← #117×AGL(1,𝔽7) #13057257
Order 1344.
660 conjugacy classes of subgroups.
The subgroup lattice has 264 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C22×C4×AGL(1,𝔽7) | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | ΓL(1,𝔽8)×#117 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6489⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #6455⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C4⋊C4×AGL(1,𝔽7) | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C22⋊C4×AGL(1,𝔽7) | C2 | 1 | 2 | yes | maximal |
| 7 | #6440⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #6435⋊C3 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C42×AGL(1,𝔽7) | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | D7×#117 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 11 | C23×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 12 | C22×C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 13 | C22×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C4×AGL(1,𝔽7) | C4 | 1 | 8 | yes | complemented |
| 15 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 4 | yes | — |
| 16 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 20 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 2 | yes | complemented |
| 21 | C22⋊C4×ΓL(1,𝔽8) | C22 | 1 | 2 | yes | — |
| 22 | C42×ΓL(1,𝔽8) | C22 | 1 | 2 | yes | complemented |
| 23 | (C22⋊Dic7)⋊C3 | C22 | 1 | 2 | yes | — |
| 24 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 4 | yes | — |
| 25 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 2 | yes | complemented |
| 26 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 4 | yes | complemented |
| 27 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 2 | yes | complemented |
| 28 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 4 | yes | complemented |
| 29 | C22×C4×D7 | C2×C3 | 1 | 1 | yes | characteristic |
| 30 | C7×#117 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 31 | #6489 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #6455 | C2×C3 | 1 | 2 | yes | complemented |
| 33 | D7×C4⋊C4 | C2×C3 | 1 | 2 | yes | complemented |
| 34 | D7×C22⋊C4 | C2×C3 | 1 | 2 | yes | — |
| 35 | #6440 | C2×C3 | 1 | 2 | yes | complemented |
| 36 | #6435 | C2×C3 | 1 | 2 | yes | complemented |
| 37 | C42×D7 | C2×C3 | 1 | 2 | yes | complemented |
| 38 | C2×C3×#117 | — | 7 | 1 | no | maximal, Hall |
| 39 | C23×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 40 | C22×AGL(1,𝔽7) | — | 2 | 4 | no | — |
| 41 | C22×AGL(1,𝔽7) | C2×C4 | 1 | 4 | yes | — |
| 42 | C22×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 43 | C22×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 44 | C2×C4×ΓL(1,𝔽8) | C2×C4 | 1 | 4 | yes | complemented |
| 45 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 4 | yes | — |
| 46 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 48 | C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | 1 | 4 | yes | complemented |
| 49 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 4 | yes | — |
| 50 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 51 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 52 | C4×AGL(1,𝔽7) | — | 2 | 8 | no | — |
| 53 | C4×AGL(1,𝔽7) | C2×C4 | 1 | 4 | yes | — |
| 54 | C4×AGL(1,𝔽7) | C2×C4 | 1 | 4 | yes | — |
| 55 | C4×AGL(1,𝔽7) | C2×C4 | 1 | 4 | yes | complemented |
| 56 | C4×AGL(1,𝔽7) | C2×C4 | 1 | 4 | yes | complemented |
| 57 | C23×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 58 | C22×C4×C7 | C22×C3 | 1 | 1 | yes | characteristic |
| 59 | C22×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | C2×C4×D7 | C3×C4 | 1 | 8 | yes | complemented |
| 61 | C2×C4×D7 | C22×C3 | 1 | 4 | yes | — |
| 62 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 63 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 64 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 66 | C7×C4⋊C4 | C22×C3 | 1 | 2 | yes | complemented |
| 67 | C7×C22⋊C4 | C22×C3 | 1 | 2 | yes | — |
| 68 | C42×C7 | C22×C3 | 1 | 2 | yes | complemented |
| 69 | C22⋊Dic7 | C22×C3 | 1 | 2 | yes | — |
| 70 | (C2×D7)⋊C4 | C22×C3 | 1 | 4 | yes | — |
| 71 | C4⋊Dic7 | C22×C3 | 1 | 2 | yes | complemented |
| 72 | Dic7⋊C4 | C22×C3 | 1 | 4 | yes | complemented |
| 73 | C4×Dic7 | C22×C3 | 1 | 2 | yes | complemented |
| 74 | C4×Dic7 | C22×C3 | 1 | 4 | yes | complemented |
| 75 | C23×C3×C4 | — | 7 | 1 | no | — |
| 76 | C3×#117 | — | 7 | 2 | no | — |
| 77 | C3×#117 | — | 7 | 2 | no | — |
| 78 | C3×#117 | — | 7 | 2 | no | — |
| 79 | C3×#117 | — | 7 | 1 | no | — |
| 80 | C3×#117 | — | 7 | 1 | no | — |
| 81 | C2×C3×C4⋊C4 | — | 7 | 2 | no | — |
| 82 | C2×C3×C22⋊C4 | — | 7 | 2 | no | — |
| 83 | C2×C3×C42 | — | 7 | 2 | no | — |
| 84 | C22×ΓL(1,𝔽8) | — | 2 | 2 | no | — |
| 85 | C22×ΓL(1,𝔽8) | C22×C4 | 1 | 2 | yes | — |
| 86 | C22×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 87 | C2×AGL(1,𝔽7) | — | 2 | 2 | no | — |
| 88 | C2×AGL(1,𝔽7) | — | 2 | 8 | no | — |
| 89 | C2×AGL(1,𝔽7) | C22×C4 | 1 | 2 | yes | — |
| 90 | C2×AGL(1,𝔽7) | C22×C4 | 1 | 2 | yes | — |
| 91 | C2×AGL(1,𝔽7) | #41 | 1 | 4 | yes | — |
| 92 | C4×ΓL(1,𝔽8) | — | 2 | 4 | no | — |
| 93 | C4×ΓL(1,𝔽8) | C22×C4 | 1 | 2 | yes | — |
| 94 | C4×ΓL(1,𝔽8) | C22×C4 | 1 | 2 | yes | — |
| 95 | ΓL(1,𝔽8)⋊C4 | — | 2 | 4 | no | — |
| 96 | ΓL(1,𝔽8)⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 97 | ΓL(1,𝔽8)⋊C4 | C22×C4 | 1 | 2 | yes | — |
| 98 | C2×#117 | — | 7 | 1 | no | Sylow |
| 99 | C23×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 100 | C22×D7 | — | 2 | 4 | no | — |
| 101 | C22×D7 | C2×C3×C4 | 1 | 4 | yes | — |
| 102 | C22×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 103 | C22×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 104 | C2×C4×C7 | C2×C3×C4 | 1 | 4 | yes | complemented |
| 105 | C2×C4×C7 | C23×C3 | 1 | 4 | yes | — |
| 106 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 107 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 108 | C2×Dic7 | C2×C3×C4 | 1 | 4 | yes | complemented |
| 109 | C2×Dic7 | C23×C3 | 1 | 4 | yes | — |
| 110 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 111 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 112 | C4×D7 | — | 2 | 8 | no | — |
| 113 | C4×D7 | C2×C3×C4 | 1 | 4 | yes | — |
| 114 | C4×D7 | C2×C3×C4 | 1 | 4 | yes | — |
| 115 | C4×D7 | C2×C3×C4 | 1 | 4 | yes | complemented |
| 116 | C4×D7 | C2×C3×C4 | 1 | 4 | yes | complemented |
| 117 | C24×C3 | — | 7 | 1 | no | — |
| 118 | C22×C3×C4 | — | 7 | 8 | no | — |
| 119 | C22×C3×C4 | — | 7 | 1 | no | — |
| 120 | C22×C3×C4 | — | 7 | 1 | no | — |
| 121 | C22×C3×C4 | — | 7 | 1 | no | — |
| 122 | C22×C3×C4 | — | 7 | 1 | no | — |
| 123 | C22×C3×C4 | — | 7 | 1 | no | — |
| 124 | C22×C3×C4 | — | 7 | 4 | no | — |
| 125 | C22×C3×C4 | — | 7 | 1 | no | — |
| 126 | C3×C4⋊C4 | — | 7 | 4 | no | — |
| 127 | C3×C4⋊C4 | — | 7 | 2 | no | — |
| 128 | C3×C4⋊C4 | — | 7 | 2 | no | — |
| 129 | C3×C22⋊C4 | — | 7 | 4 | no | — |
| 130 | C3×C22⋊C4 | — | 7 | 2 | no | — |
| 131 | C3×C22⋊C4 | — | 7 | 2 | no | — |
| 132 | C3×C42 | — | 7 | 4 | no | — |
| 133 | C3×C42 | — | 7 | 2 | no | — |
| 134 | C3×C42 | — | 7 | 2 | no | — |
| 135 | C2×ΓL(1,𝔽8) | — | 2 | 2 | no | — |
| 136 | C2×ΓL(1,𝔽8) | C23×C4 | 1 | 1 | yes | characteristic |
| 137 | C2×ΓL(1,𝔽8) | C2×#41 | 1 | 2 | yes | — |
| 138 | AGL(1,𝔽7) | — | 2 | 2 | no | — |
| 139 | AGL(1,𝔽7) | #117 | 1 | 4 | yes | direct product factor |
| 140 | C23×C4 | — | 7 | 1 | no | — |
| 141 | #117 | — | 7 | 1 | no | — |
| 142 | #117 | — | 7 | 2 | no | — |
| 143 | #117 | — | 7 | 2 | no | — |
| 144 | #117 | — | 7 | 2 | no | — |
| 145 | #117 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 146 | C2×C4⋊C4 | — | 7 | 2 | no | — |
| 147 | C2×C22⋊C4 | — | 7 | 2 | no | — |
| 148 | C2×C42 | — | 7 | 2 | no | — |
| 149 | C22×C7 | — | 2 | 2 | no | — |
| 150 | C22×C7 | C22×C3×C4 | 1 | 2 | yes | — |
| 151 | C22×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 152 | C2×D7 | — | 2 | 2 | no | — |
| 153 | C2×D7 | — | 2 | 8 | no | — |
| 154 | C2×D7 | C22×C3×C4 | 1 | 2 | yes | — |
| 155 | C2×D7 | C22×C3×C4 | 1 | 2 | yes | — |
| 156 | C2×D7 | C3×#41 | 1 | 4 | yes | — |
| 157 | C4×C7 | — | 2 | 4 | no | — |
| 158 | C4×C7 | C22×C3×C4 | 1 | 2 | yes | — |
| 159 | C4×C7 | C22×C3×C4 | 1 | 2 | yes | — |
| 160 | Dic7 | — | 2 | 4 | no | — |
| 161 | Dic7 | C22×C3×C4 | 1 | 2 | yes | — |
| 162 | Dic7 | C22×C3×C4 | 1 | 2 | yes | — |
| 163 | C23×C3 | — | 7 | 1 | no | — |
| 164 | C23×C3 | — | 7 | 4 | no | — |
| 165 | C23×C3 | — | 7 | 1 | no | — |
| 166 | C23×C3 | — | 7 | 1 | no | — |
| 167 | C23×C3 | — | 14 | 4 | no | — |
| 168 | C2×C3×C4 | — | 7 | 4 | no | — |
| 169 | C2×C3×C4 | — | 7 | 4 | no | — |
| 170 | C2×C3×C4 | — | 7 | 4 | no | — |
| 171 | C2×C3×C4 | — | 7 | 4 | no | — |
| 172 | C2×C3×C4 | — | 7 | 4 | no | — |
| 173 | C2×C3×C4 | — | 7 | 1 | no | — |
| 174 | C2×C3×C4 | — | 7 | 1 | no | — |
| 175 | C2×C3×C4 | — | 7 | 4 | no | — |
| 176 | C2×C3×C4 | — | 7 | 4 | no | — |
| 177 | C2×C3×C4 | — | 7 | 1 | no | — |
| 178 | C2×C3×C4 | — | 7 | 4 | no | — |
| 179 | C2×C3×C4 | — | 7 | 1 | no | — |
| 180 | C2×C3×C4 | — | 14 | 8 | no | — |
| 181 | ΓL(1,𝔽8) | C2×#117 | 1 | 1 | yes | characteristic, complemented, Hall |
| 182 | C24 | — | 7 | 1 | no | — |
| 183 | C22×C4 | — | 7 | 1 | no | — |
| 184 | C22×C4 | — | 7 | 8 | no | — |
| 185 | C22×C4 | — | 7 | 1 | no | — |
| 186 | C22×C4 | — | 7 | 1 | no | — |
| 187 | C22×C4 | — | 7 | 1 | no | — |
| 188 | C22×C4 | — | 7 | 1 | no | — |
| 189 | C22×C4 | — | 7 | 4 | no | — |
| 190 | C22×C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 191 | C4⋊C4 | — | 7 | 4 | no | — |
| 192 | C4⋊C4 | — | 7 | 2 | no | — |
| 193 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 2 | yes | complemented |
| 194 | C22⋊C4 | — | 7 | 2 | no | — |
| 195 | C22⋊C4 | — | 7 | 4 | no | — |
| 196 | C22⋊C4 | C2×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 197 | C42 | — | 7 | 4 | no | — |
| 198 | C42 | — | 7 | 2 | no | — |
| 199 | C42 | C2×AGL(1,𝔽7) | 1 | 2 | yes | complemented |
| 200 | C2×C7 | — | 2 | 2 | no | — |
| 201 | C2×C7 | C23×C3×C4 | 1 | 1 | yes | characteristic |
| 202 | C2×C7 | C2×C3×#41 | 1 | 2 | yes | — |
| 203 | D7 | — | 2 | 2 | no | — |
| 204 | D7 | C3×#117 | 1 | 4 | yes | complemented |
| 205 | C22×C3 | — | 7 | 2 | no | — |
| 206 | C22×C3 | — | 7 | 4 | no | — |
| 207 | C22×C3 | — | 7 | 2 | no | — |
| 208 | C22×C3 | — | 7 | 2 | no | — |
| 209 | C22×C3 | — | 7 | 1 | no | — |
| 210 | C22×C3 | — | 14 | 2 | no | — |
| 211 | C22×C3 | — | 14 | 8 | no | — |
| 212 | C22×C3 | — | 14 | 2 | no | — |
| 213 | C3×C4 | — | 7 | 2 | no | — |
| 214 | C3×C4 | — | 7 | 2 | no | — |
| 215 | C3×C4 | — | 7 | 2 | no | — |
| 216 | C3×C4 | — | 7 | 2 | no | — |
| 217 | C3×C4 | — | 14 | 4 | no | — |
| 218 | C3×C4 | — | 14 | 4 | no | — |
| 219 | C23 | — | 7 | 1 | no | — |
| 220 | C23 | — | 7 | 4 | no | — |
| 221 | C23 | — | 7 | 1 | no | — |
| 222 | C23 | — | 14 | 4 | no | — |
| 223 | C23 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 224 | C2×C4 | — | 7 | 4 | no | — |
| 225 | C2×C4 | — | 7 | 1 | no | — |
| 226 | C2×C4 | — | 7 | 1 | no | — |
| 227 | C2×C4 | — | 7 | 4 | no | — |
| 228 | C2×C4 | — | 7 | 4 | no | — |
| 229 | C2×C4 | — | 7 | 4 | no | — |
| 230 | C2×C4 | — | 7 | 4 | no | — |
| 231 | C2×C4 | — | 7 | 4 | no | — |
| 232 | C2×C4 | — | 14 | 8 | no | — |
| 233 | C2×C4 | C4×AGL(1,𝔽7) | 1 | 4 | yes | complemented |
| 234 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 4 | yes | — |
| 235 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 236 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 237 | C7 | C2×C3×#117 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 238 | C2×C3 | — | 7 | 4 | no | — |
| 239 | C2×C3 | — | 7 | 1 | no | — |
| 240 | C2×C3 | — | 7 | 2 | no | — |
| 241 | C2×C3 | — | 14 | 2 | no | — |
| 242 | C2×C3 | — | 14 | 2 | no | — |
| 243 | C22 | — | 2 | 2 | no | — |
| 244 | C22 | — | 7 | 2 | no | — |
| 245 | C22 | — | 7 | 4 | no | — |
| 246 | C22 | — | 7 | 2 | no | — |
| 247 | C22 | — | 14 | 8 | no | — |
| 248 | C22 | — | 14 | 2 | no | — |
| 249 | C22 | C2×C4×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 250 | C22 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 251 | C4 | — | 2 | 4 | no | — |
| 252 | C4 | — | 7 | 2 | no | — |
| 253 | C4 | — | 7 | 2 | no | — |
| 254 | C4 | — | 14 | 4 | no | — |
| 255 | C4 | C2×C4×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 256 | C4 | C2×C4×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 257 | C3 | — | 7 | 1 | no | Sylow |
| 258 | C2 | — | 2 | 2 | no | — |
| 259 | C2 | — | 7 | 4 | no | — |
| 260 | C2 | — | 14 | 2 | no | — |
| 261 | C2 | C22×C4×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 262 | C2 | #41×AGL(1,𝔽7) | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|
| 2. ΓL(1,𝔽8)×#117 | C2 | semidirect |
| 3. #6489⋊C3 | C2 | semidirect |
| 4. #6455⋊C3 | C2 | semidirect |
| 5. C4⋊C4×AGL(1,𝔽7) | C2 | semidirect |
| 7. #6440⋊C3 | C2 | semidirect |
| 8. #6435⋊C3 | C2 | semidirect |
| 9. C42×AGL(1,𝔽7) | C2 | semidirect |
| 10. D7×#117 | C3 | semidirect |
| 14. C2×C4×AGL(1,𝔽7) | C4 | semidirect |
| 20. C4⋊C4×ΓL(1,𝔽8) | C22 | semidirect |
| 22. C42×ΓL(1,𝔽8) | C22 | semidirect |
| 25. C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | semidirect |
| 26. (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | semidirect |
| 27. C4×ΓL(1,𝔽8)⋊C4 | C22 | semidirect |
| 28. C4×ΓL(1,𝔽8)⋊C4 | C22 | semidirect |
| 30. C7×#117 | C2×C3 | semidirect |
| 31. #6489 | C2×C3 | semidirect |
| 32. #6455 | C2×C3 | semidirect |
| 33. D7×C4⋊C4 | C2×C3 | semidirect |
| 35. #6440 | C2×C3 | semidirect |
| 36. #6435 | C2×C3 | semidirect |
| 37. C42×D7 | C2×C3 | semidirect |
| 44. C2×C4×ΓL(1,𝔽8) | C2×C4 | semidirect |
| 48. C2×ΓL(1,𝔽8)⋊C4 | C2×C4 | semidirect |
| 55. C4×AGL(1,𝔽7) | C2×C4 | semidirect |
| 56. C4×AGL(1,𝔽7) | C2×C4 | semidirect |
| 60. C2×C4×D7 | C3×C4 | semidirect |
| 66. C7×C4⋊C4 | C22×C3 | semidirect |
| 68. C42×C7 | C22×C3 | semidirect |
| 71. C4⋊Dic7 | C22×C3 | semidirect |
| 72. Dic7⋊C4 | C22×C3 | semidirect |
| 73. C4×Dic7 | C22×C3 | semidirect |
| 74. C4×Dic7 | C22×C3 | semidirect |
| 104. C2×C4×C7 | C2×C3×C4 | semidirect |
| 108. C2×Dic7 | C2×C3×C4 | semidirect |
| 115. C4×D7 | C2×C3×C4 | semidirect |
| 116. C4×D7 | C2×C3×C4 | semidirect |
| 139. AGL(1,𝔽7) | #117 | direct (N × H) |
| 145. #117 | AGL(1,𝔽7) | direct (N × H) |
| 181. ΓL(1,𝔽8) | C2×#117 | semidirect |
| 193. C4⋊C4 | C2×AGL(1,𝔽7) | semidirect |
| 199. C42 | C2×AGL(1,𝔽7) | semidirect |
| 204. D7 | C3×#117 | semidirect |
| 233. C2×C4 | C4×AGL(1,𝔽7) | semidirect |
| 237. C7 | C2×C3×#117 | semidirect |
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta