Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
670 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 77 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, complemented |
| 2 | #19143976 | C2 | 1 | 2 | yes | maximal |
| 3 | #19136250 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #19134558 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C43×#1392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #14583735 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×#13063358 | — | 2 | 2 | no | — |
| 8 | #14583470 | C22 | 1 | 2 | yes | — |
| 9 | #14583241 | — | 2 | 2 | no | — |
| 10 | #14583157 | — | 2 | 1 | no | — |
| 11 | #14583140 | — | 2 | 1 | no | — |
| 12 | #14583084 | — | 2 | 4 | no | — |
| 13 | #14583079 | — | 2 | 4 | no | — |
| 14 | #14583057 | — | 2 | 2 | no | — |
| 15 | #14582915 | — | 2 | 2 | no | — |
| 16 | #14582915 | — | 2 | 1 | no | — |
| 17 | #14582896 | — | 2 | 1 | no | — |
| 18 | #14582873 | C22 | 1 | 1 | yes | characteristic |
| 19 | #14582690 | — | 2 | 4 | no | — |
| 20 | C43×#413 | C22 | 1 | 2 | yes | — |
| 21 | C43×#408 | C22 | 1 | 1 | yes | characteristic |
| 22 | #13063373 | D4 | 1 | 2 | yes | — |
| 23 | #13063372 | — | 4 | 1 | no | — |
| 24 | #13063371 | — | 4 | 1 | no | — |
| 25 | #13063370 | — | 2 | 2 | no | — |
| 26 | #13063370 | — | 2 | 1 | no | — |
| 27 | C2×#10621898 | — | 2 | 1 | no | — |
| 28 | C2×#10621898 | — | 2 | 2 | no | — |
| 29 | #41×D43 | — | 4 | 2 | no | — |
| 30 | C22×Dic86 | D4 | 1 | 2 | yes | — |
| 31 | #13063358 | — | 2 | 8 | no | — |
| 32 | #13063358 | — | 4 | 4 | no | — |
| 33 | C2×Dic172 | — | 2 | 1 | no | — |
| 34 | C2×Dic172 | — | 2 | 1 | no | — |
| 35 | C2×Dic172 | — | 4 | 2 | no | — |
| 36 | C2×#10621873 | — | 4 | 2 | no | — |
| 37 | #13063323 | — | 2 | 2 | no | — |
| 38 | #13063312 | — | 2 | 2 | no | — |
| 39 | #13063306 | — | 2 | 2 | no | — |
| 40 | #13063306 | — | 2 | 2 | no | — |
| 41 | #13063304 | — | 2 | 2 | no | — |
| 42 | #13063304 | — | 2 | 2 | no | — |
| 43 | #13063284 | — | 2 | 1 | no | — |
| 44 | #13063284 | D4 | 1 | 2 | yes | — |
| 45 | #13063259 | — | 2 | 1 | no | — |
| 46 | #13063257 | — | 2 | 1 | no | — |
| 47 | #13063251 | — | 2 | 8 | no | — |
| 48 | #13063251 | — | 4 | 2 | no | — |
| 49 | #13063250 | — | 2 | 2 | no | — |
| 50 | #13063250 | — | 2 | 2 | no | — |
| 51 | #13063250 | — | 4 | 1 | no | — |
| 52 | #13063247 | — | 4 | 1 | no | — |
| 53 | #13063240 | — | 2 | 2 | no | — |
| 54 | C2×#41×C43 | C23 | 1 | 1 | yes | characteristic |
| 55 | C2×M16×C43 | — | 2 | 2 | no | — |
| 56 | C2×M16×C43 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×C8×C43 | D4 | 1 | 1 | yes | characteristic |
| 58 | #101×C43 | — | 2 | 2 | no | — |
| 59 | #100×C43 | D4 | 1 | 4 | yes | — |
| 60 | C22⋊C8×C43 | — | 2 | 2 | no | — |
| 61 | #41×C43 | — | 4 | 1 | no | — |
| 62 | #41×C43 | — | 4 | 1 | no | — |
| 63 | C2×Q8×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 64 | C2×D4×C43 | C2×D4 | 1 | 2 | yes | — |
| 65 | C2×D4×C43 | #41 | 1 | 1 | yes | characteristic |
| 66 | C22×C4×C43 | C2×D4 | 1 | 2 | yes | — |
| 67 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 68 | C2×C22⋊D43 | — | 4 | 2 | no | — |
| 69 | C2×C22⋊D43 | — | 4 | 1 | no | — |
| 70 | C22×Dic43 | — | 2 | 2 | no | — |
| 71 | #10621902 | — | 4 | 2 | no | — |
| 72 | Q8×D43 | — | 4 | 2 | no | — |
| 73 | #10621900 | — | 4 | 4 | no | — |
| 74 | #10621900 | — | 4 | 2 | no | — |
| 75 | D4×D43 | — | 4 | 4 | no | — |
| 76 | D4×D43 | — | 4 | 2 | no | — |
| 77 | #10621898 | — | 2 | 2 | no | — |
| 78 | #10621898 | — | 2 | 4 | no | — |
| 79 | #10621898 | — | 2 | 4 | no | — |
| 80 | #10621898 | — | 2 | 2 | no | — |
| 81 | #10621898 | — | 4 | 1 | no | — |
| 82 | #10621898 | — | 4 | 2 | no | — |
| 83 | #10621898 | — | 4 | 1 | no | — |
| 84 | C2×D172 | — | 2 | 1 | no | — |
| 85 | C2×D172 | — | 2 | 2 | no | — |
| 86 | C2×C4×D43 | — | 4 | 1 | no | — |
| 87 | C2×C4×D43 | — | 4 | 2 | no | — |
| 88 | C2×Dic86 | — | 2 | 1 | no | — |
| 89 | C2×Dic86 | — | 2 | 2 | no | — |
| 90 | C2×Dic86 | — | 2 | 2 | no | — |
| 91 | C2×Dic86 | — | 2 | 2 | no | — |
| 92 | C2×Dic86 | — | 4 | 2 | no | — |
| 93 | C2×Dic86 | — | 4 | 2 | no | — |
| 94 | M16×C43 | — | 2 | 4 | no | — |
| 95 | M16×C43 | — | 4 | 2 | no | — |
| 96 | M16×C43 | — | 4 | 1 | no | — |
| 97 | C2×C8×C43 | — | 2 | 1 | no | — |
| 98 | C2×C8×C43 | — | 2 | 1 | no | — |
| 99 | C2×C8×C43 | — | 4 | 2 | no | — |
| 100 | C2×C8×C43 | — | 4 | 1 | no | — |
| 101 | C22⋊Dic43 | — | 2 | 2 | no | — |
| 102 | C22⋊Dic43 | — | 4 | 2 | no | — |
| 103 | C22⋊Dic43 | — | 4 | 2 | no | — |
| 104 | C22⋊Dic43 | — | 4 | 1 | no | — |
| 105 | C4⋊Dic43 | — | 2 | 2 | no | — |
| 106 | C4⋊Dic43 | — | 4 | 1 | no | — |
| 107 | Dic43⋊C4 | — | 4 | 2 | no | — |
| 108 | Dic43⋊C4 | — | 4 | 2 | no | — |
| 109 | C4×Dic43 | — | 2 | 2 | no | — |
| 110 | C4×Dic43 | — | 4 | 1 | no | — |
| 111 | Dic172 | — | 4 | 8 | no | — |
| 112 | Dic172 | — | 8 | 1 | no | — |
| 113 | Dic172 | — | 8 | 1 | no | — |
| 114 | #10621873 | — | 4 | 8 | no | — |
| 115 | C23×C43 | #121 | 1 | 2 | yes | — |
| 116 | C23×C43 | #127 | 1 | 1 | yes | characteristic |
| 117 | C22×D43 | — | 4 | 2 | no | — |
| 118 | C22×D43 | — | 4 | 1 | no | — |
| 119 | Q8×C43 | — | 4 | 1 | no | — |
| 120 | D4×C43 | — | 4 | 2 | no | — |
| 121 | D4×C43 | — | 4 | 1 | no | — |
| 122 | C2×C4×C43 | — | 2 | 1 | no | — |
| 123 | C2×C4×C43 | — | 2 | 1 | no | — |
| 124 | C2×C4×C43 | — | 2 | 2 | no | — |
| 125 | C2×C4×C43 | — | 2 | 2 | no | — |
| 126 | C2×C4×C43 | #120 | 1 | 2 | yes | — |
| 127 | C2×C4×C43 | #120 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×C43 | #121 | 1 | 1 | yes | characteristic |
| 129 | C22⋊D43 | — | 4 | 4 | no | — |
| 130 | C22⋊D43 | — | 4 | 2 | no | — |
| 131 | C22⋊D43 | — | 4 | 2 | no | — |
| 132 | C2×Dic43 | — | 4 | 2 | no | — |
| 133 | C2×Dic43 | — | 4 | 1 | no | — |
| 134 | C2×Dic43 | — | 4 | 2 | no | — |
| 135 | C2×Dic43 | — | 4 | 2 | no | — |
| 136 | C2×Dic43 | — | 8 | 2 | no | — |
| 137 | C2×Dic43 | — | 8 | 1 | no | — |
| 138 | D172 | — | 2 | 4 | no | — |
| 139 | D172 | — | 2 | 2 | no | — |
| 140 | D172 | — | 4 | 1 | no | — |
| 141 | C4×D43 | — | 4 | 4 | no | — |
| 142 | C4×D43 | — | 4 | 2 | no | — |
| 143 | C4×D43 | — | 4 | 2 | no | — |
| 144 | Dic86 | — | 2 | 4 | no | — |
| 145 | Dic86 | — | 2 | 2 | no | — |
| 146 | Dic86 | — | 4 | 1 | no | — |
| 147 | Dic86 | — | 4 | 4 | no | — |
| 148 | Dic86 | — | 4 | 2 | no | — |
| 149 | Dic86 | — | 4 | 2 | no | — |
| 150 | C8×C43 | — | 4 | 4 | no | — |
| 151 | C8×C43 | — | 4 | 1 | no | — |
| 152 | C8×C43 | — | 4 | 1 | no | — |
| 153 | #13362 | — | 43 | 1 | no | maximal, Sylow |
| 154 | C22×C43 | — | 2 | 2 | no | — |
| 155 | C22×C43 | — | 2 | 1 | no | — |
| 156 | C22×C43 | — | 4 | 2 | no | — |
| 157 | C22×C43 | — | 4 | 1 | no | — |
| 158 | C22×C43 | #392 | 1 | 1 | yes | characteristic |
| 159 | C2×D43 | — | 4 | 2 | no | — |
| 160 | C2×D43 | — | 16 | 1 | no | — |
| 161 | C2×D43 | — | 16 | 2 | no | — |
| 162 | C4×C43 | — | 2 | 2 | no | — |
| 163 | C4×C43 | — | 2 | 1 | no | — |
| 164 | C4×C43 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 165 | C4×C43 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 166 | Dic43 | — | 4 | 2 | no | — |
| 167 | Dic43 | — | 8 | 2 | no | — |
| 168 | Dic43 | — | 8 | 2 | no | — |
| 169 | Dic43 | — | 16 | 1 | no | — |
| 170 | #3202 | — | 43 | 1 | no | — |
| 171 | #3022 | — | 43 | 2 | no | — |
| 172 | #2123 | — | 43 | 2 | no | — |
| 173 | #1794 | — | 43 | 1 | no | — |
| 174 | #1392 | D43 | 1 | 1 | yes | characteristic, complemented |
| 175 | C2×C43 | — | 2 | 1 | no | — |
| 176 | C2×C43 | — | 4 | 1 | no | — |
| 177 | C2×C43 | — | 4 | 2 | no | — |
| 178 | C2×C43 | #2021 | 1 | 1 | yes | characteristic |
| 179 | D43 | — | 8 | 2 | no | — |
| 180 | #585 | — | 43 | 1 | no | — |
| 181 | C2×#137 | — | 86 | 2 | no | — |
| 182 | #536 | — | 43 | 2 | no | — |
| 183 | #485 | — | 86 | 2 | no | — |
| 184 | #470 | — | 86 | 1 | no | — |
| 185 | #467 | — | 86 | 1 | no | — |
| 186 | #456 | — | 86 | 4 | no | — |
| 187 | #455 | — | 86 | 4 | no | — |
| 188 | #451 | — | 86 | 2 | no | — |
| 189 | #421 | — | 86 | 2 | no | — |
| 190 | #421 | — | 86 | 1 | no | — |
| 191 | #416 | — | 86 | 1 | no | — |
| 192 | #413 | C2×D43 | 1 | 2 | yes | — |
| 193 | #410 | — | 43 | 1 | no | — |
| 194 | #408 | C2×D43 | 1 | 1 | yes | characteristic |
| 195 | #352 | — | 86 | 4 | no | — |
| 196 | C43 | #13362 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | 2−1+4 | — | 43 | 2 | no | — |
| 198 | 2−1+4 | — | 172 | 1 | no | — |
| 199 | H(5,𝔽2) | — | 86 | 2 | no | — |
| 200 | H(5,𝔽2) | — | 86 | 1 | no | — |
| 201 | H(5,𝔽2) | — | 172 | 1 | no | — |
| 202 | C2×#41 | — | 86 | 1 | no | — |
| 203 | C2×#41 | — | 86 | 2 | no | — |
| 204 | C2×#41 | — | 172 | 2 | no | — |
| 205 | C2×#41 | C22×D43 | 1 | 1 | yes | characteristic |
| 206 | C22×Q8 | — | 43 | 2 | no | — |
| 207 | #137 | — | 86 | 8 | no | — |
| 208 | #137 | — | 172 | 4 | no | — |
| 209 | C2×Q16 | — | 86 | 1 | no | — |
| 210 | C2×Q16 | — | 86 | 1 | no | — |
| 211 | C2×Q16 | — | 172 | 2 | no | — |
| 212 | C2×SD16 | — | 172 | 2 | no | — |
| 213 | C2×M16 | — | 2 | 2 | no | — |
| 214 | C2×M16 | D172 | 1 | 1 | yes | characteristic |
| 215 | C22×C8 | D172 | 1 | 1 | yes | characteristic |
| 216 | C4⋊Q8 | — | 86 | 2 | no | — |
| 217 | #124 | — | 86 | 2 | no | — |
| 218 | #123 | — | 86 | 2 | no | — |
| 219 | #123 | — | 86 | 2 | no | — |
| 220 | C22⋊Q8 | — | 86 | 2 | no | — |
| 221 | C22⋊Q8 | — | 86 | 2 | no | — |
| 222 | #117 | — | 43 | 2 | no | — |
| 223 | #117 | — | 86 | 1 | no | — |
| 224 | #107 | — | 86 | 1 | no | — |
| 225 | #106 | — | 86 | 1 | no | — |
| 226 | #104 | — | 86 | 8 | no | — |
| 227 | #104 | — | 172 | 2 | no | — |
| 228 | #103 | — | 86 | 2 | no | — |
| 229 | #103 | — | 86 | 2 | no | — |
| 230 | #103 | — | 172 | 1 | no | — |
| 231 | #102 | — | 172 | 1 | no | — |
| 232 | #101 | — | 2 | 2 | no | — |
| 233 | #100 | D172 | 1 | 4 | yes | — |
| 234 | #99 | — | 86 | 2 | no | — |
| 235 | C22⋊C8 | — | 2 | 2 | no | — |
| 236 | #41 | — | 4 | 1 | no | — |
| 237 | #41 | — | 4 | 1 | no | — |
| 238 | #41 | — | 86 | 2 | no | — |
| 239 | #41 | — | 86 | 4 | no | — |
| 240 | #41 | — | 86 | 4 | no | — |
| 241 | #41 | — | 86 | 2 | no | — |
| 242 | #41 | — | 172 | 1 | no | — |
| 243 | #41 | — | 172 | 2 | no | — |
| 244 | #41 | — | 172 | 4 | no | — |
| 245 | #41 | — | 172 | 2 | no | — |
| 246 | #41 | — | 172 | 2 | no | — |
| 247 | #41 | — | 172 | 1 | no | — |
| 248 | C2×Q8 | — | 86 | 1 | no | — |
| 249 | C2×Q8 | — | 86 | 2 | no | — |
| 250 | C2×Q8 | — | 86 | 2 | no | — |
| 251 | C2×Q8 | — | 86 | 2 | no | — |
| 252 | C2×Q8 | — | 172 | 2 | no | — |
| 253 | C2×Q8 | — | 172 | 2 | no | — |
| 254 | C2×Q8 | — | 172 | 2 | no | — |
| 255 | C2×Q8 | D4×D43 | 1 | 1 | yes | characteristic |
| 256 | C2×D4 | — | 86 | 1 | no | — |
| 257 | C2×D4 | — | 86 | 2 | no | — |
| 258 | C2×D4 | — | 172 | 4 | no | — |
| 259 | C2×D4 | — | 172 | 2 | no | — |
| 260 | C2×D4 | — | 172 | 2 | no | — |
| 261 | C2×D4 | — | 172 | 1 | no | — |
| 262 | C2×D4 | C2×D172 | 1 | 2 | yes | — |
| 263 | C2×D4 | #10621902 | 1 | 1 | yes | characteristic |
| 264 | C22×C4 | — | 86 | 2 | no | — |
| 265 | C22×C4 | — | 172 | 1 | no | — |
| 266 | C22×C4 | — | 172 | 2 | no | — |
| 267 | C22×C4 | C2×D172 | 1 | 1 | yes | characteristic |
| 268 | C22×C4 | D4×D43 | 1 | 2 | yes | — |
| 269 | Q16 | — | 344 | 1 | no | — |
| 270 | Q16 | — | 344 | 1 | no | — |
| 271 | Q16 | — | 172 | 8 | no | — |
| 272 | SD16 | — | 172 | 8 | no | — |
| 273 | M16 | — | 2 | 4 | no | — |
| 274 | M16 | — | 4 | 2 | no | — |
| 275 | M16 | — | 4 | 1 | no | — |
| 276 | C2×C8 | — | 2 | 1 | no | — |
| 277 | C2×C8 | — | 2 | 1 | no | — |
| 278 | C2×C8 | — | 4 | 2 | no | — |
| 279 | C2×C8 | — | 4 | 1 | no | — |
| 280 | C4⋊C4 | — | 86 | 2 | no | — |
| 281 | C4⋊C4 | — | 172 | 1 | no | — |
| 282 | C4⋊C4 | — | 172 | 2 | no | — |
| 283 | C4⋊C4 | — | 172 | 2 | no | — |
| 284 | C22⋊C4 | — | 86 | 2 | no | — |
| 285 | C22⋊C4 | — | 172 | 1 | no | — |
| 286 | C22⋊C4 | — | 172 | 2 | no | — |
| 287 | C22⋊C4 | — | 172 | 2 | no | — |
| 288 | C42 | — | 86 | 2 | no | — |
| 289 | C42 | — | 172 | 1 | no | — |
| 290 | C23 | — | 172 | 2 | no | — |
| 291 | C23 | — | 172 | 1 | no | — |
| 292 | C23 | #13063300 | 1 | 2 | yes | — |
| 293 | C23 | #13063322 | 1 | 1 | yes | characteristic |
| 294 | Q8 | — | 4 | 1 | no | — |
| 295 | Q8 | — | 86 | 4 | no | — |
| 296 | Q8 | — | 86 | 2 | no | — |
| 297 | Q8 | — | 172 | 4 | no | — |
| 298 | Q8 | — | 172 | 2 | no | — |
| 299 | Q8 | — | 172 | 2 | no | — |
| 300 | Q8 | — | 172 | 1 | no | — |
| 301 | D4 | — | 4 | 2 | no | — |
| 302 | D4 | — | 4 | 1 | no | — |
| 303 | D4 | — | 86 | 4 | no | — |
| 304 | D4 | — | 86 | 2 | no | — |
| 305 | D4 | — | 172 | 4 | no | — |
| 306 | D4 | — | 172 | 2 | no | — |
| 307 | D4 | — | 172 | 2 | no | — |
| 308 | D4 | — | 172 | 1 | no | — |
| 309 | C2×C4 | — | 2 | 1 | no | — |
| 310 | C2×C4 | — | 2 | 1 | no | — |
| 311 | C2×C4 | — | 2 | 2 | no | — |
| 312 | C2×C4 | — | 2 | 2 | no | — |
| 313 | C2×C4 | — | 344 | 2 | no | — |
| 314 | C2×C4 | — | 344 | 1 | no | — |
| 315 | C2×C4 | — | 172 | 4 | no | — |
| 316 | C2×C4 | — | 172 | 2 | no | — |
| 317 | C2×C4 | — | 172 | 2 | no | — |
| 318 | C2×C4 | — | 172 | 2 | no | — |
| 319 | C2×C4 | — | 172 | 2 | no | — |
| 320 | C2×C4 | — | 172 | 1 | no | — |
| 321 | C2×C4 | — | 172 | 2 | no | — |
| 322 | C2×C4 | #13063295 | 1 | 2 | yes | — |
| 323 | C2×C4 | #13063295 | 1 | 1 | yes | characteristic |
| 324 | C2×C4 | #13063300 | 1 | 1 | yes | characteristic |
| 325 | C8 | — | 4 | 4 | no | — |
| 326 | C8 | — | 4 | 1 | no | — |
| 327 | C8 | — | 4 | 1 | no | — |
| 328 | C22 | — | 2 | 2 | no | — |
| 329 | C22 | — | 2 | 1 | no | — |
| 330 | C22 | — | 4 | 2 | no | — |
| 331 | C22 | — | 4 | 1 | no | — |
| 332 | C22 | — | 172 | 2 | no | — |
| 333 | C22 | — | 688 | 1 | no | — |
| 334 | C22 | — | 688 | 2 | no | — |
| 335 | C22 | #14582809 | 1 | 1 | yes | characteristic |
| 336 | C4 | — | 2 | 2 | no | — |
| 337 | C4 | — | 2 | 1 | no | — |
| 338 | C4 | — | 344 | 2 | no | — |
| 339 | C4 | — | 344 | 2 | no | — |
| 340 | C4 | — | 172 | 2 | no | — |
| 341 | C4 | — | 688 | 1 | no | — |
| 342 | C4 | #14583087 | 1 | 1 | yes | characteristic |
| 343 | C4 | #14583087 | 1 | 1 | yes | characteristic |
| 344 | C2 | — | 2 | 1 | no | — |
| 345 | C2 | — | 4 | 1 | no | — |
| 346 | C2 | — | 4 | 2 | no | — |
| 347 | C2 | — | 344 | 2 | no | — |
| 348 | C2 | #19135722 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19145490 | C2 | semidirect |
| 3. #19136250 | C2 | semidirect |
| 5. C43×#1392 | C2 | semidirect |
| 174. #1392 | D43 | semidirect |
| 196. C43 | #13362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145490 | 2 |
| #19143976 | 2 |
| #19136250 | 2 |
| #19134558 | 2 |
| C43×#1392 | 2 |
| #13362 | 43 |