Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
2450 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 2450 conjugacy classes of subgroups — too many to draw. Only its 70 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 | C2×C7×#997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D7×#997 | C2 | 1 | 2 | yes | maximal, direct product factor |
| 3 | C2×D7×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 4 | C22×A4×D7 | — | 4 | 3 | no | maximal |
| 5 | C7×#997 | C22 | 1 | 1 | yes | characteristic, complemented |
| 6 | C2×D7×SL(2,𝔽3) | — | 4 | 2 | no | maximal |
| 7 | C2×C7×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 8 | D7×H(5,𝔽2) | — | 3 | 4 | no | — |
| 9 | D7×H(5,𝔽2) | — | 3 | 6 | no | — |
| 10 | D7×H(5,𝔽2) | C2×C3 | 1 | 2 | yes | complemented |
| 11 | C2×#6553 | — | 3 | 2 | no | — |
| 12 | C2×D7×#41 | — | 3 | 2 | no | — |
| 13 | C2×#6548 | — | 3 | 3 | no | — |
| 14 | C22×D4×D7 | — | 3 | 3 | no | — |
| 15 | C22×#997 | — | 7 | 1 | no | maximal, Hall |
| 16 | C22×C7×A4 | — | 4 | 3 | no | — |
| 17 | C2×A4×D7 | — | 4 | 12 | no | — |
| 18 | C2×A4×D7 | — | 4 | 6 | no | — |
| 19 | C2×C7×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 20 | D7×SL(2,𝔽3) | — | 4 | 4 | no | — |
| 21 | C24×D7 | — | 3 | 1 | no | — |
| 22 | C24×D7 | A4 | 1 | 3 | yes | complemented |
| 23 | C7×H(5,𝔽2) | — | 3 | 2 | no | — |
| 24 | C7×H(5,𝔽2) | — | 3 | 3 | no | — |
| 25 | C7×H(5,𝔽2) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C7×#41 | — | 3 | 2 | no | — |
| 27 | C22×C7×D4 | — | 3 | 3 | no | — |
| 28 | C22×C22⋊D7 | — | 3 | 3 | no | — |
| 29 | C22×C22⋊D7 | — | 3 | 3 | no | — |
| 30 | #6553 | — | 3 | 12 | no | — |
| 31 | #6553 | — | 3 | 12 | no | — |
| 32 | #6553 | — | 3 | 4 | no | — |
| 33 | #6553 | — | 3 | 4 | no | — |
| 34 | D7×#41 | — | 3 | 12 | no | — |
| 35 | D7×#41 | — | 3 | 12 | no | — |
| 36 | D7×#41 | — | 3 | 4 | no | — |
| 37 | D7×#41 | — | 3 | 4 | no | — |
| 38 | C2×#1161 | — | 3 | 2 | no | — |
| 39 | C2×Q8×D7 | A4 | 1 | 2 | yes | complemented |
| 40 | #6548 | — | 3 | 6 | no | — |
| 41 | #6548 | — | 3 | 24 | no | — |
| 42 | #6548 | — | 3 | 6 | no | — |
| 43 | #6548 | — | 3 | 6 | no | — |
| 44 | #6548 | — | 3 | 6 | no | — |
| 45 | C2×#1159 | — | 3 | 6 | no | — |
| 46 | C2×D4×D7 | — | 3 | 6 | no | — |
| 47 | C2×D4×D7 | — | 3 | 12 | no | — |
| 48 | C2×D4×D7 | — | 3 | 6 | no | — |
| 49 | C2×D4×D7 | — | 3 | 24 | no | — |
| 50 | C2×D4×D7 | — | 3 | 6 | no | — |
| 51 | C2×D4×D7 | — | 3 | 6 | no | — |
| 52 | C2×D4×D7 | — | 3 | 6 | no | — |
| 53 | C2×#1157 | — | 3 | 6 | no | — |
| 54 | C22×D28 | — | 3 | 3 | no | — |
| 55 | C22×C4×D7 | — | 3 | 3 | no | — |
| 56 | C2×#997 | — | 7 | 2 | no | — |
| 57 | C2×#997 | D7 | 1 | 1 | yes | characteristic, direct product factor |
| 58 | C22×C3×D7 | — | 16 | 1 | no | — |
| 59 | C2×C7×A4 | — | 4 | 6 | no | — |
| 60 | C2×C7×A4 | — | 4 | 3 | no | — |
| 61 | A4×D7 | — | 4 | 12 | no | — |
| 62 | C7×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 63 | C22×H(5,𝔽2) | — | 7 | 1 | no | Sylow |
| 64 | C24×C7 | — | 3 | 1 | no | — |
| 65 | C24×C7 | C2×A4 | 1 | 3 | yes | complemented |
| 66 | C23×D7 | — | 3 | 3 | no | — |
| 67 | C23×D7 | — | 3 | 6 | no | — |
| 68 | C23×D7 | — | 3 | 2 | no | — |
| 69 | C23×D7 | — | 3 | 3 | no | — |
| 70 | C23×D7 | — | 3 | 3 | no | — |
| 71 | C23×D7 | — | 3 | 6 | no | — |
| 72 | C23×D7 | — | 4 | 12 | no | — |
| 73 | C23×D7 | — | 12 | 4 | no | — |
| 74 | C23×D7 | C2×A4 | 1 | 6 | yes | complemented |
| 75 | C7×#41 | — | 3 | 6 | no | — |
| 76 | C7×#41 | — | 3 | 6 | no | — |
| 77 | C7×#41 | — | 3 | 2 | no | — |
| 78 | C7×#41 | — | 3 | 2 | no | — |
| 79 | C2×C7×Q8 | C2×A4 | 1 | 2 | yes | complemented |
| 80 | C2×C7×D4 | — | 3 | 6 | no | — |
| 81 | C2×C7×D4 | — | 3 | 3 | no | — |
| 82 | C2×C7×D4 | — | 3 | 12 | no | — |
| 83 | C2×C7×D4 | — | 3 | 3 | no | — |
| 84 | C2×C7×D4 | — | 3 | 3 | no | — |
| 85 | C2×C7×D4 | — | 3 | 3 | no | — |
| 86 | C22×C4×C7 | — | 3 | 3 | no | — |
| 87 | C2×C22⋊D7 | — | 3 | 12 | no | — |
| 88 | C2×C22⋊D7 | — | 3 | 12 | no | — |
| 89 | C2×C22⋊D7 | — | 3 | 12 | no | — |
| 90 | C2×C22⋊D7 | — | 3 | 6 | no | — |
| 91 | C2×C22⋊D7 | — | 3 | 6 | no | — |
| 92 | C2×C22⋊D7 | — | 3 | 6 | no | — |
| 93 | C2×C22⋊D7 | — | 3 | 6 | no | — |
| 94 | C22×Dic7 | — | 3 | 3 | no | — |
| 95 | #1161 | — | 3 | 12 | no | — |
| 96 | #1161 | — | 3 | 4 | no | — |
| 97 | Q8×D7 | — | 3 | 4 | no | — |
| 98 | Q8×D7 | C2×A4 | 1 | 4 | yes | complemented |
| 99 | #1159 | — | 3 | 24 | no | — |
| 100 | #1159 | — | 3 | 12 | no | — |
| 101 | #1159 | — | 3 | 12 | no | — |
| 102 | D4×D7 | — | 3 | 24 | no | — |
| 103 | D4×D7 | — | 3 | 12 | no | — |
| 104 | D4×D7 | — | 3 | 12 | no | — |
| 105 | D4×D7 | — | 3 | 24 | no | — |
| 106 | D4×D7 | — | 3 | 24 | no | — |
| 107 | D4×D7 | — | 3 | 24 | no | — |
| 108 | D4×D7 | — | 3 | 24 | no | — |
| 109 | #1157 | — | 3 | 12 | no | — |
| 110 | #1157 | — | 3 | 12 | no | — |
| 111 | #1157 | — | 3 | 12 | no | — |
| 112 | #1157 | — | 3 | 12 | no | — |
| 113 | C2×D28 | — | 3 | 6 | no | — |
| 114 | C2×D28 | — | 3 | 12 | no | — |
| 115 | C2×D28 | — | 3 | 6 | no | — |
| 116 | C2×D28 | — | 3 | 6 | no | — |
| 117 | C2×C4×D7 | — | 3 | 6 | no | — |
| 118 | C2×C4×D7 | — | 3 | 6 | no | — |
| 119 | C2×C4×D7 | — | 3 | 12 | no | — |
| 120 | C2×C4×D7 | — | 3 | 6 | no | — |
| 121 | C2×C4×D7 | — | 3 | 2 | no | — |
| 122 | C2×Dic14 | — | 3 | 2 | no | — |
| 123 | C23×A4 | — | 28 | 3 | no | — |
| 124 | #997 | C2×D7 | 1 | 1 | yes | characteristic, direct product factor |
| 125 | C22×SL(2,𝔽3) | — | 28 | 2 | no | — |
| 126 | C22×C3×C7 | — | 16 | 1 | no | — |
| 127 | C2×C3×D7 | — | 16 | 4 | no | — |
| 128 | C2×C3×D7 | — | 16 | 2 | no | — |
| 129 | C7×A4 | — | 4 | 3 | no | — |
| 130 | C2×H(5,𝔽2) | — | 7 | 2 | no | — |
| 131 | C2×H(5,𝔽2) | — | 21 | 3 | no | — |
| 132 | C2×H(5,𝔽2) | — | 21 | 2 | no | — |
| 133 | C2×H(5,𝔽2) | — | 21 | 4 | no | — |
| 134 | C2×H(5,𝔽2) | — | 21 | 6 | no | — |
| 135 | C2×H(5,𝔽2) | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 136 | C22×#41 | — | 21 | 2 | no | — |
| 137 | C23×D4 | — | 21 | 3 | no | — |
| 138 | C23×C7 | — | 3 | 3 | no | — |
| 139 | C23×C7 | — | 3 | 1 | no | — |
| 140 | C23×C7 | — | 3 | 3 | no | — |
| 141 | C23×C7 | — | 3 | 3 | no | — |
| 142 | C23×C7 | — | 4 | 6 | no | — |
| 143 | C23×C7 | — | 12 | 2 | no | — |
| 144 | C23×C7 | C22×A4 | 1 | 3 | yes | complemented |
| 145 | C22×D7 | — | 3 | 3 | no | — |
| 146 | C22×D7 | — | 3 | 6 | no | — |
| 147 | C22×D7 | — | 3 | 6 | no | — |
| 148 | C22×D7 | — | 3 | 6 | no | — |
| 149 | C22×D7 | — | 3 | 6 | no | — |
| 150 | C22×D7 | — | 3 | 6 | no | — |
| 151 | C22×D7 | — | 3 | 6 | no | — |
| 152 | C22×D7 | — | 4 | 12 | no | — |
| 153 | C22×D7 | — | 6 | 12 | no | — |
| 154 | C22×D7 | — | 12 | 4 | no | — |
| 155 | C22×D7 | — | 12 | 12 | no | — |
| 156 | C22×D7 | — | 12 | 6 | no | — |
| 157 | C22×D7 | — | 12 | 12 | no | — |
| 158 | C22×D7 | — | 12 | 6 | no | — |
| 159 | C22×D7 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 160 | C7×Q8 | — | 3 | 2 | no | — |
| 161 | C7×Q8 | C22×A4 | 1 | 2 | yes | complemented |
| 162 | C7×D4 | — | 3 | 12 | no | — |
| 163 | C7×D4 | — | 3 | 6 | no | — |
| 164 | C7×D4 | — | 3 | 6 | no | — |
| 165 | C2×C4×C7 | — | 3 | 3 | no | — |
| 166 | C2×C4×C7 | — | 3 | 6 | no | — |
| 167 | C2×C4×C7 | — | 3 | 3 | no | — |
| 168 | C2×C4×C7 | — | 3 | 2 | no | — |
| 169 | C22⋊D7 | — | 3 | 24 | no | — |
| 170 | C22⋊D7 | — | 3 | 24 | no | — |
| 171 | C2×Dic7 | — | 3 | 6 | no | — |
| 172 | C2×Dic7 | — | 3 | 6 | no | — |
| 173 | C2×Dic7 | — | 3 | 2 | no | — |
| 174 | D28 | — | 3 | 12 | no | — |
| 175 | D28 | — | 3 | 12 | no | — |
| 176 | C4×D7 | — | 3 | 12 | no | — |
| 177 | C4×D7 | — | 3 | 12 | no | — |
| 178 | C4×D7 | — | 3 | 4 | no | — |
| 179 | C4×D7 | — | 3 | 4 | no | — |
| 180 | Dic14 | — | 3 | 4 | no | — |
| 181 | Dic14 | — | 3 | 4 | no | — |
| 182 | C22×A4 | — | 4 | 3 | no | — |
| 183 | C22×A4 | — | 28 | 6 | no | — |
| 184 | C22×A4 | — | 28 | 12 | no | — |
| 185 | C2×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 186 | C2×SL(2,𝔽3) | — | 28 | 4 | no | — |
| 187 | C2×C3×C7 | — | 16 | 2 | no | — |
| 188 | C2×C3×C7 | — | 16 | 1 | no | — |
| 189 | C3×D7 | — | 16 | 4 | no | — |
| 190 | C25 | — | 7 | 3 | no | — |
| 191 | C25 | — | 21 | 1 | no | — |
| 192 | H(5,𝔽2) | — | 3 | 2 | no | — |
| 193 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 194 | H(5,𝔽2) | — | 21 | 6 | no | — |
| 195 | H(5,𝔽2) | — | 21 | 24 | no | — |
| 196 | H(5,𝔽2) | — | 21 | 6 | no | — |
| 197 | H(5,𝔽2) | — | 21 | 6 | no | — |
| 198 | H(5,𝔽2) | — | 21 | 6 | no | — |
| 199 | H(5,𝔽2) | — | 21 | 4 | no | — |
| 200 | H(5,𝔽2) | — | 21 | 12 | no | — |
| 201 | H(5,𝔽2) | — | 21 | 12 | no | — |
| 202 | H(5,𝔽2) | — | 21 | 4 | no | — |
| 203 | H(5,𝔽2) | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 204 | C2×#41 | — | 3 | 2 | no | — |
| 205 | C2×#41 | — | 21 | 6 | no | — |
| 206 | C2×#41 | — | 21 | 6 | no | — |
| 207 | C2×#41 | — | 21 | 4 | no | — |
| 208 | C2×#41 | — | 21 | 4 | no | — |
| 209 | C2×#41 | — | 21 | 12 | no | — |
| 210 | C2×#41 | — | 21 | 12 | no | — |
| 211 | C2×#41 | — | 21 | 2 | no | — |
| 212 | C22×Q8 | — | 7 | 2 | no | — |
| 213 | C22×D4 | — | 3 | 3 | no | — |
| 214 | C22×D4 | — | 21 | 3 | no | — |
| 215 | C22×D4 | — | 21 | 6 | no | — |
| 216 | C22×D4 | — | 21 | 6 | no | — |
| 217 | C22×D4 | — | 21 | 6 | no | — |
| 218 | C22×D4 | — | 21 | 12 | no | — |
| 219 | C22×D4 | — | 21 | 6 | no | — |
| 220 | C22×D4 | — | 21 | 24 | no | — |
| 221 | C22×D4 | — | 21 | 6 | no | — |
| 222 | C22×D4 | — | 21 | 3 | no | — |
| 223 | C22×D4 | — | 21 | 3 | no | — |
| 224 | C23×C4 | — | 21 | 3 | no | — |
| 225 | C22×C7 | — | 3 | 3 | no | — |
| 226 | C22×C7 | — | 3 | 3 | no | — |
| 227 | C22×C7 | — | 4 | 3 | no | — |
| 228 | C22×C7 | — | 6 | 6 | no | — |
| 229 | C22×C7 | — | 12 | 3 | no | — |
| 230 | C22×C7 | — | 12 | 1 | no | — |
| 231 | C22×C7 | — | 12 | 3 | no | — |
| 232 | C22×C7 | C2×C22⋊A4 | 1 | 1 | yes | characteristic |
| 233 | C2×D7 | — | 3 | 6 | no | — |
| 234 | C2×D7 | — | 6 | 6 | no | — |
| 235 | C2×D7 | — | 6 | 12 | no | — |
| 236 | C2×D7 | — | 6 | 12 | no | — |
| 237 | C2×D7 | — | 12 | 6 | no | — |
| 238 | C2×D7 | — | 12 | 6 | no | — |
| 239 | C2×D7 | — | 12 | 6 | no | — |
| 240 | C2×D7 | — | 12 | 6 | no | — |
| 241 | C2×D7 | #997 | 1 | 4 | yes | direct product factor |
| 242 | C2×D7 | C2×C22⋊A4 | 1 | 2 | yes | — |
| 243 | C4×C7 | — | 3 | 2 | no | — |
| 244 | C4×C7 | — | 3 | 2 | no | — |
| 245 | Dic7 | — | 3 | 4 | no | — |
| 246 | C23×C3 | — | 112 | 1 | no | — |
| 247 | C2×A4 | — | 4 | 6 | no | — |
| 248 | C2×A4 | — | 4 | 3 | no | — |
| 249 | C2×A4 | — | 28 | 12 | no | — |
| 250 | SL(2,𝔽3) | — | 4 | 2 | no | — |
| 251 | C3×C7 | — | 16 | 1 | no | Hall |
| 252 | C24 | — | 3 | 1 | no | — |
| 253 | C24 | — | 7 | 6 | no | — |
| 254 | C24 | — | 21 | 3 | no | — |
| 255 | C24 | — | 21 | 2 | no | — |
| 256 | C24 | — | 21 | 6 | no | — |
| 257 | C24 | — | 21 | 3 | no | — |
| 258 | C24 | — | 21 | 3 | no | — |
| 259 | C24 | — | 21 | 6 | no | — |
| 260 | C24 | — | 28 | 12 | no | — |
| 261 | C24 | — | 84 | 4 | no | — |
| 262 | C24 | A4×D7 | 1 | 3 | yes | complemented |
| 263 | #41 | — | 3 | 6 | no | — |
| 264 | #41 | — | 3 | 6 | no | — |
| 265 | #41 | — | 3 | 2 | no | — |
| 266 | #41 | — | 3 | 2 | no | — |
| 267 | #41 | — | 21 | 12 | no | — |
| 268 | #41 | — | 21 | 12 | no | — |
| 269 | #41 | — | 21 | 12 | no | — |
| 270 | #41 | — | 21 | 12 | no | — |
| 271 | #41 | — | 21 | 12 | no | — |
| 272 | #41 | — | 21 | 12 | no | — |
| 273 | #41 | — | 21 | 24 | no | — |
| 274 | #41 | — | 21 | 12 | no | — |
| 275 | #41 | — | 21 | 4 | no | — |
| 276 | C2×Q8 | — | 7 | 4 | no | — |
| 277 | C2×Q8 | — | 21 | 2 | no | — |
| 278 | C2×Q8 | — | 21 | 4 | no | — |
| 279 | C2×Q8 | A4×D7 | 1 | 2 | yes | complemented |
| 280 | C2×D4 | — | 3 | 6 | no | — |
| 281 | C2×D4 | — | 3 | 3 | no | — |
| 282 | C2×D4 | — | 3 | 12 | no | — |
| 283 | C2×D4 | — | 3 | 3 | no | — |
| 284 | C2×D4 | — | 3 | 3 | no | — |
| 285 | C2×D4 | — | 3 | 3 | no | — |
| 286 | C2×D4 | — | 21 | 6 | no | — |
| 287 | C2×D4 | — | 21 | 12 | no | — |
| 288 | C2×D4 | — | 21 | 6 | no | — |
| 289 | C2×D4 | — | 21 | 6 | no | — |
| 290 | C2×D4 | — | 21 | 12 | no | — |
| 291 | C2×D4 | — | 21 | 12 | no | — |
| 292 | C2×D4 | — | 21 | 24 | no | — |
| 293 | C2×D4 | — | 21 | 24 | no | — |
| 294 | C2×D4 | — | 21 | 24 | no | — |
| 295 | C2×D4 | — | 21 | 24 | no | — |
| 296 | C2×D4 | — | 21 | 24 | no | — |
| 297 | C2×D4 | — | 21 | 12 | no | — |
| 298 | C2×D4 | — | 21 | 12 | no | — |
| 299 | C2×D4 | — | 21 | 6 | no | — |
| 300 | C2×D4 | — | 21 | 6 | no | — |
| 301 | C2×D4 | — | 21 | 6 | no | — |
| 302 | C2×D4 | — | 21 | 12 | no | — |
| 303 | C2×D4 | — | 21 | 6 | no | — |
| 304 | C22×C4 | — | 3 | 3 | no | — |
| 305 | C22×C4 | — | 21 | 2 | no | — |
| 306 | C22×C4 | — | 21 | 6 | no | — |
| 307 | C22×C4 | — | 21 | 12 | no | — |
| 308 | C22×C4 | — | 21 | 6 | no | — |
| 309 | C22×C4 | — | 21 | 6 | no | — |
| 310 | C22×C4 | — | 21 | 3 | no | — |
| 311 | C2×C7 | — | 6 | 3 | no | — |
| 312 | C2×C7 | — | 6 | 3 | no | — |
| 313 | C2×C7 | C2×#997 | 1 | 2 | yes | complemented |
| 314 | C2×C7 | C22×C22⋊A4 | 1 | 1 | yes | characteristic |
| 315 | D7 | — | 6 | 6 | no | — |
| 316 | D7 | C2×#997 | 1 | 4 | yes | direct product factor |
| 317 | C22×C3 | — | 16 | 1 | no | — |
| 318 | C22×C3 | — | 112 | 2 | no | — |
| 319 | C22×C3 | — | 112 | 4 | no | — |
| 320 | A4 | — | 4 | 3 | no | — |
| 321 | C23 | — | 3 | 1 | no | — |
| 322 | C23 | — | 3 | 3 | no | — |
| 323 | C23 | — | 3 | 3 | no | — |
| 324 | C23 | — | 3 | 3 | no | — |
| 325 | C23 | — | 4 | 6 | no | — |
| 326 | C23 | — | 7 | 1 | no | — |
| 327 | C23 | — | 12 | 2 | no | — |
| 328 | C23 | — | 21 | 6 | no | — |
| 329 | C23 | — | 21 | 6 | no | — |
| 330 | C23 | — | 21 | 6 | no | — |
| 331 | C23 | — | 21 | 6 | no | — |
| 332 | C23 | — | 21 | 6 | no | — |
| 333 | C23 | — | 21 | 6 | no | — |
| 334 | C23 | — | 21 | 3 | no | — |
| 335 | C23 | — | 28 | 12 | no | — |
| 336 | C23 | — | 42 | 12 | no | — |
| 337 | C23 | — | 84 | 6 | no | — |
| 338 | C23 | — | 84 | 6 | no | — |
| 339 | C23 | — | 84 | 4 | no | — |
| 340 | C23 | — | 84 | 12 | no | — |
| 341 | C23 | — | 84 | 12 | no | — |
| 342 | C23 | C2×A4×D7 | 1 | 3 | yes | complemented |
| 343 | Q8 | — | 3 | 2 | no | — |
| 344 | Q8 | — | 21 | 4 | no | — |
| 345 | Q8 | — | 21 | 4 | no | — |
| 346 | Q8 | C2×A4×D7 | 1 | 2 | yes | complemented |
| 347 | D4 | — | 3 | 6 | no | — |
| 348 | D4 | — | 3 | 6 | no | — |
| 349 | D4 | — | 3 | 12 | no | — |
| 350 | D4 | — | 21 | 12 | no | — |
| 351 | D4 | — | 21 | 12 | no | — |
| 352 | D4 | — | 21 | 24 | no | — |
| 353 | D4 | — | 21 | 24 | no | — |
| 354 | C2×C4 | — | 3 | 3 | no | — |
| 355 | C2×C4 | — | 3 | 6 | no | — |
| 356 | C2×C4 | — | 3 | 3 | no | — |
| 357 | C2×C4 | — | 3 | 2 | no | — |
| 358 | C2×C4 | — | 21 | 4 | no | — |
| 359 | C2×C4 | — | 21 | 4 | no | — |
| 360 | C2×C4 | — | 21 | 12 | no | — |
| 361 | C2×C4 | — | 21 | 12 | no | — |
| 362 | C2×C4 | — | 21 | 6 | no | — |
| 363 | C2×C4 | — | 21 | 6 | no | — |
| 364 | C2×C4 | — | 21 | 2 | no | — |
| 365 | C7 | C22×#997 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 366 | C2×C3 | — | 16 | 1 | no | — |
| 367 | C2×C3 | — | 16 | 2 | no | — |
| 368 | C2×C3 | — | 112 | 4 | no | — |
| 369 | C22 | — | 3 | 3 | no | — |
| 370 | C22 | — | 3 | 3 | no | — |
| 371 | C22 | — | 4 | 3 | no | — |
| 372 | C22 | — | 6 | 6 | no | — |
| 373 | C22 | — | 7 | 2 | no | — |
| 374 | C22 | — | 7 | 4 | no | — |
| 375 | C22 | — | 12 | 3 | no | — |
| 376 | C22 | — | 12 | 1 | no | — |
| 377 | C22 | — | 12 | 3 | no | — |
| 378 | C22 | — | 21 | 6 | no | — |
| 379 | C22 | — | 42 | 12 | no | — |
| 380 | C22 | — | 42 | 12 | no | — |
| 381 | C22 | — | 42 | 6 | no | — |
| 382 | C22 | — | 84 | 6 | no | — |
| 383 | C22 | — | 84 | 6 | no | — |
| 384 | C22 | — | 84 | 6 | no | — |
| 385 | C22 | — | 84 | 6 | no | — |
| 386 | C22 | D7×C22⋊A4 | 1 | 1 | yes | characteristic |
| 387 | C4 | — | 3 | 2 | no | — |
| 388 | C4 | — | 3 | 2 | no | — |
| 389 | C4 | — | 21 | 4 | no | — |
| 390 | C3 | — | 16 | 1 | no | Sylow |
| 391 | C2 | — | 6 | 3 | no | — |
| 392 | C2 | — | 6 | 3 | no | — |
| 393 | C2 | — | 7 | 4 | no | — |
| 394 | C2 | — | 42 | 6 | no | — |
| 395 | C2 | D7×#997 | 1 | 2 | yes | direct product factor |
| 396 | C2 | C2×D7×C22⋊A4 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D7×C22⋊A4 |
| commutator, cosocle, hypocenter | C7×H(5,𝔽2) | C22×C3 |
| Frattini | C2 | C2×D7×C22⋊A4 |
| Fitting | C2×C7×H(5,𝔽2) | C2×C3 |
| socle | C22×C7 | C2×C22⋊A4 |
| LCS | G ▷ C7×H(5,𝔽2) | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C7×#997 | C2 | semidirect |
| 2. D7×#997 | C2 | direct (N × H) |
| 3. C2×D7×H(5,𝔽2) | C3 | semidirect |
| 5. C7×#997 | C22 | semidirect |
| 7. C2×C7×H(5,𝔽2) | C2×C3 | semidirect |
| 10. D7×H(5,𝔽2) | C2×C3 | semidirect |
| 22. C24×D7 | A4 | semidirect |
| 25. C7×H(5,𝔽2) | C22×C3 | semidirect |
| 39. C2×Q8×D7 | A4 | semidirect |
| 57. C2×#997 | D7 | direct (N × H) |
| 65. C24×C7 | C2×A4 | semidirect |
| 74. C23×D7 | C2×A4 | semidirect |
| 79. C2×C7×Q8 | C2×A4 | semidirect |
| 98. Q8×D7 | C2×A4 | semidirect |
| 124. #997 | C2×D7 | direct (N × H) |
| 135. C2×H(5,𝔽2) | C3×D7 | semidirect |
| 144. C23×C7 | C22×A4 | semidirect |
| 161. C7×Q8 | C22×A4 | semidirect |
| 203. H(5,𝔽2) | C2×C3×D7 | semidirect |
| 241. C2×D7 | #997 | direct (N × H) |
| 262. C24 | A4×D7 | semidirect |
| 279. C2×Q8 | A4×D7 | semidirect |
| 313. C2×C7 | C2×#997 | semidirect |
| 316. D7 | C2×#997 | direct (N × H) |
| 342. C23 | C2×A4×D7 | semidirect |
| 346. Q8 | C2×A4×D7 | semidirect |
| 365. C7 | C22×#997 | semidirect |
| 395. C2 | D7×#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#997 | 2 |
| D7×#997 | 2 |
| C2×D7×H(5,𝔽2) | 3 |
| C22×A4×D7 | 4 |
| C2×D7×SL(2,𝔽3) | 4 |
| C22×#997 | 7 |