Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
710 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #23772805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23772801 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #23765075 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23765072 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23763363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23761521 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#3200 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #19099399 | C22 | 1 | 1 | yes | characteristic |
| 9 | #19099137 | — | 2 | 1 | no | — |
| 10 | #19099130 | — | 2 | 1 | no | — |
| 11 | #19098752 | — | 2 | 2 | no | — |
| 12 | #19098752 | — | 2 | 2 | no | — |
| 13 | #19098749 | — | 2 | 2 | no | — |
| 14 | #19098749 | — | 2 | 2 | no | — |
| 15 | #19098579 | — | 2 | 1 | no | — |
| 16 | #19098560 | — | 2 | 1 | no | — |
| 17 | #19098537 | C22 | 1 | 1 | yes | characteristic |
| 18 | #19098537 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19098537 | C22 | 1 | 1 | yes | characteristic |
| 20 | #19098536 | — | 2 | 1 | no | — |
| 21 | #19098536 | — | 2 | 1 | no | — |
| 22 | #19098358 | — | 2 | 2 | no | — |
| 23 | #19098356 | — | 2 | 2 | no | — |
| 24 | #536×C79 | C22 | 1 | 1 | yes | characteristic |
| 25 | #535×C79 | C22 | 1 | 1 | yes | characteristic |
| 26 | #485×C79 | — | 2 | 1 | no | — |
| 27 | #482×C79 | — | 2 | 1 | no | — |
| 28 | #468×C79 | — | 2 | 1 | no | — |
| 29 | #465×C79 | — | 2 | 1 | no | — |
| 30 | #450×C79 | — | 2 | 1 | no | — |
| 31 | #448×C79 | — | 2 | 1 | no | — |
| 32 | #408×C79 | C22 | 1 | 1 | yes | characteristic |
| 33 | #14579209 | — | 2 | 1 | no | — |
| 34 | #14579208 | — | 4 | 1 | no | — |
| 35 | #14579207 | — | 4 | 1 | no | — |
| 36 | #14579206 | — | 2 | 1 | no | — |
| 37 | #14579206 | — | 2 | 1 | no | — |
| 38 | #14579206 | D4 | 1 | 2 | yes | — |
| 39 | C2×#11929624 | — | 2 | 1 | no | — |
| 40 | C2×#11929624 | — | 2 | 1 | no | — |
| 41 | C2×#11929624 | — | 2 | 1 | no | — |
| 42 | #41×D79 | — | 4 | 2 | no | — |
| 43 | #14579159 | — | 4 | 1 | no | — |
| 44 | #14579157 | — | 4 | 1 | no | — |
| 45 | #14579150 | — | 4 | 1 | no | — |
| 46 | #14579148 | — | 4 | 1 | no | — |
| 47 | #14579144 | — | 2 | 4 | no | — |
| 48 | #14579137 | — | 4 | 2 | no | — |
| 49 | #14579132 | — | 4 | 2 | no | — |
| 50 | #14579130 | — | 2 | 4 | no | — |
| 51 | #14579120 | — | 2 | 1 | no | — |
| 52 | #14579120 | — | 2 | 1 | no | — |
| 53 | #14579120 | — | 2 | 1 | no | — |
| 54 | #14579087 | — | 4 | 2 | no | — |
| 55 | #14579086 | — | 4 | 1 | no | — |
| 56 | #14579083 | — | 4 | 1 | no | — |
| 57 | #14579076 | — | 2 | 1 | no | — |
| 58 | #14579076 | — | 2 | 1 | no | — |
| 59 | #14579076 | — | 2 | 1 | no | — |
| 60 | #14579076 | — | 2 | 1 | no | — |
| 61 | #14579076 | D4 | 1 | 2 | yes | — |
| 62 | #14579076 | D4 | 1 | 2 | yes | complemented |
| 63 | #14579075 | — | 2 | 4 | no | — |
| 64 | #14579075 | — | 2 | 4 | no | — |
| 65 | C2×#41×C79 | C23 | 1 | 1 | yes | characteristic |
| 66 | C22×Q8×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C22×D4×C79 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×SD16×C79 | — | 2 | 1 | no | — |
| 69 | C2×SD16×C79 | — | 2 | 1 | no | — |
| 70 | C2×M16×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 71 | C22×C8×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 72 | C4⋊Q8×C79 | — | 2 | 1 | no | — |
| 73 | #127×C79 | — | 2 | 1 | no | — |
| 74 | #124×C79 | — | 2 | 1 | no | — |
| 75 | #124×C79 | — | 2 | 1 | no | — |
| 76 | #123×C79 | — | 2 | 1 | no | — |
| 77 | #123×C79 | — | 2 | 1 | no | — |
| 78 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 79 | C22⋊Q8×C79 | — | 2 | 1 | no | — |
| 80 | #121×C79 | — | 2 | 1 | no | — |
| 81 | #121×C79 | — | 2 | 1 | no | — |
| 82 | #120×C79 | — | 2 | 1 | no | — |
| 83 | #120×C79 | — | 2 | 1 | no | — |
| 84 | #117×C79 | D4 | 1 | 1 | yes | characteristic |
| 85 | #117×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | #107×C79 | — | 2 | 1 | no | — |
| 87 | #106×C79 | — | 2 | 1 | no | — |
| 88 | #103×C79 | — | 2 | 1 | no | — |
| 89 | #103×C79 | — | 2 | 1 | no | — |
| 90 | #102×C79 | — | 2 | 1 | no | — |
| 91 | #102×C79 | — | 2 | 1 | no | — |
| 92 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 93 | C22⋊C8×C79 | — | 2 | 1 | no | — |
| 94 | #11929625 | — | 4 | 2 | no | — |
| 95 | #11929624 | — | 2 | 2 | no | — |
| 96 | #11929624 | — | 2 | 2 | no | — |
| 97 | #11929624 | — | 4 | 1 | no | — |
| 98 | #11929624 | — | 4 | 1 | no | — |
| 99 | #11929624 | — | 4 | 1 | no | — |
| 100 | #11929624 | — | 4 | 1 | no | — |
| 101 | #11929624 | — | 4 | 1 | no | — |
| 102 | #11929624 | — | 4 | 1 | no | — |
| 103 | #11929624 | — | 4 | 1 | no | — |
| 104 | #11929624 | — | 4 | 1 | no | — |
| 105 | #11929623 | — | 4 | 2 | no | — |
| 106 | #11929623 | — | 4 | 2 | no | — |
| 107 | #11929623 | — | 4 | 2 | no | — |
| 108 | C2×Dic158 | — | 2 | 1 | no | — |
| 109 | C2×Dic158 | — | 2 | 1 | no | — |
| 110 | C2×Dic158 | — | 2 | 1 | no | — |
| 111 | Q8×D79 | — | 4 | 2 | no | — |
| 112 | C2×D316 | — | 2 | 1 | no | — |
| 113 | C2×D316 | — | 2 | 1 | no | — |
| 114 | C2×D316 | — | 2 | 1 | no | — |
| 115 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 116 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 117 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 118 | C2×C22⋊D79 | — | 4 | 4 | no | — |
| 119 | D4×D79 | — | 4 | 2 | no | — |
| 120 | D4×D79 | — | 4 | 2 | no | — |
| 121 | D4×D79 | — | 4 | 2 | no | — |
| 122 | C2×C4×D79 | — | 2 | 2 | no | — |
| 123 | C2×C4×D79 | — | 2 | 2 | no | — |
| 124 | C2×C4×D79 | — | 4 | 1 | no | — |
| 125 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 126 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 127 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 128 | Dic79⋊C4 | — | 4 | 4 | no | — |
| 129 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 130 | C22⋊Dic79 | — | 2 | 2 | no | — |
| 131 | C22⋊Dic79 | — | 4 | 4 | no | — |
| 132 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 133 | (C2×D79)⋊C4 | — | 4 | 4 | no | — |
| 134 | C4×Dic79 | — | 4 | 1 | no | — |
| 135 | C4×Dic79 | — | 4 | 1 | no | — |
| 136 | C4×Dic79 | — | 4 | 1 | no | — |
| 137 | C24×C79 | — | 2 | 1 | no | — |
| 138 | #41×C79 | — | 4 | 1 | no | — |
| 139 | #41×C79 | — | 4 | 1 | no | — |
| 140 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 141 | C2×Q8×C79 | — | 2 | 1 | no | — |
| 142 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 143 | C2×Q8×C79 | — | 4 | 1 | no | — |
| 144 | C2×Q8×C79 | #41 | 1 | 1 | yes | characteristic |
| 145 | C2×D4×C79 | — | 2 | 1 | no | — |
| 146 | C2×D4×C79 | — | 2 | 1 | no | — |
| 147 | C2×D4×C79 | — | 4 | 1 | no | — |
| 148 | C2×D4×C79 | — | 4 | 1 | no | — |
| 149 | C2×D4×C79 | — | 4 | 1 | no | — |
| 150 | C2×D4×C79 | — | 4 | 1 | no | — |
| 151 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C22×C4×C79 | — | 2 | 1 | no | — |
| 155 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 156 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | SD16×C79 | — | 8 | 1 | no | — |
| 159 | SD16×C79 | — | 8 | 1 | no | — |
| 160 | M16×C79 | — | 4 | 1 | no | — |
| 161 | C2×C8×C79 | — | 2 | 1 | no | — |
| 162 | C2×C8×C79 | — | 2 | 1 | no | — |
| 163 | C2×C8×C79 | — | 4 | 1 | no | — |
| 164 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 165 | C4⋊C4×C79 | — | 2 | 1 | no | — |
| 166 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 167 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 168 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 169 | C22⋊C4×C79 | — | 2 | 1 | no | — |
| 170 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 171 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 172 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 173 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 174 | C42×C79 | — | 2 | 1 | no | — |
| 175 | C42×C79 | — | 2 | 1 | no | — |
| 176 | C23×C79 | — | 4 | 2 | no | — |
| 177 | C23×C79 | — | 4 | 1 | no | — |
| 178 | C23×C79 | — | 16 | 1 | no | — |
| 179 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 180 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 181 | C23×C79 | #127 | 1 | 1 | yes | characteristic |
| 182 | C22×D79 | — | 2 | 2 | no | — |
| 183 | C22×D79 | — | 2 | 2 | no | — |
| 184 | C22×D79 | — | 4 | 1 | no | — |
| 185 | Q8×C79 | — | 4 | 1 | no | — |
| 186 | Q8×C79 | — | 4 | 1 | no | — |
| 187 | Q8×C79 | — | 4 | 1 | no | — |
| 188 | Q8×C79 | — | 8 | 1 | no | — |
| 189 | D4×C79 | — | 4 | 1 | no | — |
| 190 | D4×C79 | — | 4 | 1 | no | — |
| 191 | D4×C79 | — | 4 | 1 | no | — |
| 192 | D4×C79 | — | 4 | 1 | no | — |
| 193 | D4×C79 | — | 4 | 1 | no | — |
| 194 | D4×C79 | — | 8 | 1 | no | — |
| 195 | D4×C79 | — | 16 | 1 | no | — |
| 196 | D4×C79 | — | 16 | 1 | no | — |
| 197 | C2×C4×C79 | — | 2 | 1 | no | — |
| 198 | C2×C4×C79 | — | 2 | 1 | no | — |
| 199 | C2×C4×C79 | — | 2 | 1 | no | — |
| 200 | C2×C4×C79 | — | 2 | 1 | no | — |
| 201 | C2×C4×C79 | — | 2 | 1 | no | — |
| 202 | C2×C4×C79 | — | 2 | 1 | no | — |
| 203 | C2×C4×C79 | — | 4 | 2 | no | — |
| 204 | C2×C4×C79 | — | 4 | 1 | no | — |
| 205 | C2×C4×C79 | — | 4 | 1 | no | — |
| 206 | C2×C4×C79 | — | 4 | 1 | no | — |
| 207 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 208 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 209 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 210 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 211 | C22⋊D79 | — | 4 | 2 | no | — |
| 212 | C22⋊D79 | — | 4 | 2 | no | — |
| 213 | C22⋊D79 | — | 4 | 2 | no | — |
| 214 | C22⋊D79 | — | 4 | 2 | no | — |
| 215 | C22⋊D79 | — | 16 | 4 | no | — |
| 216 | C2×Dic79 | — | 2 | 2 | no | — |
| 217 | C2×Dic79 | — | 2 | 2 | no | — |
| 218 | C2×Dic79 | — | 4 | 1 | no | — |
| 219 | C2×Dic79 | — | 4 | 2 | no | — |
| 220 | C2×Dic79 | — | 4 | 2 | no | — |
| 221 | C2×Dic79 | — | 8 | 1 | no | — |
| 222 | D316 | — | 2 | 2 | no | — |
| 223 | D316 | — | 4 | 1 | no | — |
| 224 | D316 | — | 4 | 1 | no | — |
| 225 | D316 | — | 4 | 1 | no | — |
| 226 | C4×D79 | — | 4 | 2 | no | — |
| 227 | C4×D79 | — | 4 | 2 | no | — |
| 228 | C4×D79 | — | 4 | 2 | no | — |
| 229 | C4×D79 | — | 4 | 2 | no | — |
| 230 | Dic158 | — | 2 | 2 | no | — |
| 231 | Dic158 | — | 4 | 1 | no | — |
| 232 | Dic158 | — | 4 | 1 | no | — |
| 233 | Dic158 | — | 4 | 1 | no | — |
| 234 | C8×C79 | — | 4 | 1 | no | — |
| 235 | C8×C79 | — | 4 | 1 | no | — |
| 236 | C22×C79 | — | 2 | 1 | no | — |
| 237 | C22×C79 | — | 2 | 1 | no | — |
| 238 | C22×C79 | — | 2 | 1 | no | — |
| 239 | C22×C79 | — | 4 | 1 | no | — |
| 240 | C22×C79 | — | 4 | 1 | no | — |
| 241 | C22×C79 | — | 4 | 1 | no | — |
| 242 | C22×C79 | — | 8 | 1 | no | — |
| 243 | C22×C79 | — | 8 | 1 | no | — |
| 244 | C22×C79 | — | 8 | 4 | no | — |
| 245 | C22×C79 | — | 8 | 1 | no | — |
| 246 | C22×C79 | #392 | 1 | 1 | yes | characteristic |
| 247 | C2×D79 | — | 4 | 2 | no | — |
| 248 | C2×D79 | — | 8 | 2 | no | — |
| 249 | C2×D79 | — | 8 | 2 | no | — |
| 250 | C2×D79 | — | 16 | 1 | no | — |
| 251 | C4×C79 | — | 2 | 1 | no | — |
| 252 | C4×C79 | — | 2 | 1 | no | — |
| 253 | C4×C79 | — | 2 | 1 | no | — |
| 254 | C4×C79 | — | 8 | 1 | no | — |
| 255 | C4×C79 | — | 8 | 1 | no | — |
| 256 | C4×C79 | — | 8 | 1 | no | — |
| 257 | C4×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 258 | C4×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 259 | Dic79 | — | 4 | 2 | no | — |
| 260 | Dic79 | — | 8 | 2 | no | — |
| 261 | Dic79 | — | 8 | 2 | no | — |
| 262 | Dic79 | — | 16 | 1 | no | — |
| 263 | #13351 | — | 79 | 1 | no | maximal, Sylow |
| 264 | C2×C79 | — | 2 | 1 | no | — |
| 265 | C2×C79 | — | 4 | 1 | no | — |
| 266 | C2×C79 | — | 4 | 1 | no | — |
| 267 | C2×C79 | — | 4 | 1 | no | — |
| 268 | C2×C79 | — | 16 | 1 | no | — |
| 269 | C2×C79 | #2021 | 1 | 1 | yes | characteristic |
| 270 | D79 | — | 8 | 2 | no | — |
| 271 | #3200 | D79 | 1 | 1 | yes | characteristic, complemented |
| 272 | #3028 | — | 79 | 1 | no | — |
| 273 | #3027 | — | 79 | 1 | no | — |
| 274 | #2129 | — | 79 | 1 | no | — |
| 275 | #2128 | — | 79 | 1 | no | — |
| 276 | #1794 | — | 79 | 1 | no | — |
| 277 | #1391 | — | 79 | 1 | no | — |
| 278 | C79 | #13351 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 279 | #585 | — | 79 | 1 | no | — |
| 280 | #536 | — | 158 | 1 | no | — |
| 281 | #536 | C2×D79 | 1 | 1 | yes | characteristic |
| 282 | #535 | — | 158 | 1 | no | — |
| 283 | #535 | C2×D79 | 1 | 1 | yes | characteristic |
| 284 | #485 | — | 2 | 1 | no | — |
| 285 | #482 | — | 2 | 1 | no | — |
| 286 | #468 | — | 2 | 1 | no | — |
| 287 | #465 | — | 2 | 1 | no | — |
| 288 | #458 | — | 158 | 2 | no | — |
| 289 | #458 | — | 158 | 2 | no | — |
| 290 | B(4,𝔽2) | — | 158 | 2 | no | — |
| 291 | B(4,𝔽2) | — | 158 | 2 | no | — |
| 292 | #450 | — | 2 | 1 | no | — |
| 293 | #448 | — | 2 | 1 | no | — |
| 294 | #421 | — | 158 | 1 | no | — |
| 295 | #416 | — | 158 | 1 | no | — |
| 296 | #410 | — | 79 | 1 | no | — |
| 297 | #410 | — | 79 | 1 | no | — |
| 298 | #410 | — | 79 | 1 | no | — |
| 299 | #410 | — | 158 | 1 | no | — |
| 300 | #410 | — | 158 | 1 | no | — |
| 301 | #408 | C2×D79 | 1 | 1 | yes | characteristic |
| 302 | #354 | — | 158 | 2 | no | — |
| 303 | #353 | — | 158 | 2 | no | — |
| 304 | 2−1+4 | — | 316 | 1 | no | — |
| 305 | 2−1+4 | — | 158 | 1 | no | — |
| 306 | H(5,𝔽2) | — | 316 | 1 | no | — |
| 307 | H(5,𝔽2) | — | 79 | 2 | no | — |
| 308 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 309 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 310 | C2×#41 | — | 316 | 2 | no | — |
| 311 | C2×#41 | — | 158 | 1 | no | — |
| 312 | C2×#41 | — | 158 | 1 | no | — |
| 313 | C2×#41 | — | 158 | 1 | no | — |
| 314 | C2×#41 | C22×D79 | 1 | 1 | yes | characteristic |
| 315 | C22×Q8 | C22⋊D79 | 1 | 1 | yes | characteristic, complemented |
| 316 | C22×D4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 317 | C2×SD16 | — | 2 | 1 | no | — |
| 318 | C2×SD16 | — | 2 | 1 | no | — |
| 319 | C2×M16 | C22⋊D79 | 1 | 1 | yes | characteristic, complemented |
| 320 | C22×C8 | C22⋊D79 | 1 | 1 | yes | characteristic, complemented |
| 321 | C4⋊Q8 | — | 2 | 1 | no | — |
| 322 | C4⋊Q8 | — | 316 | 1 | no | — |
| 323 | #127 | — | 2 | 1 | no | — |
| 324 | #127 | — | 316 | 1 | no | — |
| 325 | #124 | — | 2 | 1 | no | — |
| 326 | #124 | — | 2 | 1 | no | — |
| 327 | #124 | — | 316 | 1 | no | — |
| 328 | #124 | — | 316 | 1 | no | — |
| 329 | #123 | — | 2 | 1 | no | — |
| 330 | #123 | — | 2 | 1 | no | — |
| 331 | #123 | — | 158 | 4 | no | — |
| 332 | C22⋊Q8 | — | 2 | 1 | no | — |
| 333 | C22⋊Q8 | — | 2 | 1 | no | — |
| 334 | C22⋊Q8 | — | 316 | 2 | no | — |
| 335 | #121 | — | 2 | 1 | no | — |
| 336 | #121 | — | 2 | 1 | no | — |
| 337 | #121 | — | 316 | 2 | no | — |
| 338 | #120 | — | 2 | 1 | no | — |
| 339 | #120 | — | 2 | 1 | no | — |
| 340 | #120 | — | 158 | 4 | no | — |
| 341 | #117 | — | 158 | 1 | no | — |
| 342 | #117 | — | 158 | 1 | no | — |
| 343 | #117 | — | 158 | 1 | no | — |
| 344 | #117 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 345 | #117 | C22⋊D79 | 1 | 1 | yes | characteristic, complemented |
| 346 | #107 | — | 2 | 1 | no | — |
| 347 | #106 | — | 2 | 1 | no | — |
| 348 | #104 | — | 316 | 2 | no | — |
| 349 | #103 | — | 2 | 1 | no | — |
| 350 | #103 | — | 2 | 1 | no | — |
| 351 | #103 | — | 316 | 1 | no | — |
| 352 | #102 | — | 2 | 1 | no | — |
| 353 | #102 | — | 2 | 1 | no | — |
| 354 | #102 | — | 316 | 1 | no | — |
| 355 | #99 | — | 79 | 2 | no | — |
| 356 | #99 | — | 79 | 2 | no | — |
| 357 | #99 | — | 158 | 4 | no | — |
| 358 | #99 | — | 158 | 4 | no | — |
| 359 | #99 | — | 158 | 1 | no | — |
| 360 | #99 | — | 158 | 1 | no | — |
| 361 | #99 | — | 158 | 1 | no | — |
| 362 | #99 | — | 158 | 1 | no | — |
| 363 | C22⋊C8 | — | 2 | 1 | no | — |
| 364 | C22⋊C8 | — | 2 | 1 | no | — |
| 365 | C24 | — | 2 | 1 | no | — |
| 366 | #41 | — | 4 | 1 | no | — |
| 367 | #41 | — | 4 | 1 | no | — |
| 368 | #41 | — | 316 | 1 | no | — |
| 369 | #41 | — | 316 | 1 | no | — |
| 370 | #41 | — | 316 | 1 | no | — |
| 371 | #41 | — | 316 | 1 | no | — |
| 372 | #41 | — | 316 | 1 | no | — |
| 373 | #41 | — | 316 | 2 | no | — |
| 374 | #41 | — | 316 | 2 | no | — |
| 375 | #41 | — | 316 | 2 | no | — |
| 376 | #41 | — | 316 | 1 | no | — |
| 377 | #41 | — | 316 | 1 | no | — |
| 378 | #41 | — | 316 | 1 | no | — |
| 379 | #41 | — | 316 | 2 | no | — |
| 380 | #41 | — | 158 | 2 | no | — |
| 381 | #41 | — | 158 | 2 | no | — |
| 382 | C2×Q8 | — | 2 | 1 | no | — |
| 383 | C2×Q8 | — | 2 | 1 | no | — |
| 384 | C2×Q8 | — | 4 | 1 | no | — |
| 385 | C2×Q8 | — | 4 | 1 | no | — |
| 386 | C2×Q8 | — | 316 | 2 | no | — |
| 387 | C2×Q8 | — | 158 | 1 | no | — |
| 388 | C2×Q8 | — | 158 | 1 | no | — |
| 389 | C2×Q8 | — | 158 | 1 | no | — |
| 390 | C2×Q8 | #11929623 | 1 | 1 | yes | characteristic |
| 391 | C2×D4 | — | 2 | 1 | no | — |
| 392 | C2×D4 | — | 2 | 1 | no | — |
| 393 | C2×D4 | — | 4 | 1 | no | — |
| 394 | C2×D4 | — | 4 | 1 | no | — |
| 395 | C2×D4 | — | 4 | 1 | no | — |
| 396 | C2×D4 | — | 4 | 1 | no | — |
| 397 | C2×D4 | — | 316 | 2 | no | — |
| 398 | C2×D4 | — | 316 | 2 | no | — |
| 399 | C2×D4 | — | 316 | 2 | no | — |
| 400 | C2×D4 | — | 316 | 1 | no | — |
| 401 | C2×D4 | — | 316 | 4 | no | — |
| 402 | C2×D4 | — | 158 | 1 | no | — |
| 403 | C2×D4 | — | 158 | 1 | no | — |
| 404 | C2×D4 | — | 158 | 1 | no | — |
| 405 | C2×D4 | — | 158 | 2 | no | — |
| 406 | C2×D4 | — | 158 | 2 | no | — |
| 407 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 408 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 409 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 410 | C22×C4 | — | 2 | 1 | no | — |
| 411 | C22×C4 | — | 316 | 1 | no | — |
| 412 | C22×C4 | — | 158 | 2 | no | — |
| 413 | C22×C4 | — | 158 | 2 | no | — |
| 414 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 415 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 416 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 417 | SD16 | — | 8 | 1 | no | — |
| 418 | SD16 | — | 8 | 1 | no | — |
| 419 | M16 | — | 4 | 1 | no | — |
| 420 | C2×C8 | — | 2 | 1 | no | — |
| 421 | C2×C8 | — | 2 | 1 | no | — |
| 422 | C2×C8 | — | 4 | 1 | no | — |
| 423 | C4⋊C4 | — | 2 | 1 | no | — |
| 424 | C4⋊C4 | — | 2 | 1 | no | — |
| 425 | C4⋊C4 | — | 4 | 1 | no | — |
| 426 | C4⋊C4 | — | 4 | 1 | no | — |
| 427 | C4⋊C4 | — | 316 | 1 | no | — |
| 428 | C4⋊C4 | — | 316 | 1 | no | — |
| 429 | C4⋊C4 | — | 316 | 1 | no | — |
| 430 | C4⋊C4 | — | 316 | 4 | no | — |
| 431 | C22⋊C4 | — | 2 | 1 | no | — |
| 432 | C22⋊C4 | — | 2 | 1 | no | — |
| 433 | C22⋊C4 | — | 4 | 1 | no | — |
| 434 | C22⋊C4 | — | 4 | 1 | no | — |
| 435 | C22⋊C4 | — | 4 | 1 | no | — |
| 436 | C22⋊C4 | — | 4 | 1 | no | — |
| 437 | C22⋊C4 | — | 316 | 4 | no | — |
| 438 | C22⋊C4 | — | 316 | 4 | no | — |
| 439 | C22⋊C4 | — | 316 | 1 | no | — |
| 440 | C22⋊C4 | — | 158 | 2 | no | — |
| 441 | C22⋊C4 | — | 158 | 2 | no | — |
| 442 | C42 | — | 2 | 1 | no | — |
| 443 | C42 | — | 2 | 1 | no | — |
| 444 | C42 | — | 316 | 1 | no | — |
| 445 | C42 | — | 316 | 1 | no | — |
| 446 | C42 | — | 316 | 1 | no | — |
| 447 | C23 | — | 4 | 2 | no | — |
| 448 | C23 | — | 4 | 1 | no | — |
| 449 | C23 | — | 16 | 1 | no | — |
| 450 | C23 | — | 316 | 1 | no | — |
| 451 | C23 | — | 158 | 2 | no | — |
| 452 | C23 | — | 158 | 2 | no | — |
| 453 | C23 | #14579129 | 1 | 1 | yes | characteristic |
| 454 | C23 | #14579129 | 1 | 1 | yes | characteristic |
| 455 | C23 | #14579157 | 1 | 1 | yes | characteristic |
| 456 | Q8 | — | 4 | 1 | no | — |
| 457 | Q8 | — | 4 | 1 | no | — |
| 458 | Q8 | — | 4 | 1 | no | — |
| 459 | Q8 | — | 8 | 1 | no | — |
| 460 | Q8 | — | 316 | 1 | no | — |
| 461 | Q8 | — | 316 | 1 | no | — |
| 462 | Q8 | — | 316 | 1 | no | — |
| 463 | Q8 | — | 158 | 2 | no | — |
| 464 | D4 | — | 4 | 1 | no | — |
| 465 | D4 | — | 4 | 1 | no | — |
| 466 | D4 | — | 4 | 1 | no | — |
| 467 | D4 | — | 4 | 1 | no | — |
| 468 | D4 | — | 4 | 1 | no | — |
| 469 | D4 | — | 8 | 1 | no | — |
| 470 | D4 | — | 16 | 1 | no | — |
| 471 | D4 | — | 16 | 1 | no | — |
| 472 | D4 | — | 316 | 1 | no | — |
| 473 | D4 | — | 316 | 1 | no | — |
| 474 | D4 | — | 316 | 2 | no | — |
| 475 | D4 | — | 316 | 2 | no | — |
| 476 | D4 | — | 316 | 2 | no | — |
| 477 | D4 | — | 316 | 2 | no | — |
| 478 | D4 | — | 316 | 1 | no | — |
| 479 | D4 | — | 158 | 2 | no | — |
| 480 | D4 | — | 1264 | 4 | no | — |
| 481 | C2×C4 | — | 2 | 1 | no | — |
| 482 | C2×C4 | — | 2 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 2 | 1 | no | — |
| 486 | C2×C4 | — | 2 | 1 | no | — |
| 487 | C2×C4 | — | 4 | 2 | no | — |
| 488 | C2×C4 | — | 4 | 1 | no | — |
| 489 | C2×C4 | — | 4 | 1 | no | — |
| 490 | C2×C4 | — | 4 | 1 | no | — |
| 491 | C2×C4 | — | 316 | 2 | no | — |
| 492 | C2×C4 | — | 316 | 2 | no | — |
| 493 | C2×C4 | — | 316 | 2 | no | — |
| 494 | C2×C4 | — | 316 | 1 | no | — |
| 495 | C2×C4 | — | 316 | 2 | no | — |
| 496 | C2×C4 | — | 316 | 2 | no | — |
| 497 | C2×C4 | — | 316 | 2 | no | — |
| 498 | C2×C4 | — | 632 | 1 | no | — |
| 499 | C2×C4 | — | 158 | 2 | no | — |
| 500 | C2×C4 | — | 158 | 2 | no | — |
| 501 | C2×C4 | #14579130 | 1 | 1 | yes | characteristic |
| 502 | C2×C4 | #14579132 | 1 | 1 | yes | characteristic |
| 503 | C2×C4 | #14579133 | 1 | 1 | yes | characteristic |
| 504 | C2×C4 | #14579133 | 1 | 1 | yes | characteristic |
| 505 | C8 | — | 4 | 1 | no | — |
| 506 | C8 | — | 4 | 1 | no | — |
| 507 | C22 | — | 2 | 1 | no | — |
| 508 | C22 | — | 2 | 1 | no | — |
| 509 | C22 | — | 2 | 1 | no | — |
| 510 | C22 | — | 4 | 1 | no | — |
| 511 | C22 | — | 4 | 1 | no | — |
| 512 | C22 | — | 4 | 1 | no | — |
| 513 | C22 | — | 8 | 1 | no | — |
| 514 | C22 | — | 8 | 1 | no | — |
| 515 | C22 | — | 8 | 4 | no | — |
| 516 | C22 | — | 8 | 1 | no | — |
| 517 | C22 | — | 316 | 2 | no | — |
| 518 | C22 | — | 632 | 2 | no | — |
| 519 | C22 | — | 632 | 2 | no | — |
| 520 | C22 | — | 1264 | 1 | no | — |
| 521 | C22 | #19098471 | 1 | 1 | yes | characteristic |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 2 | 1 | no | — |
| 524 | C4 | — | 2 | 1 | no | — |
| 525 | C4 | — | 8 | 1 | no | — |
| 526 | C4 | — | 8 | 1 | no | — |
| 527 | C4 | — | 8 | 1 | no | — |
| 528 | C4 | — | 316 | 2 | no | — |
| 529 | C4 | — | 632 | 2 | no | — |
| 530 | C4 | — | 632 | 2 | no | — |
| 531 | C4 | — | 1264 | 1 | no | — |
| 532 | C4 | #19098750 | 1 | 1 | yes | characteristic |
| 533 | C4 | #19098750 | 1 | 1 | yes | characteristic |
| 534 | C2 | — | 2 | 1 | no | — |
| 535 | C2 | — | 4 | 1 | no | — |
| 536 | C2 | — | 4 | 1 | no | — |
| 537 | C2 | — | 4 | 1 | no | — |
| 538 | C2 | — | 16 | 1 | no | — |
| 539 | C2 | — | 632 | 2 | no | — |
| 540 | C2 | #23764524 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23772805 | C2 | semidirect |
| 3. #23765075 | C2 | semidirect |
| 4. #23765072 | C2 | semidirect |
| 5. #23763363 | C2 | semidirect |
| 6. #23761521 | C2 | semidirect |
| 7. C79×#3200 | C2 | semidirect |
| 62. #14579076 | D4 | semidirect |
| 66. C22×Q8×C79 | D4 | semidirect |
| 70. C2×M16×C79 | D4 | semidirect |
| 71. C22×C8×C79 | D4 | semidirect |
| 85. #117×C79 | D4 | semidirect |
| 271. #3200 | D79 | semidirect |
| 278. C79 | #13351 | semidirect |
| 315. C22×Q8 | C22⋊D79 | semidirect |
| 319. C2×M16 | C22⋊D79 | semidirect |
| 320. C22×C8 | C22⋊D79 | semidirect |
| 345. #117 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772805 | 2 |
| #23772801 | 2 |
| #23765075 | 2 |
| #23765072 | 2 |
| #23763363 | 2 |
| #23761521 | 2 |
| C79×#3200 | 2 |
| #13351 | 79 |