Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1938 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1938 conjugacy classes of subgroups — too many to draw. Only its 227 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 | #575×D79 | C2 | 1 | 3 | yes | maximal, complemented |
| 2 | #408×D79 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #23764505 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23764504 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | #23764503 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #338×D79 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#2017 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#41×D79 | C22 | 1 | 3 | yes | — |
| 9 | #19099363 | C22 | 1 | 3 | yes | complemented |
| 10 | #19099362 | — | 2 | 6 | no | — |
| 11 | #19099361 | C22 | 1 | 6 | yes | complemented |
| 12 | #19099360 | — | 2 | 6 | no | — |
| 13 | #19099359 | — | 2 | 6 | no | — |
| 14 | #137×D79 | — | 2 | 6 | no | — |
| 15 | AGL(1,ℤ/8)×D79 | — | 2 | 6 | no | — |
| 16 | #135×D79 | — | 2 | 6 | no | — |
| 17 | C2×M16×D79 | C22 | 1 | 3 | yes | — |
| 18 | C22×C8×D79 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19098531 | C22 | 1 | 3 | yes | complemented |
| 20 | #19098530 | C22 | 1 | 3 | yes | complemented |
| 21 | #19098529 | C22 | 1 | 3 | yes | complemented |
| 22 | #19098528 | — | 2 | 6 | no | — |
| 23 | C22⋊C8×D79 | — | 2 | 6 | no | — |
| 24 | C79⋊#338 | C22 | 1 | 3 | yes | complemented |
| 25 | #575×C79 | C22 | 1 | 3 | yes | complemented |
| 26 | #408×C79 | C22 | 1 | 3 | yes | complemented |
| 27 | #338×C79 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×#11929625 | D4 | 1 | 3 | yes | — |
| 29 | C2×#11929624 | — | 2 | 3 | no | — |
| 30 | C2×#11929624 | C23 | 1 | 3 | yes | — |
| 31 | C2×#11929623 | — | 2 | 3 | no | — |
| 32 | C2×#11929623 | D4 | 1 | 3 | yes | — |
| 33 | #41×D79 | — | 2 | 6 | no | — |
| 34 | #41×D79 | — | 2 | 6 | no | — |
| 35 | #41×D79 | — | 2 | 6 | no | — |
| 36 | #41×D79 | — | 2 | 6 | no | — |
| 37 | C2×Q8×D79 | D4 | 1 | 3 | yes | — |
| 38 | C2×D4×D79 | — | 2 | 3 | no | — |
| 39 | C2×D4×D79 | D4 | 1 | 3 | yes | — |
| 40 | C22×C4×D79 | — | 2 | 3 | no | — |
| 41 | C22×C4×D79 | C23 | 1 | 1 | yes | characteristic |
| 42 | #14579194 | — | 2 | 6 | no | — |
| 43 | #14579193 | — | 2 | 12 | no | — |
| 44 | #14579192 | — | 2 | 6 | no | — |
| 45 | #14579191 | — | 2 | 6 | no | — |
| 46 | #14579190 | — | 2 | 12 | no | — |
| 47 | #14579189 | — | 2 | 6 | no | — |
| 48 | #14579188 | — | 2 | 12 | no | — |
| 49 | #14579187 | — | 2 | 6 | no | — |
| 50 | #14579186 | — | 2 | 6 | no | — |
| 51 | #14579185 | — | 2 | 12 | no | — |
| 52 | #14579184 | — | 2 | 6 | no | — |
| 53 | #14579183 | — | 2 | 6 | no | — |
| 54 | #14579182 | — | 2 | 12 | no | — |
| 55 | #14579181 | — | 2 | 12 | no | — |
| 56 | #14579180 | — | 2 | 6 | no | — |
| 57 | Q16×D79 | — | 2 | 6 | no | — |
| 58 | SD16×D79 | — | 2 | 12 | no | — |
| 59 | D8×D79 | — | 2 | 6 | no | — |
| 60 | C2×#11929608 | C23 | 1 | 3 | yes | — |
| 61 | C2×#11929607 | D4 | 1 | 6 | yes | — |
| 62 | M16×D79 | — | 2 | 6 | no | — |
| 63 | M16×D79 | — | 2 | 6 | no | — |
| 64 | C22×C79⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 65 | C2×C8×D79 | — | 2 | 3 | no | — |
| 66 | C2×C8×D79 | — | 2 | 3 | no | — |
| 67 | C2×C8×D79 | D4 | 1 | 6 | yes | — |
| 68 | C22⋊(C79⋊C8) | — | 2 | 6 | no | — |
| 69 | (C2×D79)⋊C8 | — | 2 | 6 | no | — |
| 70 | (C2×D79)⋊C8 | — | 2 | 6 | no | — |
| 71 | C2×#41×C79 | C23 | 1 | 3 | yes | — |
| 72 | #137×C79 | — | 2 | 6 | no | — |
| 73 | AGL(1,ℤ/8)×C79 | — | 2 | 6 | no | — |
| 74 | #135×C79 | — | 2 | 6 | no | — |
| 75 | C2×M16×C79 | C23 | 1 | 3 | yes | — |
| 76 | C22×C8×C79 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22⋊C8×C79 | — | 2 | 6 | no | — |
| 78 | C23×D79 | — | 2 | 3 | no | — |
| 79 | C23×D79 | #41 | 1 | 1 | yes | characteristic |
| 80 | #11929625 | — | 2 | 6 | no | — |
| 81 | #11929625 | — | 2 | 6 | no | — |
| 82 | #11929624 | — | 2 | 6 | no | — |
| 83 | #11929624 | — | 2 | 6 | no | — |
| 84 | #11929624 | — | 4 | 6 | no | — |
| 85 | #11929624 | — | 4 | 6 | no | — |
| 86 | #11929623 | — | 2 | 6 | no | — |
| 87 | #11929623 | — | 2 | 6 | no | — |
| 88 | #11929623 | — | 4 | 6 | no | — |
| 89 | #11929623 | — | 4 | 6 | no | — |
| 90 | C2×Dic158 | — | 2 | 3 | no | — |
| 91 | C2×Dic158 | C2×D4 | 1 | 3 | yes | — |
| 92 | Q8×D79 | — | 2 | 6 | no | — |
| 93 | Q8×D79 | — | 2 | 6 | no | — |
| 94 | C2×D316 | — | 2 | 3 | no | — |
| 95 | C2×D316 | C2×D4 | 1 | 3 | yes | — |
| 96 | C2×C22⋊D79 | — | 2 | 3 | no | — |
| 97 | C2×C22⋊D79 | — | 2 | 3 | no | — |
| 98 | C2×C22⋊D79 | — | 2 | 3 | no | — |
| 99 | D4×D79 | — | 2 | 6 | no | — |
| 100 | D4×D79 | — | 2 | 6 | no | — |
| 101 | D4×D79 | — | 4 | 6 | no | — |
| 102 | D4×D79 | — | 4 | 6 | no | — |
| 103 | C22×Dic79 | — | 2 | 3 | no | — |
| 104 | C22×Dic79 | #41 | 1 | 1 | yes | characteristic |
| 105 | C2×C4×D79 | — | 2 | 3 | no | — |
| 106 | C2×C4×D79 | — | 2 | 3 | no | — |
| 107 | C2×C4×D79 | — | 2 | 3 | no | — |
| 108 | C2×C4×D79 | — | 4 | 3 | no | — |
| 109 | C2×C4×D79 | — | 4 | 3 | no | — |
| 110 | C2×C4×D79 | — | 4 | 3 | no | — |
| 111 | C2×C4×D79 | — | 4 | 3 | no | — |
| 112 | C2×C4×D79 | C2×D4 | 1 | 3 | yes | — |
| 113 | C2×C4×D79 | C2×D4 | 1 | 3 | yes | — |
| 114 | C2×C4×D79 | C2×D4 | 1 | 3 | yes | — |
| 115 | C2×C4×D79 | C2×D4 | 1 | 3 | yes | — |
| 116 | Dic316 | — | 2 | 6 | no | — |
| 117 | #11929614 | — | 2 | 12 | no | — |
| 118 | #11929613 | — | 2 | 12 | no | — |
| 119 | #11929612 | — | 2 | 12 | no | — |
| 120 | #11929611 | — | 2 | 12 | no | — |
| 121 | D632 | — | 2 | 6 | no | — |
| 122 | #11929609 | — | 2 | 12 | no | — |
| 123 | #11929608 | — | 2 | 6 | no | — |
| 124 | #11929607 | — | 2 | 12 | no | — |
| 125 | C2×C79⋊C8 | — | 2 | 3 | no | — |
| 126 | C2×C79⋊C8 | C2×D4 | 1 | 6 | yes | — |
| 127 | C8×D79 | — | 2 | 6 | no | — |
| 128 | C8×D79 | — | 2 | 6 | no | — |
| 129 | C8×D79 | — | 4 | 1 | no | — |
| 130 | C8×D79 | — | 4 | 3 | no | — |
| 131 | #41×C79 | — | 2 | 6 | no | — |
| 132 | #41×C79 | — | 2 | 6 | no | — |
| 133 | C2×Q8×C79 | C2×D4 | 1 | 3 | yes | — |
| 134 | C2×D4×C79 | — | 2 | 3 | no | — |
| 135 | C2×D4×C79 | C2×D4 | 1 | 3 | yes | — |
| 136 | C22×C4×C79 | — | 2 | 3 | no | — |
| 137 | C22×C4×C79 | C24 | 1 | 1 | yes | characteristic |
| 138 | Q16×C79 | — | 2 | 6 | no | — |
| 139 | SD16×C79 | — | 2 | 12 | no | — |
| 140 | D8×C79 | — | 2 | 6 | no | — |
| 141 | M16×C79 | — | 2 | 6 | no | — |
| 142 | C2×C8×C79 | — | 2 | 3 | no | — |
| 143 | C2×C8×C79 | C2×D4 | 1 | 6 | yes | — |
| 144 | C23×C79 | — | 2 | 3 | no | — |
| 145 | C23×C79 | C2×#41 | 1 | 1 | yes | characteristic |
| 146 | C22×D79 | — | 2 | 3 | no | — |
| 147 | C22×D79 | — | 4 | 2 | no | — |
| 148 | C22×D79 | — | 4 | 12 | no | — |
| 149 | C22×D79 | — | 4 | 3 | no | — |
| 150 | C22×D79 | — | 4 | 3 | no | — |
| 151 | C22×D79 | #121 | 1 | 3 | yes | — |
| 152 | C22×D79 | #121 | 1 | 3 | yes | — |
| 153 | Q8×C79 | — | 2 | 6 | no | — |
| 154 | D4×C79 | — | 2 | 6 | no | — |
| 155 | D4×C79 | — | 4 | 6 | no | — |
| 156 | C2×C4×C79 | — | 2 | 3 | no | — |
| 157 | C2×C4×C79 | — | 4 | 3 | no | — |
| 158 | C2×C4×C79 | — | 4 | 3 | no | — |
| 159 | C2×C4×C79 | C22×D4 | 1 | 3 | yes | — |
| 160 | C2×C4×C79 | C22×D4 | 1 | 3 | yes | — |
| 161 | C22⋊D79 | — | 4 | 6 | no | — |
| 162 | C22⋊D79 | — | 4 | 6 | no | — |
| 163 | C22⋊D79 | — | 4 | 6 | no | — |
| 164 | C2×Dic79 | — | 2 | 3 | no | — |
| 165 | C2×Dic79 | — | 4 | 3 | no | — |
| 166 | C2×Dic79 | — | 4 | 3 | no | — |
| 167 | C2×Dic79 | #121 | 1 | 3 | yes | — |
| 168 | C2×Dic79 | #121 | 1 | 3 | yes | — |
| 169 | D316 | — | 2 | 6 | no | — |
| 170 | D316 | — | 4 | 6 | no | — |
| 171 | C4×D79 | — | 4 | 3 | no | — |
| 172 | C4×D79 | — | 4 | 3 | no | — |
| 173 | C4×D79 | — | 4 | 3 | no | — |
| 174 | C4×D79 | — | 4 | 3 | no | — |
| 175 | C4×D79 | — | 4 | 3 | no | — |
| 176 | C4×D79 | — | 4 | 3 | no | — |
| 177 | C4×D79 | #120 | 1 | 3 | yes | — |
| 178 | C4×D79 | #120 | 1 | 3 | yes | — |
| 179 | C4×D79 | #120 | 1 | 6 | yes | — |
| 180 | C4×D79 | #127 | 1 | 1 | yes | characteristic |
| 181 | C4×D79 | #127 | 1 | 3 | yes | — |
| 182 | Dic158 | — | 2 | 6 | no | — |
| 183 | Dic158 | — | 4 | 6 | no | — |
| 184 | C8×C79 | — | 2 | 6 | no | — |
| 185 | C8×C79 | — | 4 | 1 | no | — |
| 186 | C79⋊C8 | — | 2 | 6 | no | — |
| 187 | C79⋊C8 | — | 4 | 1 | no | — |
| 188 | C22×C79 | — | 4 | 1 | no | — |
| 189 | C22×C79 | — | 4 | 6 | no | — |
| 190 | C22×C79 | — | 4 | 3 | no | — |
| 191 | C22×C79 | C2×#121 | 1 | 3 | yes | — |
| 192 | C2×D79 | — | 2 | 6 | no | — |
| 193 | C2×D79 | — | 4 | 3 | no | — |
| 194 | C2×D79 | — | 4 | 6 | no | — |
| 195 | C2×D79 | — | 4 | 3 | no | — |
| 196 | C2×D79 | — | 8 | 6 | no | — |
| 197 | C2×D79 | — | 8 | 6 | no | — |
| 198 | C2×D79 | #392 | 1 | 3 | yes | — |
| 199 | C2×D79 | #392 | 1 | 1 | yes | characteristic |
| 200 | C4×C79 | — | 4 | 3 | no | — |
| 201 | C4×C79 | C2×#120 | 1 | 3 | yes | — |
| 202 | C4×C79 | C2×#127 | 1 | 1 | yes | characteristic |
| 203 | Dic79 | — | 4 | 3 | no | — |
| 204 | Dic79 | #392 | 1 | 3 | yes | — |
| 205 | Dic79 | #392 | 1 | 1 | yes | characteristic |
| 206 | C2×#2017 | — | 79 | 1 | no | maximal, Sylow |
| 207 | C2×C79 | — | 2 | 3 | no | — |
| 208 | C2×C79 | — | 8 | 3 | no | — |
| 209 | C2×C79 | C2×#392 | 1 | 1 | yes | characteristic |
| 210 | D79 | — | 2 | 3 | no | — |
| 211 | D79 | — | 8 | 3 | no | — |
| 212 | D79 | #2017 | 1 | 2 | yes | direct product factor |
| 213 | C2×#575 | — | 79 | 3 | no | — |
| 214 | C2×#408 | — | 79 | 3 | no | — |
| 215 | #2017 | — | 79 | 3 | no | — |
| 216 | #2017 | — | 79 | 1 | no | — |
| 217 | #2017 | — | 79 | 3 | no | — |
| 218 | #2017 | D79 | 1 | 1 | yes | characteristic, direct product factor |
| 219 | C2×#338 | — | 79 | 1 | no | — |
| 220 | C79 | C2×#2017 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 221 | C22×#41 | — | 79 | 3 | no | — |
| 222 | #575 | — | 79 | 6 | no | — |
| 223 | #575 | — | 79 | 3 | no | — |
| 224 | #575 | — | 158 | 6 | no | — |
| 225 | #575 | — | 158 | 6 | no | — |
| 226 | #575 | — | 158 | 6 | no | — |
| 227 | #575 | C2×D79 | 1 | 3 | yes | complemented |
| 228 | C2×#137 | — | 158 | 6 | no | — |
| 229 | C2×AGL(1,ℤ/8) | — | 158 | 6 | no | — |
| 230 | C2×#135 | — | 158 | 6 | no | — |
| 231 | C22×M16 | — | 79 | 3 | no | — |
| 232 | C23×C8 | — | 79 | 1 | no | — |
| 233 | #408 | — | 79 | 3 | no | — |
| 234 | #408 | — | 79 | 3 | no | — |
| 235 | #408 | — | 79 | 3 | no | — |
| 236 | #408 | — | 158 | 6 | no | — |
| 237 | #408 | C2×D79 | 1 | 3 | yes | complemented |
| 238 | C2×C22⋊C8 | — | 158 | 6 | no | — |
| 239 | #338 | — | 79 | 3 | no | — |
| 240 | #338 | C2×D79 | 1 | 1 | yes | characteristic, complemented |
| 241 | C2×#41 | — | 79 | 3 | no | — |
| 242 | C2×#41 | — | 79 | 3 | no | — |
| 243 | C2×#41 | — | 79 | 3 | no | — |
| 244 | C2×#41 | — | 158 | 3 | no | — |
| 245 | C2×#41 | — | 158 | 6 | no | — |
| 246 | C2×#41 | — | 158 | 6 | no | — |
| 247 | C2×#41 | — | 158 | 6 | no | — |
| 248 | C2×#41 | — | 158 | 6 | no | — |
| 249 | C2×#41 | — | 158 | 3 | no | — |
| 250 | C2×#41 | C22×D79 | 1 | 3 | yes | — |
| 251 | C22×Q8 | — | 79 | 3 | no | — |
| 252 | C22×D4 | — | 79 | 3 | no | — |
| 253 | C22×D4 | — | 158 | 3 | no | — |
| 254 | C23×C4 | — | 79 | 1 | no | — |
| 255 | C23×C4 | — | 158 | 3 | no | — |
| 256 | #137 | — | 2 | 6 | no | — |
| 257 | #137 | — | 158 | 6 | no | — |
| 258 | #137 | — | 158 | 12 | no | — |
| 259 | #137 | — | 158 | 12 | no | — |
| 260 | #137 | — | 158 | 6 | no | — |
| 261 | #137 | — | 158 | 6 | no | — |
| 262 | AGL(1,ℤ/8) | — | 2 | 6 | no | — |
| 263 | AGL(1,ℤ/8) | — | 158 | 6 | no | — |
| 264 | AGL(1,ℤ/8) | — | 158 | 12 | no | — |
| 265 | AGL(1,ℤ/8) | — | 158 | 12 | no | — |
| 266 | AGL(1,ℤ/8) | — | 158 | 6 | no | — |
| 267 | AGL(1,ℤ/8) | — | 158 | 6 | no | — |
| 268 | #135 | — | 2 | 6 | no | — |
| 269 | #135 | — | 158 | 12 | no | — |
| 270 | #135 | — | 158 | 6 | no | — |
| 271 | #135 | — | 158 | 12 | no | — |
| 272 | #135 | — | 158 | 6 | no | — |
| 273 | #135 | — | 158 | 6 | no | — |
| 274 | C2×Q16 | — | 158 | 6 | no | — |
| 275 | C2×SD16 | — | 158 | 12 | no | — |
| 276 | C2×D8 | — | 158 | 6 | no | — |
| 277 | C2×M16 | — | 79 | 3 | no | — |
| 278 | C2×M16 | — | 79 | 6 | no | — |
| 279 | C2×M16 | — | 158 | 6 | no | — |
| 280 | C2×M16 | — | 158 | 6 | no | — |
| 281 | C2×M16 | C22×D79 | 1 | 3 | yes | — |
| 282 | C22×C8 | — | 79 | 6 | no | — |
| 283 | C22×C8 | — | 79 | 1 | no | — |
| 284 | C22×C8 | — | 158 | 3 | no | — |
| 285 | C22×C8 | — | 158 | 3 | no | — |
| 286 | C22×C8 | C22×D79 | 1 | 1 | yes | characteristic |
| 287 | C22⋊C8 | — | 2 | 6 | no | — |
| 288 | C22⋊C8 | — | 158 | 6 | no | — |
| 289 | C22⋊C8 | — | 158 | 6 | no | — |
| 290 | C22⋊C8 | — | 158 | 6 | no | — |
| 291 | C24 | — | 79 | 1 | no | — |
| 292 | C24 | — | 158 | 3 | no | — |
| 293 | #41 | — | 2 | 6 | no | — |
| 294 | #41 | — | 2 | 6 | no | — |
| 295 | #41 | — | 316 | 6 | no | — |
| 296 | #41 | — | 316 | 6 | no | — |
| 297 | #41 | — | 316 | 6 | no | — |
| 298 | #41 | — | 316 | 6 | no | — |
| 299 | #41 | — | 158 | 6 | no | — |
| 300 | #41 | — | 158 | 6 | no | — |
| 301 | #41 | — | 158 | 6 | no | — |
| 302 | #41 | — | 158 | 6 | no | — |
| 303 | #41 | — | 158 | 6 | no | — |
| 304 | #41 | — | 158 | 6 | no | — |
| 305 | C2×Q8 | — | 79 | 3 | no | — |
| 306 | C2×Q8 | — | 158 | 3 | no | — |
| 307 | C2×Q8 | — | 158 | 6 | no | — |
| 308 | C2×Q8 | — | 158 | 6 | no | — |
| 309 | C2×Q8 | D4×D79 | 1 | 3 | yes | — |
| 310 | C2×D4 | — | 2 | 3 | no | — |
| 311 | C2×D4 | — | 316 | 6 | no | — |
| 312 | C2×D4 | — | 316 | 6 | no | — |
| 313 | C2×D4 | — | 79 | 3 | no | — |
| 314 | C2×D4 | — | 158 | 3 | no | — |
| 315 | C2×D4 | — | 158 | 6 | no | — |
| 316 | C2×D4 | — | 158 | 6 | no | — |
| 317 | C2×D4 | — | 158 | 3 | no | — |
| 318 | C2×D4 | — | 158 | 3 | no | — |
| 319 | C2×D4 | — | 158 | 3 | no | — |
| 320 | C2×D4 | D4×D79 | 1 | 3 | yes | — |
| 321 | C22×C4 | — | 2 | 3 | no | — |
| 322 | C22×C4 | — | 316 | 3 | no | — |
| 323 | C22×C4 | — | 316 | 3 | no | — |
| 324 | C22×C4 | — | 316 | 3 | no | — |
| 325 | C22×C4 | — | 316 | 3 | no | — |
| 326 | C22×C4 | — | 79 | 1 | no | — |
| 327 | C22×C4 | — | 79 | 3 | no | — |
| 328 | C22×C4 | — | 79 | 3 | no | — |
| 329 | C22×C4 | — | 79 | 3 | no | — |
| 330 | C22×C4 | — | 79 | 3 | no | — |
| 331 | C22×C4 | — | 158 | 3 | no | — |
| 332 | C22×C4 | — | 158 | 3 | no | — |
| 333 | C22×C4 | — | 158 | 3 | no | — |
| 334 | C22×C4 | — | 158 | 3 | no | — |
| 335 | C22×C4 | C23×D79 | 1 | 1 | yes | characteristic |
| 336 | Q16 | — | 2 | 6 | no | — |
| 337 | Q16 | — | 158 | 6 | no | — |
| 338 | Q16 | — | 158 | 12 | no | — |
| 339 | SD16 | — | 2 | 12 | no | — |
| 340 | SD16 | — | 158 | 12 | no | — |
| 341 | SD16 | — | 158 | 12 | no | — |
| 342 | SD16 | — | 158 | 12 | no | — |
| 343 | D8 | — | 2 | 6 | no | — |
| 344 | D8 | — | 158 | 6 | no | — |
| 345 | D8 | — | 158 | 12 | no | — |
| 346 | M16 | — | 2 | 6 | no | — |
| 347 | M16 | — | 158 | 12 | no | — |
| 348 | M16 | — | 158 | 6 | no | — |
| 349 | C2×C8 | — | 2 | 3 | no | — |
| 350 | C2×C8 | — | 316 | 1 | no | — |
| 351 | C2×C8 | — | 316 | 3 | no | — |
| 352 | C2×C8 | — | 79 | 6 | no | — |
| 353 | C2×C8 | — | 158 | 6 | no | — |
| 354 | C2×C8 | — | 158 | 6 | no | — |
| 355 | C2×C8 | — | 158 | 3 | no | — |
| 356 | C2×C8 | D4×D79 | 1 | 6 | yes | — |
| 357 | C23 | — | 2 | 3 | no | — |
| 358 | C23 | — | 316 | 2 | no | — |
| 359 | C23 | — | 316 | 3 | no | — |
| 360 | C23 | — | 316 | 3 | no | — |
| 361 | C23 | — | 316 | 12 | no | — |
| 362 | C23 | — | 79 | 3 | no | — |
| 363 | C23 | — | 79 | 3 | no | — |
| 364 | C23 | — | 158 | 3 | no | — |
| 365 | C23 | #41×D79 | 1 | 1 | yes | characteristic |
| 366 | Q8 | — | 2 | 6 | no | — |
| 367 | Q8 | — | 316 | 6 | no | — |
| 368 | Q8 | — | 158 | 6 | no | — |
| 369 | D4 | — | 2 | 6 | no | — |
| 370 | D4 | — | 4 | 6 | no | — |
| 371 | D4 | — | 316 | 6 | no | — |
| 372 | D4 | — | 316 | 6 | no | — |
| 373 | D4 | — | 316 | 6 | no | — |
| 374 | D4 | — | 316 | 6 | no | — |
| 375 | D4 | — | 158 | 6 | no | — |
| 376 | C2×C4 | — | 2 | 3 | no | — |
| 377 | C2×C4 | — | 4 | 3 | no | — |
| 378 | C2×C4 | — | 4 | 3 | no | — |
| 379 | C2×C4 | — | 316 | 3 | no | — |
| 380 | C2×C4 | — | 316 | 3 | no | — |
| 381 | C2×C4 | — | 316 | 3 | no | — |
| 382 | C2×C4 | — | 316 | 3 | no | — |
| 383 | C2×C4 | — | 316 | 3 | no | — |
| 384 | C2×C4 | — | 316 | 3 | no | — |
| 385 | C2×C4 | — | 316 | 3 | no | — |
| 386 | C2×C4 | — | 316 | 3 | no | — |
| 387 | C2×C4 | — | 79 | 3 | no | — |
| 388 | C2×C4 | — | 79 | 3 | no | — |
| 389 | C2×C4 | — | 79 | 3 | no | — |
| 390 | C2×C4 | — | 79 | 3 | no | — |
| 391 | C2×C4 | — | 79 | 6 | no | — |
| 392 | C2×C4 | — | 79 | 1 | no | — |
| 393 | C2×C4 | — | 79 | 3 | no | — |
| 394 | C2×C4 | — | 158 | 3 | no | — |
| 395 | C2×C4 | C2×D4×D79 | 1 | 3 | yes | — |
| 396 | C2×C4 | C2×D4×D79 | 1 | 3 | yes | — |
| 397 | C8 | — | 2 | 6 | no | — |
| 398 | C8 | — | 4 | 1 | no | — |
| 399 | C8 | — | 316 | 1 | no | — |
| 400 | C8 | — | 158 | 6 | no | — |
| 401 | C22 | — | 4 | 1 | no | — |
| 402 | C22 | — | 4 | 6 | no | — |
| 403 | C22 | — | 4 | 3 | no | — |
| 404 | C22 | — | 316 | 6 | no | — |
| 405 | C22 | — | 316 | 3 | no | — |
| 406 | C22 | — | 316 | 3 | no | — |
| 407 | C22 | — | 79 | 1 | no | — |
| 408 | C22 | — | 79 | 3 | no | — |
| 409 | C22 | — | 632 | 6 | no | — |
| 410 | C22 | — | 632 | 6 | no | — |
| 411 | C22 | — | 158 | 6 | no | — |
| 412 | C22 | #121×D79 | 1 | 3 | yes | — |
| 413 | C4 | — | 4 | 3 | no | — |
| 414 | C4 | — | 316 | 3 | no | — |
| 415 | C4 | — | 79 | 1 | no | — |
| 416 | C4 | — | 79 | 3 | no | — |
| 417 | C4 | #120×D79 | 1 | 3 | yes | — |
| 418 | C4 | #127×D79 | 1 | 1 | yes | characteristic |
| 419 | C2 | — | 2 | 3 | no | — |
| 420 | C2 | — | 8 | 3 | no | — |
| 421 | C2 | — | 79 | 2 | no | — |
| 422 | C2 | — | 632 | 3 | no | — |
| 423 | C2 | — | 158 | 3 | no | — |
| 424 | C2 | #392×D79 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #575×D79 | C2 | semidirect |
| 2. #408×D79 | C2 | semidirect |
| 3. #23764505 | C2 | semidirect |
| 4. #23764504 | C2 | semidirect |
| 5. #23764503 | C2 | semidirect |
| 6. #338×D79 | C2 | semidirect |
| 7. C79×#2017 | C2 | semidirect |
| 9. #19099363 | C22 | semidirect |
| 11. #19099361 | C22 | semidirect |
| 19. #19098531 | C22 | semidirect |
| 20. #19098530 | C22 | semidirect |
| 21. #19098529 | C22 | semidirect |
| 24. C79⋊#338 | C22 | semidirect |
| 25. #575×C79 | C22 | semidirect |
| 26. #408×C79 | C22 | semidirect |
| 27. #338×C79 | C22 | semidirect |
| 212. D79 | #2017 | direct (N × H) |
| 218. #2017 | D79 | direct (N × H) |
| 220. C79 | C2×#2017 | semidirect |
| 227. #575 | C2×D79 | semidirect |
| 237. #408 | C2×D79 | semidirect |
| 240. #338 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×D79 | 2 |
| #408×D79 | 2 |
| #23764505 | 2 |
| #23764504 | 2 |
| #23764503 | 2 |
| #338×D79 | 2 |
| C79×#2017 | 2 |
| C2×#2017 | 79 |