
| 14 | #3273 | C22 | 1 | 4 | yes | — |
| 15 | C2×#500 | C22 | 1 | 1 | yes | characteristic, complemented |
| 16 | C2×#495 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#468 | — | 2 | 1 | no | — |
| 18 | C2×#463 | — | 2 | 1 | no | — |
| 19 | C2×#461 | — | 2 | 1 | no | — |
| 20 | C2×#452 | — | 2 | 1 | no | — |
| 21 | C2×#447 | — | 2 | 1 | no | — |
| 22 | C2×C4×D8 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#436 | C22 | 1 | 1 | yes | characteristic |
| 24 | #2243 | — | 2 | 2 | no | — |
| 25 | #2243 | C22 | 1 | 4 | yes | complemented |
| 26 | #2226 | — | 2 | 2 | no | — |
| 27 | #2226 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#367 | — | 2 | 1 | no | — |
| 29 | C2×C4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#358 | — | 2 | 1 | no | — |
| 31 | C2×#357 | — | 2 | 1 | no | — |
| 32 | C2×#357 | — | 2 | 1 | no | — |
| 33 | C2×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #1693 | — | 2 | 2 | no | — |
| 35 | #1693 | C22 | 1 | 4 | yes | complemented |
| 36 | C2×#334 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#332 | — | 2 | 1 | no | — |
| 38 | #1360 | C22 | 1 | 4 | yes | complemented |
| 39 | #1333 | C22 | 1 | 4 | yes | complemented |
| 40 | #1330 | C22 | 1 | 4 | yes | complemented |
| 41 | C22×#41 | — | 2 | 1 | no | — |
| 42 | C23×D4 | — | 2 | 1 | no | — |
| 43 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 44 | C2×AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 45 | C2×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 46 | C2×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 47 | C22×Q16 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×SD16 | — | 2 | 1 | no | — |
| 49 | C22×SD16 | — | 2 | 1 | no | — |
| 50 | C22×SD16 | — | 4 | 1 | no | — |
| 51 | C22×D8 | — | 2 | 1 | no | — |
| 52 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 53 | C22×D8 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×M16 | — | 2 | 1 | no | — |
| 55 | #546 | — | 2 | 4 | no | — |
| 56 | #546 | — | 2 | 4 | no | — |
| 57 | #546 | — | 4 | 2 | no | — |
| 58 | #546 | — | 4 | 2 | no | — |
| 59 | C2×C4⋊Q8 | — | 2 | 1 | no | — |
| 60 | C2×#124 | — | 2 | 1 | no | — |
| 61 | C2×#123 | — | 4 | 1 | no | — |
| 62 | C2×C22⋊Q8 | — | 2 | 1 | no | — |
| 63 | C2×#121 | — | 2 | 1 | no | — |
| 64 | C2×#121 | — | 4 | 1 | no | — |
| 65 | C2×#120 | — | 4 | 1 | no | — |
| 66 | C2×C4×D4 | — | 2 | 1 | no | — |
| 67 | C2×C4×D4 | D4 | 1 | 1 | yes | characteristic |
| 68 | C22×C22⋊C4 | — | 4 | 1 | no | — |
| 69 | C22×C16 | — | 2 | 1 | no | — |
| 70 | C22×C16 | — | 2 | 1 | no | — |
| 71 | #500 | — | 2 | 1 | no | — |
| 72 | #500 | — | 2 | 1 | no | — |
| 73 | #500 | — | 2 | 1 | no | — |
| 74 | #500 | C23 | 1 | 2 | yes | complemented |
| 75 | #495 | — | 2 | 1 | no | — |
| 76 | #495 | — | 2 | 1 | no | — |
| 77 | #495 | D4 | 1 | 2 | yes | — |
| 78 | #495 | C23 | 1 | 2 | yes | — |
| 79 | #468 | — | 2 | 4 | no | — |
| 80 | #468 | — | 2 | 4 | no | — |
| 81 | #463 | — | 2 | 4 | no | — |
| 82 | #463 | — | 2 | 4 | no | — |
| 83 | #461 | — | 2 | 4 | no | — |
| 84 | #461 | — | 4 | 2 | no | — |
| 85 | #452 | — | 2 | 4 | no | — |
| 86 | #452 | — | 2 | 4 | no | — |
| 87 | #447 | — | 2 | 4 | no | — |
| 88 | #447 | — | 2 | 4 | no | — |
| 89 | C4×D8 | — | 2 | 1 | no | — |
| 90 | C4×D8 | — | 2 | 1 | no | — |
| 91 | C4×D8 | D4 | 1 | 2 | yes | — |
| 92 | C4×D8 | C23 | 1 | 2 | yes | — |
| 93 | #436 | — | 2 | 1 | no | — |
| 94 | #436 | — | 2 | 1 | no | — |
| 95 | #436 | D4 | 1 | 2 | yes | — |
| 96 | #436 | C23 | 1 | 2 | yes | — |
| 97 | C2×#107 | — | 2 | 1 | no | — |
| 98 | C2×#107 | — | 2 | 1 | no | — |
| 99 | C2×#107 | D4 | 1 | 1 | yes | characteristic |
| 100 | C2×C4⋊C8 | — | 2 | 1 | no | — |
| 101 | C2×C4⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 102 | C2×#103 | — | 2 | 1 | no | — |
| 103 | C2×#103 | — | 4 | 1 | no | — |
| 104 | C2×#102 | — | 2 | 1 | no | — |
| 105 | C2×#102 | — | 2 | 1 | no | — |
| 106 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 107 | C2×C4×C8 | C23 | 1 | 1 | yes | characteristic |
| 108 | #367 | — | 2 | 4 | no | — |
| 109 | C4⋊C16 | — | 2 | 1 | no | — |
| 110 | C4⋊C16 | C23 | 1 | 2 | yes | complemented |
| 111 | #358 | — | 2 | 4 | no | — |
| 112 | #357 | — | 2 | 4 | no | — |
| 113 | #357 | — | 2 | 4 | no | — |
| 114 | #346 | — | 2 | 1 | no | — |
| 115 | #346 | C23 | 1 | 2 | yes | complemented |
| 116 | #334 | — | 2 | 1 | no | — |
| 117 | #334 | C23 | 1 | 2 | yes | complemented |
| 118 | #332 | — | 2 | 4 | no | — |
| 119 | C25 | — | 4 | 1 | no | — |
| 120 | C2×#41 | — | 2 | 4 | no | — |
| 121 | C2×#41 | — | 4 | 2 | no | — |
| 122 | C2×#41 | — | 4 | 4 | no | — |
| 123 | C2×#41 | — | 8 | 2 | no | — |
| 124 | C22×Q8 | — | 2 | 1 | no | — |
| 125 | C22×Q8 | — | 4 | 1 | no | — |
| 126 | C22×D4 | — | 2 | 4 | no | — |
| 127 | C22×D4 | — | 2 | 1 | no | — |
| 128 | C22×D4 | — | 2 | 1 | no | — |
| 129 | C22×D4 | — | 4 | 1 | no | — |
| 130 | C22×D4 | — | 4 | 2 | no | — |
| 131 | C22×D4 | — | 4 | 4 | no | — |
| 132 | C22×D4 | — | 4 | 1 | no | — |
| 133 | C22×D4 | — | 4 | 1 | no | — |
| 134 | C22×D4 | — | 8 | 2 | no | — |
| 135 | C22×D4 | D8 | 1 | 1 | yes | characteristic |
| 136 | C23×C4 | — | 2 | 1 | no | — |
| 137 | C23×C4 | — | 4 | 1 | no | — |
| 138 | C23×C4 | — | 4 | 1 | no | — |
| 139 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 140 | AGL(1,ℤ/8) | — | 4 | 16 | no | — |
| 141 | AGL(1,ℤ/8) | — | 4 | 8 | no | — |
| 142 | C2×Q16 | — | 2 | 1 | no | — |
| 143 | C2×Q16 | — | 4 | 2 | no | — |
| 144 | C2×Q16 | C2×D4 | 1 | 2 | yes | — |
| 145 | C2×SD16 | — | 2 | 4 | no | — |
| 146 | C2×SD16 | — | 2 | 2 | no | — |
| 147 | C2×SD16 | — | 2 | 2 | no | — |
| 148 | C2×SD16 | — | 4 | 4 | no | — |
| 149 | C2×SD16 | — | 4 | 4 | no | — |
| 150 | C2×SD16 | — | 4 | 2 | no | — |
| 151 | C2×SD16 | — | 4 | 2 | no | — |
| 152 | C2×SD16 | — | 8 | 4 | no | — |
| 153 | C2×D8 | — | 2 | 4 | no | — |
| 154 | C2×D8 | — | 2 | 1 | no | — |
| 155 | C2×D8 | — | 2 | 1 | no | — |
| 156 | C2×D8 | — | 2 | 2 | no | — |
| 157 | C2×D8 | — | 4 | 2 | no | — |
| 158 | C2×D8 | — | 4 | 4 | no | — |
| 159 | C2×D8 | SD16 | 1 | 4 | yes | complemented |
| 160 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 161 | C2×D8 | C2×D4 | 1 | 2 | yes | — |
| 162 | C2×M16 | — | 2 | 2 | no | — |
| 163 | C2×M16 | — | 2 | 2 | no | — |
| 164 | C2×M16 | — | 4 | 2 | no | — |
| 165 | C2×M16 | — | 4 | 2 | no | — |
| 166 | C22×C8 | — | 2 | 1 | no | — |
| 167 | C22×C8 | — | 4 | 1 | no | — |
| 168 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C22×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C4⋊Q8 | — | 2 | 2 | no | — |
| 171 | C4⋊Q8 | — | 4 | 1 | no | — |
| 172 | C4⋊Q8 | — | 4 | 1 | no | — |
| 173 | C4⋊Q8 | — | 4 | 1 | no | — |
| 174 | #124 | — | 2 | 2 | no | — |
| 175 | #124 | — | 2 | 2 | no | — |
| 176 | #124 | — | 4 | 1 | no | — |
| 177 | #124 | — | 4 | 1 | no | — |
| 178 | #123 | — | 4 | 4 | no | — |
| 179 | #123 | — | 4 | 4 | no | — |
| 180 | C22⋊Q8 | — | 2 | 4 | no | — |
| 181 | C22⋊Q8 | — | 4 | 2 | no | — |
| 182 | #121 | — | 2 | 4 | no | — |
| 183 | #121 | — | 4 | 4 | no | — |
| 184 | #121 | — | 4 | 4 | no | — |
| 185 | #121 | — | 4 | 2 | no | — |
| 186 | #120 | — | 4 | 4 | no | — |
| 187 | #120 | — | 4 | 4 | no | — |
| 188 | C4×D4 | — | 2 | 1 | no | — |
| 189 | C4×D4 | — | 2 | 2 | no | — |
| 190 | C4×D4 | — | 2 | 1 | no | — |
| 191 | C4×D4 | — | 2 | 2 | no | — |
| 192 | C4×D4 | — | 4 | 1 | no | — |
| 193 | C4×D4 | — | 4 | 1 | no | — |
| 194 | C4×D4 | D8 | 1 | 2 | yes | — |
| 195 | C4×D4 | C2×D4 | 1 | 2 | yes | — |
| 196 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 197 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 198 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 199 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 200 | C2×C4⋊C4 | D8 | 1 | 1 | yes | characteristic |
| 201 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 202 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 203 | C2×C22⋊C4 | — | 4 | 4 | no | — |
| 204 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 205 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 206 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 207 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 208 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 209 | C2×C42 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×C16 | — | 2 | 2 | no | — |
| 211 | C2×C16 | — | 2 | 2 | no | — |
| 212 | C2×C16 | — | 4 | 2 | no | — |
| 213 | C2×C16 | — | 4 | 2 | no | — |
| 214 | #107 | — | 2 | 1 | no | — |
| 215 | #107 | — | 2 | 2 | no | — |
| 216 | #107 | — | 2 | 2 | no | — |
| 217 | #107 | — | 4 | 1 | no | — |
| 218 | #107 | — | 4 | 1 | no | — |
| 219 | #107 | C2×D4 | 1 | 2 | yes | — |
| 220 | C4⋊C8 | — | 2 | 1 | no | — |
| 221 | C4⋊C8 | — | 2 | 2 | no | — |
| 222 | C4⋊C8 | — | 4 | 1 | no | — |
| 223 | C4⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 224 | #103 | — | 2 | 4 | no | — |
| 225 | #103 | — | 4 | 4 | no | — |
| 226 | #102 | — | 2 | 4 | no | — |
| 227 | #102 | — | 2 | 2 | no | — |
| 228 | #102 | — | 2 | 2 | no | — |
| 229 | C22⋊C8 | — | 2 | 2 | no | — |
| 230 | C22⋊C8 | — | 2 | 2 | no | — |
| 231 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C4×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C4×C8 | C24 | 1 | 1 | yes | characteristic |
| 235 | C24 | — | 2 | 1 | no | — |
| 236 | C24 | — | 4 | 4 | no | — |
| 237 | C24 | — | 4 | 1 | no | — |
| 238 | C24 | — | 4 | 1 | no | — |
| 239 | C24 | — | 8 | 4 | no | — |
| 240 | C24 | — | 8 | 4 | no | — |
| 241 | C24 | — | 16 | 2 | no | — |
| 242 | #41 | — | 4 | 8 | no | — |
| 243 | #41 | — | 8 | 4 | no | — |
| 244 | #41 | — | 8 | 8 | no | — |
| 245 | C2×Q8 | — | 2 | 2 | no | — |
| 246 | C2×Q8 | — | 4 | 1 | no | — |
| 247 | C2×Q8 | — | 4 | 2 | no | — |
| 248 | C2×Q8 | — | 4 | 2 | no | — |
| 249 | C2×Q8 | — | 4 | 2 | no | — |
| 250 | C2×Q8 | — | 8 | 2 | no | — |
| 251 | C2×Q8 | — | 8 | 2 | no | — |
| 252 | C2×Q8 | — | 8 | 1 | no | — |
| 253 | C2×D4 | — | 2 | 2 | no | — |
| 254 | C2×D4 | — | 2 | 2 | no | — |
| 255 | C2×D4 | — | 2 | 1 | no | — |
| 256 | C2×D4 | — | 2 | 4 | no | — |
| 257 | C2×D4 | — | 4 | 2 | no | — |
| 258 | C2×D4 | — | 4 | 4 | no | — |
| 259 | C2×D4 | — | 4 | 8 | no | — |
| 260 | C2×D4 | — | 4 | 4 | no | — |
| 261 | C2×D4 | — | 4 | 4 | no | — |
| 262 | C2×D4 | — | 4 | 1 | no | — |
| 263 | C2×D4 | — | 4 | 1 | no | — |
| 264 | C2×D4 | — | 4 | 2 | no | — |
| 265 | C2×D4 | — | 4 | 2 | no | — |
| 266 | C2×D4 | — | 4 | 2 | no | — |
| 267 | C2×D4 | — | 8 | 4 | no | — |
| 268 | C2×D4 | — | 8 | 8 | no | — |
| 269 | C2×D4 | — | 8 | 4 | no | — |
| 270 | C2×D4 | — | 8 | 4 | no | — |
| 271 | C2×D4 | — | 16 | 2 | no | — |
| 272 | C2×D4 | C2×D8 | 1 | 2 | yes | — |
| 273 | C22×C4 | — | 2 | 1 | no | — |
| 274 | C22×C4 | — | 2 | 2 | no | — |
| 275 | C22×C4 | — | 2 | 2 | no | — |
| 276 | C22×C4 | — | 4 | 4 | no | — |
| 277 | C22×C4 | — | 4 | 2 | no | — |
| 278 | C22×C4 | — | 4 | 2 | no | — |
| 279 | C22×C4 | — | 4 | 1 | no | — |
| 280 | C22×C4 | — | 4 | 1 | no | — |
| 281 | C22×C4 | — | 4 | 2 | no | — |
| 282 | C22×C4 | — | 4 | 2 | no | — |
| 283 | C22×C4 | — | 8 | 4 | no | — |
| 284 | C22×C4 | — | 8 | 1 | no | — |
| 285 | C22×C4 | — | 16 | 2 | no | — |
| 286 | C22×C4 | #120 | 1 | 1 | yes | characteristic |
| 287 | C22×C4 | C2×D8 | 1 | 1 | yes | characteristic |
| 288 | C22×C4 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 289 | Q16 | — | 4 | 2 | no | — |
| 290 | Q16 | — | 8 | 1 | no | — |
| 291 | SD16 | — | 4 | 8 | no | — |
| 292 | SD16 | — | 4 | 2 | no | — |
| 293 | SD16 | — | 4 | 2 | no | — |
| 294 | SD16 | — | 4 | 4 | no | — |
| 295 | SD16 | — | 8 | 8 | no | — |
| 296 | D8 | — | 2 | 2 | no | — |
| 297 | D8 | — | 2 | 4 | no | — |
| 298 | D8 | — | 4 | 2 | no | — |
| 299 | D8 | — | 4 | 8 | no | — |
| 300 | D8 | — | 8 | 1 | no | — |
| 301 | D8 | C2×SD16 | 1 | 4 | yes | complemented |
| 302 | M16 | — | 4 | 2 | no | — |
| 303 | M16 | — | 4 | 2 | no | — |
| 304 | M16 | — | 4 | 4 | no | — |
| 305 | C2×C8 | — | 2 | 2 | no | — |
| 306 | C2×C8 | — | 2 | 2 | no | — |
| 307 | C2×C8 | — | 4 | 2 | no | — |
| 308 | C2×C8 | — | 4 | 2 | no | — |
| 309 | C2×C8 | — | 8 | 2 | no | — |
| 310 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 311 | C2×C8 | #120 | 1 | 1 | yes | characteristic |
| 312 | C2×C8 | C2×SD16 | 1 | 2 | yes | — |
| 313 | C2×C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 314 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 315 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 316 | C4⋊C4 | — | 2 | 1 | no | — |
| 317 | C4⋊C4 | — | 2 | 2 | no | — |
| 318 | C4⋊C4 | — | 4 | 4 | no | — |
| 319 | C4⋊C4 | — | 4 | 1 | no | — |
| 320 | C4⋊C4 | — | 4 | 2 | no | — |
| 321 | C4⋊C4 | — | 4 | 2 | no | — |
| 322 | C4⋊C4 | — | 8 | 1 | no | — |
| 323 | C4⋊C4 | — | 8 | 1 | no | — |
| 324 | C4⋊C4 | C2×D8 | 1 | 2 | yes | — |
| 325 | C22⋊C4 | — | 2 | 2 | no | — |
| 326 | C22⋊C4 | — | 2 | 2 | no | — |
| 327 | C22⋊C4 | — | 4 | 4 | no | — |
| 328 | C22⋊C4 | — | 4 | 4 | no | — |
| 329 | C22⋊C4 | — | 4 | 2 | no | — |
| 330 | C22⋊C4 | — | 4 | 2 | no | — |
| 331 | C22⋊C4 | — | 4 | 2 | no | — |
| 332 | C22⋊C4 | — | 4 | 2 | no | — |
| 333 | C22⋊C4 | — | 4 | 2 | no | — |
| 334 | C22⋊C4 | — | 4 | 2 | no | — |
| 335 | C42 | #120 | 1 | 1 | yes | characteristic |
| 336 | C42 | C2×D8 | 1 | 1 | yes | characteristic |
| 337 | C42 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 338 | C42 | C22×D4 | 1 | 1 | yes | characteristic |
| 339 | C16 | — | 4 | 2 | no | — |
| 340 | C16 | — | 4 | 2 | no | — |
| 341 | C23 | — | 2 | 2 | no | — |
| 342 | C23 | — | 4 | 2 | no | — |
| 343 | C23 | — | 4 | 4 | no | — |
| 344 | C23 | — | 4 | 2 | no | — |
| 345 | C23 | — | 4 | 2 | no | — |
| 346 | C23 | — | 4 | 2 | no | — |
| 347 | C23 | — | 4 | 2 | no | — |
| 348 | C23 | — | 8 | 8 | no | — |
| 349 | C23 | — | 8 | 8 | no | — |
| 350 | C23 | — | 8 | 2 | no | — |
| 351 | C23 | — | 8 | 2 | no | — |
| 352 | C23 | — | 8 | 2 | no | — |
| 353 | C23 | — | 8 | 2 | no | — |
| 354 | C23 | — | 8 | 2 | no | — |
| 355 | C23 | — | 16 | 4 | no | — |
| 356 | C23 | — | 16 | 16 | no | — |
| 357 | C23 | #447 | 1 | 1 | yes | characteristic |
| 358 | Q8 | — | 4 | 2 | no | — |
| 359 | Q8 | — | 4 | 2 | no | — |
| 360 | Q8 | — | 8 | 2 | no | — |
| 361 | Q8 | — | 8 | 2 | no | — |
| 362 | Q8 | — | 8 | 2 | no | — |
| 363 | Q8 | — | 16 | 2 | no | — |
| 364 | D4 | — | 2 | 4 | no | — |
| 365 | D4 | — | 4 | 2 | no | — |
| 366 | D4 | — | 4 | 4 | no | — |
| 367 | D4 | — | 4 | 2 | no | — |
| 368 | D4 | — | 4 | 2 | no | — |
| 369 | D4 | — | 4 | 2 | no | — |
| 370 | D4 | — | 8 | 1 | no | — |
| 371 | D4 | — | 8 | 8 | no | — |
| 372 | D4 | — | 8 | 8 | no | — |
| 373 | D4 | — | 8 | 2 | no | — |
| 374 | D4 | — | 16 | 4 | no | — |
| 375 | C2×C4 | — | 2 | 2 | no | — |
| 376 | C2×C4 | — | 2 | 2 | no | — |
| 377 | C2×C4 | — | 2 | 2 | no | — |
| 378 | C2×C4 | — | 4 | 2 | no | — |
| 379 | C2×C4 | — | 4 | 4 | no | — |
| 380 | C2×C4 | — | 4 | 2 | no | — |
| 381 | C2×C4 | — | 4 | 2 | no | — |
| 382 | C2×C4 | — | 4 | 2 | no | — |
| 383 | C2×C4 | — | 4 | 2 | no | — |
| 384 | C2×C4 | — | 8 | 8 | no | — |
| 385 | C2×C4 | — | 8 | 2 | no | — |
| 386 | C2×C4 | — | 8 | 2 | no | — |
| 387 | C2×C4 | — | 8 | 2 | no | — |
| 388 | C2×C4 | — | 16 | 2 | no | — |
| 389 | C2×C4 | — | 16 | 2 | no | — |
| 390 | C2×C4 | — | 16 | 2 | no | — |
| 391 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 392 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 393 | C2×C4 | #447 | 1 | 1 | yes | characteristic |
| 394 | C2×C4 | #450 | 1 | 2 | yes | — |
| 395 | C2×C4 | #455 | 1 | 2 | yes | — |
| 396 | C2×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 397 | C2×C4 | C22×D8 | 1 | 1 | yes | characteristic |
| 398 | C2×C4 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 399 | C8 | — | 2 | 1 | no | — |
| 400 | C8 | — | 2 | 1 | no | — |
| 401 | C8 | — | 4 | 2 | no | — |
| 402 | C8 | — | 8 | 2 | no | — |
| 403 | C8 | #450 | 1 | 2 | yes | — |
| 404 | C8 | C22×SD16 | 1 | 1 | yes | characteristic |
| 405 | C8 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 406 | C22 | — | 4 | 2 | no | — |
| 407 | C22 | — | 4 | 4 | no | — |
| 408 | C22 | — | 4 | 2 | no | — |
| 409 | C22 | — | 4 | 2 | no | — |
| 410 | C22 | — | 8 | 4 | no | — |
| 411 | C22 | — | 8 | 8 | no | — |
| 412 | C22 | — | 8 | 2 | no | — |
| 413 | C22 | — | 8 | 2 | no | — |
| 414 | C22 | — | 8 | 2 | no | — |
| 415 | C22 | — | 8 | 2 | no | — |
| 416 | C22 | — | 8 | 2 | no | — |
| 417 | C22 | — | 16 | 16 | no | — |
| 418 | C22 | — | 16 | 4 | no | — |
| 419 | C22 | #1639 | 1 | 2 | yes | — |
| 420 | C22 | #2190 | 1 | 2 | yes | — |
| 421 | C22 | #2194 | 1 | 2 | yes | — |
| 422 | C22 | C2×#447 | 1 | 1 | yes | characteristic |
| 423 | C4 | — | 2 | 1 | no | — |
| 424 | C4 | — | 2 | 1 | no | — |
| 425 | C4 | — | 2 | 1 | no | — |
| 426 | C4 | — | 2 | 1 | no | — |
| 427 | C4 | — | 4 | 2 | no | — |
| 428 | C4 | — | 8 | 2 | no | — |
| 429 | C4 | — | 8 | 2 | no | — |
| 430 | C4 | — | 16 | 2 | no | — |
| 431 | C4 | #1639 | 1 | 2 | yes | — |
| 432 | C4 | C2×#450 | 1 | 1 | yes | characteristic |
| 433 | C4 | C2×#455 | 1 | 1 | yes | characteristic |
| 434 | C2 | — | 8 | 2 | no | — |
| 435 | C2 | — | 8 | 4 | no | — |
| 436 | C2 | — | 16 | 2 | no | — |
| 437 | C2 | #12378 | 1 | 4 | yes | direct product factor |
| 438 | C2 | C2×#1639 | 1 | 1 | yes | characteristic |
| 439 | C2 | C2×#2190 | 1 | 1 | yes | characteristic |
| 440 | C2 | C2×#2194 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C24 |
| prime radical | C2×#3273 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23 ◁ C2×C42 ◁ C2×#436 ◁ G | |
| LECS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#2243 | C2 | semidirect |
| 3. C2×#2226 | C2 | semidirect |
| 4. C2×#1693 | C2 | semidirect |
| 5. #12378 | C2 | direct (N × H) |
| 6. C2×#1360 | C2 | semidirect |
| 7. C2×#1333 | C2 | semidirect |
| 8. C2×#1330 | C2 | semidirect |
| 15. C2×#500 | C22 | semidirect |
| 25. #2243 | C22 | semidirect |
| 27. #2226 | C22 | semidirect |
| 29. C2×C4⋊C16 | C22 | semidirect |
| 33. C2×#346 | C22 | semidirect |
| 35. #1693 | C22 | semidirect |
| 36. C2×#334 | C22 | semidirect |
| 38. #1360 | C22 | semidirect |
| 39. #1333 | C22 | semidirect |
| 40. #1330 | C22 | semidirect |
| 74. #500 | C23 | semidirect |
| 110. C4⋊C16 | C23 | semidirect |
| 115. #346 | C23 | semidirect |
| 117. #334 | C23 | semidirect |
| 159. C2×D8 | SD16 | semidirect |
| 301. D8 | C2×SD16 | semidirect |
| 437. C2 | #12378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3273 | 2 |
| C2×#2243 | 2 |
| C2×#2226 | 2 |
| C2×#1693 | 2 |
| #12378 | 2 |
| C2×#1360 | 2 |
| C2×#1333 | 2 |
| C2×#1330 | 2 |