Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
400 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 43 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 | #23775178 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23765418 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #23765400 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #23762707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #23761561 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #23761552 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C79×#1403 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #19099379 | — | 2 | 1 | no | — |
| 9 | #19099374 | — | 2 | 1 | no | — |
| 10 | #19099305 | C22 | 1 | 1 | yes | characteristic |
| 11 | #19098958 | C22 | 1 | 1 | yes | characteristic |
| 12 | #19098923 | — | 2 | 1 | no | — |
| 13 | #19098836 | — | 2 | 1 | no | — |
| 14 | #19098825 | — | 2 | 1 | no | — |
| 15 | #19098750 | — | 2 | 1 | no | — |
| 16 | #19098747 | — | 2 | 1 | no | — |
| 17 | #19098738 | — | 2 | 1 | no | — |
| 18 | #19098735 | C22 | 1 | 1 | yes | characteristic |
| 19 | #19098682 | — | 2 | 1 | no | — |
| 20 | #19098359 | — | 2 | 1 | no | — |
| 21 | #19098358 | C22 | 1 | 1 | yes | characteristic |
| 22 | #19098351 | — | 2 | 1 | no | — |
| 23 | #19098302 | — | 2 | 1 | no | — |
| 24 | #455×C79 | C22 | 1 | 1 | yes | characteristic |
| 25 | #355×C79 | C22 | 1 | 1 | yes | characteristic |
| 26 | #329×C79 | C22 | 1 | 1 | yes | characteristic |
| 27 | #14579209 | D4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #14579208 | — | 2 | 1 | no | — |
| 29 | #14579194 | — | 2 | 1 | no | — |
| 30 | #14579193 | — | 4 | 1 | no | — |
| 31 | #14579191 | — | 2 | 1 | no | — |
| 32 | #14579191 | — | 4 | 1 | no | — |
| 33 | #14579190 | — | 4 | 1 | no | — |
| 34 | #14579189 | — | 4 | 1 | no | — |
| 35 | #14579187 | — | 2 | 1 | no | — |
| 36 | #14579187 | — | 4 | 1 | no | — |
| 37 | #14579182 | — | 4 | 1 | no | — |
| 38 | #14579181 | — | 2 | 1 | no | — |
| 39 | #14579181 | — | 4 | 1 | no | — |
| 40 | C2×#11929614 | — | 2 | 1 | no | — |
| 41 | Q16×D79 | — | 4 | 1 | no | — |
| 42 | C2×#11929612 | — | 2 | 1 | no | — |
| 43 | C2×#11929612 | — | 4 | 1 | no | — |
| 44 | #14579169 | — | 2 | 1 | no | — |
| 45 | #14579168 | — | 2 | 1 | no | — |
| 46 | #14579161 | D4 | 1 | 1 | yes | characteristic, complemented |
| 47 | #14579150 | — | 2 | 1 | no | — |
| 48 | #14579149 | — | 2 | 1 | no | — |
| 49 | #14579147 | — | 4 | 1 | no | — |
| 50 | #14579131 | — | 4 | 1 | no | — |
| 51 | #14579129 | — | 2 | 1 | no | — |
| 52 | #14579129 | — | 4 | 1 | no | — |
| 53 | #14579096 | — | 2 | 1 | no | — |
| 54 | #14579089 | — | 2 | 1 | no | — |
| 55 | #14579087 | — | 4 | 1 | no | — |
| 56 | #14579086 | — | 4 | 1 | no | — |
| 57 | #14579083 | — | 4 | 1 | no | — |
| 58 | #14579080 | D4 | 1 | 1 | yes | characteristic, complemented |
| 59 | #14579079 | — | 2 | 1 | no | — |
| 60 | #14579076 | — | 2 | 1 | no | — |
| 61 | #14579076 | — | 4 | 1 | no | — |
| 62 | #14579072 | D4 | 1 | 1 | yes | characteristic, complemented |
| 63 | H(5,𝔽2)×C79 | D4 | 1 | 1 | yes | characteristic |
| 64 | #137×C79 | — | 2 | 1 | no | — |
| 65 | #124×C79 | C23 | 1 | 1 | yes | characteristic |
| 66 | #104×C79 | — | 2 | 1 | no | — |
| 67 | #101×C79 | — | 2 | 1 | no | — |
| 68 | #100×C79 | D4 | 1 | 1 | yes | characteristic |
| 69 | #97×C79 | — | 2 | 1 | no | — |
| 70 | C23×D79 | — | 2 | 1 | no | — |
| 71 | #11929625 | — | 4 | 1 | no | — |
| 72 | #11929624 | — | 2 | 1 | no | — |
| 73 | #11929624 | — | 4 | 1 | no | — |
| 74 | #11929624 | — | 4 | 1 | no | — |
| 75 | #11929623 | — | 4 | 1 | no | — |
| 76 | #11929623 | — | 8 | 1 | no | — |
| 77 | C2×Dic158 | — | 2 | 1 | no | — |
| 78 | C2×Dic158 | — | 2 | 1 | no | — |
| 79 | C2×Dic158 | — | 4 | 1 | no | — |
| 80 | Q8×D79 | — | 4 | 1 | no | — |
| 81 | Q8×D79 | — | 4 | 1 | no | — |
| 82 | C2×D316 | — | 2 | 1 | no | — |
| 83 | C2×D316 | — | 2 | 1 | no | — |
| 84 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 85 | C2×C22⋊D79 | — | 8 | 1 | no | — |
| 86 | Dic316 | — | 4 | 1 | no | — |
| 87 | #11929614 | — | 2 | 1 | no | — |
| 88 | #11929614 | — | 4 | 1 | no | — |
| 89 | #11929614 | — | 4 | 1 | no | — |
| 90 | #11929614 | — | 4 | 1 | no | — |
| 91 | #11929613 | — | 4 | 1 | no | — |
| 92 | #11929613 | — | 8 | 1 | no | — |
| 93 | #11929612 | — | 2 | 1 | no | — |
| 94 | #11929612 | — | 4 | 1 | no | — |
| 95 | #11929612 | — | 4 | 1 | no | — |
| 96 | #11929612 | — | 4 | 1 | no | — |
| 97 | #11929612 | — | 4 | 1 | no | — |
| 98 | #11929611 | — | 2 | 1 | no | — |
| 99 | D632 | — | 8 | 1 | no | — |
| 100 | #11929609 | — | 2 | 1 | no | — |
| 101 | #11929609 | — | 4 | 1 | no | — |
| 102 | #11929608 | — | 2 | 1 | no | — |
| 103 | #11929608 | — | 4 | 1 | no | — |
| 104 | #11929607 | — | 4 | 1 | no | — |
| 105 | C2×C79⋊C8 | — | 2 | 1 | no | — |
| 106 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 107 | C8×D79 | — | 4 | 1 | no | — |
| 108 | C4⋊Dic79 | — | 4 | 1 | no | — |
| 109 | C22⋊Dic79 | — | 2 | 1 | no | — |
| 110 | C22⋊Dic79 | — | 4 | 1 | no | — |
| 111 | (C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 112 | (C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 113 | (C2×D79)⋊C4 | — | 4 | 1 | no | — |
| 114 | (C2×D79)⋊C4 | — | 8 | 1 | no | — |
| 115 | C4×Dic79 | — | 2 | 1 | no | — |
| 116 | #41×C79 | — | 2 | 1 | no | — |
| 117 | #41×C79 | — | 4 | 1 | no | — |
| 118 | C2×Q8×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×D4×C79 | — | 4 | 1 | no | — |
| 120 | C2×D4×C79 | — | 4 | 1 | no | — |
| 121 | C2×D4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | Q16×C79 | — | 4 | 1 | no | — |
| 123 | SD16×C79 | — | 4 | 1 | no | — |
| 124 | M16×C79 | — | 2 | 1 | no | — |
| 125 | M16×C79 | — | 4 | 1 | no | — |
| 126 | C2×C8×C79 | — | 4 | 1 | no | — |
| 127 | C22⋊C4×C79 | — | 4 | 1 | no | — |
| 128 | C42×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C23×C79 | — | 2 | 1 | no | — |
| 130 | C23×C79 | — | 4 | 1 | no | — |
| 131 | C22×D79 | — | 4 | 1 | no | — |
| 132 | C22×D79 | — | 8 | 1 | no | — |
| 133 | C22×D79 | — | 16 | 1 | no | — |
| 134 | Q8×C79 | — | 2 | 1 | no | — |
| 135 | Q8×C79 | — | 4 | 1 | no | — |
| 136 | D4×C79 | — | 2 | 1 | no | — |
| 137 | D4×C79 | — | 4 | 1 | no | — |
| 138 | D4×C79 | — | 4 | 1 | no | — |
| 139 | D4×C79 | — | 8 | 1 | no | — |
| 140 | C2×C4×C79 | — | 2 | 1 | no | — |
| 141 | C2×C4×C79 | — | 2 | 1 | no | — |
| 142 | C2×C4×C79 | — | 4 | 1 | no | — |
| 143 | C2×C4×C79 | — | 4 | 1 | no | — |
| 144 | C2×C4×C79 | #120 | 1 | 1 | yes | characteristic |
| 145 | C22⋊D79 | — | 4 | 1 | no | — |
| 146 | C22⋊D79 | — | 8 | 1 | no | — |
| 147 | C22⋊D79 | — | 16 | 1 | no | — |
| 148 | C22⋊D79 | — | 16 | 2 | no | — |
| 149 | C2×Dic79 | — | 4 | 1 | no | — |
| 150 | C2×Dic79 | — | 4 | 1 | no | — |
| 151 | C2×Dic79 | — | 8 | 1 | no | — |
| 152 | C2×Dic79 | — | 8 | 1 | no | — |
| 153 | D316 | — | 2 | 1 | no | — |
| 154 | D316 | — | 4 | 1 | no | — |
| 155 | D316 | — | 8 | 1 | no | — |
| 156 | D316 | — | 8 | 1 | no | — |
| 157 | C4×D79 | — | 4 | 1 | no | — |
| 158 | C4×D79 | — | 8 | 1 | no | — |
| 159 | C4×D79 | — | 8 | 1 | no | — |
| 160 | Dic158 | — | 2 | 1 | no | — |
| 161 | Dic158 | — | 4 | 1 | no | — |
| 162 | Dic158 | — | 4 | 1 | no | — |
| 163 | Dic158 | — | 4 | 1 | no | — |
| 164 | Dic158 | — | 8 | 1 | no | — |
| 165 | Dic158 | — | 8 | 1 | no | — |
| 166 | C8×C79 | — | 4 | 1 | no | — |
| 167 | C8×C79 | — | 8 | 1 | no | — |
| 168 | C8×C79 | — | 8 | 1 | no | — |
| 169 | C79⋊C8 | — | 2 | 1 | no | — |
| 170 | C79⋊C8 | — | 2 | 1 | no | — |
| 171 | C79⋊C8 | — | 4 | 1 | no | — |
| 172 | C22×C79 | — | 4 | 1 | no | — |
| 173 | C22×C79 | — | 4 | 1 | no | — |
| 174 | C22×C79 | — | 8 | 1 | no | — |
| 175 | C22×C79 | — | 16 | 1 | no | — |
| 176 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 177 | C2×D79 | — | 4 | 1 | no | — |
| 178 | C2×D79 | — | 8 | 1 | no | — |
| 179 | C2×D79 | — | 8 | 1 | no | — |
| 180 | C2×D79 | — | 8 | 2 | no | — |
| 181 | C2×D79 | — | 8 | 1 | no | — |
| 182 | C2×D79 | — | 16 | 1 | no | — |
| 183 | C4×C79 | — | 2 | 1 | no | — |
| 184 | C4×C79 | — | 4 | 1 | no | — |
| 185 | C4×C79 | — | 4 | 1 | no | — |
| 186 | C4×C79 | — | 4 | 1 | no | — |
| 187 | Dic79 | — | 4 | 1 | no | — |
| 188 | Dic79 | — | 8 | 1 | no | — |
| 189 | Dic79 | — | 8 | 1 | no | — |
| 190 | Dic79 | — | 16 | 1 | no | — |
| 191 | #13678 | — | 79 | 1 | no | maximal, Sylow |
| 192 | C2×C79 | — | 2 | 1 | no | — |
| 193 | C2×C79 | — | 8 | 1 | no | — |
| 194 | C2×C79 | — | 8 | 1 | no | — |
| 195 | C2×C79 | #2196 | 1 | 1 | yes | characteristic |
| 196 | D79 | — | 8 | 1 | no | — |
| 197 | D79 | — | 16 | 1 | no | — |
| 198 | #3289 | — | 79 | 1 | no | — |
| 199 | #2202 | — | 79 | 1 | no | — |
| 200 | #2199 | — | 79 | 1 | no | — |
| 201 | #1659 | — | 79 | 1 | no | — |
| 202 | #1407 | — | 79 | 1 | no | — |
| 203 | #1404 | — | 79 | 1 | no | — |
| 204 | #1403 | D79 | 1 | 1 | yes | characteristic, complemented |
| 205 | C79 | #13678 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 206 | #578 | — | 158 | 1 | no | — |
| 207 | #577 | — | 158 | 1 | no | — |
| 208 | H(3,𝔽4) | — | 79 | 1 | no | — |
| 209 | #497 | — | 79 | 1 | no | — |
| 210 | #489 | — | 158 | 1 | no | — |
| 211 | #473 | — | 158 | 1 | no | — |
| 212 | #471 | — | 158 | 1 | no | — |
| 213 | B(4,𝔽2) | — | 158 | 1 | no | — |
| 214 | #456 | — | 158 | 1 | no | — |
| 215 | #455 | C2×D79 | 1 | 1 | yes | characteristic |
| 216 | #454 | — | 79 | 1 | no | — |
| 217 | #454 | — | 158 | 1 | no | — |
| 218 | #444 | — | 158 | 1 | no | — |
| 219 | #355 | — | 158 | 1 | no | — |
| 220 | #355 | C2×D79 | 1 | 1 | yes | characteristic |
| 221 | #354 | — | 79 | 1 | no | — |
| 222 | AΣL(1,𝔽16) | — | 158 | 1 | no | — |
| 223 | #329 | — | 158 | 1 | no | — |
| 224 | #329 | C2×D79 | 1 | 1 | yes | characteristic |
| 225 | 2−1+4 | — | 79 | 1 | no | — |
| 226 | 2−1+4 | — | 158 | 1 | no | — |
| 227 | H(5,𝔽2) | D316 | 1 | 1 | yes | characteristic |
| 228 | #137 | — | 2 | 1 | no | — |
| 229 | #137 | — | 316 | 1 | no | — |
| 230 | #137 | — | 316 | 1 | no | — |
| 231 | #137 | — | 316 | 1 | no | — |
| 232 | #137 | — | 158 | 1 | no | — |
| 233 | #137 | — | 158 | 1 | no | — |
| 234 | AGL(1,ℤ/8) | — | 316 | 1 | no | — |
| 235 | AGL(1,ℤ/8) | — | 316 | 1 | no | — |
| 236 | AGL(1,ℤ/8) | — | 158 | 1 | no | — |
| 237 | #135 | — | 316 | 1 | no | — |
| 238 | #135 | — | 316 | 1 | no | — |
| 239 | #135 | — | 158 | 1 | no | — |
| 240 | C2×Q16 | — | 316 | 1 | no | — |
| 241 | C2×Q16 | — | 158 | 1 | no | — |
| 242 | C2×SD16 | — | 316 | 1 | no | — |
| 243 | C2×SD16 | — | 158 | 1 | no | — |
| 244 | #131 | — | 158 | 1 | no | — |
| 245 | #131 | — | 158 | 1 | no | — |
| 246 | C4⋊Q8 | — | 79 | 1 | no | — |
| 247 | #124 | — | 316 | 1 | no | — |
| 248 | #124 | — | 158 | 1 | no | — |
| 249 | #124 | — | 158 | 1 | no | — |
| 250 | #124 | C22×D79 | 1 | 1 | yes | characteristic |
| 251 | #120 | — | 316 | 1 | no | — |
| 252 | #120 | — | 316 | 1 | no | — |
| 253 | #120 | — | 158 | 1 | no | — |
| 254 | #108 | — | 158 | 1 | no | — |
| 255 | #104 | — | 2 | 1 | no | — |
| 256 | #104 | — | 316 | 1 | no | — |
| 257 | #104 | — | 158 | 1 | no | — |
| 258 | #103 | — | 316 | 1 | no | — |
| 259 | #102 | — | 316 | 1 | no | — |
| 260 | #101 | — | 2 | 1 | no | — |
| 261 | #101 | — | 79 | 1 | no | — |
| 262 | #101 | — | 158 | 1 | no | — |
| 263 | #100 | D316 | 1 | 1 | yes | characteristic |
| 264 | #99 | — | 316 | 1 | no | — |
| 265 | #99 | — | 158 | 1 | no | — |
| 266 | #97 | — | 2 | 1 | no | — |
| 267 | #97 | — | 79 | 1 | no | — |
| 268 | C24 | — | 158 | 1 | no | — |
| 269 | #41 | — | 2 | 1 | no | — |
| 270 | #41 | — | 4 | 1 | no | — |
| 271 | #41 | — | 316 | 1 | no | — |
| 272 | #41 | — | 316 | 1 | no | — |
| 273 | #41 | — | 316 | 1 | no | — |
| 274 | #41 | — | 316 | 1 | no | — |
| 275 | #41 | — | 632 | 1 | no | — |
| 276 | #41 | — | 158 | 1 | no | — |
| 277 | C2×Q8 | — | 316 | 1 | no | — |
| 278 | C2×Q8 | — | 316 | 1 | no | — |
| 279 | C2×Q8 | — | 316 | 1 | no | — |
| 280 | C2×Q8 | — | 158 | 1 | no | — |
| 281 | C2×Q8 | — | 158 | 1 | no | — |
| 282 | C2×Q8 | D4×D79 | 1 | 1 | yes | characteristic |
| 283 | C2×D4 | — | 4 | 1 | no | — |
| 284 | C2×D4 | — | 4 | 1 | no | — |
| 285 | C2×D4 | — | 316 | 1 | no | — |
| 286 | C2×D4 | — | 632 | 1 | no | — |
| 287 | C2×D4 | — | 158 | 1 | no | — |
| 288 | C2×D4 | — | 158 | 1 | no | — |
| 289 | C2×D4 | C2×D316 | 1 | 1 | yes | characteristic |
| 290 | Q16 | — | 4 | 1 | no | — |
| 291 | Q16 | — | 316 | 1 | no | — |
| 292 | Q16 | — | 316 | 1 | no | — |
| 293 | Q16 | — | 316 | 1 | no | — |
| 294 | Q16 | — | 316 | 1 | no | — |
| 295 | Q16 | — | 158 | 1 | no | — |
| 296 | SD16 | — | 4 | 1 | no | — |
| 297 | SD16 | — | 316 | 1 | no | — |
| 298 | SD16 | — | 316 | 1 | no | — |
| 299 | SD16 | — | 316 | 1 | no | — |
| 300 | SD16 | — | 316 | 1 | no | — |
| 301 | SD16 | — | 316 | 1 | no | — |
| 302 | SD16 | — | 632 | 1 | no | — |
| 303 | SD16 | — | 158 | 1 | no | — |
| 304 | SD16 | — | 158 | 1 | no | — |
| 305 | D8 | — | 316 | 1 | no | — |
| 306 | D8 | — | 632 | 1 | no | — |
| 307 | D8 | — | 158 | 1 | no | — |
| 308 | M16 | — | 2 | 1 | no | — |
| 309 | M16 | — | 4 | 1 | no | — |
| 310 | M16 | — | 316 | 1 | no | — |
| 311 | M16 | — | 316 | 1 | no | — |
| 312 | M16 | — | 158 | 1 | no | — |
| 313 | C2×C8 | — | 4 | 1 | no | — |
| 314 | C2×C8 | — | 316 | 1 | no | — |
| 315 | C2×C8 | — | 316 | 1 | no | — |
| 316 | C2×C8 | — | 158 | 1 | no | — |
| 317 | C4⋊C4 | — | 316 | 1 | no | — |
| 318 | C22⋊C4 | — | 4 | 1 | no | — |
| 319 | C22⋊C4 | — | 316 | 1 | no | — |
| 320 | C22⋊C4 | — | 316 | 1 | no | — |
| 321 | C22⋊C4 | — | 316 | 1 | no | — |
| 322 | C22⋊C4 | — | 316 | 1 | no | — |
| 323 | C22⋊C4 | — | 632 | 1 | no | — |
| 324 | C22⋊C4 | — | 158 | 1 | no | — |
| 325 | C42 | — | 158 | 1 | no | — |
| 326 | C42 | D4×D79 | 1 | 1 | yes | characteristic |
| 327 | C23 | — | 2 | 1 | no | — |
| 328 | C23 | — | 4 | 1 | no | — |
| 329 | C23 | — | 316 | 1 | no | — |
| 330 | C23 | — | 632 | 1 | no | — |
| 331 | C23 | — | 1264 | 1 | no | — |
| 332 | Q8 | — | 2 | 1 | no | — |
| 333 | Q8 | — | 4 | 1 | no | — |
| 334 | Q8 | — | 316 | 1 | no | — |
| 335 | Q8 | — | 316 | 1 | no | — |
| 336 | Q8 | — | 316 | 1 | no | — |
| 337 | Q8 | — | 632 | 1 | no | — |
| 338 | Q8 | — | 632 | 1 | no | — |
| 339 | Q8 | — | 158 | 1 | no | — |
| 340 | D4 | — | 2 | 1 | no | — |
| 341 | D4 | — | 4 | 1 | no | — |
| 342 | D4 | — | 4 | 1 | no | — |
| 343 | D4 | — | 8 | 1 | no | — |
| 344 | D4 | — | 316 | 1 | no | — |
| 345 | D4 | — | 316 | 1 | no | — |
| 346 | D4 | — | 632 | 1 | no | — |
| 347 | D4 | — | 632 | 1 | no | — |
| 348 | D4 | — | 632 | 1 | no | — |
| 349 | D4 | — | 158 | 1 | no | — |
| 350 | D4 | — | 1264 | 1 | no | — |
| 351 | D4 | — | 1264 | 2 | no | — |
| 352 | C2×C4 | — | 2 | 1 | no | — |
| 353 | C2×C4 | — | 2 | 1 | no | — |
| 354 | C2×C4 | — | 4 | 1 | no | — |
| 355 | C2×C4 | — | 4 | 1 | no | — |
| 356 | C2×C4 | — | 316 | 1 | no | — |
| 357 | C2×C4 | — | 316 | 1 | no | — |
| 358 | C2×C4 | — | 316 | 1 | no | — |
| 359 | C2×C4 | — | 632 | 1 | no | — |
| 360 | C2×C4 | — | 632 | 1 | no | — |
| 361 | C2×C4 | — | 632 | 1 | no | — |
| 362 | C2×C4 | — | 632 | 1 | no | — |
| 363 | C2×C4 | #14579131 | 1 | 1 | yes | characteristic |
| 364 | C8 | — | 4 | 1 | no | — |
| 365 | C8 | — | 8 | 1 | no | — |
| 366 | C8 | — | 8 | 1 | no | — |
| 367 | C8 | — | 316 | 1 | no | — |
| 368 | C8 | — | 158 | 1 | no | — |
| 369 | C8 | — | 158 | 1 | no | — |
| 370 | C22 | — | 4 | 1 | no | — |
| 371 | C22 | — | 4 | 1 | no | — |
| 372 | C22 | — | 8 | 1 | no | — |
| 373 | C22 | — | 16 | 1 | no | — |
| 374 | C22 | — | 316 | 1 | no | — |
| 375 | C22 | — | 632 | 1 | no | — |
| 376 | C22 | — | 632 | 1 | no | — |
| 377 | C22 | — | 632 | 2 | no | — |
| 378 | C22 | — | 632 | 1 | no | — |
| 379 | C22 | — | 1264 | 1 | no | — |
| 380 | C22 | #19098751 | 1 | 1 | yes | characteristic |
| 381 | C4 | — | 2 | 1 | no | — |
| 382 | C4 | — | 4 | 1 | no | — |
| 383 | C4 | — | 4 | 1 | no | — |
| 384 | C4 | — | 4 | 1 | no | — |
| 385 | C4 | — | 316 | 1 | no | — |
| 386 | C4 | — | 632 | 1 | no | — |
| 387 | C4 | — | 632 | 1 | no | — |
| 388 | C4 | — | 1264 | 1 | no | — |
| 389 | C2 | — | 2 | 1 | no | — |
| 390 | C2 | — | 8 | 1 | no | — |
| 391 | C2 | — | 8 | 1 | no | — |
| 392 | C2 | — | 632 | 1 | no | — |
| 393 | C2 | — | 1264 | 1 | no | — |
| 394 | C2 | #23765385 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23775178 | C2 | semidirect |
| 2. #23765418 | C2 | semidirect |
| 3. #23765400 | C2 | semidirect |
| 4. #23762707 | C2 | semidirect |
| 5. #23761561 | C2 | semidirect |
| 6. #23761552 | C2 | semidirect |
| 7. C79×#1403 | C2 | semidirect |
| 27. #14579209 | D4 | semidirect |
| 46. #14579161 | D4 | semidirect |
| 58. #14579080 | D4 | semidirect |
| 62. #14579072 | D4 | semidirect |
| 204. #1403 | D79 | semidirect |
| 205. C79 | #13678 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775178 | 2 |
| #23765418 | 2 |
| #23765400 | 2 |
| #23762707 | 2 |
| #23761561 | 2 |
| #23761552 | 2 |
| C79×#1403 | 2 |
| #13678 | 79 |