← #14267698
Subgroups — #14267698
Order 1792.
59452 conjugacy classes of subgroups.
The subgroup lattice has 250 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C2×C7×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11744566 | C2 | 1 | 16 | yes | maximal, complemented |
| 3 | D7×#585 | C2 | 1 | 32 | yes | maximal, complemented |
| 4 | #11744564 | C2 | 1 | 16 | yes | maximal, complemented |
| 5 | #11744563 | C2 | 1 | 12 | yes | maximal, complemented |
| 6 | #11744560 | C2 | 1 | 20 | yes | maximal, complemented |
| 7 | C2×#90616 | C2 | 1 | 30 | yes | maximal, complemented |
| 8 | C7×#585 | C22 | 1 | 16 | yes | complemented |
| 9 | C7×#585 | C22 | 1 | 16 | yes | complemented |
| 10 | C2×C7×2−1+4 | C22 | 1 | 6 | yes | complemented |
| 11 | C2×C7×H(5,𝔽2) | C22 | 1 | 10 | yes | complemented |
| 12 | C22×C7×#41 | C22 | 1 | 15 | yes | complemented |
| 13 | #90620 | C22 | 1 | 192 | yes | complemented |
| 14 | D7×2−1+4 | C22 | 1 | 192 | yes | complemented |
| 15 | #90618 | C22 | 1 | 320 | yes | complemented |
| 16 | D7×H(5,𝔽2) | C22 | 1 | 320 | yes | complemented |
| 17 | #90616 | C22 | 1 | 80 | yes | complemented |
| 18 | #90616 | C22 | 1 | 240 | yes | complemented |
| 19 | #90616 | C22 | 1 | 240 | yes | complemented |
| 20 | #90616 | C22 | 1 | 240 | yes | complemented |
| 21 | C2×#6554 | C22 | 1 | 120 | yes | complemented |
| 22 | C2×#6553 | C22 | 1 | 120 | yes | complemented |
| 23 | C2×D7×#41 | C22 | 1 | 240 | yes | complemented |
| 24 | C2×#6551 | C22 | 1 | 60 | yes | complemented |
| 25 | C2×#6548 | C22 | 1 | 180 | yes | complemented |
| 26 | C22×#1157 | C22 | 1 | 60 | yes | complemented |
| 27 | #63103 | — | 7 | 1 | no | maximal, Sylow |
| 28 | C7×2−1+4 | C23 | 1 | 96 | yes | complemented |
| 29 | C7×H(5,𝔽2) | C23 | 1 | 160 | yes | complemented |
| 30 | C2×C7×#41 | C23 | 1 | 20 | yes | complemented |
| 31 | C2×C7×#41 | C23 | 1 | 60 | yes | complemented |
| 32 | C2×C7×#41 | C23 | 1 | 120 | yes | complemented |
| 33 | C2×C7×#41 | C23 | 1 | 120 | yes | complemented |
| 34 | C22×C7×Q8 | C23 | 1 | 15 | yes | complemented |
| 35 | C22×C7×D4 | C23 | 1 | 45 | yes | complemented |
| 36 | C23×C4×C7 | C23 | 1 | 15 | yes | complemented |
| 37 | C22×C22⋊D7 | C23 | 1 | 120 | yes | complemented |
| 38 | #6554 | C23 | 1 | 320 | yes | complemented |
| 39 | #6554 | C23 | 1 | 960 | yes | complemented |
| 40 | #6553 | C23 | 1 | 320 | yes | complemented |
| 41 | #6553 | C23 | 1 | 960 | yes | complemented |
| 42 | D7×#41 | C23 | 1 | 640 | yes | complemented |
| 43 | D7×#41 | C23 | 1 | 1920 | yes | complemented |
| 44 | #6551 | C23 | 1 | 160 | yes | complemented |
| 45 | #6551 | C23 | 1 | 480 | yes | complemented |
| 46 | C2×#1161 | C23 | 1 | 240 | yes | complemented |
| 47 | C2×Q8×D7 | C23 | 1 | 240 | yes | complemented |
| 48 | #6548 | C23 | 1 | 480 | yes | complemented |
| 49 | #6548 | C23 | 1 | 1440 | yes | complemented |
| 50 | C2×#1159 | C23 | 1 | 720 | yes | complemented |
| 51 | C2×D4×D7 | C23 | 1 | 720 | yes | complemented |
| 52 | C2×#1157 | C23 | 1 | 120 | yes | complemented |
| 53 | C2×#1157 | C23 | 1 | 360 | yes | complemented |
| 54 | C2×#1157 | C23 | 1 | 360 | yes | complemented |
| 55 | C2×#1157 | C23 | 1 | 360 | yes | complemented |
| 56 | C22×D28 | C23 | 1 | 60 | yes | complemented |
| 57 | C22×C4×D7 | C23 | 1 | 120 | yes | complemented |
| 58 | C22×Dic14 | C23 | 1 | 60 | yes | complemented |
| 59 | 2−1+6 | — | 7 | 16 | no | — |
| 60 | 2−1+6 | — | 7 | 12 | no | — |
| 61 | H(7,𝔽2) | — | 7 | 16 | no | — |
| 62 | H(7,𝔽2) | — | 7 | 20 | no | — |
| 63 | C2×#585 | — | 7 | 32 | no | — |
| 64 | C2×#585 | — | 7 | 30 | no | — |
| 65 | C2×#585 | D7 | 1 | 1 | yes | characteristic, complemented |
| 66 | C24×C7 | C24 | 1 | 15 | yes | — |
| 67 | C23×D7 | C24 | 1 | 120 | yes | — |
| 68 | C7×#41 | C24 | 1 | 80 | yes | — |
| 69 | C7×#41 | C24 | 1 | 480 | yes | — |
| 70 | C7×#41 | C24 | 1 | 80 | yes | — |
| 71 | C2×C7×Q8 | C24 | 1 | 120 | yes | — |
| 72 | C2×C7×Q8 | C24 | 1 | 20 | yes | — |
| 73 | C2×C7×D4 | C24 | 1 | 360 | yes | — |
| 74 | C2×C7×D4 | C24 | 1 | 60 | yes | — |
| 75 | C22×C4×C7 | C24 | 1 | 60 | yes | — |
| 76 | C22×C4×C7 | C24 | 1 | 60 | yes | — |
| 77 | C22×C4×C7 | C24 | 1 | 15 | yes | — |
| 78 | C22×C4×C7 | C24 | 1 | 45 | yes | — |
| 79 | C2×C22⋊D7 | C24 | 1 | 240 | yes | — |
| 80 | C2×C22⋊D7 | C24 | 1 | 720 | yes | — |
| 81 | C22×Dic7 | C24 | 1 | 120 | yes | — |
| 82 | #1161 | C24 | 1 | 640 | yes | — |
| 83 | Q8×D7 | C24 | 1 | 640 | yes | — |
| 84 | #1159 | C24 | 1 | 1920 | yes | — |
| 85 | D4×D7 | C24 | 1 | 1920 | yes | — |
| 86 | #1157 | C24 | 1 | 16 | yes | — |
| 87 | #1157 | C24 | 1 | 240 | yes | — |
| 88 | #1157 | C24 | 1 | 240 | yes | — |
| 89 | #1157 | C24 | 1 | 240 | yes | — |
| 90 | #1157 | C24 | 1 | 1440 | yes | — |
| 91 | C2×D28 | C24 | 1 | 120 | yes | — |
| 92 | C2×D28 | C24 | 1 | 360 | yes | — |
| 93 | C2×C4×D7 | C24 | 1 | 240 | yes | — |
| 94 | C2×C4×D7 | C24 | 1 | 720 | yes | — |
| 95 | C2×Dic14 | C24 | 1 | 120 | yes | — |
| 96 | C2×Dic14 | C24 | 1 | 360 | yes | — |
| 97 | #585 | — | 7 | 192 | no | — |
| 98 | #585 | — | 7 | 320 | no | — |
| 99 | #585 | — | 7 | 240 | no | — |
| 100 | #585 | — | 7 | 80 | no | — |
| 101 | #585 | — | 7 | 240 | no | — |
| 102 | #585 | — | 7 | 240 | no | — |
| 103 | #585 | C2×D7 | 1 | 16 | yes | complemented |
| 104 | #585 | C2×D7 | 1 | 16 | yes | complemented |
| 105 | C2×2−1+4 | — | 7 | 192 | no | — |
| 106 | C2×2−1+4 | — | 7 | 120 | no | — |
| 107 | C2×2−1+4 | — | 7 | 60 | no | — |
| 108 | C2×2−1+4 | C2×D7 | 1 | 6 | yes | complemented |
| 109 | C2×H(5,𝔽2) | — | 7 | 320 | no | — |
| 110 | C2×H(5,𝔽2) | — | 7 | 120 | no | — |
| 111 | C2×H(5,𝔽2) | — | 7 | 180 | no | — |
| 112 | C2×H(5,𝔽2) | C2×D7 | 1 | 10 | yes | complemented |
| 113 | C22×#41 | — | 7 | 240 | no | — |
| 114 | C22×#41 | — | 7 | 60 | no | — |
| 115 | C22×#41 | C2×D7 | 1 | 15 | yes | complemented |
| 116 | C23×C7 | — | 8 | 15 | no | — |
| 117 | C23×C7 | C25 | 1 | 60 | yes | — |
| 118 | C23×C7 | C25 | 1 | 15 | yes | — |
| 119 | C22×D7 | — | 8 | 120 | no | — |
| 120 | C22×D7 | C25 | 1 | 240 | yes | — |
| 121 | C7×Q8 | C25 | 1 | 80 | yes | — |
| 122 | C7×D4 | C25 | 1 | 240 | yes | — |
| 123 | C2×C4×C7 | C25 | 1 | 30 | yes | — |
| 124 | C2×C4×C7 | C25 | 1 | 180 | yes | — |
| 125 | C2×C4×C7 | C25 | 1 | 30 | yes | — |
| 126 | C2×C4×C7 | C25 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C7 | C25 | 1 | 15 | yes | — |
| 128 | C22⋊D7 | C25 | 1 | 32 | yes | — |
| 129 | C22⋊D7 | C25 | 1 | 480 | yes | — |
| 130 | C2×Dic7 | C25 | 1 | 240 | yes | — |
| 131 | D28 | C25 | 1 | 16 | yes | — |
| 132 | D28 | C25 | 1 | 240 | yes | — |
| 133 | C4×D7 | C25 | 1 | 32 | yes | — |
| 134 | C4×D7 | C25 | 1 | 480 | yes | — |
| 135 | Dic14 | C25 | 1 | 16 | yes | — |
| 136 | Dic14 | C25 | 1 | 240 | yes | — |
| 137 | 2−1+4 | — | 7 | 960 | no | — |
| 138 | 2−1+4 | — | 7 | 320 | no | — |
| 139 | 2−1+4 | — | 7 | 480 | no | — |
| 140 | 2−1+4 | — | 7 | 160 | no | — |
| 141 | 2−1+4 | C22×D7 | 1 | 96 | yes | complemented |
| 142 | H(5,𝔽2) | — | 7 | 960 | no | — |
| 143 | H(5,𝔽2) | — | 7 | 320 | no | — |
| 144 | H(5,𝔽2) | — | 7 | 1440 | no | — |
| 145 | H(5,𝔽2) | — | 7 | 480 | no | — |
| 146 | H(5,𝔽2) | C22×D7 | 1 | 160 | yes | complemented |
| 147 | C2×#41 | — | 7 | 640 | no | — |
| 148 | C2×#41 | — | 7 | 1920 | no | — |
| 149 | C2×#41 | — | 7 | 240 | no | — |
| 150 | C2×#41 | — | 7 | 720 | no | — |
| 151 | C2×#41 | — | 7 | 360 | no | — |
| 152 | C2×#41 | — | 7 | 120 | no | — |
| 153 | C2×#41 | — | 7 | 360 | no | — |
| 154 | C2×#41 | — | 7 | 360 | no | — |
| 155 | C2×#41 | C22×D7 | 1 | 120 | yes | complemented |
| 156 | C2×#41 | C22×D7 | 1 | 20 | yes | complemented |
| 157 | C2×#41 | C22×D7 | 1 | 120 | yes | complemented |
| 158 | C2×#41 | C22×D7 | 1 | 60 | yes | complemented |
| 159 | C22×Q8 | — | 7 | 240 | no | — |
| 160 | C22×Q8 | — | 7 | 60 | no | — |
| 161 | C22×Q8 | C22×D7 | 1 | 15 | yes | complemented |
| 162 | C22×D4 | — | 7 | 120 | no | — |
| 163 | C22×D4 | — | 7 | 720 | no | — |
| 164 | C22×D4 | — | 7 | 60 | no | — |
| 165 | C22×D4 | C22×D7 | 1 | 45 | yes | complemented |
| 166 | C23×C4 | — | 7 | 120 | no | — |
| 167 | C23×C4 | C22×D7 | 1 | 15 | yes | complemented |
| 168 | C22×C7 | — | 4 | 60 | no | — |
| 169 | C22×C7 | — | 4 | 15 | no | — |
| 170 | C22×C7 | C26 | 1 | 30 | yes | — |
| 171 | C22×C7 | C26 | 1 | 1 | yes | characteristic |
| 172 | C2×D7 | — | 4 | 240 | no | — |
| 173 | C2×D7 | C26 | 1 | 32 | yes | — |
| 174 | C4×C7 | C26 | 1 | 1 | yes | characteristic |
| 175 | C4×C7 | C26 | 1 | 30 | yes | — |
| 176 | C4×C7 | C26 | 1 | 1 | yes | characteristic |
| 177 | Dic7 | C26 | 1 | 32 | yes | — |
| 178 | C24 | — | 7 | 120 | no | — |
| 179 | C24 | C23×D7 | 1 | 15 | yes | — |
| 180 | #41 | — | 7 | 640 | no | — |
| 181 | #41 | — | 7 | 1920 | no | — |
| 182 | #41 | — | 7 | 240 | no | — |
| 183 | #41 | — | 7 | 16 | no | — |
| 184 | #41 | — | 7 | 1440 | no | — |
| 185 | #41 | — | 7 | 240 | no | — |
| 186 | #41 | — | 7 | 240 | no | — |
| 187 | #41 | C23×D7 | 1 | 80 | yes | — |
| 188 | #41 | C23×D7 | 1 | 480 | yes | — |
| 189 | #41 | C23×D7 | 1 | 80 | yes | — |
| 190 | C2×Q8 | — | 7 | 640 | no | — |
| 191 | C2×Q8 | — | 7 | 360 | no | — |
| 192 | C2×Q8 | — | 7 | 120 | no | — |
| 193 | C2×Q8 | C23×D7 | 1 | 120 | yes | — |
| 194 | C2×Q8 | C23×D7 | 1 | 20 | yes | — |
| 195 | C2×D4 | — | 7 | 720 | no | — |
| 196 | C2×D4 | — | 7 | 240 | no | — |
| 197 | C2×D4 | — | 7 | 1920 | no | — |
| 198 | C2×D4 | — | 7 | 360 | no | — |
| 199 | C2×D4 | — | 7 | 120 | no | — |
| 200 | C2×D4 | C23×D7 | 1 | 360 | yes | — |
| 201 | C2×D4 | C23×D7 | 1 | 60 | yes | — |
| 202 | C22×C4 | — | 7 | 120 | no | — |
| 203 | C22×C4 | — | 7 | 240 | no | — |
| 204 | C22×C4 | — | 7 | 720 | no | — |
| 205 | C22×C4 | C23×D7 | 1 | 60 | yes | — |
| 206 | C22×C4 | C23×D7 | 1 | 15 | yes | — |
| 207 | C22×C4 | C23×D7 | 1 | 60 | yes | — |
| 208 | C22×C4 | C23×D7 | 1 | 45 | yes | — |
| 209 | C2×C7 | — | 2 | 30 | no | — |
| 210 | C2×C7 | — | 2 | 1 | no | — |
| 211 | C2×C7 | C27 | 1 | 1 | yes | characteristic |
| 212 | D7 | — | 2 | 32 | no | — |
| 213 | C23 | — | 7 | 240 | no | — |
| 214 | C23 | — | 8 | 15 | no | — |
| 215 | C23 | — | 56 | 120 | no | — |
| 216 | C23 | C24×D7 | 1 | 60 | yes | — |
| 217 | C23 | C24×D7 | 1 | 15 | yes | — |
| 218 | Q8 | — | 7 | 240 | no | — |
| 219 | Q8 | — | 7 | 16 | no | — |
| 220 | Q8 | C24×D7 | 1 | 80 | yes | — |
| 221 | D4 | — | 7 | 480 | no | — |
| 222 | D4 | — | 7 | 32 | no | — |
| 223 | D4 | — | 7 | 240 | no | — |
| 224 | D4 | — | 7 | 16 | no | — |
| 225 | D4 | C24×D7 | 1 | 240 | yes | — |
| 226 | C2×C4 | — | 7 | 240 | no | — |
| 227 | C2×C4 | — | 7 | 480 | no | — |
| 228 | C2×C4 | — | 7 | 32 | no | — |
| 229 | C2×C4 | C24×D7 | 1 | 180 | yes | — |
| 230 | C2×C4 | C24×D7 | 1 | 30 | yes | — |
| 231 | C2×C4 | C24×D7 | 1 | 15 | yes | — |
| 232 | C2×C4 | C24×D7 | 1 | 30 | yes | — |
| 233 | C2×C4 | C24×D7 | 1 | 1 | yes | characteristic |
| 234 | C7 | #63103 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 235 | C22 | — | 4 | 15 | no | — |
| 236 | C22 | — | 4 | 60 | no | — |
| 237 | C22 | — | 7 | 32 | no | — |
| 238 | C22 | — | 28 | 240 | no | — |
| 239 | C22 | C25×D7 | 1 | 30 | yes | — |
| 240 | C22 | C25×D7 | 1 | 1 | yes | characteristic |
| 241 | C4 | — | 7 | 32 | no | — |
| 242 | C4 | C25×D7 | 1 | 30 | yes | — |
| 243 | C4 | C25×D7 | 1 | 1 | yes | characteristic |
| 244 | C4 | C25×D7 | 1 | 1 | yes | characteristic |
| 245 | C2 | — | 2 | 1 | no | — |
| 246 | C2 | — | 2 | 30 | no | — |
| 247 | C2 | — | 14 | 32 | no | — |
| 248 | C2 | C26×D7 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta