Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
768 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 85 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 | #14574386 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #14572889 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #14563546 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14561996 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C19×#1293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C22×#64541 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#10597354 | — | 2 | 2 | no | — |
| 8 | C2×#10597376 | C22 | 1 | 2 | yes | — |
| 9 | #11926858 | — | 2 | 2 | no | — |
| 10 | #11926780 | — | 2 | 2 | no | — |
| 11 | #11926691 | — | 2 | 4 | no | — |
| 12 | #11926685 | — | 2 | 2 | no | — |
| 13 | #11926680 | — | 2 | 2 | no | — |
| 14 | #11926680 | — | 2 | 2 | no | — |
| 15 | #11926546 | — | 2 | 2 | no | — |
| 16 | C2×C22⋊(C19⋊C8) | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×(C2×D19)⋊C8 | — | 2 | 2 | no | — |
| 18 | #11926267 | — | 2 | 4 | no | — |
| 19 | C19×#407 | C22 | 1 | 2 | yes | — |
| 20 | C2×C19×C22⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C23×C4×C19 | C23 | 1 | 1 | yes | characteristic |
| 22 | C22×C22⋊D19 | — | 2 | 1 | no | — |
| 23 | C22×C22⋊D19 | — | 2 | 2 | no | — |
| 24 | C2×#64541 | — | 2 | 2 | no | — |
| 25 | C2×#64541 | — | 2 | 2 | no | — |
| 26 | C2×#64541 | — | 4 | 4 | no | — |
| 27 | C22×D76 | D4 | 1 | 2 | yes | — |
| 28 | C22×D76 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×C4×D19 | — | 2 | 1 | no | — |
| 30 | C22×Dic38 | D4 | 1 | 1 | yes | characteristic |
| 31 | C2×M16×C19 | — | 2 | 2 | no | — |
| 32 | C22×C8×C19 | D4 | 1 | 2 | yes | — |
| 33 | #10597376 | — | 2 | 2 | no | — |
| 34 | #10597376 | — | 2 | 2 | no | — |
| 35 | #10597376 | — | 2 | 2 | no | — |
| 36 | #10597376 | — | 2 | 2 | no | — |
| 37 | C2×(C2×D19)⋊C4 | — | 2 | 2 | no | — |
| 38 | C2×C4⋊Dic19 | D4 | 1 | 2 | yes | — |
| 39 | C22×C19⋊C8 | — | 2 | 1 | no | — |
| 40 | #10597354 | — | 4 | 8 | no | — |
| 41 | C2×D152 | — | 2 | 4 | no | — |
| 42 | C2×D152 | — | 2 | 2 | no | — |
| 43 | C2×#64516 | — | 2 | 4 | no | — |
| 44 | C19×C22⋊C8 | — | 2 | 2 | no | — |
| 45 | C19×C22⋊C8 | — | 2 | 2 | no | — |
| 46 | C19×C22⋊C8 | D4 | 1 | 4 | yes | — |
| 47 | C22⋊(C19⋊C8) | — | 2 | 2 | no | — |
| 48 | #10597278 | — | 2 | 4 | no | — |
| 49 | #10597278 | — | 2 | 4 | no | — |
| 50 | (C2×D19)⋊C8 | — | 4 | 4 | no | — |
| 51 | #10597275 | — | 2 | 2 | no | — |
| 52 | #10597273 | — | 2 | 4 | no | — |
| 53 | C24×C19 | #41 | 1 | 1 | yes | characteristic |
| 54 | C23×D19 | — | 2 | 1 | no | — |
| 55 | C23×D19 | — | 2 | 2 | no | — |
| 56 | C22×C4×C19 | — | 4 | 2 | no | — |
| 57 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 59 | C22×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 60 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 61 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 62 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 63 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 64 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 65 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 66 | C2×C22⋊D19 | — | 8 | 4 | no | — |
| 67 | C22×Dic19 | — | 2 | 1 | no | — |
| 68 | C22×Dic19 | — | 2 | 2 | no | — |
| 69 | #64541 | — | 2 | 8 | no | — |
| 70 | #64541 | — | 4 | 4 | no | — |
| 71 | #64541 | — | 4 | 4 | no | — |
| 72 | #64541 | — | 4 | 4 | no | — |
| 73 | C2×D76 | — | 2 | 2 | no | — |
| 74 | C2×D76 | — | 2 | 2 | no | — |
| 75 | C2×D76 | — | 2 | 2 | no | — |
| 76 | C2×D76 | — | 4 | 2 | no | — |
| 77 | C2×D76 | — | 4 | 4 | no | — |
| 78 | C2×C4×D19 | — | 2 | 4 | no | — |
| 79 | C2×C4×D19 | — | 4 | 2 | no | — |
| 80 | C2×C4×D19 | — | 4 | 1 | no | — |
| 81 | C2×C4×D19 | — | 4 | 1 | no | — |
| 82 | C2×Dic38 | — | 2 | 2 | no | — |
| 83 | C2×Dic38 | — | 4 | 2 | no | — |
| 84 | M16×C19 | — | 4 | 4 | no | — |
| 85 | C2×C8×C19 | — | 2 | 2 | no | — |
| 86 | C2×C8×C19 | — | 2 | 4 | no | — |
| 87 | C2×C8×C19 | — | 4 | 2 | no | — |
| 88 | (C2×D19)⋊C4 | — | 4 | 2 | no | — |
| 89 | (C2×D19)⋊C4 | — | 4 | 2 | no | — |
| 90 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 91 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 92 | C2×C19⋊C8 | — | 4 | 2 | no | — |
| 93 | C2×C19⋊C8 | — | 4 | 1 | no | — |
| 94 | D152 | — | 4 | 8 | no | — |
| 95 | D152 | — | 8 | 2 | no | — |
| 96 | #64516 | — | 4 | 8 | no | — |
| 97 | #9974 | — | 19 | 1 | no | maximal, Sylow |
| 98 | C23×C19 | — | 2 | 2 | no | — |
| 99 | C23×C19 | — | 4 | 1 | no | — |
| 100 | C23×C19 | — | 4 | 1 | no | — |
| 101 | C23×C19 | #121 | 1 | 2 | yes | — |
| 102 | C23×C19 | #121 | 1 | 1 | yes | characteristic |
| 103 | C22×D19 | — | 2 | 2 | no | — |
| 104 | C22×D19 | — | 4 | 1 | no | — |
| 105 | C22×D19 | — | 4 | 2 | no | — |
| 106 | C22×D19 | — | 4 | 1 | no | — |
| 107 | C22×D19 | — | 4 | 2 | no | — |
| 108 | C22×D19 | — | 4 | 2 | no | — |
| 109 | C22×D19 | — | 4 | 4 | no | — |
| 110 | C22×D19 | — | 8 | 2 | no | — |
| 111 | C22×D19 | — | 8 | 2 | no | — |
| 112 | C2×C4×C19 | — | 2 | 2 | no | — |
| 113 | C2×C4×C19 | — | 2 | 4 | no | — |
| 114 | C2×C4×C19 | — | 4 | 1 | no | — |
| 115 | C2×C4×C19 | — | 4 | 2 | no | — |
| 116 | C2×C4×C19 | #120 | 1 | 2 | yes | — |
| 117 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C19 | #127 | 1 | 1 | yes | characteristic |
| 119 | C22⋊D19 | — | 4 | 8 | no | — |
| 120 | C22⋊D19 | — | 8 | 4 | no | — |
| 121 | C22⋊D19 | — | 8 | 4 | no | — |
| 122 | C2×Dic19 | — | 2 | 2 | no | — |
| 123 | C2×Dic19 | — | 4 | 1 | no | — |
| 124 | C2×Dic19 | — | 4 | 1 | no | — |
| 125 | C2×Dic19 | — | 4 | 2 | no | — |
| 126 | C2×Dic19 | — | 8 | 2 | no | — |
| 127 | D76 | — | 2 | 4 | no | — |
| 128 | D76 | — | 4 | 2 | no | — |
| 129 | D76 | — | 4 | 4 | no | — |
| 130 | D76 | — | 4 | 4 | no | — |
| 131 | C4×D19 | — | 4 | 4 | no | — |
| 132 | C4×D19 | — | 4 | 4 | no | — |
| 133 | Dic38 | — | 2 | 4 | no | — |
| 134 | Dic38 | — | 4 | 2 | no | — |
| 135 | C8×C19 | — | 4 | 4 | no | — |
| 136 | C8×C19 | — | 4 | 2 | no | — |
| 137 | C19⋊C8 | — | 8 | 1 | no | — |
| 138 | #3186 | — | 19 | 1 | no | — |
| 139 | #3006 | — | 19 | 2 | no | — |
| 140 | #1780 | — | 19 | 1 | no | — |
| 141 | #1471 | — | 19 | 2 | no | — |
| 142 | #1293 | D19 | 1 | 1 | yes | characteristic, complemented |
| 143 | C22×C19 | — | 2 | 1 | no | — |
| 144 | C22×C19 | — | 2 | 1 | no | — |
| 145 | C22×C19 | — | 2 | 2 | no | — |
| 146 | C22×C19 | — | 2 | 2 | no | — |
| 147 | C22×C19 | — | 2 | 2 | no | — |
| 148 | C22×C19 | — | 8 | 2 | no | — |
| 149 | C22×C19 | #392 | 1 | 1 | yes | characteristic |
| 150 | C22×C19 | #472 | 1 | 2 | yes | — |
| 151 | C2×D19 | — | 4 | 4 | no | — |
| 152 | C2×D19 | — | 4 | 2 | no | — |
| 153 | C2×D19 | — | 8 | 2 | no | — |
| 154 | C2×D19 | — | 8 | 1 | no | — |
| 155 | C2×D19 | — | 8 | 1 | no | — |
| 156 | C2×D19 | — | 8 | 2 | no | — |
| 157 | C2×D19 | — | 8 | 2 | no | — |
| 158 | C2×D19 | — | 8 | 2 | no | — |
| 159 | C2×D19 | — | 16 | 4 | no | — |
| 160 | C4×C19 | — | 2 | 1 | no | — |
| 161 | C4×C19 | — | 2 | 2 | no | — |
| 162 | C4×C19 | B(4,𝔽2) | 1 | 2 | yes | — |
| 163 | Dic19 | — | 4 | 2 | no | — |
| 164 | Dic19 | — | 8 | 2 | no | — |
| 165 | C22×#41 | — | 19 | 1 | no | — |
| 166 | C2×AGL(1,ℤ/8) | — | 38 | 2 | no | — |
| 167 | C2×#121 | — | 19 | 2 | no | — |
| 168 | #480 | — | 38 | 2 | no | — |
| 169 | #466 | — | 38 | 2 | no | — |
| 170 | #449 | — | 38 | 4 | no | — |
| 171 | #448 | — | 38 | 2 | no | — |
| 172 | #447 | — | 38 | 2 | no | — |
| 173 | #447 | — | 38 | 2 | no | — |
| 174 | #417 | — | 38 | 2 | no | — |
| 175 | #407 | C2×D19 | 1 | 2 | yes | — |
| 176 | C2×C22⋊C8 | — | 19 | 1 | no | — |
| 177 | C2×C22⋊C8 | — | 38 | 2 | no | — |
| 178 | C2×C22⋊C8 | C2×D19 | 1 | 1 | yes | characteristic |
| 179 | #323 | — | 38 | 4 | no | — |
| 180 | C2×C19 | — | 2 | 2 | no | — |
| 181 | C2×C19 | — | 4 | 2 | no | — |
| 182 | C2×C19 | #2017 | 1 | 1 | yes | characteristic |
| 183 | C2×C19 | #2018 | 1 | 1 | yes | characteristic |
| 184 | C2×C19 | #2021 | 1 | 1 | yes | characteristic |
| 185 | D19 | — | 8 | 2 | no | — |
| 186 | D19 | — | 16 | 2 | no | — |
| 187 | C2×#41 | — | 38 | 2 | no | — |
| 188 | C2×#41 | — | 38 | 2 | no | — |
| 189 | C2×#41 | — | 76 | 4 | no | — |
| 190 | C22×Q8 | — | 19 | 1 | no | — |
| 191 | C22×D4 | — | 19 | 2 | no | — |
| 192 | C22×D4 | — | 19 | 1 | no | — |
| 193 | C22×D4 | — | 38 | 1 | no | — |
| 194 | C22×D4 | — | 38 | 2 | no | — |
| 195 | C23×C4 | — | 38 | 1 | no | — |
| 196 | C23×C4 | C22×D19 | 1 | 1 | yes | characteristic |
| 197 | AGL(1,ℤ/8) | — | 76 | 8 | no | — |
| 198 | C2×SD16 | — | 38 | 4 | no | — |
| 199 | C2×D8 | — | 38 | 4 | no | — |
| 200 | C2×D8 | — | 38 | 2 | no | — |
| 201 | C2×M16 | — | 2 | 2 | no | — |
| 202 | C22×C8 | — | 38 | 1 | no | — |
| 203 | C22×C8 | D76 | 1 | 2 | yes | — |
| 204 | #121 | — | 38 | 2 | no | — |
| 205 | #121 | — | 38 | 2 | no | — |
| 206 | #121 | — | 38 | 2 | no | — |
| 207 | #121 | — | 38 | 2 | no | — |
| 208 | C2×C4⋊C4 | — | 19 | 2 | no | — |
| 209 | C2×C22⋊C4 | — | 38 | 2 | no | — |
| 210 | #107 | — | 38 | 2 | no | — |
| 211 | #103 | — | 38 | 4 | no | — |
| 212 | #102 | — | 38 | 4 | no | — |
| 213 | #102 | — | 38 | 4 | no | — |
| 214 | C22⋊C8 | — | 2 | 2 | no | — |
| 215 | C22⋊C8 | — | 2 | 2 | no | — |
| 216 | C22⋊C8 | — | 38 | 2 | no | — |
| 217 | C22⋊C8 | — | 76 | 4 | no | — |
| 218 | C22⋊C8 | D76 | 1 | 4 | yes | — |
| 219 | C19 | #9974 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 220 | C24 | — | 38 | 1 | no | — |
| 221 | C24 | — | 38 | 2 | no | — |
| 222 | C24 | #64545 | 1 | 1 | yes | characteristic |
| 223 | #41 | — | 38 | 8 | no | — |
| 224 | #41 | — | 76 | 4 | no | — |
| 225 | #41 | — | 76 | 4 | no | — |
| 226 | #41 | — | 76 | 4 | no | — |
| 227 | C2×Q8 | — | 38 | 2 | no | — |
| 228 | C2×Q8 | — | 76 | 2 | no | — |
| 229 | C2×D4 | — | 38 | 2 | no | — |
| 230 | C2×D4 | — | 38 | 2 | no | — |
| 231 | C2×D4 | — | 38 | 2 | no | — |
| 232 | C2×D4 | — | 76 | 4 | no | — |
| 233 | C2×D4 | — | 76 | 2 | no | — |
| 234 | C2×D4 | — | 76 | 2 | no | — |
| 235 | C2×D4 | — | 76 | 2 | no | — |
| 236 | C2×D4 | — | 76 | 2 | no | — |
| 237 | C2×D4 | — | 76 | 2 | no | — |
| 238 | C2×D4 | — | 76 | 2 | no | — |
| 239 | C2×D4 | — | 152 | 4 | no | — |
| 240 | C22×C4 | — | 4 | 2 | no | — |
| 241 | C22×C4 | — | 38 | 4 | no | — |
| 242 | C22×C4 | — | 38 | 1 | no | — |
| 243 | C22×C4 | — | 38 | 2 | no | — |
| 244 | C22×C4 | — | 76 | 2 | no | — |
| 245 | C22×C4 | — | 76 | 1 | no | — |
| 246 | C22×C4 | — | 76 | 1 | no | — |
| 247 | C22×C4 | C2×D76 | 1 | 1 | yes | characteristic |
| 248 | C22×C4 | C2×D76 | 1 | 2 | yes | — |
| 249 | C22×C4 | D4×D19 | 1 | 2 | yes | — |
| 250 | C22×C4 | D4×D19 | 1 | 1 | yes | characteristic |
| 251 | SD16 | — | 76 | 8 | no | — |
| 252 | D8 | — | 76 | 8 | no | — |
| 253 | D8 | — | 152 | 2 | no | — |
| 254 | M16 | — | 4 | 4 | no | — |
| 255 | C2×C8 | — | 2 | 2 | no | — |
| 256 | C2×C8 | — | 2 | 4 | no | — |
| 257 | C2×C8 | — | 4 | 2 | no | — |
| 258 | C2×C8 | — | 76 | 2 | no | — |
| 259 | C2×C8 | — | 76 | 1 | no | — |
| 260 | C4⋊C4 | — | 38 | 2 | no | — |
| 261 | C4⋊C4 | — | 38 | 2 | no | — |
| 262 | C22⋊C4 | — | 76 | 2 | no | — |
| 263 | C22⋊C4 | — | 76 | 2 | no | — |
| 264 | C23 | — | 2 | 2 | no | — |
| 265 | C23 | — | 4 | 1 | no | — |
| 266 | C23 | — | 4 | 1 | no | — |
| 267 | C23 | — | 38 | 2 | no | — |
| 268 | C23 | — | 76 | 4 | no | — |
| 269 | C23 | — | 76 | 1 | no | — |
| 270 | C23 | — | 76 | 2 | no | — |
| 271 | C23 | — | 76 | 2 | no | — |
| 272 | C23 | — | 76 | 1 | no | — |
| 273 | C23 | — | 76 | 2 | no | — |
| 274 | C23 | — | 152 | 2 | no | — |
| 275 | C23 | — | 152 | 2 | no | — |
| 276 | C23 | #10597341 | 1 | 2 | yes | — |
| 277 | C23 | #10597341 | 1 | 1 | yes | characteristic |
| 278 | Q8 | — | 38 | 4 | no | — |
| 279 | Q8 | — | 76 | 2 | no | — |
| 280 | D4 | — | 38 | 4 | no | — |
| 281 | D4 | — | 76 | 2 | no | — |
| 282 | D4 | — | 76 | 4 | no | — |
| 283 | D4 | — | 76 | 8 | no | — |
| 284 | D4 | — | 76 | 4 | no | — |
| 285 | D4 | — | 152 | 4 | no | — |
| 286 | D4 | — | 152 | 4 | no | — |
| 287 | C2×C4 | — | 2 | 2 | no | — |
| 288 | C2×C4 | — | 2 | 4 | no | — |
| 289 | C2×C4 | — | 4 | 2 | no | — |
| 290 | C2×C4 | — | 4 | 1 | no | — |
| 291 | C2×C4 | — | 38 | 2 | no | — |
| 292 | C2×C4 | — | 76 | 4 | no | — |
| 293 | C2×C4 | — | 76 | 1 | no | — |
| 294 | C2×C4 | — | 76 | 1 | no | — |
| 295 | C2×C4 | — | 76 | 4 | no | — |
| 296 | C2×C4 | — | 76 | 2 | no | — |
| 297 | C2×C4 | — | 152 | 2 | no | — |
| 298 | C2×C4 | #10597320 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | #10597328 | 1 | 2 | yes | — |
| 300 | C2×C4 | #10597328 | 1 | 1 | yes | characteristic |
| 301 | C8 | — | 4 | 4 | no | — |
| 302 | C8 | — | 4 | 2 | no | — |
| 303 | C8 | — | 152 | 1 | no | — |
| 304 | C22 | — | 2 | 1 | no | — |
| 305 | C22 | — | 2 | 1 | no | — |
| 306 | C22 | — | 2 | 2 | no | — |
| 307 | C22 | — | 2 | 2 | no | — |
| 308 | C22 | — | 2 | 2 | no | — |
| 309 | C22 | — | 8 | 2 | no | — |
| 310 | C22 | — | 304 | 4 | no | — |
| 311 | C22 | — | 76 | 4 | no | — |
| 312 | C22 | — | 76 | 2 | no | — |
| 313 | C22 | — | 152 | 2 | no | — |
| 314 | C22 | — | 152 | 2 | no | — |
| 315 | C22 | — | 152 | 2 | no | — |
| 316 | C22 | — | 152 | 2 | no | — |
| 317 | C22 | — | 152 | 1 | no | — |
| 318 | C22 | — | 152 | 1 | no | — |
| 319 | C22 | #11926454 | 1 | 1 | yes | characteristic |
| 320 | C22 | #11926815 | 1 | 2 | yes | — |
| 321 | C4 | — | 2 | 2 | no | — |
| 322 | C4 | — | 2 | 1 | no | — |
| 323 | C4 | — | 76 | 2 | no | — |
| 324 | C4 | — | 152 | 2 | no | — |
| 325 | C4 | #11926732 | 1 | 2 | yes | — |
| 326 | C2 | — | 2 | 2 | no | — |
| 327 | C2 | — | 4 | 2 | no | — |
| 328 | C2 | — | 304 | 2 | no | — |
| 329 | C2 | — | 152 | 2 | no | — |
| 330 | C2 | #14564740 | 1 | 1 | yes | characteristic |
| 331 | C2 | #14564745 | 1 | 1 | yes | characteristic |
| 332 | C2 | #14564762 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14574386 | C2 | semidirect |
| 2. #14572889 | C2 | semidirect |
| 3. #14563546 | C2 | semidirect |
| 4. #14561996 | C2 | semidirect |
| 5. C19×#1293 | C2 | semidirect |
| 142. #1293 | D19 | semidirect |
| 219. C19 | #9974 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14574386 | 2 |
| #14572889 | 2 |
| #14563546 | 2 |
| #14561996 | 2 |
| C19×#1293 | 2 |
| #9974 | 19 |