← #35197354
Subgroups — #35197354
Order 20224.
6846 conjugacy classes of subgroups.
The subgroup lattice has 592 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23777498 | C2 | 1 | 8 | yes | maximal, complemented |
| 2 | #23777487 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #23777408 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #23777382 | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #23777262 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | #23777210 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #23777119 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #23777048 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23776828 | C2 | 1 | 6 | yes | maximal, complemented |
| 10 | #23776789 | C2 | 1 | 6 | yes | maximal, complemented |
| 11 | 2−1+4×Dic79 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | C2×#19099039 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C79×#3497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C22×Q8×D79 | C22 | 1 | 1 | yes | characteristic |
| 15 | #19099299 | C22 | 1 | 12 | yes | complemented |
| 16 | Q8×Dic158 | C22 | 1 | 4 | yes | complemented |
| 17 | #19099292 | C22 | 1 | 4 | yes | complemented |
| 18 | #19099289 | C22 | 1 | 8 | yes | complemented |
| 19 | #19099288 | C22 | 1 | 12 | yes | complemented |
| 20 | #19099284 | C22 | 1 | 24 | yes | — |
| 21 | #19099283 | C22 | 1 | 12 | yes | complemented |
| 22 | #19099282 | C22 | 1 | 24 | yes | complemented |
| 23 | #19099277 | C22 | 1 | 24 | yes | — |
| 24 | #19099270 | C22 | 1 | 12 | yes | complemented |
| 25 | #19099265 | C22 | 1 | 24 | yes | — |
| 26 | #19099255 | C22 | 1 | 24 | yes | — |
| 27 | #19099253 | C22 | 1 | 24 | yes | complemented |
| 28 | Q8×C22⋊D79 | C22 | 1 | 8 | yes | — |
| 29 | Q8×C22⋊D79 | C22 | 1 | 8 | yes | — |
| 30 | #19099220 | C22 | 1 | 8 | yes | — |
| 31 | #19099220 | C22 | 1 | 8 | yes | — |
| 32 | #19099194 | C22 | 1 | 6 | yes | — |
| 33 | #19099182 | C22 | 1 | 12 | yes | — |
| 34 | #19099182 | C22 | 1 | 12 | yes | — |
| 35 | #19099180 | C22 | 1 | 24 | yes | complemented |
| 36 | #19099174 | C22 | 1 | 12 | yes | — |
| 37 | #19099173 | C22 | 1 | 24 | yes | complemented |
| 38 | #19099167 | C22 | 1 | 12 | yes | — |
| 39 | #19099158 | C22 | 1 | 12 | yes | — |
| 40 | #19099158 | C22 | 1 | 12 | yes | — |
| 41 | #19099150 | C22 | 1 | 4 | yes | — |
| 42 | #19099150 | C22 | 1 | 12 | yes | — |
| 43 | #19099134 | C22 | 1 | 12 | yes | — |
| 44 | #19099120 | C22 | 1 | 6 | yes | — |
| 45 | #19099115 | C22 | 1 | 24 | yes | complemented |
| 46 | #19099094 | C22 | 1 | 24 | yes | — |
| 47 | #19099094 | C22 | 1 | 24 | yes | complemented |
| 48 | #19099093 | C22 | 1 | 24 | yes | — |
| 49 | #19099093 | C22 | 1 | 24 | yes | — |
| 50 | #19099070 | C22 | 1 | 12 | yes | — |
| 51 | #19099046 | C22 | 1 | 12 | yes | — |
| 52 | #19099046 | C22 | 1 | 8 | yes | complemented |
| 53 | #19099041 | C22 | 1 | 2 | yes | — |
| 54 | #19099041 | C22 | 1 | 8 | yes | complemented |
| 55 | #19099039 | C22 | 1 | 8 | yes | — |
| 56 | #19099039 | C22 | 1 | 8 | yes | — |
| 57 | #41×Dic79 | C22 | 1 | 12 | yes | — |
| 58 | #41×Dic79 | C22 | 1 | 8 | yes | complemented |
| 59 | C2×Q8×Dic79 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×Q8×Dic79 | C22 | 1 | 8 | yes | complemented |
| 61 | C2×C4×Dic158 | C22 | 1 | 3 | yes | — |
| 62 | C2×#14579126 | C22 | 1 | 3 | yes | — |
| 63 | C2×#14579119 | C22 | 1 | 3 | yes | — |
| 64 | C2×#14579118 | C22 | 1 | 3 | yes | — |
| 65 | C2×2−1+4×C79 | C22 | 1 | 2 | yes | — |
| 66 | #550×C79 | C22 | 1 | 4 | yes | complemented |
| 67 | D4×Q8×C79 | C22 | 1 | 4 | yes | complemented |
| 68 | #548×C79 | C22 | 1 | 8 | yes | complemented |
| 69 | #537×C79 | C22 | 1 | 6 | yes | — |
| 70 | #532×C79 | C22 | 1 | 6 | yes | — |
| 71 | C2×C4×Q8×C79 | C22 | 1 | 1 | yes | characteristic |
| 72 | C22×Dic158 | C23 | 1 | 3 | yes | — |
| 73 | C2×Q8×D79 | — | 2 | 8 | no | — |
| 74 | C2×Q8×D79 | C23 | 1 | 8 | yes | — |
| 75 | C22×C4×D79 | C23 | 1 | 3 | yes | — |
| 76 | #14579161 | C23 | 1 | 6 | yes | — |
| 77 | #14579161 | C23 | 1 | 6 | yes | — |
| 78 | #14579160 | C23 | 1 | 24 | yes | — |
| 79 | #14579159 | C23 | 1 | 24 | yes | — |
| 80 | #14579156 | C23 | 1 | 8 | yes | — |
| 81 | #14579156 | C23 | 1 | 24 | yes | — |
| 82 | #14579154 | C23 | 1 | 24 | yes | — |
| 83 | #14579154 | C23 | 1 | 24 | yes | — |
| 84 | #14579154 | C23 | 1 | 48 | yes | — |
| 85 | #14579153 | C23 | 1 | 12 | yes | — |
| 86 | #14579152 | C23 | 1 | 24 | yes | — |
| 87 | #14579152 | C23 | 1 | 24 | yes | — |
| 88 | #14579151 | C23 | 1 | 24 | yes | — |
| 89 | #14579151 | C23 | 1 | 24 | yes | — |
| 90 | #14579148 | C23 | 1 | 24 | yes | — |
| 91 | #14579148 | C23 | 1 | 24 | yes | — |
| 92 | #14579147 | C23 | 1 | 8 | yes | — |
| 93 | #14579147 | C23 | 1 | 24 | yes | — |
| 94 | #14579145 | C23 | 1 | 8 | yes | — |
| 95 | #14579145 | C23 | 1 | 24 | yes | — |
| 96 | #14579142 | C23 | 1 | 24 | yes | — |
| 97 | #14579142 | C23 | 1 | 24 | yes | — |
| 98 | #14579142 | C23 | 1 | 24 | yes | — |
| 99 | #14579140 | C23 | 1 | 4 | yes | — |
| 100 | #14579140 | C23 | 1 | 12 | yes | — |
| 101 | #14579140 | C23 | 1 | 24 | yes | — |
| 102 | #14579140 | C23 | 1 | 24 | yes | — |
| 103 | #14579138 | C23 | 1 | 24 | yes | — |
| 104 | #14579138 | C23 | 1 | 24 | yes | — |
| 105 | #14579137 | C23 | 1 | 12 | yes | — |
| 106 | #14579137 | C23 | 1 | 12 | yes | — |
| 107 | #14579133 | C23 | 1 | 8 | yes | — |
| 108 | #14579133 | C23 | 1 | 24 | yes | — |
| 109 | #14579132 | C23 | 1 | 12 | yes | — |
| 110 | #14579132 | C23 | 1 | 12 | yes | — |
| 111 | #14579129 | C23 | 1 | 8 | yes | — |
| 112 | Q8×Dic79 | C23 | 1 | 12 | yes | — |
| 113 | Q8×Dic79 | C23 | 1 | 12 | yes | — |
| 114 | Q8×Dic79 | C23 | 1 | 8 | yes | — |
| 115 | Q8×Dic79 | C23 | 1 | 8 | yes | — |
| 116 | Q8×Dic79 | C23 | 1 | 24 | yes | — |
| 117 | Q8×Dic79 | C23 | 1 | 8 | yes | — |
| 118 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 119 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 120 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 121 | C4×Dic158 | C23 | 1 | 12 | yes | — |
| 122 | #14579126 | C23 | 1 | 24 | yes | — |
| 123 | #14579126 | C23 | 1 | 24 | yes | — |
| 124 | D4×Dic79 | C23 | 1 | 8 | yes | — |
| 125 | D4×Dic79 | C23 | 1 | 24 | yes | — |
| 126 | D4×Dic79 | C23 | 1 | 12 | yes | — |
| 127 | D4×Dic79 | C23 | 1 | 12 | yes | — |
| 128 | D4×Dic79 | C23 | 1 | 24 | yes | — |
| 129 | D4×Dic79 | C23 | 1 | 24 | yes | — |
| 130 | C4×C22⋊D79 | C23 | 1 | 24 | yes | — |
| 131 | C4×C22⋊D79 | C23 | 1 | 24 | yes | — |
| 132 | #14579120 | C23 | 1 | 24 | yes | — |
| 133 | #14579120 | C23 | 1 | 12 | yes | — |
| 134 | #14579120 | C23 | 1 | 24 | yes | — |
| 135 | #14579119 | C23 | 1 | 24 | yes | — |
| 136 | #14579118 | C23 | 1 | 12 | yes | — |
| 137 | #14579118 | C23 | 1 | 12 | yes | — |
| 138 | #14579117 | C23 | 1 | 48 | yes | — |
| 139 | C2×C4⋊Dic79 | C23 | 1 | 24 | yes | — |
| 140 | C2×C4⋊Dic79 | C23 | 1 | 3 | yes | — |
| 141 | C2×Dic79⋊C4 | C23 | 1 | 3 | yes | — |
| 142 | C2×Dic79⋊C4 | C23 | 1 | 3 | yes | — |
| 143 | C2×(C2×D79)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×(C2×D79)⋊C4 | C23 | 1 | 3 | yes | — |
| 145 | C2×C4×Dic79 | C23 | 1 | 3 | yes | — |
| 146 | C2×C4×Dic79 | C23 | 1 | 6 | yes | — |
| 147 | C2×C4×Dic79 | C23 | 1 | 24 | yes | — |
| 148 | 2−1+4×C79 | — | 2 | 16 | no | — |
| 149 | C2×#41×C79 | C23 | 1 | 8 | yes | — |
| 150 | C2×#41×C79 | C23 | 1 | 12 | yes | — |
| 151 | C22×Q8×C79 | C23 | 1 | 8 | yes | — |
| 152 | C22×Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 153 | C4⋊Q8×C79 | C23 | 1 | 6 | yes | — |
| 154 | #127×C79 | C23 | 1 | 6 | yes | — |
| 155 | #124×C79 | C23 | 1 | 12 | yes | — |
| 156 | C22⋊Q8×C79 | C23 | 1 | 24 | yes | — |
| 157 | #121×C79 | C23 | 1 | 4 | yes | — |
| 158 | #121×C79 | C23 | 1 | 12 | yes | — |
| 159 | #121×C79 | C23 | 1 | 24 | yes | — |
| 160 | C4×Q8×C79 | C23 | 1 | 4 | yes | — |
| 161 | C4×Q8×C79 | C23 | 1 | 4 | yes | — |
| 162 | C4×D4×C79 | C23 | 1 | 12 | yes | — |
| 163 | C4×D4×C79 | C23 | 1 | 12 | yes | — |
| 164 | C2×C4⋊C4×C79 | C23 | 1 | 3 | yes | — |
| 165 | C2×C42×C79 | C23 | 1 | 3 | yes | — |
| 166 | C23×D79 | C24 | 1 | 1 | yes | characteristic |
| 167 | C2×Dic158 | — | 2 | 12 | no | — |
| 168 | C2×Dic158 | C24 | 1 | 12 | yes | — |
| 169 | C2×Dic158 | C24 | 1 | 12 | yes | — |
| 170 | C2×Dic158 | C24 | 1 | 4 | yes | — |
| 171 | Q8×D79 | — | 2 | 32 | no | — |
| 172 | C2×C22⋊D79 | C24 | 1 | 8 | yes | — |
| 173 | C2×C22⋊D79 | C24 | 1 | 8 | yes | — |
| 174 | C22×Dic79 | C24 | 1 | 3 | yes | — |
| 175 | C22×Dic79 | C24 | 1 | 1 | yes | characteristic |
| 176 | C22×Dic79 | C24 | 1 | 3 | yes | — |
| 177 | C22×Dic79 | C24 | 1 | 8 | yes | — |
| 178 | C22×Dic79 | C24 | 1 | 24 | yes | — |
| 179 | C2×C4×D79 | — | 2 | 12 | no | — |
| 180 | C2×C4×D79 | C24 | 1 | 12 | yes | — |
| 181 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 182 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 183 | C4⋊Dic79 | C24 | 1 | 24 | yes | — |
| 184 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 185 | C4⋊Dic79 | C24 | 1 | 8 | yes | — |
| 186 | C4⋊Dic79 | C24 | 1 | 12 | yes | — |
| 187 | C4⋊Dic79 | C24 | 1 | 4 | yes | — |
| 188 | Dic79⋊C4 | C24 | 1 | 12 | yes | — |
| 189 | Dic79⋊C4 | C24 | 1 | 6 | yes | — |
| 190 | Dic79⋊C4 | C24 | 1 | 6 | yes | — |
| 191 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 192 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 193 | Dic79⋊C4 | C24 | 1 | 24 | yes | — |
| 194 | Dic79⋊C4 | C24 | 1 | 8 | yes | — |
| 195 | C22⋊Dic79 | C24 | 1 | 24 | yes | — |
| 196 | C22⋊Dic79 | C24 | 1 | 8 | yes | — |
| 197 | C22⋊Dic79 | C24 | 1 | 8 | yes | — |
| 198 | C22⋊Dic79 | C24 | 1 | 24 | yes | — |
| 199 | C22⋊Dic79 | C24 | 1 | 24 | yes | — |
| 200 | (C2×D79)⋊C4 | C24 | 1 | 2 | yes | — |
| 201 | (C2×D79)⋊C4 | C24 | 1 | 2 | yes | — |
| 202 | (C2×D79)⋊C4 | C24 | 1 | 12 | yes | — |
| 203 | (C2×D79)⋊C4 | C24 | 1 | 8 | yes | — |
| 204 | (C2×D79)⋊C4 | C24 | 1 | 8 | yes | — |
| 205 | C4×Dic79 | C24 | 1 | 12 | yes | — |
| 206 | C4×Dic79 | C24 | 1 | 8 | yes | — |
| 207 | C4×Dic79 | C24 | 1 | 24 | yes | — |
| 208 | C4×Dic79 | C24 | 1 | 24 | yes | — |
| 209 | C4×Dic79 | C24 | 1 | 24 | yes | — |
| 210 | #41×C79 | — | 2 | 32 | no | — |
| 211 | #41×C79 | — | 2 | 48 | no | — |
| 212 | C2×Q8×C79 | — | 2 | 32 | no | — |
| 213 | C2×Q8×C79 | #41 | 1 | 8 | yes | — |
| 214 | C2×Q8×C79 | C24 | 1 | 12 | yes | — |
| 215 | C2×Q8×C79 | C24 | 1 | 4 | yes | — |
| 216 | C2×D4×C79 | C24 | 1 | 8 | yes | — |
| 217 | C2×D4×C79 | C24 | 1 | 12 | yes | — |
| 218 | C2×D4×C79 | C24 | 1 | 4 | yes | — |
| 219 | C2×D4×C79 | C24 | 1 | 12 | yes | — |
| 220 | C22×C4×C79 | C24 | 1 | 24 | yes | — |
| 221 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 222 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 223 | C22×C4×C79 | C24 | 1 | 3 | yes | — |
| 224 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 225 | C4⋊C4×C79 | C24 | 1 | 4 | yes | — |
| 226 | C4⋊C4×C79 | C24 | 1 | 12 | yes | — |
| 227 | C22⋊C4×C79 | C24 | 1 | 8 | yes | — |
| 228 | C22⋊C4×C79 | C24 | 1 | 24 | yes | — |
| 229 | C42×C79 | C24 | 1 | 6 | yes | — |
| 230 | C42×C79 | C24 | 1 | 6 | yes | — |
| 231 | C23×C79 | C25 | 1 | 8 | yes | — |
| 232 | C23×C79 | C25 | 1 | 1 | yes | characteristic |
| 233 | C22×D79 | — | 2 | 2 | no | — |
| 234 | C22×D79 | — | 4 | 1 | no | — |
| 235 | C22×D79 | — | 4 | 1 | no | — |
| 236 | C22×D79 | C25 | 1 | 2 | yes | — |
| 237 | Q8×C79 | — | 2 | 24 | no | — |
| 238 | Q8×C79 | C2×#41 | 1 | 16 | yes | — |
| 239 | D4×C79 | — | 2 | 16 | no | — |
| 240 | D4×C79 | — | 2 | 24 | no | — |
| 241 | D4×C79 | — | 4 | 4 | no | — |
| 242 | D4×C79 | — | 4 | 12 | no | — |
| 243 | C2×C4×C79 | — | 2 | 48 | no | — |
| 244 | C2×C4×C79 | — | 4 | 1 | no | — |
| 245 | C2×C4×C79 | — | 4 | 3 | no | — |
| 246 | C2×C4×C79 | C2×#41 | 1 | 12 | yes | — |
| 247 | C2×C4×C79 | C25 | 1 | 8 | yes | — |
| 248 | C2×C4×C79 | C25 | 1 | 6 | yes | — |
| 249 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 250 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 251 | C2×C4×C79 | C25 | 1 | 6 | yes | — |
| 252 | C22⋊D79 | — | 4 | 8 | no | — |
| 253 | C22⋊D79 | — | 4 | 8 | no | — |
| 254 | C2×Dic79 | — | 2 | 6 | no | — |
| 255 | C2×Dic79 | — | 4 | 8 | no | — |
| 256 | C2×Dic79 | — | 4 | 24 | no | — |
| 257 | C2×Dic79 | — | 4 | 1 | no | — |
| 258 | C2×Dic79 | — | 4 | 3 | no | — |
| 259 | C2×Dic79 | C25 | 1 | 2 | yes | — |
| 260 | C2×Dic79 | C25 | 1 | 6 | yes | — |
| 261 | C2×Dic79 | C25 | 1 | 8 | yes | — |
| 262 | C2×Dic79 | C25 | 1 | 8 | yes | — |
| 263 | C2×Dic79 | C25 | 1 | 6 | yes | — |
| 264 | C4×D79 | — | 2 | 24 | no | — |
| 265 | Dic158 | — | 2 | 24 | no | — |
| 266 | Dic158 | — | 4 | 12 | no | — |
| 267 | Dic158 | — | 4 | 4 | no | — |
| 268 | C22×C79 | — | 2 | 1 | no | — |
| 269 | C22×C79 | — | 2 | 1 | no | — |
| 270 | C22×C79 | — | 2 | 8 | no | — |
| 271 | C22×C79 | — | 2 | 8 | no | — |
| 272 | C22×C79 | — | 2 | 8 | no | — |
| 273 | C22×C79 | C22×#41 | 1 | 2 | yes | — |
| 274 | C22×C79 | C26 | 1 | 1 | yes | characteristic |
| 275 | C2×D79 | — | 2 | 2 | no | — |
| 276 | C2×D79 | — | 2 | 2 | no | — |
| 277 | C2×D79 | — | 2 | 2 | no | — |
| 278 | C2×D79 | — | 4 | 4 | no | — |
| 279 | C4×C79 | — | 2 | 8 | no | — |
| 280 | C4×C79 | — | 2 | 1 | no | — |
| 281 | C4×C79 | — | 2 | 6 | no | — |
| 282 | C4×C79 | — | 2 | 1 | no | — |
| 283 | C4×C79 | C22×#41 | 1 | 12 | yes | — |
| 284 | Dic79 | — | 2 | 6 | no | — |
| 285 | Dic79 | — | 2 | 8 | no | — |
| 286 | Dic79 | — | 2 | 8 | no | — |
| 287 | Dic79 | — | 2 | 6 | no | — |
| 288 | Dic79 | — | 2 | 2 | no | — |
| 289 | #62850 | — | 79 | 1 | no | maximal, Sylow |
| 290 | C2×C79 | — | 2 | 2 | no | — |
| 291 | C2×C79 | — | 4 | 8 | no | — |
| 292 | C2×C79 | C23×#41 | 1 | 1 | yes | characteristic |
| 293 | C2×C79 | 2−1+6 | 1 | 1 | yes | characteristic |
| 294 | C2×C79 | 2−1+6 | 1 | 1 | yes | characteristic |
| 295 | D79 | — | 4 | 2 | no | — |
| 296 | #3524 | — | 79 | 8 | no | — |
| 297 | #3523 | — | 79 | 8 | no | — |
| 298 | #3518 | — | 79 | 8 | no | — |
| 299 | #3516 | — | 79 | 8 | no | — |
| 300 | #3507 | — | 79 | 6 | no | — |
| 301 | #3502 | — | 79 | 1 | no | — |
| 302 | #3497 | D79 | 1 | 1 | yes | characteristic, complemented |
| 303 | #3493 | — | 79 | 6 | no | — |
| 304 | #3486 | — | 79 | 2 | no | — |
| 305 | #3461 | — | 79 | 6 | no | — |
| 306 | #3455 | — | 79 | 6 | no | — |
| 307 | C4×2−1+4 | — | 79 | 2 | no | — |
| 308 | C2×#519 | — | 79 | 1 | no | — |
| 309 | C79 | #62850 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 310 | C2×2−1+4 | C2×D79 | 1 | 2 | yes | — |
| 311 | C23×Q8 | — | 79 | 1 | no | — |
| 312 | #559 | — | 79 | 12 | no | — |
| 313 | Q82 | — | 79 | 4 | no | — |
| 314 | #557 | — | 79 | 12 | no | — |
| 315 | #557 | — | 79 | 8 | no | — |
| 316 | #557 | — | 79 | 4 | no | — |
| 317 | #556 | — | 79 | 24 | no | — |
| 318 | #556 | — | 79 | 24 | no | — |
| 319 | #556 | — | 79 | 12 | no | — |
| 320 | #555 | — | 79 | 24 | no | — |
| 321 | #554 | — | 79 | 12 | no | — |
| 322 | #553 | — | 79 | 24 | no | — |
| 323 | #552 | — | 79 | 24 | no | — |
| 324 | #552 | — | 79 | 24 | no | — |
| 325 | #550 | C2×D79 | 1 | 4 | yes | complemented |
| 326 | D4×Q8 | — | 79 | 8 | no | — |
| 327 | D4×Q8 | — | 79 | 8 | no | — |
| 328 | D4×Q8 | C2×D79 | 1 | 4 | yes | complemented |
| 329 | #548 | — | 79 | 8 | no | — |
| 330 | #548 | — | 79 | 8 | no | — |
| 331 | #548 | C2×D79 | 1 | 8 | yes | complemented |
| 332 | #544 | — | 79 | 6 | no | — |
| 333 | #542 | — | 79 | 12 | no | — |
| 334 | #542 | — | 79 | 12 | no | — |
| 335 | #542 | — | 79 | 24 | no | — |
| 336 | #541 | — | 79 | 12 | no | — |
| 337 | #541 | — | 79 | 24 | no | — |
| 338 | #540 | — | 79 | 12 | no | — |
| 339 | #539 | — | 79 | 12 | no | — |
| 340 | #539 | — | 79 | 12 | no | — |
| 341 | #538 | — | 79 | 4 | no | — |
| 342 | #538 | — | 79 | 12 | no | — |
| 343 | #537 | C2×D79 | 1 | 6 | yes | — |
| 344 | #536 | — | 79 | 12 | no | — |
| 345 | #533 | — | 79 | 24 | no | — |
| 346 | #533 | — | 79 | 6 | no | — |
| 347 | #532 | C2×D79 | 1 | 6 | yes | — |
| 348 | #529 | — | 79 | 24 | no | — |
| 349 | #529 | — | 79 | 24 | no | — |
| 350 | #529 | — | 79 | 24 | no | — |
| 351 | #529 | — | 79 | 24 | no | — |
| 352 | #525 | — | 79 | 12 | no | — |
| 353 | #520 | — | 79 | 12 | no | — |
| 354 | #520 | — | 79 | 8 | no | — |
| 355 | #519 | — | 79 | 2 | no | — |
| 356 | #519 | — | 79 | 8 | no | — |
| 357 | #519 | — | 79 | 8 | no | — |
| 358 | #519 | — | 79 | 8 | no | — |
| 359 | C4×#41 | — | 79 | 12 | no | — |
| 360 | C4×#41 | — | 79 | 8 | no | — |
| 361 | C2×C4×Q8 | — | 79 | 1 | no | — |
| 362 | C2×C4×Q8 | — | 79 | 8 | no | — |
| 363 | C2×C4×Q8 | — | 79 | 3 | no | — |
| 364 | C2×C4×Q8 | — | 79 | 3 | no | — |
| 365 | C2×C4×Q8 | C2×D79 | 1 | 1 | yes | characteristic |
| 366 | C2×#117 | — | 79 | 3 | no | — |
| 367 | C2×#117 | — | 79 | 3 | no | — |
| 368 | 2−1+4 | — | 2 | 16 | no | — |
| 369 | C2×#41 | C22×D79 | 1 | 12 | yes | — |
| 370 | C2×#41 | C22×D79 | 1 | 8 | yes | — |
| 371 | C22×Q8 | — | 79 | 8 | no | — |
| 372 | C22×Q8 | — | 79 | 3 | no | — |
| 373 | C22×Q8 | — | 158 | 8 | no | — |
| 374 | C22×Q8 | C22×D79 | 1 | 8 | yes | — |
| 375 | C22×Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 376 | C23×C4 | — | 79 | 3 | no | — |
| 377 | C4⋊Q8 | — | 79 | 24 | no | — |
| 378 | C4⋊Q8 | — | 79 | 24 | no | — |
| 379 | C4⋊Q8 | — | 79 | 6 | no | — |
| 380 | C4⋊Q8 | — | 79 | 6 | no | — |
| 381 | C4⋊Q8 | C22×D79 | 1 | 6 | yes | — |
| 382 | #127 | C22×D79 | 1 | 6 | yes | — |
| 383 | #126 | — | 79 | 8 | no | — |
| 384 | #126 | — | 79 | 24 | no | — |
| 385 | #126 | — | 79 | 24 | no | — |
| 386 | #126 | — | 79 | 24 | no | — |
| 387 | #126 | — | 79 | 48 | no | — |
| 388 | #125 | — | 79 | 24 | no | — |
| 389 | #125 | — | 79 | 24 | no | — |
| 390 | #125 | — | 79 | 24 | no | — |
| 391 | #125 | — | 79 | 24 | no | — |
| 392 | #125 | — | 79 | 12 | no | — |
| 393 | #124 | — | 79 | 24 | no | — |
| 394 | #124 | — | 79 | 24 | no | — |
| 395 | #124 | — | 79 | 8 | no | — |
| 396 | #124 | — | 79 | 24 | no | — |
| 397 | #124 | C22×D79 | 1 | 12 | yes | — |
| 398 | #123 | — | 79 | 24 | no | — |
| 399 | #123 | — | 79 | 24 | no | — |
| 400 | #123 | — | 79 | 24 | no | — |
| 401 | #123 | — | 79 | 8 | no | — |
| 402 | #123 | — | 79 | 24 | no | — |
| 403 | C22⋊Q8 | — | 79 | 12 | no | — |
| 404 | C22⋊Q8 | — | 79 | 12 | no | — |
| 405 | C22⋊Q8 | — | 79 | 12 | no | — |
| 406 | C22⋊Q8 | — | 79 | 24 | no | — |
| 407 | C22⋊Q8 | — | 79 | 4 | no | — |
| 408 | C22⋊Q8 | — | 79 | 24 | no | — |
| 409 | C22⋊Q8 | — | 79 | 24 | no | — |
| 410 | C22⋊Q8 | — | 79 | 24 | no | — |
| 411 | C22⋊Q8 | C22×D79 | 1 | 24 | yes | — |
| 412 | #121 | — | 79 | 12 | no | — |
| 413 | #121 | — | 79 | 12 | no | — |
| 414 | #121 | — | 79 | 8 | no | — |
| 415 | #121 | — | 79 | 24 | no | — |
| 416 | #121 | C22×D79 | 1 | 12 | yes | — |
| 417 | #121 | C22×D79 | 1 | 24 | yes | — |
| 418 | #121 | C22×D79 | 1 | 4 | yes | — |
| 419 | #120 | — | 79 | 8 | no | — |
| 420 | C4×Q8 | — | 79 | 8 | no | — |
| 421 | C4×Q8 | — | 79 | 12 | no | — |
| 422 | C4×Q8 | — | 79 | 8 | no | — |
| 423 | C4×Q8 | — | 79 | 24 | no | — |
| 424 | C4×Q8 | — | 79 | 12 | no | — |
| 425 | C4×Q8 | — | 79 | 8 | no | — |
| 426 | C4×Q8 | — | 79 | 24 | no | — |
| 427 | C4×Q8 | — | 79 | 24 | no | — |
| 428 | C4×Q8 | — | 79 | 12 | no | — |
| 429 | C4×Q8 | — | 79 | 12 | no | — |
| 430 | C4×Q8 | — | 79 | 12 | no | — |
| 431 | C4×Q8 | — | 79 | 12 | no | — |
| 432 | C4×Q8 | C22×D79 | 1 | 4 | yes | — |
| 433 | C4×Q8 | C22×D79 | 1 | 4 | yes | — |
| 434 | C4×D4 | — | 79 | 8 | no | — |
| 435 | C4×D4 | — | 79 | 12 | no | — |
| 436 | C4×D4 | — | 79 | 24 | no | — |
| 437 | C4×D4 | — | 79 | 12 | no | — |
| 438 | C4×D4 | — | 79 | 24 | no | — |
| 439 | C4×D4 | — | 79 | 24 | no | — |
| 440 | C4×D4 | — | 79 | 24 | no | — |
| 441 | C4×D4 | — | 79 | 24 | no | — |
| 442 | C4×D4 | C22×D79 | 1 | 12 | yes | — |
| 443 | C4×D4 | C22×D79 | 1 | 12 | yes | — |
| 444 | #117 | — | 79 | 12 | no | — |
| 445 | #117 | — | 79 | 24 | no | — |
| 446 | #117 | — | 79 | 24 | no | — |
| 447 | #117 | — | 79 | 24 | no | — |
| 448 | #117 | — | 79 | 48 | no | — |
| 449 | #117 | — | 79 | 12 | no | — |
| 450 | #117 | — | 79 | 12 | no | — |
| 451 | C2×C4⋊C4 | — | 79 | 3 | no | — |
| 452 | C2×C4⋊C4 | — | 79 | 3 | no | — |
| 453 | C2×C4⋊C4 | — | 79 | 3 | no | — |
| 454 | C2×C4⋊C4 | — | 79 | 24 | no | — |
| 455 | C2×C4⋊C4 | C22×D79 | 1 | 3 | yes | — |
| 456 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 457 | C2×C22⋊C4 | — | 79 | 3 | no | — |
| 458 | C2×C42 | — | 79 | 3 | no | — |
| 459 | C2×C42 | — | 79 | 6 | no | — |
| 460 | C2×C42 | — | 79 | 24 | no | — |
| 461 | C2×C42 | C22×D79 | 1 | 3 | yes | — |
| 462 | C24 | — | 79 | 1 | no | — |
| 463 | #41 | — | 2 | 32 | no | — |
| 464 | #41 | — | 2 | 48 | no | — |
| 465 | C2×Q8 | — | 2 | 32 | no | — |
| 466 | C2×Q8 | — | 79 | 4 | no | — |
| 467 | C2×Q8 | — | 79 | 12 | no | — |
| 468 | C2×Q8 | — | 79 | 12 | no | — |
| 469 | C2×Q8 | — | 158 | 32 | no | — |
| 470 | C2×Q8 | — | 158 | 12 | no | — |
| 471 | C2×Q8 | #11929623 | 1 | 8 | yes | — |
| 472 | C2×Q8 | C23×D79 | 1 | 12 | yes | — |
| 473 | C2×Q8 | C23×D79 | 1 | 4 | yes | — |
| 474 | C2×D4 | — | 79 | 8 | no | — |
| 475 | C2×D4 | — | 79 | 8 | no | — |
| 476 | C2×D4 | C23×D79 | 1 | 8 | yes | — |
| 477 | C2×D4 | C23×D79 | 1 | 12 | yes | — |
| 478 | C2×D4 | C23×D79 | 1 | 12 | yes | — |
| 479 | C2×D4 | C23×D79 | 1 | 4 | yes | — |
| 480 | C22×C4 | — | 79 | 1 | no | — |
| 481 | C22×C4 | — | 79 | 3 | no | — |
| 482 | C22×C4 | — | 79 | 8 | no | — |
| 483 | C22×C4 | — | 79 | 24 | no | — |
| 484 | C22×C4 | — | 79 | 3 | no | — |
| 485 | C22×C4 | — | 79 | 12 | no | — |
| 486 | C22×C4 | — | 158 | 12 | no | — |
| 487 | C22×C4 | C23×D79 | 1 | 24 | yes | — |
| 488 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 489 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 490 | C22×C4 | C23×D79 | 1 | 3 | yes | — |
| 491 | C4⋊C4 | — | 79 | 6 | no | — |
| 492 | C4⋊C4 | — | 79 | 12 | no | — |
| 493 | C4⋊C4 | — | 79 | 6 | no | — |
| 494 | C4⋊C4 | — | 79 | 24 | no | — |
| 495 | C4⋊C4 | — | 79 | 24 | no | — |
| 496 | C4⋊C4 | — | 79 | 24 | no | — |
| 497 | C4⋊C4 | — | 79 | 8 | no | — |
| 498 | C4⋊C4 | — | 79 | 12 | no | — |
| 499 | C4⋊C4 | — | 79 | 12 | no | — |
| 500 | C4⋊C4 | — | 79 | 24 | no | — |
| 501 | C4⋊C4 | — | 79 | 12 | no | — |
| 502 | C4⋊C4 | — | 79 | 8 | no | — |
| 503 | C4⋊C4 | — | 79 | 12 | no | — |
| 504 | C4⋊C4 | — | 79 | 4 | no | — |
| 505 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 506 | C4⋊C4 | C23×D79 | 1 | 4 | yes | — |
| 507 | C4⋊C4 | C23×D79 | 1 | 12 | yes | — |
| 508 | C22⋊C4 | — | 79 | 8 | no | — |
| 509 | C22⋊C4 | — | 79 | 8 | no | — |
| 510 | C22⋊C4 | — | 79 | 24 | no | — |
| 511 | C22⋊C4 | — | 79 | 24 | no | — |
| 512 | C22⋊C4 | — | 79 | 24 | no | — |
| 513 | C22⋊C4 | — | 79 | 2 | no | — |
| 514 | C22⋊C4 | — | 79 | 12 | no | — |
| 515 | C22⋊C4 | — | 79 | 2 | no | — |
| 516 | C22⋊C4 | — | 79 | 8 | no | — |
| 517 | C22⋊C4 | — | 79 | 8 | no | — |
| 518 | C22⋊C4 | C23×D79 | 1 | 24 | yes | — |
| 519 | C22⋊C4 | C23×D79 | 1 | 8 | yes | — |
| 520 | C42 | — | 79 | 12 | no | — |
| 521 | C42 | — | 79 | 8 | no | — |
| 522 | C42 | — | 79 | 24 | no | — |
| 523 | C42 | — | 79 | 24 | no | — |
| 524 | C42 | — | 79 | 24 | no | — |
| 525 | C42 | C23×D79 | 1 | 6 | yes | — |
| 526 | C42 | C23×D79 | 1 | 6 | yes | — |
| 527 | C23 | — | 316 | 1 | no | — |
| 528 | C23 | — | 316 | 1 | no | — |
| 529 | C23 | — | 79 | 2 | no | — |
| 530 | C23 | — | 158 | 2 | no | — |
| 531 | C23 | C24×D79 | 1 | 8 | yes | — |
| 532 | C23 | C24×D79 | 1 | 1 | yes | characteristic |
| 533 | Q8 | — | 2 | 24 | no | — |
| 534 | Q8 | — | 316 | 4 | no | — |
| 535 | Q8 | — | 316 | 12 | no | — |
| 536 | Q8 | — | 158 | 24 | no | — |
| 537 | Q8 | C2×#11929623 | 1 | 16 | yes | — |
| 538 | D4 | — | 2 | 16 | no | — |
| 539 | D4 | — | 2 | 24 | no | — |
| 540 | D4 | — | 4 | 4 | no | — |
| 541 | D4 | — | 4 | 12 | no | — |
| 542 | D4 | — | 316 | 8 | no | — |
| 543 | D4 | — | 316 | 8 | no | — |
| 544 | C2×C4 | — | 2 | 48 | no | — |
| 545 | C2×C4 | — | 4 | 1 | no | — |
| 546 | C2×C4 | — | 4 | 3 | no | — |
| 547 | C2×C4 | — | 316 | 3 | no | — |
| 548 | C2×C4 | — | 316 | 24 | no | — |
| 549 | C2×C4 | — | 316 | 1 | no | — |
| 550 | C2×C4 | — | 316 | 8 | no | — |
| 551 | C2×C4 | — | 79 | 6 | no | — |
| 552 | C2×C4 | — | 79 | 2 | no | — |
| 553 | C2×C4 | — | 79 | 8 | no | — |
| 554 | C2×C4 | — | 79 | 6 | no | — |
| 555 | C2×C4 | — | 79 | 8 | no | — |
| 556 | C2×C4 | — | 158 | 6 | no | — |
| 557 | C2×C4 | — | 158 | 24 | no | — |
| 558 | C2×C4 | C2×#11929623 | 1 | 12 | yes | — |
| 559 | C2×C4 | C24×D79 | 1 | 6 | yes | — |
| 560 | C2×C4 | C24×D79 | 1 | 8 | yes | — |
| 561 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 562 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 563 | C2×C4 | C24×D79 | 1 | 6 | yes | — |
| 564 | C22 | — | 2 | 1 | no | — |
| 565 | C22 | — | 2 | 1 | no | — |
| 566 | C22 | — | 2 | 8 | no | — |
| 567 | C22 | — | 2 | 8 | no | — |
| 568 | C22 | — | 2 | 8 | no | — |
| 569 | C22 | — | 316 | 4 | no | — |
| 570 | C22 | — | 158 | 2 | no | — |
| 571 | C22 | — | 158 | 2 | no | — |
| 572 | C22 | — | 158 | 2 | no | — |
| 573 | C22 | C22×#11929623 | 1 | 2 | yes | — |
| 574 | C22 | C25×D79 | 1 | 1 | yes | characteristic |
| 575 | C4 | — | 2 | 8 | no | — |
| 576 | C4 | — | 2 | 1 | no | — |
| 577 | C4 | — | 2 | 1 | no | — |
| 578 | C4 | — | 2 | 6 | no | — |
| 579 | C4 | — | 158 | 6 | no | — |
| 580 | C4 | — | 158 | 6 | no | — |
| 581 | C4 | — | 158 | 8 | no | — |
| 582 | C4 | — | 158 | 2 | no | — |
| 583 | C4 | — | 158 | 8 | no | — |
| 584 | C4 | C22×#11929623 | 1 | 12 | yes | — |
| 585 | C2 | — | 2 | 2 | no | — |
| 586 | C2 | — | 4 | 8 | no | — |
| 587 | C2 | — | 316 | 2 | no | — |
| 588 | C2 | C23×#11929623 | 1 | 1 | yes | characteristic |
| 589 | C2 | #23778212 | 1 | 1 | yes | characteristic |
| 590 | C2 | #23778213 | 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