Finite Group DatabasebetaFinite Group DatabasebetaOrder 512.
5973 conjugacy classes of subgroups.
The subgroup lattice has 368 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #63076 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #62859 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #60088 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #60070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21009 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | C2×#1909 | C2 | 1 | 12 | yes | maximal, complemented |
| 7 | #20338 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#585 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×2−1+4 | C22 | 1 | 1 | yes | characteristic |
| 10 | #3573 | — | 2 | 16 | no | — |
| 11 | C2×#568 | — | 2 | 8 | no | — |
| 12 | C2×#568 | C22 | 1 | 12 | yes | — |
| 13 | C2×#568 | C22 | 1 | 2 | yes | — |
| 14 | #3500 | C4 | 1 | 8 | yes | complemented |
| 15 | #3499 | C4 | 1 | 8 | yes | complemented |
| 16 | #3489 | — | 2 | 8 | no | — |
| 17 | #3486 | — | 2 | 2 | no | — |
| 18 | #3485 | — | 2 | 6 | no | — |
| 19 | #3449 | C22 | 1 | 6 | yes | — |
| 20 | C2×#536 | C22 | 1 | 6 | yes | — |
| 21 | #3428 | C22 | 1 | 2 | yes | — |
| 22 | #3428 | C22 | 1 | 1 | yes | characteristic |
| 23 | #2898 | — | 2 | 16 | no | — |
| 24 | #2896 | C22 | 1 | 12 | yes | complemented |
| 25 | C2×#419 | C22 | 1 | 12 | yes | complemented |
| 26 | #2884 | — | 2 | 2 | no | — |
| 27 | #2883 | — | 2 | 6 | no | — |
| 28 | C2×#410 | C22 | 1 | 12 | yes | — |
| 29 | #1910 | C22 | 1 | 16 | yes | complemented |
| 30 | #1909 | C22 | 1 | 48 | yes | complemented |
| 31 | C2×H(3,ℤ/4) | C22 | 1 | 24 | yes | complemented |
| 32 | #585 | — | 2 | 8 | no | — |
| 33 | #585 | — | 2 | 8 | no | — |
| 34 | C2×2−1+4 | — | 2 | 4 | no | — |
| 35 | C2×2−1+4 | — | 2 | 8 | no | — |
| 36 | C2×2−1+4 | — | 2 | 8 | no | — |
| 37 | C2×2−1+4 | C2×C4 | 1 | 8 | yes | — |
| 38 | C2×2−1+4 | C2×C4 | 1 | 4 | yes | — |
| 39 | C2×2−1+4 | D4 | 1 | 2 | yes | — |
| 40 | C2×H(5,𝔽2) | C2×C4 | 1 | 4 | yes | — |
| 41 | C2×H(5,𝔽2) | D4 | 1 | 6 | yes | — |
| 42 | C22×#41 | — | 2 | 3 | no | — |
| 43 | C22×#41 | D4 | 1 | 8 | yes | — |
| 44 | C22×#41 | C23 | 1 | 3 | yes | — |
| 45 | C22×#41 | C23 | 1 | 6 | yes | — |
| 46 | C22×#41 | C23 | 1 | 1 | yes | characteristic |
| 47 | C23×Q8 | — | 2 | 1 | no | — |
| 48 | C23×Q8 | C23 | 1 | 3 | yes | — |
| 49 | #568 | — | 2 | 64 | no | — |
| 50 | #568 | — | 2 | 24 | no | — |
| 51 | #568 | — | 2 | 8 | no | — |
| 52 | #568 | — | 2 | 8 | no | — |
| 53 | #568 | — | 2 | 48 | no | — |
| 54 | #568 | C23 | 1 | 16 | yes | — |
| 55 | C2×#131 | — | 2 | 64 | no | — |
| 56 | C2×#131 | — | 2 | 48 | no | — |
| 57 | C2×#131 | D4 | 1 | 16 | yes | complemented |
| 58 | C22×M16 | — | 2 | 24 | no | — |
| 59 | C22×M16 | C23 | 1 | 12 | yes | — |
| 60 | D4×Q8 | — | 2 | 16 | no | — |
| 61 | #548 | — | 2 | 16 | no | — |
| 62 | #547 | — | 2 | 48 | no | — |
| 63 | #546 | — | 2 | 48 | no | — |
| 64 | #537 | — | 2 | 12 | no | — |
| 65 | #536 | — | 2 | 12 | no | — |
| 66 | #536 | — | 2 | 12 | no | — |
| 67 | #536 | C2×C4 | 1 | 24 | yes | complemented |
| 68 | #536 | C2×C4 | 1 | 12 | yes | complemented |
| 69 | #536 | C23 | 1 | 12 | yes | — |
| 70 | #535 | C2×C4 | 1 | 12 | yes | complemented |
| 71 | #535 | C23 | 1 | 4 | yes | — |
| 72 | #534 | — | 2 | 12 | no | — |
| 73 | #532 | C2×C4 | 1 | 24 | yes | complemented |
| 74 | C2×C4⋊Q8 | C2×C4 | 1 | 12 | yes | complemented |
| 75 | C2×#124 | C2×C4 | 1 | 12 | yes | complemented |
| 76 | #525 | — | 2 | 12 | no | — |
| 77 | #525 | — | 2 | 12 | no | — |
| 78 | C2×#123 | — | 2 | 12 | no | — |
| 79 | C2×C22⋊Q8 | — | 2 | 12 | no | — |
| 80 | #520 | — | 2 | 4 | no | — |
| 81 | #520 | — | 2 | 8 | no | — |
| 82 | #519 | — | 2 | 1 | no | — |
| 83 | #519 | — | 2 | 2 | no | — |
| 84 | #518 | — | 2 | 3 | no | — |
| 85 | #518 | — | 2 | 6 | no | — |
| 86 | C4×#41 | — | 2 | 8 | no | — |
| 87 | C4×#41 | C2×C4 | 1 | 8 | yes | — |
| 88 | C2×#117 | C23 | 1 | 12 | yes | — |
| 89 | C2×#117 | C23 | 1 | 6 | yes | — |
| 90 | #419 | — | 2 | 24 | no | — |
| 91 | #419 | C23 | 1 | 24 | yes | — |
| 92 | #418 | C23 | 1 | 8 | yes | — |
| 93 | #417 | — | 2 | 24 | no | — |
| 94 | #416 | — | 2 | 24 | no | — |
| 95 | C2×#103 | — | 2 | 24 | no | — |
| 96 | #410 | — | 2 | 24 | no | — |
| 97 | #410 | C23 | 1 | 16 | yes | — |
| 98 | C2×#99 | — | 2 | 24 | no | — |
| 99 | H(3,ℤ/4) | C23 | 1 | 32 | yes | — |
| 100 | 2−1+4 | — | 2 | 32 | no | — |
| 101 | 2−1+4 | — | 2 | 16 | no | — |
| 102 | 2−1+4 | — | 2 | 64 | no | — |
| 103 | 2−1+4 | — | 4 | 16 | no | — |
| 104 | 2−1+4 | — | 4 | 16 | no | — |
| 105 | H(5,𝔽2) | — | 2 | 32 | no | — |
| 106 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 107 | C2×#41 | — | 2 | 32 | no | — |
| 108 | C2×#41 | — | 2 | 32 | no | — |
| 109 | C2×#41 | — | 2 | 24 | no | — |
| 110 | C2×#41 | — | 2 | 24 | no | — |
| 111 | C2×#41 | — | 2 | 6 | no | — |
| 112 | C2×#41 | — | 2 | 24 | no | — |
| 113 | C2×#41 | — | 2 | 12 | no | — |
| 114 | C2×#41 | — | 2 | 12 | no | — |
| 115 | C2×#41 | — | 4 | 24 | no | — |
| 116 | C2×#41 | C22⋊C4 | 1 | 24 | yes | — |
| 117 | C2×#41 | C22⋊C4 | 1 | 8 | yes | — |
| 118 | C2×#41 | C22×C4 | 1 | 12 | yes | — |
| 119 | C2×#41 | C22×C4 | 1 | 12 | yes | — |
| 120 | C2×#41 | C22×C4 | 1 | 4 | yes | — |
| 121 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 122 | C2×#41 | C2×D4 | 1 | 12 | yes | — |
| 123 | C2×#41 | C2×D4 | 1 | 4 | yes | — |
| 124 | C2×#41 | C2×D4 | 1 | 8 | yes | — |
| 125 | C2×#41 | #41 | 1 | 8 | yes | — |
| 126 | C2×#41 | C24 | 1 | 4 | yes | — |
| 127 | C22×Q8 | — | 2 | 8 | no | — |
| 128 | C22×Q8 | — | 2 | 6 | no | — |
| 129 | C22×Q8 | — | 2 | 3 | no | — |
| 130 | C22×Q8 | — | 2 | 12 | no | — |
| 131 | C22×Q8 | — | 2 | 12 | no | — |
| 132 | C22×Q8 | — | 4 | 8 | no | — |
| 133 | C22×Q8 | C22⋊C4 | 1 | 8 | yes | — |
| 134 | C22×Q8 | C22×C4 | 1 | 12 | yes | — |
| 135 | C22×Q8 | C22×C4 | 1 | 6 | yes | — |
| 136 | C22×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | C22×Q8 | C24 | 1 | 3 | yes | — |
| 138 | C22×D4 | — | 2 | 3 | no | — |
| 139 | C22×D4 | C22⋊C4 | 1 | 24 | yes | — |
| 140 | C22×D4 | C22×C4 | 1 | 6 | yes | — |
| 141 | C22×D4 | C2×D4 | 1 | 12 | yes | — |
| 142 | C22×D4 | C2×D4 | 1 | 3 | yes | — |
| 143 | C22×D4 | C24 | 1 | 1 | yes | characteristic |
| 144 | C23×C4 | — | 2 | 3 | no | — |
| 145 | C23×C4 | — | 2 | 3 | no | — |
| 146 | C23×C4 | C2×D4 | 1 | 12 | yes | — |
| 147 | C23×C4 | C24 | 1 | 3 | yes | — |
| 148 | #131 | — | 2 | 192 | no | — |
| 149 | #131 | — | 2 | 64 | no | — |
| 150 | #131 | — | 2 | 64 | no | — |
| 151 | C2×M16 | — | 2 | 96 | no | — |
| 152 | C2×M16 | — | 2 | 48 | no | — |
| 153 | C2×M16 | — | 2 | 32 | no | — |
| 154 | C2×M16 | — | 2 | 24 | no | — |
| 155 | C2×M16 | — | 2 | 24 | no | — |
| 156 | C2×M16 | C2×D4 | 1 | 24 | yes | — |
| 157 | C2×M16 | C24 | 1 | 8 | yes | — |
| 158 | C22×C8 | — | 2 | 48 | no | — |
| 159 | C22×C8 | C2×D4 | 1 | 24 | yes | — |
| 160 | C4⋊Q8 | — | 2 | 24 | no | — |
| 161 | C4⋊Q8 | C22×C4 | 1 | 24 | yes | — |
| 162 | #127 | C22×C4 | 1 | 8 | yes | — |
| 163 | #124 | — | 2 | 24 | no | — |
| 164 | #124 | C22×C4 | 1 | 24 | yes | — |
| 165 | #124 | C22×C4 | 1 | 8 | yes | — |
| 166 | #123 | — | 2 | 48 | no | — |
| 167 | #123 | — | 2 | 24 | no | — |
| 168 | #123 | — | 2 | 24 | no | — |
| 169 | C22⋊Q8 | — | 2 | 24 | no | — |
| 170 | C22⋊Q8 | — | 2 | 48 | no | — |
| 171 | C22⋊Q8 | — | 2 | 24 | no | — |
| 172 | #121 | — | 2 | 24 | no | — |
| 173 | #121 | — | 2 | 48 | no | — |
| 174 | #121 | — | 2 | 8 | no | — |
| 175 | #120 | — | 2 | 24 | no | — |
| 176 | #120 | — | 2 | 8 | no | — |
| 177 | C4×Q8 | — | 2 | 8 | no | — |
| 178 | C4×Q8 | — | 4 | 8 | no | — |
| 179 | C4×D4 | — | 2 | 24 | no | — |
| 180 | C4×D4 | — | 2 | 48 | no | — |
| 181 | C4×D4 | — | 4 | 24 | no | — |
| 182 | #117 | — | 2 | 6 | no | — |
| 183 | #117 | — | 2 | 6 | no | — |
| 184 | #117 | — | 2 | 12 | no | — |
| 185 | #117 | — | 2 | 12 | no | — |
| 186 | #117 | — | 2 | 12 | no | — |
| 187 | #117 | C22×C4 | 1 | 12 | yes | — |
| 188 | #117 | C24 | 1 | 8 | yes | — |
| 189 | #117 | C24 | 1 | 4 | yes | — |
| 190 | C2×C4⋊C4 | — | 2 | 24 | no | — |
| 191 | C2×C4⋊C4 | — | 2 | 6 | no | — |
| 192 | C2×C4⋊C4 | — | 2 | 12 | no | — |
| 193 | C2×C22⋊C4 | — | 2 | 24 | no | — |
| 194 | C2×C22⋊C4 | — | 2 | 6 | no | — |
| 195 | C2×C22⋊C4 | — | 2 | 12 | no | — |
| 196 | C2×C42 | — | 2 | 12 | no | — |
| 197 | C2×C42 | C22×C4 | 1 | 12 | yes | — |
| 198 | #103 | — | 2 | 48 | no | — |
| 199 | #102 | — | 2 | 16 | no | — |
| 200 | #99 | — | 2 | 32 | no | — |
| 201 | C24 | — | 2 | 1 | no | — |
| 202 | C24 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 203 | C24 | C22×D4 | 1 | 3 | yes | — |
| 204 | #41 | — | 2 | 32 | no | — |
| 205 | #41 | — | 2 | 96 | no | — |
| 206 | #41 | — | 2 | 48 | no | — |
| 207 | #41 | — | 2 | 24 | no | — |
| 208 | #41 | — | 2 | 48 | no | — |
| 209 | #41 | — | 2 | 24 | no | — |
| 210 | #41 | — | 2 | 8 | no | — |
| 211 | #41 | — | 2 | 8 | no | — |
| 212 | #41 | — | 2 | 48 | no | — |
| 213 | #41 | — | 4 | 96 | no | — |
| 214 | #41 | — | 4 | 12 | no | — |
| 215 | #41 | — | 4 | 12 | no | — |
| 216 | #41 | C4×D4 | 1 | 32 | yes | — |
| 217 | #41 | #120 | 1 | 16 | yes | — |
| 218 | #41 | #123 | 1 | 16 | yes | — |
| 219 | C2×Q8 | — | 2 | 32 | no | — |
| 220 | C2×Q8 | — | 2 | 12 | no | — |
| 221 | C2×Q8 | — | 2 | 24 | no | — |
| 222 | C2×Q8 | — | 2 | 3 | no | — |
| 223 | C2×Q8 | — | 2 | 48 | no | — |
| 224 | C2×Q8 | — | 2 | 6 | no | — |
| 225 | C2×Q8 | — | 2 | 6 | no | — |
| 226 | C2×Q8 | — | 4 | 32 | no | — |
| 227 | C2×Q8 | — | 4 | 12 | no | — |
| 228 | C2×Q8 | — | 4 | 12 | no | — |
| 229 | C2×Q8 | — | 4 | 12 | no | — |
| 230 | C2×Q8 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 231 | C2×Q8 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 232 | C2×Q8 | #121 | 1 | 8 | yes | — |
| 233 | C2×Q8 | C23×C4 | 1 | 6 | yes | — |
| 234 | C2×Q8 | C23×C4 | 1 | 4 | yes | — |
| 235 | C2×D4 | — | 2 | 48 | no | — |
| 236 | C2×D4 | — | 2 | 96 | no | — |
| 237 | C2×D4 | — | 2 | 12 | no | — |
| 238 | C2×D4 | — | 2 | 16 | no | — |
| 239 | C2×D4 | — | 2 | 24 | no | — |
| 240 | C2×D4 | — | 2 | 2 | no | — |
| 241 | C2×D4 | — | 2 | 1 | no | — |
| 242 | C2×D4 | — | 2 | 2 | no | — |
| 243 | C2×D4 | — | 4 | 12 | no | — |
| 244 | C2×D4 | C2×C22⋊C4 | 1 | 24 | yes | — |
| 245 | C2×D4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 246 | C2×D4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 247 | C2×D4 | #121 | 1 | 24 | yes | — |
| 248 | C2×D4 | C23×C4 | 1 | 2 | yes | — |
| 249 | C2×D4 | C23×C4 | 1 | 4 | yes | — |
| 250 | C2×D4 | C22×D4 | 1 | 8 | yes | — |
| 251 | C22×C4 | — | 2 | 24 | no | — |
| 252 | C22×C4 | — | 2 | 24 | no | — |
| 253 | C22×C4 | — | 2 | 12 | no | — |
| 254 | C22×C4 | — | 2 | 3 | no | — |
| 255 | C22×C4 | — | 2 | 12 | no | — |
| 256 | C22×C4 | — | 2 | 12 | no | — |
| 257 | C22×C4 | — | 4 | 12 | no | — |
| 258 | C22×C4 | — | 4 | 12 | no | — |
| 259 | C22×C4 | — | 4 | 12 | no | — |
| 260 | C22×C4 | C2×C22⋊C4 | 1 | 12 | yes | — |
| 261 | C22×C4 | C2×C22⋊C4 | 1 | 24 | yes | — |
| 262 | C22×C4 | C23×C4 | 1 | 6 | yes | — |
| 263 | C22×C4 | C22×D4 | 1 | 8 | yes | — |
| 264 | C22×C4 | C22×D4 | 1 | 3 | yes | — |
| 265 | C22×C4 | C22×D4 | 1 | 6 | yes | — |
| 266 | C22×C4 | C22×D4 | 1 | 12 | yes | — |
| 267 | C22×C4 | C2×#41 | 1 | 12 | yes | — |
| 268 | C22×C4 | C25 | 1 | 1 | yes | characteristic |
| 269 | M16 | — | 2 | 64 | no | — |
| 270 | M16 | — | 2 | 48 | no | — |
| 271 | M16 | — | 2 | 8 | no | — |
| 272 | M16 | — | 2 | 8 | no | — |
| 273 | C2×C8 | — | 2 | 64 | no | — |
| 274 | C2×C8 | — | 2 | 48 | no | — |
| 275 | C2×C8 | C22×D4 | 1 | 16 | yes | — |
| 276 | C4⋊C4 | — | 2 | 48 | no | — |
| 277 | C4⋊C4 | — | 2 | 12 | no | — |
| 278 | C4⋊C4 | — | 2 | 4 | no | — |
| 279 | C4⋊C4 | — | 2 | 8 | no | — |
| 280 | C4⋊C4 | — | 4 | 12 | no | — |
| 281 | C22⋊C4 | — | 2 | 48 | no | — |
| 282 | C22⋊C4 | — | 2 | 12 | no | — |
| 283 | C22⋊C4 | — | 2 | 4 | no | — |
| 284 | C22⋊C4 | — | 2 | 16 | no | — |
| 285 | C22⋊C4 | — | 2 | 8 | no | — |
| 286 | C22⋊C4 | — | 4 | 12 | no | — |
| 287 | C42 | — | 2 | 12 | no | — |
| 288 | C42 | — | 2 | 8 | no | — |
| 289 | C42 | — | 4 | 12 | no | — |
| 290 | C42 | C23×C4 | 1 | 8 | yes | — |
| 291 | C23 | — | 2 | 24 | no | — |
| 292 | C23 | — | 2 | 2 | no | — |
| 293 | C23 | — | 4 | 2 | no | — |
| 294 | C23 | — | 8 | 3 | no | — |
| 295 | C23 | — | 8 | 12 | no | — |
| 296 | C23 | — | 8 | 2 | no | — |
| 297 | C23 | C22×C22⋊C4 | 1 | 8 | yes | — |
| 298 | C23 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 299 | C23 | C2×#121 | 1 | 12 | yes | — |
| 300 | C23 | C23×D4 | 1 | 1 | yes | characteristic |
| 301 | Q8 | — | 2 | 8 | no | — |
| 302 | Q8 | — | 2 | 24 | no | — |
| 303 | Q8 | — | 2 | 12 | no | — |
| 304 | Q8 | — | 4 | 3 | no | — |
| 305 | Q8 | — | 4 | 3 | no | — |
| 306 | Q8 | — | 4 | 24 | no | — |
| 307 | Q8 | #386 | 1 | 16 | yes | — |
| 308 | D4 | — | 2 | 16 | no | — |
| 309 | D4 | — | 2 | 48 | no | — |
| 310 | D4 | — | 2 | 8 | no | — |
| 311 | D4 | — | 2 | 4 | no | — |
| 312 | D4 | — | 2 | 24 | no | — |
| 313 | D4 | — | 4 | 24 | no | — |
| 314 | D4 | — | 4 | 1 | no | — |
| 315 | D4 | — | 4 | 1 | no | — |
| 316 | D4 | — | 8 | 16 | no | — |
| 317 | D4 | #386 | 1 | 48 | yes | — |
| 318 | C2×C4 | — | 2 | 24 | no | — |
| 319 | C2×C4 | — | 2 | 8 | no | — |
| 320 | C2×C4 | — | 2 | 8 | no | — |
| 321 | C2×C4 | — | 2 | 48 | no | — |
| 322 | C2×C4 | — | 2 | 8 | no | — |
| 323 | C2×C4 | — | 2 | 6 | no | — |
| 324 | C2×C4 | — | 4 | 6 | no | — |
| 325 | C2×C4 | — | 4 | 24 | no | — |
| 326 | C2×C4 | — | 4 | 24 | no | — |
| 327 | C2×C4 | — | 4 | 8 | no | — |
| 328 | C2×C4 | — | 8 | 12 | no | — |
| 329 | C2×C4 | — | 16 | 12 | no | — |
| 330 | C2×C4 | C22×C22⋊C4 | 1 | 8 | yes | — |
| 331 | C2×C4 | C22×C22⋊C4 | 1 | 6 | yes | — |
| 332 | C2×C4 | C2×C4×D4 | 1 | 24 | yes | — |
| 333 | C2×C4 | C2×#120 | 1 | 12 | yes | — |
| 334 | C2×C4 | C2×#121 | 1 | 12 | yes | — |
| 335 | C2×C4 | C2×#123 | 1 | 12 | yes | — |
| 336 | C2×C4 | C24×C4 | 1 | 1 | yes | characteristic |
| 337 | C2×C4 | C23×D4 | 1 | 2 | yes | — |
| 338 | C2×C4 | C23×D4 | 1 | 1 | yes | characteristic |
| 339 | C2×C4 | C22×#41 | 1 | 2 | yes | — |
| 340 | C8 | — | 2 | 16 | no | — |
| 341 | C22 | — | 2 | 8 | no | — |
| 342 | C22 | — | 4 | 6 | no | — |
| 343 | C22 | — | 4 | 12 | no | — |
| 344 | C22 | — | 4 | 1 | no | — |
| 345 | C22 | — | 4 | 8 | no | — |
| 346 | C22 | — | 4 | 4 | no | — |
| 347 | C22 | — | 4 | 2 | no | — |
| 348 | C22 | — | 8 | 24 | no | — |
| 349 | C22 | — | 8 | 4 | no | — |
| 350 | C22 | C2×#386 | 1 | 12 | yes | — |
| 351 | C22 | C23×C22⋊C4 | 1 | 1 | yes | characteristic |
| 352 | C22 | C22×#121 | 1 | 2 | yes | — |
| 353 | C4 | — | 2 | 8 | no | — |
| 354 | C4 | — | 4 | 8 | no | — |
| 355 | C4 | — | 4 | 6 | no | — |
| 356 | C4 | — | 8 | 8 | no | — |
| 357 | C4 | C2×#386 | 1 | 12 | yes | — |
| 358 | C4 | C22×C4×D4 | 1 | 2 | yes | — |
| 359 | C4 | C22×#120 | 1 | 1 | yes | characteristic |
| 360 | C4 | C22×#123 | 1 | 1 | yes | characteristic |
| 361 | C2 | — | 2 | 1 | no | — |
| 362 | C2 | — | 2 | 2 | no | — |
| 363 | C2 | — | 2 | 12 | no | — |
| 364 | C2 | — | 4 | 8 | no | — |
| 365 | C2 | — | 8 | 2 | no | — |
| 366 | C2 | C22×#386 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2 | C22×#386 |
| commutator | C2×C4 | C24×C4 |
| Frattini, cosocle | C22×C4 | C25 |
| prime radical | #62859 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2 ◁ C22×#41 ◁ G | |
| LECS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #63076 | C2 | semidirect |
| 3. #60088 | C2 | semidirect |
| 4. #60070 | C2 | semidirect |
| 5. #21009 | C2 | semidirect |
| 6. C2×#1909 | C2 | semidirect |
| 7. #20338 | C2 | semidirect |
| 14. #3500 | C4 | semidirect |
| 15. #3499 | C4 | semidirect |
| 24. #2896 | C22 | semidirect |
| 25. C2×#419 | C22 | semidirect |
| 29. #1910 | C22 | semidirect |
| 30. #1909 | C22 | semidirect |
| 31. C2×H(3,ℤ/4) | C22 | semidirect |
| 57. C2×#131 | D4 | semidirect |
| 67. #536 | C2×C4 | semidirect |
| 68. #536 | C2×C4 | semidirect |
| 70. #535 | C2×C4 | semidirect |
| 73. #532 | C2×C4 | semidirect |
| 74. C2×C4⋊Q8 | C2×C4 | semidirect |
| 75. C2×#124 | C2×C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63076 | 2 |
| #62859 | 2 |
| #60088 | 2 |
| #60070 | 2 |
| #21009 | 2 |
| C2×#1909 | 2 |
| #20338 | 2 |