Finite Group DatabasebetaFinite Group DatabasebetaOrder 4864.
554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 554 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 | #14575023 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #14575016 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #14564611 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14564462 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C19×#1309 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11927101 | C22 | 1 | 1 | yes | characteristic |
| 7 | #11927094 | C22 | 1 | 2 | yes | — |
| 8 | #11926840 | — | 2 | 2 | no | — |
| 9 | #11926835 | — | 2 | 2 | no | — |
| 10 | #11926825 | — | 2 | 2 | no | — |
| 11 | #11926797 | — | 2 | 2 | no | — |
| 12 | #11926790 | — | 2 | 4 | no | — |
| 13 | #11926750 | — | 2 | 2 | no | — |
| 14 | #11926745 | — | 2 | 2 | no | — |
| 15 | #11926740 | — | 2 | 2 | no | — |
| 16 | C2×#10597282 | — | 2 | 4 | no | — |
| 17 | C42×Dic19 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11926305 | — | 2 | 2 | no | — |
| 19 | C19×#423 | C22 | 1 | 1 | yes | characteristic |
| 20 | C19×#423 | C22 | 1 | 2 | yes | — |
| 21 | C2×#64541 | — | 2 | 2 | no | — |
| 22 | C2×M16×C19 | D4 | 1 | 4 | yes | — |
| 23 | C2×M16×C19 | D4 | 1 | 2 | yes | — |
| 24 | C2×C42×C19 | C23 | 1 | 1 | yes | characteristic |
| 25 | #10597376 | — | 2 | 2 | no | — |
| 26 | #10597376 | — | 2 | 2 | no | — |
| 27 | #10597372 | — | 2 | 1 | no | — |
| 28 | #10597370 | — | 2 | 2 | no | — |
| 29 | C2×C4×Dic19 | — | 2 | 2 | no | — |
| 30 | C2×C4×Dic19 | — | 2 | 1 | no | — |
| 31 | C2×D152 | — | 2 | 2 | no | — |
| 32 | C2×#64516 | — | 2 | 4 | no | — |
| 33 | #10597321 | — | 2 | 2 | no | — |
| 34 | #10597320 | D4 | 1 | 2 | yes | — |
| 35 | C4×D76 | — | 2 | 2 | no | — |
| 36 | C4×D76 | — | 2 | 2 | no | — |
| 37 | #10597316 | — | 2 | 1 | no | — |
| 38 | #10597315 | D4 | 1 | 2 | yes | — |
| 39 | #10597315 | D4 | 1 | 2 | yes | — |
| 40 | C4×Dic38 | — | 2 | 2 | no | — |
| 41 | C19×C4⋊C8 | — | 2 | 2 | no | — |
| 42 | C19×C4⋊C8 | — | 2 | 2 | no | — |
| 43 | C19×C4⋊C8 | — | 2 | 2 | no | — |
| 44 | #10597282 | — | 4 | 8 | no | — |
| 45 | #10597278 | — | 2 | 4 | no | — |
| 46 | #10597278 | — | 2 | 4 | no | — |
| 47 | #10597275 | — | 2 | 4 | no | — |
| 48 | #10597274 | — | 2 | 2 | no | — |
| 49 | #10597273 | — | 2 | 4 | no | — |
| 50 | C22×C4×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 51 | C22×C4×C19 | C2×D4 | 1 | 2 | yes | — |
| 52 | C2×C22⋊D19 | — | 4 | 2 | no | — |
| 53 | C22×Dic19 | — | 4 | 1 | no | — |
| 54 | #64541 | — | 4 | 4 | no | — |
| 55 | #64541 | — | 4 | 4 | no | — |
| 56 | C2×D76 | — | 2 | 2 | no | — |
| 57 | C2×D76 | — | 2 | 2 | no | — |
| 58 | C2×D76 | — | 2 | 2 | no | — |
| 59 | C2×C4×D19 | — | 4 | 2 | no | — |
| 60 | C2×Dic38 | — | 2 | 2 | no | — |
| 61 | C2×Dic38 | — | 2 | 2 | no | — |
| 62 | M16×C19 | — | 4 | 2 | no | — |
| 63 | M16×C19 | — | 4 | 4 | no | — |
| 64 | C2×C8×C19 | — | 2 | 4 | no | — |
| 65 | C2×C8×C19 | — | 2 | 2 | no | — |
| 66 | C42×C19 | C2×D4 | 1 | 2 | yes | — |
| 67 | C42×C19 | C2×D4 | 1 | 1 | yes | characteristic |
| 68 | C42×C19 | #41 | 1 | 1 | yes | characteristic |
| 69 | C22⋊Dic19 | — | 4 | 1 | no | — |
| 70 | (C2×D19)⋊C4 | — | 4 | 2 | no | — |
| 71 | (C2×D19)⋊C4 | — | 4 | 2 | no | — |
| 72 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 73 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 74 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 75 | C4⋊Dic19 | — | 2 | 2 | no | — |
| 76 | Dic19⋊C4 | — | 4 | 2 | no | — |
| 77 | C4×Dic19 | — | 2 | 4 | no | — |
| 78 | C4×Dic19 | — | 2 | 2 | no | — |
| 79 | C4×Dic19 | — | 4 | 2 | no | — |
| 80 | C4×Dic19 | — | 4 | 1 | no | — |
| 81 | C4×Dic19 | — | 4 | 1 | no | — |
| 82 | D152 | — | 8 | 2 | no | — |
| 83 | #64516 | — | 8 | 4 | no | — |
| 84 | #10301 | — | 19 | 1 | no | maximal, Sylow |
| 85 | C23×C19 | #127 | 1 | 1 | yes | characteristic |
| 86 | C22×D19 | — | 4 | 2 | no | — |
| 87 | C2×C4×C19 | — | 2 | 2 | no | — |
| 88 | C2×C4×C19 | — | 2 | 2 | no | — |
| 89 | C2×C4×C19 | — | 2 | 1 | no | — |
| 90 | C2×C4×C19 | — | 2 | 1 | no | — |
| 91 | C2×C4×C19 | #120 | 1 | 2 | yes | — |
| 92 | C2×C4×C19 | #120 | 1 | 1 | yes | characteristic |
| 93 | C2×C4×C19 | #121 | 1 | 2 | yes | — |
| 94 | C2×C4×C19 | #121 | 1 | 1 | yes | characteristic |
| 95 | C22⋊D19 | — | 8 | 4 | no | — |
| 96 | C2×Dic19 | — | 4 | 4 | no | — |
| 97 | C2×Dic19 | — | 4 | 2 | no | — |
| 98 | C2×Dic19 | — | 4 | 2 | no | — |
| 99 | C2×Dic19 | — | 4 | 2 | no | — |
| 100 | D76 | — | 4 | 4 | no | — |
| 101 | D76 | — | 4 | 2 | no | — |
| 102 | D76 | — | 4 | 2 | no | — |
| 103 | D76 | — | 4 | 2 | no | — |
| 104 | D76 | — | 4 | 2 | no | — |
| 105 | C4×D19 | — | 8 | 2 | no | — |
| 106 | C4×D19 | — | 8 | 2 | no | — |
| 107 | Dic38 | — | 4 | 4 | no | — |
| 108 | Dic38 | — | 4 | 2 | no | — |
| 109 | Dic38 | — | 4 | 2 | no | — |
| 110 | C8×C19 | — | 4 | 4 | no | — |
| 111 | C8×C19 | — | 4 | 2 | no | — |
| 112 | #3254 | — | 19 | 2 | no | — |
| 113 | #3253 | — | 19 | 1 | no | — |
| 114 | #1994 | — | 19 | 1 | no | — |
| 115 | #1962 | — | 19 | 2 | no | — |
| 116 | #1309 | D19 | 1 | 1 | yes | characteristic, complemented |
| 117 | C22×C19 | — | 2 | 2 | no | — |
| 118 | C22×C19 | — | 2 | 1 | no | — |
| 119 | C22×C19 | #392 | 1 | 1 | yes | characteristic |
| 120 | C2×D19 | — | 8 | 2 | no | — |
| 121 | C2×D19 | — | 8 | 2 | no | — |
| 122 | C2×D19 | — | 8 | 2 | no | — |
| 123 | C4×C19 | — | 2 | 2 | no | — |
| 124 | C4×C19 | — | 2 | 1 | no | — |
| 125 | C4×C19 | #453 | 1 | 2 | yes | — |
| 126 | C4×C19 | #454 | 1 | 2 | yes | — |
| 127 | C4×C19 | #455 | 1 | 1 | yes | characteristic |
| 128 | C4×C19 | #456 | 1 | 1 | yes | characteristic |
| 129 | Dic19 | — | 4 | 4 | no | — |
| 130 | Dic19 | — | 8 | 2 | no | — |
| 131 | Dic19 | — | 8 | 2 | no | — |
| 132 | #533 | — | 19 | 1 | no | — |
| 133 | #532 | — | 19 | 2 | no | — |
| 134 | #477 | — | 38 | 2 | no | — |
| 135 | #476 | — | 38 | 2 | no | — |
| 136 | #474 | — | 38 | 2 | no | — |
| 137 | #469 | — | 38 | 2 | no | — |
| 138 | #468 | — | 38 | 4 | no | — |
| 139 | #461 | — | 38 | 2 | no | — |
| 140 | #460 | — | 38 | 2 | no | — |
| 141 | #459 | — | 38 | 2 | no | — |
| 142 | #423 | C2×D19 | 1 | 2 | yes | — |
| 143 | #423 | C2×D19 | 1 | 1 | yes | characteristic |
| 144 | C2×#104 | — | 38 | 4 | no | — |
| 145 | C43 | — | 19 | 1 | no | — |
| 146 | #339 | — | 38 | 2 | no | — |
| 147 | C2×C19 | — | 4 | 1 | no | — |
| 148 | C2×C19 | #2006 | 1 | 2 | yes | — |
| 149 | C2×C19 | #2007 | 1 | 1 | yes | characteristic |
| 150 | D19 | — | 16 | 2 | no | — |
| 151 | C2×#41 | — | 38 | 2 | no | — |
| 152 | C2×SD16 | — | 38 | 4 | no | — |
| 153 | C2×D8 | — | 38 | 2 | no | — |
| 154 | C2×M16 | D76 | 1 | 2 | yes | — |
| 155 | C2×M16 | D76 | 1 | 4 | yes | — |
| 156 | C4⋊Q8 | — | 19 | 2 | no | — |
| 157 | C4⋊Q8 | — | 19 | 2 | no | — |
| 158 | #127 | — | 19 | 2 | no | — |
| 159 | #125 | — | 38 | 1 | no | — |
| 160 | #124 | — | 38 | 2 | no | — |
| 161 | C22⋊Q8 | — | 38 | 2 | no | — |
| 162 | #121 | — | 38 | 2 | no | — |
| 163 | #121 | — | 38 | 2 | no | — |
| 164 | C4×Q8 | — | 38 | 2 | no | — |
| 165 | C4×D4 | — | 38 | 2 | no | — |
| 166 | C4×D4 | — | 38 | 2 | no | — |
| 167 | #117 | — | 38 | 1 | no | — |
| 168 | C2×C42 | — | 38 | 1 | no | — |
| 169 | C2×C42 | — | 38 | 2 | no | — |
| 170 | C2×C42 | C22×D19 | 1 | 1 | yes | characteristic |
| 171 | #107 | — | 38 | 4 | no | — |
| 172 | #106 | — | 38 | 2 | no | — |
| 173 | C4⋊C8 | — | 2 | 2 | no | — |
| 174 | C4⋊C8 | — | 2 | 2 | no | — |
| 175 | C4⋊C8 | — | 2 | 2 | no | — |
| 176 | #104 | — | 76 | 8 | no | — |
| 177 | #103 | — | 38 | 4 | no | — |
| 178 | #102 | — | 38 | 4 | no | — |
| 179 | #102 | — | 38 | 4 | no | — |
| 180 | C19 | #10301 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 181 | #41 | — | 76 | 4 | no | — |
| 182 | #41 | — | 76 | 4 | no | — |
| 183 | C2×Q8 | — | 38 | 2 | no | — |
| 184 | C2×Q8 | — | 38 | 2 | no | — |
| 185 | C2×D4 | — | 38 | 2 | no | — |
| 186 | C2×D4 | — | 38 | 2 | no | — |
| 187 | C2×D4 | — | 38 | 2 | no | — |
| 188 | C2×D4 | — | 76 | 2 | no | — |
| 189 | C22×C4 | — | 76 | 1 | no | — |
| 190 | C22×C4 | — | 76 | 2 | no | — |
| 191 | C22×C4 | C2×D76 | 1 | 1 | yes | characteristic |
| 192 | C22×C4 | C2×D76 | 1 | 2 | yes | — |
| 193 | SD16 | — | 152 | 4 | no | — |
| 194 | D8 | — | 152 | 2 | no | — |
| 195 | M16 | — | 4 | 4 | no | — |
| 196 | M16 | — | 4 | 2 | no | — |
| 197 | C2×C8 | — | 2 | 2 | no | — |
| 198 | C2×C8 | — | 2 | 4 | no | — |
| 199 | C4⋊C4 | — | 38 | 2 | no | — |
| 200 | C4⋊C4 | — | 38 | 2 | no | — |
| 201 | C4⋊C4 | — | 38 | 2 | no | — |
| 202 | C4⋊C4 | — | 38 | 2 | no | — |
| 203 | C4⋊C4 | — | 76 | 2 | no | — |
| 204 | C22⋊C4 | — | 76 | 1 | no | — |
| 205 | C22⋊C4 | — | 76 | 2 | no | — |
| 206 | C22⋊C4 | — | 76 | 2 | no | — |
| 207 | C42 | — | 38 | 4 | no | — |
| 208 | C42 | — | 38 | 2 | no | — |
| 209 | C42 | — | 76 | 2 | no | — |
| 210 | C42 | — | 76 | 1 | no | — |
| 211 | C42 | — | 76 | 1 | no | — |
| 212 | C42 | D4×D19 | 1 | 1 | yes | characteristic |
| 213 | C42 | D4×D19 | 1 | 2 | yes | — |
| 214 | C42 | #64545 | 1 | 1 | yes | characteristic |
| 215 | C23 | — | 76 | 2 | no | — |
| 216 | C23 | #10597320 | 1 | 1 | yes | characteristic |
| 217 | Q8 | — | 76 | 4 | no | — |
| 218 | Q8 | — | 76 | 2 | no | — |
| 219 | Q8 | — | 76 | 2 | no | — |
| 220 | D4 | — | 76 | 4 | no | — |
| 221 | D4 | — | 76 | 2 | no | — |
| 222 | D4 | — | 76 | 2 | no | — |
| 223 | D4 | — | 76 | 2 | no | — |
| 224 | D4 | — | 76 | 2 | no | — |
| 225 | D4 | — | 152 | 4 | no | — |
| 226 | C2×C4 | — | 2 | 2 | no | — |
| 227 | C2×C4 | — | 2 | 2 | no | — |
| 228 | C2×C4 | — | 2 | 1 | no | — |
| 229 | C2×C4 | — | 2 | 1 | no | — |
| 230 | C2×C4 | — | 76 | 4 | no | — |
| 231 | C2×C4 | — | 76 | 2 | no | — |
| 232 | C2×C4 | — | 76 | 2 | no | — |
| 233 | C2×C4 | — | 76 | 2 | no | — |
| 234 | C2×C4 | — | 152 | 2 | no | — |
| 235 | C2×C4 | — | 152 | 2 | no | — |
| 236 | C2×C4 | #10597328 | 1 | 2 | yes | — |
| 237 | C2×C4 | #10597328 | 1 | 1 | yes | characteristic |
| 238 | C2×C4 | #10597341 | 1 | 1 | yes | characteristic |
| 239 | C2×C4 | #10597341 | 1 | 2 | yes | — |
| 240 | C8 | — | 4 | 4 | no | — |
| 241 | C8 | — | 4 | 2 | no | — |
| 242 | C22 | — | 2 | 2 | no | — |
| 243 | C22 | — | 2 | 1 | no | — |
| 244 | C22 | — | 152 | 2 | no | — |
| 245 | C22 | — | 152 | 2 | no | — |
| 246 | C22 | — | 152 | 2 | no | — |
| 247 | C22 | #11926454 | 1 | 1 | yes | characteristic |
| 248 | C4 | — | 2 | 2 | no | — |
| 249 | C4 | — | 2 | 1 | no | — |
| 250 | C4 | — | 76 | 4 | no | — |
| 251 | C4 | — | 152 | 2 | no | — |
| 252 | C4 | — | 152 | 2 | no | — |
| 253 | C4 | #11926714 | 1 | 2 | yes | — |
| 254 | C4 | #11926719 | 1 | 2 | yes | — |
| 255 | C4 | #11926724 | 1 | 1 | yes | characteristic |
| 256 | C4 | #11926729 | 1 | 1 | yes | characteristic |
| 257 | C2 | — | 4 | 1 | no | — |
| 258 | C2 | — | 304 | 2 | no | — |
| 259 | C2 | #14564679 | 1 | 2 | yes | — |
| 260 | C2 | #14564684 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14575023 | C2 | semidirect |
| 3. #14564611 | C2 | semidirect |
| 4. #14564462 | C2 | semidirect |
| 5. C19×#1309 | C2 | semidirect |
| 116. #1309 | D19 | semidirect |
| 180. C19 | #10301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14575023 | 2 |
| #14575016 | 2 |
| #14564611 | 2 |
| #14564462 | 2 |
| C19×#1309 | 2 |
| #10301 | 19 |