Finite Group DatabasebetaFinite Group DatabasebetaOrder 2048.
1230 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 140 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×#93866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #72216534 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #72216416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72216270 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#123403 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #498572 | — | 2 | 2 | no | — |
| 7 | C2×#12515 | — | 2 | 2 | no | — |
| 8 | C2×#12515 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#12515 | C22 | 1 | 1 | yes | characteristic |
| 10 | #152994 | — | 2 | 2 | no | — |
| 11 | C2×#7459 | C22 | 1 | 2 | yes | — |
| 12 | C2×#7448 | — | 2 | 2 | no | — |
| 13 | #141263 | — | 2 | 2 | no | — |
| 14 | #137551 | — | 2 | 2 | no | — |
| 15 | #129142 | C22 | 1 | 2 | yes | — |
| 16 | #123403 | — | 2 | 2 | no | — |
| 17 | #123403 | C4 | 1 | 4 | yes | complemented |
| 18 | C2×C162 | C22 | 1 | 1 | yes | characteristic |
| 19 | #93866 | — | 2 | 2 | no | — |
| 20 | C2×#2246 | — | 2 | 2 | no | — |
| 21 | C2×#2246 | — | 2 | 2 | no | — |
| 22 | C2×#2246 | — | 4 | 4 | no | — |
| 23 | #33456 | — | 4 | 2 | no | — |
| 24 | #23201 | — | 2 | 2 | no | — |
| 25 | C2×#1712 | — | 2 | 1 | no | — |
| 26 | C2×#1712 | D4 | 1 | 2 | yes | — |
| 27 | C2×#1422 | — | 2 | 2 | no | — |
| 28 | C2×#1419 | — | 4 | 2 | no | — |
| 29 | #13617 | — | 4 | 2 | no | — |
| 30 | #13261 | — | 2 | 4 | no | — |
| 31 | #13245 | — | 4 | 2 | no | — |
| 32 | #13017 | — | 4 | 4 | no | — |
| 33 | #12670 | D4 | 1 | 2 | yes | — |
| 34 | #12664 | — | 2 | 2 | no | — |
| 35 | #12515 | — | 2 | 8 | no | — |
| 36 | #12515 | — | 2 | 1 | no | — |
| 37 | #12515 | — | 2 | 2 | no | — |
| 38 | #12515 | — | 2 | 2 | no | — |
| 39 | #12515 | — | 4 | 4 | no | — |
| 40 | #12515 | C2×C4 | 1 | 2 | yes | — |
| 41 | #12515 | C2×C4 | 1 | 2 | yes | complemented |
| 42 | #12515 | D4 | 1 | 2 | yes | — |
| 43 | C2×#1373 | D4 | 1 | 2 | yes | — |
| 44 | C2×#1357 | — | 2 | 2 | no | — |
| 45 | C2×C8×C16 | — | 2 | 1 | no | — |
| 46 | C2×C8×C16 | C23 | 1 | 1 | yes | characteristic |
| 47 | #7459 | — | 2 | 2 | no | — |
| 48 | #7459 | — | 2 | 2 | no | — |
| 49 | #7448 | — | 4 | 4 | no | — |
| 50 | #7179 | — | 2 | 2 | no | — |
| 51 | C162 | — | 2 | 1 | no | — |
| 52 | C162 | C2×C4 | 1 | 2 | yes | complemented |
| 53 | C22×D16 | — | 4 | 2 | no | — |
| 54 | C22×D16 | — | 4 | 2 | no | — |
| 55 | C22×D16 | — | 4 | 2 | no | — |
| 56 | C22×D16 | — | 4 | 2 | no | — |
| 57 | C22×D16 | — | 8 | 8 | no | — |
| 58 | C2×#493 | — | 2 | 2 | no | — |
| 59 | C2×#493 | — | 4 | 2 | no | — |
| 60 | C2×#493 | — | 4 | 2 | no | — |
| 61 | C2×#493 | — | 4 | 1 | no | — |
| 62 | #2948 | — | 4 | 4 | no | — |
| 63 | C2×M64 | — | 4 | 2 | no | — |
| 64 | #2246 | — | 2 | 4 | no | — |
| 65 | #2246 | — | 2 | 4 | no | — |
| 66 | #2246 | — | 2 | 4 | no | — |
| 67 | #2246 | — | 4 | 16 | no | — |
| 68 | #2246 | — | 4 | 2 | no | — |
| 69 | #2246 | — | 4 | 2 | no | — |
| 70 | #2246 | — | 4 | 2 | no | — |
| 71 | #2246 | — | 4 | 2 | no | — |
| 72 | #2246 | — | 4 | 2 | no | — |
| 73 | #2246 | — | 8 | 8 | no | — |
| 74 | #2177 | — | 8 | 4 | no | — |
| 75 | C4×D16 | — | 8 | 4 | no | — |
| 76 | C2×#368 | D8 | 1 | 2 | yes | — |
| 77 | #2158 | D8 | 1 | 2 | yes | — |
| 78 | C2×#364 | — | 2 | 2 | no | — |
| 79 | C2×#361 | — | 4 | 4 | no | — |
| 80 | #2140 | — | 4 | 4 | no | — |
| 81 | #2108 | — | 4 | 2 | no | — |
| 82 | C2×C4×C16 | — | 2 | 2 | no | — |
| 83 | C2×C4×C16 | C2×D4 | 1 | 2 | yes | — |
| 84 | #1978 | — | 4 | 4 | no | — |
| 85 | #1887 | — | 8 | 2 | no | — |
| 86 | #1772 | — | 2 | 2 | no | — |
| 87 | #1712 | — | 2 | 2 | no | — |
| 88 | #1712 | — | 2 | 2 | no | — |
| 89 | #1712 | — | 4 | 2 | no | — |
| 90 | #1712 | — | 4 | 2 | no | — |
| 91 | #1712 | — | 4 | 1 | no | — |
| 92 | #1712 | C22⋊C4 | 1 | 4 | yes | — |
| 93 | C2×C82 | C2×D4 | 1 | 1 | yes | characteristic |
| 94 | #1422 | — | 4 | 2 | no | — |
| 95 | #1422 | — | 4 | 2 | no | — |
| 96 | #1419 | — | 8 | 4 | no | — |
| 97 | #1415 | — | 8 | 4 | no | — |
| 98 | #1382 | — | 2 | 2 | no | — |
| 99 | #1379 | — | 4 | 2 | no | — |
| 100 | #1373 | — | 2 | 2 | no | — |
| 101 | #1373 | — | 2 | 2 | no | — |
| 102 | #1357 | — | 8 | 2 | no | — |
| 103 | C8×C16 | — | 2 | 2 | no | — |
| 104 | C8×C16 | — | 2 | 2 | no | — |
| 105 | C8×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 106 | C8×C16 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C8×C16 | #41 | 1 | 2 | yes | — |
| 108 | C22×D8 | — | 4 | 4 | no | — |
| 109 | C22×D8 | — | 8 | 4 | no | — |
| 110 | C22×D8 | — | 8 | 4 | no | — |
| 111 | C22×D8 | — | 8 | 2 | no | — |
| 112 | C2×#127 | — | 4 | 2 | no | — |
| 113 | C2×#127 | — | 8 | 1 | no | — |
| 114 | #518 | — | 8 | 2 | no | — |
| 115 | C2×D16 | — | 4 | 4 | no | — |
| 116 | C2×D16 | — | 4 | 4 | no | — |
| 117 | C2×D16 | — | 4 | 4 | no | — |
| 118 | C2×D16 | — | 4 | 4 | no | — |
| 119 | C2×D16 | — | 4 | 4 | no | — |
| 120 | C2×D16 | — | 4 | 4 | no | — |
| 121 | C2×D16 | — | 8 | 32 | no | — |
| 122 | C2×D16 | — | 8 | 2 | no | — |
| 123 | C2×D16 | — | 8 | 2 | no | — |
| 124 | C2×D16 | — | 8 | 2 | no | — |
| 125 | C2×D16 | — | 8 | 2 | no | — |
| 126 | C2×D16 | — | 8 | 2 | no | — |
| 127 | C2×D16 | — | 8 | 2 | no | — |
| 128 | C2×D16 | — | 8 | 2 | no | — |
| 129 | C2×D16 | — | 8 | 2 | no | — |
| 130 | C2×D16 | — | 8 | 2 | no | — |
| 131 | C2×D16 | — | 8 | 2 | no | — |
| 132 | C2×D16 | — | 16 | 2 | no | — |
| 133 | C2×D16 | — | 16 | 2 | no | — |
| 134 | C2×D16 | — | 16 | 2 | no | — |
| 135 | C2×D16 | — | 16 | 2 | no | — |
| 136 | C2×D16 | — | 16 | 32 | no | — |
| 137 | C2×M32 | — | 4 | 2 | no | — |
| 138 | C22×C16 | — | 2 | 4 | no | — |
| 139 | C22×C16 | C2×D8 | 1 | 2 | yes | — |
| 140 | C22×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 141 | #493 | — | 2 | 4 | no | — |
| 142 | #493 | — | 4 | 4 | no | — |
| 143 | #493 | — | 4 | 4 | no | — |
| 144 | #493 | — | 4 | 2 | no | — |
| 145 | #493 | — | 4 | 4 | no | — |
| 146 | #493 | — | 4 | 2 | no | — |
| 147 | #493 | — | 8 | 2 | no | — |
| 148 | #493 | — | 8 | 2 | no | — |
| 149 | #493 | — | 8 | 4 | no | — |
| 150 | #493 | — | 8 | 4 | no | — |
| 151 | #493 | — | 8 | 2 | no | — |
| 152 | #493 | — | 8 | 1 | no | — |
| 153 | #442 | — | 16 | 4 | no | — |
| 154 | C4×D8 | — | 8 | 8 | no | — |
| 155 | C2×#108 | — | 2 | 2 | no | — |
| 156 | #427 | — | 2 | 2 | no | — |
| 157 | #418 | — | 8 | 4 | no | — |
| 158 | C2×#100 | — | 8 | 2 | no | — |
| 159 | #405 | — | 4 | 2 | no | — |
| 160 | C2×C4×C8 | — | 2 | 1 | no | — |
| 161 | C2×C4×C8 | #120 | 1 | 1 | yes | characteristic |
| 162 | M64 | — | 8 | 2 | no | — |
| 163 | M64 | — | 8 | 2 | no | — |
| 164 | C2×C32 | — | 8 | 2 | no | — |
| 165 | #368 | — | 2 | 2 | no | — |
| 166 | #368 | — | 2 | 2 | no | — |
| 167 | #367 | — | 2 | 2 | no | — |
| 168 | #366 | D16 | 1 | 4 | yes | complemented |
| 169 | #364 | — | 4 | 2 | no | — |
| 170 | #364 | — | 4 | 2 | no | — |
| 171 | #361 | — | 16 | 4 | no | — |
| 172 | #357 | — | 8 | 8 | no | — |
| 173 | #346 | — | 8 | 2 | no | — |
| 174 | C4×C16 | — | 2 | 4 | no | — |
| 175 | C4×C16 | — | 2 | 4 | no | — |
| 176 | C4×C16 | — | 8 | 2 | no | — |
| 177 | C4×C16 | C4×D4 | 1 | 2 | yes | — |
| 178 | C4×C16 | #121 | 1 | 2 | yes | — |
| 179 | C4×C16 | #135 | 1 | 2 | yes | — |
| 180 | C4×C16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 181 | #339 | — | 4 | 2 | no | — |
| 182 | C82 | — | 2 | 1 | no | — |
| 183 | C82 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 184 | C82 | #123 | 1 | 1 | yes | characteristic |
| 185 | C22×D4 | — | 8 | 2 | no | — |
| 186 | C22×D4 | — | 16 | 2 | no | — |
| 187 | C22×D4 | — | 16 | 2 | no | — |
| 188 | C22×D4 | — | 16 | 1 | no | — |
| 189 | C2×D8 | — | 4 | 8 | no | — |
| 190 | C2×D8 | — | 8 | 8 | no | — |
| 191 | C2×D8 | — | 8 | 8 | no | — |
| 192 | C2×D8 | — | 8 | 4 | no | — |
| 193 | C2×D8 | — | 8 | 4 | no | — |
| 194 | C2×D8 | — | 8 | 4 | no | — |
| 195 | C2×D8 | — | 8 | 4 | no | — |
| 196 | C2×D8 | — | 8 | 4 | no | — |
| 197 | C2×D8 | — | 8 | 4 | no | — |
| 198 | C2×D8 | — | 16 | 16 | no | — |
| 199 | C2×D8 | — | 16 | 16 | no | — |
| 200 | C2×D8 | — | 16 | 4 | no | — |
| 201 | C2×D8 | — | 16 | 4 | no | — |
| 202 | C2×D8 | — | 16 | 2 | no | — |
| 203 | C2×D8 | — | 16 | 2 | no | — |
| 204 | C2×D8 | — | 16 | 2 | no | — |
| 205 | C2×D8 | — | 16 | 2 | no | — |
| 206 | C2×D8 | — | 16 | 2 | no | — |
| 207 | C2×M16 | — | 4 | 2 | no | — |
| 208 | C22×C8 | — | 2 | 2 | no | — |
| 209 | C22×C8 | #447 | 1 | 2 | yes | — |
| 210 | #127 | — | 4 | 4 | no | — |
| 211 | #127 | — | 8 | 2 | no | — |
| 212 | #127 | — | 8 | 2 | no | — |
| 213 | #127 | — | 16 | 2 | no | — |
| 214 | #127 | — | 16 | 2 | no | — |
| 215 | #127 | — | 16 | 1 | no | — |
| 216 | C4×D4 | — | 16 | 8 | no | — |
| 217 | #117 | — | 4 | 2 | no | — |
| 218 | C2×C22⋊C4 | — | 32 | 2 | no | — |
| 219 | C2×C42 | #453 | 1 | 1 | yes | characteristic |
| 220 | D16 | — | 8 | 4 | no | — |
| 221 | D16 | — | 8 | 4 | no | — |
| 222 | D16 | — | 8 | 4 | no | — |
| 223 | D16 | — | 8 | 4 | no | — |
| 224 | D16 | — | 8 | 4 | no | — |
| 225 | D16 | — | 8 | 4 | no | — |
| 226 | D16 | — | 16 | 4 | no | — |
| 227 | D16 | — | 16 | 4 | no | — |
| 228 | D16 | — | 16 | 4 | no | — |
| 229 | D16 | — | 16 | 64 | no | — |
| 230 | D16 | — | 16 | 4 | no | — |
| 231 | D16 | — | 16 | 2 | no | — |
| 232 | D16 | — | 16 | 2 | no | — |
| 233 | M32 | — | 8 | 2 | no | — |
| 234 | M32 | — | 8 | 2 | no | — |
| 235 | C2×C16 | — | 2 | 8 | no | — |
| 236 | C2×C16 | — | 2 | 16 | no | — |
| 237 | C2×C16 | — | 2 | 2 | no | — |
| 238 | C2×C16 | — | 2 | 2 | no | — |
| 239 | C2×C16 | — | 8 | 2 | no | — |
| 240 | C2×C16 | C4×D8 | 1 | 2 | yes | — |
| 241 | C2×C16 | #442 | 1 | 2 | yes | — |
| 242 | C2×C16 | #459 | 1 | 2 | yes | — |
| 243 | C2×C16 | #463 | 1 | 2 | yes | — |
| 244 | C2×C16 | C2×D16 | 1 | 2 | yes | — |
| 245 | C2×C16 | #508 | 1 | 2 | yes | — |
| 246 | C2×C16 | #509 | 1 | 2 | yes | — |
| 247 | C2×C16 | #509 | 1 | 2 | yes | — |
| 248 | #108 | — | 4 | 2 | no | — |
| 249 | #108 | — | 4 | 2 | no | — |
| 250 | #107 | — | 2 | 4 | no | — |
| 251 | #106 | — | 4 | 2 | no | — |
| 252 | #102 | — | 16 | 8 | no | — |
| 253 | #100 | — | 32 | 2 | no | — |
| 254 | #97 | — | 8 | 2 | no | — |
| 255 | C4×C8 | — | 2 | 2 | no | — |
| 256 | C4×C8 | — | 2 | 1 | no | — |
| 257 | C4×C8 | — | 2 | 1 | no | — |
| 258 | C4×C8 | — | 8 | 2 | no | — |
| 259 | C4×C8 | #386 | 1 | 1 | yes | characteristic |
| 260 | C4×C8 | #449 | 1 | 2 | yes | — |
| 261 | C4×C8 | #453 | 1 | 1 | yes | characteristic |
| 262 | C32 | — | 16 | 2 | no | — |
| 263 | C24 | — | 16 | 2 | no | — |
| 264 | C24 | — | 32 | 1 | no | — |
| 265 | C2×D4 | — | 8 | 4 | no | — |
| 266 | C2×D4 | — | 16 | 4 | no | — |
| 267 | C2×D4 | — | 16 | 4 | no | — |
| 268 | C2×D4 | — | 16 | 2 | no | — |
| 269 | C2×D4 | — | 16 | 4 | no | — |
| 270 | C2×D4 | — | 16 | 4 | no | — |
| 271 | C2×D4 | — | 16 | 2 | no | — |
| 272 | C2×D4 | — | 32 | 8 | no | — |
| 273 | C2×D4 | — | 32 | 8 | no | — |
| 274 | C2×D4 | — | 32 | 2 | no | — |
| 275 | C2×D4 | — | 32 | 2 | no | — |
| 276 | C2×D4 | — | 32 | 1 | no | — |
| 277 | C2×D4 | — | 32 | 2 | no | — |
| 278 | C2×D4 | — | 32 | 2 | no | — |
| 279 | C22×C4 | — | 2 | 1 | no | — |
| 280 | C22×C4 | — | 32 | 4 | no | — |
| 281 | C22×C4 | #1619 | 1 | 1 | yes | characteristic |
| 282 | D8 | — | 8 | 8 | no | — |
| 283 | D8 | — | 8 | 8 | no | — |
| 284 | D8 | — | 16 | 16 | no | — |
| 285 | D8 | — | 16 | 16 | no | — |
| 286 | D8 | — | 16 | 4 | no | — |
| 287 | D8 | — | 16 | 4 | no | — |
| 288 | D8 | — | 16 | 4 | no | — |
| 289 | D8 | — | 16 | 4 | no | — |
| 290 | D8 | — | 32 | 8 | no | — |
| 291 | D8 | — | 32 | 8 | no | — |
| 292 | D8 | — | 32 | 2 | no | — |
| 293 | D8 | — | 32 | 2 | no | — |
| 294 | M16 | — | 8 | 2 | no | — |
| 295 | M16 | — | 8 | 2 | no | — |
| 296 | C2×C8 | — | 2 | 2 | no | — |
| 297 | C2×C8 | — | 2 | 2 | no | — |
| 298 | C2×C8 | — | 2 | 8 | no | — |
| 299 | C2×C8 | — | 8 | 2 | no | — |
| 300 | C2×C8 | #1621 | 1 | 2 | yes | — |
| 301 | C2×C8 | #1879 | 1 | 2 | yes | — |
| 302 | C2×C8 | #2184 | 1 | 2 | yes | — |
| 303 | C2×C8 | #2186 | 1 | 2 | yes | — |
| 304 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 305 | C2×C8 | #2192 | 1 | 2 | yes | — |
| 306 | C4⋊C4 | — | 4 | 4 | no | — |
| 307 | C22⋊C4 | — | 8 | 2 | no | — |
| 308 | C22⋊C4 | — | 32 | 4 | no | — |
| 309 | C42 | — | 2 | 1 | no | — |
| 310 | C42 | — | 8 | 2 | no | — |
| 311 | C42 | #1620 | 1 | 1 | yes | characteristic |
| 312 | C42 | #1887 | 1 | 1 | yes | characteristic |
| 313 | C16 | — | 2 | 16 | no | — |
| 314 | C16 | — | 2 | 2 | no | — |
| 315 | C16 | — | 2 | 2 | no | — |
| 316 | C16 | — | 16 | 2 | no | — |
| 317 | C16 | C4×D16 | 1 | 2 | yes | — |
| 318 | C16 | #2177 | 1 | 2 | yes | — |
| 319 | C16 | #2206 | 1 | 2 | yes | — |
| 320 | C16 | #2210 | 1 | 2 | yes | — |
| 321 | C23 | — | 16 | 4 | no | — |
| 322 | C23 | — | 32 | 2 | no | — |
| 323 | C23 | — | 32 | 2 | no | — |
| 324 | C23 | — | 32 | 2 | no | — |
| 325 | C23 | — | 64 | 4 | no | — |
| 326 | C23 | — | 64 | 4 | no | — |
| 327 | C23 | — | 64 | 1 | no | — |
| 328 | C23 | — | 64 | 1 | no | — |
| 329 | C23 | #12310 | 1 | 1 | yes | characteristic |
| 330 | D4 | — | 16 | 8 | no | — |
| 331 | D4 | — | 32 | 8 | no | — |
| 332 | D4 | — | 32 | 8 | no | — |
| 333 | D4 | — | 32 | 4 | no | — |
| 334 | D4 | — | 32 | 4 | no | — |
| 335 | D4 | — | 64 | 4 | no | — |
| 336 | D4 | — | 64 | 4 | no | — |
| 337 | D4 | — | 64 | 2 | no | — |
| 338 | C2×C4 | — | 2 | 4 | no | — |
| 339 | C2×C4 | — | 2 | 1 | no | — |
| 340 | C2×C4 | — | 2 | 1 | no | — |
| 341 | C2×C4 | — | 8 | 4 | no | — |
| 342 | C2×C4 | — | 128 | 4 | no | — |
| 343 | C2×C4 | #9061 | 1 | 1 | yes | characteristic |
| 344 | C2×C4 | #12310 | 1 | 1 | yes | characteristic |
| 345 | C2×C4 | #12316 | 1 | 2 | yes | — |
| 346 | C2×C4 | #12317 | 1 | 2 | yes | — |
| 347 | C8 | — | 2 | 4 | no | — |
| 348 | C8 | — | 2 | 4 | no | — |
| 349 | C8 | — | 16 | 2 | no | — |
| 350 | C8 | #12328 | 1 | 2 | yes | — |
| 351 | C8 | #12329 | 1 | 2 | yes | — |
| 352 | C8 | #13012 | 1 | 2 | yes | — |
| 353 | C8 | #13017 | 1 | 2 | yes | — |
| 354 | C22 | — | 2 | 2 | no | — |
| 355 | C22 | — | 32 | 4 | no | — |
| 356 | C22 | — | 64 | 4 | no | — |
| 357 | C22 | — | 64 | 4 | no | — |
| 358 | C22 | — | 64 | 4 | no | — |
| 359 | C22 | — | 64 | 2 | no | — |
| 360 | C22 | — | 128 | 2 | no | — |
| 361 | C22 | — | 128 | 2 | no | — |
| 362 | C22 | — | 128 | 2 | no | — |
| 363 | C22 | #123275 | 1 | 1 | yes | characteristic |
| 364 | C22 | #123276 | 1 | 1 | yes | characteristic |
| 365 | C22 | #137551 | 1 | 1 | yes | characteristic |
| 366 | C4 | — | 2 | 2 | no | — |
| 367 | C4 | — | 2 | 2 | no | — |
| 368 | C4 | — | 16 | 4 | no | — |
| 369 | C4 | #123277 | 1 | 2 | yes | — |
| 370 | C4 | #137536 | 1 | 2 | yes | — |
| 371 | C2 | — | 2 | 1 | no | — |
| 372 | C2 | — | 2 | 1 | no | — |
| 373 | C2 | — | 64 | 4 | no | — |
| 374 | C2 | — | 128 | 2 | no | — |
| 375 | C2 | #72214187 | 1 | 2 | yes | — |
| 376 | C2 | #72225198 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #123275 |
| commutator | C8×C16 | C22×C4 |
| Frattini, cosocle | C2×C8×C16 | C23 |
| prime radical | C2×#123403 | C2 |
| LCS | G ▷ C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×C8×C16 ◁ G | |
| LECS | G ▷ C2×C8×C16 ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#93866 | C2 | semidirect |
| 2. #72216534 | C2 | semidirect |
| 3. #72216416 | C2 | semidirect |
| 4. #72216270 | C2 | semidirect |
| 17. #123403 | C4 | semidirect |
| 41. #12515 | C2×C4 | semidirect |
| 52. C162 | C2×C4 | semidirect |
| 168. #366 | D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#93866 | 2 |
| #72216534 | 2 |
| #72216416 | 2 |
| #72216270 | 2 |
| C2×#123403 | 2 |