Finite Group DatabasebetaFinite Group DatabasebetaOrder 1024.
2941 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 2941 conjugacy classes of subgroups — too many to draw. Only its 219 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×#31077 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #233619 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #125651 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | C2×#7115 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #60940 | — | 2 | 3 | no | — |
| 6 | C2×#3018 | — | 2 | 3 | no | — |
| 7 | #34641 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #31077 | — | 2 | 6 | no | — |
| 9 | #31077 | C22 | 1 | 4 | yes | — |
| 10 | C2×#2050 | — | 2 | 3 | no | — |
| 11 | C2×#1963 | C22 | 1 | 3 | yes | — |
| 12 | #17485 | — | 2 | 3 | no | — |
| 13 | #10012 | — | 2 | 6 | no | — |
| 14 | #10012 | C22 | 1 | 12 | yes | complemented |
| 15 | C2×#1274 | C22 | 1 | 3 | yes | complemented |
| 16 | #7115 | C22 | 1 | 12 | yes | complemented |
| 17 | C2×#585 | — | 2 | 1 | no | — |
| 18 | C2×#575 | — | 2 | 3 | no | — |
| 19 | C2×#532 | — | 2 | 3 | no | — |
| 20 | C2×#532 | D4 | 1 | 3 | yes | — |
| 21 | #3245 | — | 4 | 6 | no | — |
| 22 | #3226 | — | 4 | 3 | no | — |
| 23 | #3226 | — | 4 | 3 | no | — |
| 24 | #3205 | — | 4 | 3 | no | — |
| 25 | #3205 | — | 4 | 3 | no | — |
| 26 | #3186 | — | 4 | 6 | no | — |
| 27 | #3169 | — | 4 | 6 | no | — |
| 28 | #3100 | — | 2 | 12 | no | — |
| 29 | #3100 | — | 4 | 6 | no | — |
| 30 | #3018 | — | 2 | 12 | no | — |
| 31 | #3018 | — | 2 | 12 | no | — |
| 32 | #3018 | — | 4 | 6 | no | — |
| 33 | #3018 | — | 4 | 6 | no | — |
| 34 | C2×#456 | — | 4 | 3 | no | — |
| 35 | C2×#454 | — | 4 | 3 | no | — |
| 36 | C2×#455 | — | 4 | 3 | no | — |
| 37 | C2×#453 | — | 4 | 3 | no | — |
| 38 | C2×#431 | — | 2 | 3 | no | — |
| 39 | C2×#423 | D4 | 1 | 3 | yes | — |
| 40 | C22×#104 | — | 2 | 6 | no | — |
| 41 | C2×#413 | — | 2 | 3 | no | — |
| 42 | #2658 | — | 4 | 1 | no | — |
| 43 | #2657 | — | 4 | 1 | no | — |
| 44 | #2656 | — | 4 | 2 | no | — |
| 45 | #2397 | — | 2 | 3 | no | — |
| 46 | #2397 | C23 | 1 | 2 | yes | complemented |
| 47 | C2×#376 | C23 | 1 | 1 | yes | characteristic |
| 48 | #2050 | — | 2 | 12 | no | — |
| 49 | #2050 | — | 2 | 12 | no | — |
| 50 | #1963 | — | 2 | 6 | no | — |
| 51 | #1963 | D4 | 1 | 6 | yes | — |
| 52 | #1963 | C23 | 1 | 6 | yes | — |
| 53 | C2×#338 | — | 2 | 1 | no | — |
| 54 | #1492 | — | 4 | 6 | no | — |
| 55 | #1486 | — | 2 | 12 | no | — |
| 56 | #1480 | — | 4 | 6 | no | — |
| 57 | #1274 | — | 2 | 3 | no | — |
| 58 | #1274 | C23 | 1 | 6 | yes | complemented |
| 59 | #585 | — | 2 | 4 | no | — |
| 60 | #585 | — | 4 | 6 | no | — |
| 61 | #585 | — | 8 | 3 | no | — |
| 62 | #585 | — | 8 | 1 | no | — |
| 63 | C2×2−1+4 | — | 4 | 3 | no | — |
| 64 | C2×H(5,𝔽2) | — | 4 | 3 | no | — |
| 65 | C2×H(5,𝔽2) | — | 8 | 1 | no | — |
| 66 | C22×#41 | — | 2 | 3 | no | — |
| 67 | C22×#41 | — | 4 | 1 | no | — |
| 68 | C22×#41 | — | 8 | 3 | no | — |
| 69 | #575 | — | 2 | 12 | no | — |
| 70 | #575 | — | 4 | 12 | no | — |
| 71 | #575 | — | 8 | 3 | no | — |
| 72 | C2×#137 | — | 4 | 6 | no | — |
| 73 | C2×AGL(1,ℤ/8) | — | 4 | 6 | no | — |
| 74 | C2×#135 | — | 8 | 3 | no | — |
| 75 | C22×M16 | — | 2 | 3 | no | — |
| 76 | #532 | — | 2 | 3 | no | — |
| 77 | #532 | — | 2 | 3 | no | — |
| 78 | #532 | — | 4 | 3 | no | — |
| 79 | #532 | — | 4 | 3 | no | — |
| 80 | #532 | — | 4 | 3 | no | — |
| 81 | #532 | — | 4 | 3 | no | — |
| 82 | #532 | — | 4 | 3 | no | — |
| 83 | #532 | — | 4 | 3 | no | — |
| 84 | #532 | — | 4 | 3 | no | — |
| 85 | #532 | — | 4 | 3 | no | — |
| 86 | #532 | — | 4 | 3 | no | — |
| 87 | #532 | — | 4 | 3 | no | — |
| 88 | #532 | D8 | 1 | 6 | yes | complemented |
| 89 | #532 | C2×D4 | 1 | 6 | yes | — |
| 90 | C2×C4⋊Q8 | — | 2 | 3 | no | — |
| 91 | C2×C4⋊Q8 | D8 | 1 | 3 | yes | complemented |
| 92 | C2×#127 | — | 2 | 3 | no | — |
| 93 | C2×#127 | D8 | 1 | 3 | yes | complemented |
| 94 | C2×#124 | — | 2 | 3 | no | — |
| 95 | C2×#124 | — | 4 | 3 | no | — |
| 96 | C2×#121 | — | 2 | 6 | no | — |
| 97 | C2×#121 | — | 4 | 3 | no | — |
| 98 | C2×#121 | — | 4 | 3 | no | — |
| 99 | C2×C4×D4 | — | 2 | 6 | no | — |
| 100 | C2×C4×D4 | — | 4 | 3 | no | — |
| 101 | C2×C4×D4 | — | 4 | 3 | no | — |
| 102 | C22×C42 | C2×D4 | 1 | 3 | yes | — |
| 103 | #500 | — | 4 | 6 | no | — |
| 104 | #493 | — | 4 | 6 | no | — |
| 105 | #486 | — | 4 | 6 | no | — |
| 106 | #486 | — | 4 | 6 | no | — |
| 107 | #480 | — | 4 | 12 | no | — |
| 108 | #480 | — | 4 | 12 | no | — |
| 109 | #474 | — | 4 | 12 | no | — |
| 110 | #474 | — | 4 | 12 | no | — |
| 111 | #466 | — | 4 | 24 | no | — |
| 112 | #459 | — | 4 | 12 | no | — |
| 113 | #459 | — | 4 | 12 | no | — |
| 114 | #456 | — | 4 | 12 | no | — |
| 115 | #456 | — | 4 | 12 | no | — |
| 116 | #455 | — | 4 | 12 | no | — |
| 117 | #455 | — | 4 | 12 | no | — |
| 118 | #454 | — | 4 | 12 | no | — |
| 119 | #454 | — | 4 | 12 | no | — |
| 120 | #453 | — | 4 | 12 | no | — |
| 121 | #453 | — | 4 | 12 | no | — |
| 122 | #447 | — | 4 | 12 | no | — |
| 123 | #447 | — | 4 | 12 | no | — |
| 124 | C4×D8 | — | 4 | 24 | no | — |
| 125 | #431 | — | 2 | 6 | no | — |
| 126 | #431 | — | 2 | 6 | no | — |
| 127 | #431 | — | 4 | 3 | no | — |
| 128 | #431 | — | 4 | 3 | no | — |
| 129 | #423 | — | 2 | 3 | no | — |
| 130 | #423 | — | 4 | 3 | no | — |
| 131 | #423 | C2×D4 | 1 | 6 | yes | — |
| 132 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 133 | C2×C4⋊C8 | — | 4 | 3 | no | — |
| 134 | C2×#104 | — | 2 | 12 | no | — |
| 135 | C2×#104 | — | 2 | 12 | no | — |
| 136 | C2×#104 | — | 4 | 6 | no | — |
| 137 | C2×#104 | — | 4 | 6 | no | — |
| 138 | C2×#104 | — | 4 | 6 | no | — |
| 139 | C2×#104 | — | 4 | 6 | no | — |
| 140 | #413 | — | 2 | 12 | no | — |
| 141 | #413 | — | 4 | 6 | no | — |
| 142 | C2×#101 | — | 4 | 3 | no | — |
| 143 | C2×#100 | — | 4 | 3 | no | — |
| 144 | C2×C22⋊C8 | — | 4 | 3 | no | — |
| 145 | C2×C4×C8 | — | 2 | 6 | no | — |
| 146 | #399 | — | 4 | 2 | no | — |
| 147 | #399 | — | 4 | 6 | no | — |
| 148 | #392 | — | 4 | 2 | no | — |
| 149 | #392 | — | 4 | 6 | no | — |
| 150 | #376 | — | 4 | 1 | no | — |
| 151 | #376 | C2×D4 | 1 | 3 | yes | — |
| 152 | #376 | C24 | 1 | 1 | yes | characteristic |
| 153 | C2×#95 | — | 4 | 1 | no | — |
| 154 | #338 | — | 2 | 4 | no | — |
| 155 | D4⋊C8 | — | 4 | 24 | no | — |
| 156 | 2−1+4 | — | 4 | 12 | no | — |
| 157 | 2−1+4 | — | 8 | 12 | no | — |
| 158 | 2−1+4 | — | 8 | 6 | no | — |
| 159 | H(5,𝔽2) | — | 4 | 12 | no | — |
| 160 | H(5,𝔽2) | — | 8 | 4 | no | — |
| 161 | H(5,𝔽2) | — | 8 | 12 | no | — |
| 162 | H(5,𝔽2) | — | 8 | 6 | no | — |
| 163 | H(5,𝔽2) | — | 8 | 12 | no | — |
| 164 | C2×#41 | — | 2 | 6 | no | — |
| 165 | C2×#41 | — | 2 | 6 | no | — |
| 166 | C2×#41 | — | 4 | 3 | no | — |
| 167 | C2×#41 | — | 4 | 3 | no | — |
| 168 | C2×#41 | — | 4 | 6 | no | — |
| 169 | C2×#41 | — | 4 | 6 | no | — |
| 170 | C2×#41 | — | 4 | 6 | no | — |
| 171 | C2×#41 | — | 4 | 6 | no | — |
| 172 | C2×#41 | — | 8 | 12 | no | — |
| 173 | C2×#41 | — | 8 | 6 | no | — |
| 174 | C2×#41 | — | 8 | 12 | no | — |
| 175 | C2×#41 | — | 8 | 6 | no | — |
| 176 | C2×#41 | — | 8 | 12 | no | — |
| 177 | C2×#41 | — | 8 | 2 | no | — |
| 178 | C2×#41 | — | 8 | 12 | no | — |
| 179 | C2×#41 | — | 8 | 3 | no | — |
| 180 | C2×#41 | — | 8 | 3 | no | — |
| 181 | C2×#41 | — | 8 | 3 | no | — |
| 182 | C2×#41 | — | 8 | 3 | no | — |
| 183 | C22×Q8 | — | 2 | 3 | no | — |
| 184 | C22×Q8 | — | 4 | 1 | no | — |
| 185 | C22×Q8 | — | 8 | 3 | no | — |
| 186 | C22×D4 | — | 2 | 6 | no | — |
| 187 | C22×D4 | — | 2 | 3 | no | — |
| 188 | C22×D4 | — | 4 | 3 | no | — |
| 189 | C22×D4 | — | 4 | 3 | no | — |
| 190 | C22×D4 | — | 4 | 3 | no | — |
| 191 | C22×D4 | — | 4 | 2 | no | — |
| 192 | C22×D4 | — | 4 | 1 | no | — |
| 193 | C22×D4 | — | 8 | 3 | no | — |
| 194 | C22×D4 | — | 8 | 6 | no | — |
| 195 | C23×C4 | — | 2 | 3 | no | — |
| 196 | C23×C4 | — | 4 | 3 | no | — |
| 197 | C23×C4 | — | 4 | 2 | no | — |
| 198 | C23×C4 | — | 8 | 2 | no | — |
| 199 | C23×C4 | #120 | 1 | 1 | yes | characteristic |
| 200 | #137 | — | 4 | 24 | no | — |
| 201 | #137 | — | 8 | 12 | no | — |
| 202 | AGL(1,ℤ/8) | — | 4 | 24 | no | — |
| 203 | AGL(1,ℤ/8) | — | 8 | 12 | no | — |
| 204 | #135 | — | 8 | 12 | no | — |
| 205 | #135 | — | 8 | 12 | no | — |
| 206 | C2×Q16 | — | 8 | 3 | no | — |
| 207 | C2×SD16 | — | 8 | 6 | no | — |
| 208 | C2×D8 | — | 4 | 24 | no | — |
| 209 | C2×D8 | — | 8 | 3 | no | — |
| 210 | C2×M16 | — | 2 | 6 | no | — |
| 211 | C2×M16 | — | 4 | 3 | no | — |
| 212 | C2×M16 | — | 4 | 6 | no | — |
| 213 | C2×M16 | — | 4 | 6 | no | — |
| 214 | C22×C8 | — | 4 | 3 | no | — |
| 215 | C22×C8 | — | 4 | 6 | no | — |
| 216 | C4⋊Q8 | — | 2 | 3 | no | — |
| 217 | C4⋊Q8 | — | 4 | 3 | no | — |
| 218 | C4⋊Q8 | — | 4 | 3 | no | — |
| 219 | C4⋊Q8 | — | 4 | 3 | no | — |
| 220 | C4⋊Q8 | — | 4 | 3 | no | — |
| 221 | C4⋊Q8 | — | 4 | 3 | no | — |
| 222 | C4⋊Q8 | C2×D8 | 1 | 6 | yes | — |
| 223 | #127 | — | 2 | 3 | no | — |
| 224 | #127 | — | 4 | 3 | no | — |
| 225 | #127 | — | 4 | 3 | no | — |
| 226 | #127 | — | 4 | 3 | no | — |
| 227 | #127 | — | 4 | 3 | no | — |
| 228 | #127 | — | 4 | 3 | no | — |
| 229 | #127 | C2×D8 | 1 | 6 | yes | — |
| 230 | #124 | — | 2 | 6 | no | — |
| 231 | #124 | — | 2 | 6 | no | — |
| 232 | #124 | — | 8 | 3 | no | — |
| 233 | #124 | — | 8 | 3 | no | — |
| 234 | #124 | — | 8 | 3 | no | — |
| 235 | #124 | — | 8 | 3 | no | — |
| 236 | #124 | — | 8 | 3 | no | — |
| 237 | #121 | — | 4 | 6 | no | — |
| 238 | #121 | — | 4 | 6 | no | — |
| 239 | #121 | — | 4 | 6 | no | — |
| 240 | #121 | — | 4 | 6 | no | — |
| 241 | #121 | — | 4 | 6 | no | — |
| 242 | #121 | — | 4 | 6 | no | — |
| 243 | #121 | — | 8 | 3 | no | — |
| 244 | #121 | — | 8 | 3 | no | — |
| 245 | #121 | — | 8 | 3 | no | — |
| 246 | #121 | — | 8 | 3 | no | — |
| 247 | #121 | — | 8 | 3 | no | — |
| 248 | #121 | — | 8 | 3 | no | — |
| 249 | C4×D4 | — | 4 | 6 | no | — |
| 250 | C4×D4 | — | 4 | 6 | no | — |
| 251 | C4×D4 | — | 4 | 6 | no | — |
| 252 | C4×D4 | — | 4 | 6 | no | — |
| 253 | C4×D4 | — | 4 | 6 | no | — |
| 254 | C4×D4 | — | 4 | 6 | no | — |
| 255 | C4×D4 | — | 8 | 3 | no | — |
| 256 | C4×D4 | — | 8 | 3 | no | — |
| 257 | C4×D4 | — | 8 | 3 | no | — |
| 258 | C4×D4 | — | 8 | 3 | no | — |
| 259 | C4×D4 | — | 8 | 3 | no | — |
| 260 | C4×D4 | — | 8 | 3 | no | — |
| 261 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 262 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 263 | C2×C4⋊C4 | — | 4 | 3 | no | — |
| 264 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 265 | C2×C22⋊C4 | — | 4 | 6 | no | — |
| 266 | C2×C22⋊C4 | — | 8 | 3 | no | — |
| 267 | C2×C42 | — | 2 | 3 | no | — |
| 268 | C2×C42 | — | 2 | 3 | no | — |
| 269 | C2×C42 | — | 2 | 3 | no | — |
| 270 | C2×C42 | #120 | 1 | 3 | yes | — |
| 271 | C2×C42 | C2×D8 | 1 | 3 | yes | — |
| 272 | C2×C42 | C2×D8 | 1 | 3 | yes | — |
| 273 | C2×C42 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 274 | C2×C42 | AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 275 | C2×C42 | C22×D4 | 1 | 3 | yes | — |
| 276 | #107 | — | 4 | 24 | no | — |
| 277 | C4⋊C8 | — | 4 | 6 | no | — |
| 278 | C4⋊C8 | — | 4 | 6 | no | — |
| 279 | C4⋊C8 | — | 4 | 6 | no | — |
| 280 | C4⋊C8 | — | 8 | 3 | no | — |
| 281 | #104 | — | 4 | 12 | no | — |
| 282 | #104 | — | 4 | 12 | no | — |
| 283 | #104 | — | 4 | 12 | no | — |
| 284 | #104 | — | 4 | 12 | no | — |
| 285 | #102 | — | 4 | 24 | no | — |
| 286 | #102 | — | 4 | 24 | no | — |
| 287 | #101 | — | 4 | 12 | no | — |
| 288 | #100 | — | 4 | 12 | no | — |
| 289 | C22⋊C8 | — | 4 | 6 | no | — |
| 290 | C22⋊C8 | — | 4 | 6 | no | — |
| 291 | C4×C8 | — | 2 | 12 | no | — |
| 292 | C4×C8 | — | 4 | 6 | no | — |
| 293 | #95 | — | 4 | 3 | no | — |
| 294 | #95 | — | 4 | 1 | no | — |
| 295 | C24 | — | 4 | 3 | no | — |
| 296 | C24 | — | 4 | 2 | no | — |
| 297 | C24 | — | 8 | 2 | no | — |
| 298 | C24 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 299 | #41 | — | 4 | 12 | no | — |
| 300 | #41 | — | 4 | 12 | no | — |
| 301 | #41 | — | 4 | 12 | no | — |
| 302 | #41 | — | 4 | 12 | no | — |
| 303 | #41 | — | 8 | 24 | no | — |
| 304 | #41 | — | 8 | 24 | no | — |
| 305 | #41 | — | 8 | 8 | no | — |
| 306 | #41 | — | 8 | 8 | no | — |
| 307 | #41 | — | 8 | 24 | no | — |
| 308 | #41 | — | 8 | 24 | no | — |
| 309 | #41 | — | 8 | 6 | no | — |
| 310 | #41 | — | 8 | 6 | no | — |
| 311 | #41 | — | 8 | 6 | no | — |
| 312 | #41 | — | 8 | 6 | no | — |
| 313 | #41 | — | 16 | 3 | no | — |
| 314 | #41 | — | 16 | 3 | no | — |
| 315 | #41 | — | 16 | 6 | no | — |
| 316 | #41 | — | 16 | 1 | no | — |
| 317 | #41 | — | 16 | 3 | no | — |
| 318 | C2×Q8 | — | 2 | 6 | no | — |
| 319 | C2×Q8 | — | 4 | 3 | no | — |
| 320 | C2×Q8 | — | 4 | 6 | no | — |
| 321 | C2×Q8 | — | 4 | 6 | no | — |
| 322 | C2×Q8 | — | 8 | 12 | no | — |
| 323 | C2×Q8 | — | 8 | 2 | no | — |
| 324 | C2×Q8 | — | 8 | 12 | no | — |
| 325 | C2×Q8 | — | 8 | 3 | no | — |
| 326 | C2×Q8 | — | 8 | 3 | no | — |
| 327 | C2×D4 | — | 2 | 6 | no | — |
| 328 | C2×D4 | — | 4 | 6 | no | — |
| 329 | C2×D4 | — | 4 | 6 | no | — |
| 330 | C2×D4 | — | 4 | 6 | no | — |
| 331 | C2×D4 | — | 4 | 6 | no | — |
| 332 | C2×D4 | — | 4 | 6 | no | — |
| 333 | C2×D4 | — | 4 | 3 | no | — |
| 334 | C2×D4 | — | 4 | 6 | no | — |
| 335 | C2×D4 | — | 4 | 6 | no | — |
| 336 | C2×D4 | — | 8 | 3 | no | — |
| 337 | C2×D4 | — | 8 | 3 | no | — |
| 338 | C2×D4 | — | 8 | 3 | no | — |
| 339 | C2×D4 | — | 8 | 12 | no | — |
| 340 | C2×D4 | — | 8 | 24 | no | — |
| 341 | C2×D4 | — | 8 | 6 | no | — |
| 342 | C2×D4 | — | 8 | 24 | no | — |
| 343 | C2×D4 | — | 8 | 12 | no | — |
| 344 | C2×D4 | — | 8 | 6 | no | — |
| 345 | C2×D4 | — | 8 | 6 | no | — |
| 346 | C2×D4 | — | 8 | 6 | no | — |
| 347 | C2×D4 | — | 8 | 6 | no | — |
| 348 | C2×D4 | — | 8 | 3 | no | — |
| 349 | C2×D4 | — | 8 | 3 | no | — |
| 350 | C2×D4 | — | 16 | 6 | no | — |
| 351 | C2×D4 | — | 16 | 6 | no | — |
| 352 | C2×D4 | — | 16 | 6 | no | — |
| 353 | C22×C4 | — | 2 | 3 | no | — |
| 354 | C22×C4 | — | 2 | 3 | no | — |
| 355 | C22×C4 | — | 2 | 3 | no | — |
| 356 | C22×C4 | — | 2 | 3 | no | — |
| 357 | C22×C4 | — | 2 | 3 | no | — |
| 358 | C22×C4 | — | 2 | 3 | no | — |
| 359 | C22×C4 | — | 4 | 3 | no | — |
| 360 | C22×C4 | — | 4 | 6 | no | — |
| 361 | C22×C4 | — | 4 | 6 | no | — |
| 362 | C22×C4 | — | 4 | 2 | no | — |
| 363 | C22×C4 | — | 8 | 6 | no | — |
| 364 | C22×C4 | — | 8 | 8 | no | — |
| 365 | C22×C4 | — | 8 | 8 | no | — |
| 366 | C22×C4 | — | 8 | 3 | no | — |
| 367 | C22×C4 | — | 8 | 3 | no | — |
| 368 | C22×C4 | — | 8 | 3 | no | — |
| 369 | C22×C4 | — | 8 | 3 | no | — |
| 370 | C22×C4 | — | 8 | 6 | no | — |
| 371 | C22×C4 | — | 8 | 6 | no | — |
| 372 | C22×C4 | — | 16 | 3 | no | — |
| 373 | C22×C4 | #447 | 1 | 3 | yes | — |
| 374 | C22×C4 | #447 | 1 | 3 | yes | — |
| 375 | C22×C4 | #453 | 1 | 3 | yes | — |
| 376 | C22×C4 | #453 | 1 | 3 | yes | — |
| 377 | C22×C4 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 378 | C22×C4 | C2×#120 | 1 | 1 | yes | characteristic |
| 379 | Q16 | — | 8 | 12 | no | — |
| 380 | SD16 | — | 8 | 24 | no | — |
| 381 | D8 | — | 8 | 12 | no | — |
| 382 | D8 | — | 16 | 24 | no | — |
| 383 | M16 | — | 4 | 12 | no | — |
| 384 | M16 | — | 8 | 6 | no | — |
| 385 | C2×C8 | — | 4 | 12 | no | — |
| 386 | C2×C8 | — | 4 | 6 | no | — |
| 387 | C2×C8 | — | 8 | 3 | no | — |
| 388 | C2×C8 | — | 8 | 3 | no | — |
| 389 | C2×C8 | — | 16 | 6 | no | — |
| 390 | C4⋊C4 | — | 4 | 6 | no | — |
| 391 | C4⋊C4 | — | 4 | 6 | no | — |
| 392 | C4⋊C4 | — | 4 | 6 | no | — |
| 393 | C4⋊C4 | — | 8 | 3 | no | — |
| 394 | C4⋊C4 | — | 8 | 3 | no | — |
| 395 | C4⋊C4 | — | 8 | 3 | no | — |
| 396 | C22⋊C4 | — | 8 | 6 | no | — |
| 397 | C22⋊C4 | — | 8 | 6 | no | — |
| 398 | C22⋊C4 | — | 8 | 6 | no | — |
| 399 | C22⋊C4 | — | 8 | 6 | no | — |
| 400 | C22⋊C4 | — | 8 | 6 | no | — |
| 401 | C22⋊C4 | — | 8 | 6 | no | — |
| 402 | C42 | — | 2 | 3 | no | — |
| 403 | C42 | — | 2 | 3 | no | — |
| 404 | C42 | — | 2 | 3 | no | — |
| 405 | C42 | — | 2 | 3 | no | — |
| 406 | C42 | — | 2 | 3 | no | — |
| 407 | C42 | — | 2 | 3 | no | — |
| 408 | C42 | #447 | 1 | 3 | yes | — |
| 409 | C42 | #447 | 1 | 3 | yes | — |
| 410 | C42 | C22×D8 | 1 | 3 | yes | — |
| 411 | C42 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 412 | C23 | — | 4 | 6 | no | — |
| 413 | C23 | — | 8 | 1 | no | — |
| 414 | C23 | — | 8 | 2 | no | — |
| 415 | C23 | — | 8 | 6 | no | — |
| 416 | C23 | — | 8 | 8 | no | — |
| 417 | C23 | — | 8 | 3 | no | — |
| 418 | C23 | — | 8 | 3 | no | — |
| 419 | C23 | — | 8 | 6 | no | — |
| 420 | C23 | — | 16 | 6 | no | — |
| 421 | C23 | — | 32 | 4 | no | — |
| 422 | C23 | #1595 | 1 | 3 | yes | — |
| 423 | C23 | #1595 | 1 | 3 | yes | — |
| 424 | C23 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 425 | Q8 | — | 4 | 12 | no | — |
| 426 | Q8 | — | 8 | 8 | no | — |
| 427 | Q8 | — | 8 | 6 | no | — |
| 428 | Q8 | — | 16 | 1 | no | — |
| 429 | Q8 | — | 16 | 3 | no | — |
| 430 | D4 | — | 4 | 12 | no | — |
| 431 | D4 | — | 8 | 12 | no | — |
| 432 | D4 | — | 8 | 12 | no | — |
| 433 | D4 | — | 8 | 12 | no | — |
| 434 | D4 | — | 8 | 24 | no | — |
| 435 | D4 | — | 8 | 12 | no | — |
| 436 | D4 | — | 8 | 12 | no | — |
| 437 | D4 | — | 8 | 6 | no | — |
| 438 | D4 | — | 16 | 6 | no | — |
| 439 | D4 | — | 16 | 6 | no | — |
| 440 | D4 | — | 16 | 6 | no | — |
| 441 | D4 | — | 16 | 2 | no | — |
| 442 | D4 | — | 16 | 6 | no | — |
| 443 | D4 | — | 16 | 1 | no | — |
| 444 | D4 | — | 16 | 3 | no | — |
| 445 | C2×C4 | — | 2 | 3 | no | — |
| 446 | C2×C4 | — | 2 | 3 | no | — |
| 447 | C2×C4 | — | 2 | 3 | no | — |
| 448 | C2×C4 | — | 2 | 3 | no | — |
| 449 | C2×C4 | — | 4 | 6 | no | — |
| 450 | C2×C4 | — | 8 | 3 | no | — |
| 451 | C2×C4 | — | 8 | 3 | no | — |
| 452 | C2×C4 | — | 8 | 3 | no | — |
| 453 | C2×C4 | — | 8 | 3 | no | — |
| 454 | C2×C4 | — | 8 | 3 | no | — |
| 455 | C2×C4 | — | 8 | 3 | no | — |
| 456 | C2×C4 | — | 8 | 24 | no | — |
| 457 | C2×C4 | — | 8 | 3 | no | — |
| 458 | C2×C4 | — | 8 | 3 | no | — |
| 459 | C2×C4 | — | 8 | 6 | no | — |
| 460 | C2×C4 | — | 8 | 6 | no | — |
| 461 | C2×C4 | — | 8 | 6 | no | — |
| 462 | C2×C4 | — | 8 | 6 | no | — |
| 463 | C2×C4 | — | 8 | 6 | no | — |
| 464 | C2×C4 | — | 16 | 2 | no | — |
| 465 | C2×C4 | — | 16 | 6 | no | — |
| 466 | C2×C4 | #1595 | 1 | 3 | yes | — |
| 467 | C2×C4 | #1595 | 1 | 3 | yes | — |
| 468 | C2×C4 | #1619 | 1 | 3 | yes | — |
| 469 | C2×C4 | #1619 | 1 | 3 | yes | — |
| 470 | C2×C4 | #1619 | 1 | 6 | yes | — |
| 471 | C2×C4 | #1655 | 1 | 1 | yes | characteristic |
| 472 | C2×C4 | #1655 | 1 | 3 | yes | — |
| 473 | C2×C4 | C2×#447 | 1 | 3 | yes | — |
| 474 | C2×C4 | C2×#453 | 1 | 3 | yes | — |
| 475 | C8 | — | 8 | 12 | no | — |
| 476 | C8 | — | 8 | 6 | no | — |
| 477 | C22 | — | 4 | 1 | no | — |
| 478 | C22 | — | 4 | 3 | no | — |
| 479 | C22 | — | 4 | 3 | no | — |
| 480 | C22 | — | 8 | 6 | no | — |
| 481 | C22 | — | 16 | 6 | no | — |
| 482 | C22 | — | 16 | 6 | no | — |
| 483 | C22 | — | 16 | 6 | no | — |
| 484 | C22 | — | 16 | 6 | no | — |
| 485 | C22 | — | 16 | 2 | no | — |
| 486 | C22 | — | 32 | 3 | no | — |
| 487 | C22 | — | 32 | 8 | no | — |
| 488 | C22 | #7734 | 1 | 1 | yes | characteristic |
| 489 | C22 | #7734 | 1 | 3 | yes | — |
| 490 | C22 | C2×#1595 | 1 | 3 | yes | — |
| 491 | C4 | — | 4 | 3 | no | — |
| 492 | C4 | — | 4 | 3 | no | — |
| 493 | C4 | — | 4 | 3 | no | — |
| 494 | C4 | — | 4 | 3 | no | — |
| 495 | C4 | — | 8 | 6 | no | — |
| 496 | C4 | — | 16 | 2 | no | — |
| 497 | C4 | #7734 | 1 | 1 | yes | characteristic |
| 498 | C4 | #7734 | 1 | 3 | yes | — |
| 499 | C4 | C2×#1619 | 1 | 3 | yes | — |
| 500 | C4 | C2×#1655 | 1 | 1 | yes | characteristic |
| 501 | C2 | — | 2 | 3 | no | — |
| 502 | C2 | — | 2 | 1 | no | — |
| 503 | C2 | — | 2 | 3 | no | — |
| 504 | C2 | — | 16 | 6 | no | — |
| 505 | C2 | — | 32 | 2 | no | — |
| 506 | C2 | C2×#7734 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#1655 |
| commutator, Frattini, cosocle | #376 | C24 |
| socle | C2 | C2×#7734 |
| LCS | G ▷ #376 ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4 ◁ C23×C4 ◁ C2×#376 ◁ G | |
| LECS | G ▷ #376 ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#31077 | C2 | semidirect |
| 2. #233619 | C2 | semidirect |
| 3. #125651 | C2 | semidirect |
| 4. C2×#7115 | C2 | semidirect |
| 7. #34641 | C22 | semidirect |
| 14. #10012 | C22 | semidirect |
| 15. C2×#1274 | C22 | semidirect |
| 16. #7115 | C22 | semidirect |
| 46. #2397 | C23 | semidirect |
| 58. #1274 | C23 | semidirect |
| 88. #532 | D8 | semidirect |
| 91. C2×C4⋊Q8 | D8 | semidirect |
| 93. C2×#127 | D8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#31077 | 2 |
| #233619 | 2 |
| #125651 | 2 |
| C2×#7115 | 2 |