Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1166 conjugacy classes of subgroups.
The subgroup lattice has 550 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23777166 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23773523 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23773518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23766693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23762404 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #23762370 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #23761907 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #23761743 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C79×#1505 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#14579208 | — | 2 | 1 | no | — |
| 11 | #19099234 | — | 2 | 1 | no | — |
| 12 | #19099233 | — | 2 | 1 | no | — |
| 13 | D4×Dic158 | — | 2 | 1 | no | — |
| 14 | #19099228 | — | 2 | 1 | no | — |
| 15 | #19099222 | — | 2 | 2 | no | — |
| 16 | #19099221 | — | 2 | 2 | no | — |
| 17 | #19099141 | — | 2 | 1 | no | — |
| 18 | #19099140 | C22 | 1 | 4 | yes | — |
| 19 | #19099113 | C22 | 1 | 1 | yes | characteristic |
| 20 | #19099108 | — | 2 | 2 | no | — |
| 21 | C2×C4×Dic158 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×C4×Dic158 | C22 | 1 | 1 | yes | characteristic |
| 23 | #19098877 | C22 | 1 | 2 | yes | — |
| 24 | #19098874 | C22 | 1 | 2 | yes | — |
| 25 | #19098859 | — | 2 | 1 | no | — |
| 26 | #19098855 | — | 2 | 1 | no | — |
| 27 | #19098764 | — | 2 | 1 | no | — |
| 28 | #19098760 | — | 2 | 1 | no | — |
| 29 | #19098704 | C22 | 1 | 2 | yes | — |
| 30 | #19098701 | C22 | 1 | 2 | yes | — |
| 31 | #19098665 | — | 2 | 2 | no | — |
| 32 | #19098663 | — | 2 | 2 | no | — |
| 33 | #19098620 | C22 | 1 | 1 | yes | characteristic |
| 34 | #19098495 | — | 2 | 1 | no | — |
| 35 | #19098495 | C22 | 1 | 2 | yes | — |
| 36 | #19098484 | — | 2 | 1 | no | — |
| 37 | #19098484 | C22 | 1 | 2 | yes | — |
| 38 | C4×C4⋊Dic79 | — | 2 | 2 | no | — |
| 39 | #19098296 | C22 | 1 | 4 | yes | — |
| 40 | #19098288 | C22 | 1 | 4 | yes | — |
| 41 | #532×C79 | C22 | 1 | 1 | yes | characteristic |
| 42 | #432×C79 | C22 | 1 | 1 | yes | characteristic |
| 43 | #376×C79 | C22 | 1 | 1 | yes | characteristic |
| 44 | #327×C79 | C22 | 1 | 4 | yes | — |
| 45 | #14579208 | — | 4 | 8 | no | — |
| 46 | C2×#11929624 | — | 2 | 2 | no | — |
| 47 | C2×#11929624 | — | 2 | 1 | no | — |
| 48 | C2×#11929623 | — | 2 | 2 | no | — |
| 49 | C2×#11929623 | — | 2 | 4 | no | — |
| 50 | C22×Dic158 | — | 2 | 2 | no | — |
| 51 | C22×Dic158 | D4 | 1 | 1 | yes | characteristic |
| 52 | C22×Dic158 | C23 | 1 | 1 | yes | characteristic |
| 53 | C2×Q8×D79 | — | 2 | 2 | no | — |
| 54 | C2×#11929613 | — | 2 | 2 | no | — |
| 55 | C2×#11929612 | — | 2 | 2 | no | — |
| 56 | #14579161 | D4 | 1 | 1 | yes | characteristic |
| 57 | #14579160 | — | 2 | 2 | no | — |
| 58 | #14579158 | D4 | 1 | 1 | yes | characteristic |
| 59 | #14579157 | — | 2 | 2 | no | — |
| 60 | #14579149 | — | 2 | 1 | no | — |
| 61 | #14579147 | — | 2 | 4 | no | — |
| 62 | #14579140 | — | 2 | 2 | no | — |
| 63 | #14579139 | — | 2 | 4 | no | — |
| 64 | #14579138 | — | 2 | 4 | no | — |
| 65 | #14579137 | — | 2 | 2 | no | — |
| 66 | #14579135 | — | 2 | 2 | no | — |
| 67 | #14579135 | — | 2 | 1 | no | — |
| 68 | #14579135 | C23 | 1 | 2 | yes | — |
| 69 | #14579134 | — | 2 | 4 | no | — |
| 70 | #14579133 | — | 2 | 4 | no | — |
| 71 | #14579133 | — | 2 | 4 | no | — |
| 72 | #14579132 | — | 2 | 2 | no | — |
| 73 | C4×Dic158 | — | 2 | 1 | no | — |
| 74 | C4×Dic158 | — | 2 | 1 | no | — |
| 75 | C4×Dic158 | — | 2 | 1 | no | — |
| 76 | C4×Dic158 | — | 2 | 1 | no | — |
| 77 | C4×Dic158 | — | 2 | 1 | no | — |
| 78 | C4×Dic158 | — | 2 | 1 | no | — |
| 79 | C4×Dic158 | — | 2 | 1 | no | — |
| 80 | C4×Dic158 | — | 2 | 1 | no | — |
| 81 | C4×D316 | — | 2 | 1 | no | — |
| 82 | C4×D316 | D4 | 1 | 2 | yes | — |
| 83 | D4×Dic79 | — | 2 | 2 | no | — |
| 84 | #14579123 | — | 2 | 2 | no | — |
| 85 | (C22⋊D79)⋊C4 | — | 2 | 4 | no | — |
| 86 | C2×C4⋊Dic79 | — | 2 | 2 | no | — |
| 87 | C2×C4⋊Dic79 | — | 2 | 2 | no | — |
| 88 | C2×C4⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C4⋊Dic79 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×Dic79⋊C4 | — | 2 | 1 | no | — |
| 91 | C2×Dic79⋊C4 | C23 | 1 | 2 | yes | — |
| 92 | C2×C4×Dic79 | — | 2 | 1 | no | — |
| 93 | C2×C4×Dic79 | D4 | 1 | 2 | yes | — |
| 94 | #14579095 | — | 2 | 2 | no | — |
| 95 | #14579094 | — | 2 | 2 | no | — |
| 96 | C4⋊(C79⋊C8) | — | 2 | 1 | no | — |
| 97 | #14579086 | — | 2 | 2 | no | — |
| 98 | #14579084 | — | 2 | 2 | no | — |
| 99 | #14579083 | — | 2 | 2 | no | — |
| 100 | #14579082 | — | 2 | 2 | no | — |
| 101 | C22⋊(C79⋊C8) | C23 | 1 | 2 | yes | — |
| 102 | #14579072 | — | 2 | 1 | no | — |
| 103 | C79⋊#95 | — | 2 | 2 | no | — |
| 104 | C79⋊#95 | — | 2 | 2 | no | — |
| 105 | C2×#41×C79 | — | 2 | 1 | no | — |
| 106 | C4⋊Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 107 | #127×C79 | D4 | 1 | 1 | yes | characteristic |
| 108 | #124×C79 | — | 2 | 1 | no | — |
| 109 | #121×C79 | — | 2 | 1 | no | — |
| 110 | #121×C79 | C23 | 1 | 2 | yes | — |
| 111 | C4×D4×C79 | — | 2 | 1 | no | — |
| 112 | C4×D4×C79 | D4 | 1 | 2 | yes | — |
| 113 | C2×C42×C79 | — | 2 | 1 | no | — |
| 114 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 115 | C4⋊C8×C79 | — | 2 | 1 | no | — |
| 116 | C22⋊C8×C79 | C23 | 1 | 2 | yes | — |
| 117 | #97×C79 | — | 2 | 1 | no | — |
| 118 | #95×C79 | — | 2 | 1 | no | — |
| 119 | #95×C79 | C23 | 1 | 2 | yes | — |
| 120 | #11929624 | — | 4 | 4 | no | — |
| 121 | #11929624 | — | 4 | 8 | no | — |
| 122 | #11929623 | — | 4 | 8 | no | — |
| 123 | #11929623 | — | 4 | 8 | no | — |
| 124 | #11929623 | — | 4 | 8 | no | — |
| 125 | C2×Dic158 | — | 2 | 4 | no | — |
| 126 | C2×Dic158 | — | 2 | 4 | no | — |
| 127 | C2×Dic158 | — | 2 | 1 | no | — |
| 128 | C2×Dic158 | — | 2 | 1 | no | — |
| 129 | C2×Dic158 | — | 2 | 1 | no | — |
| 130 | C2×Dic158 | — | 2 | 1 | no | — |
| 131 | C2×Dic158 | — | 2 | 1 | no | — |
| 132 | C2×Dic158 | — | 4 | 2 | no | — |
| 133 | C2×Dic158 | — | 4 | 8 | no | — |
| 134 | Q8×D79 | — | 4 | 8 | no | — |
| 135 | C2×D316 | — | 2 | 1 | no | — |
| 136 | C2×D316 | — | 2 | 1 | no | — |
| 137 | C2×D316 | C2×D4 | 1 | 2 | yes | — |
| 138 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 139 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 140 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 141 | C22×Dic79 | — | 2 | 4 | no | — |
| 142 | C22×Dic79 | — | 2 | 1 | no | — |
| 143 | C22×Dic79 | — | 2 | 1 | no | — |
| 144 | C22×Dic79 | C2×D4 | 1 | 2 | yes | — |
| 145 | C22×Dic79 | C2×D4 | 1 | 2 | yes | — |
| 146 | C2×C4×D79 | — | 2 | 4 | no | — |
| 147 | C2×C4×D79 | — | 2 | 2 | no | — |
| 148 | #11929613 | — | 4 | 4 | no | — |
| 149 | #11929612 | — | 4 | 4 | no | — |
| 150 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 151 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 152 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 153 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 154 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 155 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 156 | C4⋊Dic79 | — | 4 | 4 | no | — |
| 157 | C4⋊Dic79 | — | 4 | 4 | no | — |
| 158 | C4⋊Dic79 | C2×D4 | 1 | 2 | yes | — |
| 159 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 160 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 161 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 162 | Dic79⋊C4 | — | 4 | 1 | no | — |
| 163 | Dic79⋊C4 | — | 4 | 1 | no | — |
| 164 | C22⋊Dic79 | — | 2 | 4 | no | — |
| 165 | (C2×D79)⋊C4 | — | 2 | 4 | no | — |
| 166 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 167 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 168 | C4×Dic79 | — | 2 | 2 | no | — |
| 169 | C4×Dic79 | — | 2 | 2 | no | — |
| 170 | C4×Dic79 | — | 4 | 1 | no | — |
| 171 | C4×Dic79 | — | 4 | 1 | no | — |
| 172 | #41×C79 | — | 4 | 4 | no | — |
| 173 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 174 | C2×D4×C79 | — | 2 | 2 | no | — |
| 175 | C2×D4×C79 | — | 2 | 1 | no | — |
| 176 | C2×D4×C79 | — | 2 | 1 | no | — |
| 177 | C2×D4×C79 | C2×D4 | 1 | 2 | yes | — |
| 178 | C22×C4×C79 | — | 2 | 2 | no | — |
| 179 | C22×C4×C79 | — | 2 | 2 | no | — |
| 180 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C8×C79 | — | 2 | 2 | no | — |
| 184 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 185 | C4⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 186 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 187 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 188 | C42×C79 | — | 2 | 4 | no | — |
| 189 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C23×C79 | — | 2 | 2 | no | — |
| 194 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 195 | C22×D79 | — | 2 | 2 | no | — |
| 196 | Q8×C79 | — | 4 | 2 | no | — |
| 197 | D4×C79 | — | 4 | 2 | no | — |
| 198 | D4×C79 | — | 4 | 2 | no | — |
| 199 | D4×C79 | — | 4 | 4 | no | — |
| 200 | D4×C79 | — | 4 | 2 | no | — |
| 201 | C2×C4×C79 | — | 2 | 2 | no | — |
| 202 | C2×C4×C79 | — | 2 | 2 | no | — |
| 203 | C2×C4×C79 | — | 2 | 4 | no | — |
| 204 | C2×C4×C79 | — | 2 | 2 | no | — |
| 205 | C2×C4×C79 | — | 4 | 1 | no | — |
| 206 | C2×C4×C79 | — | 4 | 4 | no | — |
| 207 | C2×C4×C79 | — | 4 | 2 | no | — |
| 208 | C2×C4×C79 | — | 4 | 2 | no | — |
| 209 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 211 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 212 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 213 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 214 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 215 | C22⋊D79 | — | 4 | 8 | no | — |
| 216 | C22⋊D79 | — | 4 | 4 | no | — |
| 217 | C22⋊D79 | — | 8 | 4 | no | — |
| 218 | C2×Dic79 | — | 2 | 2 | no | — |
| 219 | C2×Dic79 | — | 2 | 2 | no | — |
| 220 | C2×Dic79 | — | 2 | 2 | no | — |
| 221 | C2×Dic79 | — | 2 | 2 | no | — |
| 222 | C2×Dic79 | — | 2 | 2 | no | — |
| 223 | C2×Dic79 | — | 4 | 8 | no | — |
| 224 | C2×Dic79 | — | 4 | 1 | no | — |
| 225 | C2×Dic79 | — | 4 | 1 | no | — |
| 226 | C2×Dic79 | — | 4 | 2 | no | — |
| 227 | C2×Dic79 | — | 4 | 1 | no | — |
| 228 | C2×Dic79 | — | 4 | 2 | no | — |
| 229 | C2×Dic79 | AGL(1,ℤ/8) | 1 | 4 | yes | — |
| 230 | D316 | — | 4 | 2 | no | — |
| 231 | D316 | — | 4 | 2 | no | — |
| 232 | D316 | — | 4 | 2 | no | — |
| 233 | C4×D79 | — | 4 | 8 | no | — |
| 234 | C4×D79 | — | 4 | 4 | no | — |
| 235 | Dic158 | — | 2 | 4 | no | — |
| 236 | Dic158 | — | 2 | 4 | no | — |
| 237 | Dic158 | — | 2 | 2 | no | — |
| 238 | Dic158 | — | 2 | 2 | no | — |
| 239 | Dic158 | — | 4 | 8 | no | — |
| 240 | Dic158 | — | 4 | 1 | no | — |
| 241 | Dic158 | — | 4 | 1 | no | — |
| 242 | Dic158 | — | 4 | 2 | no | — |
| 243 | C8×C79 | — | 4 | 2 | no | — |
| 244 | C79⋊C8 | — | 4 | 2 | no | — |
| 245 | C22×C79 | — | 2 | 1 | no | — |
| 246 | C22×C79 | — | 2 | 1 | no | — |
| 247 | C22×C79 | — | 4 | 2 | no | — |
| 248 | C22×C79 | — | 4 | 2 | no | — |
| 249 | C22×C79 | — | 4 | 2 | no | — |
| 250 | C22×C79 | C2×#120 | 1 | 1 | yes | characteristic |
| 251 | C22×C79 | C2×AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 252 | C2×D79 | — | 4 | 2 | no | — |
| 253 | C2×D79 | — | 4 | 2 | no | — |
| 254 | C2×D79 | — | 4 | 2 | no | — |
| 255 | C4×C79 | — | 2 | 1 | no | — |
| 256 | C4×C79 | — | 2 | 1 | no | — |
| 257 | C4×C79 | — | 2 | 1 | no | — |
| 258 | C4×C79 | — | 2 | 1 | no | — |
| 259 | C4×C79 | — | 2 | 1 | no | — |
| 260 | C4×C79 | — | 4 | 4 | no | — |
| 261 | C4×C79 | — | 4 | 2 | no | — |
| 262 | C4×C79 | #456 | 1 | 2 | yes | — |
| 263 | Dic79 | — | 2 | 4 | no | — |
| 264 | Dic79 | — | 4 | 2 | no | — |
| 265 | Dic79 | — | 4 | 2 | no | — |
| 266 | Dic79 | — | 4 | 2 | no | — |
| 267 | Dic79 | — | 8 | 1 | no | — |
| 268 | #18187 | — | 79 | 1 | no | maximal, Sylow |
| 269 | C2×C79 | — | 2 | 2 | no | — |
| 270 | C2×C79 | — | 8 | 2 | no | — |
| 271 | C2×C79 | #3003 | 1 | 1 | yes | characteristic |
| 272 | C2×C79 | C2×#456 | 1 | 1 | yes | characteristic |
| 273 | C2×C79 | #3025 | 1 | 1 | yes | characteristic |
| 274 | D79 | — | 8 | 2 | no | — |
| 275 | #3497 | — | 79 | 1 | no | — |
| 276 | #3112 | — | 79 | 1 | no | — |
| 277 | #3112 | — | 79 | 1 | no | — |
| 278 | #2399 | — | 79 | 1 | no | — |
| 279 | #1610 | — | 79 | 4 | no | — |
| 280 | #1604 | — | 79 | 4 | no | — |
| 281 | #1505 | — | 79 | 1 | no | — |
| 282 | #1505 | D79 | 1 | 1 | yes | characteristic, complemented |
| 283 | #1467 | — | 79 | 1 | no | — |
| 284 | C79 | #18187 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 285 | C2×2−1+4 | — | 158 | 1 | no | — |
| 286 | #550 | — | 158 | 1 | no | — |
| 287 | #550 | — | 158 | 1 | no | — |
| 288 | D4×Q8 | — | 158 | 1 | no | — |
| 289 | D4×Q8 | — | 158 | 1 | no | — |
| 290 | #548 | — | 158 | 2 | no | — |
| 291 | #548 | — | 158 | 2 | no | — |
| 292 | #537 | — | 79 | 4 | no | — |
| 293 | #537 | — | 158 | 1 | no | — |
| 294 | #532 | — | 79 | 1 | no | — |
| 295 | #532 | — | 158 | 2 | no | — |
| 296 | #532 | C2×D79 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×Q8 | — | 79 | 1 | no | — |
| 298 | C2×C4×Q8 | — | 79 | 1 | no | — |
| 299 | #480 | — | 79 | 2 | no | — |
| 300 | #480 | — | 79 | 2 | no | — |
| 301 | #477 | — | 158 | 1 | no | — |
| 302 | #477 | — | 158 | 1 | no | — |
| 303 | #460 | — | 158 | 1 | no | — |
| 304 | #460 | — | 158 | 1 | no | — |
| 305 | #448 | — | 79 | 2 | no | — |
| 306 | #448 | — | 79 | 2 | no | — |
| 307 | #440 | — | 158 | 2 | no | — |
| 308 | #440 | — | 158 | 2 | no | — |
| 309 | #432 | — | 79 | 1 | no | — |
| 310 | #432 | C2×D79 | 1 | 1 | yes | characteristic |
| 311 | #398 | — | 79 | 2 | no | — |
| 312 | #398 | — | 158 | 1 | no | — |
| 313 | #395 | — | 79 | 2 | no | — |
| 314 | #395 | — | 158 | 1 | no | — |
| 315 | C4×C4⋊C4 | — | 158 | 2 | no | — |
| 316 | #376 | C2×D79 | 1 | 1 | yes | characteristic |
| 317 | #327 | — | 79 | 4 | no | — |
| 318 | #327 | C2×D79 | 1 | 4 | yes | — |
| 319 | #324 | — | 79 | 4 | no | — |
| 320 | 2−1+4 | — | 316 | 8 | no | — |
| 321 | C2×#41 | — | 2 | 1 | no | — |
| 322 | C2×#41 | — | 158 | 2 | no | — |
| 323 | C2×#41 | — | 158 | 4 | no | — |
| 324 | C2×#41 | — | 158 | 2 | no | — |
| 325 | C2×#41 | — | 158 | 1 | no | — |
| 326 | C22×Q8 | — | 79 | 1 | no | — |
| 327 | C22×Q8 | — | 79 | 1 | no | — |
| 328 | C22×Q8 | — | 158 | 2 | no | — |
| 329 | C22×Q8 | — | 158 | 2 | no | — |
| 330 | C2×SD16 | — | 158 | 2 | no | — |
| 331 | C2×SD16 | — | 158 | 2 | no | — |
| 332 | C4⋊Q8 | — | 79 | 1 | no | — |
| 333 | C4⋊Q8 | — | 158 | 2 | no | — |
| 334 | C4⋊Q8 | D316 | 1 | 1 | yes | characteristic |
| 335 | #127 | — | 79 | 1 | no | — |
| 336 | #127 | — | 158 | 2 | no | — |
| 337 | #127 | D316 | 1 | 1 | yes | characteristic |
| 338 | #124 | — | 2 | 1 | no | — |
| 339 | #124 | — | 158 | 4 | no | — |
| 340 | #124 | — | 158 | 1 | no | — |
| 341 | C22⋊Q8 | — | 158 | 4 | no | — |
| 342 | C22⋊Q8 | — | 158 | 2 | no | — |
| 343 | C22⋊Q8 | — | 158 | 2 | no | — |
| 344 | C22⋊Q8 | — | 158 | 4 | no | — |
| 345 | #121 | — | 2 | 1 | no | — |
| 346 | #121 | — | 79 | 2 | no | — |
| 347 | #121 | — | 158 | 4 | no | — |
| 348 | #121 | — | 158 | 2 | no | — |
| 349 | #121 | — | 158 | 4 | no | — |
| 350 | #121 | — | 158 | 2 | no | — |
| 351 | #121 | — | 158 | 4 | no | — |
| 352 | #121 | — | 158 | 1 | no | — |
| 353 | #121 | C22×D79 | 1 | 2 | yes | — |
| 354 | C4×Q8 | — | 158 | 1 | no | — |
| 355 | C4×Q8 | — | 158 | 1 | no | — |
| 356 | C4×Q8 | — | 158 | 1 | no | — |
| 357 | C4×Q8 | — | 158 | 1 | no | — |
| 358 | C4×Q8 | — | 158 | 1 | no | — |
| 359 | C4×Q8 | — | 158 | 1 | no | — |
| 360 | C4×Q8 | — | 158 | 1 | no | — |
| 361 | C4×Q8 | — | 158 | 1 | no | — |
| 362 | C4×D4 | — | 2 | 1 | no | — |
| 363 | C4×D4 | — | 79 | 2 | no | — |
| 364 | C4×D4 | — | 158 | 4 | no | — |
| 365 | C4×D4 | — | 158 | 2 | no | — |
| 366 | C4×D4 | — | 158 | 2 | no | — |
| 367 | C4×D4 | — | 158 | 1 | no | — |
| 368 | C4×D4 | D316 | 1 | 2 | yes | — |
| 369 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 370 | C2×C4⋊C4 | — | 79 | 2 | no | — |
| 371 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 372 | C2×C4⋊C4 | — | 158 | 2 | no | — |
| 373 | C2×C4⋊C4 | — | 158 | 2 | no | — |
| 374 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 375 | C2×C42 | — | 2 | 1 | no | — |
| 376 | C2×C42 | — | 79 | 2 | no | — |
| 377 | C2×C42 | — | 158 | 1 | no | — |
| 378 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 379 | #107 | — | 158 | 2 | no | — |
| 380 | #107 | — | 158 | 2 | no | — |
| 381 | C4⋊C8 | — | 2 | 1 | no | — |
| 382 | C4⋊C8 | — | 158 | 1 | no | — |
| 383 | #103 | — | 158 | 2 | no | — |
| 384 | #103 | — | 158 | 2 | no | — |
| 385 | #102 | — | 158 | 2 | no | — |
| 386 | #102 | — | 158 | 2 | no | — |
| 387 | C22⋊C8 | — | 79 | 2 | no | — |
| 388 | C22⋊C8 | C22×D79 | 1 | 2 | yes | — |
| 389 | #97 | — | 2 | 1 | no | — |
| 390 | #97 | — | 158 | 1 | no | — |
| 391 | #95 | — | 2 | 1 | no | — |
| 392 | #95 | — | 158 | 2 | no | — |
| 393 | #95 | — | 158 | 2 | no | — |
| 394 | #95 | C22×D79 | 1 | 2 | yes | — |
| 395 | #41 | — | 4 | 4 | no | — |
| 396 | #41 | — | 316 | 4 | no | — |
| 397 | #41 | — | 316 | 8 | no | — |
| 398 | #41 | — | 316 | 8 | no | — |
| 399 | #41 | — | 316 | 8 | no | — |
| 400 | #41 | — | 316 | 8 | no | — |
| 401 | C2×Q8 | — | 2 | 1 | no | — |
| 402 | C2×Q8 | — | 316 | 8 | no | — |
| 403 | C2×Q8 | — | 316 | 2 | no | — |
| 404 | C2×Q8 | — | 316 | 8 | no | — |
| 405 | C2×Q8 | — | 158 | 4 | no | — |
| 406 | C2×Q8 | — | 158 | 4 | no | — |
| 407 | C2×Q8 | — | 158 | 1 | no | — |
| 408 | C2×Q8 | — | 158 | 1 | no | — |
| 409 | C2×Q8 | — | 158 | 1 | no | — |
| 410 | C2×Q8 | — | 158 | 1 | no | — |
| 411 | C2×Q8 | — | 158 | 1 | no | — |
| 412 | C2×D4 | — | 2 | 2 | no | — |
| 413 | C2×D4 | — | 2 | 1 | no | — |
| 414 | C2×D4 | — | 2 | 1 | no | — |
| 415 | C2×D4 | — | 79 | 2 | no | — |
| 416 | C2×D4 | — | 158 | 4 | no | — |
| 417 | C2×D4 | — | 158 | 2 | no | — |
| 418 | C2×D4 | — | 158 | 4 | no | — |
| 419 | C2×D4 | — | 158 | 1 | no | — |
| 420 | C2×D4 | — | 158 | 1 | no | — |
| 421 | C2×D4 | C2×D316 | 1 | 2 | yes | — |
| 422 | C22×C4 | — | 2 | 2 | no | — |
| 423 | C22×C4 | — | 2 | 2 | no | — |
| 424 | C22×C4 | — | 79 | 2 | no | — |
| 425 | C22×C4 | — | 79 | 2 | no | — |
| 426 | C22×C4 | — | 158 | 4 | no | — |
| 427 | C22×C4 | — | 158 | 1 | no | — |
| 428 | C22×C4 | — | 158 | 4 | no | — |
| 429 | C22×C4 | — | 158 | 1 | no | — |
| 430 | C22×C4 | — | 158 | 2 | no | — |
| 431 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 432 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 433 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 434 | SD16 | — | 316 | 4 | no | — |
| 435 | SD16 | — | 316 | 4 | no | — |
| 436 | C2×C8 | — | 2 | 2 | no | — |
| 437 | C2×C8 | — | 158 | 2 | no | — |
| 438 | C4⋊C4 | — | 2 | 1 | no | — |
| 439 | C4⋊C4 | — | 316 | 4 | no | — |
| 440 | C4⋊C4 | — | 316 | 4 | no | — |
| 441 | C4⋊C4 | — | 316 | 1 | no | — |
| 442 | C4⋊C4 | — | 316 | 1 | no | — |
| 443 | C4⋊C4 | — | 79 | 2 | no | — |
| 444 | C4⋊C4 | — | 158 | 4 | no | — |
| 445 | C4⋊C4 | — | 158 | 1 | no | — |
| 446 | C4⋊C4 | — | 158 | 1 | no | — |
| 447 | C4⋊C4 | — | 158 | 1 | no | — |
| 448 | C4⋊C4 | — | 158 | 1 | no | — |
| 449 | C4⋊C4 | — | 158 | 1 | no | — |
| 450 | C4⋊C4 | — | 158 | 2 | no | — |
| 451 | C4⋊C4 | — | 158 | 2 | no | — |
| 452 | C4⋊C4 | C2×D316 | 1 | 2 | yes | — |
| 453 | C22⋊C4 | — | 2 | 2 | no | — |
| 454 | C22⋊C4 | — | 2 | 2 | no | — |
| 455 | C22⋊C4 | — | 158 | 4 | no | — |
| 456 | C22⋊C4 | — | 158 | 4 | no | — |
| 457 | C22⋊C4 | — | 158 | 2 | no | — |
| 458 | C22⋊C4 | — | 158 | 2 | no | — |
| 459 | C42 | — | 2 | 4 | no | — |
| 460 | C42 | — | 316 | 1 | no | — |
| 461 | C42 | — | 316 | 1 | no | — |
| 462 | C42 | — | 158 | 2 | no | — |
| 463 | C42 | — | 158 | 2 | no | — |
| 464 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 465 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 466 | C42 | C2×D316 | 1 | 1 | yes | characteristic |
| 467 | C42 | C2×D316 | 1 | 1 | yes | characteristic |
| 468 | C23 | — | 2 | 2 | no | — |
| 469 | C23 | — | 158 | 2 | no | — |
| 470 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 471 | Q8 | — | 4 | 2 | no | — |
| 472 | Q8 | — | 316 | 2 | no | — |
| 473 | Q8 | — | 316 | 1 | no | — |
| 474 | Q8 | — | 316 | 1 | no | — |
| 475 | Q8 | — | 316 | 8 | no | — |
| 476 | Q8 | — | 158 | 2 | no | — |
| 477 | Q8 | — | 158 | 2 | no | — |
| 478 | Q8 | — | 158 | 4 | no | — |
| 479 | Q8 | — | 158 | 4 | no | — |
| 480 | D4 | — | 4 | 2 | no | — |
| 481 | D4 | — | 4 | 2 | no | — |
| 482 | D4 | — | 4 | 4 | no | — |
| 483 | D4 | — | 4 | 2 | no | — |
| 484 | D4 | — | 316 | 2 | no | — |
| 485 | D4 | — | 316 | 2 | no | — |
| 486 | D4 | — | 316 | 4 | no | — |
| 487 | D4 | — | 316 | 8 | no | — |
| 488 | D4 | — | 316 | 2 | no | — |
| 489 | D4 | — | 632 | 4 | no | — |
| 490 | C2×C4 | — | 2 | 2 | no | — |
| 491 | C2×C4 | — | 2 | 2 | no | — |
| 492 | C2×C4 | — | 2 | 4 | no | — |
| 493 | C2×C4 | — | 2 | 2 | no | — |
| 494 | C2×C4 | — | 4 | 1 | no | — |
| 495 | C2×C4 | — | 4 | 4 | no | — |
| 496 | C2×C4 | — | 4 | 2 | no | — |
| 497 | C2×C4 | — | 4 | 2 | no | — |
| 498 | C2×C4 | — | 316 | 4 | no | — |
| 499 | C2×C4 | — | 316 | 8 | no | — |
| 500 | C2×C4 | — | 316 | 1 | no | — |
| 501 | C2×C4 | — | 316 | 1 | no | — |
| 502 | C2×C4 | — | 316 | 8 | no | — |
| 503 | C2×C4 | — | 316 | 2 | no | — |
| 504 | C2×C4 | — | 316 | 1 | no | — |
| 505 | C2×C4 | — | 316 | 2 | no | — |
| 506 | C2×C4 | — | 79 | 4 | no | — |
| 507 | C2×C4 | — | 158 | 2 | no | — |
| 508 | C2×C4 | — | 158 | 2 | no | — |
| 509 | C2×C4 | — | 158 | 2 | no | — |
| 510 | C2×C4 | — | 158 | 2 | no | — |
| 511 | C2×C4 | — | 158 | 2 | no | — |
| 512 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 515 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 516 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 517 | C2×C4 | C22×D316 | 1 | 1 | yes | characteristic |
| 518 | C8 | — | 4 | 2 | no | — |
| 519 | C8 | — | 316 | 2 | no | — |
| 520 | C22 | — | 2 | 1 | no | — |
| 521 | C22 | — | 2 | 1 | no | — |
| 522 | C22 | — | 4 | 2 | no | — |
| 523 | C22 | — | 4 | 2 | no | — |
| 524 | C22 | — | 4 | 2 | no | — |
| 525 | C22 | — | 316 | 2 | no | — |
| 526 | C22 | — | 316 | 2 | no | — |
| 527 | C22 | — | 316 | 2 | no | — |
| 528 | C22 | C2×#14579131 | 1 | 1 | yes | characteristic |
| 529 | C22 | AGL(1,ℤ/8)×D79 | 1 | 2 | yes | — |
| 530 | C4 | — | 2 | 1 | no | — |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 2 | 1 | no | — |
| 533 | C4 | — | 2 | 1 | no | — |
| 534 | C4 | — | 2 | 1 | no | — |
| 535 | C4 | — | 4 | 4 | no | — |
| 536 | C4 | — | 4 | 2 | no | — |
| 537 | C4 | — | 316 | 2 | no | — |
| 538 | C4 | — | 316 | 2 | no | — |
| 539 | C4 | — | 316 | 2 | no | — |
| 540 | C4 | — | 632 | 1 | no | — |
| 541 | C4 | — | 158 | 4 | no | — |
| 542 | C4 | #19098747 | 1 | 2 | yes | — |
| 543 | C2 | — | 2 | 2 | no | — |
| 544 | C2 | — | 8 | 2 | no | — |
| 545 | C2 | — | 632 | 2 | no | — |
| 546 | C2 | #23772629 | 1 | 1 | yes | characteristic |
| 547 | C2 | C2×#19098747 | 1 | 1 | yes | characteristic |
| 548 | C2 | #23772794 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23773523 | C2 | semidirect |
| 3. #23773518 | C2 | semidirect |
| 4. #23766693 | C2 | semidirect |
| 5. #23762404 | C2 | semidirect |
| 6. #23762370 | C2 | semidirect |
| 7. #23761907 | C2 | semidirect |
| 8. #23761743 | C2 | semidirect |
| 9. C79×#1505 | C2 | semidirect |
| 282. #1505 | D79 | semidirect |
| 284. C79 | #18187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777166 | 2 |
| #23773523 | 2 |
| #23773518 | 2 |
| #23766693 | 2 |
| #23762404 | 2 |
| #23762370 | 2 |
| #23761907 | 2 |
| #23761743 | 2 |
| C79×#1505 | 2 |
| #18187 | 79 |