← #72230256
Subgroups — #72230256
Order 2688.
11984 conjugacy classes of subgroups.
The subgroup lattice has 244 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 | 12 | yes | maximal, complemented |
| 3 | H(5,𝔽2)×AGL(1,𝔽7) | C2 | 1 | 20 | yes | maximal, complemented |
| 4 | #13062154 | C2 | 1 | 15 | yes | maximal, complemented |
| 5 | C2×#10621518 | C2 | 1 | 15 | yes | maximal, complemented |
| 6 | #11744566 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 7 | ΓL(1,𝔽8)×2−1+4 | C22 | 1 | 6 | yes | complemented |
| 8 | ΓL(1,𝔽8)×H(5,𝔽2) | C22 | 1 | 10 | yes | complemented |
| 9 | C2×#41×ΓL(1,𝔽8) | C22 | 1 | 15 | yes | complemented |
| 10 | #10621519 | C22 | 1 | 20 | yes | complemented |
| 11 | #10621518 | C22 | 1 | 60 | yes | complemented |
| 12 | #10621518 | C22 | 1 | 120 | yes | complemented |
| 13 | #41×AGL(1,𝔽7) | C22 | 1 | 120 | yes | complemented |
| 14 | #10621516 | C22 | 1 | 30 | yes | complemented |
| 15 | C2×#66659 | C22 | 1 | 30 | yes | complemented |
| 16 | #6548⋊C3 | C22 | 1 | 90 | yes | complemented |
| 17 | C2×D4×AGL(1,𝔽7) | C22 | 1 | 90 | yes | complemented |
| 18 | C2×#1157⋊C3 | C22 | 1 | 45 | yes | complemented |
| 19 | C22×C4⋊AGL(1,𝔽7) | C22 | 1 | 15 | yes | complemented |
| 20 | C7×#585 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #90620 | C2×C3 | 1 | 12 | yes | complemented |
| 22 | D7×H(5,𝔽2) | C2×C3 | 1 | 20 | yes | complemented |
| 23 | #90616 | C2×C3 | 1 | 15 | yes | complemented |
| 24 | C2×#6553 | C2×C3 | 1 | 15 | yes | complemented |
| 25 | C3×H(7,𝔽2) | — | 7 | 1 | no | maximal, Hall |
| 26 | C23×AGL(1,𝔽7) | C23 | 1 | 30 | yes | complemented |
| 27 | #41×ΓL(1,𝔽8) | C23 | 1 | 60 | yes | complemented |
| 28 | #41×ΓL(1,𝔽8) | C23 | 1 | 20 | yes | complemented |
| 29 | C2×Q8×ΓL(1,𝔽8) | C23 | 1 | 15 | yes | complemented |
| 30 | C2×D4×ΓL(1,𝔽8) | C23 | 1 | 45 | yes | complemented |
| 31 | C22×C4×ΓL(1,𝔽8) | C23 | 1 | 15 | yes | complemented |
| 32 | C2×(C22⋊D7)⋊C3 | C23 | 1 | 90 | yes | complemented |
| 33 | #66659 | C23 | 1 | 120 | yes | complemented |
| 34 | Q8×AGL(1,𝔽7) | C23 | 1 | 40 | yes | complemented |
| 35 | #1159⋊C3 | C23 | 1 | 120 | yes | complemented |
| 36 | D4×AGL(1,𝔽7) | C23 | 1 | 360 | yes | complemented |
| 37 | #1157⋊C3 | C23 | 1 | 60 | yes | complemented |
| 38 | #1157⋊C3 | C23 | 1 | 180 | yes | complemented |
| 39 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 45 | yes | complemented |
| 40 | C2×C4⋊AGL(1,𝔽7) | C23 | 1 | 90 | yes | complemented |
| 41 | C2×C4×AGL(1,𝔽7) | C23 | 1 | 90 | yes | complemented |
| 42 | C2×ΓL(1,𝔽8)⋊Q8 | C23 | 1 | 15 | yes | complemented |
| 43 | C7×2−1+4 | C22×C3 | 1 | 6 | yes | complemented |
| 44 | C7×H(5,𝔽2) | C22×C3 | 1 | 10 | yes | complemented |
| 45 | C2×C7×#41 | C22×C3 | 1 | 15 | yes | complemented |
| 46 | #6554 | C22×C3 | 1 | 20 | yes | complemented |
| 47 | #6553 | C22×C3 | 1 | 60 | yes | complemented |
| 48 | #6553 | C22×C3 | 1 | 120 | yes | complemented |
| 49 | D7×#41 | C22×C3 | 1 | 120 | yes | complemented |
| 50 | #6551 | C22×C3 | 1 | 30 | yes | complemented |
| 51 | C2×#1161 | C22×C3 | 1 | 30 | yes | complemented |
| 52 | #6548 | C22×C3 | 1 | 90 | yes | complemented |
| 53 | C2×D4×D7 | C22×C3 | 1 | 90 | yes | complemented |
| 54 | C2×#1157 | C22×C3 | 1 | 45 | yes | complemented |
| 55 | C22×D28 | C22×C3 | 1 | 15 | yes | complemented |
| 56 | C3×#585 | — | 7 | 12 | no | — |
| 57 | C3×#585 | — | 7 | 15 | no | — |
| 58 | C3×#585 | — | 14 | 1 | no | — |
| 59 | C2×C3×H(5,𝔽2) | — | 7 | 20 | no | — |
| 60 | C2×C3×H(5,𝔽2) | — | 7 | 15 | no | — |
| 61 | C23×ΓL(1,𝔽8) | C24 | 1 | 15 | yes | — |
| 62 | C22×AGL(1,𝔽7) | — | 8 | 30 | no | — |
| 63 | C22×AGL(1,𝔽7) | C24 | 1 | 90 | yes | — |
| 64 | Q8×ΓL(1,𝔽8) | C24 | 1 | 20 | yes | — |
| 65 | D4×ΓL(1,𝔽8) | C24 | 1 | 60 | yes | — |
| 66 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 15 | yes | — |
| 67 | C2×C4×ΓL(1,𝔽8) | C24 | 1 | 45 | yes | — |
| 68 | (C22⋊D7)⋊C3 | C24 | 1 | 120 | yes | — |
| 69 | C2×ΓL(1,𝔽8)⋊C4 | C24 | 1 | 30 | yes | — |
| 70 | C4⋊AGL(1,𝔽7) | C24 | 1 | 10 | yes | — |
| 71 | C4⋊AGL(1,𝔽7) | C24 | 1 | 90 | yes | — |
| 72 | C4×AGL(1,𝔽7) | C24 | 1 | 120 | yes | — |
| 73 | ΓL(1,𝔽8)⋊Q8 | C24 | 1 | 6 | yes | — |
| 74 | ΓL(1,𝔽8)⋊Q8 | C24 | 1 | 30 | yes | — |
| 75 | H(7,𝔽2) | — | 7 | 1 | no | Sylow |
| 76 | C23×D7 | C23×C3 | 1 | 30 | yes | complemented |
| 77 | C7×#41 | C23×C3 | 1 | 60 | yes | complemented |
| 78 | C7×#41 | C23×C3 | 1 | 20 | yes | complemented |
| 79 | C2×C7×Q8 | C23×C3 | 1 | 15 | yes | complemented |
| 80 | C2×C7×D4 | C23×C3 | 1 | 45 | yes | complemented |
| 81 | C22×C4×C7 | C23×C3 | 1 | 15 | yes | complemented |
| 82 | C2×C22⋊D7 | C23×C3 | 1 | 90 | yes | complemented |
| 83 | #1161 | C23×C3 | 1 | 120 | yes | complemented |
| 84 | Q8×D7 | C23×C3 | 1 | 40 | yes | complemented |
| 85 | #1159 | C23×C3 | 1 | 120 | yes | complemented |
| 86 | D4×D7 | C23×C3 | 1 | 360 | yes | complemented |
| 87 | #1157 | C23×C3 | 1 | 60 | yes | complemented |
| 88 | #1157 | C23×C3 | 1 | 180 | yes | complemented |
| 89 | C2×D28 | C23×C3 | 1 | 45 | yes | complemented |
| 90 | C2×D28 | C23×C3 | 1 | 90 | yes | complemented |
| 91 | C2×C4×D7 | C23×C3 | 1 | 90 | yes | complemented |
| 92 | C2×Dic14 | C23×C3 | 1 | 15 | yes | complemented |
| 93 | C3×2−1+4 | — | 7 | 20 | no | — |
| 94 | C3×2−1+4 | — | 7 | 30 | no | — |
| 95 | C3×2−1+4 | — | 14 | 6 | no | — |
| 96 | C3×H(5,𝔽2) | — | 7 | 120 | no | — |
| 97 | C3×H(5,𝔽2) | — | 7 | 60 | no | — |
| 98 | C3×H(5,𝔽2) | — | 7 | 90 | no | — |
| 99 | C3×H(5,𝔽2) | — | 14 | 10 | no | — |
| 100 | C2×C3×#41 | — | 7 | 120 | no | — |
| 101 | C2×C3×#41 | — | 7 | 30 | no | — |
| 102 | C2×C3×#41 | — | 7 | 45 | no | — |
| 103 | C2×C3×#41 | — | 14 | 15 | no | — |
| 104 | C22×C3×D4 | — | 7 | 90 | no | — |
| 105 | C22×C3×D4 | — | 7 | 15 | no | — |
| 106 | C22×ΓL(1,𝔽8) | — | 4 | 15 | no | — |
| 107 | C22×ΓL(1,𝔽8) | C25 | 1 | 15 | yes | — |
| 108 | C2×AGL(1,𝔽7) | — | 4 | 90 | no | — |
| 109 | C2×AGL(1,𝔽7) | C25 | 1 | 20 | yes | — |
| 110 | C4×ΓL(1,𝔽8) | C25 | 1 | 1 | yes | characteristic |
| 111 | C4×ΓL(1,𝔽8) | C25 | 1 | 15 | yes | — |
| 112 | ΓL(1,𝔽8)⋊C4 | C25 | 1 | 12 | yes | — |
| 113 | #585 | — | 7 | 12 | no | — |
| 114 | #585 | — | 7 | 15 | no | — |
| 115 | #585 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 116 | C2×H(5,𝔽2) | — | 7 | 20 | no | — |
| 117 | C2×H(5,𝔽2) | — | 7 | 15 | no | — |
| 118 | C23×C7 | C24×C3 | 1 | 15 | yes | — |
| 119 | C22×D7 | — | 8 | 30 | no | — |
| 120 | C22×D7 | C24×C3 | 1 | 90 | yes | — |
| 121 | C7×Q8 | C24×C3 | 1 | 20 | yes | — |
| 122 | C7×D4 | C24×C3 | 1 | 60 | yes | — |
| 123 | C2×C4×C7 | C24×C3 | 1 | 15 | yes | — |
| 124 | C2×C4×C7 | C24×C3 | 1 | 45 | yes | — |
| 125 | C22⋊D7 | C24×C3 | 1 | 120 | yes | — |
| 126 | C2×Dic7 | C24×C3 | 1 | 30 | yes | — |
| 127 | D28 | C24×C3 | 1 | 10 | yes | — |
| 128 | D28 | C24×C3 | 1 | 90 | yes | — |
| 129 | C4×D7 | C24×C3 | 1 | 120 | yes | — |
| 130 | Dic14 | C24×C3 | 1 | 6 | yes | — |
| 131 | Dic14 | C24×C3 | 1 | 30 | yes | — |
| 132 | C24×C3 | — | 7 | 30 | no | — |
| 133 | C3×#41 | — | 7 | 120 | no | — |
| 134 | C3×#41 | — | 7 | 120 | no | — |
| 135 | C3×#41 | — | 7 | 180 | no | — |
| 136 | C3×#41 | — | 7 | 60 | no | — |
| 137 | C3×#41 | — | 14 | 60 | no | — |
| 138 | C3×#41 | — | 14 | 20 | no | — |
| 139 | C2×C3×Q8 | — | 7 | 40 | no | — |
| 140 | C2×C3×Q8 | — | 7 | 15 | no | — |
| 141 | C2×C3×Q8 | — | 14 | 15 | no | — |
| 142 | C2×C3×D4 | — | 7 | 90 | no | — |
| 143 | C2×C3×D4 | — | 7 | 360 | no | — |
| 144 | C2×C3×D4 | — | 7 | 90 | no | — |
| 145 | C2×C3×D4 | — | 7 | 45 | no | — |
| 146 | C2×C3×D4 | — | 14 | 45 | no | — |
| 147 | C22×C3×C4 | — | 7 | 90 | no | — |
| 148 | C22×C3×C4 | — | 14 | 15 | no | — |
| 149 | C2×ΓL(1,𝔽8) | — | 2 | 15 | no | — |
| 150 | C2×ΓL(1,𝔽8) | C26 | 1 | 1 | yes | characteristic |
| 151 | AGL(1,𝔽7) | — | 2 | 20 | no | — |
| 152 | 2−1+4 | — | 7 | 20 | no | — |
| 153 | 2−1+4 | — | 7 | 30 | no | — |
| 154 | 2−1+4 | C2×AGL(1,𝔽7) | 1 | 6 | yes | complemented |
| 155 | H(5,𝔽2) | — | 7 | 120 | no | — |
| 156 | H(5,𝔽2) | — | 7 | 60 | no | — |
| 157 | H(5,𝔽2) | — | 7 | 90 | no | — |
| 158 | H(5,𝔽2) | C2×AGL(1,𝔽7) | 1 | 10 | yes | complemented |
| 159 | C2×#41 | — | 7 | 120 | no | — |
| 160 | C2×#41 | — | 7 | 30 | no | — |
| 161 | C2×#41 | — | 7 | 45 | no | — |
| 162 | C2×#41 | C2×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 163 | C22×D4 | — | 7 | 90 | no | — |
| 164 | C22×D4 | — | 7 | 15 | no | — |
| 165 | C22×C7 | — | 4 | 15 | no | — |
| 166 | C22×C7 | C25×C3 | 1 | 15 | yes | — |
| 167 | C2×D7 | — | 4 | 90 | no | — |
| 168 | C2×D7 | C25×C3 | 1 | 20 | yes | — |
| 169 | C4×C7 | C25×C3 | 1 | 1 | yes | characteristic |
| 170 | C4×C7 | C25×C3 | 1 | 15 | yes | — |
| 171 | Dic7 | C25×C3 | 1 | 12 | yes | — |
| 172 | C23×C3 | — | 7 | 90 | no | — |
| 173 | C23×C3 | — | 14 | 15 | no | — |
| 174 | C23×C3 | — | 56 | 30 | no | — |
| 175 | C3×Q8 | — | 7 | 30 | no | — |
| 176 | C3×Q8 | — | 7 | 6 | no | — |
| 177 | C3×Q8 | — | 14 | 20 | no | — |
| 178 | C3×D4 | — | 7 | 120 | no | — |
| 179 | C3×D4 | — | 7 | 90 | no | — |
| 180 | C3×D4 | — | 7 | 10 | no | — |
| 181 | C3×D4 | — | 14 | 60 | no | — |
| 182 | C2×C3×C4 | — | 7 | 30 | no | — |
| 183 | C2×C3×C4 | — | 7 | 120 | no | — |
| 184 | C2×C3×C4 | — | 14 | 45 | no | — |
| 185 | C2×C3×C4 | — | 14 | 15 | no | — |
| 186 | ΓL(1,𝔽8) | H(7,𝔽2) | 1 | 1 | yes | characteristic, complemented, Hall |
| 187 | C24 | — | 7 | 30 | no | — |
| 188 | #41 | — | 7 | 120 | no | — |
| 189 | #41 | — | 7 | 120 | no | — |
| 190 | #41 | — | 7 | 180 | no | — |
| 191 | #41 | — | 7 | 60 | no | — |
| 192 | #41 | C22×AGL(1,𝔽7) | 1 | 60 | yes | complemented |
| 193 | #41 | C22×AGL(1,𝔽7) | 1 | 20 | yes | complemented |
| 194 | C2×Q8 | — | 7 | 40 | no | — |
| 195 | C2×Q8 | — | 7 | 15 | no | — |
| 196 | C2×Q8 | C22×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 197 | C2×D4 | — | 7 | 90 | no | — |
| 198 | C2×D4 | — | 7 | 360 | no | — |
| 199 | C2×D4 | — | 7 | 90 | no | — |
| 200 | C2×D4 | — | 7 | 45 | no | — |
| 201 | C2×D4 | C22×AGL(1,𝔽7) | 1 | 45 | yes | complemented |
| 202 | C22×C4 | — | 7 | 90 | no | — |
| 203 | C22×C4 | C22×AGL(1,𝔽7) | 1 | 15 | yes | complemented |
| 204 | C2×C7 | — | 2 | 15 | no | — |
| 205 | C2×C7 | C26×C3 | 1 | 1 | yes | characteristic |
| 206 | D7 | — | 2 | 20 | no | — |
| 207 | C22×C3 | — | 7 | 20 | no | — |
| 208 | C22×C3 | — | 14 | 15 | no | — |
| 209 | C22×C3 | — | 28 | 90 | no | — |
| 210 | C22×C3 | — | 56 | 15 | no | — |
| 211 | C3×C4 | — | 7 | 12 | no | — |
| 212 | C3×C4 | — | 14 | 15 | no | — |
| 213 | C3×C4 | — | 14 | 1 | no | — |
| 214 | C23 | — | 7 | 90 | no | — |
| 215 | C23 | — | 56 | 30 | no | — |
| 216 | C23 | C23×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 217 | Q8 | — | 7 | 30 | no | — |
| 218 | Q8 | — | 7 | 6 | no | — |
| 219 | Q8 | C23×AGL(1,𝔽7) | 1 | 20 | yes | — |
| 220 | D4 | — | 7 | 120 | no | — |
| 221 | D4 | — | 7 | 90 | no | — |
| 222 | D4 | — | 7 | 10 | no | — |
| 223 | D4 | C23×AGL(1,𝔽7) | 1 | 60 | yes | — |
| 224 | C2×C4 | — | 7 | 30 | no | — |
| 225 | C2×C4 | — | 7 | 120 | no | — |
| 226 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 45 | yes | — |
| 227 | C2×C4 | C23×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 228 | C7 | C3×H(7,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 229 | C2×C3 | — | 14 | 20 | no | — |
| 230 | C2×C3 | — | 14 | 1 | no | — |
| 231 | C2×C3 | — | 28 | 15 | no | — |
| 232 | C22 | — | 4 | 15 | no | — |
| 233 | C22 | — | 7 | 20 | no | — |
| 234 | C22 | — | 28 | 90 | no | — |
| 235 | C22 | C24×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 236 | C4 | — | 7 | 12 | no | — |
| 237 | C4 | C24×AGL(1,𝔽7) | 1 | 15 | yes | — |
| 238 | C4 | C24×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 239 | C3 | — | 14 | 1 | no | Sylow |
| 240 | C2 | — | 2 | 15 | no | — |
| 241 | C2 | — | 14 | 20 | no | — |
| 242 | 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. H(5,𝔽2)×AGL(1,𝔽7) | C2 | semidirect |
| 4. #13062154 | C2 | semidirect |
| 5. C2×#10621518 | C2 | semidirect |
| 6. #11744566 | C3 | semidirect |
| 7. ΓL(1,𝔽8)×2−1+4 | C22 | semidirect |
| 8. ΓL(1,𝔽8)×H(5,𝔽2) | C22 | semidirect |
| 9. C2×#41×ΓL(1,𝔽8) | C22 | semidirect |
| 10. #10621519 | C22 | semidirect |
| 11. #10621518 | C22 | semidirect |
| 12. #10621518 | C22 | semidirect |
| 13. #41×AGL(1,𝔽7) | C22 | semidirect |
| 14. #10621516 | C22 | semidirect |
| 15. C2×#66659 | C22 | semidirect |
| 16. #6548⋊C3 | C22 | semidirect |
| 17. C2×D4×AGL(1,𝔽7) | C22 | semidirect |
| 18. C2×#1157⋊C3 | C22 | semidirect |
| 19. C22×C4⋊AGL(1,𝔽7) | C22 | semidirect |
| 20. C7×#585 | C2×C3 | semidirect |
| 21. #90620 | C2×C3 | semidirect |
| 22. D7×H(5,𝔽2) | C2×C3 | semidirect |
| 23. #90616 | C2×C3 | semidirect |
| 24. C2×#6553 | C2×C3 | semidirect |
| 26. C23×AGL(1,𝔽7) | C23 | semidirect |
| 27. #41×ΓL(1,𝔽8) | C23 | semidirect |
| 28. #41×ΓL(1,𝔽8) | C23 | semidirect |
| 29. C2×Q8×ΓL(1,𝔽8) | C23 | semidirect |
| 30. C2×D4×ΓL(1,𝔽8) | C23 | semidirect |
| 31. C22×C4×ΓL(1,𝔽8) | C23 | semidirect |
| 32. C2×(C22⋊D7)⋊C3 | C23 | semidirect |
| 33. #66659 | C23 | semidirect |
| 34. Q8×AGL(1,𝔽7) | C23 | semidirect |
| 35. #1159⋊C3 | C23 | semidirect |
| 36. D4×AGL(1,𝔽7) | C23 | semidirect |
| 37. #1157⋊C3 | C23 | semidirect |
| 38. #1157⋊C3 | C23 | semidirect |
| 39. C2×C4⋊AGL(1,𝔽7) | C23 | semidirect |
| 40. C2×C4⋊AGL(1,𝔽7) | C23 | semidirect |
| 41. C2×C4×AGL(1,𝔽7) | C23 | semidirect |
| 42. C2×ΓL(1,𝔽8)⋊Q8 | C23 | semidirect |
| 43. C7×2−1+4 | C22×C3 | semidirect |
| 44. C7×H(5,𝔽2) | C22×C3 | semidirect |
| 45. C2×C7×#41 | C22×C3 | semidirect |
| 46. #6554 | C22×C3 | semidirect |
| 47. #6553 | C22×C3 | semidirect |
| 48. #6553 | C22×C3 | semidirect |
| 49. D7×#41 | C22×C3 | semidirect |
| 50. #6551 | C22×C3 | semidirect |
| 51. C2×#1161 | C22×C3 | semidirect |
| 52. #6548 | C22×C3 | semidirect |
| 53. C2×D4×D7 | C22×C3 | semidirect |
| 54. C2×#1157 | C22×C3 | semidirect |
| 55. C22×D28 | C22×C3 | semidirect |
| 76. C23×D7 | C23×C3 | semidirect |
| 77. C7×#41 | C23×C3 | semidirect |
| 78. C7×#41 | C23×C3 | semidirect |
| 79. C2×C7×Q8 | C23×C3 | semidirect |
| 80. C2×C7×D4 | C23×C3 | semidirect |
| 81. C22×C4×C7 | C23×C3 | semidirect |
| 82. C2×C22⋊D7 | C23×C3 | semidirect |
| 83. #1161 | C23×C3 | semidirect |
| 84. Q8×D7 | C23×C3 | semidirect |
| 85. #1159 | C23×C3 | semidirect |
| 86. D4×D7 | C23×C3 | semidirect |
| 87. #1157 | C23×C3 | semidirect |
| 88. #1157 | C23×C3 | semidirect |
| 89. C2×D28 | C23×C3 | semidirect |
| 90. C2×D28 | C23×C3 | semidirect |
| 91. C2×C4×D7 | C23×C3 | semidirect |
| 92. C2×Dic14 | C23×C3 | semidirect |
| 115. #585 | AGL(1,𝔽7) | semidirect |
| 154. 2−1+4 | C2×AGL(1,𝔽7) | semidirect |
| 158. H(5,𝔽2) | C2×AGL(1,𝔽7) | semidirect |
| 162. C2×#41 | C2×AGL(1,𝔽7) | semidirect |
| 186. ΓL(1,𝔽8) | H(7,𝔽2) | semidirect |
| 192. #41 | C22×AGL(1,𝔽7) | semidirect |
| 193. #41 | C22×AGL(1,𝔽7) | semidirect |
| 196. C2×Q8 | C22×AGL(1,𝔽7) | semidirect |
| 201. C2×D4 | C22×AGL(1,𝔽7) | semidirect |
| 203. C22×C4 | C22×AGL(1,𝔽7) | semidirect |
| 228. C7 | C3×H(7,𝔽2) | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta