Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
1885 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#3416 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62624 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #60472 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #60471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #33619 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #33618 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #33617 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | C2×#2223 | C2 | 1 | 6 | yes | maximal, complemented |
| 9 | #33414 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #33393 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #33392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #3586 | — | 2 | 1 | no | — |
| 13 | #3585 | — | 2 | 1 | no | — |
| 14 | C2×#578 | C22 | 1 | 1 | yes | characteristic |
| 15 | C2×#576 | C22 | 1 | 1 | yes | characteristic |
| 16 | #3573 | C22 | 1 | 1 | yes | characteristic |
| 17 | #3416 | — | 2 | 4 | no | — |
| 18 | #3416 | — | 2 | 4 | no | — |
| 19 | C2×#510 | C22 | 1 | 3 | yes | complemented |
| 20 | C2×#509 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×#508 | C22 | 1 | 3 | yes | complemented |
| 22 | C22×SD32 | C22 | 1 | 3 | yes | complemented |
| 23 | #3407 | — | 2 | 4 | no | — |
| 24 | #3407 | C22 | 1 | 1 | yes | characteristic |
| 25 | #3407 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×#504 | — | 2 | 4 | no | — |
| 27 | C2×#504 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#504 | C22 | 1 | 6 | yes | complemented |
| 29 | #3069 | — | 2 | 6 | no | — |
| 30 | #3068 | — | 2 | 6 | no | — |
| 31 | #3067 | C22 | 1 | 6 | yes | — |
| 32 | #3067 | C22 | 1 | 6 | yes | complemented |
| 33 | C2×#473 | C22 | 1 | 6 | yes | complemented |
| 34 | C2×#472 | C22 | 1 | 6 | yes | — |
| 35 | #2916 | C22 | 1 | 1 | yes | characteristic |
| 36 | #2916 | C22 | 1 | 1 | yes | characteristic |
| 37 | #2889 | — | 2 | 1 | no | — |
| 38 | #2888 | — | 2 | 1 | no | — |
| 39 | #2223 | C22 | 1 | 12 | yes | complemented |
| 40 | #2223 | C22 | 1 | 24 | yes | complemented |
| 41 | #2223 | C22 | 1 | 4 | yes | complemented |
| 42 | #2222 | C22 | 1 | 12 | yes | complemented |
| 43 | #2221 | C22 | 1 | 12 | yes | complemented |
| 44 | #2161 | C22 | 1 | 6 | yes | complemented |
| 45 | C2×#368 | C22 | 1 | 6 | yes | complemented |
| 46 | #2148 | C22 | 1 | 6 | yes | complemented |
| 47 | #2148 | C22 | 1 | 6 | yes | complemented |
| 48 | C2×#362 | C22 | 1 | 6 | yes | complemented |
| 49 | C2×#361 | C22 | 1 | 6 | yes | complemented |
| 50 | #585 | D4 | 1 | 1 | yes | characteristic |
| 51 | C2×2−1+4 | — | 2 | 1 | no | — |
| 52 | C2×H(5,𝔽2) | — | 2 | 1 | no | — |
| 53 | #578 | — | 2 | 4 | no | — |
| 54 | #578 | — | 2 | 4 | no | — |
| 55 | #578 | — | 4 | 4 | no | — |
| 56 | #577 | — | 4 | 4 | no | — |
| 57 | #577 | — | 4 | 4 | no | — |
| 58 | #576 | — | 2 | 4 | no | — |
| 59 | #576 | — | 2 | 4 | no | — |
| 60 | #576 | — | 4 | 4 | no | — |
| 61 | #575 | — | 2 | 6 | no | — |
| 62 | #575 | — | 2 | 6 | no | — |
| 63 | C2×#137 | — | 2 | 6 | no | — |
| 64 | C2×#137 | — | 2 | 3 | no | — |
| 65 | C2×AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 66 | C2×AGL(1,ℤ/8) | — | 2 | 3 | no | — |
| 67 | C2×#135 | C23 | 1 | 3 | yes | — |
| 68 | C2×#135 | C23 | 1 | 3 | yes | — |
| 69 | C22×Q16 | C23 | 1 | 3 | yes | — |
| 70 | C22×D8 | C23 | 1 | 3 | yes | — |
| 71 | #568 | — | 2 | 4 | no | — |
| 72 | #568 | — | 2 | 1 | no | — |
| 73 | #568 | — | 2 | 1 | no | — |
| 74 | #568 | D4 | 1 | 6 | yes | — |
| 75 | #568 | D4 | 1 | 1 | yes | characteristic |
| 76 | C2×#131 | — | 2 | 4 | no | — |
| 77 | C2×#131 | C23 | 1 | 6 | yes | — |
| 78 | C2×#131 | C23 | 1 | 1 | yes | characteristic |
| 79 | #510 | — | 2 | 12 | no | — |
| 80 | #509 | — | 2 | 12 | no | — |
| 81 | #508 | — | 2 | 6 | no | — |
| 82 | #508 | — | 2 | 6 | no | — |
| 83 | C2×Q32 | C23 | 1 | 3 | yes | — |
| 84 | C2×SD32 | — | 2 | 6 | no | — |
| 85 | C2×SD32 | — | 2 | 6 | no | — |
| 86 | C2×SD32 | C23 | 1 | 3 | yes | — |
| 87 | C2×SD32 | C23 | 1 | 6 | yes | — |
| 88 | C2×SD32 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×D16 | C23 | 1 | 3 | yes | — |
| 90 | #504 | — | 2 | 4 | no | — |
| 91 | #504 | — | 2 | 12 | no | — |
| 92 | #504 | — | 2 | 6 | no | — |
| 93 | #504 | — | 2 | 6 | no | — |
| 94 | #504 | D4 | 1 | 4 | yes | — |
| 95 | #504 | D4 | 1 | 4 | yes | — |
| 96 | #504 | C23 | 1 | 4 | yes | — |
| 97 | #504 | C23 | 1 | 12 | yes | — |
| 98 | C2×M32 | — | 2 | 12 | no | — |
| 99 | C2×M32 | — | 2 | 6 | no | — |
| 100 | C2×M32 | C23 | 1 | 6 | yes | — |
| 101 | C2×M32 | C23 | 1 | 3 | yes | — |
| 102 | C22×C16 | — | 2 | 6 | no | — |
| 103 | C22×C16 | C23 | 1 | 3 | yes | — |
| 104 | #473 | — | 2 | 12 | no | — |
| 105 | #473 | C23 | 1 | 4 | yes | — |
| 106 | #473 | C23 | 1 | 12 | yes | — |
| 107 | #472 | — | 2 | 12 | no | — |
| 108 | #472 | C23 | 1 | 4 | yes | — |
| 109 | #472 | C23 | 1 | 12 | yes | — |
| 110 | #471 | — | 2 | 12 | no | — |
| 111 | #471 | — | 2 | 12 | no | — |
| 112 | #430 | — | 2 | 3 | no | — |
| 113 | #430 | — | 2 | 3 | no | — |
| 114 | C2×#108 | C23 | 1 | 6 | yes | — |
| 115 | C2×#108 | C23 | 1 | 6 | yes | — |
| 116 | #413 | — | 2 | 6 | no | — |
| 117 | #413 | — | 2 | 6 | no | — |
| 118 | C2×#101 | — | 2 | 6 | no | — |
| 119 | C2×#100 | — | 2 | 6 | no | — |
| 120 | #368 | C23 | 1 | 4 | yes | — |
| 121 | #368 | C23 | 1 | 12 | yes | — |
| 122 | #362 | C23 | 1 | 12 | yes | — |
| 123 | #362 | C23 | 1 | 4 | yes | — |
| 124 | #361 | C23 | 1 | 12 | yes | — |
| 125 | #361 | C23 | 1 | 4 | yes | — |
| 126 | 2−1+4 | — | 2 | 1 | no | — |
| 127 | 2−1+4 | — | 4 | 4 | no | — |
| 128 | 2−1+4 | — | 4 | 4 | no | — |
| 129 | 2−1+4 | D8 | 1 | 4 | yes | — |
| 130 | H(5,𝔽2) | — | 2 | 3 | no | — |
| 131 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 132 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 133 | H(5,𝔽2) | D8 | 1 | 4 | yes | — |
| 134 | C2×#41 | — | 2 | 4 | no | — |
| 135 | C2×#41 | — | 2 | 3 | no | — |
| 136 | C2×#41 | — | 2 | 3 | no | — |
| 137 | C2×#41 | — | 4 | 1 | no | — |
| 138 | C2×#41 | — | 4 | 3 | no | — |
| 139 | C2×#41 | C2×D4 | 1 | 6 | yes | — |
| 140 | C2×#41 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | C22×Q8 | — | 2 | 3 | no | — |
| 142 | C22×Q8 | — | 4 | 1 | no | — |
| 143 | C22×D4 | — | 2 | 3 | no | — |
| 144 | C22×D4 | — | 4 | 3 | no | — |
| 145 | #137 | — | 2 | 12 | no | — |
| 146 | #137 | — | 2 | 4 | no | — |
| 147 | #137 | — | 4 | 12 | no | — |
| 148 | #137 | — | 4 | 6 | no | — |
| 149 | #137 | — | 4 | 6 | no | — |
| 150 | #137 | — | 4 | 12 | no | — |
| 151 | AGL(1,ℤ/8) | — | 2 | 12 | no | — |
| 152 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 153 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 154 | AGL(1,ℤ/8) | — | 4 | 6 | no | — |
| 155 | AGL(1,ℤ/8) | — | 4 | 6 | no | — |
| 156 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 157 | #135 | — | 2 | 6 | no | — |
| 158 | #135 | — | 2 | 6 | no | — |
| 159 | #135 | — | 2 | 6 | no | — |
| 160 | #135 | — | 2 | 6 | no | — |
| 161 | #135 | — | 4 | 12 | no | — |
| 162 | #135 | — | 4 | 12 | no | — |
| 163 | C2×Q16 | — | 2 | 6 | no | — |
| 164 | C2×Q16 | — | 2 | 3 | no | — |
| 165 | C2×Q16 | — | 2 | 6 | no | — |
| 166 | C2×Q16 | — | 4 | 6 | no | — |
| 167 | C2×Q16 | C24 | 1 | 3 | yes | — |
| 168 | C2×Q16 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×SD16 | — | 2 | 3 | no | — |
| 170 | C2×SD16 | — | 2 | 3 | no | — |
| 171 | C2×SD16 | — | 4 | 6 | no | — |
| 172 | C2×SD16 | — | 4 | 6 | no | — |
| 173 | C2×D8 | — | 2 | 6 | no | — |
| 174 | C2×D8 | — | 2 | 3 | no | — |
| 175 | C2×D8 | — | 2 | 6 | no | — |
| 176 | C2×D8 | — | 4 | 6 | no | — |
| 177 | C2×D8 | C24 | 1 | 3 | yes | — |
| 178 | C2×D8 | C24 | 1 | 1 | yes | characteristic |
| 179 | #131 | — | 2 | 4 | no | — |
| 180 | #131 | — | 2 | 12 | no | — |
| 181 | #131 | — | 2 | 6 | no | — |
| 182 | #131 | — | 2 | 6 | no | — |
| 183 | #131 | — | 4 | 4 | no | — |
| 184 | #131 | — | 4 | 4 | no | — |
| 185 | #131 | C2×D4 | 1 | 12 | yes | — |
| 186 | #131 | C2×D4 | 1 | 4 | yes | — |
| 187 | #131 | #41 | 1 | 4 | yes | — |
| 188 | #131 | C24 | 1 | 4 | yes | — |
| 189 | C2×M16 | — | 2 | 12 | no | — |
| 190 | C2×M16 | — | 2 | 6 | no | — |
| 191 | C2×M16 | — | 2 | 6 | no | — |
| 192 | C2×M16 | — | 2 | 6 | no | — |
| 193 | C2×M16 | C2×D4 | 1 | 6 | yes | — |
| 194 | C2×M16 | C2×D4 | 1 | 3 | yes | — |
| 195 | C22×C8 | — | 2 | 6 | no | — |
| 196 | C22×C8 | C24 | 1 | 3 | yes | — |
| 197 | Q32 | — | 2 | 6 | no | — |
| 198 | SD32 | — | 2 | 3 | no | — |
| 199 | SD32 | — | 2 | 3 | no | — |
| 200 | SD32 | — | 2 | 12 | no | — |
| 201 | SD32 | — | 2 | 1 | no | — |
| 202 | SD32 | — | 2 | 1 | no | — |
| 203 | D16 | — | 2 | 6 | no | — |
| 204 | M32 | — | 2 | 6 | no | — |
| 205 | M32 | — | 2 | 12 | no | — |
| 206 | M32 | — | 2 | 4 | no | — |
| 207 | M32 | C2×D4 | 1 | 12 | yes | — |
| 208 | M32 | C24 | 1 | 4 | yes | — |
| 209 | C2×C16 | — | 2 | 6 | no | — |
| 210 | C2×C16 | — | 2 | 4 | no | — |
| 211 | C2×C16 | — | 2 | 12 | no | — |
| 212 | C2×C16 | C2×D4 | 1 | 6 | yes | — |
| 213 | C2×C16 | C2×D4 | 1 | 6 | yes | — |
| 214 | C2×C16 | C24 | 1 | 1 | yes | characteristic |
| 215 | C2×C16 | C24 | 1 | 3 | yes | — |
| 216 | #108 | — | 2 | 6 | no | — |
| 217 | #108 | — | 2 | 6 | no | — |
| 218 | #108 | C24 | 1 | 4 | yes | — |
| 219 | #108 | C24 | 1 | 4 | yes | — |
| 220 | #101 | — | 2 | 12 | no | — |
| 221 | #101 | — | 2 | 4 | no | — |
| 222 | #100 | — | 2 | 12 | no | — |
| 223 | #100 | — | 2 | 4 | no | — |
| 224 | C24 | — | 4 | 3 | no | — |
| 225 | #41 | — | 2 | 4 | no | — |
| 226 | #41 | — | 2 | 12 | no | — |
| 227 | #41 | — | 2 | 6 | no | — |
| 228 | #41 | — | 2 | 6 | no | — |
| 229 | #41 | — | 4 | 6 | no | — |
| 230 | #41 | — | 4 | 6 | no | — |
| 231 | #41 | — | 4 | 6 | no | — |
| 232 | #41 | — | 4 | 6 | no | — |
| 233 | #41 | — | 8 | 4 | no | — |
| 234 | #41 | — | 8 | 12 | no | — |
| 235 | #41 | #121 | 1 | 4 | yes | — |
| 236 | #41 | C2×D8 | 1 | 12 | yes | — |
| 237 | #41 | C2×D8 | 1 | 4 | yes | — |
| 238 | #41 | C22×D4 | 1 | 4 | yes | — |
| 239 | C2×Q8 | — | 2 | 4 | no | — |
| 240 | C2×Q8 | — | 2 | 1 | no | — |
| 241 | C2×Q8 | — | 2 | 3 | no | — |
| 242 | C2×Q8 | — | 4 | 3 | no | — |
| 243 | C2×Q8 | — | 4 | 6 | no | — |
| 244 | C2×Q8 | — | 4 | 6 | no | — |
| 245 | C2×Q8 | — | 8 | 4 | no | — |
| 246 | C2×Q8 | C2×D8 | 1 | 6 | yes | — |
| 247 | C2×Q8 | #135 | 1 | 1 | yes | characteristic |
| 248 | C2×D4 | — | 2 | 6 | no | — |
| 249 | C2×D4 | — | 2 | 12 | no | — |
| 250 | C2×D4 | — | 2 | 3 | no | — |
| 251 | C2×D4 | — | 2 | 1 | no | — |
| 252 | C2×D4 | — | 4 | 3 | no | — |
| 253 | C2×D4 | — | 4 | 3 | no | — |
| 254 | C2×D4 | — | 4 | 6 | no | — |
| 255 | C2×D4 | — | 4 | 6 | no | — |
| 256 | C2×D4 | — | 4 | 3 | no | — |
| 257 | C2×D4 | — | 8 | 12 | no | — |
| 258 | C2×D4 | C2×D8 | 1 | 6 | yes | — |
| 259 | C2×D4 | #135 | 1 | 3 | yes | — |
| 260 | C22×C4 | — | 2 | 6 | no | — |
| 261 | C22×C4 | — | 4 | 3 | no | — |
| 262 | C22×C4 | — | 4 | 3 | no | — |
| 263 | C22×C4 | — | 4 | 3 | no | — |
| 264 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 265 | Q16 | — | 2 | 3 | no | — |
| 266 | Q16 | — | 2 | 1 | no | — |
| 267 | Q16 | — | 2 | 3 | no | — |
| 268 | Q16 | — | 2 | 1 | no | — |
| 269 | Q16 | — | 4 | 12 | no | — |
| 270 | Q16 | — | 4 | 4 | no | — |
| 271 | Q16 | — | 4 | 6 | no | — |
| 272 | SD16 | — | 4 | 12 | no | — |
| 273 | SD16 | — | 4 | 4 | no | — |
| 274 | SD16 | — | 4 | 12 | no | — |
| 275 | SD16 | — | 4 | 4 | no | — |
| 276 | SD16 | — | 4 | 6 | no | — |
| 277 | SD16 | — | 4 | 6 | no | — |
| 278 | D8 | — | 2 | 1 | no | — |
| 279 | D8 | — | 2 | 3 | no | — |
| 280 | D8 | — | 2 | 3 | no | — |
| 281 | D8 | — | 2 | 1 | no | — |
| 282 | D8 | — | 4 | 12 | no | — |
| 283 | D8 | — | 4 | 4 | no | — |
| 284 | D8 | — | 4 | 6 | no | — |
| 285 | M16 | — | 2 | 6 | no | — |
| 286 | M16 | — | 2 | 12 | no | — |
| 287 | M16 | — | 2 | 4 | no | — |
| 288 | M16 | — | 2 | 4 | no | — |
| 289 | M16 | — | 2 | 4 | no | — |
| 290 | M16 | — | 4 | 6 | no | — |
| 291 | M16 | — | 4 | 6 | no | — |
| 292 | M16 | #121 | 1 | 12 | yes | — |
| 293 | M16 | C22×D4 | 1 | 4 | yes | — |
| 294 | C2×C8 | — | 2 | 6 | no | — |
| 295 | C2×C8 | — | 2 | 12 | no | — |
| 296 | C2×C8 | — | 2 | 4 | no | — |
| 297 | C2×C8 | — | 4 | 6 | no | — |
| 298 | C2×C8 | — | 4 | 6 | no | — |
| 299 | C2×C8 | C22×D4 | 1 | 3 | yes | — |
| 300 | C2×C8 | C22×D4 | 1 | 6 | yes | — |
| 301 | C2×C8 | C2×#41 | 1 | 6 | yes | — |
| 302 | C2×C8 | C25 | 1 | 1 | yes | characteristic |
| 303 | C16 | — | 2 | 4 | no | — |
| 304 | C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 305 | C16 | C22×D4 | 1 | 6 | yes | — |
| 306 | C16 | C22×D4 | 1 | 1 | yes | characteristic |
| 307 | C23 | — | 2 | 6 | no | — |
| 308 | C23 | — | 4 | 1 | no | — |
| 309 | C23 | — | 4 | 3 | no | — |
| 310 | C23 | — | 8 | 6 | no | — |
| 311 | C23 | — | 32 | 3 | no | — |
| 312 | C23 | C2×#135 | 1 | 3 | yes | — |
| 313 | Q8 | — | 2 | 6 | no | — |
| 314 | Q8 | — | 4 | 1 | no | — |
| 315 | Q8 | — | 4 | 3 | no | — |
| 316 | Q8 | — | 4 | 3 | no | — |
| 317 | Q8 | — | 4 | 1 | no | — |
| 318 | Q8 | — | 8 | 6 | no | — |
| 319 | Q8 | #466 | 1 | 4 | yes | — |
| 320 | Q8 | C22×D8 | 1 | 4 | yes | — |
| 321 | D4 | — | 2 | 12 | no | — |
| 322 | D4 | — | 2 | 4 | no | — |
| 323 | D4 | — | 2 | 6 | no | — |
| 324 | D4 | — | 4 | 3 | no | — |
| 325 | D4 | — | 4 | 1 | no | — |
| 326 | D4 | — | 4 | 3 | no | — |
| 327 | D4 | — | 4 | 1 | no | — |
| 328 | D4 | — | 8 | 6 | no | — |
| 329 | D4 | — | 8 | 6 | no | — |
| 330 | D4 | — | 8 | 6 | no | — |
| 331 | D4 | #466 | 1 | 12 | yes | — |
| 332 | D4 | C22×D8 | 1 | 4 | yes | — |
| 333 | C2×C4 | — | 2 | 6 | no | — |
| 334 | C2×C4 | — | 2 | 4 | no | — |
| 335 | C2×C4 | — | 2 | 12 | no | — |
| 336 | C2×C4 | — | 4 | 1 | no | — |
| 337 | C2×C4 | — | 4 | 3 | no | — |
| 338 | C2×C4 | — | 8 | 6 | no | — |
| 339 | C2×C4 | — | 8 | 6 | no | — |
| 340 | C2×C4 | — | 8 | 6 | no | — |
| 341 | C2×C4 | C2×#121 | 1 | 6 | yes | — |
| 342 | C2×C4 | C22×D8 | 1 | 6 | yes | — |
| 343 | C2×C4 | C2×#135 | 1 | 3 | yes | — |
| 344 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 345 | C8 | — | 2 | 4 | no | — |
| 346 | C8 | — | 4 | 4 | no | — |
| 347 | C8 | — | 4 | 4 | no | — |
| 348 | C8 | C2×#121 | 1 | 6 | yes | — |
| 349 | C8 | C23×D4 | 1 | 1 | yes | characteristic |
| 350 | C8 | C22×#41 | 1 | 1 | yes | characteristic |
| 351 | C22 | — | 2 | 4 | no | — |
| 352 | C22 | — | 4 | 3 | no | — |
| 353 | C22 | — | 8 | 6 | no | — |
| 354 | C22 | — | 8 | 1 | no | — |
| 355 | C22 | — | 8 | 3 | no | — |
| 356 | C22 | — | 16 | 1 | no | — |
| 357 | C22 | — | 16 | 3 | no | — |
| 358 | C22 | — | 32 | 6 | no | — |
| 359 | C22 | C2×#466 | 1 | 6 | yes | — |
| 360 | C22 | C22×#135 | 1 | 1 | yes | characteristic |
| 361 | C4 | — | 2 | 4 | no | — |
| 362 | C4 | — | 8 | 1 | no | — |
| 363 | C4 | — | 8 | 3 | no | — |
| 364 | C4 | C2×#466 | 1 | 6 | yes | — |
| 365 | C4 | C22×#121 | 1 | 1 | yes | characteristic |
| 366 | C4 | C23×D8 | 1 | 1 | yes | characteristic |
| 367 | C2 | — | 2 | 1 | no | — |
| 368 | C2 | — | 2 | 6 | no | — |
| 369 | C2 | — | 4 | 4 | no | — |
| 370 | C2 | — | 16 | 1 | no | — |
| 371 | C2 | — | 16 | 3 | no | — |
| 372 | C2 | C22×#466 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#466 |
| commutator, Frattini, cosocle | C2×C8 | C25 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #3573 ◁ G | |
| LECS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#3416 | C2 | semidirect |
| 2. #62624 | C2 | semidirect |
| 3. #60472 | C2 | semidirect |
| 4. #60471 | C2 | semidirect |
| 5. #33619 | C2 | semidirect |
| 6. #33618 | C2 | semidirect |
| 7. #33617 | C2 | semidirect |
| 8. C2×#2223 | C2 | semidirect |
| 9. #33414 | C2 | semidirect |
| 10. #33393 | C2 | semidirect |
| 11. #33392 | C2 | semidirect |
| 19. C2×#510 | C22 | semidirect |
| 20. C2×#509 | C22 | semidirect |
| 21. C2×#508 | C22 | semidirect |
| 22. C22×SD32 | C22 | semidirect |
| 25. #3407 | C22 | semidirect |
| 28. C2×#504 | C22 | semidirect |
| 32. #3067 | C22 | semidirect |
| 33. C2×#473 | C22 | semidirect |
| 39. #2223 | C22 | semidirect |
| 40. #2223 | C22 | semidirect |
| 41. #2223 | C22 | semidirect |
| 42. #2222 | C22 | semidirect |
| 43. #2221 | C22 | semidirect |
| 44. #2161 | C22 | semidirect |
| 45. C2×#368 | C22 | semidirect |
| 46. #2148 | C22 | semidirect |
| 47. #2148 | C22 | semidirect |
| 48. C2×#362 | C22 | semidirect |
| 49. C2×#361 | C22 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3416 | 2 |
| #62624 | 2 |
| #60472 | 2 |
| #60471 | 2 |
| #33619 | 2 |
| #33618 | 2 |
| #33617 | 2 |
| C2×#2223 | 2 |
| #33414 | 2 |
| #33393 | 2 |
| #33392 | 2 |