Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
844 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 89 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 | C2×#19098751 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #23766538 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#19098351 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23763356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23763347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23761524 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#1390 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14579206 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14579131 | — | 2 | 1 | no | — |
| 10 | C2×#14579129 | C22 | 1 | 1 | yes | characteristic |
| 11 | #19098751 | — | 2 | 2 | no | — |
| 12 | #19098751 | C4 | 1 | 4 | yes | complemented |
| 13 | C2×#14579087 | — | 2 | 1 | no | — |
| 14 | #19098565 | — | 2 | 1 | no | — |
| 15 | C2×#14579076 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#14579075 | — | 2 | 1 | no | — |
| 17 | C2×#14579075 | — | 2 | 1 | no | — |
| 18 | #19098466 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19098463 | — | 2 | 1 | no | — |
| 20 | #19098457 | — | 2 | 1 | no | — |
| 21 | #19098455 | — | 2 | 1 | no | — |
| 22 | #19098452 | — | 2 | 1 | no | — |
| 23 | #19098442 | — | 2 | 1 | no | — |
| 24 | #19098442 | — | 2 | 1 | no | — |
| 25 | #19098418 | — | 2 | 1 | no | — |
| 26 | #19098351 | — | 2 | 2 | no | — |
| 27 | C2×#100×C79 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#99×C79 | C22 | 1 | 1 | yes | characteristic |
| 29 | #386×C79 | C22 | 1 | 1 | yes | characteristic |
| 30 | C24×D79 | D4 | 1 | 1 | yes | characteristic |
| 31 | #14579206 | — | 2 | 1 | no | — |
| 32 | #14579206 | — | 2 | 1 | no | — |
| 33 | #14579206 | — | 2 | 1 | no | — |
| 34 | #14579206 | — | 4 | 2 | no | — |
| 35 | #14579206 | C2×C4 | 1 | 2 | yes | — |
| 36 | C2×#11929624 | — | 2 | 1 | no | — |
| 37 | C2×#11929623 | — | 4 | 1 | no | — |
| 38 | C22×D316 | — | 4 | 1 | no | — |
| 39 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 40 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 41 | C22×C22⋊D79 | — | 2 | 1 | no | — |
| 42 | C2×D4×D79 | — | 4 | 1 | no | — |
| 43 | #14579131 | — | 2 | 4 | no | — |
| 44 | #14579131 | — | 4 | 2 | no | — |
| 45 | #14579129 | — | 2 | 1 | no | — |
| 46 | #14579129 | — | 2 | 1 | no | — |
| 47 | #14579129 | C2×C4 | 1 | 2 | yes | — |
| 48 | #14579129 | D4 | 1 | 2 | yes | — |
| 49 | C2×C4⋊Dic79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 50 | C2×Dic79⋊C4 | — | 2 | 1 | no | — |
| 51 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 52 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 53 | C2×C22⋊Dic79 | — | 2 | 1 | no | — |
| 54 | C2×C22⋊Dic79 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 56 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 57 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 58 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 59 | C2×(C2×D79)⋊C4 | — | 2 | 1 | no | — |
| 60 | C2×(C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 61 | C2×(C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 62 | C2×C4×Dic79 | — | 2 | 1 | no | — |
| 63 | C2×C4×Dic79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | #14579087 | — | 4 | 2 | no | — |
| 65 | #14579086 | — | 4 | 1 | no | — |
| 66 | #14579083 | — | 4 | 1 | no | — |
| 67 | #14579076 | — | 2 | 1 | no | — |
| 68 | #14579076 | — | 2 | 1 | no | — |
| 69 | #14579075 | — | 2 | 4 | no | — |
| 70 | #14579075 | — | 4 | 2 | no | — |
| 71 | C79⋊#95 | — | 2 | 1 | no | — |
| 72 | C79⋊#95 | — | 2 | 1 | no | — |
| 73 | C79⋊#95 | — | 4 | 1 | no | — |
| 74 | C22×D4×C79 | C23 | 1 | 1 | yes | characteristic |
| 75 | C23×C4×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 76 | C2×M16×C79 | — | 2 | 1 | no | — |
| 77 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 78 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 79 | C2×C22⋊C4×C79 | D4 | 1 | 1 | yes | characteristic, complemented |
| 80 | #100×C79 | — | 2 | 1 | no | — |
| 81 | #100×C79 | — | 2 | 1 | no | — |
| 82 | #99×C79 | — | 2 | 1 | no | — |
| 83 | #99×C79 | C2×C4 | 1 | 2 | yes | — |
| 84 | #95×C79 | — | 2 | 1 | no | — |
| 85 | C23×D79 | — | 2 | 1 | no | — |
| 86 | C23×D79 | — | 2 | 1 | no | — |
| 87 | C23×D79 | — | 2 | 1 | no | — |
| 88 | C23×D79 | — | 2 | 1 | no | — |
| 89 | C23×D79 | — | 4 | 1 | no | — |
| 90 | C23×D79 | — | 4 | 1 | no | — |
| 91 | C23×D79 | — | 8 | 1 | no | — |
| 92 | C23×D79 | — | 8 | 1 | no | — |
| 93 | C23×D79 | C22⋊C4 | 1 | 2 | yes | complemented |
| 94 | #11929624 | — | 2 | 2 | no | — |
| 95 | #11929624 | — | 2 | 2 | no | — |
| 96 | #11929624 | — | 4 | 1 | no | — |
| 97 | #11929624 | — | 4 | 1 | no | — |
| 98 | #11929623 | — | 4 | 2 | no | — |
| 99 | #11929623 | — | 4 | 2 | no | — |
| 100 | #11929623 | — | 4 | 2 | no | — |
| 101 | #11929623 | — | 4 | 2 | no | — |
| 102 | C2×Dic158 | — | 2 | 1 | no | — |
| 103 | C2×D316 | — | 2 | 1 | no | — |
| 104 | C2×D316 | — | 4 | 4 | no | — |
| 105 | C2×D316 | — | 8 | 2 | no | — |
| 106 | C2×D316 | — | 8 | 2 | no | — |
| 107 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 108 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 109 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 110 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 111 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 112 | C2×C22⋊D79 | — | 2 | 2 | no | — |
| 113 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 114 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 115 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 116 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 117 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 118 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 119 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 120 | C2×C22⋊D79 | — | 8 | 1 | no | — |
| 121 | C2×C22⋊D79 | — | 8 | 1 | no | — |
| 122 | D4×D79 | — | 4 | 2 | no | — |
| 123 | D4×D79 | — | 4 | 2 | no | — |
| 124 | D4×D79 | — | 4 | 2 | no | — |
| 125 | D4×D79 | — | 4 | 2 | no | — |
| 126 | C22×Dic79 | — | 2 | 1 | no | — |
| 127 | C22×Dic79 | — | 2 | 1 | no | — |
| 128 | C22×Dic79 | — | 2 | 1 | no | — |
| 129 | C22×Dic79 | — | 2 | 1 | no | — |
| 130 | C22×Dic79 | — | 2 | 1 | no | — |
| 131 | C22×Dic79 | — | 4 | 1 | no | — |
| 132 | C2×C4×D79 | — | 4 | 1 | no | — |
| 133 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 134 | Dic79⋊C4 | — | 8 | 1 | no | — |
| 135 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 136 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 137 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 138 | C22⋊Dic79 | — | 8 | 1 | no | — |
| 139 | C22⋊Dic79 | — | 8 | 1 | no | — |
| 140 | C22⋊Dic79 | C22⋊C4 | 1 | 2 | yes | complemented |
| 141 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 142 | (C2×D79)⋊C4 | — | 2 | 2 | no | — |
| 143 | (C2×D79)⋊C4 | — | 4 | 4 | no | — |
| 144 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 145 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 146 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 147 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 148 | (C2×D79)⋊C4 | — | 8 | 2 | no | — |
| 149 | C4×Dic79 | — | 4 | 1 | no | — |
| 150 | C4×Dic79 | — | 8 | 1 | no | — |
| 151 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C24×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 153 | C2×D4×C79 | — | 4 | 1 | no | — |
| 154 | C2×D4×C79 | — | 4 | 1 | no | — |
| 155 | C2×D4×C79 | C22×C4 | 1 | 1 | yes | characteristic |
| 156 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×D4×C79 | #41 | 1 | 1 | yes | characteristic |
| 158 | C2×D4×C79 | #41 | 1 | 1 | yes | characteristic |
| 159 | C22×C4×C79 | — | 2 | 1 | no | — |
| 160 | C22×C4×C79 | — | 2 | 1 | no | — |
| 161 | C22×C4×C79 | — | 4 | 1 | no | — |
| 162 | C22×C4×C79 | — | 4 | 1 | no | — |
| 163 | C22×C4×C79 | — | 8 | 1 | no | — |
| 164 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 165 | M16×C79 | — | 4 | 1 | no | — |
| 166 | M16×C79 | — | 4 | 1 | no | — |
| 167 | C2×C8×C79 | — | 4 | 1 | no | — |
| 168 | C22⋊C4×C79 | — | 2 | 2 | no | — |
| 169 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 170 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 171 | C22⋊C4×C79 | — | 8 | 1 | no | — |
| 172 | C23×C79 | — | 2 | 1 | no | — |
| 173 | C23×C79 | — | 2 | 1 | no | — |
| 174 | C23×C79 | — | 2 | 1 | no | — |
| 175 | C23×C79 | — | 2 | 1 | no | — |
| 176 | C23×C79 | — | 4 | 1 | no | — |
| 177 | C23×C79 | — | 4 | 1 | no | — |
| 178 | C23×C79 | — | 4 | 1 | no | — |
| 179 | C23×C79 | — | 4 | 1 | no | — |
| 180 | C23×C79 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 181 | C23×C79 | C4×D4 | 1 | 1 | yes | characteristic |
| 182 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 183 | C23×C79 | #121 | 1 | 1 | yes | characteristic |
| 184 | C23×C79 | #123 | 1 | 1 | yes | characteristic |
| 185 | C22×D79 | — | 2 | 2 | no | — |
| 186 | C22×D79 | — | 2 | 2 | no | — |
| 187 | C22×D79 | — | 2 | 2 | no | — |
| 188 | C22×D79 | — | 4 | 2 | no | — |
| 189 | C22×D79 | — | 4 | 1 | no | — |
| 190 | C22×D79 | — | 4 | 1 | no | — |
| 191 | C22×D79 | — | 4 | 1 | no | — |
| 192 | C22×D79 | — | 4 | 1 | no | — |
| 193 | C22×D79 | — | 4 | 2 | no | — |
| 194 | C22×D79 | — | 4 | 2 | no | — |
| 195 | C22×D79 | — | 4 | 1 | no | — |
| 196 | C22×D79 | — | 4 | 1 | no | — |
| 197 | C22×D79 | — | 4 | 1 | no | — |
| 198 | C22×D79 | — | 4 | 1 | no | — |
| 199 | C22×D79 | — | 4 | 1 | no | — |
| 200 | C22×D79 | — | 8 | 2 | no | — |
| 201 | C22×D79 | — | 8 | 1 | no | — |
| 202 | C22×D79 | — | 8 | 2 | no | — |
| 203 | C22×D79 | — | 8 | 4 | no | — |
| 204 | C22×D79 | — | 8 | 1 | no | — |
| 205 | C22×D79 | — | 8 | 1 | no | — |
| 206 | C22×D79 | — | 8 | 1 | no | — |
| 207 | C22×D79 | — | 8 | 1 | no | — |
| 208 | C22×D79 | — | 8 | 1 | no | — |
| 209 | C22×D79 | — | 8 | 1 | no | — |
| 210 | D4×C79 | — | 4 | 1 | no | — |
| 211 | D4×C79 | — | 4 | 1 | no | — |
| 212 | D4×C79 | — | 4 | 1 | no | — |
| 213 | D4×C79 | — | 4 | 1 | no | — |
| 214 | C2×C4×C79 | — | 2 | 1 | no | — |
| 215 | C2×C4×C79 | — | 2 | 1 | no | — |
| 216 | C2×C4×C79 | — | 4 | 1 | no | — |
| 217 | C2×C4×C79 | — | 4 | 2 | no | — |
| 218 | C2×C4×C79 | — | 4 | 1 | no | — |
| 219 | C2×C4×C79 | — | 4 | 1 | no | — |
| 220 | C2×C4×C79 | — | 4 | 1 | no | — |
| 221 | C2×C4×C79 | — | 4 | 2 | no | — |
| 222 | C2×C4×C79 | — | 4 | 1 | no | — |
| 223 | C2×C4×C79 | — | 4 | 1 | no | — |
| 224 | C2×C4×C79 | — | 8 | 1 | no | — |
| 225 | C2×C4×C79 | — | 8 | 1 | no | — |
| 226 | C2×C4×C79 | — | 8 | 1 | no | — |
| 227 | C2×C4×C79 | C4×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C79 | #121 | 1 | 1 | yes | characteristic |
| 229 | C22⋊D79 | — | 4 | 2 | no | — |
| 230 | C22⋊D79 | — | 4 | 2 | no | — |
| 231 | C22⋊D79 | — | 4 | 2 | no | — |
| 232 | C22⋊D79 | — | 4 | 2 | no | — |
| 233 | C22⋊D79 | — | 4 | 2 | no | — |
| 234 | C22⋊D79 | — | 4 | 2 | no | — |
| 235 | C22⋊D79 | — | 8 | 2 | no | — |
| 236 | C22⋊D79 | — | 8 | 2 | no | — |
| 237 | C2×Dic79 | — | 2 | 2 | no | — |
| 238 | C2×Dic79 | — | 2 | 2 | no | — |
| 239 | C2×Dic79 | — | 2 | 2 | no | — |
| 240 | C2×Dic79 | — | 4 | 1 | no | — |
| 241 | C2×Dic79 | — | 4 | 1 | no | — |
| 242 | C2×Dic79 | — | 4 | 1 | no | — |
| 243 | C2×Dic79 | — | 4 | 1 | no | — |
| 244 | C2×Dic79 | — | 4 | 1 | no | — |
| 245 | C2×Dic79 | — | 4 | 1 | no | — |
| 246 | C2×Dic79 | — | 4 | 1 | no | — |
| 247 | C2×Dic79 | — | 4 | 1 | no | — |
| 248 | C2×Dic79 | — | 4 | 1 | no | — |
| 249 | C2×Dic79 | — | 4 | 1 | no | — |
| 250 | C2×Dic79 | — | 4 | 1 | no | — |
| 251 | C2×Dic79 | — | 8 | 1 | no | — |
| 252 | C2×Dic79 | — | 8 | 1 | no | — |
| 253 | C2×Dic79 | — | 8 | 1 | no | — |
| 254 | D316 | — | 2 | 2 | no | — |
| 255 | D316 | — | 4 | 1 | no | — |
| 256 | D316 | — | 8 | 8 | no | — |
| 257 | C4×D79 | — | 4 | 2 | no | — |
| 258 | C4×D79 | — | 4 | 2 | no | — |
| 259 | Dic158 | — | 2 | 2 | no | — |
| 260 | Dic158 | — | 4 | 1 | no | — |
| 261 | C8×C79 | — | 8 | 1 | no | — |
| 262 | C22×C79 | — | 2 | 1 | no | — |
| 263 | C22×C79 | — | 2 | 1 | no | — |
| 264 | C22×C79 | — | 2 | 1 | no | — |
| 265 | C22×C79 | — | 2 | 1 | no | — |
| 266 | C22×C79 | — | 2 | 1 | no | — |
| 267 | C22×C79 | — | 2 | 1 | no | — |
| 268 | C22×C79 | — | 4 | 1 | no | — |
| 269 | C22×C79 | — | 4 | 1 | no | — |
| 270 | C22×C79 | — | 4 | 1 | no | — |
| 271 | C22×C79 | — | 4 | 1 | no | — |
| 272 | C22×C79 | — | 4 | 1 | no | — |
| 273 | C22×C79 | — | 4 | 1 | no | — |
| 274 | C22×C79 | — | 4 | 1 | no | — |
| 275 | C22×C79 | — | 4 | 1 | no | — |
| 276 | C22×C79 | — | 8 | 1 | no | — |
| 277 | C22×C79 | — | 8 | 1 | no | — |
| 278 | C22×C79 | #386 | 1 | 1 | yes | characteristic |
| 279 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 280 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 281 | C2×D79 | — | 4 | 2 | no | — |
| 282 | C2×D79 | — | 4 | 2 | no | — |
| 283 | C2×D79 | — | 4 | 4 | no | — |
| 284 | C2×D79 | — | 4 | 2 | no | — |
| 285 | C2×D79 | — | 4 | 2 | no | — |
| 286 | C2×D79 | — | 8 | 1 | no | — |
| 287 | C2×D79 | — | 8 | 1 | no | — |
| 288 | C2×D79 | — | 8 | 2 | no | — |
| 289 | C2×D79 | — | 8 | 2 | no | — |
| 290 | C2×D79 | — | 8 | 1 | no | — |
| 291 | C2×D79 | — | 8 | 1 | no | — |
| 292 | C2×D79 | — | 8 | 1 | no | — |
| 293 | C2×D79 | — | 8 | 1 | no | — |
| 294 | C2×D79 | — | 8 | 2 | no | — |
| 295 | C2×D79 | — | 8 | 2 | no | — |
| 296 | C2×D79 | — | 8 | 2 | no | — |
| 297 | C2×D79 | — | 16 | 1 | no | — |
| 298 | C2×D79 | — | 16 | 1 | no | — |
| 299 | C4×C79 | — | 2 | 1 | no | — |
| 300 | C4×C79 | — | 2 | 1 | no | — |
| 301 | C4×C79 | — | 8 | 1 | no | — |
| 302 | C4×C79 | — | 8 | 2 | no | — |
| 303 | C4×C79 | — | 8 | 1 | no | — |
| 304 | Dic79 | — | 4 | 2 | no | — |
| 305 | Dic79 | — | 4 | 2 | no | — |
| 306 | Dic79 | — | 8 | 1 | no | — |
| 307 | Dic79 | — | 8 | 1 | no | — |
| 308 | Dic79 | — | 16 | 1 | no | — |
| 309 | #13043 | — | 79 | 1 | no | maximal, Sylow |
| 310 | C2×C79 | — | 2 | 1 | no | — |
| 311 | C2×C79 | — | 2 | 1 | no | — |
| 312 | C2×C79 | — | 4 | 1 | no | — |
| 313 | C2×C79 | — | 4 | 1 | no | — |
| 314 | C2×C79 | — | 4 | 1 | no | — |
| 315 | C2×C79 | — | 4 | 1 | no | — |
| 316 | C2×C79 | #1889 | 1 | 1 | yes | characteristic |
| 317 | C2×C79 | #2199 | 1 | 1 | yes | characteristic |
| 318 | C2×C79 | #2200 | 1 | 1 | yes | characteristic |
| 319 | D79 | — | 8 | 2 | no | — |
| 320 | D79 | — | 8 | 2 | no | — |
| 321 | C2×B(4,𝔽2) | — | 79 | 1 | no | — |
| 322 | #2375 | — | 79 | 1 | no | — |
| 323 | C2×AΣL(1,𝔽16) | — | 79 | 1 | no | — |
| 324 | #1792 | — | 79 | 1 | no | — |
| 325 | #1790 | — | 79 | 1 | no | — |
| 326 | #1393 | — | 79 | 1 | no | — |
| 327 | #1390 | D79 | 1 | 1 | yes | characteristic, complemented |
| 328 | C79 | #13043 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 329 | C2×H(5,𝔽2) | — | 79 | 1 | no | — |
| 330 | C2×#120 | — | 79 | 1 | no | — |
| 331 | C2×#120 | — | 158 | 1 | no | — |
| 332 | B(4,𝔽2) | — | 79 | 4 | no | — |
| 333 | B(4,𝔽2) | — | 158 | 2 | no | — |
| 334 | C2×#104 | — | 158 | 1 | no | — |
| 335 | #417 | — | 158 | 1 | no | — |
| 336 | C2×#100 | C2×D79 | 1 | 1 | yes | characteristic |
| 337 | C2×#99 | — | 79 | 1 | no | — |
| 338 | C2×#99 | — | 158 | 1 | no | — |
| 339 | C2×#99 | — | 158 | 1 | no | — |
| 340 | C2×#99 | C2×D79 | 1 | 1 | yes | characteristic |
| 341 | #390 | — | 79 | 1 | no | — |
| 342 | #390 | — | 158 | 1 | no | — |
| 343 | #388 | — | 158 | 1 | no | — |
| 344 | #388 | — | 158 | 1 | no | — |
| 345 | #388 | — | 158 | 1 | no | — |
| 346 | #386 | — | 158 | 1 | no | — |
| 347 | #386 | — | 158 | 1 | no | — |
| 348 | #386 | C2×D79 | 1 | 1 | yes | characteristic |
| 349 | #379 | — | 158 | 1 | no | — |
| 350 | AΣL(1,𝔽16) | — | 158 | 2 | no | — |
| 351 | C25 | — | 79 | 1 | no | — |
| 352 | H(5,𝔽2) | — | 316 | 2 | no | — |
| 353 | H(5,𝔽2) | — | 79 | 2 | no | — |
| 354 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 355 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 356 | H(5,𝔽2) | — | 158 | 1 | no | — |
| 357 | C2×#41 | — | 316 | 1 | no | — |
| 358 | C2×#41 | — | 158 | 1 | no | — |
| 359 | C22×D4 | — | 316 | 1 | no | — |
| 360 | C22×D4 | — | 316 | 1 | no | — |
| 361 | C22×D4 | — | 158 | 1 | no | — |
| 362 | C22×D4 | — | 158 | 1 | no | — |
| 363 | C22×D4 | — | 158 | 1 | no | — |
| 364 | C22×D4 | C22×D79 | 1 | 1 | yes | characteristic |
| 365 | C23×C4 | D316 | 1 | 1 | yes | characteristic, complemented |
| 366 | C2×M16 | — | 2 | 1 | no | — |
| 367 | #120 | — | 316 | 2 | no | — |
| 368 | #120 | — | 79 | 2 | no | — |
| 369 | #120 | — | 79 | 2 | no | — |
| 370 | #120 | — | 158 | 4 | no | — |
| 371 | #120 | — | 158 | 1 | no | — |
| 372 | #120 | — | 158 | 1 | no | — |
| 373 | C2×C4⋊C4 | — | 79 | 1 | no | — |
| 374 | C2×C4⋊C4 | — | 158 | 1 | no | — |
| 375 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 376 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 377 | C2×C22⋊C4 | — | 316 | 1 | no | — |
| 378 | C2×C22⋊C4 | — | 316 | 1 | no | — |
| 379 | C2×C22⋊C4 | — | 79 | 1 | no | — |
| 380 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 381 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 382 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 383 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 384 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 385 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 386 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 387 | C2×C22⋊C4 | — | 158 | 1 | no | — |
| 388 | C2×C22⋊C4 | D316 | 1 | 1 | yes | characteristic, complemented |
| 389 | C2×C42 | — | 79 | 1 | no | — |
| 390 | C2×C42 | — | 158 | 1 | no | — |
| 391 | #104 | — | 316 | 2 | no | — |
| 392 | #103 | — | 316 | 1 | no | — |
| 393 | #102 | — | 316 | 1 | no | — |
| 394 | #100 | — | 2 | 1 | no | — |
| 395 | #100 | — | 2 | 1 | no | — |
| 396 | #99 | — | 2 | 1 | no | — |
| 397 | #99 | — | 316 | 2 | no | — |
| 398 | #99 | — | 158 | 4 | no | — |
| 399 | #99 | — | 158 | 1 | no | — |
| 400 | #99 | — | 158 | 1 | no | — |
| 401 | #99 | C4×D79 | 1 | 2 | yes | — |
| 402 | #95 | — | 2 | 1 | no | — |
| 403 | #95 | — | 316 | 1 | no | — |
| 404 | #95 | — | 158 | 1 | no | — |
| 405 | #95 | — | 158 | 1 | no | — |
| 406 | C24 | — | 316 | 1 | no | — |
| 407 | C24 | — | 316 | 1 | no | — |
| 408 | C24 | — | 79 | 2 | no | — |
| 409 | C24 | — | 632 | 1 | no | — |
| 410 | C24 | — | 632 | 1 | no | — |
| 411 | C24 | — | 158 | 1 | no | — |
| 412 | C24 | — | 158 | 1 | no | — |
| 413 | C24 | — | 158 | 1 | no | — |
| 414 | C24 | — | 158 | 1 | no | — |
| 415 | C24 | D4×D79 | 1 | 1 | yes | characteristic |
| 416 | C24 | C2×D316 | 1 | 1 | yes | characteristic |
| 417 | #41 | — | 316 | 1 | no | — |
| 418 | #41 | — | 316 | 2 | no | — |
| 419 | #41 | — | 316 | 2 | no | — |
| 420 | #41 | — | 316 | 2 | no | — |
| 421 | #41 | — | 316 | 1 | no | — |
| 422 | #41 | — | 316 | 2 | no | — |
| 423 | #41 | — | 158 | 2 | no | — |
| 424 | #41 | — | 158 | 2 | no | — |
| 425 | C2×Q8 | — | 158 | 1 | no | — |
| 426 | C2×D4 | — | 4 | 1 | no | — |
| 427 | C2×D4 | — | 4 | 1 | no | — |
| 428 | C2×D4 | — | 316 | 4 | no | — |
| 429 | C2×D4 | — | 316 | 2 | no | — |
| 430 | C2×D4 | — | 316 | 2 | no | — |
| 431 | C2×D4 | — | 316 | 2 | no | — |
| 432 | C2×D4 | — | 316 | 2 | no | — |
| 433 | C2×D4 | — | 316 | 1 | no | — |
| 434 | C2×D4 | — | 316 | 1 | no | — |
| 435 | C2×D4 | — | 316 | 1 | no | — |
| 436 | C2×D4 | — | 316 | 1 | no | — |
| 437 | C2×D4 | — | 316 | 1 | no | — |
| 438 | C2×D4 | — | 316 | 1 | no | — |
| 439 | C2×D4 | — | 316 | 1 | no | — |
| 440 | C2×D4 | — | 632 | 2 | no | — |
| 441 | C2×D4 | — | 632 | 2 | no | — |
| 442 | C2×D4 | — | 632 | 1 | no | — |
| 443 | C2×D4 | — | 632 | 1 | no | — |
| 444 | C2×D4 | — | 158 | 1 | no | — |
| 445 | C2×D4 | — | 158 | 2 | no | — |
| 446 | C2×D4 | — | 158 | 2 | no | — |
| 447 | C2×D4 | — | 158 | 2 | no | — |
| 448 | C2×D4 | — | 158 | 2 | no | — |
| 449 | C2×D4 | — | 158 | 2 | no | — |
| 450 | C2×D4 | — | 158 | 2 | no | — |
| 451 | C2×D4 | C2×C4×D79 | 1 | 1 | yes | characteristic |
| 452 | C2×D4 | D4×D79 | 1 | 1 | yes | characteristic |
| 453 | C2×D4 | #11929624 | 1 | 1 | yes | characteristic |
| 454 | C2×D4 | #11929625 | 1 | 1 | yes | characteristic |
| 455 | C22×C4 | — | 2 | 1 | no | — |
| 456 | C22×C4 | — | 2 | 1 | no | — |
| 457 | C22×C4 | — | 4 | 1 | no | — |
| 458 | C22×C4 | — | 4 | 1 | no | — |
| 459 | C22×C4 | — | 8 | 1 | no | — |
| 460 | C22×C4 | — | 316 | 1 | no | — |
| 461 | C22×C4 | — | 316 | 1 | no | — |
| 462 | C22×C4 | — | 158 | 1 | no | — |
| 463 | C22×C4 | — | 158 | 1 | no | — |
| 464 | C22×C4 | — | 158 | 1 | no | — |
| 465 | C22×C4 | — | 158 | 1 | no | — |
| 466 | C22×C4 | — | 158 | 1 | no | — |
| 467 | C22×C4 | D4×D79 | 1 | 1 | yes | characteristic |
| 468 | M16 | — | 4 | 1 | no | — |
| 469 | M16 | — | 4 | 1 | no | — |
| 470 | C2×C8 | — | 4 | 1 | no | — |
| 471 | C4⋊C4 | — | 316 | 1 | no | — |
| 472 | C4⋊C4 | — | 632 | 1 | no | — |
| 473 | C22⋊C4 | — | 2 | 2 | no | — |
| 474 | C22⋊C4 | — | 4 | 1 | no | — |
| 475 | C22⋊C4 | — | 4 | 1 | no | — |
| 476 | C22⋊C4 | — | 8 | 1 | no | — |
| 477 | C22⋊C4 | — | 316 | 4 | no | — |
| 478 | C22⋊C4 | — | 316 | 1 | no | — |
| 479 | C22⋊C4 | — | 316 | 1 | no | — |
| 480 | C22⋊C4 | — | 79 | 2 | no | — |
| 481 | C22⋊C4 | — | 632 | 1 | no | — |
| 482 | C22⋊C4 | — | 632 | 1 | no | — |
| 483 | C22⋊C4 | — | 632 | 1 | no | — |
| 484 | C22⋊C4 | — | 632 | 1 | no | — |
| 485 | C22⋊C4 | — | 632 | 2 | no | — |
| 486 | C22⋊C4 | — | 632 | 1 | no | — |
| 487 | C22⋊C4 | — | 632 | 1 | no | — |
| 488 | C22⋊C4 | — | 158 | 1 | no | — |
| 489 | C22⋊C4 | — | 158 | 2 | no | — |
| 490 | C22⋊C4 | — | 158 | 2 | no | — |
| 491 | C42 | — | 316 | 1 | no | — |
| 492 | C42 | — | 632 | 1 | no | — |
| 493 | C23 | — | 2 | 1 | no | — |
| 494 | C23 | — | 2 | 1 | no | — |
| 495 | C23 | — | 2 | 1 | no | — |
| 496 | C23 | — | 2 | 1 | no | — |
| 497 | C23 | — | 4 | 1 | no | — |
| 498 | C23 | — | 4 | 1 | no | — |
| 499 | C23 | — | 4 | 1 | no | — |
| 500 | C23 | — | 4 | 1 | no | — |
| 501 | C23 | — | 316 | 2 | no | — |
| 502 | C23 | — | 316 | 1 | no | — |
| 503 | C23 | — | 316 | 1 | no | — |
| 504 | C23 | — | 316 | 1 | no | — |
| 505 | C23 | — | 316 | 1 | no | — |
| 506 | C23 | — | 316 | 1 | no | — |
| 507 | C23 | — | 316 | 1 | no | — |
| 508 | C23 | — | 316 | 2 | no | — |
| 509 | C23 | — | 316 | 2 | no | — |
| 510 | C23 | — | 316 | 1 | no | — |
| 511 | C23 | — | 316 | 1 | no | — |
| 512 | C23 | — | 316 | 1 | no | — |
| 513 | C23 | — | 632 | 1 | no | — |
| 514 | C23 | — | 632 | 2 | no | — |
| 515 | C23 | — | 632 | 2 | no | — |
| 516 | C23 | — | 632 | 1 | no | — |
| 517 | C23 | — | 632 | 1 | no | — |
| 518 | C23 | — | 632 | 1 | no | — |
| 519 | C23 | — | 632 | 1 | no | — |
| 520 | C23 | — | 632 | 1 | no | — |
| 521 | C23 | — | 632 | 1 | no | — |
| 522 | C23 | — | 632 | 4 | no | — |
| 523 | C23 | — | 158 | 2 | no | — |
| 524 | C23 | — | 158 | 2 | no | — |
| 525 | C23 | — | 158 | 2 | no | — |
| 526 | C23 | C22⋊C4×D79 | 1 | 1 | yes | characteristic |
| 527 | C23 | C4×D316 | 1 | 1 | yes | characteristic |
| 528 | C23 | #14579131 | 1 | 1 | yes | characteristic |
| 529 | C23 | #14579136 | 1 | 1 | yes | characteristic |
| 530 | C23 | #14579146 | 1 | 1 | yes | characteristic |
| 531 | Q8 | — | 316 | 1 | no | — |
| 532 | Q8 | — | 158 | 2 | no | — |
| 533 | D4 | — | 4 | 1 | no | — |
| 534 | D4 | — | 4 | 1 | no | — |
| 535 | D4 | — | 4 | 1 | no | — |
| 536 | D4 | — | 4 | 1 | no | — |
| 537 | D4 | — | 316 | 1 | no | — |
| 538 | D4 | — | 316 | 2 | no | — |
| 539 | D4 | — | 316 | 2 | no | — |
| 540 | D4 | — | 316 | 2 | no | — |
| 541 | D4 | — | 316 | 2 | no | — |
| 542 | D4 | — | 316 | 2 | no | — |
| 543 | D4 | — | 316 | 2 | no | — |
| 544 | D4 | — | 632 | 8 | no | — |
| 545 | D4 | — | 632 | 2 | no | — |
| 546 | D4 | — | 632 | 2 | no | — |
| 547 | D4 | — | 158 | 2 | no | — |
| 548 | C2×C4 | — | 2 | 1 | no | — |
| 549 | C2×C4 | — | 2 | 1 | no | — |
| 550 | C2×C4 | — | 4 | 1 | no | — |
| 551 | C2×C4 | — | 4 | 2 | no | — |
| 552 | C2×C4 | — | 4 | 1 | no | — |
| 553 | C2×C4 | — | 4 | 1 | no | — |
| 554 | C2×C4 | — | 4 | 1 | no | — |
| 555 | C2×C4 | — | 4 | 2 | no | — |
| 556 | C2×C4 | — | 4 | 1 | no | — |
| 557 | C2×C4 | — | 4 | 1 | no | — |
| 558 | C2×C4 | — | 8 | 1 | no | — |
| 559 | C2×C4 | — | 8 | 1 | no | — |
| 560 | C2×C4 | — | 8 | 1 | no | — |
| 561 | C2×C4 | — | 316 | 2 | no | — |
| 562 | C2×C4 | — | 316 | 2 | no | — |
| 563 | C2×C4 | — | 316 | 1 | no | — |
| 564 | C2×C4 | — | 316 | 1 | no | — |
| 565 | C2×C4 | — | 316 | 1 | no | — |
| 566 | C2×C4 | — | 316 | 1 | no | — |
| 567 | C2×C4 | — | 316 | 1 | no | — |
| 568 | C2×C4 | — | 316 | 1 | no | — |
| 569 | C2×C4 | — | 316 | 1 | no | — |
| 570 | C2×C4 | — | 316 | 1 | no | — |
| 571 | C2×C4 | — | 316 | 1 | no | — |
| 572 | C2×C4 | — | 316 | 1 | no | — |
| 573 | C2×C4 | — | 316 | 1 | no | — |
| 574 | C2×C4 | — | 632 | 1 | no | — |
| 575 | C2×C4 | — | 632 | 1 | no | — |
| 576 | C2×C4 | — | 632 | 1 | no | — |
| 577 | C2×C4 | — | 158 | 2 | no | — |
| 578 | C2×C4 | — | 158 | 2 | no | — |
| 579 | C2×C4 | — | 158 | 2 | no | — |
| 580 | C2×C4 | #14579123 | 1 | 1 | yes | characteristic |
| 581 | C2×C4 | #14579134 | 1 | 1 | yes | characteristic |
| 582 | C8 | — | 8 | 1 | no | — |
| 583 | C22 | — | 2 | 1 | no | — |
| 584 | C22 | — | 2 | 1 | no | — |
| 585 | C22 | — | 2 | 1 | no | — |
| 586 | C22 | — | 2 | 1 | no | — |
| 587 | C22 | — | 2 | 1 | no | — |
| 588 | C22 | — | 2 | 1 | no | — |
| 589 | C22 | — | 4 | 1 | no | — |
| 590 | C22 | — | 4 | 1 | no | — |
| 591 | C22 | — | 4 | 1 | no | — |
| 592 | C22 | — | 4 | 1 | no | — |
| 593 | C22 | — | 4 | 1 | no | — |
| 594 | C22 | — | 4 | 1 | no | — |
| 595 | C22 | — | 4 | 1 | no | — |
| 596 | C22 | — | 4 | 1 | no | — |
| 597 | C22 | — | 8 | 1 | no | — |
| 598 | C22 | — | 8 | 1 | no | — |
| 599 | C22 | — | 316 | 2 | no | — |
| 600 | C22 | — | 316 | 2 | no | — |
| 601 | C22 | — | 316 | 4 | no | — |
| 602 | C22 | — | 316 | 2 | no | — |
| 603 | C22 | — | 316 | 2 | no | — |
| 604 | C22 | — | 632 | 1 | no | — |
| 605 | C22 | — | 632 | 1 | no | — |
| 606 | C22 | — | 632 | 2 | no | — |
| 607 | C22 | — | 632 | 2 | no | — |
| 608 | C22 | — | 632 | 2 | no | — |
| 609 | C22 | — | 632 | 2 | no | — |
| 610 | C22 | — | 632 | 2 | no | — |
| 611 | C22 | — | 632 | 1 | no | — |
| 612 | C22 | — | 632 | 1 | no | — |
| 613 | C22 | — | 632 | 1 | no | — |
| 614 | C22 | — | 632 | 1 | no | — |
| 615 | C22 | — | 1264 | 1 | no | — |
| 616 | C22 | — | 1264 | 1 | no | — |
| 617 | C22 | #19098441 | 1 | 1 | yes | characteristic |
| 618 | C22 | #19098751 | 1 | 1 | yes | characteristic |
| 619 | C22 | #19098751 | 1 | 1 | yes | characteristic |
| 620 | C4 | — | 2 | 1 | no | — |
| 621 | C4 | — | 2 | 1 | no | — |
| 622 | C4 | — | 8 | 1 | no | — |
| 623 | C4 | — | 8 | 2 | no | — |
| 624 | C4 | — | 8 | 1 | no | — |
| 625 | C4 | — | 316 | 2 | no | — |
| 626 | C4 | — | 316 | 2 | no | — |
| 627 | C4 | — | 632 | 1 | no | — |
| 628 | C4 | — | 632 | 1 | no | — |
| 629 | C4 | — | 1264 | 1 | no | — |
| 630 | C2 | — | 2 | 1 | no | — |
| 631 | C2 | — | 2 | 1 | no | — |
| 632 | C2 | — | 4 | 1 | no | — |
| 633 | C2 | — | 4 | 1 | no | — |
| 634 | C2 | — | 4 | 1 | no | — |
| 635 | C2 | — | 4 | 1 | no | — |
| 636 | C2 | — | 632 | 2 | no | — |
| 637 | C2 | — | 632 | 2 | no | — |
| 638 | C2 | #23763807 | 1 | 1 | yes | characteristic |
| 639 | C2 | #23765402 | 1 | 1 | yes | characteristic |
| 640 | C2 | #23765408 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23766538 | C2 | semidirect |
| 3. C2×#19098351 | C2 | semidirect |
| 4. #23763356 | C2 | semidirect |
| 5. #23763347 | C2 | semidirect |
| 6. #23761524 | C2 | semidirect |
| 7. C79×#1390 | C2 | semidirect |
| 12. #19098751 | C4 | semidirect |
| 49. C2×C4⋊Dic79 | D4 | semidirect |
| 63. C2×C4×Dic79 | D4 | semidirect |
| 75. C23×C4×C79 | D4 | semidirect |
| 79. C2×C22⋊C4×C79 | D4 | semidirect |
| 93. C23×D79 | C22⋊C4 | semidirect |
| 140. C22⋊Dic79 | C22⋊C4 | semidirect |
| 327. #1390 | D79 | semidirect |
| 328. C79 | #13043 | semidirect |
| 365. C23×C4 | D316 | semidirect |
| 388. C2×C22⋊C4 | D316 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098751 | 2 |
| #23766538 | 2 |
| C2×#19098351 | 2 |
| #23763356 | 2 |
| #23763347 | 2 |
| #23761524 | 2 |
| C79×#1390 | 2 |
| #13043 | 79 |