Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
5942 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 5942 conjugacy classes of subgroups — too many to draw. Only its 323 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 | C24×D172 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#14583052 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | #19142882 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19134527 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C43×#1779 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C25×D43 | — | 2 | 1 | no | — |
| 7 | C23×D172 | — | 2 | 24 | no | — |
| 8 | C23×D172 | — | 2 | 3 | no | — |
| 9 | C23×D172 | C22 | 1 | 6 | yes | — |
| 10 | C22×#10621873 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×#13063304 | C22 | 1 | 3 | yes | complemented |
| 12 | #14583052 | — | 2 | 24 | no | — |
| 13 | C2×#13063247 | C22 | 1 | 12 | yes | complemented |
| 14 | #14582772 | — | 2 | 3 | no | — |
| 15 | #14582759 | C22 | 1 | 3 | yes | complemented |
| 16 | #14582755 | — | 2 | 1 | no | — |
| 17 | C24×C4×C43 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C22⋊C8×C43 | C22 | 1 | 6 | yes | complemented |
| 19 | C24×D43 | — | 2 | 24 | no | — |
| 20 | C24×D43 | — | 2 | 6 | no | — |
| 21 | C24×D43 | — | 4 | 12 | no | — |
| 22 | C24×D43 | — | 4 | 4 | no | — |
| 23 | C22×Dic86 | C23 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×D172 | — | 2 | 24 | no | — |
| 25 | C22×D172 | — | 2 | 48 | no | — |
| 26 | C22×D172 | — | 2 | 128 | no | — |
| 27 | C22×D172 | — | 2 | 6 | no | — |
| 28 | C22×D172 | — | 2 | 12 | no | — |
| 29 | C22×D172 | — | 2 | 48 | no | — |
| 30 | C22×D172 | D4 | 1 | 24 | yes | — |
| 31 | C22×D172 | C23 | 1 | 4 | yes | — |
| 32 | C2×#10621873 | — | 2 | 24 | no | — |
| 33 | #13063304 | — | 2 | 12 | no | — |
| 34 | C2×C4⋊Dic43 | C23 | 1 | 3 | yes | complemented |
| 35 | C2×Dic43⋊C4 | — | 2 | 3 | no | — |
| 36 | C2×C22⋊Dic43 | — | 2 | 3 | no | — |
| 37 | C2×C22⋊Dic43 | — | 2 | 3 | no | — |
| 38 | #13063247 | — | 2 | 24 | no | — |
| 39 | C43⋊#95 | — | 2 | 3 | no | — |
| 40 | C25×C43 | D4 | 1 | 1 | yes | characteristic |
| 41 | C23×C4×C43 | — | 2 | 12 | no | — |
| 42 | C23×C4×C43 | D4 | 1 | 3 | yes | — |
| 43 | C23×C4×C43 | C23 | 1 | 3 | yes | — |
| 44 | C22×C8×C43 | C23 | 1 | 4 | yes | complemented |
| 45 | C22⋊C8×C43 | — | 2 | 12 | no | — |
| 46 | C24×C43 | — | 2 | 6 | no | — |
| 47 | C24×C43 | — | 2 | 6 | no | — |
| 48 | C24×C43 | SD16 | 1 | 4 | yes | complemented |
| 49 | C24×C43 | C2×D4 | 1 | 3 | yes | — |
| 50 | C23×D43 | — | 2 | 64 | no | — |
| 51 | C23×D43 | — | 2 | 48 | no | — |
| 52 | C23×D43 | — | 2 | 24 | no | — |
| 53 | C23×D43 | — | 2 | 4 | no | — |
| 54 | C23×D43 | — | 4 | 96 | no | — |
| 55 | C23×D43 | — | 4 | 24 | no | — |
| 56 | C23×D43 | — | 4 | 96 | no | — |
| 57 | C23×D43 | — | 4 | 12 | no | — |
| 58 | C23×D43 | — | 4 | 12 | no | — |
| 59 | C22×C4×C43 | — | 2 | 32 | no | — |
| 60 | C22×C4×C43 | — | 2 | 12 | no | — |
| 61 | C22×C4×C43 | — | 2 | 12 | no | — |
| 62 | C22×C4×C43 | — | 2 | 6 | no | — |
| 63 | C22×C4×C43 | C2×D4 | 1 | 12 | yes | — |
| 64 | C22×C4×C43 | C2×D4 | 1 | 3 | yes | — |
| 65 | C22×C4×C43 | C24 | 1 | 1 | yes | characteristic |
| 66 | C22×Dic43 | — | 2 | 3 | no | — |
| 67 | C22×Dic43 | — | 2 | 1 | no | — |
| 68 | C2×D172 | — | 2 | 192 | no | — |
| 69 | C2×D172 | — | 2 | 96 | no | — |
| 70 | C2×D172 | — | 2 | 48 | no | — |
| 71 | C2×D172 | — | 2 | 24 | no | — |
| 72 | C2×D172 | — | 2 | 12 | no | — |
| 73 | C2×D172 | — | 2 | 96 | no | — |
| 74 | C2×D172 | C2×D4 | 1 | 24 | yes | — |
| 75 | C2×Dic86 | — | 2 | 6 | no | — |
| 76 | C2×C8×C43 | — | 2 | 12 | no | — |
| 77 | C22⋊Dic43 | — | 4 | 6 | no | — |
| 78 | C22⋊Dic43 | — | 4 | 6 | no | — |
| 79 | C4⋊Dic43 | — | 2 | 6 | no | — |
| 80 | Dic43⋊C4 | — | 4 | 6 | no | — |
| 81 | #10621873 | — | 4 | 16 | no | — |
| 82 | C23×C43 | — | 2 | 8 | no | — |
| 83 | C23×C43 | — | 2 | 24 | no | — |
| 84 | C23×C43 | — | 2 | 6 | no | — |
| 85 | C23×C43 | — | 2 | 6 | no | — |
| 86 | C23×C43 | — | 2 | 24 | no | — |
| 87 | C23×C43 | #120 | 1 | 6 | yes | — |
| 88 | C23×C43 | C2×SD16 | 1 | 6 | yes | — |
| 89 | C23×C43 | AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 90 | C23×C43 | C22×D4 | 1 | 1 | yes | characteristic |
| 91 | C22×D43 | — | 2 | 96 | no | — |
| 92 | C22×D43 | — | 2 | 24 | no | — |
| 93 | C22×D43 | — | 4 | 256 | no | — |
| 94 | C22×D43 | — | 4 | 96 | no | — |
| 95 | C22×D43 | — | 4 | 48 | no | — |
| 96 | C22×D43 | — | 4 | 96 | no | — |
| 97 | C22×D43 | — | 4 | 4 | no | — |
| 98 | C22×D43 | — | 4 | 12 | no | — |
| 99 | C22×D43 | — | 4 | 48 | no | — |
| 100 | C2×C4×C43 | — | 2 | 24 | no | — |
| 101 | C2×C4×C43 | — | 2 | 6 | no | — |
| 102 | C2×C4×C43 | — | 2 | 24 | no | — |
| 103 | C2×C4×C43 | #120 | 1 | 6 | yes | — |
| 104 | C2×C4×C43 | C22×D4 | 1 | 6 | yes | — |
| 105 | C2×Dic43 | — | 4 | 3 | no | — |
| 106 | C2×Dic43 | — | 4 | 3 | no | — |
| 107 | C2×Dic43 | — | 4 | 6 | no | — |
| 108 | D172 | — | 2 | 96 | no | — |
| 109 | D172 | — | 2 | 24 | no | — |
| 110 | D172 | #120 | 1 | 16 | yes | — |
| 111 | Dic86 | — | 4 | 4 | no | — |
| 112 | C8×C43 | — | 4 | 4 | no | — |
| 113 | #32881 | — | 43 | 1 | no | maximal, Sylow |
| 114 | C22×C43 | — | 2 | 32 | no | — |
| 115 | C22×C43 | — | 2 | 6 | no | — |
| 116 | C22×C43 | — | 2 | 12 | no | — |
| 117 | C22×C43 | — | 2 | 6 | no | — |
| 118 | C22×C43 | — | 2 | 12 | no | — |
| 119 | C22×C43 | #450 | 1 | 12 | yes | complemented |
| 120 | C22×C43 | C2×#120 | 1 | 3 | yes | — |
| 121 | C22×C43 | C22×SD16 | 1 | 1 | yes | characteristic |
| 122 | C22×C43 | C2×AGL(1,ℤ/8) | 1 | 3 | yes | — |
| 123 | C2×D43 | — | 2 | 16 | no | — |
| 124 | C2×D43 | — | 4 | 192 | no | — |
| 125 | C2×D43 | — | 4 | 24 | no | — |
| 126 | C2×D43 | — | 4 | 24 | no | — |
| 127 | C4×C43 | — | 2 | 6 | no | — |
| 128 | C4×C43 | C2×#120 | 1 | 4 | yes | — |
| 129 | Dic43 | — | 8 | 1 | no | — |
| 130 | Dic43 | — | 8 | 3 | no | — |
| 131 | C24×D4 | — | 43 | 1 | no | — |
| 132 | C2×#450 | — | 43 | 6 | no | — |
| 133 | #2848 | — | 43 | 1 | no | — |
| 134 | #1786 | — | 43 | 6 | no | — |
| 135 | #1779 | D43 | 1 | 1 | yes | characteristic, complemented |
| 136 | C2×C43 | — | 2 | 12 | no | — |
| 137 | C2×C43 | #2846 | 1 | 1 | yes | characteristic |
| 138 | C2×C43 | C2×#450 | 1 | 3 | yes | — |
| 139 | C2×C43 | #3003 | 1 | 3 | yes | — |
| 140 | D43 | — | 4 | 16 | no | — |
| 141 | C26 | — | 86 | 1 | no | — |
| 142 | C23×D4 | — | 43 | 6 | no | — |
| 143 | C23×D4 | — | 86 | 24 | no | — |
| 144 | C23×D4 | — | 86 | 3 | no | — |
| 145 | C24×C4 | C2×D43 | 1 | 1 | yes | characteristic |
| 146 | C22×SD16 | — | 43 | 4 | no | — |
| 147 | C2×C22⋊Q8 | — | 43 | 3 | no | — |
| 148 | #450 | — | 86 | 24 | no | — |
| 149 | C2×#102 | — | 43 | 12 | no | — |
| 150 | C2×C22⋊C8 | C2×D43 | 1 | 6 | yes | complemented |
| 151 | #385 | — | 86 | 3 | no | — |
| 152 | #380 | — | 43 | 3 | no | — |
| 153 | #379 | — | 86 | 1 | no | — |
| 154 | C43 | #32881 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 155 | C25 | — | 86 | 24 | no | — |
| 156 | C25 | — | 86 | 6 | no | — |
| 157 | C25 | — | 172 | 12 | no | — |
| 158 | C25 | — | 172 | 4 | no | — |
| 159 | C25 | D172 | 1 | 1 | yes | characteristic |
| 160 | C22×Q8 | — | 43 | 1 | no | — |
| 161 | C22×D4 | — | 43 | 24 | no | — |
| 162 | C22×D4 | — | 43 | 4 | no | — |
| 163 | C22×D4 | — | 86 | 48 | no | — |
| 164 | C22×D4 | — | 86 | 128 | no | — |
| 165 | C22×D4 | — | 86 | 24 | no | — |
| 166 | C22×D4 | — | 86 | 48 | no | — |
| 167 | C22×D4 | — | 86 | 6 | no | — |
| 168 | C22×D4 | — | 86 | 12 | no | — |
| 169 | C23×C4 | — | 2 | 12 | no | — |
| 170 | C23×C4 | D172 | 1 | 3 | yes | — |
| 171 | C23×C4 | C22×D43 | 1 | 3 | yes | — |
| 172 | C2×SD16 | — | 86 | 24 | no | — |
| 173 | C22×C8 | C22×D43 | 1 | 4 | yes | complemented |
| 174 | C22⋊Q8 | — | 86 | 12 | no | — |
| 175 | C2×C4⋊C4 | — | 43 | 3 | no | — |
| 176 | C2×C4⋊C4 | — | 86 | 3 | no | — |
| 177 | C2×C22⋊C4 | — | 86 | 3 | no | — |
| 178 | C2×C22⋊C4 | — | 86 | 3 | no | — |
| 179 | #102 | — | 86 | 24 | no | — |
| 180 | C22⋊C8 | — | 2 | 12 | no | — |
| 181 | #95 | — | 86 | 3 | no | — |
| 182 | C24 | — | 2 | 6 | no | — |
| 183 | C24 | — | 2 | 6 | no | — |
| 184 | C24 | — | 86 | 64 | no | — |
| 185 | C24 | — | 86 | 48 | no | — |
| 186 | C24 | — | 86 | 24 | no | — |
| 187 | C24 | — | 86 | 4 | no | — |
| 188 | C24 | — | 172 | 96 | no | — |
| 189 | C24 | — | 172 | 96 | no | — |
| 190 | C24 | — | 172 | 24 | no | — |
| 191 | C24 | — | 172 | 12 | no | — |
| 192 | C24 | — | 172 | 12 | no | — |
| 193 | C24 | #10621873 | 1 | 4 | yes | complemented |
| 194 | C24 | C2×D172 | 1 | 3 | yes | — |
| 195 | C2×Q8 | — | 86 | 6 | no | — |
| 196 | C2×D4 | — | 43 | 24 | no | — |
| 197 | C2×D4 | — | 86 | 96 | no | — |
| 198 | C2×D4 | — | 86 | 192 | no | — |
| 199 | C2×D4 | — | 86 | 48 | no | — |
| 200 | C2×D4 | — | 86 | 96 | no | — |
| 201 | C2×D4 | — | 86 | 24 | no | — |
| 202 | C2×D4 | — | 86 | 12 | no | — |
| 203 | C22×C4 | — | 2 | 32 | no | — |
| 204 | C22×C4 | — | 2 | 6 | no | — |
| 205 | C22×C4 | — | 2 | 12 | no | — |
| 206 | C22×C4 | — | 2 | 12 | no | — |
| 207 | C22×C4 | — | 86 | 3 | no | — |
| 208 | C22×C4 | — | 86 | 1 | no | — |
| 209 | C22×C4 | C2×D172 | 1 | 3 | yes | — |
| 210 | C22×C4 | D4×D43 | 1 | 12 | yes | — |
| 211 | C22×C4 | C23×D43 | 1 | 1 | yes | characteristic |
| 212 | SD16 | — | 172 | 16 | no | — |
| 213 | C2×C8 | — | 2 | 12 | no | — |
| 214 | C4⋊C4 | — | 86 | 6 | no | — |
| 215 | C4⋊C4 | — | 172 | 6 | no | — |
| 216 | C22⋊C4 | — | 172 | 6 | no | — |
| 217 | C22⋊C4 | — | 172 | 6 | no | — |
| 218 | C23 | — | 2 | 8 | no | — |
| 219 | C23 | — | 2 | 24 | no | — |
| 220 | C23 | — | 2 | 24 | no | — |
| 221 | C23 | — | 2 | 6 | no | — |
| 222 | C23 | — | 2 | 6 | no | — |
| 223 | C23 | — | 86 | 96 | no | — |
| 224 | C23 | — | 86 | 24 | no | — |
| 225 | C23 | — | 172 | 256 | no | — |
| 226 | C23 | — | 172 | 96 | no | — |
| 227 | C23 | — | 172 | 48 | no | — |
| 228 | C23 | — | 172 | 96 | no | — |
| 229 | C23 | — | 172 | 48 | no | — |
| 230 | C23 | — | 172 | 4 | no | — |
| 231 | C23 | — | 172 | 12 | no | — |
| 232 | C23 | #13063295 | 1 | 6 | yes | — |
| 233 | C23 | C2×#10621873 | 1 | 6 | yes | — |
| 234 | C23 | #13063353 | 1 | 6 | yes | — |
| 235 | C23 | C22×D172 | 1 | 1 | yes | characteristic |
| 236 | Q8 | — | 172 | 4 | no | — |
| 237 | D4 | — | 43 | 16 | no | — |
| 238 | D4 | — | 86 | 96 | no | — |
| 239 | D4 | — | 86 | 24 | no | — |
| 240 | C2×C4 | — | 2 | 24 | no | — |
| 241 | C2×C4 | — | 2 | 6 | no | — |
| 242 | C2×C4 | — | 2 | 24 | no | — |
| 243 | C2×C4 | — | 172 | 3 | no | — |
| 244 | C2×C4 | — | 172 | 3 | no | — |
| 245 | C2×C4 | — | 172 | 6 | no | — |
| 246 | C2×C4 | #13063295 | 1 | 6 | yes | — |
| 247 | C2×C4 | C2×D4×D43 | 1 | 6 | yes | — |
| 248 | C8 | — | 4 | 4 | no | — |
| 249 | C22 | — | 2 | 32 | no | — |
| 250 | C22 | — | 2 | 12 | no | — |
| 251 | C22 | — | 2 | 6 | no | — |
| 252 | C22 | — | 2 | 12 | no | — |
| 253 | C22 | — | 2 | 6 | no | — |
| 254 | C22 | — | 86 | 16 | no | — |
| 255 | C22 | — | 172 | 192 | no | — |
| 256 | C22 | — | 172 | 24 | no | — |
| 257 | C22 | — | 172 | 24 | no | — |
| 258 | C22 | #14583052 | 1 | 12 | yes | complemented |
| 259 | C22 | C2×#13063295 | 1 | 3 | yes | — |
| 260 | C22 | C22×#10621873 | 1 | 1 | yes | characteristic |
| 261 | C22 | C2×#13063353 | 1 | 3 | yes | — |
| 262 | C4 | — | 2 | 6 | no | — |
| 263 | C4 | — | 344 | 3 | no | — |
| 264 | C4 | — | 344 | 1 | no | — |
| 265 | C4 | #120×D43 | 1 | 4 | yes | — |
| 266 | C2 | — | 2 | 12 | no | — |
| 267 | C2 | — | 172 | 16 | no | — |
| 268 | C2 | #19142873 | 1 | 1 | yes | characteristic |
| 269 | C2 | C2×#14583052 | 1 | 3 | yes | — |
| 270 | C2 | #19143825 | 1 | 3 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#14583052 | C2 | semidirect |
| 3. #19142882 | C2 | semidirect |
| 4. #19134527 | C2 | semidirect |
| 5. C43×#1779 | C2 | semidirect |
| 10. C22×#10621873 | C22 | semidirect |
| 11. C2×#13063304 | C22 | semidirect |
| 13. C2×#13063247 | C22 | semidirect |
| 15. #14582759 | C22 | semidirect |
| 18. C2×C22⋊C8×C43 | C22 | semidirect |
| 23. C22×Dic86 | C23 | semidirect |
| 34. C2×C4⋊Dic43 | C23 | semidirect |
| 44. C22×C8×C43 | C23 | semidirect |
| 48. C24×C43 | SD16 | semidirect |
| 119. C22×C43 | #450 | semidirect |
| 135. #1779 | D43 | semidirect |
| 150. C2×C22⋊C8 | C2×D43 | semidirect |
| 154. C43 | #32881 | semidirect |
| 173. C22×C8 | C22×D43 | semidirect |
| 193. C24 | #10621873 | semidirect |
| 258. C22 | #14583052 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D172 | 2 |
| C2×#14583052 | 2 |
| #19142882 | 2 |
| #19134527 | 2 |
| C43×#1779 | 2 |
| #32881 | 43 |