Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2002 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 2002 conjugacy classes of subgroups — too many to draw. Only its 282 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×#3484 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C7×#3026 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | C7×#2021 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | C7×#1913 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | C7×#1781 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C7×H(5,𝔽2) | C22 | 1 | 2 | yes | complemented |
| 7 | C23×C7×D4 | C22 | 1 | 1 | yes | characteristic |
| 8 | C7×#546 | — | 2 | 8 | no | — |
| 9 | C7×D42 | — | 2 | 8 | no | — |
| 10 | C7×#535 | — | 2 | 2 | no | — |
| 11 | C7×#534 | — | 2 | 2 | no | — |
| 12 | C7×#534 | C22 | 1 | 4 | yes | — |
| 13 | C7×#534 | C22 | 1 | 4 | yes | complemented |
| 14 | C7×#525 | — | 2 | 2 | no | — |
| 15 | C2×C7×#120 | — | 2 | 2 | no | — |
| 16 | C2×C7×#120 | C22 | 1 | 4 | yes | complemented |
| 17 | C7×#518 | C22 | 1 | 2 | yes | complemented |
| 18 | C7×#458 | — | 2 | 8 | no | — |
| 19 | C7×B(4,𝔽2) | — | 2 | 8 | no | — |
| 20 | C2×C7×#99 | C22 | 1 | 8 | yes | complemented |
| 21 | C2×C7×#99 | C22 | 1 | 4 | yes | complemented |
| 22 | C7×#379 | C22 | 1 | 2 | yes | complemented |
| 23 | C7×#342 | C22 | 1 | 4 | yes | complemented |
| 24 | #23895 | C7 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 25 | C25×C7 | D4 | 1 | 1 | yes | characteristic, complemented |
| 26 | C25×C7 | C23 | 1 | 1 | yes | characteristic |
| 27 | C7×H(5,𝔽2) | — | 2 | 8 | no | — |
| 28 | C7×H(5,𝔽2) | — | 4 | 4 | no | — |
| 29 | C2×C7×#41 | — | 2 | 2 | no | — |
| 30 | C2×C7×#41 | — | 2 | 4 | no | — |
| 31 | C22×C7×D4 | — | 2 | 2 | no | — |
| 32 | C22×C7×D4 | — | 2 | 4 | no | — |
| 33 | C22×C7×D4 | — | 2 | 4 | no | — |
| 34 | C22×C7×D4 | — | 2 | 4 | no | — |
| 35 | C22×C7×D4 | — | 2 | 8 | no | — |
| 36 | C22×C7×D4 | — | 4 | 2 | no | — |
| 37 | C22×C7×D4 | D4 | 1 | 2 | yes | complemented |
| 38 | C22×C7×D4 | C23 | 1 | 2 | yes | — |
| 39 | C22×C7×D4 | C23 | 1 | 4 | yes | — |
| 40 | C23×C4×C7 | D4 | 1 | 1 | yes | characteristic, complemented |
| 41 | C7×#127 | — | 2 | 4 | no | — |
| 42 | C7×#124 | — | 2 | 4 | no | — |
| 43 | C7×#123 | — | 2 | 4 | no | — |
| 44 | C7×#123 | — | 2 | 4 | no | — |
| 45 | C7×#123 | — | 2 | 8 | no | — |
| 46 | C7×#123 | D4 | 1 | 8 | yes | complemented |
| 47 | C7×C22⋊Q8 | — | 2 | 4 | no | — |
| 48 | C7×#121 | — | 2 | 4 | no | — |
| 49 | C7×#121 | — | 2 | 8 | no | — |
| 50 | C7×#121 | — | 2 | 8 | no | — |
| 51 | C7×#121 | — | 2 | 8 | no | — |
| 52 | C7×#121 | — | 4 | 4 | no | — |
| 53 | C7×#120 | — | 2 | 8 | no | — |
| 54 | C7×#120 | — | 2 | 4 | no | — |
| 55 | C7×#120 | — | 2 | 4 | no | — |
| 56 | C7×#120 | — | 2 | 4 | no | — |
| 57 | C7×#120 | — | 2 | 4 | no | — |
| 58 | C7×#120 | — | 2 | 8 | no | — |
| 59 | C7×#120 | — | 2 | 8 | no | — |
| 60 | C7×#120 | D4 | 1 | 8 | yes | complemented |
| 61 | C4×C7×D4 | — | 2 | 8 | no | — |
| 62 | C4×C7×D4 | — | 2 | 8 | no | — |
| 63 | C7×#117 | — | 2 | 2 | no | — |
| 64 | C2×C7×C22⋊C4 | — | 2 | 4 | no | — |
| 65 | C2×C7×C22⋊C4 | — | 2 | 2 | no | — |
| 66 | C2×C7×C22⋊C4 | — | 2 | 4 | no | — |
| 67 | C2×C7×C22⋊C4 | — | 4 | 2 | no | — |
| 68 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 69 | C2×C7×C22⋊C4 | C23 | 1 | 4 | yes | — |
| 70 | C7×#99 | — | 2 | 8 | no | — |
| 71 | C7×#99 | — | 2 | 16 | no | — |
| 72 | #3484 | C2×C7 | 1 | 2 | yes | complemented |
| 73 | #3026 | C2×C7 | 1 | 4 | yes | complemented |
| 74 | #2021 | C2×C7 | 1 | 4 | yes | complemented |
| 75 | #1913 | C2×C7 | 1 | 4 | yes | complemented |
| 76 | #1781 | C2×C7 | 1 | 1 | yes | characteristic, complemented |
| 77 | C24×C7 | — | 2 | 2 | no | — |
| 78 | C24×C7 | — | 2 | 4 | no | — |
| 79 | C24×C7 | — | 2 | 4 | no | — |
| 80 | C24×C7 | — | 2 | 2 | no | — |
| 81 | C24×C7 | — | 4 | 1 | no | — |
| 82 | C24×C7 | — | 8 | 2 | no | — |
| 83 | C24×C7 | — | 8 | 2 | no | — |
| 84 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 85 | C24×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | C24×C7 | C2×D4 | 1 | 2 | yes | — |
| 87 | C24×C7 | C2×D4 | 1 | 4 | yes | complemented |
| 88 | C24×C7 | C24 | 1 | 1 | yes | characteristic |
| 89 | C7×#41 | — | 4 | 16 | no | — |
| 90 | C7×#41 | — | 4 | 4 | no | — |
| 91 | C7×#41 | — | 4 | 4 | no | — |
| 92 | C2×C7×Q8 | — | 2 | 2 | no | — |
| 93 | C2×C7×D4 | — | 2 | 4 | no | — |
| 94 | C2×C7×D4 | — | 2 | 4 | no | — |
| 95 | C2×C7×D4 | — | 2 | 8 | no | — |
| 96 | C2×C7×D4 | — | 2 | 4 | no | — |
| 97 | C2×C7×D4 | — | 2 | 2 | no | — |
| 98 | C2×C7×D4 | — | 2 | 4 | no | — |
| 99 | C2×C7×D4 | — | 2 | 8 | no | — |
| 100 | C2×C7×D4 | — | 2 | 4 | no | — |
| 101 | C2×C7×D4 | — | 2 | 4 | no | — |
| 102 | C2×C7×D4 | — | 2 | 8 | no | — |
| 103 | C2×C7×D4 | — | 2 | 8 | no | — |
| 104 | C2×C7×D4 | — | 2 | 8 | no | — |
| 105 | C2×C7×D4 | — | 2 | 4 | no | — |
| 106 | C2×C7×D4 | — | 4 | 2 | no | — |
| 107 | C2×C7×D4 | — | 4 | 16 | no | — |
| 108 | C2×C7×D4 | — | 4 | 16 | no | — |
| 109 | C2×C7×D4 | — | 4 | 4 | no | — |
| 110 | C2×C7×D4 | — | 4 | 4 | no | — |
| 111 | C2×C7×D4 | — | 4 | 4 | no | — |
| 112 | C2×C7×D4 | — | 8 | 8 | no | — |
| 113 | C2×C7×D4 | — | 8 | 8 | no | — |
| 114 | C2×C7×D4 | C2×D4 | 1 | 8 | yes | — |
| 115 | C22×C4×C7 | — | 2 | 2 | no | — |
| 116 | C22×C4×C7 | — | 2 | 4 | no | — |
| 117 | C22×C4×C7 | — | 2 | 4 | no | — |
| 118 | C22×C4×C7 | — | 2 | 4 | no | — |
| 119 | C22×C4×C7 | — | 2 | 4 | no | — |
| 120 | C22×C4×C7 | — | 2 | 4 | no | — |
| 121 | C22×C4×C7 | — | 4 | 1 | no | — |
| 122 | C22×C4×C7 | C2×D4 | 1 | 2 | yes | — |
| 123 | C22×C4×C7 | C2×D4 | 1 | 4 | yes | complemented |
| 124 | C7×C4⋊C4 | — | 2 | 4 | no | — |
| 125 | C7×C4⋊C4 | — | 2 | 8 | no | — |
| 126 | C7×C4⋊C4 | — | 4 | 4 | no | — |
| 127 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 128 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 129 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 130 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 131 | C7×C22⋊C4 | — | 2 | 4 | no | — |
| 132 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 133 | C7×C22⋊C4 | — | 2 | 8 | no | — |
| 134 | C7×C22⋊C4 | — | 4 | 8 | no | — |
| 135 | C7×C22⋊C4 | — | 8 | 4 | no | — |
| 136 | C7×C22⋊C4 | C2×D4 | 1 | 8 | yes | complemented |
| 137 | C42×C7 | — | 2 | 4 | no | — |
| 138 | C2×H(5,𝔽2) | C22×C7 | 1 | 2 | yes | complemented |
| 139 | C23×D4 | C22×C7 | 1 | 1 | yes | characteristic |
| 140 | #546 | — | 2 | 8 | no | — |
| 141 | D42 | — | 2 | 8 | no | — |
| 142 | #535 | — | 2 | 2 | no | — |
| 143 | #534 | — | 2 | 2 | no | — |
| 144 | #534 | C22×C7 | 1 | 4 | yes | — |
| 145 | #534 | C22×C7 | 1 | 4 | yes | complemented |
| 146 | #525 | — | 2 | 2 | no | — |
| 147 | C2×#120 | — | 2 | 2 | no | — |
| 148 | C2×#120 | C22×C7 | 1 | 4 | yes | complemented |
| 149 | #518 | C22×C7 | 1 | 2 | yes | complemented |
| 150 | #458 | — | 2 | 8 | no | — |
| 151 | B(4,𝔽2) | — | 2 | 8 | no | — |
| 152 | C2×#99 | C22×C7 | 1 | 8 | yes | complemented |
| 153 | C2×#99 | C22×C7 | 1 | 4 | yes | complemented |
| 154 | #379 | C22×C7 | 1 | 2 | yes | complemented |
| 155 | #342 | C22×C7 | 1 | 4 | yes | complemented |
| 156 | C23×C7 | — | 2 | 2 | no | — |
| 157 | C23×C7 | — | 2 | 2 | no | — |
| 158 | C23×C7 | — | 2 | 1 | no | — |
| 159 | C23×C7 | — | 2 | 2 | no | — |
| 160 | C23×C7 | — | 2 | 2 | no | — |
| 161 | C23×C7 | — | 2 | 4 | no | — |
| 162 | C23×C7 | — | 2 | 1 | no | — |
| 163 | C23×C7 | — | 2 | 8 | no | — |
| 164 | C23×C7 | — | 4 | 2 | no | — |
| 165 | C23×C7 | — | 4 | 4 | no | — |
| 166 | C23×C7 | — | 4 | 4 | no | — |
| 167 | C23×C7 | — | 4 | 8 | no | — |
| 168 | C23×C7 | — | 4 | 8 | no | — |
| 169 | C23×C7 | — | 4 | 4 | no | — |
| 170 | C23×C7 | — | 4 | 4 | no | — |
| 171 | C23×C7 | — | 8 | 2 | no | — |
| 172 | C23×C7 | — | 8 | 1 | no | — |
| 173 | C23×C7 | — | 8 | 1 | no | — |
| 174 | C23×C7 | — | 8 | 2 | no | — |
| 175 | C23×C7 | — | 8 | 4 | no | — |
| 176 | C23×C7 | — | 8 | 2 | no | — |
| 177 | C23×C7 | — | 8 | 4 | no | — |
| 178 | C23×C7 | — | 8 | 4 | no | — |
| 179 | C23×C7 | — | 8 | 4 | no | — |
| 180 | C23×C7 | — | 8 | 2 | no | — |
| 181 | C23×C7 | #120 | 1 | 4 | yes | — |
| 182 | C23×C7 | C22×D4 | 1 | 1 | yes | characteristic |
| 183 | C23×C7 | C22×D4 | 1 | 4 | yes | — |
| 184 | C23×C7 | H(5,𝔽2) | 1 | 2 | yes | — |
| 185 | C7×Q8 | — | 4 | 4 | no | — |
| 186 | C7×D4 | — | 2 | 16 | no | — |
| 187 | C7×D4 | — | 4 | 8 | no | — |
| 188 | C7×D4 | — | 4 | 4 | no | — |
| 189 | C7×D4 | — | 4 | 8 | no | — |
| 190 | C7×D4 | — | 4 | 16 | no | — |
| 191 | C7×D4 | — | 4 | 4 | no | — |
| 192 | C7×D4 | — | 4 | 4 | no | — |
| 193 | C7×D4 | — | 4 | 8 | no | — |
| 194 | C7×D4 | — | 8 | 8 | no | — |
| 195 | C7×D4 | — | 8 | 8 | no | — |
| 196 | C7×D4 | — | 16 | 4 | no | — |
| 197 | C2×C4×C7 | — | 2 | 2 | no | — |
| 198 | C2×C4×C7 | — | 2 | 2 | no | — |
| 199 | C2×C4×C7 | — | 2 | 8 | no | — |
| 200 | C2×C4×C7 | — | 2 | 4 | no | — |
| 201 | C2×C4×C7 | — | 2 | 8 | no | — |
| 202 | C2×C4×C7 | — | 4 | 4 | no | — |
| 203 | C2×C4×C7 | — | 4 | 8 | no | — |
| 204 | C2×C4×C7 | — | 4 | 4 | no | — |
| 205 | C2×C4×C7 | — | 4 | 4 | no | — |
| 206 | C2×C4×C7 | — | 8 | 4 | no | — |
| 207 | C2×C4×C7 | — | 8 | 4 | no | — |
| 208 | C2×C4×C7 | — | 8 | 4 | no | — |
| 209 | C2×C4×C7 | #120 | 1 | 4 | yes | — |
| 210 | C25 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 211 | C25 | C23×C7 | 1 | 1 | yes | characteristic |
| 212 | H(5,𝔽2) | — | 2 | 8 | no | — |
| 213 | H(5,𝔽2) | — | 4 | 4 | no | — |
| 214 | C2×#41 | — | 2 | 2 | no | — |
| 215 | C2×#41 | — | 2 | 4 | no | — |
| 216 | C22×D4 | — | 2 | 2 | no | — |
| 217 | C22×D4 | — | 2 | 4 | no | — |
| 218 | C22×D4 | — | 2 | 4 | no | — |
| 219 | C22×D4 | — | 2 | 4 | no | — |
| 220 | C22×D4 | — | 2 | 8 | no | — |
| 221 | C22×D4 | — | 4 | 2 | no | — |
| 222 | C22×D4 | C7×D4 | 1 | 2 | yes | complemented |
| 223 | C22×D4 | C23×C7 | 1 | 2 | yes | — |
| 224 | C22×D4 | C23×C7 | 1 | 4 | yes | — |
| 225 | C23×C4 | C7×D4 | 1 | 1 | yes | characteristic, complemented |
| 226 | #127 | — | 2 | 4 | no | — |
| 227 | #124 | — | 2 | 4 | no | — |
| 228 | #123 | — | 2 | 4 | no | — |
| 229 | #123 | — | 2 | 4 | no | — |
| 230 | #123 | — | 2 | 8 | no | — |
| 231 | #123 | C7×D4 | 1 | 8 | yes | complemented |
| 232 | C22⋊Q8 | — | 2 | 4 | no | — |
| 233 | #121 | — | 2 | 4 | no | — |
| 234 | #121 | — | 2 | 8 | no | — |
| 235 | #121 | — | 2 | 8 | no | — |
| 236 | #121 | — | 2 | 8 | no | — |
| 237 | #121 | — | 4 | 4 | no | — |
| 238 | #120 | — | 2 | 8 | no | — |
| 239 | #120 | — | 2 | 4 | no | — |
| 240 | #120 | — | 2 | 4 | no | — |
| 241 | #120 | — | 2 | 4 | no | — |
| 242 | #120 | — | 2 | 4 | no | — |
| 243 | #120 | — | 2 | 8 | no | — |
| 244 | #120 | — | 2 | 8 | no | — |
| 245 | #120 | C7×D4 | 1 | 8 | yes | complemented |
| 246 | C4×D4 | — | 2 | 8 | no | — |
| 247 | C4×D4 | — | 2 | 8 | no | — |
| 248 | #117 | — | 2 | 2 | no | — |
| 249 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 250 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 251 | C2×C22⋊C4 | — | 2 | 4 | no | — |
| 252 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 253 | C2×C22⋊C4 | C23×C7 | 1 | 4 | yes | — |
| 254 | C2×C22⋊C4 | C23×C7 | 1 | 4 | yes | — |
| 255 | #99 | — | 2 | 8 | no | — |
| 256 | #99 | — | 2 | 16 | no | — |
| 257 | C22×C7 | — | 2 | 4 | no | — |
| 258 | C22×C7 | — | 2 | 2 | no | — |
| 259 | C22×C7 | — | 2 | 4 | no | — |
| 260 | C22×C7 | — | 4 | 2 | no | — |
| 261 | C22×C7 | — | 4 | 4 | no | — |
| 262 | C22×C7 | — | 4 | 1 | no | — |
| 263 | C22×C7 | — | 4 | 4 | no | — |
| 264 | C22×C7 | — | 4 | 4 | no | — |
| 265 | C22×C7 | — | 4 | 2 | no | — |
| 266 | C22×C7 | — | 4 | 1 | no | — |
| 267 | C22×C7 | — | 4 | 8 | no | — |
| 268 | C22×C7 | — | 4 | 4 | no | — |
| 269 | C22×C7 | — | 4 | 2 | no | — |
| 270 | C22×C7 | — | 4 | 1 | no | — |
| 271 | C22×C7 | — | 4 | 4 | no | — |
| 272 | C22×C7 | — | 4 | 1 | no | — |
| 273 | C22×C7 | — | 8 | 2 | no | — |
| 274 | C22×C7 | — | 8 | 8 | no | — |
| 275 | C22×C7 | — | 8 | 8 | no | — |
| 276 | C22×C7 | — | 8 | 8 | no | — |
| 277 | C22×C7 | — | 16 | 4 | no | — |
| 278 | C22×C7 | C2×#120 | 1 | 2 | yes | — |
| 279 | C22×C7 | #534 | 1 | 1 | yes | characteristic |
| 280 | C22×C7 | D42 | 1 | 4 | yes | — |
| 281 | C4×C7 | — | 2 | 4 | no | — |
| 282 | C4×C7 | — | 4 | 8 | no | — |
| 283 | C4×C7 | — | 4 | 4 | no | — |
| 284 | C4×C7 | — | 8 | 4 | no | — |
| 285 | C24 | — | 2 | 2 | no | — |
| 286 | C24 | — | 2 | 4 | no | — |
| 287 | C24 | — | 2 | 4 | no | — |
| 288 | C24 | — | 2 | 2 | no | — |
| 289 | C24 | — | 4 | 1 | no | — |
| 290 | C24 | — | 8 | 2 | no | — |
| 291 | C24 | — | 8 | 2 | no | — |
| 292 | C24 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 293 | C24 | C2×C7×D4 | 1 | 1 | yes | characteristic |
| 294 | C24 | C2×C7×D4 | 1 | 2 | yes | — |
| 295 | C24 | C2×C7×D4 | 1 | 4 | yes | complemented |
| 296 | C24 | C24×C7 | 1 | 1 | yes | characteristic |
| 297 | #41 | — | 4 | 16 | no | — |
| 298 | #41 | — | 4 | 4 | no | — |
| 299 | #41 | — | 4 | 4 | no | — |
| 300 | C2×Q8 | — | 2 | 2 | no | — |
| 301 | C2×D4 | — | 2 | 4 | no | — |
| 302 | C2×D4 | — | 2 | 4 | no | — |
| 303 | C2×D4 | — | 2 | 8 | no | — |
| 304 | C2×D4 | — | 2 | 4 | no | — |
| 305 | C2×D4 | — | 2 | 2 | no | — |
| 306 | C2×D4 | — | 2 | 4 | no | — |
| 307 | C2×D4 | — | 2 | 8 | no | — |
| 308 | C2×D4 | — | 2 | 4 | no | — |
| 309 | C2×D4 | — | 2 | 4 | no | — |
| 310 | C2×D4 | — | 2 | 8 | no | — |
| 311 | C2×D4 | — | 2 | 8 | no | — |
| 312 | C2×D4 | — | 2 | 8 | no | — |
| 313 | C2×D4 | — | 2 | 4 | no | — |
| 314 | C2×D4 | — | 4 | 2 | no | — |
| 315 | C2×D4 | — | 4 | 16 | no | — |
| 316 | C2×D4 | — | 4 | 16 | no | — |
| 317 | C2×D4 | — | 4 | 4 | no | — |
| 318 | C2×D4 | — | 4 | 4 | no | — |
| 319 | C2×D4 | — | 4 | 4 | no | — |
| 320 | C2×D4 | — | 8 | 8 | no | — |
| 321 | C2×D4 | — | 8 | 8 | no | — |
| 322 | C2×D4 | C2×C7×D4 | 1 | 8 | yes | — |
| 323 | C22×C4 | — | 2 | 2 | no | — |
| 324 | C22×C4 | — | 2 | 4 | no | — |
| 325 | C22×C4 | — | 2 | 4 | no | — |
| 326 | C22×C4 | — | 2 | 4 | no | — |
| 327 | C22×C4 | — | 2 | 4 | no | — |
| 328 | C22×C4 | — | 2 | 4 | no | — |
| 329 | C22×C4 | — | 4 | 1 | no | — |
| 330 | C22×C4 | C2×C7×D4 | 1 | 2 | yes | — |
| 331 | C22×C4 | C2×C7×D4 | 1 | 4 | yes | complemented |
| 332 | C4⋊C4 | — | 2 | 4 | no | — |
| 333 | C4⋊C4 | — | 2 | 8 | no | — |
| 334 | C4⋊C4 | — | 4 | 4 | no | — |
| 335 | C22⋊C4 | — | 2 | 8 | no | — |
| 336 | C22⋊C4 | — | 2 | 4 | no | — |
| 337 | C22⋊C4 | — | 2 | 8 | no | — |
| 338 | C22⋊C4 | — | 2 | 8 | no | — |
| 339 | C22⋊C4 | — | 2 | 4 | no | — |
| 340 | C22⋊C4 | — | 2 | 8 | no | — |
| 341 | C22⋊C4 | — | 2 | 8 | no | — |
| 342 | C22⋊C4 | — | 4 | 8 | no | — |
| 343 | C22⋊C4 | — | 8 | 4 | no | — |
| 344 | C22⋊C4 | C2×C7×D4 | 1 | 8 | yes | complemented |
| 345 | C42 | — | 2 | 4 | no | — |
| 346 | C2×C7 | — | 2 | 2 | no | — |
| 347 | C2×C7 | — | 2 | 4 | no | — |
| 348 | C2×C7 | — | 2 | 1 | no | — |
| 349 | C2×C7 | — | 4 | 2 | no | — |
| 350 | C2×C7 | — | 4 | 4 | no | — |
| 351 | C2×C7 | — | 8 | 1 | no | — |
| 352 | C2×C7 | — | 8 | 4 | no | — |
| 353 | C2×C7 | #2403 | 1 | 1 | yes | characteristic |
| 354 | C23 | — | 2 | 2 | no | — |
| 355 | C23 | — | 2 | 2 | no | — |
| 356 | C23 | — | 2 | 1 | no | — |
| 357 | C23 | — | 2 | 2 | no | — |
| 358 | C23 | — | 2 | 2 | no | — |
| 359 | C23 | — | 2 | 4 | no | — |
| 360 | C23 | — | 2 | 1 | no | — |
| 361 | C23 | — | 2 | 8 | no | — |
| 362 | C23 | — | 4 | 2 | no | — |
| 363 | C23 | — | 4 | 4 | no | — |
| 364 | C23 | — | 4 | 4 | no | — |
| 365 | C23 | — | 4 | 8 | no | — |
| 366 | C23 | — | 4 | 8 | no | — |
| 367 | C23 | — | 4 | 4 | no | — |
| 368 | C23 | — | 4 | 4 | no | — |
| 369 | C23 | — | 8 | 2 | no | — |
| 370 | C23 | — | 8 | 1 | no | — |
| 371 | C23 | — | 8 | 1 | no | — |
| 372 | C23 | — | 8 | 2 | no | — |
| 373 | C23 | — | 8 | 4 | no | — |
| 374 | C23 | — | 8 | 2 | no | — |
| 375 | C23 | — | 8 | 4 | no | — |
| 376 | C23 | — | 8 | 4 | no | — |
| 377 | C23 | — | 8 | 4 | no | — |
| 378 | C23 | — | 8 | 2 | no | — |
| 379 | C23 | C7×#120 | 1 | 4 | yes | — |
| 380 | C23 | C22×C7×D4 | 1 | 1 | yes | characteristic |
| 381 | C23 | C22×C7×D4 | 1 | 4 | yes | — |
| 382 | C23 | C7×H(5,𝔽2) | 1 | 2 | yes | — |
| 383 | Q8 | — | 4 | 4 | no | — |
| 384 | D4 | — | 2 | 16 | no | — |
| 385 | D4 | — | 4 | 8 | no | — |
| 386 | D4 | — | 4 | 4 | no | — |
| 387 | D4 | — | 4 | 8 | no | — |
| 388 | D4 | — | 4 | 16 | no | — |
| 389 | D4 | — | 4 | 4 | no | — |
| 390 | D4 | — | 4 | 4 | no | — |
| 391 | D4 | — | 4 | 8 | no | — |
| 392 | D4 | — | 8 | 8 | no | — |
| 393 | D4 | — | 8 | 8 | no | — |
| 394 | D4 | — | 16 | 4 | no | — |
| 395 | C2×C4 | — | 2 | 2 | no | — |
| 396 | C2×C4 | — | 2 | 2 | no | — |
| 397 | C2×C4 | — | 2 | 8 | no | — |
| 398 | C2×C4 | — | 2 | 4 | no | — |
| 399 | C2×C4 | — | 2 | 8 | no | — |
| 400 | C2×C4 | — | 4 | 4 | no | — |
| 401 | C2×C4 | — | 4 | 8 | no | — |
| 402 | C2×C4 | — | 4 | 4 | no | — |
| 403 | C2×C4 | — | 4 | 4 | no | — |
| 404 | C2×C4 | — | 8 | 4 | no | — |
| 405 | C2×C4 | — | 8 | 4 | no | — |
| 406 | C2×C4 | — | 8 | 4 | no | — |
| 407 | C2×C4 | C7×#120 | 1 | 4 | yes | — |
| 408 | C7 | #23895 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 409 | C22 | — | 2 | 4 | no | — |
| 410 | C22 | — | 2 | 2 | no | — |
| 411 | C22 | — | 2 | 4 | no | — |
| 412 | C22 | — | 4 | 2 | no | — |
| 413 | C22 | — | 4 | 4 | no | — |
| 414 | C22 | — | 4 | 1 | no | — |
| 415 | C22 | — | 4 | 4 | no | — |
| 416 | C22 | — | 4 | 4 | no | — |
| 417 | C22 | — | 4 | 2 | no | — |
| 418 | C22 | — | 4 | 1 | no | — |
| 419 | C22 | — | 4 | 8 | no | — |
| 420 | C22 | — | 4 | 4 | no | — |
| 421 | C22 | — | 4 | 2 | no | — |
| 422 | C22 | — | 4 | 1 | no | — |
| 423 | C22 | — | 4 | 4 | no | — |
| 424 | C22 | — | 4 | 1 | no | — |
| 425 | C22 | — | 8 | 2 | no | — |
| 426 | C22 | — | 8 | 8 | no | — |
| 427 | C22 | — | 8 | 8 | no | — |
| 428 | C22 | — | 8 | 8 | no | — |
| 429 | C22 | — | 16 | 4 | no | — |
| 430 | C22 | C2×C7×#120 | 1 | 2 | yes | — |
| 431 | C22 | C7×#534 | 1 | 1 | yes | characteristic |
| 432 | C22 | C7×D42 | 1 | 4 | yes | — |
| 433 | C4 | — | 2 | 4 | no | — |
| 434 | C4 | — | 4 | 8 | no | — |
| 435 | C4 | — | 4 | 4 | no | — |
| 436 | C4 | — | 8 | 4 | no | — |
| 437 | C2 | — | 2 | 2 | no | — |
| 438 | C2 | — | 2 | 4 | no | — |
| 439 | C2 | — | 2 | 1 | no | — |
| 440 | C2 | — | 4 | 2 | no | — |
| 441 | C2 | — | 4 | 4 | no | — |
| 442 | C2 | — | 8 | 1 | no | — |
| 443 | C2 | — | 8 | 4 | no | — |
| 444 | C2 | C7×#2403 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3484 | C2 | semidirect |
| 2. C7×#3026 | C2 | semidirect |
| 3. C7×#2021 | C2 | semidirect |
| 4. C7×#1913 | C2 | semidirect |
| 5. C7×#1781 | C2 | semidirect |
| 6. C2×C7×H(5,𝔽2) | C22 | semidirect |
| 13. C7×#534 | C22 | semidirect |
| 16. C2×C7×#120 | C22 | semidirect |
| 17. C7×#518 | C22 | semidirect |
| 20. C2×C7×#99 | C22 | semidirect |
| 21. C2×C7×#99 | C22 | semidirect |
| 22. C7×#379 | C22 | semidirect |
| 23. C7×#342 | C22 | semidirect |
| 24. #23895 | C7 | direct (N × H) |
| 25. C25×C7 | D4 | semidirect |
| 37. C22×C7×D4 | D4 | semidirect |
| 40. C23×C4×C7 | D4 | semidirect |
| 46. C7×#123 | D4 | semidirect |
| 60. C7×#120 | D4 | semidirect |
| 72. #3484 | C2×C7 | semidirect |
| 73. #3026 | C2×C7 | semidirect |
| 74. #2021 | C2×C7 | semidirect |
| 75. #1913 | C2×C7 | semidirect |
| 76. #1781 | C2×C7 | semidirect |
| 87. C24×C7 | C2×D4 | semidirect |
| 123. C22×C4×C7 | C2×D4 | semidirect |
| 136. C7×C22⋊C4 | C2×D4 | semidirect |
| 138. C2×H(5,𝔽2) | C22×C7 | semidirect |
| 145. #534 | C22×C7 | semidirect |
| 148. C2×#120 | C22×C7 | semidirect |
| 149. #518 | C22×C7 | semidirect |
| 152. C2×#99 | C22×C7 | semidirect |
| 153. C2×#99 | C22×C7 | semidirect |
| 154. #379 | C22×C7 | semidirect |
| 155. #342 | C22×C7 | semidirect |
| 210. C25 | C7×D4 | semidirect |
| 222. C22×D4 | C7×D4 | semidirect |
| 225. C23×C4 | C7×D4 | semidirect |
| 231. #123 | C7×D4 | semidirect |
| 245. #120 | C7×D4 | semidirect |
| 295. C24 | C2×C7×D4 | semidirect |
| 331. C22×C4 | C2×C7×D4 | semidirect |
| 344. C22⋊C4 | C2×C7×D4 | semidirect |
| 408. C7 | #23895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3484 | 2 |
| C7×#3026 | 2 |
| C7×#2021 | 2 |
| C7×#1913 | 2 |
| C7×#1781 | 2 |
| #23895 | 7 |