Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
374 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 374 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 | #19146034 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #19136509 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #19135851 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #19132611 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C43×#1323 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C22×D344 | C22 | 1 | 1 | yes | characteristic |
| 7 | #14583504 | — | 2 | 1 | no | — |
| 8 | C2×D688 | — | 2 | 2 | no | — |
| 9 | #14583200 | — | 2 | 2 | no | — |
| 10 | #14583152 | — | 2 | 1 | no | — |
| 11 | #14583135 | C22 | 1 | 2 | yes | — |
| 12 | #14583095 | — | 2 | 2 | no | — |
| 13 | #14582903 | — | 2 | 1 | no | — |
| 14 | C2×#13063241 | — | 2 | 1 | no | — |
| 15 | #14582701 | — | 2 | 2 | no | — |
| 16 | #14582664 | C22 | 1 | 1 | yes | characteristic |
| 17 | C43×#424 | C22 | 1 | 1 | yes | characteristic |
| 18 | C43×C22⋊C16 | C22 | 1 | 2 | yes | — |
| 19 | C22×D172 | — | 2 | 1 | no | — |
| 20 | C2×D344 | — | 2 | 2 | no | — |
| 21 | C2×D344 | — | 2 | 1 | no | — |
| 22 | C2×D344 | — | 4 | 2 | no | — |
| 23 | C2×D344 | D4 | 1 | 2 | yes | — |
| 24 | C2×#10621877 | — | 2 | 1 | no | — |
| 25 | #13063322 | — | 2 | 1 | no | — |
| 26 | #13063317 | — | 2 | 1 | no | — |
| 27 | #13063310 | — | 4 | 2 | no | — |
| 28 | #13063299 | — | 2 | 2 | no | — |
| 29 | #13063298 | — | 4 | 2 | no | — |
| 30 | C4×D172 | — | 2 | 2 | no | — |
| 31 | D688 | — | 4 | 4 | no | — |
| 32 | #13063259 | D4 | 1 | 2 | yes | — |
| 33 | #13063257 | — | 2 | 1 | no | — |
| 34 | #13063247 | — | 2 | 2 | no | — |
| 35 | #13063247 | — | 2 | 2 | no | — |
| 36 | #13063245 | — | 4 | 2 | no | — |
| 37 | #13063241 | — | 4 | 2 | no | — |
| 38 | C2×M16×C43 | D4 | 1 | 1 | yes | characteristic |
| 39 | C22×C8×C43 | C23 | 1 | 1 | yes | characteristic |
| 40 | #117×C43 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×C16×C43 | — | 2 | 2 | no | — |
| 42 | C4⋊C8×C43 | — | 2 | 2 | no | — |
| 43 | C23×D43 | — | 4 | 1 | no | — |
| 44 | C22×C4×C43 | C2×D4 | 1 | 1 | yes | characteristic |
| 45 | C2×C22⋊D43 | — | 4 | 2 | no | — |
| 46 | C2×D172 | — | 2 | 2 | no | — |
| 47 | C2×D172 | — | 2 | 2 | no | — |
| 48 | C2×D172 | — | 4 | 1 | no | — |
| 49 | C2×D172 | — | 4 | 2 | no | — |
| 50 | C2×D172 | — | 4 | 1 | no | — |
| 51 | C2×D172 | — | 4 | 1 | no | — |
| 52 | C2×D172 | — | 4 | 1 | no | — |
| 53 | C2×D172 | — | 4 | 1 | no | — |
| 54 | C2×C4×D43 | — | 4 | 2 | no | — |
| 55 | M16×C43 | — | 4 | 1 | no | — |
| 56 | C2×C8×C43 | — | 2 | 1 | no | — |
| 57 | C2×C8×C43 | — | 4 | 1 | no | — |
| 58 | C2×C8×C43 | C2×D4 | 1 | 2 | yes | — |
| 59 | C4⋊C4×C43 | D8 | 1 | 2 | yes | — |
| 60 | C22⋊C4×C43 | — | 2 | 1 | no | — |
| 61 | C42×C43 | — | 2 | 1 | no | — |
| 62 | (C2×D43)⋊C4 | — | 4 | 2 | no | — |
| 63 | (C2×D43)⋊C4 | — | 4 | 2 | no | — |
| 64 | C4⋊Dic43 | — | 2 | 2 | no | — |
| 65 | Dic43⋊C4 | — | 4 | 2 | no | — |
| 66 | #10621877 | — | 4 | 1 | no | — |
| 67 | #10621877 | — | 4 | 1 | no | — |
| 68 | C2×C43⋊C8 | — | 4 | 1 | no | — |
| 69 | D344 | — | 2 | 4 | no | — |
| 70 | D344 | — | 4 | 2 | no | — |
| 71 | D344 | — | 4 | 2 | no | — |
| 72 | D344 | — | 8 | 1 | no | — |
| 73 | C16×C43 | — | 4 | 2 | no | — |
| 74 | C23×C43 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 75 | C22×D43 | — | 4 | 2 | no | — |
| 76 | C22×D43 | — | 4 | 2 | no | — |
| 77 | C22×D43 | — | 8 | 1 | no | — |
| 78 | C22×D43 | — | 8 | 1 | no | — |
| 79 | C22×D43 | — | 16 | 2 | no | — |
| 80 | C2×C4×C43 | — | 2 | 1 | no | — |
| 81 | C2×C4×C43 | — | 2 | 1 | no | — |
| 82 | C2×C4×C43 | — | 2 | 2 | no | — |
| 83 | C2×C4×C43 | #120 | 1 | 1 | yes | characteristic |
| 84 | C2×C4×C43 | C2×D8 | 1 | 1 | yes | characteristic |
| 85 | C22⋊D43 | — | 16 | 2 | no | — |
| 86 | C2×Dic43 | — | 4 | 2 | no | — |
| 87 | D172 | — | 4 | 2 | no | — |
| 88 | D172 | — | 4 | 2 | no | — |
| 89 | D172 | — | 4 | 2 | no | — |
| 90 | D172 | — | 4 | 2 | no | — |
| 91 | D172 | — | 8 | 1 | no | — |
| 92 | D172 | — | 8 | 1 | no | — |
| 93 | D172 | — | 16 | 2 | no | — |
| 94 | C4×D43 | — | 16 | 2 | no | — |
| 95 | C8×C43 | — | 2 | 2 | no | — |
| 96 | C8×C43 | — | 4 | 1 | no | — |
| 97 | C43⋊C8 | — | 8 | 1 | no | — |
| 98 | #12164 | — | 43 | 1 | no | maximal, Sylow |
| 99 | C22×C43 | — | 2 | 1 | no | — |
| 100 | C22×C43 | — | 2 | 2 | no | — |
| 101 | C22×C43 | #447 | 1 | 1 | yes | characteristic |
| 102 | C2×D43 | — | 8 | 2 | no | — |
| 103 | C2×D43 | — | 8 | 2 | no | — |
| 104 | C2×D43 | — | 8 | 2 | no | — |
| 105 | C2×D43 | — | 8 | 2 | no | — |
| 106 | C2×D43 | — | 16 | 2 | no | — |
| 107 | C2×D43 | — | 16 | 2 | no | — |
| 108 | C2×D43 | — | 16 | 2 | no | — |
| 109 | C4×C43 | — | 2 | 1 | no | — |
| 110 | C4×C43 | — | 4 | 2 | no | — |
| 111 | C4×C43 | #454 | 1 | 1 | yes | characteristic |
| 112 | C4×C43 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 113 | Dic43 | — | 8 | 2 | no | — |
| 114 | #3259 | — | 43 | 1 | no | — |
| 115 | #2184 | — | 43 | 2 | no | — |
| 116 | #2045 | — | 43 | 1 | no | — |
| 117 | #1349 | — | 43 | 2 | no | — |
| 118 | #1323 | D43 | 1 | 1 | yes | characteristic, complemented |
| 119 | C2×C43 | — | 4 | 1 | no | — |
| 120 | C2×C43 | #1598 | 1 | 1 | yes | characteristic |
| 121 | C2×C43 | #2192 | 1 | 2 | yes | — |
| 122 | D43 | — | 16 | 2 | no | — |
| 123 | D43 | — | 16 | 2 | no | — |
| 124 | C22×D8 | — | 43 | 1 | no | — |
| 125 | #540 | — | 86 | 1 | no | — |
| 126 | C2×D16 | — | 86 | 2 | no | — |
| 127 | #478 | — | 86 | 2 | no | — |
| 128 | #469 | — | 86 | 1 | no | — |
| 129 | #466 | — | 43 | 2 | no | — |
| 130 | #459 | — | 86 | 2 | no | — |
| 131 | #424 | C2×D43 | 1 | 1 | yes | characteristic |
| 132 | #418 | — | 86 | 1 | no | — |
| 133 | C2×#100 | — | 86 | 1 | no | — |
| 134 | #357 | — | 86 | 2 | no | — |
| 135 | C22⋊C16 | C2×D43 | 1 | 2 | yes | — |
| 136 | #341 | — | 43 | 1 | no | — |
| 137 | C43 | #12164 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 138 | C22×D4 | — | 86 | 1 | no | — |
| 139 | C2×D8 | — | 43 | 2 | no | — |
| 140 | C2×D8 | — | 86 | 1 | no | — |
| 141 | C2×D8 | — | 86 | 2 | no | — |
| 142 | C2×D8 | — | 172 | 2 | no | — |
| 143 | C2×M16 | — | 86 | 1 | no | — |
| 144 | C2×M16 | D172 | 1 | 1 | yes | characteristic |
| 145 | C22×C8 | C22×D43 | 1 | 1 | yes | characteristic |
| 146 | #127 | — | 86 | 1 | no | — |
| 147 | #125 | — | 86 | 1 | no | — |
| 148 | #123 | — | 172 | 2 | no | — |
| 149 | #121 | — | 86 | 2 | no | — |
| 150 | #121 | — | 172 | 2 | no | — |
| 151 | C4×D4 | — | 86 | 2 | no | — |
| 152 | #117 | D172 | 1 | 1 | yes | characteristic |
| 153 | D16 | — | 172 | 4 | no | — |
| 154 | C2×C16 | — | 2 | 2 | no | — |
| 155 | #107 | — | 43 | 2 | no | — |
| 156 | #106 | — | 86 | 1 | no | — |
| 157 | C4⋊C8 | — | 2 | 2 | no | — |
| 158 | #102 | — | 86 | 2 | no | — |
| 159 | #102 | — | 86 | 2 | no | — |
| 160 | #102 | — | 172 | 2 | no | — |
| 161 | #100 | — | 172 | 2 | no | — |
| 162 | C24 | — | 172 | 1 | no | — |
| 163 | C2×D4 | — | 86 | 2 | no | — |
| 164 | C2×D4 | — | 86 | 2 | no | — |
| 165 | C2×D4 | — | 172 | 1 | no | — |
| 166 | C2×D4 | — | 172 | 1 | no | — |
| 167 | C2×D4 | — | 172 | 1 | no | — |
| 168 | C2×D4 | — | 172 | 2 | no | — |
| 169 | C2×D4 | — | 172 | 2 | no | — |
| 170 | C2×D4 | — | 172 | 1 | no | — |
| 171 | C2×D4 | — | 172 | 1 | no | — |
| 172 | C22×C4 | — | 172 | 2 | no | — |
| 173 | C22×C4 | C2×D172 | 1 | 1 | yes | characteristic |
| 174 | D8 | — | 86 | 4 | no | — |
| 175 | D8 | — | 344 | 1 | no | — |
| 176 | D8 | — | 172 | 2 | no | — |
| 177 | D8 | — | 172 | 2 | no | — |
| 178 | M16 | — | 4 | 1 | no | — |
| 179 | M16 | — | 172 | 1 | no | — |
| 180 | M16 | — | 172 | 1 | no | — |
| 181 | C2×C8 | — | 2 | 1 | no | — |
| 182 | C2×C8 | — | 4 | 1 | no | — |
| 183 | C2×C8 | — | 172 | 1 | no | — |
| 184 | C2×C8 | D4×D43 | 1 | 2 | yes | — |
| 185 | C4⋊C4 | — | 86 | 2 | no | — |
| 186 | C4⋊C4 | — | 172 | 2 | no | — |
| 187 | C4⋊C4 | D344 | 1 | 2 | yes | — |
| 188 | C22⋊C4 | — | 2 | 1 | no | — |
| 189 | C22⋊C4 | — | 172 | 2 | no | — |
| 190 | C22⋊C4 | — | 172 | 2 | no | — |
| 191 | C42 | — | 2 | 1 | no | — |
| 192 | C16 | — | 4 | 2 | no | — |
| 193 | C23 | — | 344 | 1 | no | — |
| 194 | C23 | — | 344 | 1 | no | — |
| 195 | C23 | — | 172 | 2 | no | — |
| 196 | C23 | — | 172 | 2 | no | — |
| 197 | C23 | — | 688 | 2 | no | — |
| 198 | C23 | #13063353 | 1 | 1 | yes | characteristic |
| 199 | D4 | — | 344 | 1 | no | — |
| 200 | D4 | — | 344 | 1 | no | — |
| 201 | D4 | — | 172 | 2 | no | — |
| 202 | D4 | — | 172 | 2 | no | — |
| 203 | D4 | — | 172 | 2 | no | — |
| 204 | D4 | — | 172 | 2 | no | — |
| 205 | D4 | — | 688 | 2 | no | — |
| 206 | D4 | — | 688 | 2 | no | — |
| 207 | C2×C4 | — | 2 | 1 | no | — |
| 208 | C2×C4 | — | 2 | 1 | no | — |
| 209 | C2×C4 | — | 2 | 2 | no | — |
| 210 | C2×C4 | — | 172 | 2 | no | — |
| 211 | C2×C4 | — | 688 | 2 | no | — |
| 212 | C2×C4 | #13063295 | 1 | 1 | yes | characteristic |
| 213 | C2×C4 | C2×D344 | 1 | 1 | yes | characteristic |
| 214 | C8 | — | 2 | 2 | no | — |
| 215 | C8 | — | 4 | 1 | no | — |
| 216 | C8 | — | 344 | 1 | no | — |
| 217 | C22 | — | 2 | 2 | no | — |
| 218 | C22 | — | 2 | 1 | no | — |
| 219 | C22 | — | 344 | 2 | no | — |
| 220 | C22 | — | 344 | 2 | no | — |
| 221 | C22 | — | 344 | 2 | no | — |
| 222 | C22 | — | 344 | 2 | no | — |
| 223 | C22 | — | 688 | 2 | no | — |
| 224 | C22 | — | 688 | 2 | no | — |
| 225 | C22 | — | 688 | 2 | no | — |
| 226 | C22 | #14583035 | 1 | 1 | yes | characteristic |
| 227 | C4 | — | 2 | 1 | no | — |
| 228 | C4 | — | 4 | 2 | no | — |
| 229 | C4 | — | 344 | 2 | no | — |
| 230 | C4 | #14583074 | 1 | 1 | yes | characteristic |
| 231 | C4 | #14583087 | 1 | 1 | yes | characteristic |
| 232 | C2 | — | 4 | 1 | no | — |
| 233 | C2 | — | 688 | 2 | no | — |
| 234 | C2 | — | 688 | 2 | no | — |
| 235 | C2 | #19133532 | 1 | 1 | yes | characteristic |
| 236 | C2 | #19136554 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19146034 | C2 | semidirect |
| 2. #19136509 | C2 | semidirect |
| 3. #19135851 | C2 | semidirect |
| 4. #19132611 | C2 | semidirect |
| 5. C43×#1323 | C2 | semidirect |
| 118. #1323 | D43 | semidirect |
| 137. C43 | #12164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19146034 | 2 |
| #19136509 | 2 |
| #19135851 | 2 |
| #19132611 | 2 |
| C43×#1323 | 2 |
| #12164 | 43 |