← AGL(1,𝔽7)×#543 #72277480
Order 2688.
2592 conjugacy classes of subgroups.
The subgroup lattice has 304 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | ΓL(1,𝔽8)×#543 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #90325⋊C3 | C2 | 1 | 12 | yes | maximal, complemented |
| 3 | C22⋊Q8×AGL(1,𝔽7) | C2 | 1 | 12 | yes | maximal, complemented |
| 4 | C2×C22⋊C4×AGL(1,𝔽7) | C2 | 1 | 3 | yes | maximal |
| 5 | #90174⋊C3 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | D7×#543 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | C24×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 8 | C2×Q8×AGL(1,𝔽7) | C22 | 1 | 4 | yes | complemented |
| 9 | C22×C4×AGL(1,𝔽7) | C22 | 1 | 6 | yes | — |
| 10 | ΓL(1,𝔽8)×C22⋊Q8 | C22 | 1 | 12 | yes | complemented |
| 11 | C2×C22⋊C4×ΓL(1,𝔽8) | C22 | 1 | 3 | yes | — |
| 12 | C2×(C22⋊Dic7)⋊C3 | C22 | 1 | 3 | yes | — |
| 13 | #6509⋊C3 | C22 | 1 | 12 | yes | complemented |
| 14 | C2×(C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 6 | yes | — |
| 15 | #6487⋊C3 | C22 | 1 | 12 | yes | complemented |
| 16 | #6460⋊C3 | C22 | 1 | 12 | yes | complemented |
| 17 | #6459⋊C3 | C22 | 1 | 24 | yes | complemented |
| 18 | C4⋊C4×AGL(1,𝔽7) | C22 | 1 | 12 | yes | complemented |
| 19 | C22⋊C4×AGL(1,𝔽7) | C22 | 1 | 12 | yes | — |
| 20 | C22⋊C4×AGL(1,𝔽7) | C22 | 1 | 12 | yes | — |
| 21 | #6441⋊C3 | C22 | 1 | 24 | yes | complemented |
| 22 | C7×#543 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 23 | #90325 | C2×C3 | 1 | 12 | yes | complemented |
| 24 | D7×C22⋊Q8 | C2×C3 | 1 | 12 | yes | complemented |
| 25 | C2×D7×C22⋊C4 | C2×C3 | 1 | 3 | yes | — |
| 26 | #90174 | C2×C3 | 1 | 3 | yes | complemented |
| 27 | C2×C3×#543 | — | 7 | 1 | no | maximal, Hall |
| 28 | C24×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 29 | C23×AGL(1,𝔽7) | — | 4 | 4 | no | — |
| 30 | C23×AGL(1,𝔽7) | Q8 | 1 | 8 | yes | complemented |
| 31 | C23×AGL(1,𝔽7) | C23 | 1 | 3 | yes | — |
| 32 | C23×AGL(1,𝔽7) | C23 | 1 | 3 | yes | — |
| 33 | C2×Q8×ΓL(1,𝔽8) | C23 | 1 | 4 | yes | complemented |
| 34 | C22×C4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | — |
| 35 | C22×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 6 | yes | — |
| 36 | Q8×AGL(1,𝔽7) | — | 4 | 8 | no | — |
| 37 | C2×C4×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 38 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 12 | yes | — |
| 39 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 12 | yes | — |
| 40 | C2×ΓL(1,𝔽8)⋊Q8 | C23 | 1 | 12 | yes | complemented |
| 41 | C4⋊C4×ΓL(1,𝔽8) | C23 | 1 | 12 | yes | complemented |
| 42 | C22⋊C4×ΓL(1,𝔽8) | C23 | 1 | 12 | yes | — |
| 43 | (C22⋊Dic7)⋊C3 | C23 | 1 | 12 | yes | — |
| 44 | (C2×AGL(1,𝔽7))⋊C4 | C23 | 1 | 24 | yes | — |
| 45 | C4⋊(ΓL(1,𝔽8)⋊C4) | C23 | 1 | 12 | yes | complemented |
| 46 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C23 | 1 | 24 | yes | complemented |
| 47 | C24×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 48 | C2×Q8×D7 | C22×C3 | 1 | 4 | yes | complemented |
| 49 | C22×C4×D7 | C22×C3 | 1 | 6 | yes | — |
| 50 | C7×C22⋊Q8 | C22×C3 | 1 | 12 | yes | complemented |
| 51 | C2×C7×C22⋊C4 | C22×C3 | 1 | 3 | yes | — |
| 52 | C2×C22⋊Dic7 | C22×C3 | 1 | 3 | yes | — |
| 53 | #6509 | C22×C3 | 1 | 12 | yes | complemented |
| 54 | C2×(C2×D7)⋊C4 | C22×C3 | 1 | 6 | yes | — |
| 55 | #6487 | C22×C3 | 1 | 12 | yes | complemented |
| 56 | #6460 | C22×C3 | 1 | 12 | yes | complemented |
| 57 | #6459 | C22×C3 | 1 | 24 | yes | complemented |
| 58 | D7×C4⋊C4 | C22×C3 | 1 | 12 | yes | complemented |
| 59 | D7×C22⋊C4 | C22×C3 | 1 | 12 | yes | — |
| 60 | D7×C22⋊C4 | C22×C3 | 1 | 12 | yes | — |
| 61 | #6441 | C22×C3 | 1 | 24 | yes | complemented |
| 62 | C3×#543 | — | 7 | 12 | no | — |
| 63 | C3×#543 | — | 7 | 3 | no | — |
| 64 | C3×#543 | — | 7 | 1 | no | — |
| 65 | C2×C3×C22⋊Q8 | — | 7 | 12 | no | — |
| 66 | C22×C3×C22⋊C4 | — | 7 | 3 | no | — |
| 67 | C23×ΓL(1,𝔽8) | — | 4 | 2 | no | — |
| 68 | C23×ΓL(1,𝔽8) | C2×Q8 | 1 | 4 | yes | complemented |
| 69 | C23×ΓL(1,𝔽8) | C24 | 1 | 3 | yes | — |
| 70 | C22×AGL(1,𝔽7) | — | 2 | 12 | no | — |
| 71 | C22×AGL(1,𝔽7) | — | 4 | 16 | no | — |
| 72 | C22×AGL(1,𝔽7) | — | 4 | 6 | no | — |
| 73 | C22×AGL(1,𝔽7) | C2×Q8 | 1 | 12 | yes | — |
| 74 | C22×AGL(1,𝔽7) | C2×Q8 | 1 | 12 | yes | complemented |
| 75 | C22×AGL(1,𝔽7) | C24 | 1 | 3 | yes | — |
| 76 | C22×AGL(1,𝔽7) | C24 | 1 | 1 | yes | characteristic |
| 77 | Q8×ΓL(1,𝔽8) | — | 4 | 4 | no | — |
| 78 | C2×C4×ΓL(1,𝔽8) | — | 4 | 6 | no | — |
| 79 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 12 | yes | — |
| 80 | C2×ΓL(1,𝔽8)⋊C4 | — | 4 | 6 | no | — |
| 81 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 12 | yes | — |
| 82 | C4×AGL(1,𝔽7) | — | 2 | 24 | no | — |
| 83 | C4×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 84 | ΓL(1,𝔽8)⋊Q8 | — | 4 | 12 | no | — |
| 85 | C2×#543 | — | 7 | 1 | no | Sylow |
| 86 | C24×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 87 | C23×D7 | — | 4 | 4 | no | — |
| 88 | C23×D7 | C3×Q8 | 1 | 8 | yes | complemented |
| 89 | C23×D7 | C23×C3 | 1 | 3 | yes | — |
| 90 | C23×D7 | C23×C3 | 1 | 3 | yes | — |
| 91 | C2×C7×Q8 | C23×C3 | 1 | 4 | yes | complemented |
| 92 | C22×C4×C7 | C23×C3 | 1 | 6 | yes | — |
| 93 | C22×Dic7 | C23×C3 | 1 | 6 | yes | — |
| 94 | Q8×D7 | — | 4 | 8 | no | — |
| 95 | C2×C4×D7 | — | 4 | 12 | no | — |
| 96 | C2×C4×D7 | C23×C3 | 1 | 12 | yes | — |
| 97 | C2×C4×D7 | C23×C3 | 1 | 12 | yes | — |
| 98 | C2×Dic14 | C23×C3 | 1 | 12 | yes | complemented |
| 99 | C7×C4⋊C4 | C23×C3 | 1 | 12 | yes | complemented |
| 100 | C7×C22⋊C4 | C23×C3 | 1 | 12 | yes | — |
| 101 | C22⋊Dic7 | C23×C3 | 1 | 12 | yes | — |
| 102 | (C2×D7)⋊C4 | C23×C3 | 1 | 24 | yes | — |
| 103 | C4⋊Dic7 | C23×C3 | 1 | 12 | yes | complemented |
| 104 | Dic7⋊C4 | C23×C3 | 1 | 24 | yes | complemented |
| 105 | C25×C3 | — | 7 | 1 | no | — |
| 106 | C22×C3×Q8 | — | 7 | 4 | no | — |
| 107 | C23×C3×C4 | — | 7 | 6 | no | — |
| 108 | C3×C22⋊Q8 | — | 7 | 24 | no | — |
| 109 | C3×C22⋊Q8 | — | 7 | 24 | no | — |
| 110 | C3×C22⋊Q8 | — | 7 | 12 | no | — |
| 111 | C3×C22⋊Q8 | — | 7 | 12 | no | — |
| 112 | C3×C22⋊Q8 | — | 7 | 12 | no | — |
| 113 | C3×C22⋊Q8 | — | 7 | 12 | no | — |
| 114 | C2×C3×C4⋊C4 | — | 7 | 12 | no | — |
| 115 | C2×C3×C22⋊C4 | — | 7 | 12 | no | — |
| 116 | C2×C3×C22⋊C4 | — | 7 | 12 | no | — |
| 117 | C2×C3×C22⋊C4 | — | 7 | 6 | no | — |
| 118 | C2×C3×C22⋊C4 | — | 7 | 3 | no | — |
| 119 | C2×C3×C22⋊C4 | — | 7 | 3 | no | — |
| 120 | C22×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 121 | C22×ΓL(1,𝔽8) | — | 4 | 4 | no | — |
| 122 | C22×ΓL(1,𝔽8) | C22×Q8 | 1 | 6 | yes | — |
| 123 | C22×ΓL(1,𝔽8) | C25 | 1 | 1 | yes | characteristic |
| 124 | C2×AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 125 | C2×AGL(1,𝔽7) | — | 2 | 24 | no | — |
| 126 | C2×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 127 | C2×AGL(1,𝔽7) | C22×Q8 | 1 | 6 | yes | — |
| 128 | C2×AGL(1,𝔽7) | C22×Q8 | 1 | 2 | yes | — |
| 129 | C2×AGL(1,𝔽7) | H(5,𝔽2) | 1 | 4 | yes | — |
| 130 | C4×ΓL(1,𝔽8) | — | 2 | 12 | no | — |
| 131 | ΓL(1,𝔽8)⋊C4 | — | 2 | 12 | no | — |
| 132 | #543 | — | 7 | 12 | no | — |
| 133 | #543 | — | 7 | 3 | no | — |
| 134 | #543 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 135 | C2×C22⋊Q8 | — | 7 | 12 | no | — |
| 136 | C22×C22⋊C4 | — | 7 | 3 | no | — |
| 137 | C23×C7 | — | 4 | 2 | no | — |
| 138 | C23×C7 | C2×C3×Q8 | 1 | 4 | yes | complemented |
| 139 | C23×C7 | C24×C3 | 1 | 3 | yes | — |
| 140 | C22×D7 | — | 2 | 12 | no | — |
| 141 | C22×D7 | — | 4 | 16 | no | — |
| 142 | C22×D7 | — | 4 | 6 | no | — |
| 143 | C22×D7 | C2×C3×Q8 | 1 | 12 | yes | — |
| 144 | C22×D7 | C2×C3×Q8 | 1 | 12 | yes | complemented |
| 145 | C22×D7 | C24×C3 | 1 | 3 | yes | — |
| 146 | C22×D7 | C24×C3 | 1 | 1 | yes | characteristic |
| 147 | C7×Q8 | — | 4 | 4 | no | — |
| 148 | C2×C4×C7 | — | 4 | 6 | no | — |
| 149 | C2×C4×C7 | C24×C3 | 1 | 12 | yes | — |
| 150 | C2×Dic7 | — | 4 | 6 | no | — |
| 151 | C2×Dic7 | C24×C3 | 1 | 12 | yes | — |
| 152 | C4×D7 | — | 2 | 24 | no | — |
| 153 | C4×D7 | — | 4 | 12 | no | — |
| 154 | Dic14 | — | 4 | 12 | no | — |
| 155 | C24×C3 | — | 7 | 3 | no | — |
| 156 | C24×C3 | — | 7 | 3 | no | — |
| 157 | C24×C3 | — | 7 | 8 | no | — |
| 158 | C24×C3 | — | 7 | 1 | no | — |
| 159 | C24×C3 | — | 28 | 4 | no | — |
| 160 | C2×C3×Q8 | — | 7 | 12 | no | — |
| 161 | C2×C3×Q8 | — | 7 | 4 | no | — |
| 162 | C2×C3×Q8 | — | 28 | 8 | no | — |
| 163 | C22×C3×C4 | — | 7 | 12 | no | — |
| 164 | C22×C3×C4 | — | 7 | 12 | no | — |
| 165 | C22×C3×C4 | — | 7 | 6 | no | — |
| 166 | C22×C3×C4 | — | 7 | 6 | no | — |
| 167 | C22×C3×C4 | — | 28 | 12 | no | — |
| 168 | C3×C4⋊C4 | — | 7 | 24 | no | — |
| 169 | C3×C4⋊C4 | — | 7 | 12 | no | — |
| 170 | C3×C4⋊C4 | — | 7 | 12 | no | — |
| 171 | C3×C22⋊C4 | — | 7 | 24 | no | — |
| 172 | C3×C22⋊C4 | — | 7 | 12 | no | — |
| 173 | C3×C22⋊C4 | — | 7 | 12 | no | — |
| 174 | C2×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 175 | C2×ΓL(1,𝔽8) | C23×Q8 | 1 | 1 | yes | characteristic |
| 176 | C2×ΓL(1,𝔽8) | C2×H(5,𝔽2) | 1 | 2 | yes | — |
| 177 | AGL(1,𝔽7) | — | 2 | 6 | no | — |
| 178 | AGL(1,𝔽7) | #543 | 1 | 4 | yes | direct product factor |
| 179 | C25 | — | 7 | 1 | no | — |
| 180 | C22×Q8 | — | 7 | 4 | no | — |
| 181 | C23×C4 | — | 7 | 6 | no | — |
| 182 | C22⋊Q8 | — | 7 | 12 | no | — |
| 183 | C22⋊Q8 | — | 7 | 12 | no | — |
| 184 | C22⋊Q8 | — | 7 | 24 | no | — |
| 185 | C22⋊Q8 | — | 7 | 12 | no | — |
| 186 | C22⋊Q8 | — | 7 | 24 | no | — |
| 187 | C22⋊Q8 | C2×AGL(1,𝔽7) | 1 | 12 | yes | complemented |
| 188 | C2×C4⋊C4 | — | 7 | 12 | no | — |
| 189 | C2×C22⋊C4 | — | 7 | 3 | no | — |
| 190 | C2×C22⋊C4 | — | 7 | 6 | no | — |
| 191 | C2×C22⋊C4 | — | 7 | 12 | no | — |
| 192 | C2×C22⋊C4 | — | 7 | 12 | no | — |
| 193 | C2×C22⋊C4 | C2×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 194 | C22×C7 | — | 2 | 6 | no | — |
| 195 | C22×C7 | — | 4 | 4 | no | — |
| 196 | C22×C7 | C22×C3×Q8 | 1 | 6 | yes | — |
| 197 | C22×C7 | C25×C3 | 1 | 1 | yes | characteristic |
| 198 | C2×D7 | — | 2 | 6 | no | — |
| 199 | C2×D7 | — | 2 | 24 | no | — |
| 200 | C2×D7 | — | 4 | 12 | no | — |
| 201 | C2×D7 | C22×C3×Q8 | 1 | 6 | yes | — |
| 202 | C2×D7 | C22×C3×Q8 | 1 | 2 | yes | — |
| 203 | C2×D7 | C3×H(5,𝔽2) | 1 | 4 | yes | — |
| 204 | C4×C7 | — | 2 | 12 | no | — |
| 205 | Dic7 | — | 2 | 12 | no | — |
| 206 | C23×C3 | — | 7 | 1 | no | — |
| 207 | C23×C3 | — | 7 | 12 | no | — |
| 208 | C23×C3 | — | 7 | 3 | no | — |
| 209 | C23×C3 | — | 7 | 12 | no | — |
| 210 | C23×C3 | — | 7 | 4 | no | — |
| 211 | C23×C3 | — | 7 | 3 | no | — |
| 212 | C23×C3 | — | 14 | 12 | no | — |
| 213 | C23×C3 | — | 28 | 2 | no | — |
| 214 | C23×C3 | — | 28 | 6 | no | — |
| 215 | C23×C3 | — | 28 | 16 | no | — |
| 216 | C3×Q8 | — | 28 | 4 | no | — |
| 217 | C3×Q8 | — | 28 | 12 | no | — |
| 218 | C2×C3×C4 | — | 7 | 12 | no | — |
| 219 | C2×C3×C4 | — | 7 | 12 | no | — |
| 220 | C2×C3×C4 | — | 14 | 24 | no | — |
| 221 | C2×C3×C4 | — | 28 | 6 | no | — |
| 222 | C2×C3×C4 | — | 28 | 12 | no | — |
| 223 | C2×C3×C4 | — | 28 | 6 | no | — |
| 224 | ΓL(1,𝔽8) | C2×#543 | 1 | 1 | yes | characteristic, complemented, Hall |
| 225 | C24 | — | 7 | 3 | no | — |
| 226 | C24 | — | 7 | 8 | no | — |
| 227 | C24 | — | 7 | 3 | no | — |
| 228 | C24 | — | 28 | 4 | no | — |
| 229 | C24 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 230 | C2×Q8 | — | 7 | 12 | no | — |
| 231 | C2×Q8 | — | 28 | 8 | no | — |
| 232 | C2×Q8 | C22×AGL(1,𝔽7) | 1 | 4 | yes | complemented |
| 233 | C22×C4 | — | 7 | 6 | no | — |
| 234 | C22×C4 | — | 7 | 12 | no | — |
| 235 | C22×C4 | — | 7 | 12 | no | — |
| 236 | C22×C4 | — | 28 | 12 | no | — |
| 237 | C22×C4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 238 | C4⋊C4 | — | 7 | 24 | no | — |
| 239 | C4⋊C4 | — | 7 | 12 | no | — |
| 240 | C4⋊C4 | C22×AGL(1,𝔽7) | 1 | 12 | yes | complemented |
| 241 | C22⋊C4 | — | 7 | 12 | no | — |
| 242 | C22⋊C4 | — | 7 | 24 | no | — |
| 243 | C22⋊C4 | C22×AGL(1,𝔽7) | 1 | 12 | yes | — |
| 244 | C2×C7 | — | 2 | 6 | no | — |
| 245 | C2×C7 | C23×C3×Q8 | 1 | 1 | yes | characteristic |
| 246 | C2×C7 | C2×C3×H(5,𝔽2) | 1 | 2 | yes | — |
| 247 | D7 | — | 2 | 6 | no | — |
| 248 | D7 | C3×#543 | 1 | 4 | yes | complemented |
| 249 | C22×C3 | — | 7 | 4 | no | — |
| 250 | C22×C3 | — | 7 | 2 | no | — |
| 251 | C22×C3 | — | 7 | 6 | no | — |
| 252 | C22×C3 | — | 7 | 6 | no | — |
| 253 | C22×C3 | — | 7 | 1 | no | — |
| 254 | C22×C3 | — | 14 | 6 | no | — |
| 255 | C22×C3 | — | 14 | 6 | no | — |
| 256 | C22×C3 | — | 14 | 24 | no | — |
| 257 | C22×C3 | — | 28 | 4 | no | — |
| 258 | C22×C3 | — | 28 | 12 | no | — |
| 259 | C3×C4 | — | 14 | 12 | no | — |
| 260 | C3×C4 | — | 14 | 12 | no | — |
| 261 | C23 | — | 4 | 2 | no | — |
| 262 | C23 | — | 7 | 1 | no | — |
| 263 | C23 | — | 7 | 12 | no | — |
| 264 | C23 | — | 7 | 3 | no | — |
| 265 | C23 | — | 7 | 12 | no | — |
| 266 | C23 | — | 14 | 12 | no | — |
| 267 | C23 | — | 28 | 6 | no | — |
| 268 | C23 | — | 28 | 16 | no | — |
| 269 | C23 | Q8×AGL(1,𝔽7) | 1 | 4 | yes | complemented |
| 270 | C23 | C23×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 271 | Q8 | — | 4 | 4 | no | — |
| 272 | Q8 | — | 28 | 12 | no | — |
| 273 | C2×C4 | — | 4 | 6 | no | — |
| 274 | C2×C4 | — | 7 | 12 | no | — |
| 275 | C2×C4 | — | 14 | 24 | no | — |
| 276 | C2×C4 | — | 28 | 12 | no | — |
| 277 | C2×C4 | — | 28 | 6 | no | — |
| 278 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 12 | yes | — |
| 279 | C7 | C2×C3×#543 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 280 | C2×C3 | — | 7 | 4 | no | — |
| 281 | C2×C3 | — | 7 | 1 | no | — |
| 282 | C2×C3 | — | 7 | 2 | no | — |
| 283 | C2×C3 | — | 14 | 6 | no | — |
| 284 | C2×C3 | — | 14 | 6 | no | — |
| 285 | C22 | — | 2 | 6 | no | — |
| 286 | C22 | — | 4 | 4 | no | — |
| 287 | C22 | — | 7 | 2 | no | — |
| 288 | C22 | — | 7 | 4 | no | — |
| 289 | C22 | — | 7 | 6 | no | — |
| 290 | C22 | — | 14 | 24 | no | — |
| 291 | C22 | — | 14 | 6 | no | — |
| 292 | C22 | — | 28 | 12 | no | — |
| 293 | C22 | C2×Q8×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 294 | C22 | C24×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 295 | C4 | — | 2 | 12 | no | — |
| 296 | C4 | — | 14 | 12 | no | — |
| 297 | C3 | — | 7 | 1 | no | Sylow |
| 298 | C2 | — | 2 | 6 | no | — |
| 299 | C2 | — | 7 | 4 | no | — |
| 300 | C2 | — | 14 | 6 | no | — |
| 301 | C2 | C22×Q8×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 302 | C2 | H(5,𝔽2)×AGL(1,𝔽7) | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 1. ΓL(1,𝔽8)×#543 | C2 | semidirect |
| 2. #90325⋊C3 | C2 | semidirect |
| 3. C22⋊Q8×AGL(1,𝔽7) | C2 | semidirect |
| 5. #90174⋊C3 | C2 | semidirect |
| 6. D7×#543 | C3 | semidirect |
| 8. C2×Q8×AGL(1,𝔽7) | C22 | semidirect |
| 10. ΓL(1,𝔽8)×C22⋊Q8 | C22 | semidirect |
| 13. #6509⋊C3 | C22 | semidirect |
| 15. #6487⋊C3 | C22 | semidirect |
| 16. #6460⋊C3 | C22 | semidirect |
| 17. #6459⋊C3 | C22 | semidirect |
| 18. C4⋊C4×AGL(1,𝔽7) | C22 | semidirect |
| 21. #6441⋊C3 | C22 | semidirect |
| 22. C7×#543 | C2×C3 | semidirect |
| 23. #90325 | C2×C3 | semidirect |
| 24. D7×C22⋊Q8 | C2×C3 | semidirect |
| 26. #90174 | C2×C3 | semidirect |
| 30. C23×AGL(1,𝔽7) | Q8 | semidirect |
| 33. C2×Q8×ΓL(1,𝔽8) | C23 | semidirect |
| 40. C2×ΓL(1,𝔽8)⋊Q8 | C23 | semidirect |
| 41. C4⋊C4×ΓL(1,𝔽8) | C23 | semidirect |
| 45. C4⋊(ΓL(1,𝔽8)⋊C4) | C23 | semidirect |
| 46. (ΓL(1,𝔽8)⋊C4)⋊C4 | C23 | semidirect |
| 48. C2×Q8×D7 | C22×C3 | semidirect |
| 50. C7×C22⋊Q8 | C22×C3 | semidirect |
| 53. #6509 | C22×C3 | semidirect |
| 55. #6487 | C22×C3 | semidirect |
| 56. #6460 | C22×C3 | semidirect |
| 57. #6459 | C22×C3 | semidirect |
| 58. D7×C4⋊C4 | C22×C3 | semidirect |
| 61. #6441 | C22×C3 | semidirect |
| 68. C23×ΓL(1,𝔽8) | C2×Q8 | semidirect |
| 74. C22×AGL(1,𝔽7) | C2×Q8 | semidirect |
| 88. C23×D7 | C3×Q8 | semidirect |
| 91. C2×C7×Q8 | C23×C3 | semidirect |
| 98. C2×Dic14 | C23×C3 | semidirect |
| 99. C7×C4⋊C4 | C23×C3 | semidirect |
| 103. C4⋊Dic7 | C23×C3 | semidirect |
| 104. Dic7⋊C4 | C23×C3 | semidirect |
| 134. #543 | AGL(1,𝔽7) | direct (N × H) |
| 138. C23×C7 | C2×C3×Q8 | semidirect |
| 144. C22×D7 | C2×C3×Q8 | semidirect |
| 178. AGL(1,𝔽7) | #543 | direct (N × H) |
| 187. C22⋊Q8 | C2×AGL(1,𝔽7) | semidirect |
| 224. ΓL(1,𝔽8) | C2×#543 | semidirect |
| 232. C2×Q8 | C22×AGL(1,𝔽7) | semidirect |
| 240. C4⋊C4 | C22×AGL(1,𝔽7) | semidirect |
| 248. D7 | C3×#543 | semidirect |
| 269. C23 | Q8×AGL(1,𝔽7) | semidirect |
| 279. C7 | C2×C3×#543 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta