Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
440 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 83 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 | #513315 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #512951 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #512945 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#7540 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #153560 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #153432 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #94764 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#2262 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#2262 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#2258 | C22 | 1 | 1 | yes | characteristic |
| 11 | #33617 | — | 2 | 1 | no | — |
| 12 | #33610 | — | 2 | 1 | no | — |
| 13 | #13743 | — | 2 | 1 | no | — |
| 14 | #13743 | — | 2 | 1 | no | — |
| 15 | #13742 | — | 2 | 1 | no | — |
| 16 | #13742 | — | 2 | 1 | no | — |
| 17 | #13741 | — | 2 | 2 | no | — |
| 18 | C2×M128 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×M128 | C22 | 1 | 1 | yes | characteristic |
| 20 | #13702 | — | 2 | 2 | no | — |
| 21 | #13701 | — | 2 | 1 | no | — |
| 22 | #13700 | — | 2 | 1 | no | — |
| 23 | #13698 | — | 2 | 1 | no | — |
| 24 | #13697 | — | 2 | 1 | no | — |
| 25 | #13696 | — | 2 | 2 | no | — |
| 26 | C2×#1425 | C22 | 1 | 1 | yes | characteristic |
| 27 | C2×#1424 | C22 | 1 | 1 | yes | characteristic |
| 28 | #13625 | — | 2 | 1 | no | — |
| 29 | #13616 | — | 2 | 1 | no | — |
| 30 | #7540 | — | 2 | 2 | no | — |
| 31 | #7539 | — | 2 | 2 | no | — |
| 32 | #7514 | — | 2 | 2 | no | — |
| 33 | C2×#508 | — | 2 | 1 | no | — |
| 34 | C2×#508 | — | 2 | 1 | no | — |
| 35 | C2×#504 | D4 | 1 | 1 | yes | characteristic |
| 36 | #3067 | — | 4 | 1 | no | — |
| 37 | #3061 | — | 4 | 1 | no | — |
| 38 | #2262 | — | 2 | 1 | no | — |
| 39 | #2262 | — | 2 | 1 | no | — |
| 40 | #2262 | — | 2 | 1 | no | — |
| 41 | #2262 | — | 2 | 1 | no | — |
| 42 | #2262 | — | 2 | 1 | no | — |
| 43 | #2262 | — | 2 | 1 | no | — |
| 44 | #2262 | — | 2 | 1 | no | — |
| 45 | #2262 | — | 2 | 1 | no | — |
| 46 | C2×Q64 | D4 | 1 | 1 | yes | characteristic |
| 47 | C2×Q64 | D4 | 1 | 1 | yes | characteristic, complemented |
| 48 | C2×SD64 | — | 2 | 1 | no | — |
| 49 | C2×SD64 | — | 2 | 1 | no | — |
| 50 | C2×D32 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×D32 | D4 | 1 | 1 | yes | characteristic, complemented |
| 52 | #2258 | — | 2 | 1 | no | — |
| 53 | #2258 | — | 2 | 1 | no | — |
| 54 | #2258 | — | 2 | 1 | no | — |
| 55 | #2258 | — | 2 | 1 | no | — |
| 56 | C2×M64 | — | 2 | 1 | no | — |
| 57 | C2×M64 | D4 | 1 | 1 | yes | characteristic |
| 58 | C22×C32 | — | 2 | 1 | no | — |
| 59 | C22×C32 | C23 | 1 | 1 | yes | characteristic |
| 60 | #2223 | — | 4 | 2 | no | — |
| 61 | #2222 | — | 2 | 2 | no | — |
| 62 | #2221 | — | 2 | 2 | no | — |
| 63 | #2220 | — | 4 | 2 | no | — |
| 64 | #2216 | — | 2 | 2 | no | — |
| 65 | #2215 | — | 2 | 2 | no | — |
| 66 | C2×#368 | — | 2 | 1 | no | — |
| 67 | C2×#366 | — | 2 | 1 | no | — |
| 68 | #2148 | — | 4 | 1 | no | — |
| 69 | #2139 | — | 4 | 1 | no | — |
| 70 | Q128 | — | 2 | 2 | no | — |
| 71 | SD128 | — | 2 | 2 | no | — |
| 72 | SD128 | — | 2 | 2 | no | — |
| 73 | D64 | — | 2 | 2 | no | — |
| 74 | M128 | — | 2 | 1 | no | — |
| 75 | M128 | — | 2 | 1 | no | — |
| 76 | M128 | — | 2 | 1 | no | — |
| 77 | M128 | — | 2 | 1 | no | — |
| 78 | C2×C64 | — | 2 | 1 | no | — |
| 79 | C2×C64 | D4 | 1 | 2 | yes | complemented |
| 80 | #1425 | — | 2 | 1 | no | — |
| 81 | #1425 | D4 | 1 | 2 | yes | complemented |
| 82 | #1424 | — | 2 | 1 | no | — |
| 83 | #1424 | D4 | 1 | 2 | yes | — |
| 84 | #1420 | — | 2 | 2 | no | — |
| 85 | #1419 | — | 2 | 2 | no | — |
| 86 | #1416 | — | 2 | 2 | no | — |
| 87 | #1415 | — | 2 | 2 | no | — |
| 88 | #575 | — | 8 | 1 | no | — |
| 89 | C2×#135 | — | 4 | 1 | no | — |
| 90 | C2×#135 | — | 4 | 1 | no | — |
| 91 | C2×#131 | D8 | 1 | 1 | yes | characteristic |
| 92 | #537 | — | 8 | 1 | no | — |
| 93 | #508 | — | 4 | 1 | no | — |
| 94 | #508 | — | 4 | 1 | no | — |
| 95 | #508 | — | 4 | 1 | no | — |
| 96 | #508 | — | 4 | 1 | no | — |
| 97 | #508 | — | 4 | 1 | no | — |
| 98 | #508 | — | 4 | 1 | no | — |
| 99 | #508 | — | 4 | 1 | no | — |
| 100 | #508 | — | 4 | 1 | no | — |
| 101 | C2×Q32 | — | 2 | 1 | no | — |
| 102 | C2×Q32 | — | 2 | 1 | no | — |
| 103 | C2×SD32 | — | 4 | 1 | no | — |
| 104 | C2×SD32 | — | 4 | 1 | no | — |
| 105 | C2×D16 | — | 2 | 1 | no | — |
| 106 | C2×D16 | — | 2 | 1 | no | — |
| 107 | #504 | — | 2 | 1 | no | — |
| 108 | #504 | — | 2 | 1 | no | — |
| 109 | #504 | — | 2 | 1 | no | — |
| 110 | #504 | — | 2 | 1 | no | — |
| 111 | C2×M32 | — | 2 | 1 | no | — |
| 112 | C2×M32 | D8 | 1 | 1 | yes | characteristic |
| 113 | C22×C16 | — | 2 | 1 | no | — |
| 114 | C22×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 115 | #473 | — | 4 | 2 | no | — |
| 116 | #472 | — | 4 | 2 | no | — |
| 117 | #471 | — | 8 | 2 | no | — |
| 118 | #468 | — | 8 | 2 | no | — |
| 119 | #467 | — | 4 | 2 | no | — |
| 120 | #466 | — | 4 | 2 | no | — |
| 121 | C2×#108 | — | 4 | 1 | no | — |
| 122 | C2×#107 | — | 4 | 1 | no | — |
| 123 | #417 | — | 8 | 1 | no | — |
| 124 | #413 | — | 8 | 1 | no | — |
| 125 | Q64 | — | 2 | 1 | no | — |
| 126 | Q64 | — | 2 | 1 | no | — |
| 127 | Q64 | — | 2 | 1 | no | — |
| 128 | Q64 | — | 2 | 1 | no | — |
| 129 | SD64 | — | 4 | 1 | no | — |
| 130 | SD64 | — | 4 | 1 | no | — |
| 131 | SD64 | — | 4 | 1 | no | — |
| 132 | SD64 | — | 4 | 1 | no | — |
| 133 | D32 | — | 2 | 1 | no | — |
| 134 | D32 | — | 2 | 1 | no | — |
| 135 | D32 | — | 2 | 1 | no | — |
| 136 | D32 | — | 2 | 1 | no | — |
| 137 | M64 | — | 2 | 1 | no | — |
| 138 | M64 | — | 2 | 1 | no | — |
| 139 | M64 | — | 4 | 1 | no | — |
| 140 | M64 | — | 4 | 1 | no | — |
| 141 | C2×C32 | — | 2 | 1 | no | — |
| 142 | C2×C32 | — | 4 | 1 | no | — |
| 143 | C2×C32 | — | 4 | 1 | no | — |
| 144 | C2×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C2×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C32 | #41 | 1 | 1 | yes | characteristic |
| 150 | #368 | — | 2 | 2 | no | — |
| 151 | #368 | — | 4 | 1 | no | — |
| 152 | #366 | — | 2 | 2 | no | — |
| 153 | #366 | — | 4 | 1 | no | — |
| 154 | #362 | — | 4 | 2 | no | — |
| 155 | #361 | — | 4 | 2 | no | — |
| 156 | #358 | — | 4 | 2 | no | — |
| 157 | #357 | — | 4 | 2 | no | — |
| 158 | C64 | — | 2 | 2 | no | — |
| 159 | C64 | — | 4 | 1 | no | — |
| 160 | C2×#41 | — | 8 | 1 | no | — |
| 161 | C2×#41 | — | 8 | 1 | no | — |
| 162 | C2×#41 | D16 | 1 | 1 | yes | characteristic |
| 163 | #137 | — | 8 | 2 | no | — |
| 164 | #137 | — | 16 | 1 | no | — |
| 165 | AGL(1,ℤ/8) | — | 8 | 2 | no | — |
| 166 | AGL(1,ℤ/8) | — | 16 | 1 | no | — |
| 167 | #135 | — | 8 | 1 | no | — |
| 168 | #135 | — | 8 | 1 | no | — |
| 169 | #135 | — | 8 | 1 | no | — |
| 170 | #135 | — | 8 | 1 | no | — |
| 171 | #135 | — | 8 | 1 | no | — |
| 172 | #135 | — | 8 | 1 | no | — |
| 173 | #135 | — | 8 | 1 | no | — |
| 174 | #135 | — | 8 | 1 | no | — |
| 175 | #135 | — | 16 | 2 | no | — |
| 176 | C2×Q16 | — | 4 | 1 | no | — |
| 177 | C2×Q16 | — | 4 | 1 | no | — |
| 178 | C2×SD16 | — | 8 | 1 | no | — |
| 179 | C2×SD16 | — | 8 | 1 | no | — |
| 180 | C2×D8 | — | 4 | 1 | no | — |
| 181 | C2×D8 | — | 4 | 1 | no | — |
| 182 | #131 | — | 2 | 1 | no | — |
| 183 | #131 | — | 2 | 1 | no | — |
| 184 | #131 | — | 2 | 1 | no | — |
| 185 | #131 | — | 2 | 1 | no | — |
| 186 | C2×M16 | — | 2 | 1 | no | — |
| 187 | C2×M16 | — | 8 | 1 | no | — |
| 188 | C2×M16 | D16 | 1 | 1 | yes | characteristic |
| 189 | C22×C8 | — | 2 | 1 | no | — |
| 190 | C22×C8 | C2×D8 | 1 | 1 | yes | characteristic |
| 191 | C22⋊Q8 | — | 8 | 2 | no | — |
| 192 | C22⋊Q8 | — | 16 | 1 | no | — |
| 193 | #121 | — | 8 | 2 | no | — |
| 194 | #121 | — | 16 | 2 | no | — |
| 195 | #121 | — | 16 | 1 | no | — |
| 196 | C2×C4⋊C4 | — | 8 | 1 | no | — |
| 197 | Q32 | — | 4 | 1 | no | — |
| 198 | Q32 | — | 4 | 1 | no | — |
| 199 | Q32 | — | 4 | 1 | no | — |
| 200 | Q32 | — | 4 | 1 | no | — |
| 201 | SD32 | — | 8 | 1 | no | — |
| 202 | SD32 | — | 8 | 1 | no | — |
| 203 | SD32 | — | 8 | 1 | no | — |
| 204 | SD32 | — | 8 | 1 | no | — |
| 205 | D16 | — | 4 | 1 | no | — |
| 206 | D16 | — | 4 | 1 | no | — |
| 207 | D16 | — | 4 | 1 | no | — |
| 208 | D16 | — | 4 | 1 | no | — |
| 209 | M32 | — | 2 | 1 | no | — |
| 210 | M32 | — | 2 | 1 | no | — |
| 211 | M32 | — | 4 | 1 | no | — |
| 212 | M32 | — | 4 | 1 | no | — |
| 213 | C2×C16 | — | 2 | 1 | no | — |
| 214 | C2×C16 | — | 4 | 1 | no | — |
| 215 | C2×C16 | — | 4 | 1 | no | — |
| 216 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 217 | C2×C16 | #120 | 1 | 1 | yes | characteristic |
| 218 | C2×C16 | #121 | 1 | 1 | yes | characteristic |
| 219 | C2×C16 | #135 | 1 | 1 | yes | characteristic |
| 220 | C2×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 221 | C2×C16 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 222 | #108 | — | 4 | 2 | no | — |
| 223 | #108 | — | 8 | 1 | no | — |
| 224 | #107 | — | 4 | 2 | no | — |
| 225 | #107 | — | 8 | 1 | no | — |
| 226 | #103 | — | 8 | 2 | no | — |
| 227 | #102 | — | 8 | 2 | no | — |
| 228 | #101 | — | 8 | 2 | no | — |
| 229 | #100 | — | 8 | 2 | no | — |
| 230 | C32 | — | 4 | 1 | no | — |
| 231 | C32 | #120 | 1 | 1 | yes | characteristic |
| 232 | C32 | #121 | 1 | 1 | yes | characteristic |
| 233 | C32 | #121 | 1 | 1 | yes | characteristic |
| 234 | C32 | #127 | 1 | 1 | yes | characteristic |
| 235 | #41 | — | 2 | 1 | no | — |
| 236 | #41 | — | 2 | 1 | no | — |
| 237 | #41 | — | 2 | 1 | no | — |
| 238 | #41 | — | 2 | 1 | no | — |
| 239 | #41 | — | 16 | 1 | no | — |
| 240 | #41 | — | 16 | 1 | no | — |
| 241 | #41 | — | 16 | 1 | no | — |
| 242 | #41 | — | 16 | 1 | no | — |
| 243 | #41 | — | 16 | 1 | no | — |
| 244 | #41 | — | 16 | 1 | no | — |
| 245 | #41 | — | 16 | 1 | no | — |
| 246 | #41 | — | 16 | 1 | no | — |
| 247 | C2×Q8 | — | 8 | 1 | no | — |
| 248 | C2×Q8 | — | 8 | 1 | no | — |
| 249 | C2×Q8 | D32 | 1 | 1 | yes | characteristic |
| 250 | C2×D4 | — | 2 | 1 | no | — |
| 251 | C2×D4 | — | 8 | 1 | no | — |
| 252 | C2×D4 | — | 8 | 1 | no | — |
| 253 | C2×D4 | — | 16 | 1 | no | — |
| 254 | C2×D4 | — | 16 | 1 | no | — |
| 255 | C2×D4 | — | 16 | 2 | no | — |
| 256 | C2×D4 | D32 | 1 | 1 | yes | characteristic |
| 257 | C22×C4 | — | 2 | 1 | no | — |
| 258 | C22×C4 | — | 16 | 1 | no | — |
| 259 | C22×C4 | — | 16 | 1 | no | — |
| 260 | C22×C4 | — | 16 | 1 | no | — |
| 261 | C22×C4 | C2×D16 | 1 | 1 | yes | characteristic |
| 262 | Q16 | — | 8 | 1 | no | — |
| 263 | Q16 | — | 8 | 1 | no | — |
| 264 | Q16 | — | 8 | 1 | no | — |
| 265 | Q16 | — | 8 | 1 | no | — |
| 266 | Q16 | — | 16 | 2 | no | — |
| 267 | SD16 | — | 16 | 2 | no | — |
| 268 | SD16 | — | 16 | 2 | no | — |
| 269 | SD16 | — | 16 | 1 | no | — |
| 270 | SD16 | — | 16 | 1 | no | — |
| 271 | SD16 | — | 16 | 1 | no | — |
| 272 | SD16 | — | 16 | 1 | no | — |
| 273 | D8 | — | 8 | 1 | no | — |
| 274 | D8 | — | 8 | 1 | no | — |
| 275 | D8 | — | 8 | 1 | no | — |
| 276 | D8 | — | 8 | 1 | no | — |
| 277 | D8 | — | 16 | 2 | no | — |
| 278 | M16 | — | 2 | 1 | no | — |
| 279 | M16 | — | 2 | 1 | no | — |
| 280 | M16 | — | 4 | 1 | no | — |
| 281 | M16 | — | 4 | 1 | no | — |
| 282 | M16 | — | 8 | 2 | no | — |
| 283 | M16 | — | 16 | 1 | no | — |
| 284 | C2×C8 | — | 2 | 1 | no | — |
| 285 | C2×C8 | — | 4 | 1 | no | — |
| 286 | C2×C8 | — | 4 | 1 | no | — |
| 287 | C2×C8 | — | 16 | 1 | no | — |
| 288 | C2×C8 | #447 | 1 | 1 | yes | characteristic |
| 289 | C2×C8 | #447 | 1 | 1 | yes | characteristic |
| 290 | C2×C8 | #466 | 1 | 1 | yes | characteristic |
| 291 | C2×C8 | #508 | 1 | 1 | yes | characteristic |
| 292 | C2×C8 | #509 | 1 | 1 | yes | characteristic |
| 293 | C2×C8 | #509 | 1 | 1 | yes | characteristic |
| 294 | C4⋊C4 | — | 8 | 2 | no | — |
| 295 | C4⋊C4 | — | 16 | 2 | no | — |
| 296 | C4⋊C4 | — | 16 | 1 | no | — |
| 297 | C22⋊C4 | — | 16 | 2 | no | — |
| 298 | C22⋊C4 | — | 16 | 2 | no | — |
| 299 | C16 | — | 4 | 1 | no | — |
| 300 | C16 | #392 | 1 | 1 | yes | characteristic |
| 301 | C16 | #449 | 1 | 1 | yes | characteristic |
| 302 | C16 | #449 | 1 | 1 | yes | characteristic |
| 303 | C16 | #469 | 1 | 1 | yes | characteristic |
| 304 | C23 | — | 2 | 1 | no | — |
| 305 | C23 | — | 16 | 1 | no | — |
| 306 | C23 | — | 16 | 1 | no | — |
| 307 | C23 | #2263 | 1 | 1 | yes | characteristic |
| 308 | Q8 | — | 2 | 1 | no | — |
| 309 | Q8 | — | 2 | 1 | no | — |
| 310 | Q8 | — | 16 | 1 | no | — |
| 311 | Q8 | — | 16 | 1 | no | — |
| 312 | Q8 | — | 16 | 1 | no | — |
| 313 | Q8 | — | 16 | 1 | no | — |
| 314 | D4 | — | 2 | 1 | no | — |
| 315 | D4 | — | 2 | 1 | no | — |
| 316 | D4 | — | 4 | 1 | no | — |
| 317 | D4 | — | 4 | 1 | no | — |
| 318 | D4 | — | 16 | 1 | no | — |
| 319 | D4 | — | 16 | 1 | no | — |
| 320 | D4 | — | 16 | 1 | no | — |
| 321 | D4 | — | 16 | 1 | no | — |
| 322 | D4 | — | 32 | 1 | no | — |
| 323 | D4 | — | 32 | 1 | no | — |
| 324 | D4 | — | 32 | 1 | no | — |
| 325 | D4 | — | 32 | 1 | no | — |
| 326 | D4 | — | 64 | 2 | no | — |
| 327 | C2×C4 | — | 2 | 1 | no | — |
| 328 | C2×C4 | — | 4 | 1 | no | — |
| 329 | C2×C4 | — | 4 | 1 | no | — |
| 330 | C2×C4 | — | 16 | 2 | no | — |
| 331 | C2×C4 | — | 16 | 1 | no | — |
| 332 | C2×C4 | — | 16 | 1 | no | — |
| 333 | C2×C4 | — | 32 | 1 | no | — |
| 334 | C2×C4 | — | 32 | 1 | no | — |
| 335 | C2×C4 | — | 32 | 1 | no | — |
| 336 | C2×C4 | — | 32 | 1 | no | — |
| 337 | C2×C4 | — | 64 | 1 | no | — |
| 338 | C2×C4 | #2184 | 1 | 1 | yes | characteristic |
| 339 | C2×C4 | #2184 | 1 | 1 | yes | characteristic |
| 340 | C2×C4 | #2215 | 1 | 1 | yes | characteristic |
| 341 | C2×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 342 | C2×C4 | #2262 | 1 | 1 | yes | characteristic |
| 343 | C2×C4 | #2263 | 1 | 1 | yes | characteristic |
| 344 | C8 | — | 4 | 1 | no | — |
| 345 | C8 | — | 16 | 2 | no | — |
| 346 | C8 | #1999 | 1 | 1 | yes | characteristic |
| 347 | C8 | #2186 | 1 | 1 | yes | characteristic |
| 348 | C8 | #2186 | 1 | 1 | yes | characteristic |
| 349 | C8 | #2218 | 1 | 1 | yes | characteristic |
| 350 | C22 | — | 4 | 1 | no | — |
| 351 | C22 | — | 4 | 2 | no | — |
| 352 | C22 | — | 4 | 1 | no | — |
| 353 | C22 | — | 32 | 1 | no | — |
| 354 | C22 | — | 32 | 1 | no | — |
| 355 | C22 | — | 32 | 1 | no | — |
| 356 | C22 | — | 32 | 1 | no | — |
| 357 | C22 | — | 64 | 1 | no | — |
| 358 | C22 | #13661 | 1 | 1 | yes | characteristic |
| 359 | C22 | #13663 | 1 | 1 | yes | characteristic |
| 360 | C22 | #13697 | 1 | 1 | yes | characteristic |
| 361 | C4 | — | 4 | 1 | no | — |
| 362 | C4 | — | 32 | 2 | no | — |
| 363 | C4 | — | 32 | 1 | no | — |
| 364 | C4 | — | 32 | 1 | no | — |
| 365 | C4 | #13304 | 1 | 1 | yes | characteristic |
| 366 | C4 | #13661 | 1 | 1 | yes | characteristic |
| 367 | C4 | #13663 | 1 | 1 | yes | characteristic |
| 368 | C4 | #13694 | 1 | 1 | yes | characteristic |
| 369 | C2 | — | 2 | 1 | no | — |
| 370 | C2 | — | 2 | 1 | no | — |
| 371 | C2 | — | 2 | 1 | no | — |
| 372 | C2 | — | 8 | 1 | no | — |
| 373 | C2 | — | 64 | 1 | no | — |
| 374 | C2 | — | 64 | 1 | no | — |
| 375 | C2 | #153078 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #153078 |
| commutator, Frattini, cosocle | C22×C32 | C23 |
| LCS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ C2×#504 ◁ C2×#2258 ◁ G | |
| LECS | G ▷ C22×C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #513315 | C2 | semidirect |
| 2. #512951 | C2 | semidirect |
| 3. #512945 | C2 | semidirect |
| 4. C2×#7540 | C2 | semidirect |
| 5. #153560 | C2 | semidirect |
| 6. #153432 | C2 | semidirect |
| 7. #94764 | C2 | semidirect |
| 47. C2×Q64 | D4 | semidirect |
| 51. C2×D32 | D4 | semidirect |
| 79. C2×C64 | D4 | semidirect |
| 81. #1425 | D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #513315 | 2 |
| #512951 | 2 |
| #512945 | 2 |
| C2×#7540 | 2 |
| #153560 | 2 |
| #153432 | 2 |
| #94764 | 2 |