← #34273580
Subgroups — #34273580
Order 20224.
610 conjugacy classes of subgroups.
The subgroup lattice has 410 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23774356 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23773531 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23773427 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #23772480 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23762843 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23762829 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23762769 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23762747 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23762181 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #23762064 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#1553 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #19099120 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×C4×Dic158 | C22 | 1 | 1 | yes | characteristic |
| 14 | #19098942 | C22 | 1 | 1 | yes | characteristic |
| 15 | #19098935 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19098913 | C22 | 1 | 1 | yes | characteristic |
| 17 | #19098909 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19098894 | — | 2 | 1 | no | — |
| 19 | #19098879 | — | 2 | 1 | no | — |
| 20 | #19098849 | C22 | 1 | 2 | yes | — |
| 21 | #19098845 | C22 | 1 | 2 | yes | — |
| 22 | #19098782 | — | 2 | 2 | no | — |
| 23 | #19098774 | C22 | 1 | 2 | yes | — |
| 24 | #19098760 | C22 | 1 | 2 | yes | — |
| 25 | #19098725 | — | 2 | 2 | no | — |
| 26 | #19098721 | — | 2 | 1 | no | — |
| 27 | #19098701 | — | 2 | 1 | no | — |
| 28 | C8×Dic158 | — | 2 | 2 | no | — |
| 29 | #19098687 | C22 | 1 | 2 | yes | — |
| 30 | #19098687 | C22 | 1 | 2 | yes | — |
| 31 | #19098671 | — | 2 | 2 | no | — |
| 32 | C4×#11929612 | — | 2 | 2 | no | — |
| 33 | #19098616 | C22 | 1 | 1 | yes | characteristic |
| 34 | #19098616 | C22 | 1 | 1 | yes | characteristic |
| 35 | #19098613 | — | 2 | 2 | no | — |
| 36 | #19098315 | C22 | 1 | 2 | yes | — |
| 37 | #19098313 | C22 | 1 | 2 | yes | — |
| 38 | #19098310 | C22 | 1 | 2 | yes | — |
| 39 | #19098308 | C22 | 1 | 2 | yes | — |
| 40 | #532×C79 | C22 | 1 | 1 | yes | characteristic |
| 41 | #432×C79 | C22 | 1 | 1 | yes | characteristic |
| 42 | #431×C79 | C22 | 1 | 1 | yes | characteristic |
| 43 | #332×C79 | C22 | 1 | 2 | yes | — |
| 44 | #331×C79 | C22 | 1 | 2 | yes | — |
| 45 | C22×Dic158 | D4 | 1 | 1 | yes | characteristic |
| 46 | C2×Dic316 | — | 2 | 2 | no | — |
| 47 | C2×#11929614 | — | 2 | 2 | no | — |
| 48 | C2×#11929612 | — | 2 | 2 | no | — |
| 49 | C2×#11929612 | — | 2 | 2 | no | — |
| 50 | #14579161 | C23 | 1 | 1 | yes | characteristic |
| 51 | #14579161 | C23 | 1 | 1 | yes | characteristic |
| 52 | #14579153 | — | 2 | 1 | no | — |
| 53 | #14579140 | — | 2 | 1 | no | — |
| 54 | #14579140 | — | 2 | 1 | no | — |
| 55 | C4×Dic158 | — | 2 | 1 | no | — |
| 56 | C4×Dic158 | — | 2 | 1 | no | — |
| 57 | C4×Dic158 | — | 2 | 1 | no | — |
| 58 | C4×Dic158 | — | 2 | 1 | no | — |
| 59 | C4×Dic158 | D4 | 1 | 2 | yes | — |
| 60 | C4×Dic158 | C23 | 1 | 2 | yes | — |
| 61 | #14579120 | — | 2 | 1 | no | — |
| 62 | C2×C4⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 63 | C2×Dic79⋊C4 | — | 2 | 1 | no | — |
| 64 | C2×C4×Dic79 | — | 2 | 1 | no | — |
| 65 | #14579093 | — | 2 | 2 | no | — |
| 66 | #14579092 | — | 2 | 2 | no | — |
| 67 | C4⋊(C79⋊C8) | D4 | 1 | 2 | yes | — |
| 68 | C4⋊(C79⋊C8) | C23 | 1 | 2 | yes | — |
| 69 | Dic79⋊C8 | — | 2 | 2 | no | — |
| 70 | Dic79⋊C8 | — | 2 | 2 | no | — |
| 71 | #14579086 | — | 2 | 2 | no | — |
| 72 | #14579086 | — | 2 | 2 | no | — |
| 73 | #14579085 | — | 2 | 2 | no | — |
| 74 | #14579084 | — | 2 | 2 | no | — |
| 75 | #14579082 | — | 2 | 2 | no | — |
| 76 | #14579082 | — | 2 | 2 | no | — |
| 77 | C22⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 78 | C22⋊(C79⋊C8) | D4 | 1 | 2 | yes | — |
| 79 | C4×C79⋊C8 | — | 2 | 1 | no | — |
| 80 | C4×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 81 | C4×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 82 | C8×Dic79 | — | 2 | 2 | no | — |
| 83 | C8×Dic79 | — | 2 | 2 | no | — |
| 84 | C2×#41×C79 | — | 2 | 1 | no | — |
| 85 | C4⋊Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 86 | #127×C79 | C23 | 1 | 1 | yes | characteristic |
| 87 | #124×C79 | — | 2 | 1 | no | — |
| 88 | #121×C79 | — | 2 | 1 | no | — |
| 89 | #121×C79 | — | 2 | 1 | no | — |
| 90 | C4×D4×C79 | — | 2 | 1 | no | — |
| 91 | C4×D4×C79 | — | 2 | 1 | no | — |
| 92 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4⋊C8×C79 | C23 | 1 | 2 | yes | — |
| 94 | C4⋊C8×C79 | C23 | 1 | 2 | yes | — |
| 95 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 96 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 97 | #97×C79 | — | 2 | 1 | no | — |
| 98 | C4×C8×C79 | — | 2 | 1 | no | — |
| 99 | C2×Dic158 | — | 2 | 4 | no | — |
| 100 | C2×Dic158 | — | 2 | 1 | no | — |
| 101 | C2×Dic158 | — | 2 | 1 | no | — |
| 102 | C2×Dic158 | — | 2 | 1 | no | — |
| 103 | C2×Dic158 | C2×D4 | 1 | 2 | yes | — |
| 104 | C22×Dic79 | — | 2 | 1 | no | — |
| 105 | C22×Dic79 | — | 2 | 1 | no | — |
| 106 | Dic316 | — | 4 | 4 | no | — |
| 107 | #11929614 | — | 8 | 2 | no | — |
| 108 | #11929612 | — | 4 | 4 | no | — |
| 109 | #11929612 | — | 8 | 2 | no | — |
| 110 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 111 | C2×C79⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 112 | C2×C79⋊C8 | C2×D4 | 1 | 2 | yes | — |
| 113 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 114 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 115 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 116 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 117 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 118 | C4⋊Dic79 | C2×D4 | 1 | 2 | yes | — |
| 119 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 120 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 121 | Dic79⋊C4 | — | 4 | 1 | no | — |
| 122 | Dic79⋊C4 | — | 4 | 1 | no | — |
| 123 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 124 | C4×Dic79 | — | 2 | 2 | no | — |
| 125 | C4×Dic79 | — | 2 | 2 | no | — |
| 126 | C4×Dic79 | — | 4 | 1 | no | — |
| 127 | #41×C79 | — | 8 | 2 | no | — |
| 128 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 129 | C2×D4×C79 | — | 2 | 1 | no | — |
| 130 | C2×D4×C79 | — | 2 | 1 | no | — |
| 131 | C2×D4×C79 | — | 2 | 1 | no | — |
| 132 | C2×D4×C79 | — | 4 | 1 | no | — |
| 133 | C22×C4×C79 | — | 4 | 1 | no | — |
| 134 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C22×C4×C79 | #41 | 1 | 1 | yes | characteristic |
| 137 | C2×C8×C79 | — | 2 | 2 | no | — |
| 138 | C2×C8×C79 | — | 2 | 2 | no | — |
| 139 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 140 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 141 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 142 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 143 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C42×C79 | #41 | 1 | 1 | yes | characteristic |
| 146 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 147 | C23×C79 | — | 4 | 1 | no | — |
| 148 | C23×C79 | #121 | 1 | 1 | yes | characteristic |
| 149 | Q8×C79 | — | 4 | 2 | no | — |
| 150 | D4×C79 | — | 4 | 2 | no | — |
| 151 | D4×C79 | — | 4 | 2 | no | — |
| 152 | D4×C79 | — | 8 | 1 | no | — |
| 153 | D4×C79 | — | 8 | 2 | no | — |
| 154 | C2×C4×C79 | — | 2 | 2 | no | — |
| 155 | C2×C4×C79 | — | 2 | 2 | no | — |
| 156 | C2×C4×C79 | — | 4 | 1 | no | — |
| 157 | C2×C4×C79 | — | 4 | 1 | no | — |
| 158 | C2×C4×C79 | — | 8 | 2 | no | — |
| 159 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 160 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 161 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C79 | C2×#41 | 1 | 1 | yes | characteristic |
| 165 | C2×Dic79 | — | 2 | 4 | no | — |
| 166 | C2×Dic79 | — | 2 | 2 | no | — |
| 167 | C2×Dic79 | — | 2 | 2 | no | — |
| 168 | C2×Dic79 | — | 4 | 1 | no | — |
| 169 | C2×Dic79 | — | 4 | 1 | no | — |
| 170 | C2×Dic79 | — | 8 | 1 | no | — |
| 171 | Dic158 | — | 2 | 4 | no | — |
| 172 | Dic158 | — | 2 | 2 | no | — |
| 173 | Dic158 | — | 4 | 2 | no | — |
| 174 | Dic158 | — | 4 | 2 | no | — |
| 175 | Dic158 | #135 | 1 | 4 | yes | — |
| 176 | C8×C79 | — | 4 | 2 | no | — |
| 177 | C8×C79 | — | 4 | 2 | no | — |
| 178 | C79⋊C8 | — | 2 | 2 | no | — |
| 179 | C79⋊C8 | — | 2 | 2 | no | — |
| 180 | C79⋊C8 | — | 4 | 2 | no | — |
| 181 | C22×C79 | — | 2 | 1 | no | — |
| 182 | C22×C79 | — | 2 | 1 | no | — |
| 183 | C22×C79 | — | 2 | 1 | no | — |
| 184 | C22×C79 | — | 8 | 1 | no | — |
| 185 | C22×C79 | — | 8 | 1 | no | — |
| 186 | C22×C79 | — | 8 | 1 | no | — |
| 187 | C22×C79 | C2×#121 | 1 | 1 | yes | characteristic |
| 188 | C4×C79 | — | 2 | 1 | no | — |
| 189 | C4×C79 | — | 2 | 1 | no | — |
| 190 | C4×C79 | — | 2 | 1 | no | — |
| 191 | C4×C79 | — | 2 | 1 | no | — |
| 192 | C4×C79 | — | 8 | 1 | no | — |
| 193 | C4×C79 | C2×#135 | 1 | 2 | yes | — |
| 194 | C4×C79 | #577 | 1 | 2 | yes | — |
| 195 | Dic79 | — | 2 | 4 | no | — |
| 196 | Dic79 | — | 4 | 2 | no | — |
| 197 | Dic79 | — | 8 | 1 | no | — |
| 198 | Dic79 | — | 8 | 1 | no | — |
| 199 | #19400 | — | 79 | 1 | no | maximal, Sylow |
| 200 | C2×C79 | — | 4 | 1 | no | — |
| 201 | C2×C79 | — | 16 | 1 | no | — |
| 202 | C2×C79 | #3043 | 1 | 1 | yes | characteristic |
| 203 | C2×C79 | #3050 | 1 | 1 | yes | characteristic |
| 204 | C2×C79 | #3069 | 1 | 1 | yes | characteristic |
| 205 | #3210 | — | 79 | 1 | no | — |
| 206 | #3113 | — | 79 | 1 | no | — |
| 207 | #3103 | — | 79 | 1 | no | — |
| 208 | #2982 | — | 79 | 1 | no | — |
| 209 | #1682 | — | 79 | 2 | no | — |
| 210 | #1680 | — | 79 | 2 | no | — |
| 211 | #1670 | — | 79 | 2 | no | — |
| 212 | #1666 | — | 79 | 2 | no | — |
| 213 | #1572 | — | 79 | 1 | no | — |
| 214 | #1553 | D79 | 1 | 1 | yes | characteristic |
| 215 | #1544 | — | 79 | 1 | no | — |
| 216 | C79 | #19400 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 217 | #533 | — | 79 | 1 | no | — |
| 218 | #532 | C2×D79 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×Q8 | — | 79 | 1 | no | — |
| 220 | #494 | — | 79 | 1 | no | — |
| 221 | #492 | — | 79 | 1 | no | — |
| 222 | #487 | — | 79 | 1 | no | — |
| 223 | #486 | — | 79 | 1 | no | — |
| 224 | #483 | — | 158 | 1 | no | — |
| 225 | #481 | — | 158 | 1 | no | — |
| 226 | #475 | — | 79 | 2 | no | — |
| 227 | #475 | — | 79 | 2 | no | — |
| 228 | #464 | — | 158 | 2 | no | — |
| 229 | #462 | — | 79 | 2 | no | — |
| 230 | #460 | — | 79 | 2 | no | — |
| 231 | #452 | — | 158 | 2 | no | — |
| 232 | #451 | — | 158 | 1 | no | — |
| 233 | #448 | — | 158 | 1 | no | — |
| 234 | C8×Q8 | — | 79 | 2 | no | — |
| 235 | C8×Q8 | — | 79 | 2 | no | — |
| 236 | C8×Q8 | — | 158 | 2 | no | — |
| 237 | #441 | — | 158 | 2 | no | — |
| 238 | C4×SD16 | — | 158 | 2 | no | — |
| 239 | #432 | C2×D79 | 1 | 1 | yes | characteristic |
| 240 | #431 | — | 79 | 1 | no | — |
| 241 | #431 | — | 79 | 1 | no | — |
| 242 | #431 | — | 158 | 2 | no | — |
| 243 | #431 | C2×D79 | 1 | 1 | yes | characteristic |
| 244 | #335 | — | 79 | 2 | no | — |
| 245 | #334 | — | 79 | 2 | no | — |
| 246 | #332 | — | 79 | 2 | no | — |
| 247 | #332 | — | 79 | 2 | no | — |
| 248 | #332 | C2×D79 | 1 | 2 | yes | — |
| 249 | #331 | C2×D79 | 1 | 2 | yes | — |
| 250 | C2×#41 | — | 2 | 1 | no | — |
| 251 | C22×Q8 | — | 79 | 1 | no | — |
| 252 | C2×Q16 | — | 158 | 2 | no | — |
| 253 | C2×Q16 | — | 158 | 2 | no | — |
| 254 | C2×SD16 | — | 158 | 2 | no | — |
| 255 | C2×SD16 | — | 158 | 2 | no | — |
| 256 | C4⋊Q8 | — | 79 | 1 | no | — |
| 257 | C4⋊Q8 | — | 79 | 1 | no | — |
| 258 | C4⋊Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 259 | #127 | C22×D79 | 1 | 1 | yes | characteristic |
| 260 | #125 | — | 158 | 1 | no | — |
| 261 | #124 | — | 2 | 1 | no | — |
| 262 | C22⋊Q8 | — | 158 | 1 | no | — |
| 263 | C22⋊Q8 | — | 158 | 1 | no | — |
| 264 | #121 | — | 2 | 1 | no | — |
| 265 | #121 | — | 2 | 1 | no | — |
| 266 | C4×Q8 | — | 79 | 2 | no | — |
| 267 | C4×Q8 | — | 79 | 2 | no | — |
| 268 | C4×Q8 | — | 158 | 1 | no | — |
| 269 | C4×Q8 | — | 158 | 1 | no | — |
| 270 | C4×Q8 | — | 158 | 1 | no | — |
| 271 | C4×Q8 | — | 158 | 1 | no | — |
| 272 | C4×D4 | — | 2 | 1 | no | — |
| 273 | C4×D4 | — | 2 | 1 | no | — |
| 274 | #117 | — | 158 | 1 | no | — |
| 275 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 276 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 277 | C2×C42 | — | 158 | 1 | no | — |
| 278 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 279 | #106 | — | 158 | 2 | no | — |
| 280 | #106 | — | 158 | 2 | no | — |
| 281 | C4⋊C8 | — | 79 | 2 | no | — |
| 282 | C4⋊C8 | — | 79 | 2 | no | — |
| 283 | C4⋊C8 | — | 158 | 2 | no | — |
| 284 | C4⋊C8 | — | 158 | 2 | no | — |
| 285 | C4⋊C8 | C22×D79 | 1 | 2 | yes | — |
| 286 | C4⋊C8 | C22×D79 | 1 | 2 | yes | — |
| 287 | #103 | — | 158 | 2 | no | — |
| 288 | #103 | — | 158 | 2 | no | — |
| 289 | #103 | — | 158 | 2 | no | — |
| 290 | #103 | — | 158 | 2 | no | — |
| 291 | #102 | — | 158 | 2 | no | — |
| 292 | #102 | — | 158 | 2 | no | — |
| 293 | C22⋊C8 | — | 2 | 1 | no | — |
| 294 | C22⋊C8 | — | 2 | 1 | no | — |
| 295 | C22⋊C8 | — | 79 | 2 | no | — |
| 296 | C22⋊C8 | — | 158 | 1 | no | — |
| 297 | #97 | — | 2 | 1 | no | — |
| 298 | C4×C8 | — | 2 | 1 | no | — |
| 299 | C4×C8 | — | 79 | 1 | no | — |
| 300 | C4×C8 | — | 79 | 1 | no | — |
| 301 | C4×C8 | — | 158 | 2 | no | — |
| 302 | C4×C8 | — | 158 | 2 | no | — |
| 303 | C4×C8 | — | 158 | 1 | no | — |
| 304 | #41 | — | 8 | 2 | no | — |
| 305 | C2×Q8 | — | 2 | 1 | no | — |
| 306 | C2×Q8 | — | 79 | 2 | no | — |
| 307 | C2×Q8 | — | 158 | 4 | no | — |
| 308 | C2×Q8 | — | 158 | 1 | no | — |
| 309 | C2×Q8 | — | 158 | 1 | no | — |
| 310 | C2×Q8 | — | 158 | 1 | no | — |
| 311 | C2×D4 | — | 2 | 1 | no | — |
| 312 | C2×D4 | — | 2 | 1 | no | — |
| 313 | C2×D4 | — | 2 | 1 | no | — |
| 314 | C2×D4 | — | 4 | 1 | no | — |
| 315 | C22×C4 | — | 4 | 1 | no | — |
| 316 | C22×C4 | — | 158 | 1 | no | — |
| 317 | C22×C4 | — | 158 | 1 | no | — |
| 318 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 319 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 320 | C22×C4 | #11929624 | 1 | 1 | yes | characteristic |
| 321 | Q16 | — | 316 | 4 | no | — |
| 322 | Q16 | — | 632 | 2 | no | — |
| 323 | SD16 | — | 316 | 4 | no | — |
| 324 | SD16 | — | 632 | 2 | no | — |
| 325 | C2×C8 | — | 2 | 2 | no | — |
| 326 | C2×C8 | — | 2 | 2 | no | — |
| 327 | C2×C8 | — | 79 | 2 | no | — |
| 328 | C2×C8 | — | 79 | 2 | no | — |
| 329 | C2×C8 | — | 158 | 2 | no | — |
| 330 | C4⋊C4 | — | 2 | 1 | no | — |
| 331 | C4⋊C4 | — | 2 | 1 | no | — |
| 332 | C4⋊C4 | — | 316 | 1 | no | — |
| 333 | C4⋊C4 | — | 316 | 1 | no | — |
| 334 | C4⋊C4 | — | 79 | 2 | no | — |
| 335 | C4⋊C4 | — | 158 | 1 | no | — |
| 336 | C4⋊C4 | — | 158 | 1 | no | — |
| 337 | C4⋊C4 | — | 158 | 1 | no | — |
| 338 | C4⋊C4 | — | 158 | 1 | no | — |
| 339 | C4⋊C4 | — | 158 | 2 | no | — |
| 340 | C4⋊C4 | — | 158 | 2 | no | — |
| 341 | C4⋊C4 | — | 158 | 1 | no | — |
| 342 | C22⋊C4 | — | 4 | 1 | no | — |
| 343 | C22⋊C4 | — | 4 | 1 | no | — |
| 344 | C22⋊C4 | — | 316 | 1 | no | — |
| 345 | C42 | — | 316 | 1 | no | — |
| 346 | C42 | — | 158 | 2 | no | — |
| 347 | C42 | — | 158 | 2 | no | — |
| 348 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 349 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 350 | C42 | #11929624 | 1 | 1 | yes | characteristic |
| 351 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 352 | C23 | — | 4 | 1 | no | — |
| 353 | C23 | #14579134 | 1 | 1 | yes | characteristic |
| 354 | Q8 | — | 4 | 2 | no | — |
| 355 | Q8 | — | 316 | 2 | no | — |
| 356 | Q8 | — | 316 | 2 | no | — |
| 357 | Q8 | — | 79 | 4 | no | — |
| 358 | Q8 | — | 158 | 4 | no | — |
| 359 | Q8 | — | 158 | 2 | no | — |
| 360 | D4 | — | 4 | 2 | no | — |
| 361 | D4 | — | 4 | 2 | no | — |
| 362 | D4 | — | 8 | 1 | no | — |
| 363 | D4 | — | 8 | 2 | no | — |
| 364 | C2×C4 | — | 2 | 2 | no | — |
| 365 | C2×C4 | — | 2 | 2 | no | — |
| 366 | C2×C4 | — | 4 | 1 | no | — |
| 367 | C2×C4 | — | 4 | 1 | no | — |
| 368 | C2×C4 | — | 8 | 2 | no | — |
| 369 | C2×C4 | — | 316 | 1 | no | — |
| 370 | C2×C4 | — | 316 | 1 | no | — |
| 371 | C2×C4 | — | 632 | 1 | no | — |
| 372 | C2×C4 | — | 158 | 2 | no | — |
| 373 | C2×C4 | — | 158 | 4 | no | — |
| 374 | C2×C4 | — | 158 | 2 | no | — |
| 375 | C2×C4 | #14579134 | 1 | 1 | yes | characteristic |
| 376 | C2×C4 | #14579134 | 1 | 1 | yes | characteristic |
| 377 | C2×C4 | #14579134 | 1 | 1 | yes | characteristic |
| 378 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 379 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 380 | C2×C4 | C2×#11929624 | 1 | 1 | yes | characteristic |
| 381 | C8 | — | 4 | 2 | no | — |
| 382 | C8 | — | 4 | 2 | no | — |
| 383 | C8 | — | 316 | 2 | no | — |
| 384 | C8 | — | 158 | 2 | no | — |
| 385 | C8 | — | 158 | 2 | no | — |
| 386 | C22 | — | 2 | 1 | no | — |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 2 | 1 | no | — |
| 389 | C22 | — | 8 | 1 | no | — |
| 390 | C22 | — | 8 | 1 | no | — |
| 391 | C22 | — | 8 | 1 | no | — |
| 392 | C22 | C2×#14579134 | 1 | 1 | yes | characteristic |
| 393 | C4 | — | 2 | 1 | no | — |
| 394 | C4 | — | 2 | 1 | no | — |
| 395 | C4 | — | 2 | 1 | no | — |
| 396 | C4 | — | 2 | 1 | no | — |
| 397 | C4 | — | 8 | 1 | no | — |
| 398 | C4 | — | 316 | 2 | no | — |
| 399 | C4 | — | 632 | 1 | no | — |
| 400 | C4 | — | 632 | 1 | no | — |
| 401 | C4 | — | 158 | 4 | no | — |
| 402 | C4 | #135×D79 | 1 | 2 | yes | — |
| 403 | C4 | #19099373 | 1 | 2 | yes | — |
| 404 | C2 | — | 4 | 1 | no | — |
| 405 | C2 | — | 16 | 1 | no | — |
| 406 | C2 | #23772920 | 1 | 1 | yes | characteristic |
| 407 | C2 | #23772980 | 1 | 1 | yes | characteristic |
| 408 | C2 | #23773140 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta