← #35158171
Subgroups — #35158171
Order 20224.
1878 conjugacy classes of subgroups.
The subgroup lattice has 456 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #23776792 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #23774088 | C2 | 1 | 8 | yes | maximal, complemented |
| 3 | #23774073 | C2 | 1 | 8 | yes | maximal, complemented |
| 4 | #23773846 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23773725 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23773010 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #23772982 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #23772200 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #23772171 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×#19098520 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C79×#3162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#14579183 | C22 | 1 | 2 | yes | — |
| 13 | C2×#14579183 | C22 | 1 | 2 | yes | — |
| 14 | C22×#11929607 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C8×D79 | C22 | 1 | 1 | yes | characteristic |
| 16 | #19099187 | C22 | 1 | 8 | yes | — |
| 17 | #19099176 | C22 | 1 | 4 | yes | — |
| 18 | #19099169 | C22 | 1 | 4 | yes | — |
| 19 | #19099162 | — | 2 | 4 | no | — |
| 20 | #19099153 | — | 2 | 4 | no | — |
| 21 | #19099113 | C22 | 1 | 2 | yes | — |
| 22 | #19099100 | — | 2 | 8 | no | — |
| 23 | #19099075 | C22 | 1 | 4 | yes | — |
| 24 | #19099031 | C22 | 1 | 4 | yes | — |
| 25 | C2×#14579118 | C22 | 1 | 1 | yes | characteristic |
| 26 | #19098957 | C22 | 1 | 4 | yes | complemented |
| 27 | #19098952 | C22 | 1 | 4 | yes | complemented |
| 28 | #19098920 | C22 | 1 | 8 | yes | complemented |
| 29 | #19098915 | C22 | 1 | 4 | yes | complemented |
| 30 | #19098911 | C22 | 1 | 4 | yes | complemented |
| 31 | #19098822 | C22 | 1 | 4 | yes | — |
| 32 | #19098817 | C22 | 1 | 4 | yes | — |
| 33 | #19098810 | C22 | 1 | 8 | yes | — |
| 34 | #19098805 | C22 | 1 | 4 | yes | — |
| 35 | #19098800 | C22 | 1 | 4 | yes | — |
| 36 | #19098793 | C22 | 1 | 8 | yes | — |
| 37 | #19098674 | C22 | 1 | 4 | yes | complemented |
| 38 | #19098669 | C22 | 1 | 4 | yes | complemented |
| 39 | #19098662 | C22 | 1 | 8 | yes | complemented |
| 40 | #19098657 | C22 | 1 | 4 | yes | complemented |
| 41 | #19098650 | C22 | 1 | 8 | yes | complemented |
| 42 | #19098645 | C22 | 1 | 4 | yes | complemented |
| 43 | #19098557 | C22 | 1 | 4 | yes | — |
| 44 | #19098557 | C22 | 1 | 4 | yes | — |
| 45 | #19098520 | C22 | 1 | 8 | yes | — |
| 46 | C2×#14579071 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×C79⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×C8×Dic79 | C22 | 1 | 1 | yes | characteristic |
| 49 | #533×C79 | C22 | 1 | 2 | yes | — |
| 50 | #501×C79 | C22 | 1 | 8 | yes | complemented |
| 51 | #427×C79 | C22 | 1 | 2 | yes | — |
| 52 | #427×C79 | C22 | 1 | 2 | yes | — |
| 53 | C2×#97×C79 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#11929624 | C23 | 1 | 4 | yes | — |
| 55 | C22×C4×D79 | C23 | 1 | 1 | yes | characteristic |
| 56 | #14579183 | — | 2 | 8 | no | — |
| 57 | #14579183 | — | 2 | 8 | no | — |
| 58 | C2×Dic316 | C23 | 1 | 2 | yes | — |
| 59 | C2×Dic316 | C23 | 1 | 2 | yes | — |
| 60 | C2×#11929613 | C23 | 1 | 4 | yes | — |
| 61 | C2×#11929613 | C23 | 1 | 4 | yes | — |
| 62 | C2×D632 | C23 | 1 | 2 | yes | — |
| 63 | C2×D632 | C23 | 1 | 2 | yes | — |
| 64 | C2×#11929607 | — | 2 | 4 | no | — |
| 65 | C2×#11929607 | C23 | 1 | 4 | yes | — |
| 66 | C22×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 67 | C22×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×C8×D79 | — | 2 | 4 | no | — |
| 69 | C2×C8×D79 | C23 | 1 | 4 | yes | — |
| 70 | #14579161 | C23 | 1 | 2 | yes | — |
| 71 | #14579158 | C23 | 1 | 2 | yes | — |
| 72 | #14579156 | — | 2 | 8 | no | — |
| 73 | #14579156 | — | 2 | 8 | no | — |
| 74 | #14579152 | — | 2 | 8 | no | — |
| 75 | #14579150 | — | 2 | 8 | no | — |
| 76 | #14579149 | C23 | 1 | 4 | yes | — |
| 77 | #14579146 | — | 2 | 8 | no | — |
| 78 | #14579146 | — | 2 | 8 | no | — |
| 79 | #14579145 | — | 2 | 4 | no | — |
| 80 | #14579141 | C23 | 1 | 8 | yes | — |
| 81 | #14579137 | — | 2 | 8 | no | — |
| 82 | #14579136 | — | 2 | 8 | no | — |
| 83 | #14579136 | C23 | 1 | 8 | yes | — |
| 84 | #14579135 | — | 2 | 4 | no | — |
| 85 | #14579131 | — | 2 | 4 | no | — |
| 86 | #14579126 | C23 | 1 | 8 | yes | — |
| 87 | C4×D316 | — | 2 | 4 | no | — |
| 88 | C4×D316 | — | 2 | 8 | no | — |
| 89 | #14579123 | C23 | 1 | 8 | yes | — |
| 90 | (C22⋊D79)⋊C4 | — | 2 | 8 | no | — |
| 91 | #14579118 | — | 2 | 4 | no | — |
| 92 | #14579118 | D4 | 1 | 4 | yes | — |
| 93 | #14579118 | C23 | 1 | 4 | yes | — |
| 94 | C2×Dic79⋊C4 | D4 | 1 | 2 | yes | — |
| 95 | C2×(C2×D79)⋊C4 | D4 | 1 | 2 | yes | — |
| 96 | C2×C4×Dic79 | C23 | 1 | 1 | yes | characteristic |
| 97 | C42×D79 | — | 2 | 4 | no | — |
| 98 | #14579084 | C23 | 1 | 8 | yes | — |
| 99 | #14579084 | C23 | 1 | 8 | yes | — |
| 100 | #14579081 | C23 | 1 | 8 | yes | — |
| 101 | #14579081 | C23 | 1 | 8 | yes | — |
| 102 | #14579071 | C23 | 1 | 4 | yes | — |
| 103 | C4×C79⋊C8 | C23 | 1 | 4 | yes | — |
| 104 | C8×Dic79 | C23 | 1 | 4 | yes | — |
| 105 | C22×C8×C79 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22×C8×C79 | C23 | 1 | 1 | yes | characteristic |
| 107 | C4⋊Q8×C79 | C23 | 1 | 4 | yes | — |
| 108 | #125×C79 | C23 | 1 | 4 | yes | — |
| 109 | C22⋊Q8×C79 | — | 2 | 4 | no | — |
| 110 | C4×Q8×C79 | — | 2 | 4 | no | — |
| 111 | #117×C79 | C23 | 1 | 4 | yes | — |
| 112 | C2×C42×C79 | C23 | 1 | 1 | yes | characteristic |
| 113 | #107×C79 | C23 | 1 | 4 | yes | — |
| 114 | #107×C79 | C23 | 1 | 4 | yes | — |
| 115 | #106×C79 | C23 | 1 | 4 | yes | — |
| 116 | #106×C79 | C23 | 1 | 4 | yes | — |
| 117 | #97×C79 | C23 | 1 | 4 | yes | — |
| 118 | C23×D79 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | #11929624 | — | 2 | 8 | no | — |
| 120 | #11929624 | — | 2 | 8 | no | — |
| 121 | C2×Dic158 | C24 | 1 | 4 | yes | — |
| 122 | C2×D316 | — | 2 | 8 | no | — |
| 123 | C2×D316 | — | 2 | 4 | no | — |
| 124 | C2×D316 | C24 | 1 | 4 | yes | — |
| 125 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 126 | C22×Dic79 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C22×Dic79 | C2×D4 | 1 | 2 | yes | — |
| 128 | C2×C4×D79 | — | 2 | 8 | no | — |
| 129 | C2×C4×D79 | — | 2 | 4 | no | — |
| 130 | C2×C4×D79 | — | 2 | 2 | no | — |
| 131 | C2×C4×D79 | — | 2 | 2 | no | — |
| 132 | C2×C4×D79 | C2×D4 | 1 | 2 | yes | — |
| 133 | C2×C4×D79 | C24 | 1 | 2 | yes | — |
| 134 | Dic316 | — | 2 | 4 | no | — |
| 135 | Dic316 | — | 2 | 4 | no | — |
| 136 | #11929613 | — | 2 | 8 | no | — |
| 137 | #11929613 | — | 2 | 8 | no | — |
| 138 | D632 | — | 2 | 4 | no | — |
| 139 | D632 | — | 2 | 4 | no | — |
| 140 | #11929607 | — | 2 | 8 | no | — |
| 141 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 142 | C2×C79⋊C8 | — | 2 | 2 | no | — |
| 143 | C2×C79⋊C8 | C24 | 1 | 2 | yes | — |
| 144 | C2×C79⋊C8 | C24 | 1 | 2 | yes | — |
| 145 | C8×D79 | — | 2 | 8 | no | — |
| 146 | C4⋊Dic79 | — | 2 | 8 | no | — |
| 147 | C4⋊Dic79 | — | 2 | 4 | no | — |
| 148 | Dic79⋊C4 | — | 2 | 8 | no | — |
| 149 | Dic79⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 150 | (C2×D79)⋊C4 | — | 2 | 8 | no | — |
| 151 | (C2×D79)⋊C4 | — | 2 | 8 | no | — |
| 152 | (C2×D79)⋊C4 | — | 2 | 8 | no | — |
| 153 | (C2×D79)⋊C4 | — | 2 | 8 | no | — |
| 154 | (C2×D79)⋊C4 | C2×D4 | 1 | 8 | yes | — |
| 155 | C4×Dic79 | — | 2 | 8 | no | — |
| 156 | C4×Dic79 | C2×D4 | 1 | 2 | yes | — |
| 157 | C4×Dic79 | C24 | 1 | 2 | yes | — |
| 158 | C2×Q8×C79 | — | 2 | 4 | no | — |
| 159 | C22×C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 160 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 161 | C2×C8×C79 | #41 | 1 | 4 | yes | — |
| 162 | C2×C8×C79 | #41 | 1 | 4 | yes | — |
| 163 | C2×C8×C79 | C24 | 1 | 2 | yes | — |
| 164 | C2×C8×C79 | C24 | 1 | 2 | yes | — |
| 165 | C4⋊C4×C79 | — | 2 | 8 | no | — |
| 166 | C4⋊C4×C79 | — | 2 | 4 | no | — |
| 167 | C4⋊C4×C79 | C24 | 1 | 8 | yes | — |
| 168 | C22⋊C4×C79 | — | 2 | 4 | no | — |
| 169 | C42×C79 | — | 2 | 4 | no | — |
| 170 | C42×C79 | C2×D4 | 1 | 2 | yes | — |
| 171 | C42×C79 | C24 | 1 | 2 | yes | — |
| 172 | C23×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 173 | C22×D79 | — | 2 | 2 | no | — |
| 174 | C22×D79 | — | 2 | 4 | no | — |
| 175 | C22×D79 | — | 4 | 2 | no | — |
| 176 | C22×D79 | C22×D4 | 1 | 2 | yes | — |
| 177 | Q8×C79 | — | 8 | 4 | no | — |
| 178 | C2×C4×C79 | — | 2 | 8 | no | — |
| 179 | C2×C4×C79 | — | 4 | 2 | no | — |
| 180 | C2×C4×C79 | C22×D4 | 1 | 4 | yes | — |
| 181 | C2×C4×C79 | C22×D4 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×C79 | C2×#41 | 1 | 2 | yes | — |
| 183 | C2×C4×C79 | C2×#41 | 1 | 2 | yes | — |
| 184 | C2×C4×C79 | C25 | 1 | 1 | yes | characteristic |
| 185 | C22⋊D79 | — | 4 | 8 | no | — |
| 186 | C2×Dic79 | — | 2 | 2 | no | — |
| 187 | C2×Dic79 | — | 2 | 4 | no | — |
| 188 | C2×Dic79 | — | 4 | 2 | no | — |
| 189 | C2×Dic79 | C22×D4 | 1 | 4 | yes | — |
| 190 | C2×Dic79 | C22×D4 | 1 | 2 | yes | — |
| 191 | D316 | — | 2 | 4 | no | — |
| 192 | D316 | — | 2 | 4 | no | — |
| 193 | D316 | — | 8 | 4 | no | — |
| 194 | D316 | — | 8 | 8 | no | — |
| 195 | C4×D79 | — | 2 | 4 | no | — |
| 196 | C4×D79 | — | 2 | 2 | no | — |
| 197 | C4×D79 | — | 2 | 2 | no | — |
| 198 | C4×D79 | — | 4 | 8 | no | — |
| 199 | C4×D79 | — | 8 | 8 | no | — |
| 200 | Dic158 | — | 2 | 4 | no | — |
| 201 | Dic158 | — | 2 | 4 | no | — |
| 202 | C8×C79 | C2×#41 | 1 | 4 | yes | — |
| 203 | C8×C79 | C2×#41 | 1 | 4 | yes | — |
| 204 | C79⋊C8 | — | 2 | 2 | no | — |
| 205 | C79⋊C8 | — | 2 | 2 | no | — |
| 206 | C22×C79 | — | 2 | 2 | no | — |
| 207 | C22×C79 | #532 | 1 | 2 | yes | — |
| 208 | C22×C79 | C23×D4 | 1 | 1 | yes | characteristic |
| 209 | C2×D79 | — | 2 | 4 | no | — |
| 210 | C2×D79 | — | 2 | 2 | no | — |
| 211 | C2×D79 | — | 4 | 4 | no | — |
| 212 | C2×D79 | — | 4 | 8 | no | — |
| 213 | C2×D79 | — | 4 | 4 | no | — |
| 214 | C4×C79 | — | 2 | 4 | no | — |
| 215 | C4×C79 | — | 4 | 8 | no | — |
| 216 | C4×C79 | #532 | 1 | 2 | yes | — |
| 217 | C4×C79 | C22×#41 | 1 | 1 | yes | characteristic |
| 218 | C4×C79 | C22×#41 | 1 | 1 | yes | characteristic |
| 219 | Dic79 | — | 2 | 4 | no | — |
| 220 | Dic79 | — | 2 | 2 | no | — |
| 221 | Dic79 | — | 4 | 4 | no | — |
| 222 | #60685 | — | 79 | 1 | no | maximal, Sylow |
| 223 | C2×C79 | — | 2 | 2 | no | — |
| 224 | C2×C79 | C2×#532 | 1 | 1 | yes | characteristic |
| 225 | C2×C79 | #3584 | 1 | 2 | yes | — |
| 226 | D79 | — | 4 | 2 | no | — |
| 227 | D79 | — | 8 | 4 | no | — |
| 228 | #3455 | — | 79 | 2 | no | — |
| 229 | #3179 | — | 79 | 8 | no | — |
| 230 | #3178 | — | 79 | 8 | no | — |
| 231 | #3162 | D79 | 1 | 1 | yes | characteristic, complemented |
| 232 | #3150 | — | 79 | 1 | no | — |
| 233 | #3131 | — | 79 | 2 | no | — |
| 234 | #3054 | — | 79 | 2 | no | — |
| 235 | #3050 | — | 79 | 2 | no | — |
| 236 | #2943 | — | 79 | 2 | no | — |
| 237 | C4×#135 | — | 79 | 2 | no | — |
| 238 | C2×#405 | — | 79 | 1 | no | — |
| 239 | C79 | #60685 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 240 | C2×#135 | — | 79 | 2 | no | — |
| 241 | C2×#135 | — | 79 | 2 | no | — |
| 242 | C22×M16 | — | 79 | 1 | no | — |
| 243 | C23×C8 | — | 79 | 1 | no | — |
| 244 | #542 | — | 79 | 8 | no | — |
| 245 | #541 | — | 79 | 4 | no | — |
| 246 | #540 | — | 79 | 4 | no | — |
| 247 | #539 | — | 158 | 4 | no | — |
| 248 | #538 | — | 158 | 4 | no | — |
| 249 | #533 | C2×D79 | 1 | 2 | yes | — |
| 250 | #532 | — | 79 | 2 | no | — |
| 251 | #529 | — | 158 | 8 | no | — |
| 252 | #525 | — | 79 | 4 | no | — |
| 253 | C4×#41 | — | 79 | 4 | no | — |
| 254 | C2×#117 | — | 79 | 1 | no | — |
| 255 | #501 | C2×D79 | 1 | 8 | yes | complemented |
| 256 | #497 | — | 79 | 4 | no | — |
| 257 | #496 | — | 79 | 4 | no | — |
| 258 | #488 | — | 79 | 8 | no | — |
| 259 | #487 | — | 79 | 4 | no | — |
| 260 | #486 | — | 79 | 4 | no | — |
| 261 | #470 | — | 79 | 4 | no | — |
| 262 | #469 | — | 79 | 4 | no | — |
| 263 | #468 | — | 79 | 8 | no | — |
| 264 | #467 | — | 79 | 4 | no | — |
| 265 | #466 | — | 79 | 4 | no | — |
| 266 | #465 | — | 79 | 8 | no | — |
| 267 | #442 | — | 79 | 4 | no | — |
| 268 | #441 | — | 79 | 4 | no | — |
| 269 | #440 | — | 79 | 8 | no | — |
| 270 | C4×Q16 | — | 79 | 4 | no | — |
| 271 | C4×SD16 | — | 79 | 8 | no | — |
| 272 | C4×D8 | — | 79 | 4 | no | — |
| 273 | #427 | C2×D79 | 1 | 2 | yes | — |
| 274 | #427 | C2×D79 | 1 | 2 | yes | — |
| 275 | #416 | — | 79 | 4 | no | — |
| 276 | #416 | — | 79 | 4 | no | — |
| 277 | #405 | — | 79 | 8 | no | — |
| 278 | C2×#97 | — | 79 | 1 | no | — |
| 279 | C2×#97 | C2×D79 | 1 | 1 | yes | characteristic |
| 280 | C2×C4×C8 | — | 79 | 1 | no | — |
| 281 | C2×C4×C8 | — | 79 | 1 | no | — |
| 282 | C2×#41 | — | 79 | 4 | no | — |
| 283 | C23×C4 | — | 79 | 1 | no | — |
| 284 | #135 | — | 158 | 8 | no | — |
| 285 | #135 | — | 158 | 8 | no | — |
| 286 | C2×Q16 | — | 79 | 2 | no | — |
| 287 | C2×Q16 | — | 79 | 2 | no | — |
| 288 | C2×SD16 | — | 79 | 4 | no | — |
| 289 | C2×SD16 | — | 79 | 4 | no | — |
| 290 | C2×D8 | — | 79 | 2 | no | — |
| 291 | C2×D8 | — | 79 | 2 | no | — |
| 292 | C2×M16 | — | 79 | 4 | no | — |
| 293 | C2×M16 | — | 158 | 4 | no | — |
| 294 | C22×C8 | — | 79 | 1 | no | — |
| 295 | C22×C8 | — | 79 | 1 | no | — |
| 296 | C22×C8 | — | 79 | 4 | no | — |
| 297 | C22×C8 | — | 158 | 4 | no | — |
| 298 | C22×C8 | C22×D79 | 1 | 1 | yes | characteristic |
| 299 | C22×C8 | C22×D79 | 1 | 1 | yes | characteristic |
| 300 | C4⋊Q8 | — | 79 | 2 | no | — |
| 301 | C4⋊Q8 | C22×D79 | 1 | 4 | yes | — |
| 302 | #127 | — | 79 | 2 | no | — |
| 303 | #126 | — | 158 | 8 | no | — |
| 304 | #126 | — | 158 | 8 | no | — |
| 305 | #125 | — | 158 | 8 | no | — |
| 306 | #125 | C22×D79 | 1 | 4 | yes | — |
| 307 | #124 | — | 79 | 4 | no | — |
| 308 | #124 | — | 158 | 8 | no | — |
| 309 | #123 | — | 158 | 4 | no | — |
| 310 | #123 | — | 158 | 8 | no | — |
| 311 | #123 | — | 158 | 8 | no | — |
| 312 | C22⋊Q8 | — | 2 | 4 | no | — |
| 313 | C22⋊Q8 | — | 79 | 8 | no | — |
| 314 | C22⋊Q8 | — | 158 | 8 | no | — |
| 315 | #121 | — | 79 | 8 | no | — |
| 316 | #121 | — | 158 | 8 | no | — |
| 317 | #121 | — | 158 | 4 | no | — |
| 318 | #120 | — | 158 | 4 | no | — |
| 319 | C4×Q8 | — | 2 | 4 | no | — |
| 320 | C4×Q8 | — | 79 | 8 | no | — |
| 321 | C4×D4 | — | 79 | 8 | no | — |
| 322 | C4×D4 | — | 158 | 8 | no | — |
| 323 | C4×D4 | — | 158 | 8 | no | — |
| 324 | C4×D4 | — | 158 | 4 | no | — |
| 325 | #117 | — | 79 | 4 | no | — |
| 326 | #117 | — | 79 | 4 | no | — |
| 327 | #117 | — | 158 | 4 | no | — |
| 328 | #117 | C22×D79 | 1 | 4 | yes | — |
| 329 | C2×C4⋊C4 | — | 79 | 2 | no | — |
| 330 | C2×C22⋊C4 | — | 79 | 2 | no | — |
| 331 | C2×C42 | — | 79 | 1 | no | — |
| 332 | C2×C42 | — | 158 | 4 | no | — |
| 333 | C2×C42 | C22×D79 | 1 | 1 | yes | characteristic |
| 334 | #107 | C22×D79 | 1 | 4 | yes | — |
| 335 | #107 | C22×D79 | 1 | 4 | yes | — |
| 336 | #106 | C22×D79 | 1 | 4 | yes | — |
| 337 | #106 | C22×D79 | 1 | 4 | yes | — |
| 338 | #103 | — | 79 | 8 | no | — |
| 339 | #103 | — | 79 | 8 | no | — |
| 340 | #102 | — | 79 | 8 | no | — |
| 341 | #102 | — | 79 | 8 | no | — |
| 342 | #97 | — | 79 | 4 | no | — |
| 343 | #97 | C22×D79 | 1 | 4 | yes | — |
| 344 | C4×C8 | — | 79 | 4 | no | — |
| 345 | C4×C8 | — | 79 | 4 | no | — |
| 346 | C24 | — | 79 | 1 | no | — |
| 347 | #41 | — | 158 | 8 | no | — |
| 348 | #41 | — | 158 | 8 | no | — |
| 349 | C2×Q8 | — | 2 | 4 | no | — |
| 350 | C2×Q8 | — | 79 | 4 | no | — |
| 351 | C2×D4 | — | 79 | 4 | no | — |
| 352 | C2×D4 | — | 158 | 8 | no | — |
| 353 | C2×D4 | — | 158 | 4 | no | — |
| 354 | C2×D4 | — | 158 | 4 | no | — |
| 355 | C22×C4 | — | 79 | 2 | no | — |
| 356 | C22×C4 | — | 79 | 1 | no | — |
| 357 | C22×C4 | — | 79 | 2 | no | — |
| 358 | C22×C4 | — | 79 | 2 | no | — |
| 359 | C22×C4 | — | 158 | 8 | no | — |
| 360 | C22×C4 | — | 158 | 4 | no | — |
| 361 | C22×C4 | — | 158 | 2 | no | — |
| 362 | C22×C4 | — | 158 | 2 | no | — |
| 363 | C22×C4 | D4×D79 | 1 | 2 | yes | — |
| 364 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 365 | Q16 | — | 158 | 4 | no | — |
| 366 | Q16 | — | 158 | 4 | no | — |
| 367 | SD16 | — | 158 | 8 | no | — |
| 368 | SD16 | — | 158 | 8 | no | — |
| 369 | D8 | — | 158 | 4 | no | — |
| 370 | D8 | — | 158 | 4 | no | — |
| 371 | M16 | — | 158 | 8 | no | — |
| 372 | C2×C8 | — | 79 | 2 | no | — |
| 373 | C2×C8 | — | 79 | 2 | no | — |
| 374 | C2×C8 | — | 158 | 2 | no | — |
| 375 | C2×C8 | — | 158 | 2 | no | — |
| 376 | C2×C8 | — | 158 | 8 | no | — |
| 377 | C2×C8 | #11929625 | 1 | 4 | yes | — |
| 378 | C2×C8 | #11929625 | 1 | 4 | yes | — |
| 379 | C2×C8 | C23×D79 | 1 | 2 | yes | — |
| 380 | C2×C8 | C23×D79 | 1 | 2 | yes | — |
| 381 | C4⋊C4 | — | 2 | 8 | no | — |
| 382 | C4⋊C4 | — | 2 | 4 | no | — |
| 383 | C4⋊C4 | — | 79 | 8 | no | — |
| 384 | C4⋊C4 | — | 158 | 8 | no | — |
| 385 | C4⋊C4 | — | 158 | 8 | no | — |
| 386 | C4⋊C4 | — | 158 | 4 | no | — |
| 387 | C4⋊C4 | C23×D79 | 1 | 8 | yes | — |
| 388 | C22⋊C4 | — | 2 | 4 | no | — |
| 389 | C22⋊C4 | — | 79 | 8 | no | — |
| 390 | C22⋊C4 | — | 158 | 8 | no | — |
| 391 | C22⋊C4 | — | 158 | 8 | no | — |
| 392 | C22⋊C4 | — | 158 | 8 | no | — |
| 393 | C22⋊C4 | — | 158 | 8 | no | — |
| 394 | C42 | — | 2 | 4 | no | — |
| 395 | C42 | — | 79 | 2 | no | — |
| 396 | C42 | — | 79 | 2 | no | — |
| 397 | C42 | — | 158 | 8 | no | — |
| 398 | C42 | D4×D79 | 1 | 2 | yes | — |
| 399 | C42 | C23×D79 | 1 | 2 | yes | — |
| 400 | C23 | — | 316 | 2 | no | — |
| 401 | C23 | — | 79 | 2 | no | — |
| 402 | C23 | — | 158 | 4 | no | — |
| 403 | C23 | — | 158 | 2 | no | — |
| 404 | C23 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 405 | Q8 | — | 8 | 4 | no | — |
| 406 | Q8 | — | 158 | 4 | no | — |
| 407 | Q8 | — | 158 | 4 | no | — |
| 408 | D4 | — | 316 | 8 | no | — |
| 409 | D4 | — | 632 | 4 | no | — |
| 410 | D4 | — | 632 | 8 | no | — |
| 411 | D4 | — | 158 | 4 | no | — |
| 412 | D4 | — | 158 | 4 | no | — |
| 413 | C2×C4 | — | 2 | 8 | no | — |
| 414 | C2×C4 | — | 4 | 2 | no | — |
| 415 | C2×C4 | — | 316 | 8 | no | — |
| 416 | C2×C4 | — | 316 | 2 | no | — |
| 417 | C2×C4 | — | 79 | 4 | no | — |
| 418 | C2×C4 | — | 79 | 2 | no | — |
| 419 | C2×C4 | — | 632 | 8 | no | — |
| 420 | C2×C4 | — | 158 | 4 | no | — |
| 421 | C2×C4 | — | 158 | 2 | no | — |
| 422 | C2×C4 | — | 158 | 4 | no | — |
| 423 | C2×C4 | — | 158 | 2 | no | — |
| 424 | C2×C4 | — | 158 | 2 | no | — |
| 425 | C2×C4 | C2×D4×D79 | 1 | 4 | yes | — |
| 426 | C2×C4 | C2×D4×D79 | 1 | 1 | yes | characteristic |
| 427 | C2×C4 | C2×#11929625 | 1 | 2 | yes | — |
| 428 | C2×C4 | C2×#11929625 | 1 | 2 | yes | — |
| 429 | C2×C4 | C24×D79 | 1 | 1 | yes | characteristic |
| 430 | C8 | — | 158 | 2 | no | — |
| 431 | C8 | — | 158 | 2 | no | — |
| 432 | C8 | C2×#11929625 | 1 | 4 | yes | — |
| 433 | C8 | C2×#11929625 | 1 | 4 | yes | — |
| 434 | C22 | — | 2 | 2 | no | — |
| 435 | C22 | — | 316 | 4 | no | — |
| 436 | C22 | — | 316 | 8 | no | — |
| 437 | C22 | — | 316 | 4 | no | — |
| 438 | C22 | — | 158 | 4 | no | — |
| 439 | C22 | — | 158 | 2 | no | — |
| 440 | C22 | #19099114 | 1 | 2 | yes | — |
| 441 | C22 | C22×D4×D79 | 1 | 1 | yes | characteristic |
| 442 | C4 | — | 2 | 4 | no | — |
| 443 | C4 | — | 4 | 8 | no | — |
| 444 | C4 | — | 316 | 4 | no | — |
| 445 | C4 | — | 158 | 4 | no | — |
| 446 | C4 | — | 158 | 2 | no | — |
| 447 | C4 | #19099114 | 1 | 2 | yes | — |
| 448 | C4 | C22×#11929625 | 1 | 1 | yes | characteristic |
| 449 | C4 | C22×#11929625 | 1 | 1 | yes | characteristic |
| 450 | C2 | — | 2 | 2 | no | — |
| 451 | C2 | — | 316 | 2 | no | — |
| 452 | C2 | — | 632 | 4 | no | — |
| 453 | C2 | C2×#19099114 | 1 | 1 | yes | characteristic |
| 454 | C2 | #23778173 | 1 | 2 | yes | — |
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