← AGL(1,𝔽7)×#585 #72230191
Order 2688.
11912 conjugacy classes of subgroups.
The subgroup lattice has 328 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | ΓL(1,𝔽8)×#585 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13062158 | C2 | 1 | 6 | yes | maximal, complemented |
| 3 | 2−1+4×AGL(1,𝔽7) | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | #13062156 | C2 | 1 | 10 | yes | maximal, complemented |
| 5 | H(5,𝔽2)×AGL(1,𝔽7) | C2 | 1 | 10 | yes | maximal, complemented |
| 6 | #13062154 | C2 | 1 | 15 | yes | maximal, complemented |
| 7 | C2×#41×AGL(1,𝔽7) | C2 | 1 | 15 | yes | maximal, complemented |
| 8 | D7×#585 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | ΓL(1,𝔽8)×2−1+4 | C22 | 1 | 6 | yes | complemented |
| 10 | ΓL(1,𝔽8)×H(5,𝔽2) | C22 | 1 | 10 | yes | complemented |
| 11 | C2×#41×ΓL(1,𝔽8) | C22 | 1 | 15 | yes | complemented |
| 12 | #10621519 | C22 | 1 | 60 | yes | complemented |
| 13 | #10621518 | C22 | 1 | 60 | yes | complemented |
| 14 | #41×AGL(1,𝔽7) | C22 | 1 | 20 | yes | complemented |
| 15 | #41×AGL(1,𝔽7) | C22 | 1 | 60 | yes | complemented |
| 16 | #41×AGL(1,𝔽7) | C22 | 1 | 60 | yes | complemented |
| 17 | #41×AGL(1,𝔽7) | C22 | 1 | 60 | yes | complemented |
| 18 | #10621516 | C22 | 1 | 30 | yes | complemented |
| 19 | C2×#66659 | C22 | 1 | 15 | yes | complemented |
| 20 | C2×Q8×AGL(1,𝔽7) | C22 | 1 | 15 | yes | complemented |
| 21 | #6548⋊C3 | C22 | 1 | 90 | yes | complemented |
| 22 | C2×#1159⋊C3 | C22 | 1 | 45 | yes | complemented |
| 23 | C2×D4×AGL(1,𝔽7) | C22 | 1 | 45 | yes | complemented |
| 24 | C2×#1157⋊C3 | C22 | 1 | 45 | yes | complemented |
| 25 | C22×C4×AGL(1,𝔽7) | C22 | 1 | 15 | yes | complemented |
| 26 | C7×#585 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #90620 | C2×C3 | 1 | 6 | yes | complemented |
| 28 | D7×2−1+4 | C2×C3 | 1 | 6 | yes | complemented |
| 29 | #90618 | C2×C3 | 1 | 10 | yes | complemented |
| 30 | D7×H(5,𝔽2) | C2×C3 | 1 | 10 | yes | complemented |
| 31 | #90616 | C2×C3 | 1 | 15 | yes | complemented |
| 32 | C2×D7×#41 | C2×C3 | 1 | 15 | yes | complemented |
| 33 | C2×C3×#585 | — | 7 | 1 | no | maximal, Hall |
| 34 | C23×AGL(1,𝔽7) | C23 | 1 | 15 | yes | — |
| 35 | #41×ΓL(1,𝔽8) | C23 | 1 | 20 | yes | complemented |
| 36 | #41×ΓL(1,𝔽8) | C23 | 1 | 60 | yes | complemented |
| 37 | C2×Q8×ΓL(1,𝔽8) | C23 | 1 | 15 | yes | complemented |
| 38 | C2×D4×ΓL(1,𝔽8) | C23 | 1 | 45 | yes | complemented |
| 39 | C22×C4×ΓL(1,𝔽8) | C23 | 1 | 15 | yes | complemented |
| 40 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 90 | yes | complemented |
| 41 | C22×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 15 | yes | complemented |
| 42 | #66659 | C23 | 1 | 20 | yes | complemented |
| 43 | #66659 | C23 | 1 | 60 | yes | complemented |
| 44 | Q8×AGL(1,𝔽7) | C23 | 1 | 20 | yes | — |
| 45 | Q8×AGL(1,𝔽7) | C23 | 1 | 60 | yes | complemented |
| 46 | #1159⋊C3 | C23 | 1 | 60 | yes | complemented |
| 47 | #1159⋊C3 | C23 | 1 | 180 | yes | complemented |
| 48 | D4×AGL(1,𝔽7) | C23 | 1 | 60 | yes | — |
| 49 | D4×AGL(1,𝔽7) | C23 | 1 | 180 | yes | complemented |
| 50 | #1157⋊C3 | C23 | 1 | 60 | yes | complemented |
| 51 | #1157⋊C3 | C23 | 1 | 180 | yes | complemented |
| 52 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 45 | yes | complemented |
| 53 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 15 | yes | — |
| 54 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 45 | yes | — |
| 55 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 45 | yes | complemented |
| 56 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 45 | yes | complemented |
| 57 | C2×ΓL(1,𝔽8)⋊Q8 | C23 | 1 | 45 | yes | complemented |
| 58 | C7×2−1+4 | C22×C3 | 1 | 6 | yes | complemented |
| 59 | C7×H(5,𝔽2) | C22×C3 | 1 | 10 | yes | complemented |
| 60 | C2×C7×#41 | C22×C3 | 1 | 15 | yes | complemented |
| 61 | #6554 | C22×C3 | 1 | 60 | yes | complemented |
| 62 | #6553 | C22×C3 | 1 | 60 | yes | complemented |
| 63 | D7×#41 | C22×C3 | 1 | 20 | yes | complemented |
| 64 | D7×#41 | C22×C3 | 1 | 60 | yes | complemented |
| 65 | D7×#41 | C22×C3 | 1 | 60 | yes | complemented |
| 66 | D7×#41 | C22×C3 | 1 | 60 | yes | complemented |
| 67 | #6551 | C22×C3 | 1 | 30 | yes | complemented |
| 68 | C2×#1161 | C22×C3 | 1 | 15 | yes | complemented |
| 69 | C2×Q8×D7 | C22×C3 | 1 | 15 | yes | complemented |
| 70 | #6548 | C22×C3 | 1 | 90 | yes | complemented |
| 71 | C2×#1159 | C22×C3 | 1 | 45 | yes | complemented |
| 72 | C2×D4×D7 | C22×C3 | 1 | 45 | yes | complemented |
| 73 | C2×#1157 | C22×C3 | 1 | 45 | yes | complemented |
| 74 | C22×C4×D7 | C22×C3 | 1 | 15 | yes | complemented |
| 75 | C3×#585 | — | 7 | 6 | no | — |
| 76 | C3×#585 | — | 7 | 10 | no | — |
| 77 | C3×#585 | — | 7 | 15 | no | — |
| 78 | C3×#585 | — | 14 | 1 | no | — |
| 79 | C2×C3×2−1+4 | — | 7 | 6 | no | — |
| 80 | C2×C3×H(5,𝔽2) | — | 7 | 10 | no | — |
| 81 | C22×C3×#41 | — | 7 | 15 | no | — |
| 82 | C23×ΓL(1,𝔽8) | C24 | 1 | 15 | yes | — |
| 83 | C22×AGL(1,𝔽7) | — | 4 | 30 | no | — |
| 84 | C22×AGL(1,𝔽7) | C24 | 1 | 15 | yes | — |
| 85 | C22×AGL(1,𝔽7) | C24 | 1 | 45 | yes | — |
| 86 | Q8×ΓL(1,𝔽8) | C24 | 1 | 20 | yes | — |
| 87 | D4×ΓL(1,𝔽8) | C24 | 1 | 60 | yes | — |
| 88 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 45 | yes | — |
| 89 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 15 | yes | — |
| 90 | (C22⋊D7)⋊C3 | C24 | 1 | 120 | yes | — |
| 91 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 45 | yes | — |
| 92 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 15 | yes | — |
| 93 | C4⋊AGL(1,𝔽7) | C24 | 1 | 60 | yes | — |
| 94 | C4×AGL(1,𝔽7) | C24 | 1 | 1 | yes | characteristic |
| 95 | C4×AGL(1,𝔽7) | C24 | 1 | 15 | yes | — |
| 96 | C4×AGL(1,𝔽7) | C24 | 1 | 15 | yes | — |
| 97 | C4×AGL(1,𝔽7) | C24 | 1 | 15 | yes | — |
| 98 | C4×AGL(1,𝔽7) | C24 | 1 | 90 | yes | — |
| 99 | ΓL(1,𝔽8)⋊Q8 | C24 | 1 | 60 | yes | — |
| 100 | C2×#585 | — | 7 | 1 | no | Sylow |
| 101 | C23×D7 | C23×C3 | 1 | 15 | yes | — |
| 102 | C7×#41 | C23×C3 | 1 | 20 | yes | complemented |
| 103 | C7×#41 | C23×C3 | 1 | 60 | yes | complemented |
| 104 | C2×C7×Q8 | C23×C3 | 1 | 15 | yes | complemented |
| 105 | C2×C7×D4 | C23×C3 | 1 | 45 | yes | complemented |
| 106 | C22×C4×C7 | C23×C3 | 1 | 15 | yes | complemented |
| 107 | C2×C22⋊D7 | C23×C3 | 1 | 90 | yes | complemented |
| 108 | C22×Dic7 | C23×C3 | 1 | 15 | yes | complemented |
| 109 | #1161 | C23×C3 | 1 | 20 | yes | complemented |
| 110 | #1161 | C23×C3 | 1 | 60 | yes | complemented |
| 111 | Q8×D7 | C23×C3 | 1 | 20 | yes | — |
| 112 | Q8×D7 | C23×C3 | 1 | 60 | yes | complemented |
| 113 | #1159 | C23×C3 | 1 | 60 | yes | complemented |
| 114 | #1159 | C23×C3 | 1 | 180 | yes | complemented |
| 115 | D4×D7 | C23×C3 | 1 | 60 | yes | — |
| 116 | D4×D7 | C23×C3 | 1 | 180 | yes | complemented |
| 117 | #1157 | C23×C3 | 1 | 60 | yes | complemented |
| 118 | #1157 | C23×C3 | 1 | 180 | yes | complemented |
| 119 | C2×D28 | C23×C3 | 1 | 45 | yes | complemented |
| 120 | C2×C4×D7 | C23×C3 | 1 | 15 | yes | — |
| 121 | C2×C4×D7 | C23×C3 | 1 | 45 | yes | — |
| 122 | C2×C4×D7 | C23×C3 | 1 | 45 | yes | complemented |
| 123 | C2×C4×D7 | C23×C3 | 1 | 45 | yes | complemented |
| 124 | C2×Dic14 | C23×C3 | 1 | 45 | yes | complemented |
| 125 | C3×2−1+4 | — | 7 | 60 | no | — |
| 126 | C3×2−1+4 | — | 7 | 30 | no | — |
| 127 | C3×2−1+4 | — | 14 | 6 | no | — |
| 128 | C3×H(5,𝔽2) | — | 7 | 60 | no | — |
| 129 | C3×H(5,𝔽2) | — | 7 | 90 | no | — |
| 130 | C3×H(5,𝔽2) | — | 14 | 10 | no | — |
| 131 | C2×C3×#41 | — | 7 | 20 | no | — |
| 132 | C2×C3×#41 | — | 7 | 60 | no | — |
| 133 | C2×C3×#41 | — | 7 | 60 | no | — |
| 134 | C2×C3×#41 | — | 7 | 60 | no | — |
| 135 | C2×C3×#41 | — | 7 | 15 | no | — |
| 136 | C2×C3×#41 | — | 7 | 45 | no | — |
| 137 | C2×C3×#41 | — | 7 | 45 | no | — |
| 138 | C2×C3×#41 | — | 14 | 15 | no | — |
| 139 | C22×C3×Q8 | — | 7 | 15 | no | — |
| 140 | C22×C3×D4 | — | 7 | 45 | no | — |
| 141 | C23×C3×C4 | — | 7 | 15 | no | — |
| 142 | C22×ΓL(1,𝔽8) | — | 4 | 15 | no | — |
| 143 | C22×ΓL(1,𝔽8) | C25 | 1 | 15 | yes | — |
| 144 | C2×AGL(1,𝔽7) | — | 2 | 30 | no | — |
| 145 | C2×AGL(1,𝔽7) | — | 4 | 45 | no | — |
| 146 | C2×AGL(1,𝔽7) | C25 | 1 | 15 | yes | — |
| 147 | C2×AGL(1,𝔽7) | C25 | 1 | 1 | yes | characteristic |
| 148 | C4×ΓL(1,𝔽8) | C25 | 1 | 15 | yes | — |
| 149 | C4×ΓL(1,𝔽8) | C25 | 1 | 1 | yes | characteristic |
| 150 | ΓL(1,𝔽8)⋊C4 | C25 | 1 | 15 | yes | — |
| 151 | ΓL(1,𝔽8)⋊C4 | C25 | 1 | 1 | yes | characteristic |
| 152 | #585 | — | 7 | 6 | no | — |
| 153 | #585 | — | 7 | 10 | no | — |
| 154 | #585 | — | 7 | 15 | no | — |
| 155 | #585 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 156 | C2×2−1+4 | — | 7 | 6 | no | — |
| 157 | C2×H(5,𝔽2) | — | 7 | 10 | no | — |
| 158 | C22×#41 | — | 7 | 15 | no | — |
| 159 | C23×C7 | C24×C3 | 1 | 15 | yes | — |
| 160 | C22×D7 | — | 4 | 30 | no | — |
| 161 | C22×D7 | C24×C3 | 1 | 15 | yes | — |
| 162 | C22×D7 | C24×C3 | 1 | 45 | yes | — |
| 163 | C7×Q8 | C24×C3 | 1 | 20 | yes | — |
| 164 | C7×D4 | C24×C3 | 1 | 60 | yes | — |
| 165 | C2×C4×C7 | C24×C3 | 1 | 45 | yes | — |
| 166 | C2×C4×C7 | C24×C3 | 1 | 15 | yes | — |
| 167 | C22⋊D7 | C24×C3 | 1 | 120 | yes | — |
| 168 | C2×Dic7 | C24×C3 | 1 | 45 | yes | — |
| 169 | C2×Dic7 | C24×C3 | 1 | 15 | yes | — |
| 170 | D28 | C24×C3 | 1 | 60 | yes | — |
| 171 | C4×D7 | C24×C3 | 1 | 1 | yes | characteristic |
| 172 | C4×D7 | C24×C3 | 1 | 15 | yes | — |
| 173 | C4×D7 | C24×C3 | 1 | 15 | yes | — |
| 174 | C4×D7 | C24×C3 | 1 | 15 | yes | — |
| 175 | C4×D7 | C24×C3 | 1 | 90 | yes | — |
| 176 | Dic14 | C24×C3 | 1 | 60 | yes | — |
| 177 | C24×C3 | — | 7 | 15 | no | — |
| 178 | C3×#41 | — | 7 | 20 | no | — |
| 179 | C3×#41 | — | 7 | 60 | no | — |
| 180 | C3×#41 | — | 7 | 60 | no | — |
| 181 | C3×#41 | — | 7 | 180 | no | — |
| 182 | C3×#41 | — | 7 | 60 | no | — |
| 183 | C3×#41 | — | 7 | 180 | no | — |
| 184 | C3×#41 | — | 14 | 20 | no | — |
| 185 | C3×#41 | — | 14 | 60 | no | — |
| 186 | C2×C3×Q8 | — | 7 | 20 | no | — |
| 187 | C2×C3×Q8 | — | 7 | 60 | no | — |
| 188 | C2×C3×Q8 | — | 7 | 45 | no | — |
| 189 | C2×C3×Q8 | — | 14 | 15 | no | — |
| 190 | C2×C3×D4 | — | 7 | 90 | no | — |
| 191 | C2×C3×D4 | — | 7 | 60 | no | — |
| 192 | C2×C3×D4 | — | 7 | 180 | no | — |
| 193 | C2×C3×D4 | — | 7 | 45 | no | — |
| 194 | C2×C3×D4 | — | 14 | 45 | no | — |
| 195 | C22×C3×C4 | — | 7 | 15 | no | — |
| 196 | C22×C3×C4 | — | 7 | 15 | no | — |
| 197 | C22×C3×C4 | — | 7 | 45 | no | — |
| 198 | C22×C3×C4 | — | 7 | 45 | no | — |
| 199 | C22×C3×C4 | — | 7 | 45 | no | — |
| 200 | C22×C3×C4 | — | 14 | 15 | no | — |
| 201 | C2×ΓL(1,𝔽8) | — | 2 | 15 | no | — |
| 202 | C2×ΓL(1,𝔽8) | C26 | 1 | 1 | yes | characteristic |
| 203 | AGL(1,𝔽7) | — | 2 | 15 | no | — |
| 204 | AGL(1,𝔽7) | #585 | 1 | 2 | yes | direct product factor |
| 205 | 2−1+4 | — | 7 | 60 | no | — |
| 206 | 2−1+4 | — | 7 | 30 | no | — |
| 207 | 2−1+4 | C2×AGL(1,𝔽7) | 1 | 6 | yes | complemented |
| 208 | H(5,𝔽2) | — | 7 | 60 | no | — |
| 209 | H(5,𝔽2) | — | 7 | 90 | no | — |
| 210 | H(5,𝔽2) | C2×AGL(1,𝔽7) | 1 | 10 | yes | complemented |
| 211 | C2×#41 | — | 7 | 20 | no | — |
| 212 | C2×#41 | — | 7 | 60 | no | — |
| 213 | C2×#41 | — | 7 | 60 | no | — |
| 214 | C2×#41 | — | 7 | 60 | no | — |
| 215 | C2×#41 | — | 7 | 15 | no | — |
| 216 | C2×#41 | — | 7 | 45 | no | — |
| 217 | C2×#41 | — | 7 | 45 | no | — |
| 218 | C2×#41 | C2×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 219 | C22×Q8 | — | 7 | 15 | no | — |
| 220 | C22×D4 | — | 7 | 45 | no | — |
| 221 | C23×C4 | — | 7 | 15 | no | — |
| 222 | C22×C7 | — | 4 | 15 | no | — |
| 223 | C22×C7 | C25×C3 | 1 | 15 | yes | — |
| 224 | C2×D7 | — | 2 | 30 | no | — |
| 225 | C2×D7 | — | 4 | 45 | no | — |
| 226 | C2×D7 | C25×C3 | 1 | 15 | yes | — |
| 227 | C2×D7 | C25×C3 | 1 | 1 | yes | characteristic |
| 228 | C4×C7 | C25×C3 | 1 | 15 | yes | — |
| 229 | C4×C7 | C25×C3 | 1 | 1 | yes | characteristic |
| 230 | Dic7 | C25×C3 | 1 | 15 | yes | — |
| 231 | Dic7 | C25×C3 | 1 | 1 | yes | characteristic |
| 232 | C23×C3 | — | 7 | 15 | no | — |
| 233 | C23×C3 | — | 7 | 45 | no | — |
| 234 | C23×C3 | — | 14 | 15 | no | — |
| 235 | C23×C3 | — | 28 | 30 | no | — |
| 236 | C3×Q8 | — | 7 | 60 | no | — |
| 237 | C3×Q8 | — | 14 | 20 | no | — |
| 238 | C3×D4 | — | 7 | 120 | no | — |
| 239 | C3×D4 | — | 7 | 60 | no | — |
| 240 | C3×D4 | — | 14 | 60 | no | — |
| 241 | C2×C3×C4 | — | 7 | 15 | no | — |
| 242 | C2×C3×C4 | — | 7 | 45 | no | — |
| 243 | C2×C3×C4 | — | 7 | 1 | no | — |
| 244 | C2×C3×C4 | — | 7 | 15 | no | — |
| 245 | C2×C3×C4 | — | 7 | 15 | no | — |
| 246 | C2×C3×C4 | — | 7 | 15 | no | — |
| 247 | C2×C3×C4 | — | 7 | 90 | no | — |
| 248 | C2×C3×C4 | — | 14 | 15 | no | — |
| 249 | C2×C3×C4 | — | 14 | 45 | no | — |
| 250 | ΓL(1,𝔽8) | C2×#585 | 1 | 1 | yes | characteristic, complemented, Hall |
| 251 | C24 | — | 7 | 15 | no | — |
| 252 | #41 | — | 7 | 20 | no | — |
| 253 | #41 | — | 7 | 60 | no | — |
| 254 | #41 | — | 7 | 60 | no | — |
| 255 | #41 | — | 7 | 180 | no | — |
| 256 | #41 | — | 7 | 60 | no | — |
| 257 | #41 | — | 7 | 180 | no | — |
| 258 | #41 | C22×AGL(1,𝔽7) | 1 | 20 | yes | complemented |
| 259 | #41 | C22×AGL(1,𝔽7) | 1 | 60 | yes | complemented |
| 260 | C2×Q8 | — | 7 | 20 | no | — |
| 261 | C2×Q8 | — | 7 | 60 | no | — |
| 262 | C2×Q8 | — | 7 | 45 | no | — |
| 263 | C2×Q8 | C22×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 264 | C2×D4 | — | 7 | 90 | no | — |
| 265 | C2×D4 | — | 7 | 60 | no | — |
| 266 | C2×D4 | — | 7 | 180 | no | — |
| 267 | C2×D4 | — | 7 | 45 | no | — |
| 268 | C2×D4 | C22×AGL(1,𝔽7) | 1 | 45 | yes | complemented |
| 269 | C22×C4 | — | 7 | 15 | no | — |
| 270 | C22×C4 | — | 7 | 15 | no | — |
| 271 | C22×C4 | — | 7 | 45 | no | — |
| 272 | C22×C4 | — | 7 | 45 | no | — |
| 273 | C22×C4 | — | 7 | 45 | no | — |
| 274 | C22×C4 | C22×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 275 | C2×C7 | — | 2 | 15 | no | — |
| 276 | C2×C7 | C26×C3 | 1 | 1 | yes | characteristic |
| 277 | D7 | — | 2 | 15 | no | — |
| 278 | D7 | C3×#585 | 1 | 2 | yes | complemented |
| 279 | C22×C3 | — | 7 | 1 | no | — |
| 280 | C22×C3 | — | 7 | 15 | no | — |
| 281 | C22×C3 | — | 14 | 30 | no | — |
| 282 | C22×C3 | — | 14 | 15 | no | — |
| 283 | C22×C3 | — | 28 | 45 | no | — |
| 284 | C22×C3 | — | 56 | 15 | no | — |
| 285 | C3×C4 | — | 7 | 1 | no | — |
| 286 | C3×C4 | — | 7 | 15 | no | — |
| 287 | C3×C4 | — | 14 | 15 | no | — |
| 288 | C3×C4 | — | 14 | 1 | no | — |
| 289 | C23 | — | 7 | 15 | no | — |
| 290 | C23 | — | 7 | 45 | no | — |
| 291 | C23 | — | 28 | 30 | no | — |
| 292 | C23 | C23×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 293 | Q8 | — | 7 | 60 | no | — |
| 294 | Q8 | C23×AGL(1,𝔽7) | 1 | 20 | yes | — |
| 295 | D4 | — | 7 | 120 | no | — |
| 296 | D4 | — | 7 | 60 | no | — |
| 297 | D4 | C23×AGL(1,𝔽7) | 1 | 60 | yes | — |
| 298 | C2×C4 | — | 7 | 15 | no | — |
| 299 | C2×C4 | — | 7 | 45 | no | — |
| 300 | C2×C4 | — | 7 | 15 | no | — |
| 301 | C2×C4 | — | 7 | 15 | no | — |
| 302 | C2×C4 | — | 7 | 90 | no | — |
| 303 | C2×C4 | — | 7 | 1 | no | — |
| 304 | C2×C4 | — | 7 | 15 | no | — |
| 305 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 45 | yes | — |
| 306 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 307 | C7 | C2×C3×#585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 308 | C2×C3 | — | 7 | 2 | no | — |
| 309 | C2×C3 | — | 14 | 15 | no | — |
| 310 | C2×C3 | — | 14 | 1 | no | — |
| 311 | C2×C3 | — | 28 | 15 | no | — |
| 312 | C22 | — | 4 | 15 | no | — |
| 313 | C22 | — | 7 | 1 | no | — |
| 314 | C22 | — | 7 | 15 | no | — |
| 315 | C22 | — | 14 | 30 | no | — |
| 316 | C22 | — | 28 | 45 | no | — |
| 317 | C22 | C24×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 318 | C4 | — | 7 | 1 | no | — |
| 319 | C4 | — | 7 | 15 | no | — |
| 320 | C4 | C24×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 321 | C4 | C24×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 322 | C3 | — | 14 | 1 | no | Sylow |
| 323 | C2 | — | 2 | 15 | no | — |
| 324 | C2 | — | 7 | 2 | no | — |
| 325 | C2 | — | 14 | 15 | no | — |
| 326 | C2 | C25×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. ΓL(1,𝔽8)×#585 | C2 | semidirect |
| 2. #13062158 | C2 | semidirect |
| 3. 2−1+4×AGL(1,𝔽7) | C2 | semidirect |
| 4. #13062156 | C2 | semidirect |
| 5. H(5,𝔽2)×AGL(1,𝔽7) | C2 | semidirect |
| 6. #13062154 | C2 | semidirect |
| 7. C2×#41×AGL(1,𝔽7) | C2 | semidirect |
| 8. D7×#585 | C3 | semidirect |
| 9. ΓL(1,𝔽8)×2−1+4 | C22 | semidirect |
| 10. ΓL(1,𝔽8)×H(5,𝔽2) | C22 | semidirect |
| 11. C2×#41×ΓL(1,𝔽8) | C22 | semidirect |
| 12. #10621519 | C22 | semidirect |
| 13. #10621518 | C22 | semidirect |
| 14. #41×AGL(1,𝔽7) | C22 | semidirect |
| 15. #41×AGL(1,𝔽7) | C22 | semidirect |
| 16. #41×AGL(1,𝔽7) | C22 | semidirect |
| 17. #41×AGL(1,𝔽7) | C22 | semidirect |
| 18. #10621516 | C22 | semidirect |
| 19. C2×#66659 | C22 | semidirect |
| 20. C2×Q8×AGL(1,𝔽7) | C22 | semidirect |
| 21. #6548⋊C3 | C22 | semidirect |
| 22. C2×#1159⋊C3 | C22 | semidirect |
| 23. C2×D4×AGL(1,𝔽7) | C22 | semidirect |
| 24. C2×#1157⋊C3 | C22 | semidirect |
| 25. C22×C4×AGL(1,𝔽7) | C22 | semidirect |
| 26. C7×#585 | C2×C3 | semidirect |
| 27. #90620 | C2×C3 | semidirect |
| 28. D7×2−1+4 | C2×C3 | semidirect |
| 29. #90618 | C2×C3 | semidirect |
| 30. D7×H(5,𝔽2) | C2×C3 | semidirect |
| 31. #90616 | C2×C3 | semidirect |
| 32. C2×D7×#41 | C2×C3 | semidirect |
| 35. #41×ΓL(1,𝔽8) | C23 | semidirect |
| 36. #41×ΓL(1,𝔽8) | C23 | semidirect |
| 37. C2×Q8×ΓL(1,𝔽8) | C23 | semidirect |
| 38. C2×D4×ΓL(1,𝔽8) | C23 | semidirect |
| 39. C22×C4×ΓL(1,𝔽8) | C23 | semidirect |
| 40. C2×(C22⋊D7)⋊C3 | C23 | semidirect |
| 41. C22×ΓL(1,𝔽8)⋊C4 | C23 | semidirect |
| 42. #66659 | C23 | semidirect |
| 43. #66659 | C23 | semidirect |
| 45. Q8×AGL(1,𝔽7) | C23 | semidirect |
| 46. #1159⋊C3 | C23 | semidirect |
| 47. #1159⋊C3 | C23 | semidirect |
| 49. D4×AGL(1,𝔽7) | C23 | semidirect |
| 50. #1157⋊C3 | C23 | semidirect |
| 51. #1157⋊C3 | C23 | semidirect |
| 52. C2×C4⋊AGL(1,𝔽7) | C23 | semidirect |
| 55. C2×C4×AGL(1,𝔽7) | C23 | semidirect |
| 56. C2×C4×AGL(1,𝔽7) | C23 | semidirect |
| 57. C2×ΓL(1,𝔽8)⋊Q8 | C23 | semidirect |
| 58. C7×2−1+4 | C22×C3 | semidirect |
| 59. C7×H(5,𝔽2) | C22×C3 | semidirect |
| 60. C2×C7×#41 | C22×C3 | semidirect |
| 61. #6554 | C22×C3 | semidirect |
| 62. #6553 | C22×C3 | semidirect |
| 63. D7×#41 | C22×C3 | semidirect |
| 64. D7×#41 | C22×C3 | semidirect |
| 65. D7×#41 | C22×C3 | semidirect |
| 66. D7×#41 | C22×C3 | semidirect |
| 67. #6551 | C22×C3 | semidirect |
| 68. C2×#1161 | C22×C3 | semidirect |
| 69. C2×Q8×D7 | C22×C3 | semidirect |
| 70. #6548 | C22×C3 | semidirect |
| 71. C2×#1159 | C22×C3 | semidirect |
| 72. C2×D4×D7 | C22×C3 | semidirect |
| 73. C2×#1157 | C22×C3 | semidirect |
| 74. C22×C4×D7 | C22×C3 | semidirect |
| 102. C7×#41 | C23×C3 | semidirect |
| 103. C7×#41 | C23×C3 | semidirect |
| 104. C2×C7×Q8 | C23×C3 | semidirect |
| 105. C2×C7×D4 | C23×C3 | semidirect |
| 106. C22×C4×C7 | C23×C3 | semidirect |
| 107. C2×C22⋊D7 | C23×C3 | semidirect |
| 108. C22×Dic7 | C23×C3 | semidirect |
| 109. #1161 | C23×C3 | semidirect |
| 110. #1161 | C23×C3 | semidirect |
| 112. Q8×D7 | C23×C3 | semidirect |
| 113. #1159 | C23×C3 | semidirect |
| 114. #1159 | C23×C3 | semidirect |
| 116. D4×D7 | C23×C3 | semidirect |
| 117. #1157 | C23×C3 | semidirect |
| 118. #1157 | C23×C3 | semidirect |
| 119. C2×D28 | C23×C3 | semidirect |
| 122. C2×C4×D7 | C23×C3 | semidirect |
| 123. C2×C4×D7 | C23×C3 | semidirect |
| 124. C2×Dic14 | C23×C3 | semidirect |
| 155. #585 | AGL(1,𝔽7) | direct (N × H) |
| 204. AGL(1,𝔽7) | #585 | direct (N × H) |
| 207. 2−1+4 | C2×AGL(1,𝔽7) | semidirect |
| 210. H(5,𝔽2) | C2×AGL(1,𝔽7) | semidirect |
| 218. C2×#41 | C2×AGL(1,𝔽7) | semidirect |
| 250. ΓL(1,𝔽8) | C2×#585 | semidirect |
| 258. #41 | C22×AGL(1,𝔽7) | semidirect |
| 259. #41 | C22×AGL(1,𝔽7) | semidirect |
| 263. C2×Q8 | C22×AGL(1,𝔽7) | semidirect |
| 268. C2×D4 | C22×AGL(1,𝔽7) | semidirect |
| 274. C22×C4 | C22×AGL(1,𝔽7) | semidirect |
| 278. D7 | C3×#585 | semidirect |
| 307. C7 | C2×C3×#585 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta