← #35160788
Subgroups — #35160788
Order 20224.
1666 conjugacy classes of subgroups.
The subgroup lattice has 664 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23777286 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23774668 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #23774559 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #23774559 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #23774551 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23774544 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23773942 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #23773910 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #23773782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C2×#19098915 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #23773369 | C2 | 1 | 4 | yes | maximal |
| 12 | #23773236 | C2 | 1 | 4 | yes | maximal, complemented |
| 13 | #23772044 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | C79×#3503 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #19099291 | — | 2 | 1 | no | — |
| 16 | #19099291 | — | 2 | 1 | no | — |
| 17 | #19099283 | — | 2 | 1 | no | — |
| 18 | #19099283 | — | 2 | 1 | no | — |
| 19 | #19099253 | — | 2 | 2 | no | — |
| 20 | #19099253 | — | 2 | 2 | no | — |
| 21 | #19099175 | C22 | 1 | 4 | yes | — |
| 22 | #19099134 | C22 | 1 | 2 | yes | — |
| 23 | #19099120 | C22 | 1 | 2 | yes | — |
| 24 | #19099120 | C22 | 1 | 2 | yes | — |
| 25 | #19099120 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#14579161 | C22 | 1 | 1 | yes | characteristic |
| 27 | #19099040 | C22 | 1 | 2 | yes | — |
| 28 | #19098969 | C22 | 1 | 4 | yes | — |
| 29 | #19098966 | C22 | 1 | 1 | yes | characteristic |
| 30 | #19098966 | C22 | 1 | 2 | yes | — |
| 31 | #19098966 | C22 | 1 | 1 | yes | characteristic |
| 32 | #19098962 | C22 | 1 | 4 | yes | — |
| 33 | #19098959 | C22 | 1 | 1 | yes | characteristic |
| 34 | #19098959 | C22 | 1 | 2 | yes | — |
| 35 | #19098959 | C22 | 1 | 1 | yes | characteristic |
| 36 | #19098933 | C22 | 1 | 4 | yes | — |
| 37 | #19098915 | C22 | 1 | 2 | yes | — |
| 38 | #19098915 | C22 | 1 | 2 | yes | — |
| 39 | #19098915 | C22 | 1 | 4 | yes | — |
| 40 | #19098915 | C22 | 1 | 2 | yes | — |
| 41 | #19098915 | C22 | 1 | 2 | yes | — |
| 42 | #19098904 | C22 | 1 | 8 | yes | — |
| 43 | #19098904 | C22 | 1 | 8 | yes | — |
| 44 | #19098898 | C22 | 1 | 8 | yes | — |
| 45 | #19098893 | C22 | 1 | 8 | yes | — |
| 46 | #19098867 | C22 | 1 | 8 | yes | — |
| 47 | #19098867 | C22 | 1 | 8 | yes | — |
| 48 | #19098855 | C22 | 1 | 8 | yes | — |
| 49 | #19098845 | C22 | 1 | 8 | yes | — |
| 50 | #19098624 | C22 | 1 | 4 | yes | — |
| 51 | #19098616 | C22 | 1 | 2 | yes | — |
| 52 | #19098616 | C22 | 1 | 2 | yes | — |
| 53 | #19098603 | C22 | 1 | 4 | yes | — |
| 54 | #19098599 | C22 | 1 | 4 | yes | — |
| 55 | #19098590 | C22 | 1 | 2 | yes | — |
| 56 | #19098571 | C22 | 1 | 4 | yes | — |
| 57 | C2×#14579084 | C22 | 1 | 4 | yes | — |
| 58 | #19098530 | C22 | 1 | 2 | yes | — |
| 59 | C4×#11929608 | C22 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×C79⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 61 | Q82×C79 | — | 2 | 1 | no | — |
| 62 | #557×C79 | — | 2 | 1 | no | — |
| 63 | #554×C79 | — | 2 | 2 | no | — |
| 64 | #554×C79 | — | 2 | 1 | no | — |
| 65 | D4×Q8×C79 | — | 2 | 2 | no | — |
| 66 | D4×Q8×C79 | — | 2 | 1 | no | — |
| 67 | #544×C79 | C22 | 1 | 2 | yes | — |
| 68 | #544×C79 | C22 | 1 | 4 | yes | — |
| 69 | #533×C79 | C22 | 1 | 1 | yes | characteristic |
| 70 | #533×C79 | C22 | 1 | 2 | yes | — |
| 71 | C2×C4⋊Q8×C79 | C22 | 1 | 1 | yes | characteristic |
| 72 | C2×C4⋊Q8×C79 | C22 | 1 | 2 | yes | — |
| 73 | #520×C79 | C22 | 1 | 2 | yes | — |
| 74 | C4×#41×C79 | C22 | 1 | 1 | yes | characteristic |
| 75 | C22×Dic158 | C23 | 1 | 2 | yes | — |
| 76 | C2×#11929608 | C23 | 1 | 2 | yes | — |
| 77 | C22×C79⋊C8 | C23 | 1 | 2 | yes | — |
| 78 | #14579161 | — | 2 | 1 | no | — |
| 79 | #14579161 | — | 2 | 1 | no | — |
| 80 | #14579161 | C23 | 1 | 2 | yes | — |
| 81 | #14579161 | C23 | 1 | 2 | yes | — |
| 82 | #14579161 | C23 | 1 | 1 | yes | characteristic |
| 83 | #14579161 | C23 | 1 | 1 | yes | characteristic |
| 84 | #14579159 | — | 2 | 2 | no | — |
| 85 | #14579154 | — | 2 | 4 | no | — |
| 86 | #14579154 | — | 2 | 4 | no | — |
| 87 | #14579153 | — | 2 | 2 | no | — |
| 88 | #14579153 | — | 2 | 2 | no | — |
| 89 | #14579153 | C23 | 1 | 2 | yes | — |
| 90 | #14579151 | — | 2 | 4 | no | — |
| 91 | #14579151 | — | 2 | 4 | no | — |
| 92 | #14579148 | — | 2 | 2 | no | — |
| 93 | #14579142 | — | 2 | 4 | no | — |
| 94 | #14579140 | — | 2 | 1 | no | — |
| 95 | #14579140 | — | 2 | 1 | no | — |
| 96 | #14579140 | — | 2 | 2 | no | — |
| 97 | #14579140 | — | 2 | 2 | no | — |
| 98 | #14579140 | C23 | 1 | 4 | yes | — |
| 99 | #14579140 | C23 | 1 | 4 | yes | — |
| 100 | C4×Dic158 | — | 2 | 2 | no | — |
| 101 | C4×Dic158 | — | 2 | 2 | no | — |
| 102 | C4×Dic158 | — | 2 | 1 | no | — |
| 103 | C4×Dic158 | — | 2 | 1 | no | — |
| 104 | C4×Dic158 | C23 | 1 | 4 | yes | — |
| 105 | C4×Dic158 | C23 | 1 | 4 | yes | — |
| 106 | #14579126 | — | 2 | 2 | no | — |
| 107 | #14579126 | — | 2 | 2 | no | — |
| 108 | #14579120 | — | 2 | 2 | no | — |
| 109 | #14579120 | — | 2 | 2 | no | — |
| 110 | #14579120 | C23 | 1 | 2 | yes | — |
| 111 | #14579117 | — | 2 | 4 | no | — |
| 112 | C2×C4⋊Dic79 | — | 2 | 1 | no | — |
| 113 | C2×C4⋊Dic79 | — | 2 | 1 | no | — |
| 114 | #14579094 | C23 | 1 | 4 | yes | — |
| 115 | #14579094 | C23 | 1 | 8 | yes | — |
| 116 | #14579094 | C23 | 1 | 4 | yes | — |
| 117 | #14579092 | C23 | 1 | 4 | yes | — |
| 118 | #14579092 | C23 | 1 | 8 | yes | — |
| 119 | #14579092 | C23 | 1 | 4 | yes | — |
| 120 | C4⋊(C79⋊C8) | C23 | 1 | 4 | yes | — |
| 121 | C4⋊(C79⋊C8) | C23 | 1 | 4 | yes | — |
| 122 | #14579084 | C23 | 1 | 8 | yes | — |
| 123 | #14579084 | C23 | 1 | 8 | yes | — |
| 124 | #14579084 | C23 | 1 | 8 | yes | — |
| 125 | #14579084 | C23 | 1 | 8 | yes | — |
| 126 | C22⋊(C79⋊C8) | C23 | 1 | 4 | yes | — |
| 127 | C22⋊(C79⋊C8) | C23 | 1 | 4 | yes | — |
| 128 | #14579072 | C23 | 1 | 2 | yes | — |
| 129 | C4×C79⋊C8 | C23 | 1 | 2 | yes | — |
| 130 | C4×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4×C79⋊C8 | C23 | 1 | 2 | yes | — |
| 132 | C4×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 133 | C2×#41×C79 | C23 | 1 | 1 | yes | characteristic |
| 134 | C22×Q8×C79 | — | 2 | 1 | no | — |
| 135 | C22×Q8×C79 | — | 2 | 2 | no | — |
| 136 | C4⋊Q8×C79 | — | 2 | 2 | no | — |
| 137 | C4⋊Q8×C79 | — | 2 | 4 | no | — |
| 138 | C4⋊Q8×C79 | — | 2 | 2 | no | — |
| 139 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 140 | C4⋊Q8×C79 | — | 2 | 2 | no | — |
| 141 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 142 | C4⋊Q8×C79 | C23 | 1 | 2 | yes | — |
| 143 | C4⋊Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4⋊Q8×C79 | C23 | 1 | 1 | yes | characteristic |
| 145 | C4⋊Q8×C79 | C23 | 1 | 2 | yes | — |
| 146 | C4⋊Q8×C79 | C23 | 1 | 4 | yes | — |
| 147 | #125×C79 | — | 2 | 2 | no | — |
| 148 | #125×C79 | — | 2 | 4 | no | — |
| 149 | #125×C79 | C23 | 1 | 2 | yes | — |
| 150 | #125×C79 | C23 | 1 | 4 | yes | — |
| 151 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 152 | C22⋊Q8×C79 | — | 2 | 2 | no | — |
| 153 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 154 | C22⋊Q8×C79 | — | 2 | 2 | no | — |
| 155 | C22⋊Q8×C79 | — | 2 | 4 | no | — |
| 156 | C22⋊Q8×C79 | — | 2 | 4 | no | — |
| 157 | C22⋊Q8×C79 | — | 2 | 4 | no | — |
| 158 | C4×Q8×C79 | — | 2 | 2 | no | — |
| 159 | C4×Q8×C79 | — | 2 | 2 | no | — |
| 160 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 161 | C4×Q8×C79 | — | 2 | 2 | no | — |
| 162 | C4×Q8×C79 | — | 2 | 1 | no | — |
| 163 | C4×Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 164 | C4×Q8×C79 | D4 | 1 | 1 | yes | characteristic |
| 165 | C4×D4×C79 | — | 2 | 4 | no | — |
| 166 | C4×D4×C79 | — | 2 | 2 | no | — |
| 167 | C4×D4×C79 | D4 | 1 | 2 | yes | — |
| 168 | C4×D4×C79 | D4 | 1 | 2 | yes | — |
| 169 | C4×D4×C79 | D4 | 1 | 1 | yes | characteristic |
| 170 | C4×D4×C79 | D4 | 1 | 1 | yes | characteristic |
| 171 | #117×C79 | C23 | 1 | 4 | yes | — |
| 172 | #117×C79 | C23 | 1 | 2 | yes | — |
| 173 | #117×C79 | C23 | 1 | 2 | yes | — |
| 174 | #117×C79 | C23 | 1 | 1 | yes | characteristic |
| 175 | C2×C4⋊C4×C79 | — | 2 | 1 | no | — |
| 176 | C2×C4⋊C4×C79 | — | 2 | 2 | no | — |
| 177 | C2×C4⋊C4×C79 | C23 | 1 | 4 | yes | — |
| 178 | C2×C4⋊C4×C79 | C23 | 1 | 2 | yes | — |
| 179 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 180 | C2×C42×C79 | C23 | 1 | 2 | yes | — |
| 181 | C2×Dic158 | — | 2 | 2 | no | — |
| 182 | C2×Dic158 | — | 2 | 1 | no | — |
| 183 | C2×Dic158 | — | 2 | 1 | no | — |
| 184 | C2×Dic158 | — | 2 | 8 | no | — |
| 185 | C2×Dic158 | C24 | 1 | 4 | yes | — |
| 186 | C22×Dic79 | — | 2 | 2 | no | — |
| 187 | #11929608 | — | 2 | 4 | no | — |
| 188 | C2×C79⋊C8 | — | 2 | 4 | no | — |
| 189 | C2×C79⋊C8 | C24 | 1 | 2 | yes | — |
| 190 | C2×C79⋊C8 | C24 | 1 | 2 | yes | — |
| 191 | C2×C79⋊C8 | C24 | 1 | 4 | yes | — |
| 192 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 193 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 194 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 195 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 196 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 197 | C4⋊Dic79 | — | 2 | 1 | no | — |
| 198 | C4⋊Dic79 | C24 | 1 | 2 | yes | — |
| 199 | C4⋊Dic79 | C24 | 1 | 2 | yes | — |
| 200 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 201 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 202 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 203 | Dic79⋊C4 | — | 2 | 2 | no | — |
| 204 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 205 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 206 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 207 | C22⋊Dic79 | — | 2 | 4 | no | — |
| 208 | C22⋊Dic79 | — | 2 | 4 | no | — |
| 209 | C4×Dic79 | — | 2 | 4 | no | — |
| 210 | C4×Dic79 | — | 2 | 4 | no | — |
| 211 | C4×Dic79 | — | 2 | 2 | no | — |
| 212 | #41×C79 | — | 2 | 4 | no | — |
| 213 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 214 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 215 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 216 | C2×Q8×C79 | — | 2 | 4 | no | — |
| 217 | C2×Q8×C79 | — | 2 | 2 | no | — |
| 218 | C2×Q8×C79 | — | 8 | 2 | no | — |
| 219 | C2×Q8×C79 | — | 8 | 4 | no | — |
| 220 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×D4×C79 | C2×D4 | 1 | 2 | yes | — |
| 222 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C22×C4×C79 | — | 2 | 4 | no | — |
| 224 | C22×C4×C79 | — | 2 | 2 | no | — |
| 225 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 226 | C22×C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 227 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 228 | C22×C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 229 | C22×C4×C79 | C24 | 1 | 2 | yes | — |
| 230 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 231 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 232 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 233 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 234 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 235 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 236 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 237 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 238 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 239 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 240 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 241 | C4⋊C4×C79 | — | 2 | 2 | no | — |
| 242 | C4⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C4⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 244 | C4⋊C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C4⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 246 | C4⋊C4×C79 | C24 | 1 | 2 | yes | — |
| 247 | C4⋊C4×C79 | C24 | 1 | 4 | yes | — |
| 248 | C4⋊C4×C79 | C24 | 1 | 2 | yes | — |
| 249 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 250 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 251 | C22⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 252 | C22⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 253 | C22⋊C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 254 | C42×C79 | — | 2 | 4 | no | — |
| 255 | C42×C79 | — | 2 | 2 | no | — |
| 256 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 257 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 258 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 261 | C42×C79 | C24 | 1 | 1 | yes | characteristic |
| 262 | C42×C79 | C24 | 1 | 2 | yes | — |
| 263 | C23×C79 | C22×D4 | 1 | 2 | yes | — |
| 264 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 265 | Q8×C79 | — | 2 | 2 | no | — |
| 266 | Q8×C79 | — | 4 | 4 | no | — |
| 267 | Q8×C79 | — | 4 | 2 | no | — |
| 268 | Q8×C79 | — | 4 | 2 | no | — |
| 269 | Q8×C79 | — | 8 | 4 | no | — |
| 270 | Q8×C79 | — | 8 | 2 | no | — |
| 271 | D4×C79 | — | 2 | 4 | no | — |
| 272 | D4×C79 | — | 2 | 2 | no | — |
| 273 | C2×C4×C79 | — | 2 | 2 | no | — |
| 274 | C2×C4×C79 | — | 2 | 4 | no | — |
| 275 | C2×C4×C79 | — | 2 | 2 | no | — |
| 276 | C2×C4×C79 | — | 2 | 4 | no | — |
| 277 | C2×C4×C79 | — | 2 | 4 | no | — |
| 278 | C2×C4×C79 | — | 2 | 2 | no | — |
| 279 | C2×C4×C79 | — | 2 | 4 | no | — |
| 280 | C2×C4×C79 | — | 2 | 2 | no | — |
| 281 | C2×C4×C79 | — | 8 | 2 | no | — |
| 282 | C2×C4×C79 | — | 8 | 4 | no | — |
| 283 | C2×C4×C79 | C22×D4 | 1 | 2 | yes | — |
| 284 | C2×C4×C79 | C22×D4 | 1 | 2 | yes | — |
| 285 | C2×C4×C79 | C22×D4 | 1 | 2 | yes | — |
| 286 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 287 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C79 | 2−1+4 | 1 | 4 | yes | — |
| 292 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 293 | C2×Dic79 | — | 2 | 2 | no | — |
| 294 | C2×Dic79 | — | 2 | 2 | no | — |
| 295 | C2×Dic79 | — | 2 | 4 | no | — |
| 296 | C2×Dic79 | — | 4 | 4 | no | — |
| 297 | Dic158 | — | 2 | 8 | no | — |
| 298 | Dic158 | — | 4 | 4 | no | — |
| 299 | Dic158 | — | 4 | 2 | no | — |
| 300 | Dic158 | — | 4 | 2 | no | — |
| 301 | C79⋊C8 | — | 2 | 2 | no | — |
| 302 | C79⋊C8 | — | 2 | 2 | no | — |
| 303 | C79⋊C8 | — | 2 | 4 | no | — |
| 304 | C22×C79 | — | 2 | 1 | no | — |
| 305 | C22×C79 | — | 2 | 1 | no | — |
| 306 | C22×C79 | — | 2 | 2 | no | — |
| 307 | C22×C79 | — | 2 | 2 | no | — |
| 308 | C22×C79 | — | 2 | 2 | no | — |
| 309 | C22×C79 | #536 | 1 | 2 | yes | — |
| 310 | C22×C79 | C23×D4 | 1 | 1 | yes | characteristic |
| 311 | C4×C79 | — | 2 | 2 | no | — |
| 312 | C4×C79 | — | 2 | 2 | no | — |
| 313 | C4×C79 | — | 2 | 1 | no | — |
| 314 | C4×C79 | — | 2 | 2 | no | — |
| 315 | C4×C79 | — | 2 | 1 | no | — |
| 316 | C4×C79 | — | 4 | 4 | no | — |
| 317 | C4×C79 | — | 4 | 2 | no | — |
| 318 | C4×C79 | — | 4 | 2 | no | — |
| 319 | C4×C79 | #536 | 1 | 2 | yes | — |
| 320 | C4×C79 | #577 | 1 | 2 | yes | — |
| 321 | C4×C79 | #578 | 1 | 2 | yes | — |
| 322 | C4×C79 | C2×2−1+4 | 1 | 2 | yes | — |
| 323 | Dic79 | — | 4 | 4 | no | — |
| 324 | Dic79 | — | 4 | 2 | no | — |
| 325 | Dic79 | — | 4 | 2 | no | — |
| 326 | #60878 | — | 79 | 1 | no | maximal, Sylow |
| 327 | C2×C79 | — | 2 | 2 | no | — |
| 328 | C2×C79 | — | 4 | 2 | no | — |
| 329 | C2×C79 | C2×#536 | 1 | 1 | yes | characteristic |
| 330 | C2×C79 | C2×#577 | 1 | 1 | yes | characteristic |
| 331 | C2×C79 | C2×#578 | 1 | 1 | yes | characteristic |
| 332 | #3509 | — | 79 | 1 | no | — |
| 333 | #3503 | D79 | 1 | 1 | yes | characteristic |
| 334 | #3242 | — | 79 | 8 | no | — |
| 335 | #3231 | — | 79 | 2 | no | — |
| 336 | #3231 | — | 79 | 2 | no | — |
| 337 | #3230 | — | 79 | 2 | no | — |
| 338 | #3229 | — | 79 | 2 | no | — |
| 339 | #3165 | — | 79 | 1 | no | — |
| 340 | #3160 | — | 79 | 1 | no | — |
| 341 | #3139 | — | 79 | 1 | no | — |
| 342 | C2×#487 | — | 79 | 1 | no | — |
| 343 | #3097 | — | 79 | 4 | no | — |
| 344 | #3082 | — | 79 | 4 | no | — |
| 345 | #2922 | — | 79 | 1 | no | — |
| 346 | C79 | #60878 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 347 | Q82 | — | 2 | 1 | no | — |
| 348 | #557 | — | 2 | 1 | no | — |
| 349 | #557 | — | 158 | 1 | no | — |
| 350 | #557 | — | 158 | 1 | no | — |
| 351 | #556 | — | 158 | 1 | no | — |
| 352 | #556 | — | 158 | 1 | no | — |
| 353 | #554 | — | 2 | 2 | no | — |
| 354 | #554 | — | 2 | 1 | no | — |
| 355 | #552 | — | 158 | 2 | no | — |
| 356 | #552 | — | 158 | 2 | no | — |
| 357 | D4×Q8 | — | 2 | 2 | no | — |
| 358 | D4×Q8 | — | 2 | 1 | no | — |
| 359 | #544 | C2×D79 | 1 | 2 | yes | — |
| 360 | #544 | C2×D79 | 1 | 4 | yes | — |
| 361 | #541 | — | 79 | 4 | no | — |
| 362 | #536 | — | 79 | 2 | no | — |
| 363 | #533 | — | 79 | 1 | no | — |
| 364 | #533 | — | 79 | 2 | no | — |
| 365 | #533 | — | 79 | 2 | no | — |
| 366 | #533 | C2×D79 | 1 | 1 | yes | characteristic |
| 367 | #533 | C2×D79 | 1 | 2 | yes | — |
| 368 | C2×C4⋊Q8 | — | 79 | 1 | no | — |
| 369 | C2×C4⋊Q8 | C2×D79 | 1 | 1 | yes | characteristic |
| 370 | C2×C4⋊Q8 | C2×D79 | 1 | 2 | yes | — |
| 371 | #520 | C2×D79 | 1 | 2 | yes | — |
| 372 | #519 | — | 79 | 2 | no | — |
| 373 | C4×#41 | C2×D79 | 1 | 1 | yes | characteristic |
| 374 | #501 | — | 79 | 4 | no | — |
| 375 | #500 | — | 79 | 1 | no | — |
| 376 | #500 | — | 79 | 1 | no | — |
| 377 | #500 | — | 79 | 2 | no | — |
| 378 | #499 | — | 79 | 4 | no | — |
| 379 | #498 | — | 79 | 1 | no | — |
| 380 | #498 | — | 79 | 1 | no | — |
| 381 | #498 | — | 79 | 2 | no | — |
| 382 | #491 | — | 79 | 4 | no | — |
| 383 | #487 | — | 79 | 2 | no | — |
| 384 | #487 | — | 79 | 2 | no | — |
| 385 | #487 | — | 79 | 4 | no | — |
| 386 | #487 | — | 79 | 2 | no | — |
| 387 | #487 | — | 79 | 2 | no | — |
| 388 | #485 | — | 79 | 8 | no | — |
| 389 | #485 | — | 79 | 8 | no | — |
| 390 | #484 | — | 79 | 8 | no | — |
| 391 | #483 | — | 79 | 8 | no | — |
| 392 | #479 | — | 79 | 8 | no | — |
| 393 | #479 | — | 79 | 8 | no | — |
| 394 | #477 | — | 79 | 8 | no | — |
| 395 | #475 | — | 79 | 8 | no | — |
| 396 | #433 | — | 79 | 4 | no | — |
| 397 | #431 | — | 79 | 2 | no | — |
| 398 | #431 | — | 79 | 2 | no | — |
| 399 | #428 | — | 79 | 4 | no | — |
| 400 | #427 | — | 79 | 4 | no | — |
| 401 | #424 | — | 79 | 2 | no | — |
| 402 | #419 | — | 79 | 4 | no | — |
| 403 | C2×#103 | — | 79 | 4 | no | — |
| 404 | #408 | — | 79 | 2 | no | — |
| 405 | C4×M16 | — | 79 | 1 | no | — |
| 406 | C2×C4×C8 | — | 79 | 1 | no | — |
| 407 | C2×#41 | C22×D79 | 1 | 1 | yes | characteristic |
| 408 | C22×Q8 | — | 2 | 1 | no | — |
| 409 | C22×Q8 | — | 2 | 2 | no | — |
| 410 | C22×Q8 | — | 79 | 2 | no | — |
| 411 | C2×M16 | — | 79 | 2 | no | — |
| 412 | C22×C8 | — | 79 | 2 | no | — |
| 413 | C4⋊Q8 | — | 2 | 2 | no | — |
| 414 | C4⋊Q8 | — | 2 | 4 | no | — |
| 415 | C4⋊Q8 | — | 2 | 2 | no | — |
| 416 | C4⋊Q8 | — | 2 | 1 | no | — |
| 417 | C4⋊Q8 | — | 2 | 2 | no | — |
| 418 | C4⋊Q8 | — | 2 | 1 | no | — |
| 419 | C4⋊Q8 | — | 79 | 1 | no | — |
| 420 | C4⋊Q8 | — | 79 | 1 | no | — |
| 421 | C4⋊Q8 | — | 79 | 2 | no | — |
| 422 | C4⋊Q8 | — | 79 | 2 | no | — |
| 423 | C4⋊Q8 | — | 158 | 2 | no | — |
| 424 | C4⋊Q8 | — | 158 | 1 | no | — |
| 425 | C4⋊Q8 | — | 158 | 1 | no | — |
| 426 | C4⋊Q8 | C22×D79 | 1 | 2 | yes | — |
| 427 | C4⋊Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 428 | C4⋊Q8 | C22×D79 | 1 | 4 | yes | — |
| 429 | C4⋊Q8 | C22×D79 | 1 | 2 | yes | — |
| 430 | C4⋊Q8 | C22×D79 | 1 | 1 | yes | characteristic |
| 431 | #126 | — | 158 | 4 | no | — |
| 432 | #126 | — | 158 | 4 | no | — |
| 433 | #125 | — | 2 | 2 | no | — |
| 434 | #125 | — | 2 | 4 | no | — |
| 435 | #125 | — | 79 | 2 | no | — |
| 436 | #125 | — | 158 | 4 | no | — |
| 437 | #125 | — | 158 | 4 | no | — |
| 438 | #125 | — | 158 | 2 | no | — |
| 439 | #125 | — | 158 | 2 | no | — |
| 440 | #125 | C22×D79 | 1 | 4 | yes | — |
| 441 | #125 | C22×D79 | 1 | 2 | yes | — |
| 442 | #124 | — | 158 | 2 | no | — |
| 443 | #123 | — | 158 | 4 | no | — |
| 444 | C22⋊Q8 | — | 2 | 1 | no | — |
| 445 | C22⋊Q8 | — | 2 | 2 | no | — |
| 446 | C22⋊Q8 | — | 2 | 1 | no | — |
| 447 | C22⋊Q8 | — | 2 | 2 | no | — |
| 448 | C22⋊Q8 | — | 2 | 4 | no | — |
| 449 | C22⋊Q8 | — | 2 | 4 | no | — |
| 450 | C22⋊Q8 | — | 2 | 4 | no | — |
| 451 | C22⋊Q8 | — | 79 | 4 | no | — |
| 452 | C22⋊Q8 | — | 79 | 4 | no | — |
| 453 | C22⋊Q8 | — | 158 | 1 | no | — |
| 454 | C22⋊Q8 | — | 158 | 1 | no | — |
| 455 | C22⋊Q8 | — | 158 | 2 | no | — |
| 456 | C22⋊Q8 | — | 158 | 2 | no | — |
| 457 | C4×Q8 | — | 2 | 2 | no | — |
| 458 | C4×Q8 | — | 2 | 2 | no | — |
| 459 | C4×Q8 | — | 2 | 1 | no | — |
| 460 | C4×Q8 | — | 2 | 2 | no | — |
| 461 | C4×Q8 | — | 2 | 1 | no | — |
| 462 | C4×Q8 | — | 79 | 4 | no | — |
| 463 | C4×Q8 | — | 79 | 4 | no | — |
| 464 | C4×Q8 | — | 158 | 2 | no | — |
| 465 | C4×Q8 | — | 158 | 2 | no | — |
| 466 | C4×Q8 | — | 158 | 2 | no | — |
| 467 | C4×Q8 | — | 158 | 2 | no | — |
| 468 | C4×Q8 | — | 158 | 1 | no | — |
| 469 | C4×Q8 | — | 158 | 1 | no | — |
| 470 | C4×Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 471 | C4×Q8 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 472 | C4×D4 | — | 2 | 4 | no | — |
| 473 | C4×D4 | — | 2 | 2 | no | — |
| 474 | C4×D4 | C22⋊D79 | 1 | 2 | yes | — |
| 475 | C4×D4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 476 | C4×D4 | C22⋊D79 | 1 | 2 | yes | — |
| 477 | C4×D4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 478 | #117 | — | 79 | 2 | no | — |
| 479 | #117 | — | 158 | 2 | no | — |
| 480 | #117 | — | 158 | 2 | no | — |
| 481 | #117 | — | 158 | 4 | no | — |
| 482 | #117 | C22×D79 | 1 | 2 | yes | — |
| 483 | #117 | C22×D79 | 1 | 4 | yes | — |
| 484 | #117 | C22×D79 | 1 | 1 | yes | characteristic |
| 485 | #117 | C22×D79 | 1 | 2 | yes | — |
| 486 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 487 | C2×C4⋊C4 | — | 2 | 2 | no | — |
| 488 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 489 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 490 | C2×C4⋊C4 | C22×D79 | 1 | 2 | yes | — |
| 491 | C2×C4⋊C4 | C22×D79 | 1 | 4 | yes | — |
| 492 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 493 | C2×C42 | C22×D79 | 1 | 2 | yes | — |
| 494 | #107 | — | 79 | 4 | no | — |
| 495 | #107 | — | 79 | 4 | no | — |
| 496 | #107 | — | 79 | 8 | no | — |
| 497 | #106 | — | 79 | 4 | no | — |
| 498 | #106 | — | 79 | 4 | no | — |
| 499 | #106 | — | 79 | 8 | no | — |
| 500 | C4⋊C8 | — | 79 | 4 | no | — |
| 501 | C4⋊C8 | — | 79 | 4 | no | — |
| 502 | #103 | — | 79 | 8 | no | — |
| 503 | #103 | — | 79 | 8 | no | — |
| 504 | #103 | — | 79 | 8 | no | — |
| 505 | #103 | — | 79 | 8 | no | — |
| 506 | C22⋊C8 | — | 79 | 4 | no | — |
| 507 | C22⋊C8 | — | 79 | 4 | no | — |
| 508 | #97 | — | 79 | 2 | no | — |
| 509 | C4×C8 | — | 79 | 1 | no | — |
| 510 | C4×C8 | — | 79 | 1 | no | — |
| 511 | C4×C8 | — | 79 | 2 | no | — |
| 512 | C4×C8 | — | 79 | 2 | no | — |
| 513 | #41 | — | 2 | 4 | no | — |
| 514 | C2×Q8 | — | 2 | 1 | no | — |
| 515 | C2×Q8 | — | 2 | 2 | no | — |
| 516 | C2×Q8 | — | 2 | 1 | no | — |
| 517 | C2×Q8 | — | 2 | 4 | no | — |
| 518 | C2×Q8 | — | 2 | 2 | no | — |
| 519 | C2×Q8 | — | 8 | 2 | no | — |
| 520 | C2×Q8 | — | 8 | 4 | no | — |
| 521 | C2×Q8 | — | 79 | 4 | no | — |
| 522 | C2×Q8 | — | 158 | 8 | no | — |
| 523 | C2×Q8 | — | 158 | 1 | no | — |
| 524 | C2×Q8 | — | 158 | 1 | no | — |
| 525 | C2×Q8 | — | 158 | 2 | no | — |
| 526 | C2×Q8 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 527 | C2×D4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 528 | C2×D4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 529 | C22×C4 | — | 2 | 4 | no | — |
| 530 | C22×C4 | — | 2 | 2 | no | — |
| 531 | C22×C4 | — | 158 | 2 | no | — |
| 532 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 533 | C22×C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 534 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 535 | C22×C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 536 | C22×C4 | C23×D79 | 1 | 2 | yes | — |
| 537 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 538 | M16 | — | 158 | 4 | no | — |
| 539 | C2×C8 | — | 79 | 2 | no | — |
| 540 | C2×C8 | — | 79 | 2 | no | — |
| 541 | C2×C8 | — | 79 | 4 | no | — |
| 542 | C2×C8 | — | 158 | 4 | no | — |
| 543 | C4⋊C4 | — | 2 | 2 | no | — |
| 544 | C4⋊C4 | — | 2 | 1 | no | — |
| 545 | C4⋊C4 | — | 2 | 4 | no | — |
| 546 | C4⋊C4 | — | 2 | 2 | no | — |
| 547 | C4⋊C4 | — | 2 | 4 | no | — |
| 548 | C4⋊C4 | — | 2 | 2 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 2 | 4 | no | — |
| 551 | C4⋊C4 | — | 2 | 2 | no | — |
| 552 | C4⋊C4 | — | 2 | 4 | no | — |
| 553 | C4⋊C4 | — | 2 | 2 | no | — |
| 554 | C4⋊C4 | — | 79 | 2 | no | — |
| 555 | C4⋊C4 | — | 79 | 2 | no | — |
| 556 | C4⋊C4 | — | 158 | 4 | no | — |
| 557 | C4⋊C4 | — | 158 | 4 | no | — |
| 558 | C4⋊C4 | — | 158 | 4 | no | — |
| 559 | C4⋊C4 | — | 158 | 4 | no | — |
| 560 | C4⋊C4 | — | 158 | 2 | no | — |
| 561 | C4⋊C4 | — | 158 | 2 | no | — |
| 562 | C4⋊C4 | — | 158 | 2 | no | — |
| 563 | C4⋊C4 | — | 158 | 2 | no | — |
| 564 | C4⋊C4 | — | 158 | 2 | no | — |
| 565 | C4⋊C4 | — | 158 | 2 | no | — |
| 566 | C4⋊C4 | — | 158 | 1 | no | — |
| 567 | C4⋊C4 | — | 158 | 1 | no | — |
| 568 | C4⋊C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 569 | C4⋊C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 570 | C4⋊C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 571 | C4⋊C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 572 | C4⋊C4 | C23×D79 | 1 | 4 | yes | — |
| 573 | C4⋊C4 | C23×D79 | 1 | 2 | yes | — |
| 574 | C4⋊C4 | C23×D79 | 1 | 2 | yes | — |
| 575 | C22⋊C4 | — | 2 | 4 | no | — |
| 576 | C22⋊C4 | — | 2 | 2 | no | — |
| 577 | C22⋊C4 | — | 158 | 2 | no | — |
| 578 | C22⋊C4 | — | 158 | 4 | no | — |
| 579 | C22⋊C4 | — | 158 | 4 | no | — |
| 580 | C22⋊C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 581 | C22⋊C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 582 | C22⋊C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 583 | C42 | — | 2 | 4 | no | — |
| 584 | C42 | — | 2 | 2 | no | — |
| 585 | C42 | — | 158 | 2 | no | — |
| 586 | C42 | — | 158 | 4 | no | — |
| 587 | C42 | — | 158 | 4 | no | — |
| 588 | C42 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 589 | C42 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 590 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 591 | C42 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 592 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 593 | C42 | C23×D79 | 1 | 1 | yes | characteristic |
| 594 | C42 | C23×D79 | 1 | 2 | yes | — |
| 595 | C23 | C22×C22⋊D79 | 1 | 2 | yes | — |
| 596 | C23 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 597 | Q8 | — | 2 | 2 | no | — |
| 598 | Q8 | — | 4 | 4 | no | — |
| 599 | Q8 | — | 4 | 2 | no | — |
| 600 | Q8 | — | 4 | 2 | no | — |
| 601 | Q8 | — | 8 | 4 | no | — |
| 602 | Q8 | — | 8 | 2 | no | — |
| 603 | Q8 | — | 316 | 4 | no | — |
| 604 | Q8 | — | 316 | 2 | no | — |
| 605 | Q8 | — | 316 | 2 | no | — |
| 606 | Q8 | — | 158 | 8 | no | — |
| 607 | D4 | — | 2 | 4 | no | — |
| 608 | D4 | — | 2 | 2 | no | — |
| 609 | C2×C4 | — | 2 | 4 | no | — |
| 610 | C2×C4 | — | 2 | 2 | no | — |
| 611 | C2×C4 | — | 2 | 4 | no | — |
| 612 | C2×C4 | — | 2 | 2 | no | — |
| 613 | C2×C4 | — | 2 | 4 | no | — |
| 614 | C2×C4 | — | 2 | 2 | no | — |
| 615 | C2×C4 | — | 2 | 4 | no | — |
| 616 | C2×C4 | — | 2 | 2 | no | — |
| 617 | C2×C4 | — | 8 | 2 | no | — |
| 618 | C2×C4 | — | 8 | 4 | no | — |
| 619 | C2×C4 | — | 316 | 4 | no | — |
| 620 | C2×C4 | — | 158 | 2 | no | — |
| 621 | C2×C4 | — | 158 | 2 | no | — |
| 622 | C2×C4 | — | 158 | 4 | no | — |
| 623 | C2×C4 | C22×C22⋊D79 | 1 | 2 | yes | — |
| 624 | C2×C4 | C22×C22⋊D79 | 1 | 2 | yes | — |
| 625 | C2×C4 | C22×C22⋊D79 | 1 | 2 | yes | — |
| 626 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 627 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 628 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 629 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 630 | C2×C4 | C22×C22⋊D79 | 1 | 1 | yes | characteristic |
| 631 | C2×C4 | #14579209 | 1 | 4 | yes | — |
| 632 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 633 | C8 | — | 158 | 2 | no | — |
| 634 | C8 | — | 158 | 2 | no | — |
| 635 | C8 | — | 158 | 4 | no | — |
| 636 | C22 | — | 2 | 1 | no | — |
| 637 | C22 | — | 2 | 1 | no | — |
| 638 | C22 | — | 2 | 2 | no | — |
| 639 | C22 | — | 2 | 2 | no | — |
| 640 | C22 | — | 2 | 2 | no | — |
| 641 | C22 | #19099137 | 1 | 2 | yes | — |
| 642 | C22 | C23×C22⋊D79 | 1 | 1 | yes | characteristic |
| 643 | C4 | — | 2 | 2 | no | — |
| 644 | C4 | — | 2 | 1 | no | — |
| 645 | C4 | — | 2 | 2 | no | — |
| 646 | C4 | — | 2 | 1 | no | — |
| 647 | C4 | — | 2 | 2 | no | — |
| 648 | C4 | — | 4 | 4 | no | — |
| 649 | C4 | — | 4 | 2 | no | — |
| 650 | C4 | — | 4 | 2 | no | — |
| 651 | C4 | — | 316 | 2 | no | — |
| 652 | C4 | — | 316 | 2 | no | — |
| 653 | C4 | — | 316 | 4 | no | — |
| 654 | C4 | #19099137 | 1 | 2 | yes | — |
| 655 | C4 | #19099374 | 1 | 2 | yes | — |
| 656 | C4 | #19099378 | 1 | 2 | yes | — |
| 657 | C4 | C2×#14579209 | 1 | 2 | yes | — |
| 658 | C2 | — | 2 | 2 | no | — |
| 659 | C2 | — | 4 | 2 | no | — |
| 660 | C2 | C2×#19099137 | 1 | 1 | yes | characteristic |
| 661 | C2 | C2×#19099374 | 1 | 1 | yes | characteristic |
| 662 | C2 | C2×#19099378 | 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