Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
1178 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #7623644 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #152169 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #150879 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #149671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #134775 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#3415 | C4 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#3415 | C22 | 1 | 1 | yes | characteristic |
| 8 | #61089 | — | 2 | 1 | no | — |
| 9 | #33853 | — | 2 | 2 | no | — |
| 10 | D4×D16 | — | 2 | 2 | no | — |
| 11 | #33840 | — | 2 | 4 | no | — |
| 12 | C2×#2246 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #33607 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #33607 | C22 | 1 | 1 | yes | characteristic |
| 15 | #33582 | — | 2 | 1 | no | — |
| 16 | #33522 | — | 2 | 1 | no | — |
| 17 | #33522 | — | 2 | 1 | no | — |
| 18 | C4×#508 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #33434 | C22 | 1 | 1 | yes | characteristic |
| 20 | #13622 | — | 2 | 2 | no | — |
| 21 | #13617 | — | 2 | 2 | no | — |
| 22 | #13556 | C22 | 1 | 2 | yes | complemented |
| 23 | #12839 | C22 | 1 | 2 | yes | complemented |
| 24 | #12807 | — | 2 | 1 | no | — |
| 25 | #7422 | — | 2 | 4 | no | — |
| 26 | #7364 | — | 2 | 1 | no | — |
| 27 | #7337 | — | 2 | 1 | no | — |
| 28 | #7228 | — | 2 | 1 | no | — |
| 29 | C2×#576 | — | 2 | 1 | no | — |
| 30 | C2×#576 | — | 2 | 1 | no | — |
| 31 | #3498 | — | 4 | 1 | no | — |
| 32 | #3415 | — | 4 | 2 | no | — |
| 33 | #3415 | — | 4 | 2 | no | — |
| 34 | #3415 | — | 4 | 2 | no | — |
| 35 | #3415 | — | 4 | 2 | no | — |
| 36 | C2×#509 | — | 2 | 2 | no | — |
| 37 | C2×#509 | — | 2 | 1 | no | — |
| 38 | C2×#509 | — | 2 | 1 | no | — |
| 39 | C2×#509 | — | 2 | 2 | no | — |
| 40 | C2×#508 | — | 2 | 1 | no | — |
| 41 | C2×#508 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | C2×#508 | D4 | 1 | 2 | yes | — |
| 43 | C22×D16 | — | 2 | 1 | no | — |
| 44 | C22×D16 | — | 2 | 1 | no | — |
| 45 | C22×D16 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | C22×D16 | C2×C4 | 1 | 1 | yes | characteristic |
| 47 | C22×D16 | D4 | 1 | 2 | yes | — |
| 48 | C2×#504 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×#504 | C23 | 1 | 1 | yes | characteristic |
| 50 | #3287 | — | 2 | 4 | no | — |
| 51 | D4×D8 | — | 2 | 4 | no | — |
| 52 | #3274 | — | 4 | 4 | no | — |
| 53 | C2×#493 | — | 2 | 1 | no | — |
| 54 | #3058 | — | 2 | 1 | no | — |
| 55 | #3058 | — | 2 | 1 | no | — |
| 56 | #3038 | — | 4 | 1 | no | — |
| 57 | #3008 | — | 4 | 1 | no | — |
| 58 | #3008 | — | 4 | 1 | no | — |
| 59 | C4×#135 | — | 2 | 1 | no | — |
| 60 | #2931 | D4 | 1 | 1 | yes | characteristic |
| 61 | C2×M64 | — | 2 | 2 | no | — |
| 62 | #2246 | — | 2 | 2 | no | — |
| 63 | #2246 | — | 2 | 2 | no | — |
| 64 | #2218 | — | 2 | 2 | no | — |
| 65 | #2218 | D4 | 1 | 4 | yes | — |
| 66 | #2215 | — | 2 | 2 | no | — |
| 67 | #2215 | — | 2 | 2 | no | — |
| 68 | #2207 | — | 2 | 4 | no | — |
| 69 | #2206 | — | 2 | 4 | no | — |
| 70 | #2186 | — | 2 | 4 | no | — |
| 71 | #2186 | — | 2 | 4 | no | — |
| 72 | #2184 | — | 2 | 4 | no | — |
| 73 | #2184 | — | 2 | 4 | no | — |
| 74 | C4×Q32 | — | 2 | 1 | no | — |
| 75 | C4×SD32 | — | 2 | 2 | no | — |
| 76 | C4×D16 | — | 2 | 1 | no | — |
| 77 | #2169 | — | 2 | 2 | no | — |
| 78 | D4×C16 | — | 2 | 2 | no | — |
| 79 | #2158 | — | 2 | 2 | no | — |
| 80 | #2158 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #2150 | D4 | 1 | 1 | yes | characteristic |
| 82 | #2140 | — | 2 | 1 | no | — |
| 83 | #2140 | — | 2 | 1 | no | — |
| 84 | #2138 | — | 2 | 1 | no | — |
| 85 | #2126 | — | 4 | 1 | no | — |
| 86 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 87 | #2113 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C4×C16 | C2×C4 | 1 | 1 | yes | characteristic |
| 89 | #1812 | — | 2 | 2 | no | — |
| 90 | #1418 | — | 4 | 4 | no | — |
| 91 | #1415 | — | 4 | 4 | no | — |
| 92 | #1400 | — | 2 | 2 | no | — |
| 93 | #1400 | — | 2 | 2 | no | — |
| 94 | #1391 | — | 4 | 1 | no | — |
| 95 | #1384 | — | 2 | 2 | no | — |
| 96 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 97 | C2×H(5,𝔽2) | — | 4 | 1 | no | — |
| 98 | #576 | — | 4 | 4 | no | — |
| 99 | #576 | — | 4 | 4 | no | — |
| 100 | #576 | — | 8 | 2 | no | — |
| 101 | #576 | — | 8 | 2 | no | — |
| 102 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 103 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 104 | C2×AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 105 | C2×AGL(1,ℤ/8) | — | 4 | 2 | no | — |
| 106 | C2×#135 | — | 2 | 2 | no | — |
| 107 | C2×#135 | — | 2 | 1 | no | — |
| 108 | C2×#135 | — | 2 | 2 | no | — |
| 109 | C22×D8 | — | 2 | 2 | no | — |
| 110 | C22×D8 | — | 2 | 1 | no | — |
| 111 | C22×D8 | — | 2 | 1 | no | — |
| 112 | C22×D8 | — | 2 | 2 | no | — |
| 113 | C22×D8 | — | 4 | 1 | no | — |
| 114 | C2×#131 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C2×#131 | C2×D4 | 1 | 1 | yes | characteristic |
| 116 | #550 | — | 4 | 4 | no | — |
| 117 | D42 | — | 4 | 4 | no | — |
| 118 | D42 | — | 8 | 4 | no | — |
| 119 | #535 | — | 4 | 1 | no | — |
| 120 | #535 | — | 4 | 1 | no | — |
| 121 | #535 | — | 8 | 1 | no | — |
| 122 | #535 | — | 8 | 1 | no | — |
| 123 | #532 | — | 8 | 1 | no | — |
| 124 | #532 | D8 | 1 | 1 | yes | characteristic |
| 125 | C2×#127 | — | 4 | 1 | no | — |
| 126 | C2×#127 | — | 8 | 1 | no | — |
| 127 | C4×#41 | — | 4 | 1 | no | — |
| 128 | #509 | — | 4 | 8 | no | — |
| 129 | #509 | — | 4 | 8 | no | — |
| 130 | #509 | — | 4 | 4 | no | — |
| 131 | #509 | — | 4 | 4 | no | — |
| 132 | #508 | — | 2 | 2 | no | — |
| 133 | #508 | — | 2 | 4 | no | — |
| 134 | #508 | — | 2 | 2 | no | — |
| 135 | #508 | — | 4 | 2 | no | — |
| 136 | #508 | — | 4 | 2 | no | — |
| 137 | #508 | — | 4 | 2 | no | — |
| 138 | C2×Q32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 139 | C2×SD32 | — | 2 | 2 | no | — |
| 140 | C2×SD32 | — | 2 | 1 | no | — |
| 141 | C2×SD32 | — | 2 | 2 | no | — |
| 142 | C2×D16 | — | 2 | 4 | no | — |
| 143 | C2×D16 | — | 2 | 2 | no | — |
| 144 | C2×D16 | — | 2 | 4 | no | — |
| 145 | C2×D16 | — | 2 | 1 | no | — |
| 146 | C2×D16 | — | 2 | 1 | no | — |
| 147 | C2×D16 | — | 2 | 2 | no | — |
| 148 | C2×D16 | — | 4 | 1 | no | — |
| 149 | C2×D16 | — | 4 | 1 | no | — |
| 150 | C2×D16 | — | 4 | 2 | no | — |
| 151 | C2×D16 | — | 4 | 1 | no | — |
| 152 | C2×D16 | — | 4 | 1 | no | — |
| 153 | C2×D16 | — | 4 | 2 | no | — |
| 154 | C2×D16 | — | 4 | 2 | no | — |
| 155 | C2×D16 | — | 8 | 2 | no | — |
| 156 | C2×D16 | C22⋊C4 | 1 | 2 | yes | — |
| 157 | C2×D16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 158 | C2×D16 | C22⋊C4 | 1 | 2 | yes | — |
| 159 | #504 | — | 4 | 1 | no | — |
| 160 | #504 | — | 4 | 1 | no | — |
| 161 | #504 | — | 4 | 1 | no | — |
| 162 | #504 | — | 4 | 1 | no | — |
| 163 | C2×M32 | — | 2 | 1 | no | — |
| 164 | C2×M32 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C2×M32 | C2×D4 | 1 | 2 | yes | — |
| 166 | C2×M32 | C2×D4 | 1 | 1 | yes | characteristic |
| 167 | C22×C16 | — | 2 | 1 | no | — |
| 168 | C22×C16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 169 | C22×C16 | C22×C4 | 1 | 1 | yes | characteristic |
| 170 | C22×C16 | C2×D4 | 1 | 2 | yes | — |
| 171 | #493 | — | 2 | 4 | no | — |
| 172 | #493 | — | 4 | 2 | no | — |
| 173 | #469 | — | 4 | 2 | no | — |
| 174 | #469 | — | 4 | 2 | no | — |
| 175 | #466 | — | 2 | 4 | no | — |
| 176 | #466 | — | 2 | 4 | no | — |
| 177 | #460 | — | 4 | 4 | no | — |
| 178 | #459 | — | 4 | 4 | no | — |
| 179 | #449 | — | 4 | 4 | no | — |
| 180 | #449 | — | 4 | 4 | no | — |
| 181 | #447 | — | 4 | 4 | no | — |
| 182 | #447 | — | 4 | 4 | no | — |
| 183 | C4×Q16 | — | 2 | 2 | no | — |
| 184 | C4×SD16 | — | 4 | 2 | no | — |
| 185 | C4×D8 | — | 2 | 2 | no | — |
| 186 | #436 | — | 2 | 2 | no | — |
| 187 | C8×D4 | — | 2 | 2 | no | — |
| 188 | #427 | — | 2 | 1 | no | — |
| 189 | #427 | — | 4 | 2 | no | — |
| 190 | #423 | SD16 | 1 | 1 | yes | characteristic |
| 191 | #418 | — | 4 | 1 | no | — |
| 192 | #418 | — | 4 | 1 | no | — |
| 193 | #416 | — | 4 | 1 | no | — |
| 194 | #410 | — | 4 | 2 | no | — |
| 195 | #408 | D8 | 1 | 1 | yes | characteristic |
| 196 | #408 | SD16 | 1 | 1 | yes | characteristic |
| 197 | C2×C4×C8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 198 | M64 | — | 4 | 2 | no | — |
| 199 | M64 | — | 4 | 2 | no | — |
| 200 | C2×C32 | — | 4 | 2 | no | — |
| 201 | #367 | — | 4 | 2 | no | — |
| 202 | #367 | C22⋊C4 | 1 | 2 | yes | — |
| 203 | #366 | — | 2 | 1 | no | — |
| 204 | #366 | — | 4 | 2 | no | — |
| 205 | C4⋊C16 | — | 2 | 2 | no | — |
| 206 | #358 | — | 2 | 2 | no | — |
| 207 | #357 | — | 2 | 2 | no | — |
| 208 | #357 | — | 2 | 4 | no | — |
| 209 | #357 | — | 2 | 4 | no | — |
| 210 | #354 | — | 8 | 1 | no | — |
| 211 | #353 | — | 8 | 1 | no | — |
| 212 | C22⋊C16 | — | 2 | 2 | no | — |
| 213 | C22⋊C16 | — | 2 | 2 | no | — |
| 214 | C4×C16 | — | 2 | 1 | no | — |
| 215 | C4×C16 | — | 2 | 1 | no | — |
| 216 | H(3,ℤ/4) | — | 4 | 2 | no | — |
| 217 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 218 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 219 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 220 | H(5,𝔽2) | — | 16 | 2 | no | — |
| 221 | C2×#41 | — | 4 | 2 | no | — |
| 222 | C2×#41 | — | 4 | 1 | no | — |
| 223 | C2×#41 | — | 4 | 2 | no | — |
| 224 | C2×#41 | — | 8 | 1 | no | — |
| 225 | C2×#41 | — | 8 | 1 | no | — |
| 226 | C2×#41 | #102 | 1 | 1 | yes | characteristic |
| 227 | C2×#41 | C2×D8 | 1 | 1 | yes | characteristic |
| 228 | C22×D4 | — | 4 | 2 | no | — |
| 229 | C22×D4 | — | 4 | 1 | no | — |
| 230 | C22×D4 | — | 4 | 1 | no | — |
| 231 | C22×D4 | — | 4 | 2 | no | — |
| 232 | C22×D4 | — | 8 | 2 | no | — |
| 233 | C22×D4 | — | 8 | 2 | no | — |
| 234 | C22×D4 | — | 8 | 4 | no | — |
| 235 | C22×D4 | — | 8 | 1 | no | — |
| 236 | C22×D4 | — | 8 | 1 | no | — |
| 237 | C22×D4 | — | 8 | 2 | no | — |
| 238 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 239 | AGL(1,ℤ/8) | — | 8 | 8 | no | — |
| 240 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 241 | AGL(1,ℤ/8) | — | 8 | 4 | no | — |
| 242 | #135 | — | 2 | 4 | no | — |
| 243 | #135 | — | 4 | 2 | no | — |
| 244 | #135 | — | 4 | 4 | no | — |
| 245 | #135 | — | 4 | 4 | no | — |
| 246 | #135 | — | 8 | 2 | no | — |
| 247 | #135 | — | 8 | 2 | no | — |
| 248 | C2×Q16 | — | 2 | 1 | no | — |
| 249 | C2×SD16 | — | 4 | 2 | no | — |
| 250 | C2×SD16 | — | 4 | 1 | no | — |
| 251 | C2×SD16 | — | 4 | 2 | no | — |
| 252 | C2×D8 | — | 2 | 1 | no | — |
| 253 | C2×D8 | — | 2 | 2 | no | — |
| 254 | C2×D8 | — | 2 | 2 | no | — |
| 255 | C2×D8 | — | 4 | 4 | no | — |
| 256 | C2×D8 | — | 4 | 2 | no | — |
| 257 | C2×D8 | — | 4 | 2 | no | — |
| 258 | C2×D8 | — | 4 | 2 | no | — |
| 259 | C2×D8 | — | 4 | 2 | no | — |
| 260 | C2×D8 | — | 4 | 2 | no | — |
| 261 | C2×D8 | — | 4 | 4 | no | — |
| 262 | C2×D8 | — | 4 | 4 | no | — |
| 263 | C2×D8 | — | 4 | 1 | no | — |
| 264 | C2×D8 | — | 4 | 1 | no | — |
| 265 | C2×D8 | — | 4 | 2 | no | — |
| 266 | C2×D8 | — | 8 | 2 | no | — |
| 267 | C2×D8 | — | 8 | 2 | no | — |
| 268 | C2×D8 | — | 16 | 2 | no | — |
| 269 | #131 | — | 4 | 1 | no | — |
| 270 | #131 | — | 4 | 1 | no | — |
| 271 | #131 | — | 4 | 1 | no | — |
| 272 | #131 | — | 4 | 1 | no | — |
| 273 | C2×M16 | — | 2 | 1 | no | — |
| 274 | C2×M16 | #102 | 1 | 1 | yes | characteristic |
| 275 | C2×M16 | C2×SD16 | 1 | 1 | yes | characteristic |
| 276 | C2×M16 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 277 | C22×C8 | — | 2 | 1 | no | — |
| 278 | C22×C8 | #102 | 1 | 1 | yes | characteristic |
| 279 | C22×C8 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 280 | C22×C8 | #120 | 1 | 2 | yes | — |
| 281 | C4⋊Q8 | SD32 | 1 | 1 | yes | characteristic |
| 282 | #127 | — | 4 | 4 | no | — |
| 283 | #127 | — | 8 | 4 | no | — |
| 284 | #127 | — | 8 | 1 | no | — |
| 285 | #127 | — | 8 | 1 | no | — |
| 286 | #127 | — | 8 | 1 | no | — |
| 287 | #127 | — | 8 | 1 | no | — |
| 288 | #127 | D16 | 1 | 1 | yes | characteristic |
| 289 | #124 | — | 8 | 1 | no | — |
| 290 | #124 | — | 8 | 1 | no | — |
| 291 | #124 | D16 | 1 | 1 | yes | characteristic |
| 292 | #124 | SD32 | 1 | 1 | yes | characteristic |
| 293 | #121 | — | 2 | 2 | no | — |
| 294 | #121 | — | 4 | 4 | no | — |
| 295 | #121 | — | 4 | 4 | no | — |
| 296 | #121 | — | 8 | 4 | no | — |
| 297 | #121 | — | 8 | 4 | no | — |
| 298 | #121 | — | 8 | 4 | no | — |
| 299 | #120 | — | 8 | 4 | no | — |
| 300 | #120 | — | 8 | 4 | no | — |
| 301 | #120 | — | 8 | 2 | no | — |
| 302 | #120 | — | 8 | 2 | no | — |
| 303 | C4×Q8 | — | 4 | 2 | no | — |
| 304 | C4×D4 | — | 2 | 2 | no | — |
| 305 | C4×D4 | — | 4 | 2 | no | — |
| 306 | C4×D4 | — | 8 | 4 | no | — |
| 307 | C4×D4 | — | 8 | 2 | no | — |
| 308 | #117 | — | 4 | 1 | no | — |
| 309 | #117 | — | 8 | 1 | no | — |
| 310 | #117 | — | 8 | 2 | no | — |
| 311 | C2×C42 | — | 8 | 1 | no | — |
| 312 | C2×C42 | #102 | 1 | 1 | yes | characteristic |
| 313 | Q32 | — | 2 | 1 | no | — |
| 314 | Q32 | #99 | 1 | 2 | yes | — |
| 315 | SD32 | — | 2 | 4 | no | — |
| 316 | SD32 | — | 4 | 4 | no | — |
| 317 | SD32 | — | 4 | 4 | no | — |
| 318 | D16 | — | 2 | 1 | no | — |
| 319 | D16 | — | 2 | 2 | no | — |
| 320 | D16 | — | 2 | 2 | no | — |
| 321 | D16 | — | 4 | 4 | no | — |
| 322 | D16 | — | 4 | 2 | no | — |
| 323 | D16 | — | 4 | 2 | no | — |
| 324 | D16 | — | 4 | 4 | no | — |
| 325 | D16 | — | 4 | 1 | no | — |
| 326 | D16 | — | 4 | 1 | no | — |
| 327 | D16 | — | 8 | 4 | no | — |
| 328 | D16 | #99 | 1 | 2 | yes | — |
| 329 | M32 | — | 4 | 1 | no | — |
| 330 | M32 | — | 4 | 2 | no | — |
| 331 | M32 | — | 4 | 2 | no | — |
| 332 | M32 | — | 4 | 1 | no | — |
| 333 | C2×C16 | — | 2 | 2 | no | — |
| 334 | C2×C16 | — | 2 | 2 | no | — |
| 335 | C2×C16 | — | 2 | 1 | no | — |
| 336 | C2×C16 | — | 2 | 1 | no | — |
| 337 | C2×C16 | — | 2 | 1 | no | — |
| 338 | C2×C16 | — | 2 | 1 | no | — |
| 339 | C2×C16 | — | 4 | 1 | no | — |
| 340 | C2×C16 | — | 4 | 1 | no | — |
| 341 | C2×C16 | — | 4 | 1 | no | — |
| 342 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 343 | C2×C16 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 344 | C2×C16 | #120 | 1 | 2 | yes | — |
| 345 | #107 | — | 2 | 2 | no | — |
| 346 | #107 | — | 8 | 2 | no | — |
| 347 | #106 | — | 4 | 1 | no | — |
| 348 | #106 | — | 8 | 2 | no | — |
| 349 | C4⋊C8 | — | 2 | 2 | no | — |
| 350 | #103 | — | 4 | 2 | no | — |
| 351 | #102 | — | 4 | 2 | no | — |
| 352 | #102 | — | 4 | 4 | no | — |
| 353 | #102 | — | 4 | 4 | no | — |
| 354 | #99 | — | 8 | 2 | no | — |
| 355 | #99 | — | 8 | 2 | no | — |
| 356 | C22⋊C8 | — | 2 | 2 | no | — |
| 357 | C22⋊C8 | — | 2 | 2 | no | — |
| 358 | C4×C8 | — | 2 | 1 | no | — |
| 359 | C4×C8 | — | 2 | 1 | no | — |
| 360 | C32 | — | 8 | 2 | no | — |
| 361 | C24 | — | 8 | 2 | no | — |
| 362 | C24 | — | 8 | 1 | no | — |
| 363 | C24 | — | 8 | 1 | no | — |
| 364 | C24 | — | 8 | 2 | no | — |
| 365 | #41 | — | 4 | 1 | no | — |
| 366 | #41 | — | 4 | 1 | no | — |
| 367 | #41 | — | 4 | 1 | no | — |
| 368 | #41 | — | 4 | 1 | no | — |
| 369 | #41 | — | 4 | 4 | no | — |
| 370 | #41 | — | 8 | 2 | no | — |
| 371 | #41 | — | 8 | 4 | no | — |
| 372 | #41 | — | 8 | 4 | no | — |
| 373 | #41 | — | 16 | 2 | no | — |
| 374 | #41 | — | 16 | 2 | no | — |
| 375 | #41 | — | 16 | 4 | no | — |
| 376 | #41 | — | 16 | 4 | no | — |
| 377 | C2×Q8 | — | 4 | 1 | no | — |
| 378 | C2×Q8 | #357 | 1 | 1 | yes | characteristic |
| 379 | C2×Q8 | C2×SD32 | 1 | 1 | yes | characteristic |
| 380 | C2×D4 | — | 2 | 1 | no | — |
| 381 | C2×D4 | — | 2 | 2 | no | — |
| 382 | C2×D4 | — | 4 | 1 | no | — |
| 383 | C2×D4 | — | 4 | 2 | no | — |
| 384 | C2×D4 | — | 4 | 2 | no | — |
| 385 | C2×D4 | — | 8 | 4 | no | — |
| 386 | C2×D4 | — | 8 | 2 | no | — |
| 387 | C2×D4 | — | 8 | 2 | no | — |
| 388 | C2×D4 | — | 8 | 2 | no | — |
| 389 | C2×D4 | — | 8 | 2 | no | — |
| 390 | C2×D4 | — | 8 | 4 | no | — |
| 391 | C2×D4 | — | 8 | 2 | no | — |
| 392 | C2×D4 | — | 8 | 4 | no | — |
| 393 | C2×D4 | — | 8 | 4 | no | — |
| 394 | C2×D4 | — | 8 | 1 | no | — |
| 395 | C2×D4 | — | 8 | 2 | no | — |
| 396 | C2×D4 | — | 8 | 2 | no | — |
| 397 | C2×D4 | — | 8 | 4 | no | — |
| 398 | C2×D4 | — | 8 | 4 | no | — |
| 399 | C2×D4 | — | 8 | 1 | no | — |
| 400 | C2×D4 | — | 8 | 1 | no | — |
| 401 | C2×D4 | — | 8 | 2 | no | — |
| 402 | C2×D4 | — | 16 | 2 | no | — |
| 403 | C2×D4 | — | 16 | 2 | no | — |
| 404 | C2×D4 | — | 16 | 4 | no | — |
| 405 | C2×D4 | — | 16 | 4 | no | — |
| 406 | C2×D4 | — | 16 | 8 | no | — |
| 407 | C2×D4 | — | 16 | 8 | no | — |
| 408 | C2×D4 | — | 32 | 4 | no | — |
| 409 | C2×D4 | — | 32 | 8 | no | — |
| 410 | C2×D4 | #357 | 1 | 1 | yes | characteristic |
| 411 | C2×D4 | C2×D16 | 1 | 1 | yes | characteristic |
| 412 | C2×D4 | #509 | 1 | 2 | yes | — |
| 413 | C22×C4 | — | 2 | 1 | no | — |
| 414 | C22×C4 | — | 2 | 1 | no | — |
| 415 | C22×C4 | — | 8 | 2 | no | — |
| 416 | C22×C4 | — | 8 | 2 | no | — |
| 417 | C22×C4 | — | 8 | 1 | no | — |
| 418 | C22×C4 | — | 8 | 2 | no | — |
| 419 | C22×C4 | C2×#102 | 1 | 1 | yes | characteristic |
| 420 | C22×C4 | #447 | 1 | 2 | yes | — |
| 421 | Q16 | — | 2 | 2 | no | — |
| 422 | Q16 | — | 4 | 1 | no | — |
| 423 | SD16 | — | 4 | 4 | no | — |
| 424 | SD16 | — | 8 | 4 | no | — |
| 425 | SD16 | — | 8 | 4 | no | — |
| 426 | D8 | — | 2 | 2 | no | — |
| 427 | D8 | — | 4 | 1 | no | — |
| 428 | D8 | — | 4 | 2 | no | — |
| 429 | D8 | — | 4 | 2 | no | — |
| 430 | D8 | — | 4 | 2 | no | — |
| 431 | D8 | — | 4 | 2 | no | — |
| 432 | D8 | — | 8 | 4 | no | — |
| 433 | D8 | — | 8 | 2 | no | — |
| 434 | D8 | — | 8 | 2 | no | — |
| 435 | D8 | — | 8 | 4 | no | — |
| 436 | D8 | — | 16 | 4 | no | — |
| 437 | M16 | — | 4 | 1 | no | — |
| 438 | M16 | — | 4 | 2 | no | — |
| 439 | M16 | — | 4 | 2 | no | — |
| 440 | M16 | — | 4 | 1 | no | — |
| 441 | C2×C8 | — | 2 | 2 | no | — |
| 442 | C2×C8 | — | 2 | 1 | no | — |
| 443 | C2×C8 | — | 2 | 2 | no | — |
| 444 | C2×C8 | — | 2 | 1 | no | — |
| 445 | C2×C8 | — | 2 | 1 | no | — |
| 446 | C2×C8 | — | 2 | 1 | no | — |
| 447 | C2×C8 | — | 4 | 1 | no | — |
| 448 | C2×C8 | — | 4 | 1 | no | — |
| 449 | C2×C8 | — | 4 | 1 | no | — |
| 450 | C2×C8 | #379 | 1 | 1 | yes | characteristic |
| 451 | C2×C8 | #418 | 1 | 1 | yes | characteristic |
| 452 | C2×C8 | #450 | 1 | 2 | yes | — |
| 453 | C4⋊C4 | — | 2 | 2 | no | — |
| 454 | C4⋊C4 | — | 4 | 2 | no | — |
| 455 | C4⋊C4 | — | 8 | 2 | no | — |
| 456 | C4⋊C4 | — | 16 | 2 | no | — |
| 457 | C22⋊C4 | — | 2 | 2 | no | — |
| 458 | C22⋊C4 | — | 2 | 2 | no | — |
| 459 | C22⋊C4 | — | 8 | 2 | no | — |
| 460 | C22⋊C4 | — | 8 | 4 | no | — |
| 461 | C22⋊C4 | — | 8 | 1 | no | — |
| 462 | C22⋊C4 | — | 8 | 4 | no | — |
| 463 | C22⋊C4 | — | 16 | 2 | no | — |
| 464 | C42 | — | 2 | 1 | no | — |
| 465 | C42 | — | 8 | 2 | no | — |
| 466 | C42 | — | 8 | 1 | no | — |
| 467 | C42 | — | 16 | 2 | no | — |
| 468 | C42 | #357 | 1 | 1 | yes | characteristic |
| 469 | C42 | #357 | 1 | 1 | yes | characteristic |
| 470 | C16 | — | 2 | 2 | no | — |
| 471 | C16 | — | 2 | 1 | no | — |
| 472 | C16 | — | 4 | 1 | no | — |
| 473 | C16 | — | 4 | 1 | no | — |
| 474 | C16 | C2×#99 | 1 | 1 | yes | characteristic |
| 475 | C16 | C2×#99 | 1 | 1 | yes | characteristic |
| 476 | C23 | — | 2 | 1 | no | — |
| 477 | C23 | — | 8 | 1 | no | — |
| 478 | C23 | — | 8 | 2 | no | — |
| 479 | C23 | — | 8 | 2 | no | — |
| 480 | C23 | — | 16 | 4 | no | — |
| 481 | C23 | — | 16 | 2 | no | — |
| 482 | C23 | — | 16 | 2 | no | — |
| 483 | C23 | — | 16 | 4 | no | — |
| 484 | C23 | — | 32 | 2 | no | — |
| 485 | C23 | — | 32 | 2 | no | — |
| 486 | C23 | — | 32 | 4 | no | — |
| 487 | C23 | — | 32 | 4 | no | — |
| 488 | C23 | #2140 | 1 | 1 | yes | characteristic |
| 489 | C23 | #2184 | 1 | 2 | yes | — |
| 490 | Q8 | — | 4 | 1 | no | — |
| 491 | Q8 | — | 4 | 1 | no | — |
| 492 | Q8 | — | 4 | 2 | no | — |
| 493 | Q8 | — | 8 | 1 | no | — |
| 494 | D4 | — | 4 | 1 | no | — |
| 495 | D4 | — | 4 | 2 | no | — |
| 496 | D4 | — | 4 | 1 | no | — |
| 497 | D4 | — | 4 | 4 | no | — |
| 498 | D4 | — | 4 | 2 | no | — |
| 499 | D4 | — | 4 | 2 | no | — |
| 500 | D4 | — | 8 | 4 | no | — |
| 501 | D4 | — | 8 | 2 | no | — |
| 502 | D4 | — | 8 | 2 | no | — |
| 503 | D4 | — | 8 | 1 | no | — |
| 504 | D4 | — | 8 | 2 | no | — |
| 505 | D4 | — | 8 | 2 | no | — |
| 506 | D4 | — | 16 | 4 | no | — |
| 507 | D4 | — | 16 | 2 | no | — |
| 508 | D4 | — | 16 | 2 | no | — |
| 509 | D4 | — | 16 | 8 | no | — |
| 510 | D4 | — | 16 | 4 | no | — |
| 511 | D4 | — | 16 | 4 | no | — |
| 512 | D4 | — | 16 | 4 | no | — |
| 513 | D4 | — | 32 | 4 | no | — |
| 514 | D4 | — | 32 | 4 | no | — |
| 515 | D4 | — | 32 | 4 | no | — |
| 516 | C2×C4 | — | 2 | 1 | no | — |
| 517 | C2×C4 | — | 2 | 2 | no | — |
| 518 | C2×C4 | — | 2 | 1 | no | — |
| 519 | C2×C4 | — | 2 | 2 | no | — |
| 520 | C2×C4 | — | 2 | 1 | no | — |
| 521 | C2×C4 | — | 2 | 1 | no | — |
| 522 | C2×C4 | — | 2 | 1 | no | — |
| 523 | C2×C4 | — | 4 | 2 | no | — |
| 524 | C2×C4 | — | 4 | 1 | no | — |
| 525 | C2×C4 | — | 4 | 1 | no | — |
| 526 | C2×C4 | — | 8 | 4 | no | — |
| 527 | C2×C4 | — | 8 | 1 | no | — |
| 528 | C2×C4 | — | 8 | 2 | no | — |
| 529 | C2×C4 | — | 16 | 4 | no | — |
| 530 | C2×C4 | — | 16 | 4 | no | — |
| 531 | C2×C4 | — | 16 | 4 | no | — |
| 532 | C2×C4 | — | 32 | 2 | no | — |
| 533 | C2×C4 | #1786 | 1 | 1 | yes | characteristic |
| 534 | C2×C4 | C2×#357 | 1 | 1 | yes | characteristic |
| 535 | C2×C4 | #2187 | 1 | 2 | yes | — |
| 536 | C8 | — | 2 | 1 | no | — |
| 537 | C8 | — | 2 | 2 | no | — |
| 538 | C8 | — | 4 | 1 | no | — |
| 539 | C8 | — | 4 | 1 | no | — |
| 540 | C8 | #1781 | 1 | 1 | yes | characteristic |
| 541 | C8 | #1795 | 1 | 1 | yes | characteristic |
| 542 | C22 | — | 2 | 2 | no | — |
| 543 | C22 | — | 2 | 1 | no | — |
| 544 | C22 | — | 4 | 1 | no | — |
| 545 | C22 | — | 4 | 2 | no | — |
| 546 | C22 | — | 4 | 2 | no | — |
| 547 | C22 | — | 4 | 1 | no | — |
| 548 | C22 | — | 8 | 2 | no | — |
| 549 | C22 | — | 16 | 2 | no | — |
| 550 | C22 | — | 16 | 4 | no | — |
| 551 | C22 | — | 16 | 4 | no | — |
| 552 | C22 | — | 16 | 2 | no | — |
| 553 | C22 | — | 16 | 2 | no | — |
| 554 | C22 | — | 64 | 4 | no | — |
| 555 | C22 | — | 64 | 2 | no | — |
| 556 | C22 | — | 64 | 2 | no | — |
| 557 | C22 | — | 64 | 4 | no | — |
| 558 | C22 | #12731 | 1 | 1 | yes | characteristic |
| 559 | C4 | — | 2 | 2 | no | — |
| 560 | C4 | — | 2 | 1 | no | — |
| 561 | C4 | — | 2 | 2 | no | — |
| 562 | C4 | — | 4 | 1 | no | — |
| 563 | C4 | — | 4 | 1 | no | — |
| 564 | C4 | — | 8 | 2 | no | — |
| 565 | C4 | — | 16 | 2 | no | — |
| 566 | C4 | — | 64 | 2 | no | — |
| 567 | C4 | #8375 | 1 | 1 | yes | characteristic |
| 568 | C4 | #12741 | 1 | 1 | yes | characteristic |
| 569 | C2 | — | 2 | 1 | no | — |
| 570 | C2 | — | 4 | 2 | no | — |
| 571 | C2 | — | 4 | 1 | no | — |
| 572 | C2 | — | 8 | 1 | no | — |
| 573 | C2 | — | 16 | 2 | no | — |
| 574 | C2 | — | 32 | 2 | no | — |
| 575 | C2 | — | 32 | 2 | no | — |
| 576 | C2 | #130718 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | #130718 |
| commutator | C22×C16 | C22×C4 |
| Frattini, cosocle | C2×#504 | C23 |
| prime radical | #7623644 | C2 |
| LCS | G ▷ C22×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×#131 ◁ #33434 ◁ G | |
| LECS | G ▷ C2×#504 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #152169 | C2 | semidirect |
| 3. #150879 | C2 | semidirect |
| 4. #149671 | C2 | semidirect |
| 5. #134775 | C2 | semidirect |
| 6. C2×#3415 | C4 | semidirect |
| 12. C2×#2246 | C4 | semidirect |
| 13. #33607 | C4 | semidirect |
| 18. C4×#508 | C4 | semidirect |
| 22. #13556 | C22 | semidirect |
| 23. #12839 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #7623644 | 2 |
| #152169 | 2 |
| #150879 | 2 |
| #149671 | 2 |
| #134775 | 2 |