Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1661 conjugacy classes of subgroups.
The subgroup lattice has 421 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | Q8×AGL(1,ℤ/8) | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×Q8×D8 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #29886 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #28699 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #28217 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #25489 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #24720 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #23716 | C2 | 1 | 3 | yes | maximal |
| 10 | #22746 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | Q8×#100 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | Q8×#41 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×D4×Q8 | C22 | 1 | 2 | yes | — |
| 14 | #3386 | — | 2 | 6 | no | — |
| 15 | #3384 | — | 2 | 6 | no | — |
| 16 | Q8×SD16 | — | 2 | 2 | no | — |
| 17 | Q8×D8 | — | 2 | 1 | no | — |
| 18 | Q8×D8 | — | 2 | 1 | no | — |
| 19 | Q8×D8 | — | 2 | 3 | no | — |
| 20 | Q8×D8 | — | 2 | 3 | no | — |
| 21 | Q8×D8 | — | 2 | 2 | no | — |
| 22 | #3165 | C22 | 1 | 6 | yes | — |
| 23 | C2×#500 | C22 | 1 | 3 | yes | — |
| 24 | #3079 | C22 | 1 | 6 | yes | — |
| 25 | #3077 | C22 | 1 | 6 | yes | — |
| 26 | C2×#474 | C22 | 1 | 6 | yes | — |
| 27 | #2986 | — | 2 | 3 | no | — |
| 28 | #2985 | — | 2 | 3 | no | — |
| 29 | #2984 | — | 2 | 1 | no | — |
| 30 | #2982 | — | 2 | 1 | no | — |
| 31 | Q8×M16 | C22 | 1 | 1 | yes | characteristic |
| 32 | Q8×M16 | C22 | 1 | 2 | yes | — |
| 33 | #2962 | C22 | 1 | 3 | yes | — |
| 34 | #2960 | C22 | 1 | 3 | yes | — |
| 35 | C2×C8×Q8 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×AGL(1,ℤ/8) | C22 | 1 | 6 | yes | — |
| 37 | C2×C4×D8 | C22 | 1 | 3 | yes | — |
| 38 | #2925 | C22 | 1 | 3 | yes | — |
| 39 | #2922 | C22 | 1 | 3 | yes | — |
| 40 | #2089 | C22 | 1 | 3 | yes | — |
| 41 | #2089 | C22 | 1 | 6 | yes | — |
| 42 | #2089 | C22 | 1 | 6 | yes | — |
| 43 | #2078 | C22 | 1 | 6 | yes | — |
| 44 | #2078 | C22 | 1 | 3 | yes | — |
| 45 | #2063 | C22 | 1 | 6 | yes | — |
| 46 | #2051 | C22 | 1 | 6 | yes | — |
| 47 | #2045 | C22 | 1 | 3 | yes | — |
| 48 | #2018 | C22 | 1 | 1 | yes | characteristic |
| 49 | #1997 | C22 | 1 | 6 | yes | — |
| 50 | #1997 | C22 | 1 | 6 | yes | — |
| 51 | #1952 | C22 | 1 | 12 | yes | — |
| 52 | #1950 | C22 | 1 | 6 | yes | — |
| 53 | #1931 | C22 | 1 | 12 | yes | — |
| 54 | #1837 | C22 | 1 | 3 | yes | — |
| 55 | #1800 | C22 | 1 | 6 | yes | — |
| 56 | C4×#108 | C22 | 1 | 3 | yes | — |
| 57 | C4×#100 | C22 | 1 | 6 | yes | — |
| 58 | C23×Q8 | — | 2 | 2 | no | — |
| 59 | C2×AGL(1,ℤ/8) | C23 | 1 | 2 | yes | — |
| 60 | C22×D8 | C23 | 1 | 1 | yes | characteristic |
| 61 | Q82 | D4 | 1 | 1 | yes | characteristic |
| 62 | #557 | D4 | 1 | 3 | yes | — |
| 63 | #554 | — | 2 | 3 | no | — |
| 64 | #554 | D4 | 1 | 3 | yes | — |
| 65 | D4×Q8 | — | 2 | 1 | no | — |
| 66 | D4×Q8 | — | 2 | 2 | no | — |
| 67 | D4×Q8 | — | 2 | 6 | no | — |
| 68 | D4×Q8 | — | 2 | 2 | no | — |
| 69 | D4×Q8 | — | 2 | 6 | no | — |
| 70 | D4×Q8 | D4 | 1 | 1 | yes | characteristic |
| 71 | #533 | — | 2 | 3 | no | — |
| 72 | #533 | C23 | 1 | 3 | yes | — |
| 73 | C2×C4⋊Q8 | C23 | 1 | 6 | yes | — |
| 74 | C2×C22⋊Q8 | — | 2 | 6 | no | — |
| 75 | C4×#41 | C23 | 1 | 3 | yes | — |
| 76 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 77 | C2×C4×Q8 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C4×D4 | C23 | 1 | 6 | yes | — |
| 79 | #501 | — | 2 | 12 | no | — |
| 80 | #500 | — | 2 | 6 | no | — |
| 81 | #500 | — | 2 | 3 | no | — |
| 82 | #500 | — | 2 | 3 | no | — |
| 83 | #500 | — | 2 | 3 | no | — |
| 84 | #500 | — | 2 | 3 | no | — |
| 85 | #498 | — | 2 | 6 | no | — |
| 86 | #478 | — | 2 | 12 | no | — |
| 87 | #477 | — | 2 | 6 | no | — |
| 88 | #476 | — | 2 | 6 | no | — |
| 89 | #476 | — | 2 | 6 | no | — |
| 90 | #475 | — | 2 | 6 | no | — |
| 91 | #474 | — | 2 | 6 | no | — |
| 92 | #474 | — | 2 | 6 | no | — |
| 93 | #474 | — | 2 | 6 | no | — |
| 94 | #474 | — | 2 | 6 | no | — |
| 95 | #474 | — | 2 | 12 | no | — |
| 96 | #446 | — | 2 | 6 | no | — |
| 97 | #446 | — | 2 | 3 | no | — |
| 98 | #446 | — | 2 | 3 | no | — |
| 99 | #446 | — | 2 | 6 | no | — |
| 100 | #446 | — | 2 | 3 | no | — |
| 101 | #446 | — | 2 | 3 | no | — |
| 102 | C8×Q8 | — | 2 | 2 | no | — |
| 103 | C8×Q8 | — | 2 | 1 | no | — |
| 104 | C8×Q8 | — | 2 | 3 | no | — |
| 105 | C8×Q8 | — | 2 | 3 | no | — |
| 106 | C8×Q8 | — | 2 | 3 | no | — |
| 107 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 108 | C8×Q8 | D4 | 1 | 1 | yes | characteristic |
| 109 | C8×Q8 | D4 | 1 | 3 | yes | — |
| 110 | C8×Q8 | D4 | 1 | 3 | yes | — |
| 111 | #442 | — | 2 | 6 | no | — |
| 112 | #440 | — | 2 | 6 | no | — |
| 113 | C4×SD16 | — | 2 | 6 | no | — |
| 114 | C4×D8 | — | 2 | 6 | no | — |
| 115 | C4×D8 | — | 2 | 3 | no | — |
| 116 | C4×D8 | — | 2 | 3 | no | — |
| 117 | C4×D8 | — | 2 | 3 | no | — |
| 118 | C4×D8 | — | 2 | 3 | no | — |
| 119 | #433 | — | 2 | 6 | no | — |
| 120 | #433 | — | 2 | 3 | no | — |
| 121 | #433 | — | 2 | 3 | no | — |
| 122 | #432 | — | 2 | 3 | no | — |
| 123 | #431 | — | 2 | 3 | no | — |
| 124 | #431 | — | 2 | 3 | no | — |
| 125 | #431 | — | 2 | 3 | no | — |
| 126 | C2×#108 | C23 | 1 | 6 | yes | — |
| 127 | #428 | C23 | 1 | 12 | yes | — |
| 128 | #428 | C23 | 1 | 6 | yes | — |
| 129 | C2×#107 | C23 | 1 | 3 | yes | — |
| 130 | C2×#107 | C23 | 1 | 6 | yes | — |
| 131 | #424 | C23 | 1 | 3 | yes | — |
| 132 | #424 | C23 | 1 | 3 | yes | — |
| 133 | #423 | C23 | 1 | 6 | yes | — |
| 134 | #423 | C23 | 1 | 3 | yes | — |
| 135 | C2×C4⋊C8 | C23 | 1 | 3 | yes | — |
| 136 | #418 | C23 | 1 | 6 | yes | — |
| 137 | #417 | C23 | 1 | 6 | yes | — |
| 138 | C2×#102 | C23 | 1 | 6 | yes | — |
| 139 | C2×#100 | C23 | 1 | 6 | yes | — |
| 140 | C2×#100 | C23 | 1 | 2 | yes | — |
| 141 | #408 | C23 | 1 | 3 | yes | — |
| 142 | #408 | C23 | 1 | 1 | yes | characteristic |
| 143 | #405 | C23 | 1 | 6 | yes | — |
| 144 | C4×M16 | C23 | 1 | 6 | yes | — |
| 145 | C4×M16 | C23 | 1 | 3 | yes | — |
| 146 | C2×C4×C8 | C23 | 1 | 3 | yes | — |
| 147 | #343 | C23 | 1 | 6 | yes | — |
| 148 | #343 | C23 | 1 | 12 | yes | — |
| 149 | #343 | C23 | 1 | 6 | yes | — |
| 150 | #341 | C23 | 1 | 3 | yes | — |
| 151 | #341 | C23 | 1 | 6 | yes | — |
| 152 | #341 | C23 | 1 | 1 | yes | characteristic |
| 153 | C2×#41 | C24 | 1 | 1 | yes | characteristic |
| 154 | C22×Q8 | — | 2 | 1 | no | — |
| 155 | C22×Q8 | — | 2 | 6 | no | — |
| 156 | C22×Q8 | — | 4 | 6 | no | — |
| 157 | C22×Q8 | — | 4 | 2 | no | — |
| 158 | C22×Q8 | — | 8 | 8 | no | — |
| 159 | C22×Q8 | #41 | 1 | 1 | yes | characteristic |
| 160 | C22×D4 | C24 | 1 | 2 | yes | — |
| 161 | C23×C4 | — | 2 | 6 | no | — |
| 162 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 163 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 164 | C2×SD16 | — | 2 | 2 | no | — |
| 165 | C2×D8 | — | 2 | 2 | no | — |
| 166 | C2×D8 | — | 2 | 4 | no | — |
| 167 | C2×D8 | — | 2 | 1 | no | — |
| 168 | C2×D8 | — | 2 | 1 | no | — |
| 169 | C2×M16 | C24 | 1 | 6 | yes | — |
| 170 | C2×M16 | C24 | 1 | 1 | yes | characteristic |
| 171 | C2×M16 | C24 | 1 | 3 | yes | — |
| 172 | C2×M16 | C24 | 1 | 2 | yes | — |
| 173 | C22×C8 | C24 | 1 | 1 | yes | characteristic |
| 174 | C22×C8 | C24 | 1 | 3 | yes | — |
| 175 | C4⋊Q8 | — | 2 | 3 | no | — |
| 176 | C4⋊Q8 | — | 2 | 3 | no | — |
| 177 | C4⋊Q8 | — | 2 | 6 | no | — |
| 178 | C4⋊Q8 | — | 2 | 6 | no | — |
| 179 | C4⋊Q8 | — | 2 | 6 | no | — |
| 180 | C4⋊Q8 | — | 2 | 6 | no | — |
| 181 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 182 | C4⋊Q8 | C2×D4 | 1 | 3 | yes | — |
| 183 | #125 | — | 2 | 6 | no | — |
| 184 | #125 | C2×D4 | 1 | 6 | yes | — |
| 185 | C22⋊Q8 | — | 2 | 3 | no | — |
| 186 | C22⋊Q8 | — | 2 | 3 | no | — |
| 187 | C22⋊Q8 | — | 2 | 3 | no | — |
| 188 | C22⋊Q8 | — | 2 | 3 | no | — |
| 189 | C22⋊Q8 | — | 2 | 6 | no | — |
| 190 | C22⋊Q8 | — | 4 | 6 | no | — |
| 191 | C22⋊Q8 | — | 4 | 12 | no | — |
| 192 | C22⋊Q8 | — | 4 | 6 | no | — |
| 193 | C4×Q8 | — | 2 | 1 | no | — |
| 194 | C4×Q8 | — | 2 | 3 | no | — |
| 195 | C4×Q8 | — | 2 | 3 | no | — |
| 196 | C4×Q8 | — | 2 | 3 | no | — |
| 197 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 198 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 199 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 201 | C4×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C4×Q8 | C2×D4 | 1 | 3 | yes | — |
| 203 | C4×D4 | — | 2 | 3 | no | — |
| 204 | C4×D4 | — | 2 | 3 | no | — |
| 205 | C4×D4 | — | 2 | 6 | no | — |
| 206 | C4×D4 | — | 2 | 6 | no | — |
| 207 | C4×D4 | — | 2 | 6 | no | — |
| 208 | C4×D4 | — | 2 | 6 | no | — |
| 209 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 210 | C4×D4 | C2×D4 | 1 | 3 | yes | — |
| 211 | #117 | — | 2 | 3 | no | — |
| 212 | #117 | C24 | 1 | 3 | yes | — |
| 213 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 214 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 215 | C2×C4⋊C4 | #41 | 1 | 3 | yes | — |
| 216 | C2×C4⋊C4 | C24 | 1 | 6 | yes | — |
| 217 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 218 | C2×C42 | — | 2 | 3 | no | — |
| 219 | C2×C42 | C24 | 1 | 3 | yes | — |
| 220 | #108 | — | 2 | 12 | no | — |
| 221 | #107 | — | 2 | 3 | no | — |
| 222 | #107 | — | 2 | 3 | no | — |
| 223 | #107 | — | 2 | 6 | no | — |
| 224 | #107 | — | 2 | 6 | no | — |
| 225 | #107 | — | 2 | 6 | no | — |
| 226 | #107 | — | 2 | 12 | no | — |
| 227 | #106 | — | 2 | 6 | no | — |
| 228 | #106 | — | 2 | 12 | no | — |
| 229 | C4⋊C8 | — | 2 | 3 | no | — |
| 230 | C4⋊C8 | — | 2 | 3 | no | — |
| 231 | C4⋊C8 | — | 2 | 3 | no | — |
| 232 | C4⋊C8 | — | 2 | 3 | no | — |
| 233 | C4⋊C8 | — | 2 | 3 | no | — |
| 234 | C4⋊C8 | — | 2 | 3 | no | — |
| 235 | C4⋊C8 | — | 2 | 6 | no | — |
| 236 | C4⋊C8 | — | 2 | 6 | no | — |
| 237 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 238 | C4⋊C8 | C2×D4 | 1 | 3 | yes | — |
| 239 | C4⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 240 | #103 | — | 2 | 6 | no | — |
| 241 | #102 | — | 2 | 6 | no | — |
| 242 | #102 | — | 2 | 6 | no | — |
| 243 | #102 | — | 2 | 6 | no | — |
| 244 | #102 | — | 2 | 6 | no | — |
| 245 | #102 | — | 2 | 6 | no | — |
| 246 | #100 | — | 2 | 12 | no | — |
| 247 | #100 | — | 2 | 4 | no | — |
| 248 | C22⋊C8 | — | 2 | 3 | no | — |
| 249 | C22⋊C8 | — | 2 | 1 | no | — |
| 250 | C22⋊C8 | — | 2 | 1 | no | — |
| 251 | C22⋊C8 | — | 2 | 3 | no | — |
| 252 | #97 | — | 2 | 6 | no | — |
| 253 | #97 | — | 2 | 3 | no | — |
| 254 | #97 | — | 2 | 6 | no | — |
| 255 | C4×C8 | — | 2 | 6 | no | — |
| 256 | C4×C8 | — | 2 | 3 | no | — |
| 257 | C4×C8 | — | 2 | 6 | no | — |
| 258 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 259 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 260 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 261 | C4×C8 | C2×D4 | 1 | 3 | yes | — |
| 262 | C24 | — | 2 | 2 | no | — |
| 263 | #41 | — | 2 | 2 | no | — |
| 264 | #41 | — | 2 | 2 | no | — |
| 265 | C2×Q8 | — | 2 | 4 | no | — |
| 266 | C2×Q8 | — | 2 | 3 | no | — |
| 267 | C2×Q8 | — | 2 | 3 | no | — |
| 268 | C2×Q8 | — | 4 | 4 | no | — |
| 269 | C2×Q8 | — | 4 | 6 | no | — |
| 270 | C2×Q8 | — | 4 | 6 | no | — |
| 271 | C2×Q8 | — | 8 | 12 | no | — |
| 272 | C2×Q8 | — | 8 | 24 | no | — |
| 273 | C2×Q8 | — | 8 | 8 | no | — |
| 274 | C2×Q8 | #121 | 1 | 3 | yes | — |
| 275 | C2×Q8 | #121 | 1 | 1 | yes | characteristic |
| 276 | C2×Q8 | C22×D4 | 1 | 1 | yes | characteristic |
| 277 | C2×D4 | — | 2 | 1 | no | — |
| 278 | C2×D4 | — | 2 | 2 | no | — |
| 279 | C2×D4 | — | 2 | 2 | no | — |
| 280 | C2×D4 | — | 2 | 2 | no | — |
| 281 | C2×D4 | — | 2 | 2 | no | — |
| 282 | C2×D4 | — | 2 | 2 | no | — |
| 283 | C2×D4 | C22×D4 | 1 | 1 | yes | characteristic |
| 284 | C2×D4 | 2−1+4 | 1 | 4 | yes | — |
| 285 | C22×C4 | — | 2 | 3 | no | — |
| 286 | C22×C4 | — | 2 | 1 | no | — |
| 287 | C22×C4 | — | 2 | 3 | no | — |
| 288 | C22×C4 | — | 2 | 6 | no | — |
| 289 | C22×C4 | — | 4 | 6 | no | — |
| 290 | C22×C4 | — | 4 | 6 | no | — |
| 291 | C22×C4 | — | 8 | 12 | no | — |
| 292 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 293 | C22×C4 | C2×#41 | 1 | 3 | yes | — |
| 294 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 295 | SD16 | — | 2 | 8 | no | — |
| 296 | D8 | — | 2 | 4 | no | — |
| 297 | D8 | — | 2 | 4 | no | — |
| 298 | D8 | — | 2 | 8 | no | — |
| 299 | M16 | — | 2 | 2 | no | — |
| 300 | M16 | — | 2 | 6 | no | — |
| 301 | M16 | — | 2 | 6 | no | — |
| 302 | M16 | — | 2 | 2 | no | — |
| 303 | M16 | — | 2 | 6 | no | — |
| 304 | M16 | 2−1+4 | 1 | 4 | yes | — |
| 305 | C2×C8 | — | 2 | 2 | no | — |
| 306 | C2×C8 | — | 2 | 6 | no | — |
| 307 | C2×C8 | — | 2 | 2 | no | — |
| 308 | C2×C8 | — | 2 | 3 | no | — |
| 309 | C2×C8 | — | 2 | 1 | no | — |
| 310 | C2×C8 | — | 2 | 6 | no | — |
| 311 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 312 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×C8 | C22×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 315 | C4⋊C4 | — | 2 | 6 | no | — |
| 316 | C4⋊C4 | — | 2 | 3 | no | — |
| 317 | C4⋊C4 | — | 2 | 3 | no | — |
| 318 | C4⋊C4 | — | 2 | 3 | no | — |
| 319 | C4⋊C4 | — | 2 | 3 | no | — |
| 320 | C4⋊C4 | — | 2 | 6 | no | — |
| 321 | C4⋊C4 | — | 2 | 6 | no | — |
| 322 | C4⋊C4 | — | 2 | 6 | no | — |
| 323 | C4⋊C4 | — | 4 | 6 | no | — |
| 324 | C4⋊C4 | — | 4 | 6 | no | — |
| 325 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 326 | C4⋊C4 | #121 | 1 | 6 | yes | — |
| 327 | C4⋊C4 | #121 | 1 | 3 | yes | — |
| 328 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 329 | C4⋊C4 | C22×D4 | 1 | 3 | yes | — |
| 330 | C22⋊C4 | — | 2 | 3 | no | — |
| 331 | C22⋊C4 | — | 2 | 3 | no | — |
| 332 | C22⋊C4 | — | 2 | 3 | no | — |
| 333 | C22⋊C4 | — | 4 | 6 | no | — |
| 334 | C22⋊C4 | — | 4 | 6 | no | — |
| 335 | C42 | — | 2 | 3 | no | — |
| 336 | C42 | — | 2 | 3 | no | — |
| 337 | C42 | — | 2 | 3 | no | — |
| 338 | C42 | C22×D4 | 1 | 3 | yes | — |
| 339 | C42 | C22×D4 | 1 | 3 | yes | — |
| 340 | C42 | C22×D4 | 1 | 3 | yes | — |
| 341 | C42 | C22×D4 | 1 | 3 | yes | — |
| 342 | C23 | — | 2 | 1 | no | — |
| 343 | C23 | — | 2 | 4 | no | — |
| 344 | C23 | — | 4 | 2 | no | — |
| 345 | C23 | — | 4 | 2 | no | — |
| 346 | C23 | — | 8 | 2 | no | — |
| 347 | C23 | — | 8 | 2 | no | — |
| 348 | C23 | C22×#41 | 1 | 1 | yes | characteristic |
| 349 | Q8 | — | 2 | 6 | no | — |
| 350 | Q8 | — | 2 | 2 | no | — |
| 351 | Q8 | — | 4 | 6 | no | — |
| 352 | Q8 | — | 8 | 3 | no | — |
| 353 | Q8 | — | 8 | 12 | no | — |
| 354 | Q8 | — | 8 | 12 | no | — |
| 355 | Q8 | #472 | 1 | 4 | yes | — |
| 356 | D4 | — | 2 | 4 | no | — |
| 357 | D4 | — | 2 | 2 | no | — |
| 358 | D4 | — | 2 | 4 | no | — |
| 359 | D4 | — | 4 | 2 | no | — |
| 360 | D4 | — | 4 | 2 | no | — |
| 361 | D4 | — | 4 | 2 | no | — |
| 362 | C2×C4 | — | 2 | 6 | no | — |
| 363 | C2×C4 | — | 2 | 1 | no | — |
| 364 | C2×C4 | — | 2 | 3 | no | — |
| 365 | C2×C4 | — | 2 | 3 | no | — |
| 366 | C2×C4 | — | 4 | 3 | no | — |
| 367 | C2×C4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 4 | 1 | no | — |
| 369 | C2×C4 | — | 4 | 6 | no | — |
| 370 | C2×C4 | — | 4 | 6 | no | — |
| 371 | C2×C4 | — | 8 | 3 | no | — |
| 372 | C2×C4 | — | 8 | 12 | no | — |
| 373 | C2×C4 | — | 8 | 12 | no | — |
| 374 | C2×C4 | — | 8 | 6 | no | — |
| 375 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 376 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 377 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 378 | C2×C4 | C2×#121 | 1 | 3 | yes | — |
| 379 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 381 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 382 | C2×C4 | C2×2−1+4 | 1 | 2 | yes | — |
| 383 | C8 | — | 2 | 1 | no | — |
| 384 | C8 | — | 2 | 1 | no | — |
| 385 | C8 | — | 2 | 4 | no | — |
| 386 | C8 | — | 2 | 3 | no | — |
| 387 | C8 | — | 2 | 3 | no | — |
| 388 | C8 | — | 4 | 3 | no | — |
| 389 | C8 | — | 4 | 6 | no | — |
| 390 | C8 | — | 4 | 1 | no | — |
| 391 | C22 | — | 2 | 1 | no | — |
| 392 | C22 | — | 2 | 1 | no | — |
| 393 | C22 | — | 4 | 1 | no | — |
| 394 | C22 | — | 4 | 1 | no | — |
| 395 | C22 | — | 4 | 1 | no | — |
| 396 | C22 | — | 4 | 4 | no | — |
| 397 | C22 | — | 8 | 4 | no | — |
| 398 | C22 | — | 8 | 4 | no | — |
| 399 | C22 | — | 8 | 2 | no | — |
| 400 | C22 | — | 8 | 2 | no | — |
| 401 | C22 | C22×#121 | 1 | 1 | yes | characteristic |
| 402 | C22 | #3523 | 1 | 2 | yes | — |
| 403 | C4 | — | 2 | 3 | no | — |
| 404 | C4 | — | 2 | 3 | no | — |
| 405 | C4 | — | 2 | 3 | no | — |
| 406 | C4 | — | 4 | 3 | no | — |
| 407 | C4 | — | 4 | 3 | no | — |
| 408 | C4 | — | 4 | 1 | no | — |
| 409 | C4 | — | 8 | 6 | no | — |
| 410 | C4 | C2×#472 | 1 | 6 | yes | — |
| 411 | C4 | #3486 | 1 | 1 | yes | characteristic |
| 412 | C4 | #3486 | 1 | 2 | yes | — |
| 413 | C4 | #3499 | 1 | 1 | yes | characteristic |
| 414 | C2 | — | 2 | 2 | no | — |
| 415 | C2 | — | 8 | 1 | no | — |
| 416 | C2 | — | 8 | 4 | no | — |
| 417 | C2 | #35700 | 1 | 1 | yes | characteristic |
| 418 | C2 | C22×#472 | 1 | 1 | yes | characteristic |
| 419 | C2 | #60472 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#121 |
| commutator, Frattini, cosocle | C22×C4 | C25 |
| prime radical | #2018 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22 ◁ C2×C4×Q8 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×Q8×D8 | C2 | semidirect |
| 3. #60253 | C2 | semidirect |
| 4. #29886 | C2 | semidirect |
| 5. #28699 | C2 | semidirect |
| 6. #28217 | C2 | semidirect |
| 7. #25489 | C2 | semidirect |
| 8. #24720 | C2 | semidirect |
| 10. #22746 | C2 | semidirect |
| 11. Q8×#100 | C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×AGL(1,ℤ/8) | 2 |
| C2×Q8×D8 | 2 |
| #60253 | 2 |
| #29886 | 2 |
| #28699 | 2 |
| #28217 | 2 |
| #25489 | 2 |
| #24720 | 2 |
| #23716 | 2 |
| #22746 | 2 |
| Q8×#100 | 2 |