Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
390 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 59 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 | #19145490 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #19136531 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #19135716 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #19132614 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C43×#1315 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#13063355 | — | 2 | 1 | no | — |
| 7 | C22×Dic172 | C22 | 1 | 1 | yes | characteristic |
| 8 | #14583470 | — | 2 | 1 | no | — |
| 9 | C2×Dic344 | — | 2 | 2 | no | — |
| 10 | #14583241 | — | 2 | 2 | no | — |
| 11 | #14583157 | — | 2 | 1 | no | — |
| 12 | #14583140 | C22 | 1 | 2 | yes | — |
| 13 | #14583057 | — | 2 | 2 | no | — |
| 14 | C2×#13063243 | — | 2 | 1 | no | — |
| 15 | #14582704 | — | 2 | 2 | no | — |
| 16 | #14582664 | C22 | 1 | 1 | yes | characteristic |
| 17 | C43×#408 | C22 | 1 | 1 | yes | characteristic |
| 18 | C43×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 19 | C22×Dic86 | — | 2 | 1 | no | — |
| 20 | C22×Dic86 | — | 2 | 1 | no | — |
| 21 | #13063355 | — | 4 | 2 | no | — |
| 22 | #13063355 | — | 4 | 2 | no | — |
| 23 | C2×Dic172 | — | 2 | 2 | no | — |
| 24 | C2×Dic172 | — | 2 | 1 | no | — |
| 25 | C2×Dic172 | — | 4 | 2 | no | — |
| 26 | C2×Dic172 | D4 | 1 | 2 | yes | — |
| 27 | C2×#10621885 | — | 4 | 1 | no | — |
| 28 | C2×#10621883 | — | 4 | 1 | no | — |
| 29 | C2×#10621877 | — | 2 | 1 | no | — |
| 30 | #13063323 | — | 4 | 1 | no | — |
| 31 | #13063312 | — | 4 | 1 | no | — |
| 32 | #13063306 | — | 4 | 1 | no | — |
| 33 | #13063306 | — | 4 | 1 | no | — |
| 34 | #13063304 | — | 2 | 2 | no | — |
| 35 | #13063304 | — | 2 | 2 | no | — |
| 36 | #13063284 | — | 2 | 1 | no | — |
| 37 | Dic344 | — | 4 | 4 | no | — |
| 38 | #13063259 | D4 | 1 | 2 | yes | — |
| 39 | #13063257 | — | 2 | 1 | no | — |
| 40 | #13063250 | — | 2 | 2 | no | — |
| 41 | #13063250 | — | 2 | 2 | no | — |
| 42 | #13063243 | — | 4 | 2 | no | — |
| 43 | C2×#41×C43 | D4 | 1 | 1 | yes | characteristic |
| 44 | C2×M16×C43 | D4 | 1 | 1 | yes | characteristic |
| 45 | C22×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C16×C43 | — | 2 | 2 | no | — |
| 47 | C22⋊C8×C43 | — | 2 | 2 | no | — |
| 48 | #41×C43 | — | 4 | 1 | no | — |
| 49 | #41×C43 | — | 4 | 1 | no | — |
| 50 | C2×Q8×C43 | D8 | 1 | 1 | yes | characteristic |
| 51 | C2×D4×C43 | — | 2 | 1 | no | — |
| 52 | C2×D4×C43 | D8 | 1 | 1 | yes | characteristic |
| 53 | C22×C4×C43 | — | 2 | 1 | no | — |
| 54 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 55 | C22×Dic43 | — | 4 | 1 | no | — |
| 56 | C22×Dic43 | — | 4 | 1 | no | — |
| 57 | C2×Dic86 | — | 2 | 2 | no | — |
| 58 | C2×Dic86 | — | 2 | 2 | no | — |
| 59 | C2×Dic86 | — | 4 | 1 | no | — |
| 60 | C2×Dic86 | — | 4 | 1 | no | — |
| 61 | C2×Dic86 | — | 4 | 1 | no | — |
| 62 | C2×Dic86 | — | 4 | 1 | no | — |
| 63 | C2×Dic86 | — | 4 | 1 | no | — |
| 64 | C2×Dic86 | — | 4 | 1 | no | — |
| 65 | C2×Dic86 | — | 8 | 1 | no | — |
| 66 | C2×Dic86 | — | 8 | 1 | no | — |
| 67 | M16×C43 | — | 4 | 1 | no | — |
| 68 | C2×C8×C43 | — | 2 | 1 | no | — |
| 69 | C2×C8×C43 | — | 4 | 1 | no | — |
| 70 | C2×C8×C43 | C2×D4 | 1 | 2 | yes | — |
| 71 | C22⋊Dic43 | — | 4 | 1 | no | — |
| 72 | C22⋊Dic43 | — | 4 | 2 | no | — |
| 73 | C22⋊Dic43 | — | 4 | 2 | no | — |
| 74 | #10621885 | — | 4 | 4 | no | — |
| 75 | #10621883 | — | 4 | 4 | no | — |
| 76 | C4⋊Dic43 | — | 2 | 2 | no | — |
| 77 | Dic43⋊C4 | — | 4 | 2 | no | — |
| 78 | Dic43⋊C4 | — | 4 | 2 | no | — |
| 79 | C4×Dic43 | — | 4 | 1 | no | — |
| 80 | #10621877 | — | 2 | 2 | no | — |
| 81 | #10621877 | — | 4 | 1 | no | — |
| 82 | C2×C43⋊C8 | — | 4 | 1 | no | — |
| 83 | Dic172 | — | 2 | 4 | no | — |
| 84 | Dic172 | — | 4 | 2 | no | — |
| 85 | Dic172 | — | 4 | 2 | no | — |
| 86 | Dic172 | — | 8 | 1 | no | — |
| 87 | C16×C43 | — | 4 | 2 | no | — |
| 88 | C23×C43 | — | 2 | 1 | no | — |
| 89 | C23×C43 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 90 | Q8×C43 | — | 4 | 1 | no | — |
| 91 | D4×C43 | — | 4 | 1 | no | — |
| 92 | D4×C43 | — | 8 | 1 | no | — |
| 93 | C2×C4×C43 | — | 2 | 1 | no | — |
| 94 | C2×C4×C43 | — | 2 | 1 | no | — |
| 95 | C2×C4×C43 | — | 2 | 1 | no | — |
| 96 | C2×C4×C43 | — | 4 | 1 | no | — |
| 97 | C2×C4×C43 | — | 4 | 1 | no | — |
| 98 | C2×C4×C43 | #120 | 1 | 1 | yes | characteristic |
| 99 | C2×C4×C43 | C2×D8 | 1 | 1 | yes | characteristic |
| 100 | C2×Dic43 | — | 4 | 2 | no | — |
| 101 | C2×Dic43 | — | 4 | 2 | no | — |
| 102 | C2×Dic43 | — | 4 | 2 | no | — |
| 103 | C2×Dic43 | — | 8 | 1 | no | — |
| 104 | C2×Dic43 | — | 8 | 2 | no | — |
| 105 | C2×Dic43 | — | 8 | 1 | no | — |
| 106 | Dic86 | — | 4 | 2 | no | — |
| 107 | Dic86 | — | 4 | 2 | no | — |
| 108 | Dic86 | — | 4 | 2 | no | — |
| 109 | Dic86 | — | 4 | 2 | no | — |
| 110 | Dic86 | — | 8 | 1 | no | — |
| 111 | Dic86 | — | 8 | 2 | no | — |
| 112 | Dic86 | — | 8 | 1 | no | — |
| 113 | C8×C43 | — | 2 | 2 | no | — |
| 114 | C8×C43 | — | 4 | 1 | no | — |
| 115 | C43⋊C8 | — | 4 | 2 | no | — |
| 116 | #12112 | — | 43 | 1 | no | maximal, Sylow |
| 117 | C22×C43 | — | 2 | 1 | no | — |
| 118 | C22×C43 | — | 2 | 2 | no | — |
| 119 | C22×C43 | — | 4 | 1 | no | — |
| 120 | C22×C43 | — | 4 | 2 | no | — |
| 121 | C22×C43 | #447 | 1 | 1 | yes | characteristic |
| 122 | C4×C43 | — | 2 | 1 | no | — |
| 123 | C4×C43 | — | 4 | 1 | no | — |
| 124 | C4×C43 | #453 | 1 | 1 | yes | characteristic |
| 125 | C4×C43 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 126 | Dic43 | — | 8 | 2 | no | — |
| 127 | Dic43 | — | 8 | 2 | no | — |
| 128 | Dic43 | — | 8 | 2 | no | — |
| 129 | #3202 | — | 43 | 1 | no | — |
| 130 | #2188 | — | 43 | 2 | no | — |
| 131 | #2020 | — | 43 | 1 | no | — |
| 132 | #1350 | — | 43 | 2 | no | — |
| 133 | #1315 | D43 | 1 | 1 | yes | characteristic |
| 134 | C2×C43 | — | 4 | 1 | no | — |
| 135 | C2×C43 | — | 8 | 1 | no | — |
| 136 | C2×C43 | #1595 | 1 | 1 | yes | characteristic |
| 137 | C2×C43 | #2195 | 1 | 2 | yes | — |
| 138 | C2×#137 | — | 86 | 1 | no | — |
| 139 | C22×Q16 | — | 43 | 1 | no | — |
| 140 | #536 | — | 86 | 1 | no | — |
| 141 | C2×Q32 | — | 86 | 2 | no | — |
| 142 | #485 | — | 86 | 2 | no | — |
| 143 | #470 | — | 86 | 1 | no | — |
| 144 | #467 | — | 43 | 2 | no | — |
| 145 | #451 | — | 86 | 2 | no | — |
| 146 | C2×#101 | — | 86 | 1 | no | — |
| 147 | #408 | C2×D43 | 1 | 1 | yes | characteristic |
| 148 | #358 | — | 86 | 2 | no | — |
| 149 | C22⋊C16 | C2×D43 | 1 | 2 | yes | — |
| 150 | #341 | — | 43 | 1 | no | — |
| 151 | C43 | #12112 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 152 | C2×#41 | D172 | 1 | 1 | yes | characteristic |
| 153 | C22×Q8 | — | 86 | 1 | no | — |
| 154 | C22×Q8 | — | 86 | 1 | no | — |
| 155 | #137 | — | 172 | 2 | no | — |
| 156 | #137 | — | 172 | 2 | no | — |
| 157 | C2×Q16 | — | 43 | 2 | no | — |
| 158 | C2×Q16 | — | 86 | 1 | no | — |
| 159 | C2×Q16 | — | 86 | 2 | no | — |
| 160 | C2×Q16 | — | 172 | 2 | no | — |
| 161 | C2×Q16 | — | 172 | 1 | no | — |
| 162 | C2×SD16 | — | 172 | 1 | no | — |
| 163 | C2×M16 | — | 86 | 1 | no | — |
| 164 | C2×M16 | D172 | 1 | 1 | yes | characteristic |
| 165 | C22×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 166 | C4⋊Q8 | — | 172 | 1 | no | — |
| 167 | #124 | — | 172 | 1 | no | — |
| 168 | #123 | — | 172 | 1 | no | — |
| 169 | #123 | — | 172 | 1 | no | — |
| 170 | C22⋊Q8 | — | 86 | 2 | no | — |
| 171 | C22⋊Q8 | — | 86 | 2 | no | — |
| 172 | #117 | — | 86 | 1 | no | — |
| 173 | Q32 | — | 172 | 4 | no | — |
| 174 | C2×C16 | — | 2 | 2 | no | — |
| 175 | #107 | — | 43 | 2 | no | — |
| 176 | #106 | — | 86 | 1 | no | — |
| 177 | #103 | — | 86 | 2 | no | — |
| 178 | #103 | — | 86 | 2 | no | — |
| 179 | #101 | — | 172 | 2 | no | — |
| 180 | C22⋊C8 | — | 2 | 2 | no | — |
| 181 | #41 | — | 4 | 1 | no | — |
| 182 | #41 | — | 4 | 1 | no | — |
| 183 | C2×Q8 | — | 86 | 2 | no | — |
| 184 | C2×Q8 | — | 86 | 2 | no | — |
| 185 | C2×Q8 | — | 344 | 1 | no | — |
| 186 | C2×Q8 | — | 344 | 1 | no | — |
| 187 | C2×Q8 | — | 172 | 1 | no | — |
| 188 | C2×Q8 | — | 172 | 1 | no | — |
| 189 | C2×Q8 | — | 172 | 1 | no | — |
| 190 | C2×Q8 | — | 172 | 1 | no | — |
| 191 | C2×Q8 | — | 172 | 1 | no | — |
| 192 | C2×Q8 | — | 172 | 1 | no | — |
| 193 | C2×Q8 | D344 | 1 | 1 | yes | characteristic |
| 194 | C2×D4 | — | 2 | 1 | no | — |
| 195 | C2×D4 | D344 | 1 | 1 | yes | characteristic |
| 196 | C22×C4 | — | 2 | 1 | no | — |
| 197 | C22×C4 | — | 172 | 1 | no | — |
| 198 | C22×C4 | — | 172 | 1 | no | — |
| 199 | C22×C4 | C2×D172 | 1 | 1 | yes | characteristic |
| 200 | Q16 | — | 86 | 4 | no | — |
| 201 | Q16 | — | 344 | 1 | no | — |
| 202 | Q16 | — | 172 | 2 | no | — |
| 203 | Q16 | — | 172 | 2 | no | — |
| 204 | Q16 | — | 172 | 4 | no | — |
| 205 | SD16 | — | 172 | 4 | no | — |
| 206 | M16 | — | 4 | 1 | no | — |
| 207 | M16 | — | 86 | 2 | no | — |
| 208 | M16 | — | 172 | 1 | no | — |
| 209 | C2×C8 | — | 2 | 1 | no | — |
| 210 | C2×C8 | — | 4 | 1 | no | — |
| 211 | C2×C8 | — | 172 | 1 | no | — |
| 212 | C2×C8 | D4×D43 | 1 | 2 | yes | — |
| 213 | C4⋊C4 | — | 86 | 2 | no | — |
| 214 | C4⋊C4 | — | 172 | 2 | no | — |
| 215 | C4⋊C4 | — | 172 | 2 | no | — |
| 216 | C22⋊C4 | — | 172 | 1 | no | — |
| 217 | C22⋊C4 | — | 172 | 2 | no | — |
| 218 | C22⋊C4 | — | 172 | 2 | no | — |
| 219 | C42 | — | 172 | 1 | no | — |
| 220 | C16 | — | 4 | 2 | no | — |
| 221 | C23 | — | 2 | 1 | no | — |
| 222 | C23 | #13063353 | 1 | 1 | yes | characteristic |
| 223 | Q8 | — | 4 | 1 | no | — |
| 224 | Q8 | — | 344 | 1 | no | — |
| 225 | Q8 | — | 344 | 2 | no | — |
| 226 | Q8 | — | 344 | 1 | no | — |
| 227 | Q8 | — | 172 | 2 | no | — |
| 228 | Q8 | — | 172 | 2 | no | — |
| 229 | Q8 | — | 172 | 2 | no | — |
| 230 | Q8 | — | 172 | 2 | no | — |
| 231 | D4 | — | 4 | 1 | no | — |
| 232 | D4 | — | 8 | 1 | no | — |
| 233 | C2×C4 | — | 2 | 1 | no | — |
| 234 | C2×C4 | — | 2 | 1 | no | — |
| 235 | C2×C4 | — | 2 | 1 | no | — |
| 236 | C2×C4 | — | 4 | 1 | no | — |
| 237 | C2×C4 | — | 4 | 1 | no | — |
| 238 | C2×C4 | — | 344 | 1 | no | — |
| 239 | C2×C4 | — | 344 | 2 | no | — |
| 240 | C2×C4 | — | 344 | 1 | no | — |
| 241 | C2×C4 | — | 172 | 2 | no | — |
| 242 | C2×C4 | — | 172 | 2 | no | — |
| 243 | C2×C4 | — | 172 | 2 | no | — |
| 244 | C2×C4 | #13063295 | 1 | 1 | yes | characteristic |
| 245 | C2×C4 | C2×D344 | 1 | 1 | yes | characteristic |
| 246 | C8 | — | 2 | 2 | no | — |
| 247 | C8 | — | 4 | 1 | no | — |
| 248 | C8 | — | 172 | 2 | no | — |
| 249 | C22 | — | 2 | 2 | no | — |
| 250 | C22 | — | 2 | 1 | no | — |
| 251 | C22 | — | 4 | 2 | no | — |
| 252 | C22 | — | 4 | 1 | no | — |
| 253 | C22 | #14583035 | 1 | 1 | yes | characteristic |
| 254 | C4 | — | 2 | 1 | no | — |
| 255 | C4 | — | 4 | 1 | no | — |
| 256 | C4 | — | 344 | 2 | no | — |
| 257 | C4 | — | 344 | 2 | no | — |
| 258 | C4 | — | 344 | 2 | no | — |
| 259 | C4 | #14583069 | 1 | 1 | yes | characteristic |
| 260 | C4 | #14583087 | 1 | 1 | yes | characteristic |
| 261 | C2 | — | 4 | 1 | no | — |
| 262 | C2 | — | 8 | 1 | no | — |
| 263 | C2 | #19133515 | 1 | 1 | yes | characteristic |
| 264 | C2 | #19136575 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #19136531 | C2 | semidirect |
| 4. #19132614 | C2 | semidirect |
| 151. C43 | #12112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145490 | 2 |
| #19136531 | 2 |
| #19135716 | 2 |
| #19132614 | 2 |
| C43×#1315 | 2 |
| #12112 | 43 |