Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
726 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 63 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 | #23764441 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #23762334 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #23761403 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #23761332 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C79×#2679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×#14579187 | — | 2 | 1 | no | — |
| 7 | #19099144 | C22 | 1 | 1 | yes | characteristic, complemented |
| 8 | #19098697 | — | 2 | 2 | no | — |
| 9 | C2×#14579089 | — | 2 | 1 | no | — |
| 10 | #19098332 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #19098296 | — | 2 | 2 | no | — |
| 12 | #19098289 | C22 | 1 | 2 | yes | complemented |
| 13 | C2×#120×C79 | — | 2 | 2 | no | — |
| 14 | C2×#120×C79 | — | 2 | 1 | no | — |
| 15 | #394×C79 | — | 2 | 2 | no | — |
| 16 | #394×C79 | C22 | 1 | 2 | yes | — |
| 17 | #390×C79 | — | 2 | 1 | no | — |
| 18 | #390×C79 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#11929624 | — | 2 | 1 | no | — |
| 20 | #14579187 | — | 4 | 2 | no | — |
| 21 | #14579187 | — | 4 | 2 | no | — |
| 22 | C2×#11929612 | — | 4 | 1 | no | — |
| 23 | C2×#11929609 | — | 4 | 1 | no | — |
| 24 | C2×#11929609 | — | 4 | 2 | no | — |
| 25 | C2×#11929608 | — | 2 | 1 | no | — |
| 26 | #14579141 | — | 4 | 1 | no | — |
| 27 | #14579136 | — | 4 | 1 | no | — |
| 28 | #14579135 | — | 2 | 2 | no | — |
| 29 | #14579089 | — | 4 | 2 | no | — |
| 30 | #14579082 | — | 4 | 2 | no | — |
| 31 | C22⋊(C79⋊C8) | — | 2 | 2 | no | — |
| 32 | C25×C79 | — | 2 | 1 | no | — |
| 33 | C22×D4×C79 | — | 2 | 1 | no | — |
| 34 | C22×D4×C79 | — | 2 | 2 | no | — |
| 35 | C22×D4×C79 | D4 | 1 | 1 | yes | characteristic |
| 36 | C22×D4×C79 | D4 | 1 | 2 | yes | — |
| 37 | #120×C79 | — | 4 | 8 | no | — |
| 38 | #120×C79 | — | 4 | 2 | no | — |
| 39 | #120×C79 | — | 4 | 2 | no | — |
| 40 | C2×C4⋊C4×C79 | — | 2 | 1 | no | — |
| 41 | C2×C4⋊C4×C79 | C23 | 1 | 1 | yes | characteristic |
| 42 | C2×C22⋊C4×C79 | — | 2 | 2 | no | — |
| 43 | C2×C22⋊C4×C79 | — | 2 | 1 | no | — |
| 44 | C2×C22⋊C4×C79 | — | 2 | 2 | no | — |
| 45 | C2×C22⋊C4×C79 | — | 2 | 2 | no | — |
| 46 | C2×C22⋊C4×C79 | — | 2 | 2 | no | — |
| 47 | C2×C42×C79 | D4 | 1 | 1 | yes | characteristic |
| 48 | #95×C79 | D4 | 1 | 2 | yes | — |
| 49 | #11929624 | — | 4 | 1 | no | — |
| 50 | #11929624 | — | 4 | 1 | no | — |
| 51 | #11929624 | — | 4 | 1 | no | — |
| 52 | #11929624 | — | 4 | 1 | no | — |
| 53 | C2×Dic158 | — | 2 | 1 | no | — |
| 54 | C2×D316 | — | 2 | 1 | no | — |
| 55 | C2×D316 | — | 2 | 2 | no | — |
| 56 | C2×C22⋊D79 | — | 4 | 1 | no | — |
| 57 | C2×C4×D79 | — | 4 | 1 | no | — |
| 58 | #11929612 | — | 4 | 4 | no | — |
| 59 | #11929609 | — | 4 | 4 | no | — |
| 60 | #11929609 | — | 8 | 4 | no | — |
| 61 | #11929608 | — | 2 | 2 | no | — |
| 62 | #11929608 | — | 4 | 1 | no | — |
| 63 | C2×C79⋊C8 | — | 4 | 1 | no | — |
| 64 | C2×C79⋊C8 | — | 4 | 2 | no | — |
| 65 | C4⋊Dic79 | — | 2 | 2 | no | — |
| 66 | (C2×D79)⋊C4 | — | 4 | 2 | no | — |
| 67 | C24×C79 | — | 2 | 2 | no | — |
| 68 | C24×C79 | — | 2 | 1 | no | — |
| 69 | C24×C79 | — | 4 | 4 | no | — |
| 70 | C24×C79 | — | 4 | 2 | no | — |
| 71 | C24×C79 | — | 8 | 2 | no | — |
| 72 | C24×C79 | — | 8 | 1 | no | — |
| 73 | C24×C79 | — | 8 | 1 | no | — |
| 74 | C2×D4×C79 | — | 2 | 4 | no | — |
| 75 | C2×D4×C79 | — | 2 | 1 | no | — |
| 76 | C2×D4×C79 | — | 4 | 2 | no | — |
| 77 | C2×D4×C79 | — | 4 | 1 | no | — |
| 78 | C2×D4×C79 | — | 4 | 1 | no | — |
| 79 | C2×D4×C79 | — | 4 | 4 | no | — |
| 80 | C2×D4×C79 | — | 4 | 4 | no | — |
| 81 | C2×D4×C79 | — | 4 | 4 | no | — |
| 82 | C2×D4×C79 | — | 8 | 1 | no | — |
| 83 | C2×D4×C79 | — | 8 | 1 | no | — |
| 84 | C2×D4×C79 | — | 8 | 2 | no | — |
| 85 | C2×D4×C79 | D8 | 1 | 2 | yes | complemented |
| 86 | C22×C4×C79 | — | 2 | 1 | no | — |
| 87 | C22×C4×C79 | — | 2 | 2 | no | — |
| 88 | C22×C4×C79 | C2×D4 | 1 | 1 | yes | characteristic |
| 89 | C22×C4×C79 | C2×D4 | 1 | 2 | yes | — |
| 90 | C4⋊C4×C79 | — | 4 | 1 | no | — |
| 91 | C4⋊C4×C79 | — | 8 | 1 | no | — |
| 92 | C22⋊C4×C79 | — | 4 | 4 | no | — |
| 93 | C22⋊C4×C79 | — | 4 | 4 | no | — |
| 94 | C22⋊C4×C79 | — | 4 | 4 | no | — |
| 95 | C22⋊C4×C79 | — | 4 | 2 | no | — |
| 96 | C22⋊C4×C79 | — | 4 | 2 | no | — |
| 97 | C22⋊C4×C79 | — | 4 | 2 | no | — |
| 98 | C42×C79 | — | 4 | 1 | no | — |
| 99 | C23×C79 | — | 2 | 4 | no | — |
| 100 | C23×C79 | — | 2 | 2 | no | — |
| 101 | C23×C79 | — | 4 | 2 | no | — |
| 102 | C23×C79 | — | 4 | 2 | no | — |
| 103 | C23×C79 | — | 4 | 2 | no | — |
| 104 | C23×C79 | — | 4 | 2 | no | — |
| 105 | C23×C79 | — | 4 | 2 | no | — |
| 106 | C23×C79 | — | 4 | 2 | no | — |
| 107 | C23×C79 | — | 4 | 1 | no | — |
| 108 | C23×C79 | — | 4 | 2 | no | — |
| 109 | C23×C79 | — | 4 | 1 | no | — |
| 110 | C23×C79 | — | 4 | 2 | no | — |
| 111 | C23×C79 | — | 8 | 8 | no | — |
| 112 | C23×C79 | — | 8 | 4 | no | — |
| 113 | C23×C79 | — | 8 | 8 | no | — |
| 114 | C23×C79 | — | 8 | 4 | no | — |
| 115 | C23×C79 | — | 8 | 4 | no | — |
| 116 | C23×C79 | #120 | 1 | 1 | yes | characteristic |
| 117 | C22×D79 | — | 4 | 1 | no | — |
| 118 | D4×C79 | — | 4 | 2 | no | — |
| 119 | D4×C79 | — | 4 | 4 | no | — |
| 120 | D4×C79 | — | 8 | 1 | no | — |
| 121 | D4×C79 | — | 8 | 4 | no | — |
| 122 | D4×C79 | — | 8 | 2 | no | — |
| 123 | D4×C79 | — | 8 | 8 | no | — |
| 124 | C2×C4×C79 | — | 2 | 1 | no | — |
| 125 | C2×C4×C79 | — | 2 | 1 | no | — |
| 126 | C2×C4×C79 | — | 2 | 2 | no | — |
| 127 | C2×C4×C79 | — | 2 | 2 | no | — |
| 128 | C2×C4×C79 | — | 4 | 1 | no | — |
| 129 | C2×C4×C79 | — | 4 | 1 | no | — |
| 130 | C2×C4×C79 | — | 4 | 2 | no | — |
| 131 | C2×C4×C79 | — | 4 | 2 | no | — |
| 132 | C2×C4×C79 | — | 4 | 2 | no | — |
| 133 | C2×C4×C79 | — | 4 | 2 | no | — |
| 134 | C2×C4×C79 | C2×D8 | 1 | 1 | yes | characteristic |
| 135 | C2×C4×C79 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 136 | C22⋊D79 | — | 8 | 1 | no | — |
| 137 | C22⋊D79 | — | 8 | 1 | no | — |
| 138 | C2×Dic79 | — | 4 | 1 | no | — |
| 139 | D316 | — | 4 | 1 | no | — |
| 140 | D316 | — | 4 | 1 | no | — |
| 141 | D316 | — | 8 | 2 | no | — |
| 142 | C4×D79 | — | 8 | 1 | no | — |
| 143 | C4×D79 | — | 8 | 1 | no | — |
| 144 | Dic158 | — | 4 | 1 | no | — |
| 145 | Dic158 | — | 4 | 1 | no | — |
| 146 | C79⋊C8 | — | 4 | 2 | no | — |
| 147 | C79⋊C8 | — | 8 | 2 | no | — |
| 148 | C22×C79 | — | 2 | 1 | no | — |
| 149 | C22×C79 | — | 2 | 1 | no | — |
| 150 | C22×C79 | — | 4 | 4 | no | — |
| 151 | C22×C79 | — | 4 | 4 | no | — |
| 152 | C22×C79 | — | 4 | 4 | no | — |
| 153 | C22×C79 | — | 4 | 2 | no | — |
| 154 | C22×C79 | — | 4 | 4 | no | — |
| 155 | C22×C79 | — | 8 | 2 | no | — |
| 156 | C22×C79 | — | 8 | 2 | no | — |
| 157 | C22×C79 | — | 8 | 2 | no | — |
| 158 | C22×C79 | — | 8 | 16 | no | — |
| 159 | C22×C79 | — | 8 | 2 | no | — |
| 160 | C22×C79 | — | 8 | 1 | no | — |
| 161 | C22×C79 | — | 8 | 1 | no | — |
| 162 | C22×C79 | — | 8 | 2 | no | — |
| 163 | C22×C79 | #447 | 1 | 1 | yes | characteristic |
| 164 | C22×C79 | #453 | 1 | 1 | yes | characteristic |
| 165 | C22×C79 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 166 | C2×D79 | — | 8 | 1 | no | — |
| 167 | C2×D79 | — | 8 | 1 | no | — |
| 168 | C2×D79 | — | 8 | 1 | no | — |
| 169 | C4×C79 | — | 2 | 1 | no | — |
| 170 | C4×C79 | — | 2 | 1 | no | — |
| 171 | C4×C79 | — | 4 | 2 | no | — |
| 172 | C4×C79 | — | 4 | 2 | no | — |
| 173 | C4×C79 | — | 8 | 2 | no | — |
| 174 | Dic79 | — | 8 | 1 | no | — |
| 175 | #12096 | — | 79 | 1 | no | maximal, Sylow |
| 176 | C2×C79 | — | 2 | 1 | no | — |
| 177 | C2×C79 | — | 2 | 1 | no | — |
| 178 | C2×C79 | — | 8 | 2 | no | — |
| 179 | C2×C79 | — | 8 | 4 | no | — |
| 180 | C2×C79 | #1595 | 1 | 1 | yes | characteristic |
| 181 | C2×C79 | #2196 | 1 | 1 | yes | characteristic |
| 182 | C2×C79 | #2202 | 1 | 1 | yes | characteristic |
| 183 | D79 | — | 16 | 1 | no | — |
| 184 | #2679 | D79 | 1 | 1 | yes | characteristic, complemented |
| 185 | #2006 | — | 79 | 1 | no | — |
| 186 | #1598 | — | 79 | 2 | no | — |
| 187 | #1345 | — | 79 | 2 | no | — |
| 188 | #1318 | — | 79 | 1 | no | — |
| 189 | C79 | #12096 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 190 | C2×AGL(1,ℤ/8) | — | 158 | 1 | no | — |
| 191 | #537 | — | 79 | 1 | no | — |
| 192 | C2×#120 | — | 2 | 2 | no | — |
| 193 | C2×#120 | — | 2 | 1 | no | — |
| 194 | #447 | — | 158 | 2 | no | — |
| 195 | C2×#104 | — | 158 | 1 | no | — |
| 196 | #394 | — | 2 | 2 | no | — |
| 197 | #394 | C2×D79 | 1 | 2 | yes | — |
| 198 | #390 | — | 2 | 1 | no | — |
| 199 | #390 | C2×D79 | 1 | 1 | yes | characteristic |
| 200 | #343 | — | 79 | 1 | no | — |
| 201 | #327 | — | 158 | 2 | no | — |
| 202 | #324 | — | 79 | 2 | no | — |
| 203 | C25 | — | 2 | 1 | no | — |
| 204 | C2×#41 | — | 158 | 1 | no | — |
| 205 | C22×D4 | — | 2 | 1 | no | — |
| 206 | C22×D4 | — | 2 | 2 | no | — |
| 207 | C22×D4 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 208 | C22×D4 | C22⋊D79 | 1 | 2 | yes | — |
| 209 | AGL(1,ℤ/8) | — | 316 | 2 | no | — |
| 210 | AGL(1,ℤ/8) | — | 316 | 2 | no | — |
| 211 | C2×SD16 | — | 316 | 1 | no | — |
| 212 | C2×D8 | — | 316 | 1 | no | — |
| 213 | C2×D8 | — | 316 | 2 | no | — |
| 214 | C2×M16 | — | 158 | 1 | no | — |
| 215 | C22⋊Q8 | — | 316 | 1 | no | — |
| 216 | #121 | — | 316 | 1 | no | — |
| 217 | #121 | — | 158 | 2 | no | — |
| 218 | #120 | — | 4 | 8 | no | — |
| 219 | #120 | — | 4 | 2 | no | — |
| 220 | #120 | — | 4 | 2 | no | — |
| 221 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 222 | C2×C4⋊C4 | C22×D79 | 1 | 1 | yes | characteristic |
| 223 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 224 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 225 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 226 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 227 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 228 | C2×C42 | C22⋊D79 | 1 | 1 | yes | characteristic |
| 229 | #104 | — | 316 | 2 | no | — |
| 230 | #102 | — | 316 | 2 | no | — |
| 231 | C22⋊C8 | — | 158 | 2 | no | — |
| 232 | #95 | C22⋊D79 | 1 | 2 | yes | — |
| 233 | C24 | — | 2 | 2 | no | — |
| 234 | C24 | — | 2 | 1 | no | — |
| 235 | C24 | — | 4 | 4 | no | — |
| 236 | C24 | — | 4 | 2 | no | — |
| 237 | C24 | — | 8 | 2 | no | — |
| 238 | C24 | — | 8 | 1 | no | — |
| 239 | C24 | — | 8 | 1 | no | — |
| 240 | #41 | — | 316 | 1 | no | — |
| 241 | #41 | — | 316 | 1 | no | — |
| 242 | #41 | — | 316 | 1 | no | — |
| 243 | #41 | — | 316 | 1 | no | — |
| 244 | C2×Q8 | — | 158 | 1 | no | — |
| 245 | C2×D4 | — | 2 | 4 | no | — |
| 246 | C2×D4 | — | 2 | 1 | no | — |
| 247 | C2×D4 | — | 4 | 2 | no | — |
| 248 | C2×D4 | — | 4 | 1 | no | — |
| 249 | C2×D4 | — | 4 | 1 | no | — |
| 250 | C2×D4 | — | 4 | 4 | no | — |
| 251 | C2×D4 | — | 4 | 4 | no | — |
| 252 | C2×D4 | — | 4 | 4 | no | — |
| 253 | C2×D4 | — | 8 | 1 | no | — |
| 254 | C2×D4 | — | 8 | 1 | no | — |
| 255 | C2×D4 | — | 8 | 2 | no | — |
| 256 | C2×D4 | — | 316 | 1 | no | — |
| 257 | C2×D4 | — | 158 | 1 | no | — |
| 258 | C2×D4 | — | 158 | 2 | no | — |
| 259 | C2×D4 | #11929609 | 1 | 2 | yes | complemented |
| 260 | C22×C4 | — | 2 | 1 | no | — |
| 261 | C22×C4 | — | 2 | 2 | no | — |
| 262 | C22×C4 | — | 316 | 1 | no | — |
| 263 | C22×C4 | C2×C22⋊D79 | 1 | 1 | yes | characteristic |
| 264 | C22×C4 | C2×C22⋊D79 | 1 | 2 | yes | — |
| 265 | SD16 | — | 316 | 4 | no | — |
| 266 | D8 | — | 316 | 4 | no | — |
| 267 | D8 | — | 632 | 4 | no | — |
| 268 | M16 | — | 316 | 1 | no | — |
| 269 | M16 | — | 158 | 2 | no | — |
| 270 | C2×C8 | — | 316 | 1 | no | — |
| 271 | C2×C8 | — | 316 | 2 | no | — |
| 272 | C4⋊C4 | — | 4 | 1 | no | — |
| 273 | C4⋊C4 | — | 8 | 1 | no | — |
| 274 | C4⋊C4 | — | 158 | 2 | no | — |
| 275 | C22⋊C4 | — | 4 | 4 | no | — |
| 276 | C22⋊C4 | — | 4 | 4 | no | — |
| 277 | C22⋊C4 | — | 4 | 4 | no | — |
| 278 | C22⋊C4 | — | 4 | 2 | no | — |
| 279 | C22⋊C4 | — | 4 | 2 | no | — |
| 280 | C22⋊C4 | — | 4 | 2 | no | — |
| 281 | C22⋊C4 | — | 316 | 2 | no | — |
| 282 | C42 | — | 4 | 1 | no | — |
| 283 | C23 | — | 2 | 4 | no | — |
| 284 | C23 | — | 2 | 2 | no | — |
| 285 | C23 | — | 4 | 2 | no | — |
| 286 | C23 | — | 4 | 2 | no | — |
| 287 | C23 | — | 4 | 2 | no | — |
| 288 | C23 | — | 4 | 2 | no | — |
| 289 | C23 | — | 4 | 2 | no | — |
| 290 | C23 | — | 4 | 2 | no | — |
| 291 | C23 | — | 4 | 1 | no | — |
| 292 | C23 | — | 4 | 2 | no | — |
| 293 | C23 | — | 4 | 2 | no | — |
| 294 | C23 | — | 4 | 1 | no | — |
| 295 | C23 | — | 8 | 8 | no | — |
| 296 | C23 | — | 8 | 4 | no | — |
| 297 | C23 | — | 8 | 8 | no | — |
| 298 | C23 | — | 8 | 4 | no | — |
| 299 | C23 | — | 8 | 4 | no | — |
| 300 | C23 | — | 316 | 1 | no | — |
| 301 | C23 | #14579130 | 1 | 1 | yes | characteristic |
| 302 | Q8 | — | 316 | 1 | no | — |
| 303 | Q8 | — | 316 | 1 | no | — |
| 304 | D4 | — | 4 | 2 | no | — |
| 305 | D4 | — | 4 | 4 | no | — |
| 306 | D4 | — | 8 | 1 | no | — |
| 307 | D4 | — | 8 | 4 | no | — |
| 308 | D4 | — | 8 | 2 | no | — |
| 309 | D4 | — | 8 | 8 | no | — |
| 310 | D4 | — | 316 | 1 | no | — |
| 311 | D4 | — | 316 | 1 | no | — |
| 312 | D4 | — | 632 | 2 | no | — |
| 313 | D4 | — | 632 | 1 | no | — |
| 314 | D4 | — | 632 | 1 | no | — |
| 315 | C2×C4 | — | 2 | 1 | no | — |
| 316 | C2×C4 | — | 2 | 1 | no | — |
| 317 | C2×C4 | — | 2 | 2 | no | — |
| 318 | C2×C4 | — | 2 | 2 | no | — |
| 319 | C2×C4 | — | 4 | 1 | no | — |
| 320 | C2×C4 | — | 4 | 1 | no | — |
| 321 | C2×C4 | — | 4 | 2 | no | — |
| 322 | C2×C4 | — | 4 | 2 | no | — |
| 323 | C2×C4 | — | 4 | 2 | no | — |
| 324 | C2×C4 | — | 4 | 2 | no | — |
| 325 | C2×C4 | — | 316 | 1 | no | — |
| 326 | C2×C4 | — | 632 | 1 | no | — |
| 327 | C2×C4 | — | 632 | 1 | no | — |
| 328 | C2×C4 | C2×#11929609 | 1 | 1 | yes | characteristic |
| 329 | C2×C4 | #14579187 | 1 | 1 | yes | characteristic |
| 330 | C8 | — | 316 | 2 | no | — |
| 331 | C8 | — | 632 | 2 | no | — |
| 332 | C22 | — | 2 | 1 | no | — |
| 333 | C22 | — | 2 | 1 | no | — |
| 334 | C22 | — | 4 | 4 | no | — |
| 335 | C22 | — | 4 | 4 | no | — |
| 336 | C22 | — | 4 | 4 | no | — |
| 337 | C22 | — | 4 | 4 | no | — |
| 338 | C22 | — | 4 | 2 | no | — |
| 339 | C22 | — | 8 | 2 | no | — |
| 340 | C22 | — | 8 | 2 | no | — |
| 341 | C22 | — | 8 | 2 | no | — |
| 342 | C22 | — | 8 | 16 | no | — |
| 343 | C22 | — | 8 | 1 | no | — |
| 344 | C22 | — | 8 | 2 | no | — |
| 345 | C22 | — | 8 | 2 | no | — |
| 346 | C22 | — | 8 | 1 | no | — |
| 347 | C22 | — | 632 | 1 | no | — |
| 348 | C22 | — | 632 | 1 | no | — |
| 349 | C22 | — | 632 | 1 | no | — |
| 350 | C22 | #19098697 | 1 | 1 | yes | characteristic |
| 351 | C22 | #19098731 | 1 | 1 | yes | characteristic |
| 352 | C22 | #19098750 | 1 | 1 | yes | characteristic |
| 353 | C4 | — | 2 | 1 | no | — |
| 354 | C4 | — | 2 | 1 | no | — |
| 355 | C4 | — | 4 | 2 | no | — |
| 356 | C4 | — | 4 | 2 | no | — |
| 357 | C4 | — | 8 | 2 | no | — |
| 358 | C4 | — | 632 | 1 | no | — |
| 359 | C2 | — | 2 | 1 | no | — |
| 360 | C2 | — | 2 | 1 | no | — |
| 361 | C2 | — | 8 | 4 | no | — |
| 362 | C2 | — | 8 | 2 | no | — |
| 363 | C2 | — | 1264 | 1 | no | — |
| 364 | C2 | #23762318 | 1 | 1 | yes | characteristic |
| 365 | C2 | #23765384 | 1 | 1 | yes | characteristic |
| 366 | C2 | #23765417 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23764441 | C2 | semidirect |
| 2. #23762334 | C2 | semidirect |
| 3. #23761403 | C2 | semidirect |
| 4. #23761332 | C2 | semidirect |
| 5. C79×#2679 | C2 | semidirect |
| 7. #19099144 | C22 | semidirect |
| 10. #19098332 | C22 | semidirect |
| 12. #19098289 | C22 | semidirect |
| 85. C2×D4×C79 | D8 | semidirect |
| 184. #2679 | D79 | semidirect |
| 189. C79 | #12096 | semidirect |
| 259. C2×D4 | #11929609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764441 | 2 |
| #23762334 | 2 |
| #23761403 | 2 |
| #23761332 | 2 |
| C79×#2679 | 2 |
| #12096 | 79 |