Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1440 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1440 conjugacy classes of subgroups — too many to draw. Only its 231 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 | #23777035 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23771876 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #23763944 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #23763815 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #23763509 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #23763321 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#1783 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14579206 | C22 | 1 | 1 | yes | characteristic |
| 9 | #19099329 | C22 | 1 | 4 | yes | complemented |
| 10 | #19099207 | — | 2 | 4 | no | — |
| 11 | D4×C22⋊D79 | — | 2 | 4 | no | — |
| 12 | #19099130 | C22 | 1 | 2 | yes | — |
| 13 | #19099122 | C4 | 1 | 4 | yes | — |
| 14 | #19099074 | C22 | 1 | 2 | yes | — |
| 15 | C2×#14579130 | C4 | 1 | 4 | yes | — |
| 16 | #19099038 | C22 | 1 | 1 | yes | characteristic |
| 17 | #19098545 | C22 | 1 | 4 | yes | complemented |
| 18 | #19098544 | — | 2 | 4 | no | — |
| 19 | C2×#14579078 | C22 | 1 | 2 | yes | — |
| 20 | C2×#14579078 | C22 | 1 | 2 | yes | complemented |
| 21 | #100×D79 | — | 2 | 4 | no | — |
| 22 | #19098527 | C22 | 1 | 2 | yes | complemented |
| 23 | #19098335 | C22 | 1 | 4 | yes | complemented |
| 24 | #19098334 | C22 | 1 | 4 | yes | complemented |
| 25 | C23×D4×C79 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#100×C79 | C22 | 1 | 2 | yes | — |
| 27 | C2×#100×C79 | C22 | 1 | 2 | yes | complemented |
| 28 | #407×C79 | C22 | 1 | 2 | yes | complemented |
| 29 | #14579206 | — | 4 | 2 | no | — |
| 30 | #14579206 | — | 4 | 2 | no | — |
| 31 | C2×#11929624 | C23 | 1 | 2 | yes | — |
| 32 | C2×#11929623 | D4 | 1 | 4 | yes | — |
| 33 | C22×C22⋊D79 | — | 2 | 4 | no | — |
| 34 | C22×C22⋊D79 | C2×C4 | 1 | 4 | yes | — |
| 35 | C2×D4×D79 | D4 | 1 | 4 | yes | — |
| 36 | #14579169 | — | 4 | 4 | no | — |
| 37 | #14579167 | — | 4 | 4 | no | — |
| 38 | C2×#11929608 | C23 | 1 | 4 | yes | — |
| 39 | M16×D79 | — | 2 | 8 | no | — |
| 40 | #14579157 | — | 2 | 2 | no | — |
| 41 | #14579148 | — | 2 | 2 | no | — |
| 42 | #14579144 | C2×C4 | 1 | 4 | yes | — |
| 43 | #14579142 | — | 2 | 4 | no | — |
| 44 | #14579140 | — | 2 | 2 | no | — |
| 45 | #14579135 | — | 2 | 2 | no | — |
| 46 | #14579133 | — | 2 | 8 | no | — |
| 47 | #14579132 | — | 2 | 4 | no | — |
| 48 | #14579130 | — | 2 | 8 | no | — |
| 49 | #14579130 | C2×C4 | 1 | 4 | yes | — |
| 50 | #14579130 | C2×C4 | 1 | 8 | yes | — |
| 51 | #14579129 | — | 2 | 4 | no | — |
| 52 | D4×Dic79 | — | 2 | 4 | no | — |
| 53 | C4×C22⋊D79 | — | 2 | 4 | no | — |
| 54 | #14579120 | C23 | 1 | 2 | yes | — |
| 55 | C2×C22⋊Dic79 | — | 2 | 4 | no | — |
| 56 | C2×C22⋊Dic79 | C2×C4 | 1 | 4 | yes | — |
| 57 | #14579079 | — | 2 | 4 | no | — |
| 58 | #14579078 | — | 2 | 4 | no | — |
| 59 | #14579078 | — | 4 | 2 | no | — |
| 60 | #14579077 | — | 2 | 4 | no | — |
| 61 | C22⋊(C79⋊C8) | — | 4 | 2 | no | — |
| 62 | C25×C79 | C2×C4 | 1 | 2 | yes | — |
| 63 | C22×D4×C79 | — | 2 | 4 | no | — |
| 64 | C22×D4×C79 | — | 4 | 2 | no | — |
| 65 | C22×D4×C79 | — | 4 | 2 | no | — |
| 66 | C22×D4×C79 | C2×C4 | 1 | 2 | yes | — |
| 67 | C22×D4×C79 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×D4×C79 | C23 | 1 | 1 | yes | characteristic |
| 69 | C23×C4×C79 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×M16×C79 | C23 | 1 | 4 | yes | — |
| 71 | #100×C79 | — | 2 | 4 | no | — |
| 72 | #100×C79 | — | 4 | 2 | no | — |
| 73 | C22⋊C8×C79 | — | 4 | 2 | no | — |
| 74 | C23×D79 | C22⋊C4 | 1 | 4 | yes | — |
| 75 | #11929624 | — | 2 | 4 | no | — |
| 76 | #11929624 | — | 2 | 4 | no | — |
| 77 | #11929623 | — | 4 | 8 | no | — |
| 78 | C2×Dic158 | C2×D4 | 1 | 2 | yes | — |
| 79 | C2×D316 | C2×D4 | 1 | 2 | yes | — |
| 80 | C2×C22⋊D79 | — | 2 | 4 | no | — |
| 81 | C2×C22⋊D79 | — | 2 | 8 | no | — |
| 82 | C2×C22⋊D79 | — | 4 | 4 | no | — |
| 83 | C2×C22⋊D79 | — | 4 | 4 | no | — |
| 84 | C2×C22⋊D79 | — | 8 | 8 | no | — |
| 85 | C2×C22⋊D79 | C22⋊C4 | 1 | 8 | yes | — |
| 86 | C2×C22⋊D79 | C22×C4 | 1 | 4 | yes | — |
| 87 | D4×D79 | — | 4 | 8 | no | — |
| 88 | C22×Dic79 | — | 2 | 4 | no | — |
| 89 | C22×Dic79 | C22⋊C4 | 1 | 4 | yes | — |
| 90 | C2×C4×D79 | C2×D4 | 1 | 4 | yes | — |
| 91 | #11929608 | — | 2 | 4 | no | — |
| 92 | #11929608 | — | 2 | 4 | no | — |
| 93 | #11929607 | — | 4 | 8 | no | — |
| 94 | C2×C79⋊C8 | — | 2 | 4 | no | — |
| 95 | C8×D79 | — | 4 | 8 | no | — |
| 96 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 97 | Dic79⋊C4 | — | 2 | 4 | no | — |
| 98 | C22⋊Dic79 | — | 2 | 4 | no | — |
| 99 | C22⋊Dic79 | — | 2 | 8 | no | — |
| 100 | C22⋊Dic79 | — | 2 | 4 | no | — |
| 101 | C22⋊Dic79 | C22×C4 | 1 | 4 | yes | — |
| 102 | (C2×D79)⋊C4 | — | 2 | 4 | no | — |
| 103 | C4×Dic79 | — | 2 | 2 | no | — |
| 104 | C24×C79 | — | 2 | 4 | no | — |
| 105 | C24×C79 | — | 4 | 2 | no | — |
| 106 | C24×C79 | — | 4 | 2 | no | — |
| 107 | C24×C79 | — | 8 | 4 | no | — |
| 108 | C24×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 109 | C24×C79 | C22×C4 | 1 | 2 | yes | — |
| 110 | C24×C79 | C22×C4 | 1 | 2 | yes | — |
| 111 | C2×D4×C79 | — | 2 | 4 | no | — |
| 112 | C2×D4×C79 | — | 2 | 2 | no | — |
| 113 | C2×D4×C79 | — | 2 | 2 | no | — |
| 114 | C2×D4×C79 | — | 2 | 2 | no | — |
| 115 | C2×D4×C79 | — | 2 | 2 | no | — |
| 116 | C2×D4×C79 | — | 2 | 2 | no | — |
| 117 | C2×D4×C79 | — | 4 | 2 | no | — |
| 118 | C2×D4×C79 | — | 4 | 2 | no | — |
| 119 | C2×D4×C79 | — | 4 | 16 | no | — |
| 120 | C2×D4×C79 | C2×D4 | 1 | 4 | yes | — |
| 121 | C22×C4×C79 | — | 2 | 2 | no | — |
| 122 | C22×C4×C79 | — | 2 | 2 | no | — |
| 123 | C22×C4×C79 | — | 2 | 2 | no | — |
| 124 | C22×C4×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 125 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 126 | M16×C79 | — | 2 | 4 | no | — |
| 127 | M16×C79 | — | 2 | 4 | no | — |
| 128 | C2×C8×C79 | — | 2 | 4 | no | — |
| 129 | C23×C79 | — | 2 | 1 | no | — |
| 130 | C23×C79 | — | 2 | 1 | no | — |
| 131 | C23×C79 | — | 2 | 1 | no | — |
| 132 | C23×C79 | — | 2 | 2 | no | — |
| 133 | C23×C79 | — | 2 | 2 | no | — |
| 134 | C23×C79 | — | 2 | 2 | no | — |
| 135 | C23×C79 | — | 2 | 2 | no | — |
| 136 | C23×C79 | — | 2 | 2 | no | — |
| 137 | C23×C79 | — | 4 | 2 | no | — |
| 138 | C23×C79 | — | 4 | 8 | no | — |
| 139 | C23×C79 | — | 4 | 8 | no | — |
| 140 | C23×C79 | — | 8 | 4 | no | — |
| 141 | C23×C79 | — | 8 | 4 | no | — |
| 142 | C23×C79 | — | 8 | 2 | no | — |
| 143 | C23×C79 | — | 8 | 2 | no | — |
| 144 | C23×C79 | — | 8 | 4 | no | — |
| 145 | C23×C79 | — | 8 | 4 | no | — |
| 146 | C23×C79 | — | 8 | 4 | no | — |
| 147 | C23×C79 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 148 | C23×C79 | C23×C4 | 1 | 1 | yes | characteristic |
| 149 | C22×D79 | — | 4 | 4 | no | — |
| 150 | C22×D79 | — | 8 | 4 | no | — |
| 151 | C22×D79 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 152 | D4×C79 | — | 2 | 8 | no | — |
| 153 | D4×C79 | — | 4 | 8 | no | — |
| 154 | D4×C79 | — | 4 | 4 | no | — |
| 155 | C2×C4×C79 | — | 2 | 1 | no | — |
| 156 | C2×C4×C79 | — | 2 | 1 | no | — |
| 157 | C2×C4×C79 | — | 2 | 1 | no | — |
| 158 | C2×C4×C79 | — | 4 | 4 | no | — |
| 159 | C2×C4×C79 | C22×D4 | 1 | 2 | yes | — |
| 160 | C2×C4×C79 | H(5,𝔽2) | 1 | 2 | yes | — |
| 161 | C2×C4×C79 | H(5,𝔽2) | 1 | 2 | yes | — |
| 162 | C22⋊D79 | — | 2 | 4 | no | — |
| 163 | C22⋊D79 | — | 2 | 4 | no | — |
| 164 | C22⋊D79 | — | 4 | 8 | no | — |
| 165 | C22⋊D79 | — | 4 | 8 | no | — |
| 166 | C22⋊D79 | — | 8 | 8 | no | — |
| 167 | C2×Dic79 | — | 2 | 4 | no | — |
| 168 | C2×Dic79 | — | 4 | 4 | no | — |
| 169 | C2×Dic79 | — | 8 | 4 | no | — |
| 170 | C2×Dic79 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 171 | D316 | — | 2 | 4 | no | — |
| 172 | C4×D79 | — | 2 | 8 | no | — |
| 173 | Dic158 | — | 2 | 4 | no | — |
| 174 | C8×C79 | — | 4 | 4 | no | — |
| 175 | C79⋊C8 | — | 4 | 4 | no | — |
| 176 | C22×C79 | — | 2 | 2 | no | — |
| 177 | C22×C79 | — | 2 | 2 | no | — |
| 178 | C22×C79 | — | 2 | 2 | no | — |
| 179 | C22×C79 | — | 2 | 4 | no | — |
| 180 | C22×C79 | — | 4 | 1 | no | — |
| 181 | C22×C79 | — | 4 | 4 | no | — |
| 182 | C22×C79 | — | 4 | 1 | no | — |
| 183 | C22×C79 | — | 4 | 1 | no | — |
| 184 | C22×C79 | — | 4 | 1 | no | — |
| 185 | C22×C79 | — | 4 | 4 | no | — |
| 186 | C22×C79 | — | 4 | 1 | no | — |
| 187 | C22×C79 | — | 4 | 2 | no | — |
| 188 | C22×C79 | — | 8 | 2 | no | — |
| 189 | C22×C79 | — | 8 | 2 | no | — |
| 190 | C22×C79 | — | 8 | 2 | no | — |
| 191 | C22×C79 | — | 8 | 2 | no | — |
| 192 | C22×C79 | — | 8 | 16 | no | — |
| 193 | C22×C79 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 194 | C22×C79 | #518 | 1 | 1 | yes | characteristic |
| 195 | C22×C79 | #518 | 1 | 1 | yes | characteristic |
| 196 | C2×D79 | — | 2 | 4 | no | — |
| 197 | C2×D79 | — | 4 | 4 | no | — |
| 198 | C2×D79 | — | 16 | 4 | no | — |
| 199 | C4×C79 | — | 4 | 1 | no | — |
| 200 | C4×C79 | #534 | 1 | 4 | yes | — |
| 201 | Dic79 | — | 2 | 4 | no | — |
| 202 | Dic79 | — | 4 | 4 | no | — |
| 203 | #21778 | — | 79 | 1 | no | maximal, Sylow |
| 204 | C2×C79 | — | 2 | 1 | no | — |
| 205 | C2×C79 | — | 2 | 1 | no | — |
| 206 | C2×C79 | — | 2 | 1 | no | — |
| 207 | C2×C79 | — | 4 | 4 | no | — |
| 208 | C2×C79 | — | 4 | 2 | no | — |
| 209 | C2×C79 | — | 8 | 2 | no | — |
| 210 | C2×C79 | #2308 | 1 | 1 | yes | characteristic |
| 211 | D79 | — | 4 | 4 | no | — |
| 212 | #3484 | — | 79 | 1 | no | — |
| 213 | #2888 | — | 79 | 2 | no | — |
| 214 | #1914 | — | 79 | 4 | no | — |
| 215 | #1891 | — | 79 | 4 | no | — |
| 216 | #1829 | — | 79 | 2 | no | — |
| 217 | #1783 | — | 79 | 1 | no | — |
| 218 | #1783 | D79 | 1 | 1 | yes | characteristic, complemented |
| 219 | C79 | #21778 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 220 | C2×H(5,𝔽2) | — | 79 | 1 | no | — |
| 221 | C23×D4 | C2×D79 | 1 | 1 | yes | characteristic |
| 222 | #568 | — | 79 | 4 | no | — |
| 223 | #546 | — | 158 | 4 | no | — |
| 224 | D42 | — | 158 | 4 | no | — |
| 225 | #535 | — | 79 | 2 | no | — |
| 226 | #534 | — | 79 | 4 | no | — |
| 227 | #525 | — | 79 | 2 | no | — |
| 228 | C2×#120 | — | 79 | 4 | no | — |
| 229 | #518 | — | 79 | 1 | no | — |
| 230 | #413 | — | 79 | 4 | no | — |
| 231 | #413 | — | 158 | 4 | no | — |
| 232 | C2×#100 | — | 79 | 2 | no | — |
| 233 | C2×#100 | — | 79 | 2 | no | — |
| 234 | C2×#100 | — | 158 | 4 | no | — |
| 235 | C2×#100 | C2×D79 | 1 | 2 | yes | — |
| 236 | C2×#100 | C2×D79 | 1 | 2 | yes | complemented |
| 237 | #407 | — | 79 | 2 | no | — |
| 238 | #407 | C2×D79 | 1 | 2 | yes | complemented |
| 239 | #344 | — | 79 | 4 | no | — |
| 240 | #344 | — | 79 | 4 | no | — |
| 241 | C25 | C4×D79 | 1 | 2 | yes | — |
| 242 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 243 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 244 | C2×#41 | — | 79 | 4 | no | — |
| 245 | C2×#41 | — | 79 | 2 | no | — |
| 246 | C22×D4 | — | 2 | 4 | no | — |
| 247 | C22×D4 | — | 4 | 2 | no | — |
| 248 | C22×D4 | — | 4 | 2 | no | — |
| 249 | C22×D4 | — | 79 | 4 | no | — |
| 250 | C22×D4 | — | 79 | 4 | no | — |
| 251 | C22×D4 | — | 158 | 4 | no | — |
| 252 | C22×D4 | C4×D79 | 1 | 2 | yes | — |
| 253 | C22×D4 | C22×D79 | 1 | 1 | yes | characteristic |
| 254 | C22×D4 | C22×D79 | 1 | 1 | yes | characteristic |
| 255 | C23×C4 | C22×D79 | 1 | 1 | yes | characteristic |
| 256 | #131 | — | 316 | 4 | no | — |
| 257 | #131 | — | 316 | 4 | no | — |
| 258 | C2×M16 | — | 79 | 4 | no | — |
| 259 | C2×M16 | — | 158 | 8 | no | — |
| 260 | C2×M16 | C22×D79 | 1 | 4 | yes | — |
| 261 | #127 | — | 158 | 2 | no | — |
| 262 | #124 | — | 158 | 2 | no | — |
| 263 | #123 | — | 79 | 4 | no | — |
| 264 | #123 | — | 158 | 4 | no | — |
| 265 | C22⋊Q8 | — | 158 | 2 | no | — |
| 266 | #121 | — | 158 | 2 | no | — |
| 267 | #121 | — | 158 | 4 | no | — |
| 268 | #121 | — | 158 | 8 | no | — |
| 269 | #120 | — | 79 | 4 | no | — |
| 270 | #120 | — | 79 | 8 | no | — |
| 271 | #120 | — | 158 | 4 | no | — |
| 272 | #120 | — | 158 | 8 | no | — |
| 273 | C4×D4 | — | 158 | 4 | no | — |
| 274 | C4×D4 | — | 158 | 4 | no | — |
| 275 | #117 | — | 79 | 2 | no | — |
| 276 | C2×C22⋊C4 | — | 79 | 4 | no | — |
| 277 | C2×C22⋊C4 | — | 158 | 4 | no | — |
| 278 | #101 | — | 158 | 4 | no | — |
| 279 | #100 | — | 2 | 4 | no | — |
| 280 | #100 | — | 4 | 2 | no | — |
| 281 | #100 | — | 316 | 2 | no | — |
| 282 | #100 | — | 158 | 4 | no | — |
| 283 | #100 | — | 158 | 4 | no | — |
| 284 | C22⋊C8 | — | 4 | 2 | no | — |
| 285 | C22⋊C8 | — | 316 | 2 | no | — |
| 286 | C24 | — | 2 | 4 | no | — |
| 287 | C24 | — | 4 | 2 | no | — |
| 288 | C24 | — | 4 | 2 | no | — |
| 289 | C24 | — | 8 | 4 | no | — |
| 290 | C24 | — | 79 | 4 | no | — |
| 291 | C24 | C2×C4×D79 | 1 | 1 | yes | characteristic |
| 292 | C24 | C2×C4×D79 | 1 | 2 | yes | — |
| 293 | C24 | C2×C4×D79 | 1 | 2 | yes | — |
| 294 | #41 | — | 316 | 8 | no | — |
| 295 | #41 | — | 158 | 4 | no | — |
| 296 | #41 | — | 158 | 4 | no | — |
| 297 | C2×Q8 | — | 79 | 2 | no | — |
| 298 | C2×D4 | — | 2 | 4 | no | — |
| 299 | C2×D4 | — | 2 | 2 | no | — |
| 300 | C2×D4 | — | 2 | 2 | no | — |
| 301 | C2×D4 | — | 2 | 2 | no | — |
| 302 | C2×D4 | — | 2 | 2 | no | — |
| 303 | C2×D4 | — | 2 | 2 | no | — |
| 304 | C2×D4 | — | 4 | 2 | no | — |
| 305 | C2×D4 | — | 4 | 2 | no | — |
| 306 | C2×D4 | — | 4 | 16 | no | — |
| 307 | C2×D4 | — | 316 | 4 | no | — |
| 308 | C2×D4 | — | 316 | 4 | no | — |
| 309 | C2×D4 | — | 316 | 8 | no | — |
| 310 | C2×D4 | — | 79 | 8 | no | — |
| 311 | C2×D4 | — | 79 | 4 | no | — |
| 312 | C2×D4 | — | 79 | 2 | no | — |
| 313 | C2×D4 | — | 632 | 8 | no | — |
| 314 | C2×D4 | — | 158 | 4 | no | — |
| 315 | C2×D4 | — | 158 | 8 | no | — |
| 316 | C2×D4 | D4×D79 | 1 | 4 | yes | — |
| 317 | C22×C4 | — | 2 | 2 | no | — |
| 318 | C22×C4 | — | 2 | 2 | no | — |
| 319 | C22×C4 | — | 2 | 2 | no | — |
| 320 | C22×C4 | — | 79 | 4 | no | — |
| 321 | C22×C4 | — | 79 | 4 | no | — |
| 322 | C22×C4 | — | 158 | 4 | no | — |
| 323 | C22×C4 | C2×C4×D79 | 1 | 1 | yes | characteristic |
| 324 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 325 | M16 | — | 2 | 4 | no | — |
| 326 | M16 | — | 2 | 4 | no | — |
| 327 | M16 | — | 316 | 8 | no | — |
| 328 | M16 | — | 158 | 4 | no | — |
| 329 | M16 | — | 158 | 4 | no | — |
| 330 | C2×C8 | — | 2 | 4 | no | — |
| 331 | C2×C8 | — | 316 | 8 | no | — |
| 332 | C2×C8 | — | 158 | 4 | no | — |
| 333 | C4⋊C4 | — | 158 | 4 | no | — |
| 334 | C4⋊C4 | — | 158 | 2 | no | — |
| 335 | C22⋊C4 | — | 79 | 4 | no | — |
| 336 | C22⋊C4 | — | 158 | 4 | no | — |
| 337 | C22⋊C4 | — | 158 | 4 | no | — |
| 338 | C22⋊C4 | — | 158 | 8 | no | — |
| 339 | C22⋊C4 | — | 158 | 4 | no | — |
| 340 | C42 | — | 158 | 2 | no | — |
| 341 | C23 | — | 2 | 1 | no | — |
| 342 | C23 | — | 2 | 1 | no | — |
| 343 | C23 | — | 2 | 1 | no | — |
| 344 | C23 | — | 2 | 2 | no | — |
| 345 | C23 | — | 2 | 2 | no | — |
| 346 | C23 | — | 2 | 2 | no | — |
| 347 | C23 | — | 2 | 2 | no | — |
| 348 | C23 | — | 2 | 2 | no | — |
| 349 | C23 | — | 4 | 2 | no | — |
| 350 | C23 | — | 4 | 8 | no | — |
| 351 | C23 | — | 4 | 8 | no | — |
| 352 | C23 | — | 8 | 4 | no | — |
| 353 | C23 | — | 8 | 4 | no | — |
| 354 | C23 | — | 8 | 2 | no | — |
| 355 | C23 | — | 8 | 2 | no | — |
| 356 | C23 | — | 8 | 4 | no | — |
| 357 | C23 | — | 8 | 4 | no | — |
| 358 | C23 | — | 8 | 4 | no | — |
| 359 | C23 | — | 316 | 4 | no | — |
| 360 | C23 | — | 79 | 4 | no | — |
| 361 | C23 | — | 632 | 4 | no | — |
| 362 | C23 | C22⋊C4×D79 | 1 | 4 | yes | — |
| 363 | C23 | C22×C4×D79 | 1 | 1 | yes | characteristic |
| 364 | Q8 | — | 158 | 4 | no | — |
| 365 | D4 | — | 2 | 8 | no | — |
| 366 | D4 | — | 4 | 8 | no | — |
| 367 | D4 | — | 4 | 4 | no | — |
| 368 | D4 | — | 316 | 8 | no | — |
| 369 | D4 | — | 316 | 8 | no | — |
| 370 | D4 | — | 632 | 8 | no | — |
| 371 | D4 | — | 158 | 4 | no | — |
| 372 | D4 | — | 158 | 4 | no | — |
| 373 | D4 | — | 158 | 4 | no | — |
| 374 | C2×C4 | — | 2 | 1 | no | — |
| 375 | C2×C4 | — | 2 | 1 | no | — |
| 376 | C2×C4 | — | 2 | 1 | no | — |
| 377 | C2×C4 | — | 4 | 4 | no | — |
| 378 | C2×C4 | — | 316 | 4 | no | — |
| 379 | C2×C4 | — | 79 | 4 | no | — |
| 380 | C2×C4 | — | 632 | 4 | no | — |
| 381 | C2×C4 | — | 158 | 4 | no | — |
| 382 | C2×C4 | — | 158 | 8 | no | — |
| 383 | C2×C4 | C2×D4×D79 | 1 | 2 | yes | — |
| 384 | C2×C4 | #14579206 | 1 | 2 | yes | — |
| 385 | C2×C4 | #14579206 | 1 | 2 | yes | — |
| 386 | C8 | — | 4 | 4 | no | — |
| 387 | C8 | — | 316 | 4 | no | — |
| 388 | C22 | — | 2 | 2 | no | — |
| 389 | C22 | — | 2 | 2 | no | — |
| 390 | C22 | — | 2 | 2 | no | — |
| 391 | C22 | — | 2 | 4 | no | — |
| 392 | C22 | — | 4 | 1 | no | — |
| 393 | C22 | — | 4 | 4 | no | — |
| 394 | C22 | — | 4 | 1 | no | — |
| 395 | C22 | — | 4 | 1 | no | — |
| 396 | C22 | — | 4 | 1 | no | — |
| 397 | C22 | — | 4 | 4 | no | — |
| 398 | C22 | — | 4 | 1 | no | — |
| 399 | C22 | — | 4 | 2 | no | — |
| 400 | C22 | — | 8 | 2 | no | — |
| 401 | C22 | — | 8 | 2 | no | — |
| 402 | C22 | — | 8 | 2 | no | — |
| 403 | C22 | — | 8 | 2 | no | — |
| 404 | C22 | — | 8 | 16 | no | — |
| 405 | C22 | — | 316 | 4 | no | — |
| 406 | C22 | — | 158 | 4 | no | — |
| 407 | C22 | — | 1264 | 4 | no | — |
| 408 | C22 | C2×C22⋊C4×D79 | 1 | 1 | yes | characteristic |
| 409 | C22 | #19099036 | 1 | 1 | yes | characteristic |
| 410 | C22 | #19099036 | 1 | 1 | yes | characteristic |
| 411 | C4 | — | 4 | 1 | no | — |
| 412 | C4 | — | 316 | 4 | no | — |
| 413 | C4 | — | 158 | 4 | no | — |
| 414 | C4 | #19099123 | 1 | 4 | yes | — |
| 415 | C2 | — | 2 | 1 | no | — |
| 416 | C2 | — | 2 | 1 | no | — |
| 417 | C2 | — | 2 | 1 | no | — |
| 418 | C2 | — | 4 | 2 | no | — |
| 419 | C2 | — | 4 | 4 | no | — |
| 420 | C2 | — | 8 | 2 | no | — |
| 421 | C2 | — | 316 | 4 | no | — |
| 422 | C2 | #23765976 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23771876 | C2 | semidirect |
| 3. #23763944 | C2 | semidirect |
| 4. #23763815 | C2 | semidirect |
| 5. #23763509 | C2 | semidirect |
| 6. #23763321 | C2 | semidirect |
| 7. C79×#1783 | C2 | semidirect |
| 9. #19099329 | C22 | semidirect |
| 17. #19098545 | C22 | semidirect |
| 20. C2×#14579078 | C22 | semidirect |
| 22. #19098527 | C22 | semidirect |
| 23. #19098335 | C22 | semidirect |
| 24. #19098334 | C22 | semidirect |
| 27. C2×#100×C79 | C22 | semidirect |
| 28. #407×C79 | C22 | semidirect |
| 218. #1783 | D79 | semidirect |
| 219. C79 | #21778 | semidirect |
| 236. C2×#100 | C2×D79 | semidirect |
| 238. #407 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777035 | 2 |
| #23771876 | 2 |
| #23763944 | 2 |
| #23763815 | 2 |
| #23763509 | 2 |
| #23763321 | 2 |
| C79×#1783 | 2 |
| #21778 | 79 |