Finite Group DatabasebetaFinite Group DatabasebetaOrder 5376.
22372 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 22372 conjugacy classes of subgroups — too many to draw. Only its 143 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×C22⋊#997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C22×D7×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 3 | C2×D7×C22⋊A4 | — | 4 | 3 | no | maximal |
| 4 | D7×#997 | — | 4 | 16 | no | maximal |
| 5 | D7×C22⋊SL(2,𝔽3) | — | 4 | 2 | no | maximal |
| 6 | C22×C7×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×D7×H(5,𝔽2) | — | 3 | 16 | no | — |
| 8 | C2×D7×H(5,𝔽2) | — | 3 | 16 | no | — |
| 9 | C22×#6553 | — | 3 | 2 | no | — |
| 10 | C22×D7×#41 | — | 3 | 2 | no | — |
| 11 | C22×#6548 | — | 3 | 3 | no | — |
| 12 | C23×D4×D7 | — | 3 | 3 | no | — |
| 13 | C2×C22⋊#997 | — | 7 | 1 | no | maximal, Hall |
| 14 | C2×C7×C22⋊A4 | — | 4 | 3 | no | — |
| 15 | D7×C22⋊A4 | — | 4 | 6 | no | — |
| 16 | C7×#997 | — | 4 | 16 | no | — |
| 17 | C7×C22⋊SL(2,𝔽3) | — | 4 | 2 | no | — |
| 18 | C25×D7 | — | 3 | 1 | no | — |
| 19 | C25×D7 | A4 | 1 | 3 | yes | complemented |
| 20 | C2×C7×H(5,𝔽2) | — | 3 | 16 | no | — |
| 21 | C22×C7×#41 | — | 3 | 2 | no | — |
| 22 | C23×C7×D4 | — | 3 | 3 | no | — |
| 23 | C23×C22⋊D7 | — | 3 | 3 | no | — |
| 24 | C23×C22⋊D7 | — | 3 | 3 | no | — |
| 25 | D7×H(5,𝔽2) | — | 3 | 96 | no | — |
| 26 | D7×H(5,𝔽2) | — | 3 | 32 | no | — |
| 27 | D7×H(5,𝔽2) | — | 3 | 144 | no | — |
| 28 | D7×H(5,𝔽2) | — | 3 | 48 | no | — |
| 29 | D7×H(5,𝔽2) | — | 3 | 16 | no | — |
| 30 | D7×H(5,𝔽2) | A4 | 1 | 16 | yes | complemented |
| 31 | C2×#6553 | — | 3 | 96 | no | — |
| 32 | C2×D7×#41 | — | 3 | 48 | no | — |
| 33 | C2×D7×#41 | — | 3 | 48 | no | — |
| 34 | C22×#1161 | — | 3 | 2 | no | — |
| 35 | C22×Q8×D7 | A4 | 1 | 2 | yes | complemented |
| 36 | C2×#6548 | — | 3 | 144 | no | — |
| 37 | C22×#1159 | — | 3 | 6 | no | — |
| 38 | C22×D4×D7 | — | 3 | 6 | no | — |
| 39 | C22×D4×D7 | — | 3 | 12 | no | — |
| 40 | C22×D4×D7 | — | 3 | 72 | no | — |
| 41 | C22×D4×D7 | — | 3 | 72 | no | — |
| 42 | C22×#1157 | — | 3 | 6 | no | — |
| 43 | C23×D28 | — | 3 | 3 | no | — |
| 44 | C23×C4×D7 | — | 3 | 3 | no | — |
| 45 | C22⋊#997 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 46 | C7×C22⋊A4 | — | 4 | 3 | no | — |
| 47 | C2×A4×D7 | — | 16 | 1 | no | — |
| 48 | C2×A4×D7 | — | 16 | 12 | no | — |
| 49 | D7×SL(2,𝔽3) | — | 16 | 8 | no | — |
| 50 | C23×H(5,𝔽2) | — | 7 | 1 | no | Sylow |
| 51 | C25×C7 | — | 3 | 1 | no | — |
| 52 | C25×C7 | C2×A4 | 1 | 3 | yes | complemented |
| 53 | C24×D7 | — | 3 | 3 | no | — |
| 54 | C24×D7 | — | 3 | 12 | no | — |
| 55 | C24×D7 | — | 3 | 12 | no | — |
| 56 | C24×D7 | — | 3 | 3 | no | — |
| 57 | C24×D7 | — | 3 | 12 | no | — |
| 58 | C24×D7 | — | 3 | 3 | no | — |
| 59 | C24×D7 | — | 3 | 12 | no | — |
| 60 | C24×D7 | — | 4 | 6 | no | — |
| 61 | C24×D7 | — | 12 | 6 | no | — |
| 62 | C24×D7 | — | 12 | 2 | no | — |
| 63 | C24×D7 | — | 12 | 6 | no | — |
| 64 | C7×H(5,𝔽2) | — | 3 | 32 | no | — |
| 65 | C7×H(5,𝔽2) | — | 3 | 48 | no | — |
| 66 | C7×H(5,𝔽2) | C2×A4 | 1 | 16 | yes | complemented |
| 67 | C2×C7×#41 | — | 3 | 48 | no | — |
| 68 | C22×C7×Q8 | C2×A4 | 1 | 2 | yes | complemented |
| 69 | C22×C7×D4 | — | 3 | 6 | no | — |
| 70 | C22×C7×D4 | — | 3 | 72 | no | — |
| 71 | C23×C4×C7 | — | 3 | 3 | no | — |
| 72 | C22×C22⋊D7 | — | 3 | 12 | no | — |
| 73 | C22×C22⋊D7 | — | 3 | 72 | no | — |
| 74 | C22×C22⋊D7 | — | 3 | 72 | no | — |
| 75 | C23×Dic7 | — | 3 | 3 | no | — |
| 76 | #6553 | — | 3 | 96 | no | — |
| 77 | #6553 | — | 3 | 288 | no | — |
| 78 | #6553 | — | 3 | 96 | no | — |
| 79 | #6553 | — | 3 | 32 | no | — |
| 80 | D7×#41 | — | 3 | 288 | no | — |
| 81 | D7×#41 | — | 3 | 96 | no | — |
| 82 | D7×#41 | — | 3 | 96 | no | — |
| 83 | D7×#41 | — | 3 | 32 | no | — |
| 84 | C2×#1161 | — | 3 | 48 | no | — |
| 85 | C2×Q8×D7 | — | 3 | 8 | no | — |
| 86 | C2×Q8×D7 | — | 3 | 8 | no | — |
| 87 | #6548 | — | 3 | 288 | no | — |
| 88 | #6548 | — | 3 | 288 | no | — |
| 89 | #6548 | — | 3 | 144 | no | — |
| 90 | #6548 | — | 3 | 48 | no | — |
| 91 | C2×#1159 | — | 3 | 144 | no | — |
| 92 | C2×D4×D7 | — | 3 | 72 | no | — |
| 93 | C2×D4×D7 | — | 3 | 72 | no | — |
| 94 | C2×D4×D7 | — | 3 | 288 | no | — |
| 95 | C2×D4×D7 | — | 3 | 288 | no | — |
| 96 | C2×D4×D7 | — | 3 | 144 | no | — |
| 97 | C2×D4×D7 | — | 3 | 144 | no | — |
| 98 | C2×D4×D7 | — | 3 | 144 | no | — |
| 99 | C2×D4×D7 | — | 3 | 48 | no | — |
| 100 | C2×#1157 | — | 3 | 144 | no | — |
| 101 | C22×D28 | — | 3 | 6 | no | — |
| 102 | C22×D28 | — | 3 | 72 | no | — |
| 103 | C22×C4×D7 | — | 3 | 6 | no | — |
| 104 | C22×C4×D7 | — | 3 | 36 | no | — |
| 105 | C22×C4×D7 | — | 3 | 36 | no | — |
| 106 | C22×C4×D7 | — | 3 | 2 | no | — |
| 107 | C22×Dic14 | — | 3 | 2 | no | — |
| 108 | C22×C22⋊A4 | — | 28 | 3 | no | — |
| 109 | C2×#997 | — | 28 | 16 | no | — |
| 110 | C2×C22⋊SL(2,𝔽3) | — | 28 | 2 | no | — |
| 111 | C2×C7×A4 | — | 16 | 1 | no | — |
| 112 | C2×C7×A4 | — | 16 | 12 | no | — |
| 113 | A4×D7 | — | 16 | 24 | no | — |
| 114 | A4×D7 | — | 16 | 2 | no | — |
| 115 | C7×SL(2,𝔽3) | — | 16 | 8 | no | — |
| 116 | C22×H(5,𝔽2) | — | 21 | 3 | no | — |
| 117 | C22×H(5,𝔽2) | — | 21 | 2 | no | — |
| 118 | C22×H(5,𝔽2) | — | 21 | 16 | no | — |
| 119 | C22×H(5,𝔽2) | — | 21 | 16 | no | — |
| 120 | C22×H(5,𝔽2) | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 121 | C23×#41 | — | 21 | 2 | no | — |
| 122 | C24×D4 | — | 21 | 3 | no | — |
| 123 | C24×C7 | — | 3 | 12 | no | — |
| 124 | C24×C7 | — | 3 | 3 | no | — |
| 125 | C24×C7 | — | 3 | 12 | no | — |
| 126 | C24×C7 | — | 4 | 3 | no | — |
| 127 | C24×C7 | — | 12 | 3 | no | — |
| 128 | C24×C7 | — | 12 | 1 | no | — |
| 129 | C24×C7 | — | 12 | 3 | no | — |
| 130 | C23×D7 | — | 3 | 18 | no | — |
| 131 | C23×D7 | — | 3 | 18 | no | — |
| 132 | C23×D7 | — | 3 | 3 | no | — |
| 133 | C23×D7 | — | 3 | 36 | no | — |
| 134 | C23×D7 | — | 3 | 36 | no | — |
| 135 | C23×D7 | — | 3 | 48 | no | — |
| 136 | C23×D7 | — | 3 | 36 | no | — |
| 137 | C23×D7 | — | 3 | 12 | no | — |
| 138 | C23×D7 | — | 3 | 16 | no | — |
| 139 | C23×D7 | — | 3 | 12 | no | — |
| 140 | C23×D7 | — | 6 | 18 | no | — |
| 141 | C23×D7 | — | 6 | 6 | no | — |
| 142 | C23×D7 | — | 12 | 24 | no | — |
| 143 | C23×D7 | — | 12 | 24 | no | — |
| 144 | C23×D7 | — | 12 | 24 | no | — |
| 145 | C23×D7 | — | 12 | 24 | no | — |
| 146 | C23×D7 | — | 12 | 24 | no | — |
| 147 | C23×D7 | — | 12 | 24 | no | — |
| 148 | C23×D7 | — | 12 | 24 | no | — |
| 149 | C23×D7 | — | 12 | 24 | no | — |
| 150 | C23×D7 | — | 12 | 9 | no | — |
| 151 | C23×D7 | — | 12 | 9 | no | — |
| 152 | C23×D7 | — | 12 | 3 | no | — |
| 153 | C23×D7 | — | 12 | 3 | no | — |
| 154 | C23×D7 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 155 | C23×D7 | C22⋊A4 | 1 | 12 | yes | complemented |
| 156 | C7×#41 | — | 3 | 96 | no | — |
| 157 | C7×#41 | — | 3 | 32 | no | — |
| 158 | C2×C7×Q8 | — | 3 | 8 | no | — |
| 159 | C2×C7×D4 | — | 3 | 72 | no | — |
| 160 | C2×C7×D4 | — | 3 | 144 | no | — |
| 161 | C2×C7×D4 | — | 3 | 48 | no | — |
| 162 | C22×C4×C7 | — | 3 | 36 | no | — |
| 163 | C22×C4×C7 | — | 3 | 2 | no | — |
| 164 | C2×C22⋊D7 | — | 3 | 144 | no | — |
| 165 | C2×C22⋊D7 | — | 3 | 144 | no | — |
| 166 | C2×C22⋊D7 | — | 3 | 144 | no | — |
| 167 | C2×C22⋊D7 | — | 3 | 48 | no | — |
| 168 | C2×C22⋊D7 | — | 3 | 48 | no | — |
| 169 | C22×Dic7 | — | 3 | 36 | no | — |
| 170 | C22×Dic7 | — | 3 | 2 | no | — |
| 171 | #1161 | — | 3 | 96 | no | — |
| 172 | #1161 | — | 3 | 32 | no | — |
| 173 | Q8×D7 | — | 3 | 8 | no | — |
| 174 | Q8×D7 | — | 3 | 24 | no | — |
| 175 | Q8×D7 | — | 3 | 8 | no | — |
| 176 | Q8×D7 | C22⋊A4 | 1 | 8 | yes | complemented |
| 177 | #1159 | — | 3 | 288 | no | — |
| 178 | #1159 | — | 3 | 96 | no | — |
| 179 | D4×D7 | — | 3 | 288 | no | — |
| 180 | D4×D7 | — | 3 | 96 | no | — |
| 181 | D4×D7 | — | 3 | 576 | no | — |
| 182 | D4×D7 | — | 3 | 192 | no | — |
| 183 | #1157 | — | 3 | 288 | no | — |
| 184 | #1157 | — | 3 | 96 | no | — |
| 185 | C2×D28 | — | 3 | 72 | no | — |
| 186 | C2×D28 | — | 3 | 144 | no | — |
| 187 | C2×D28 | — | 3 | 48 | no | — |
| 188 | C2×C4×D7 | — | 3 | 12 | no | — |
| 189 | C2×C4×D7 | — | 3 | 12 | no | — |
| 190 | C2×C4×D7 | — | 3 | 72 | no | — |
| 191 | C2×C4×D7 | — | 3 | 144 | no | — |
| 192 | C2×C4×D7 | — | 3 | 48 | no | — |
| 193 | C2×Dic14 | — | 3 | 24 | no | — |
| 194 | C2×C22⋊A4 | — | 4 | 3 | no | — |
| 195 | C2×C22⋊A4 | — | 28 | 6 | no | — |
| 196 | #997 | — | 4 | 16 | no | — |
| 197 | C22⋊SL(2,𝔽3) | — | 4 | 2 | no | — |
| 198 | C2×C3×D7 | — | 64 | 1 | no | — |
| 199 | C7×A4 | — | 16 | 12 | no | — |
| 200 | C7×A4 | — | 16 | 1 | no | — |
| 201 | C26 | — | 7 | 3 | no | — |
| 202 | C26 | — | 21 | 1 | no | — |
| 203 | C2×H(5,𝔽2) | — | 3 | 16 | no | — |
| 204 | C2×H(5,𝔽2) | — | 7 | 16 | no | — |
| 205 | C2×H(5,𝔽2) | — | 21 | 144 | no | — |
| 206 | C2×H(5,𝔽2) | — | 21 | 96 | no | — |
| 207 | C2×H(5,𝔽2) | — | 21 | 48 | no | — |
| 208 | C2×H(5,𝔽2) | — | 21 | 32 | no | — |
| 209 | C2×H(5,𝔽2) | — | 21 | 96 | no | — |
| 210 | C2×H(5,𝔽2) | — | 21 | 144 | no | — |
| 211 | C2×H(5,𝔽2) | — | 21 | 16 | no | — |
| 212 | C22×#41 | — | 3 | 2 | no | — |
| 213 | C22×#41 | — | 21 | 6 | no | — |
| 214 | C22×#41 | — | 21 | 6 | no | — |
| 215 | C22×#41 | — | 21 | 48 | no | — |
| 216 | C22×#41 | — | 21 | 48 | no | — |
| 217 | C22×#41 | — | 21 | 2 | no | — |
| 218 | C23×Q8 | — | 7 | 2 | no | — |
| 219 | C23×D4 | — | 3 | 3 | no | — |
| 220 | C23×D4 | — | 21 | 3 | no | — |
| 221 | C23×D4 | — | 21 | 6 | no | — |
| 222 | C23×D4 | — | 21 | 12 | no | — |
| 223 | C23×D4 | — | 21 | 72 | no | — |
| 224 | C23×D4 | — | 21 | 72 | no | — |
| 225 | C23×D4 | — | 21 | 3 | no | — |
| 226 | C23×D4 | — | 21 | 3 | no | — |
| 227 | C24×C4 | — | 21 | 3 | no | — |
| 228 | C23×C7 | — | 3 | 18 | no | — |
| 229 | C23×C7 | — | 3 | 12 | no | — |
| 230 | C23×C7 | — | 3 | 16 | no | — |
| 231 | C23×C7 | — | 6 | 9 | no | — |
| 232 | C23×C7 | — | 6 | 3 | no | — |
| 233 | C23×C7 | — | 12 | 12 | no | — |
| 234 | C23×C7 | — | 12 | 12 | no | — |
| 235 | C23×C7 | — | 12 | 12 | no | — |
| 236 | C23×C7 | — | 12 | 12 | no | — |
| 237 | C23×C7 | C2×C22⋊A4 | 1 | 1 | yes | characteristic |
| 238 | C23×C7 | C2×C22⋊A4 | 1 | 12 | yes | complemented |
| 239 | C22×D7 | — | 3 | 1 | no | — |
| 240 | C22×D7 | — | 3 | 1 | no | — |
| 241 | C22×D7 | — | 3 | 2 | no | — |
| 242 | C22×D7 | — | 3 | 18 | no | — |
| 243 | C22×D7 | — | 3 | 36 | no | — |
| 244 | C22×D7 | — | 3 | 36 | no | — |
| 245 | C22×D7 | — | 3 | 48 | no | — |
| 246 | C22×D7 | — | 3 | 12 | no | — |
| 247 | C22×D7 | — | 3 | 12 | no | — |
| 248 | C22×D7 | — | 4 | 24 | no | — |
| 249 | C22×D7 | — | 6 | 36 | no | — |
| 250 | C22×D7 | — | 6 | 36 | no | — |
| 251 | C22×D7 | — | 6 | 36 | no | — |
| 252 | C22×D7 | — | 6 | 36 | no | — |
| 253 | C22×D7 | — | 6 | 9 | no | — |
| 254 | C22×D7 | — | 6 | 3 | no | — |
| 255 | C22×D7 | — | 12 | 24 | no | — |
| 256 | C22×D7 | — | 12 | 96 | no | — |
| 257 | C22×D7 | — | 12 | 72 | no | — |
| 258 | C22×D7 | — | 12 | 24 | no | — |
| 259 | C22×D7 | — | 12 | 32 | no | — |
| 260 | C22×D7 | — | 12 | 36 | no | — |
| 261 | C22×D7 | — | 12 | 36 | no | — |
| 262 | C22×D7 | — | 12 | 36 | no | — |
| 263 | C22×D7 | — | 12 | 36 | no | — |
| 264 | C22×D7 | #997 | 1 | 2 | yes | complemented |
| 265 | C7×Q8 | — | 3 | 8 | no | — |
| 266 | C7×Q8 | C2×C22⋊A4 | 1 | 8 | yes | complemented |
| 267 | C7×D4 | — | 3 | 96 | no | — |
| 268 | C2×C4×C7 | — | 3 | 12 | no | — |
| 269 | C2×C4×C7 | — | 3 | 48 | no | — |
| 270 | C22⋊D7 | — | 3 | 192 | no | — |
| 271 | C2×Dic7 | — | 3 | 12 | no | — |
| 272 | C2×Dic7 | — | 3 | 48 | no | — |
| 273 | D28 | — | 3 | 96 | no | — |
| 274 | C4×D7 | — | 3 | 24 | no | — |
| 275 | C4×D7 | — | 3 | 96 | no | — |
| 276 | C4×D7 | — | 3 | 8 | no | — |
| 277 | Dic14 | — | 3 | 24 | no | — |
| 278 | Dic14 | — | 3 | 8 | no | — |
| 279 | C22⋊A4 | — | 4 | 3 | no | — |
| 280 | C22×A4 | — | 112 | 1 | no | — |
| 281 | C22×A4 | — | 112 | 12 | no | — |
| 282 | C2×SL(2,𝔽3) | — | 112 | 8 | no | — |
| 283 | C2×C3×C7 | — | 64 | 1 | no | — |
| 284 | C3×D7 | — | 64 | 2 | no | — |
| 285 | C25 | — | 3 | 1 | no | — |
| 286 | C25 | — | 21 | 3 | no | — |
| 287 | C25 | — | 21 | 12 | no | — |
| 288 | C25 | — | 21 | 12 | no | — |
| 289 | C25 | — | 21 | 12 | no | — |
| 290 | C25 | — | 21 | 3 | no | — |
| 291 | C25 | — | 21 | 3 | no | — |
| 292 | C25 | — | 21 | 12 | no | — |
| 293 | C25 | — | 28 | 6 | no | — |
| 294 | C25 | — | 84 | 6 | no | — |
| 295 | C25 | — | 84 | 2 | no | — |
| 296 | C25 | — | 84 | 6 | no | — |
| 297 | C25 | A4×D7 | 1 | 3 | yes | complemented |
| 298 | H(5,𝔽2) | — | 3 | 32 | no | — |
| 299 | H(5,𝔽2) | — | 3 | 48 | no | — |
| 300 | H(5,𝔽2) | — | 21 | 288 | no | — |
| 301 | H(5,𝔽2) | — | 21 | 288 | no | — |
| 302 | H(5,𝔽2) | — | 21 | 144 | no | — |
| 303 | H(5,𝔽2) | — | 21 | 48 | no | — |
| 304 | H(5,𝔽2) | — | 21 | 32 | no | — |
| 305 | H(5,𝔽2) | — | 21 | 96 | no | — |
| 306 | H(5,𝔽2) | — | 21 | 288 | no | — |
| 307 | H(5,𝔽2) | — | 21 | 96 | no | — |
| 308 | H(5,𝔽2) | A4×D7 | 1 | 16 | yes | complemented |
| 309 | C2×#41 | — | 3 | 48 | no | — |
| 310 | C2×#41 | — | 21 | 144 | no | — |
| 311 | C2×#41 | — | 21 | 144 | no | — |
| 312 | C2×#41 | — | 21 | 48 | no | — |
| 313 | C2×#41 | — | 21 | 32 | no | — |
| 314 | C2×#41 | — | 21 | 96 | no | — |
| 315 | C2×#41 | — | 21 | 288 | no | — |
| 316 | C2×#41 | — | 21 | 96 | no | — |
| 317 | C22×Q8 | — | 21 | 2 | no | — |
| 318 | C22×Q8 | — | 21 | 8 | no | — |
| 319 | C22×Q8 | — | 21 | 8 | no | — |
| 320 | C22×Q8 | A4×D7 | 1 | 2 | yes | complemented |
| 321 | C22×D4 | — | 3 | 6 | no | — |
| 322 | C22×D4 | — | 3 | 72 | no | — |
| 323 | C22×D4 | — | 21 | 6 | no | — |
| 324 | C22×D4 | — | 21 | 72 | no | — |
| 325 | C22×D4 | — | 21 | 48 | no | — |
| 326 | C22×D4 | — | 21 | 72 | no | — |
| 327 | C22×D4 | — | 21 | 72 | no | — |
| 328 | C22×D4 | — | 21 | 288 | no | — |
| 329 | C22×D4 | — | 21 | 144 | no | — |
| 330 | C22×D4 | — | 21 | 288 | no | — |
| 331 | C22×D4 | — | 21 | 144 | no | — |
| 332 | C22×D4 | — | 21 | 144 | no | — |
| 333 | C22×D4 | — | 21 | 12 | no | — |
| 334 | C22×D4 | — | 21 | 72 | no | — |
| 335 | C22×D4 | — | 21 | 72 | no | — |
| 336 | C23×C4 | — | 3 | 3 | no | — |
| 337 | C23×C4 | — | 21 | 2 | no | — |
| 338 | C23×C4 | — | 21 | 36 | no | — |
| 339 | C23×C4 | — | 21 | 36 | no | — |
| 340 | C23×C4 | — | 21 | 6 | no | — |
| 341 | C23×C4 | — | 21 | 3 | no | — |
| 342 | C22×C7 | — | 3 | 1 | no | — |
| 343 | C22×C7 | — | 3 | 1 | no | — |
| 344 | C22×C7 | — | 3 | 12 | no | — |
| 345 | C22×C7 | — | 4 | 12 | no | — |
| 346 | C22×C7 | — | 6 | 18 | no | — |
| 347 | C22×C7 | — | 6 | 18 | no | — |
| 348 | C22×C7 | — | 12 | 12 | no | — |
| 349 | C22×C7 | — | 12 | 16 | no | — |
| 350 | C22×C7 | C2×#997 | 1 | 1 | yes | characteristic, complemented |
| 351 | C2×D7 | — | 3 | 2 | no | — |
| 352 | C2×D7 | — | 3 | 1 | no | — |
| 353 | C2×D7 | — | 3 | 2 | no | — |
| 354 | C2×D7 | — | 3 | 2 | no | — |
| 355 | C2×D7 | — | 3 | 2 | no | — |
| 356 | C2×D7 | — | 3 | 12 | no | — |
| 357 | C2×D7 | — | 6 | 72 | no | — |
| 358 | C2×D7 | — | 6 | 18 | no | — |
| 359 | C2×D7 | — | 6 | 18 | no | — |
| 360 | C2×D7 | — | 6 | 24 | no | — |
| 361 | C2×D7 | — | 12 | 36 | no | — |
| 362 | C2×D7 | — | 12 | 48 | no | — |
| 363 | C2×D7 | — | 12 | 12 | no | — |
| 364 | C2×D7 | C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 365 | C4×C7 | — | 3 | 8 | no | — |
| 366 | Dic7 | — | 3 | 8 | no | — |
| 367 | C2×A4 | — | 16 | 1 | no | — |
| 368 | C2×A4 | — | 16 | 12 | no | — |
| 369 | C2×A4 | — | 112 | 2 | no | — |
| 370 | C2×A4 | — | 112 | 24 | no | — |
| 371 | SL(2,𝔽3) | — | 16 | 8 | no | — |
| 372 | C3×C7 | — | 64 | 1 | no | Hall |
| 373 | C24 | — | 3 | 12 | no | — |
| 374 | C24 | — | 3 | 3 | no | — |
| 375 | C24 | — | 3 | 12 | no | — |
| 376 | C24 | — | 4 | 3 | no | — |
| 377 | C24 | — | 7 | 1 | no | — |
| 378 | C24 | — | 7 | 12 | no | — |
| 379 | C24 | — | 12 | 3 | no | — |
| 380 | C24 | — | 12 | 3 | no | — |
| 381 | C24 | — | 12 | 1 | no | — |
| 382 | C24 | — | 21 | 18 | no | — |
| 383 | C24 | — | 21 | 18 | no | — |
| 384 | C24 | — | 21 | 36 | no | — |
| 385 | C24 | — | 21 | 36 | no | — |
| 386 | C24 | — | 21 | 16 | no | — |
| 387 | C24 | — | 21 | 12 | no | — |
| 388 | C24 | — | 21 | 48 | no | — |
| 389 | C24 | — | 21 | 36 | no | — |
| 390 | C24 | — | 21 | 3 | no | — |
| 391 | C24 | — | 21 | 12 | no | — |
| 392 | C24 | — | 42 | 6 | no | — |
| 393 | C24 | — | 42 | 18 | no | — |
| 394 | C24 | — | 84 | 9 | no | — |
| 395 | C24 | — | 84 | 9 | no | — |
| 396 | C24 | — | 84 | 3 | no | — |
| 397 | C24 | — | 84 | 3 | no | — |
| 398 | C24 | — | 84 | 24 | no | — |
| 399 | C24 | — | 84 | 24 | no | — |
| 400 | C24 | — | 84 | 24 | no | — |
| 401 | C24 | — | 84 | 24 | no | — |
| 402 | C24 | — | 84 | 24 | no | — |
| 403 | C24 | — | 84 | 24 | no | — |
| 404 | C24 | — | 84 | 24 | no | — |
| 405 | C24 | — | 84 | 24 | no | — |
| 406 | #41 | — | 3 | 96 | no | — |
| 407 | #41 | — | 3 | 32 | no | — |
| 408 | #41 | — | 21 | 96 | no | — |
| 409 | #41 | — | 21 | 288 | no | — |
| 410 | #41 | — | 21 | 96 | no | — |
| 411 | #41 | — | 21 | 288 | no | — |
| 412 | #41 | — | 21 | 96 | no | — |
| 413 | #41 | — | 21 | 32 | no | — |
| 414 | C2×Q8 | — | 3 | 8 | no | — |
| 415 | C2×Q8 | — | 7 | 8 | no | — |
| 416 | C2×Q8 | — | 21 | 24 | no | — |
| 417 | C2×Q8 | — | 21 | 8 | no | — |
| 418 | C2×Q8 | — | 21 | 24 | no | — |
| 419 | C2×Q8 | — | 21 | 8 | no | — |
| 420 | C2×D4 | — | 3 | 72 | no | — |
| 421 | C2×D4 | — | 3 | 144 | no | — |
| 422 | C2×D4 | — | 3 | 48 | no | — |
| 423 | C2×D4 | — | 21 | 72 | no | — |
| 424 | C2×D4 | — | 21 | 144 | no | — |
| 425 | C2×D4 | — | 21 | 48 | no | — |
| 426 | C2×D4 | — | 21 | 96 | no | — |
| 427 | C2×D4 | — | 21 | 288 | no | — |
| 428 | C2×D4 | — | 21 | 576 | no | — |
| 429 | C2×D4 | — | 21 | 192 | no | — |
| 430 | C2×D4 | — | 21 | 144 | no | — |
| 431 | C2×D4 | — | 21 | 144 | no | — |
| 432 | C2×D4 | — | 21 | 144 | no | — |
| 433 | C2×D4 | — | 21 | 48 | no | — |
| 434 | C2×D4 | — | 21 | 48 | no | — |
| 435 | C22×C4 | — | 3 | 36 | no | — |
| 436 | C22×C4 | — | 3 | 2 | no | — |
| 437 | C22×C4 | — | 21 | 12 | no | — |
| 438 | C22×C4 | — | 21 | 12 | no | — |
| 439 | C22×C4 | — | 21 | 72 | no | — |
| 440 | C22×C4 | — | 21 | 48 | no | — |
| 441 | C22×C4 | — | 21 | 144 | no | — |
| 442 | C22×C4 | — | 21 | 36 | no | — |
| 443 | C22×C4 | — | 21 | 2 | no | — |
| 444 | C2×C7 | — | 3 | 1 | no | — |
| 445 | C2×C7 | — | 3 | 1 | no | — |
| 446 | C2×C7 | — | 6 | 12 | no | — |
| 447 | C2×C7 | C2×C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 448 | D7 | — | 3 | 2 | no | — |
| 449 | D7 | — | 6 | 12 | no | — |
| 450 | D7 | C22⋊#997 | 1 | 2 | yes | direct product factor |
| 451 | C22×C3 | — | 448 | 1 | no | — |
| 452 | A4 | — | 16 | 12 | no | — |
| 453 | A4 | — | 16 | 1 | no | — |
| 454 | C23 | — | 3 | 18 | no | — |
| 455 | C23 | — | 3 | 12 | no | — |
| 456 | C23 | — | 3 | 16 | no | — |
| 457 | C23 | — | 6 | 9 | no | — |
| 458 | C23 | — | 6 | 3 | no | — |
| 459 | C23 | — | 7 | 2 | no | — |
| 460 | C23 | — | 12 | 12 | no | — |
| 461 | C23 | — | 12 | 12 | no | — |
| 462 | C23 | — | 12 | 12 | no | — |
| 463 | C23 | — | 12 | 12 | no | — |
| 464 | C23 | — | 21 | 1 | no | — |
| 465 | C23 | — | 21 | 12 | no | — |
| 466 | C23 | — | 21 | 1 | no | — |
| 467 | C23 | — | 21 | 2 | no | — |
| 468 | C23 | — | 21 | 18 | no | — |
| 469 | C23 | — | 21 | 36 | no | — |
| 470 | C23 | — | 21 | 36 | no | — |
| 471 | C23 | — | 21 | 48 | no | — |
| 472 | C23 | — | 21 | 12 | no | — |
| 473 | C23 | — | 28 | 24 | no | — |
| 474 | C23 | — | 42 | 9 | no | — |
| 475 | C23 | — | 42 | 36 | no | — |
| 476 | C23 | — | 42 | 36 | no | — |
| 477 | C23 | — | 42 | 36 | no | — |
| 478 | C23 | — | 42 | 36 | no | — |
| 479 | C23 | — | 42 | 3 | no | — |
| 480 | C23 | — | 84 | 24 | no | — |
| 481 | C23 | — | 84 | 36 | no | — |
| 482 | C23 | — | 84 | 36 | no | — |
| 483 | C23 | — | 84 | 36 | no | — |
| 484 | C23 | — | 84 | 36 | no | — |
| 485 | C23 | — | 84 | 24 | no | — |
| 486 | C23 | — | 84 | 32 | no | — |
| 487 | C23 | — | 84 | 72 | no | — |
| 488 | C23 | — | 84 | 96 | no | — |
| 489 | C23 | D7×C22⋊A4 | 1 | 1 | yes | characteristic |
| 490 | C23 | D7×C22⋊A4 | 1 | 12 | yes | complemented |
| 491 | Q8 | — | 3 | 8 | no | — |
| 492 | Q8 | — | 21 | 8 | no | — |
| 493 | Q8 | — | 21 | 24 | no | — |
| 494 | Q8 | D7×C22⋊A4 | 1 | 8 | yes | complemented |
| 495 | D4 | — | 3 | 96 | no | — |
| 496 | D4 | — | 21 | 96 | no | — |
| 497 | D4 | — | 21 | 192 | no | — |
| 498 | C2×C4 | — | 3 | 12 | no | — |
| 499 | C2×C4 | — | 3 | 48 | no | — |
| 500 | C2×C4 | — | 21 | 8 | no | — |
| 501 | C2×C4 | — | 21 | 24 | no | — |
| 502 | C2×C4 | — | 21 | 96 | no | — |
| 503 | C2×C4 | — | 21 | 12 | no | — |
| 504 | C2×C4 | — | 21 | 48 | no | — |
| 505 | C7 | C2×C22⋊#997 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 506 | C2×C3 | — | 64 | 1 | no | — |
| 507 | C2×C3 | — | 448 | 2 | no | — |
| 508 | C22 | — | 3 | 1 | no | — |
| 509 | C22 | — | 3 | 1 | no | — |
| 510 | C22 | — | 3 | 12 | no | — |
| 511 | C22 | — | 4 | 12 | no | — |
| 512 | C22 | — | 6 | 18 | no | — |
| 513 | C22 | — | 6 | 18 | no | — |
| 514 | C22 | — | 7 | 1 | no | — |
| 515 | C22 | — | 12 | 12 | no | — |
| 516 | C22 | — | 12 | 16 | no | — |
| 517 | C22 | — | 21 | 2 | no | — |
| 518 | C22 | — | 21 | 2 | no | — |
| 519 | C22 | — | 21 | 2 | no | — |
| 520 | C22 | — | 21 | 2 | no | — |
| 521 | C22 | — | 21 | 1 | no | — |
| 522 | C22 | — | 21 | 12 | no | — |
| 523 | C22 | — | 42 | 18 | no | — |
| 524 | C22 | — | 42 | 18 | no | — |
| 525 | C22 | — | 42 | 24 | no | — |
| 526 | C22 | — | 42 | 72 | no | — |
| 527 | C22 | — | 84 | 12 | no | — |
| 528 | C22 | — | 84 | 36 | no | — |
| 529 | C22 | — | 84 | 48 | no | — |
| 530 | C22 | D7×#997 | 1 | 1 | yes | characteristic, complemented |
| 531 | C4 | — | 3 | 8 | no | — |
| 532 | C4 | — | 21 | 8 | no | — |
| 533 | C3 | — | 64 | 1 | no | Sylow |
| 534 | C2 | — | 3 | 1 | no | — |
| 535 | C2 | — | 3 | 1 | no | — |
| 536 | C2 | — | 6 | 12 | no | — |
| 537 | C2 | — | 7 | 2 | no | — |
| 538 | C2 | — | 21 | 2 | no | — |
| 539 | C2 | — | 42 | 12 | no | — |
| 540 | C2 | D7×C22⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×C22⋊(C22⋊A4) |
| commutator, Fitting, cosocle, hypocenter | C22×C7×H(5,𝔽2) | C2×C3 |
| socle | C23×C7 | C2×C22⋊A4 |
| LCS | G ▷ C22×C7×H(5,𝔽2) | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×C22⋊#997 | C2 | semidirect |
| 2. C22×D7×H(5,𝔽2) | C3 | semidirect |
| 6. C22×C7×H(5,𝔽2) | C2×C3 | semidirect |
| 19. C25×D7 | A4 | semidirect |
| 30. D7×H(5,𝔽2) | A4 | semidirect |
| 35. C22×Q8×D7 | A4 | semidirect |
| 45. C22⋊#997 | D7 | direct (N × H) |
| 52. C25×C7 | C2×A4 | semidirect |
| 66. C7×H(5,𝔽2) | C2×A4 | semidirect |
| 68. C22×C7×Q8 | C2×A4 | semidirect |
| 120. C22×H(5,𝔽2) | C3×D7 | semidirect |
| 155. C23×D7 | C22⋊A4 | semidirect |
| 176. Q8×D7 | C22⋊A4 | semidirect |
| 238. C23×C7 | C2×C22⋊A4 | semidirect |
| 264. C22×D7 | #997 | semidirect |
| 266. C7×Q8 | C2×C22⋊A4 | semidirect |
| 297. C25 | A4×D7 | semidirect |
| 308. H(5,𝔽2) | A4×D7 | semidirect |
| 320. C22×Q8 | A4×D7 | semidirect |
| 350. C22×C7 | C2×#997 | semidirect |
| 450. D7 | C22⋊#997 | direct (N × H) |
| 490. C23 | D7×C22⋊A4 | semidirect |
| 494. Q8 | D7×C22⋊A4 | semidirect |
| 505. C7 | C2×C22⋊#997 | semidirect |
| 530. C22 | D7×#997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C22⋊#997 | 2 |
| C22×D7×H(5,𝔽2) | 3 |
| C2×D7×C22⋊A4 | 4 |
| D7×#997 | 4 |
| D7×C22⋊SL(2,𝔽3) | 4 |
| C2×C22⋊#997 | 7 |