Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
702 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C7×#3199 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C7×#3021 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C7×#2122 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | C7×#1794 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C7×#585 | C22 | 1 | 1 | yes | characteristic |
| 7 | C2×C7×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 8 | C7×#535 | C22 | 1 | 2 | yes | — |
| 9 | C7×#482 | — | 2 | 2 | no | — |
| 10 | C7×#469 | — | 2 | 1 | no | — |
| 11 | C7×#466 | — | 2 | 1 | no | — |
| 12 | C7×#454 | — | 2 | 4 | no | — |
| 13 | C7×#453 | — | 2 | 4 | no | — |
| 14 | C7×#447 | — | 2 | 2 | no | — |
| 15 | C7×#421 | — | 2 | 2 | no | — |
| 16 | C7×#421 | — | 2 | 1 | no | — |
| 17 | C7×#416 | — | 2 | 1 | no | — |
| 18 | C7×#413 | C22 | 1 | 2 | yes | — |
| 19 | C7×#410 | C22 | 1 | 1 | yes | characteristic |
| 20 | C7×#408 | C22 | 1 | 1 | yes | characteristic |
| 21 | C7×AΣL(1,𝔽16) | — | 2 | 4 | no | — |
| 22 | #13360 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 23 | C7×2−1+4 | — | 4 | 1 | no | — |
| 24 | C7×2−1+4 | D4 | 1 | 2 | yes | — |
| 25 | C7×H(5,𝔽2) | — | 2 | 2 | no | — |
| 26 | C7×H(5,𝔽2) | — | 2 | 1 | no | — |
| 27 | C7×H(5,𝔽2) | — | 4 | 1 | no | — |
| 28 | C2×C7×#41 | — | 2 | 1 | no | — |
| 29 | C2×C7×#41 | — | 2 | 2 | no | — |
| 30 | C2×C7×#41 | — | 4 | 2 | no | — |
| 31 | C2×C7×#41 | C23 | 1 | 1 | yes | characteristic |
| 32 | C22×C7×D4 | D4 | 1 | 2 | yes | — |
| 33 | C7×AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 34 | C7×AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 35 | C2×C7×SD16 | — | 4 | 2 | no | — |
| 36 | C2×C7×D8 | — | 2 | 1 | no | — |
| 37 | C2×C7×D8 | — | 2 | 1 | no | — |
| 38 | C2×C7×D8 | — | 4 | 2 | no | — |
| 39 | C2×C7×M16 | — | 2 | 2 | no | — |
| 40 | C2×C7×M16 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×C7×C8 | D4 | 1 | 1 | yes | characteristic |
| 42 | C7×#127 | — | 2 | 2 | no | — |
| 43 | C7×#124 | — | 2 | 2 | no | — |
| 44 | C7×#121 | — | 2 | 2 | no | — |
| 45 | C7×#121 | — | 2 | 2 | no | — |
| 46 | C7×#120 | — | 2 | 2 | no | — |
| 47 | C7×#120 | — | 2 | 2 | no | — |
| 48 | C7×#117 | — | 2 | 1 | no | — |
| 49 | C7×#117 | D4 | 1 | 2 | yes | — |
| 50 | C7×#107 | — | 2 | 1 | no | — |
| 51 | C7×#106 | — | 2 | 1 | no | — |
| 52 | C7×#104 | — | 2 | 8 | no | — |
| 53 | C7×#104 | — | 4 | 2 | no | — |
| 54 | C7×#103 | — | 4 | 1 | no | — |
| 55 | C7×#102 | — | 2 | 2 | no | — |
| 56 | C7×#102 | — | 2 | 2 | no | — |
| 57 | C7×#102 | — | 4 | 1 | no | — |
| 58 | C7×#101 | — | 2 | 2 | no | — |
| 59 | C7×#100 | D4 | 1 | 4 | yes | — |
| 60 | C7×#99 | — | 2 | 2 | no | — |
| 61 | C7×C22⋊C8 | — | 2 | 2 | no | — |
| 62 | #3199 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 63 | #3021 | C2×C7 | 1 | 2 | yes | complemented |
| 64 | #2122 | C2×C7 | 1 | 2 | yes | complemented |
| 65 | #1794 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 66 | #1392 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 67 | C24×C7 | — | 2 | 2 | no | — |
| 68 | C7×#41 | — | 2 | 2 | no | — |
| 69 | C7×#41 | — | 2 | 4 | no | — |
| 70 | C7×#41 | — | 2 | 4 | no | — |
| 71 | C7×#41 | — | 2 | 2 | no | — |
| 72 | C7×#41 | — | 4 | 1 | no | — |
| 73 | C7×#41 | — | 4 | 1 | no | — |
| 74 | C7×#41 | — | 4 | 1 | no | — |
| 75 | C7×#41 | — | 4 | 2 | no | — |
| 76 | C7×#41 | — | 4 | 2 | no | — |
| 77 | C7×#41 | — | 4 | 4 | no | — |
| 78 | C7×#41 | — | 4 | 2 | no | — |
| 79 | C7×#41 | — | 4 | 1 | no | — |
| 80 | C2×C7×Q8 | — | 2 | 1 | no | — |
| 81 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 82 | C2×C7×Q8 | — | 4 | 2 | no | — |
| 83 | C2×C7×Q8 | C2×D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C7×D4 | — | 2 | 1 | no | — |
| 85 | C2×C7×D4 | — | 2 | 2 | no | — |
| 86 | C2×C7×D4 | — | 2 | 2 | no | — |
| 87 | C2×C7×D4 | — | 2 | 2 | no | — |
| 88 | C2×C7×D4 | — | 4 | 2 | no | — |
| 89 | C2×C7×D4 | — | 4 | 2 | no | — |
| 90 | C2×C7×D4 | — | 4 | 4 | no | — |
| 91 | C2×C7×D4 | — | 4 | 2 | no | — |
| 92 | C2×C7×D4 | — | 4 | 2 | no | — |
| 93 | C2×C7×D4 | — | 4 | 1 | no | — |
| 94 | C2×C7×D4 | — | 4 | 2 | no | — |
| 95 | C2×C7×D4 | — | 4 | 2 | no | — |
| 96 | C2×C7×D4 | C2×D4 | 1 | 2 | yes | — |
| 97 | C2×C7×D4 | #41 | 1 | 1 | yes | characteristic |
| 98 | C22×C4×C7 | — | 4 | 1 | no | — |
| 99 | C22×C4×C7 | — | 4 | 2 | no | — |
| 100 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 101 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 102 | C7×SD16 | — | 4 | 8 | no | — |
| 103 | C7×D8 | — | 4 | 8 | no | — |
| 104 | C7×D8 | — | 8 | 1 | no | — |
| 105 | C7×D8 | — | 8 | 1 | no | — |
| 106 | C7×M16 | — | 2 | 4 | no | — |
| 107 | C7×M16 | — | 4 | 2 | no | — |
| 108 | C7×M16 | — | 4 | 1 | no | — |
| 109 | C2×C7×C8 | — | 2 | 1 | no | — |
| 110 | C2×C7×C8 | — | 2 | 1 | no | — |
| 111 | C2×C7×C8 | — | 4 | 2 | no | — |
| 112 | C2×C7×C8 | — | 4 | 1 | no | — |
| 113 | C7×C4⋊C4 | — | 2 | 2 | no | — |
| 114 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 115 | C7×C22⋊C4 | — | 2 | 2 | no | — |
| 116 | C7×C22⋊C4 | — | 4 | 2 | no | — |
| 117 | C7×C22⋊C4 | — | 4 | 2 | no | — |
| 118 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 119 | C42×C7 | — | 2 | 2 | no | — |
| 120 | C42×C7 | — | 4 | 1 | no | — |
| 121 | #585 | C22×C7 | 1 | 1 | yes | characteristic |
| 122 | C2×AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 123 | #535 | C22×C7 | 1 | 2 | yes | — |
| 124 | #482 | — | 2 | 2 | no | — |
| 125 | #469 | — | 2 | 1 | no | — |
| 126 | #466 | — | 2 | 1 | no | — |
| 127 | #454 | — | 2 | 4 | no | — |
| 128 | #453 | — | 2 | 4 | no | — |
| 129 | #447 | — | 2 | 2 | no | — |
| 130 | #421 | — | 2 | 2 | no | — |
| 131 | #421 | — | 2 | 1 | no | — |
| 132 | #416 | — | 2 | 1 | no | — |
| 133 | #413 | C22×C7 | 1 | 2 | yes | — |
| 134 | #410 | C22×C7 | 1 | 1 | yes | characteristic |
| 135 | #408 | C22×C7 | 1 | 1 | yes | characteristic |
| 136 | AΣL(1,𝔽16) | — | 2 | 4 | no | — |
| 137 | C23×C7 | — | 4 | 1 | no | — |
| 138 | C23×C7 | — | 4 | 2 | no | — |
| 139 | C23×C7 | — | 4 | 2 | no | — |
| 140 | C23×C7 | — | 8 | 2 | no | — |
| 141 | C23×C7 | — | 16 | 2 | no | — |
| 142 | C23×C7 | #121 | 1 | 2 | yes | — |
| 143 | C23×C7 | #127 | 1 | 1 | yes | characteristic |
| 144 | C7×Q8 | — | 2 | 4 | no | — |
| 145 | C7×Q8 | — | 2 | 2 | no | — |
| 146 | C7×Q8 | — | 4 | 1 | no | — |
| 147 | C7×Q8 | — | 4 | 1 | no | — |
| 148 | C7×D4 | — | 2 | 4 | no | — |
| 149 | C7×D4 | — | 2 | 2 | no | — |
| 150 | C7×D4 | — | 4 | 2 | no | — |
| 151 | C7×D4 | — | 4 | 1 | no | — |
| 152 | C7×D4 | — | 4 | 4 | no | — |
| 153 | C7×D4 | — | 4 | 2 | no | — |
| 154 | C7×D4 | — | 4 | 4 | no | — |
| 155 | C7×D4 | — | 4 | 2 | no | — |
| 156 | C7×D4 | — | 4 | 1 | no | — |
| 157 | C7×D4 | — | 4 | 2 | no | — |
| 158 | C7×D4 | — | 4 | 2 | no | — |
| 159 | C7×D4 | — | 16 | 2 | no | — |
| 160 | C7×D4 | — | 16 | 2 | no | — |
| 161 | C2×C4×C7 | — | 2 | 1 | no | — |
| 162 | C2×C4×C7 | — | 2 | 1 | no | — |
| 163 | C2×C4×C7 | — | 2 | 2 | no | — |
| 164 | C2×C4×C7 | — | 2 | 2 | no | — |
| 165 | C2×C4×C7 | — | 4 | 4 | no | — |
| 166 | C2×C4×C7 | — | 4 | 2 | no | — |
| 167 | C2×C4×C7 | — | 4 | 1 | no | — |
| 168 | C2×C4×C7 | — | 4 | 2 | no | — |
| 169 | C2×C4×C7 | — | 4 | 2 | no | — |
| 170 | C2×C4×C7 | — | 4 | 2 | no | — |
| 171 | C2×C4×C7 | — | 8 | 1 | no | — |
| 172 | C2×C4×C7 | #120 | 1 | 2 | yes | — |
| 173 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 174 | C2×C4×C7 | #121 | 1 | 1 | yes | characteristic |
| 175 | C7×C8 | — | 4 | 4 | no | — |
| 176 | C7×C8 | — | 4 | 1 | no | — |
| 177 | C7×C8 | — | 4 | 1 | no | — |
| 178 | 2−1+4 | — | 4 | 1 | no | — |
| 179 | 2−1+4 | C7×D4 | 1 | 2 | yes | — |
| 180 | H(5,𝔽2) | — | 2 | 2 | no | — |
| 181 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 182 | H(5,𝔽2) | — | 4 | 1 | no | — |
| 183 | C2×#41 | — | 2 | 2 | no | — |
| 184 | C2×#41 | — | 2 | 1 | no | — |
| 185 | C2×#41 | — | 4 | 2 | no | — |
| 186 | C2×#41 | C23×C7 | 1 | 1 | yes | characteristic |
| 187 | C22×D4 | C7×D4 | 1 | 2 | yes | — |
| 188 | AGL(1,ℤ/8) | — | 2 | 8 | no | — |
| 189 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 190 | C2×SD16 | — | 4 | 2 | no | — |
| 191 | C2×D8 | — | 2 | 1 | no | — |
| 192 | C2×D8 | — | 2 | 1 | no | — |
| 193 | C2×D8 | — | 4 | 2 | no | — |
| 194 | C2×M16 | — | 2 | 2 | no | — |
| 195 | C2×M16 | C7×D4 | 1 | 1 | yes | characteristic |
| 196 | C22×C8 | C7×D4 | 1 | 1 | yes | characteristic |
| 197 | #127 | — | 2 | 2 | no | — |
| 198 | #124 | — | 2 | 2 | no | — |
| 199 | #121 | — | 2 | 2 | no | — |
| 200 | #121 | — | 2 | 2 | no | — |
| 201 | #120 | — | 2 | 2 | no | — |
| 202 | #120 | — | 2 | 2 | no | — |
| 203 | #117 | — | 2 | 1 | no | — |
| 204 | #117 | C7×D4 | 1 | 2 | yes | — |
| 205 | #107 | — | 2 | 1 | no | — |
| 206 | #106 | — | 2 | 1 | no | — |
| 207 | #104 | — | 2 | 8 | no | — |
| 208 | #104 | — | 4 | 2 | no | — |
| 209 | #103 | — | 4 | 1 | no | — |
| 210 | #102 | — | 2 | 2 | no | — |
| 211 | #102 | — | 2 | 2 | no | — |
| 212 | #102 | — | 4 | 1 | no | — |
| 213 | #101 | — | 2 | 2 | no | — |
| 214 | #100 | C7×D4 | 1 | 4 | yes | — |
| 215 | #99 | — | 2 | 2 | no | — |
| 216 | C22⋊C8 | — | 2 | 2 | no | — |
| 217 | C22×C7 | — | 2 | 1 | no | — |
| 218 | C22×C7 | — | 2 | 2 | no | — |
| 219 | C22×C7 | — | 4 | 1 | no | — |
| 220 | C22×C7 | — | 4 | 2 | no | — |
| 221 | C22×C7 | — | 4 | 2 | no | — |
| 222 | C22×C7 | — | 8 | 2 | no | — |
| 223 | C22×C7 | — | 8 | 2 | no | — |
| 224 | C22×C7 | — | 8 | 2 | no | — |
| 225 | C22×C7 | — | 16 | 1 | no | — |
| 226 | C22×C7 | — | 16 | 2 | no | — |
| 227 | C22×C7 | — | 16 | 4 | no | — |
| 228 | C22×C7 | #392 | 1 | 1 | yes | characteristic |
| 229 | C4×C7 | — | 2 | 2 | no | — |
| 230 | C4×C7 | — | 2 | 1 | no | — |
| 231 | C4×C7 | — | 4 | 2 | no | — |
| 232 | C4×C7 | — | 8 | 2 | no | — |
| 233 | C4×C7 | — | 16 | 1 | no | — |
| 234 | C4×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 235 | C4×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | C24 | — | 2 | 2 | no | — |
| 237 | #41 | — | 2 | 2 | no | — |
| 238 | #41 | — | 2 | 4 | no | — |
| 239 | #41 | — | 2 | 4 | no | — |
| 240 | #41 | — | 2 | 2 | no | — |
| 241 | #41 | — | 4 | 1 | no | — |
| 242 | #41 | — | 4 | 1 | no | — |
| 243 | #41 | — | 4 | 1 | no | — |
| 244 | #41 | — | 4 | 2 | no | — |
| 245 | #41 | — | 4 | 2 | no | — |
| 246 | #41 | — | 4 | 4 | no | — |
| 247 | #41 | — | 4 | 2 | no | — |
| 248 | #41 | — | 4 | 1 | no | — |
| 249 | C2×Q8 | — | 2 | 1 | no | — |
| 250 | C2×Q8 | — | 2 | 2 | no | — |
| 251 | C2×Q8 | — | 4 | 2 | no | — |
| 252 | C2×Q8 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 253 | C2×D4 | — | 2 | 1 | no | — |
| 254 | C2×D4 | — | 2 | 2 | no | — |
| 255 | C2×D4 | — | 2 | 2 | no | — |
| 256 | C2×D4 | — | 2 | 2 | no | — |
| 257 | C2×D4 | — | 4 | 2 | no | — |
| 258 | C2×D4 | — | 4 | 2 | no | — |
| 259 | C2×D4 | — | 4 | 4 | no | — |
| 260 | C2×D4 | — | 4 | 2 | no | — |
| 261 | C2×D4 | — | 4 | 2 | no | — |
| 262 | C2×D4 | — | 4 | 1 | no | — |
| 263 | C2×D4 | — | 4 | 2 | no | — |
| 264 | C2×D4 | — | 4 | 2 | no | — |
| 265 | C2×D4 | C2×C7×D4 | 1 | 2 | yes | — |
| 266 | C2×D4 | C7×#41 | 1 | 1 | yes | characteristic |
| 267 | C22×C4 | — | 4 | 1 | no | — |
| 268 | C22×C4 | — | 4 | 2 | no | — |
| 269 | C22×C4 | C2×C7×D4 | 1 | 2 | yes | — |
| 270 | C22×C4 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 271 | SD16 | — | 4 | 8 | no | — |
| 272 | D8 | — | 4 | 8 | no | — |
| 273 | D8 | — | 8 | 1 | no | — |
| 274 | D8 | — | 8 | 1 | no | — |
| 275 | M16 | — | 2 | 4 | no | — |
| 276 | M16 | — | 4 | 2 | no | — |
| 277 | M16 | — | 4 | 1 | no | — |
| 278 | C2×C8 | — | 2 | 1 | no | — |
| 279 | C2×C8 | — | 2 | 1 | no | — |
| 280 | C2×C8 | — | 4 | 2 | no | — |
| 281 | C2×C8 | — | 4 | 1 | no | — |
| 282 | C4⋊C4 | — | 2 | 2 | no | — |
| 283 | C4⋊C4 | — | 4 | 1 | no | — |
| 284 | C22⋊C4 | — | 2 | 2 | no | — |
| 285 | C22⋊C4 | — | 4 | 2 | no | — |
| 286 | C22⋊C4 | — | 4 | 2 | no | — |
| 287 | C22⋊C4 | — | 4 | 1 | no | — |
| 288 | C42 | — | 2 | 2 | no | — |
| 289 | C42 | — | 4 | 1 | no | — |
| 290 | C2×C7 | — | 2 | 1 | no | — |
| 291 | C2×C7 | — | 4 | 1 | no | — |
| 292 | C2×C7 | — | 4 | 2 | no | — |
| 293 | C2×C7 | — | 8 | 2 | no | — |
| 294 | C2×C7 | — | 16 | 2 | no | — |
| 295 | C2×C7 | #2021 | 1 | 1 | yes | characteristic |
| 296 | C23 | — | 4 | 1 | no | — |
| 297 | C23 | — | 4 | 2 | no | — |
| 298 | C23 | — | 4 | 2 | no | — |
| 299 | C23 | — | 8 | 2 | no | — |
| 300 | C23 | — | 16 | 2 | no | — |
| 301 | C23 | C7×#121 | 1 | 2 | yes | — |
| 302 | C23 | C7×#127 | 1 | 1 | yes | characteristic |
| 303 | Q8 | — | 2 | 4 | no | — |
| 304 | Q8 | — | 2 | 2 | no | — |
| 305 | Q8 | — | 4 | 1 | no | — |
| 306 | Q8 | — | 4 | 1 | no | — |
| 307 | D4 | — | 2 | 4 | no | — |
| 308 | D4 | — | 2 | 2 | no | — |
| 309 | D4 | — | 4 | 2 | no | — |
| 310 | D4 | — | 4 | 1 | no | — |
| 311 | D4 | — | 4 | 4 | no | — |
| 312 | D4 | — | 4 | 2 | no | — |
| 313 | D4 | — | 4 | 4 | no | — |
| 314 | D4 | — | 4 | 2 | no | — |
| 315 | D4 | — | 4 | 1 | no | — |
| 316 | D4 | — | 4 | 2 | no | — |
| 317 | D4 | — | 4 | 2 | no | — |
| 318 | D4 | — | 16 | 2 | no | — |
| 319 | D4 | — | 16 | 2 | no | — |
| 320 | C2×C4 | — | 2 | 1 | no | — |
| 321 | C2×C4 | — | 2 | 1 | no | — |
| 322 | C2×C4 | — | 2 | 2 | no | — |
| 323 | C2×C4 | — | 2 | 2 | no | — |
| 324 | C2×C4 | — | 4 | 4 | no | — |
| 325 | C2×C4 | — | 4 | 2 | no | — |
| 326 | C2×C4 | — | 4 | 1 | no | — |
| 327 | C2×C4 | — | 4 | 2 | no | — |
| 328 | C2×C4 | — | 4 | 2 | no | — |
| 329 | C2×C4 | — | 4 | 2 | no | — |
| 330 | C2×C4 | — | 8 | 1 | no | — |
| 331 | C2×C4 | C7×#120 | 1 | 2 | yes | — |
| 332 | C2×C4 | C7×#120 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C7×#121 | 1 | 1 | yes | characteristic |
| 334 | C8 | — | 4 | 4 | no | — |
| 335 | C8 | — | 4 | 1 | no | — |
| 336 | C8 | — | 4 | 1 | no | — |
| 337 | C7 | #13360 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 338 | C22 | — | 2 | 1 | no | — |
| 339 | C22 | — | 2 | 2 | no | — |
| 340 | C22 | — | 4 | 1 | no | — |
| 341 | C22 | — | 4 | 2 | no | — |
| 342 | C22 | — | 4 | 2 | no | — |
| 343 | C22 | — | 8 | 2 | no | — |
| 344 | C22 | — | 8 | 2 | no | — |
| 345 | C22 | — | 8 | 2 | no | — |
| 346 | C22 | — | 16 | 1 | no | — |
| 347 | C22 | — | 16 | 2 | no | — |
| 348 | C22 | — | 16 | 4 | no | — |
| 349 | C22 | C7×#392 | 1 | 1 | yes | characteristic |
| 350 | C4 | — | 2 | 2 | no | — |
| 351 | C4 | — | 2 | 1 | no | — |
| 352 | C4 | — | 4 | 2 | no | — |
| 353 | C4 | — | 8 | 2 | no | — |
| 354 | C4 | — | 16 | 1 | no | — |
| 355 | C4 | C7×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 356 | C4 | C7×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 357 | C2 | — | 2 | 1 | no | — |
| 358 | C2 | — | 4 | 1 | no | — |
| 359 | C2 | — | 4 | 2 | no | — |
| 360 | C2 | — | 8 | 2 | no | — |
| 361 | C2 | — | 16 | 2 | no | — |
| 362 | C2 | C7×#2021 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2021 |
| commutator, Frattini, cosocle | C2×#41 | C23×C7 |
| LCS | G ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×#41 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3199 | C2 | semidirect |
| 2. C7×#3021 | C2 | semidirect |
| 3. C7×#2122 | C2 | semidirect |
| 4. C7×#1794 | C2 | semidirect |
| 5. C7×#1392 | C2 | semidirect |
| 22. #13360 | C7 | direct (N × H) |
| 62. #3199 | C2×C7 | semidirect |
| 63. #3021 | C2×C7 | semidirect |
| 64. #2122 | C2×C7 | semidirect |
| 65. #1794 | C2×C7 | semidirect |
| 66. #1392 | C2×C7 | semidirect |
| 337. C7 | #13360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3199 | 2 |
| C7×#3021 | 2 |
| C7×#2122 | 2 |
| C7×#1794 | 2 |
| C7×#1392 | 2 |
| #13360 | 7 |