Finite Group DatabasebetaFinite Group DatabasebetaOrder 2688.
2036 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 2036 conjugacy classes of subgroups — too many to draw. Only its 189 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 | H(5,𝔽2)×D21 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #120×D21 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C3×C7×B(4,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13056881 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13056669 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #99×D21 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #13056378 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | D7×B(4,𝔽2) | — | 3 | 1 | no | maximal, Hall |
| 9 | C24×D21 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×C7×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #10621662 | — | 2 | 3 | no | — |
| 12 | #41×D21 | — | 2 | 3 | no | — |
| 13 | #10621657 | — | 2 | 3 | no | — |
| 14 | #10621657 | C22 | 1 | 3 | yes | complemented |
| 15 | C2×D4×D21 | — | 2 | 3 | no | — |
| 16 | C2×D4×D21 | — | 2 | 3 | no | — |
| 17 | C2×D4×D21 | C22 | 1 | 3 | yes | — |
| 18 | C3×C7×#120 | C22 | 1 | 3 | yes | complemented |
| 19 | #10621436 | C22 | 1 | 3 | yes | complemented |
| 20 | #10621420 | — | 2 | 3 | no | — |
| 21 | #10621420 | C22 | 1 | 3 | yes | complemented |
| 22 | #10621365 | — | 2 | 3 | no | — |
| 23 | #10621365 | C22 | 1 | 3 | yes | complemented |
| 24 | C22⋊C4×D21 | — | 2 | 3 | no | — |
| 25 | C22⋊C4×D21 | C22 | 1 | 3 | yes | complemented |
| 26 | C3×C7×#99 | C22 | 1 | 3 | yes | complemented |
| 27 | #10620673 | C22 | 1 | 3 | yes | complemented |
| 28 | #10620645 | C22 | 1 | 6 | yes | complemented |
| 29 | D7×H(5,𝔽2) | — | 3 | 1 | no | — |
| 30 | D7×#120 | — | 3 | 3 | no | — |
| 31 | C7×B(4,𝔽2) | D3 | 1 | 1 | yes | characteristic, complemented |
| 32 | #90016 | — | 3 | 1 | no | — |
| 33 | #89804 | — | 3 | 3 | no | — |
| 34 | D7×#99 | — | 3 | 3 | no | — |
| 35 | #89513 | — | 3 | 3 | no | — |
| 36 | D3×B(4,𝔽2) | — | 7 | 1 | no | maximal, Hall |
| 37 | C24×C3×C7 | C23 | 1 | 1 | yes | characteristic, complemented |
| 38 | C23×D21 | — | 2 | 1 | no | — |
| 39 | C23×D21 | — | 2 | 3 | no | — |
| 40 | C23×D21 | — | 2 | 3 | no | — |
| 41 | C23×D21 | — | 4 | 4 | no | — |
| 42 | C23×D21 | D4 | 1 | 3 | yes | complemented |
| 43 | C23×D21 | C23 | 1 | 1 | yes | characteristic |
| 44 | C23×D21 | C23 | 1 | 1 | yes | characteristic, complemented |
| 45 | C3×C7×#41 | — | 2 | 3 | no | — |
| 46 | C2×C3×C7×D4 | — | 2 | 3 | no | — |
| 47 | C2×C3×C7×D4 | — | 2 | 3 | no | — |
| 48 | C2×C3×C7×D4 | C23 | 1 | 3 | yes | — |
| 49 | C2×#4268 | — | 2 | 3 | no | — |
| 50 | C2×#4268 | — | 2 | 3 | no | — |
| 51 | C2×#4268 | — | 2 | 3 | no | — |
| 52 | C2×#4268 | — | 2 | 3 | no | — |
| 53 | C2×#4268 | D4 | 1 | 3 | yes | complemented |
| 54 | C2×#4268 | C23 | 1 | 3 | yes | — |
| 55 | #66732 | — | 2 | 3 | no | — |
| 56 | Q8×D21 | — | 2 | 1 | no | — |
| 57 | #66730 | — | 2 | 3 | no | — |
| 58 | #66730 | — | 2 | 6 | no | — |
| 59 | D4×D21 | — | 2 | 3 | no | — |
| 60 | D4×D21 | — | 2 | 6 | no | — |
| 61 | D4×D21 | — | 2 | 6 | no | — |
| 62 | D4×D21 | — | 2 | 6 | no | — |
| 63 | D4×D21 | — | 2 | 6 | no | — |
| 64 | D4×D21 | — | 4 | 12 | no | — |
| 65 | #66728 | — | 2 | 6 | no | — |
| 66 | #66728 | — | 2 | 3 | no | — |
| 67 | C2×D84 | — | 2 | 3 | no | — |
| 68 | C2×D84 | — | 2 | 3 | no | — |
| 69 | C2×D84 | D4 | 1 | 3 | yes | complemented |
| 70 | C2×C4×D21 | — | 2 | 3 | no | — |
| 71 | C2×C4×D21 | — | 2 | 3 | no | — |
| 72 | C2×C4×D21 | D4 | 1 | 3 | yes | complemented |
| 73 | C3×C7×C22⋊C4 | — | 2 | 3 | no | — |
| 74 | C3×C7×C22⋊C4 | C23 | 1 | 3 | yes | complemented |
| 75 | #66636 | — | 2 | 3 | no | — |
| 76 | #66636 | C23 | 1 | 3 | yes | complemented |
| 77 | #66631 | — | 2 | 3 | no | — |
| 78 | #66631 | — | 2 | 3 | no | — |
| 79 | #66631 | — | 2 | 3 | no | — |
| 80 | C24×D7 | — | 3 | 1 | no | — |
| 81 | C7×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | #6553 | — | 6 | 3 | no | — |
| 83 | D7×#41 | — | 6 | 3 | no | — |
| 84 | #6548 | — | 3 | 3 | no | — |
| 85 | #6548 | — | 6 | 3 | no | — |
| 86 | C2×D4×D7 | — | 3 | 3 | no | — |
| 87 | C2×D4×D7 | — | 6 | 3 | no | — |
| 88 | C2×D4×D7 | — | 6 | 3 | no | — |
| 89 | C7×#120 | C2×D3 | 1 | 3 | yes | complemented |
| 90 | #6516 | — | 3 | 3 | no | — |
| 91 | #6500 | — | 3 | 3 | no | — |
| 92 | #6500 | — | 6 | 3 | no | — |
| 93 | #6445 | — | 3 | 3 | no | — |
| 94 | #6445 | — | 6 | 3 | no | — |
| 95 | D7×C22⋊C4 | — | 3 | 3 | no | — |
| 96 | D7×C22⋊C4 | — | 6 | 3 | no | — |
| 97 | C7×#99 | C2×D3 | 1 | 3 | yes | complemented |
| 98 | #6408 | — | 3 | 3 | no | — |
| 99 | #6380 | — | 3 | 6 | no | — |
| 100 | D3×H(5,𝔽2) | — | 7 | 1 | no | — |
| 101 | D3×#120 | — | 7 | 3 | no | — |
| 102 | C3×B(4,𝔽2) | D7 | 1 | 1 | yes | characteristic, complemented |
| 103 | #5244 | — | 7 | 1 | no | — |
| 104 | #5032 | — | 7 | 3 | no | — |
| 105 | D3×#99 | — | 7 | 3 | no | — |
| 106 | #4741 | — | 7 | 3 | no | — |
| 107 | C23×C3×C7 | — | 2 | 1 | no | — |
| 108 | C23×C3×C7 | — | 2 | 3 | no | — |
| 109 | C23×C3×C7 | — | 4 | 2 | no | — |
| 110 | C23×C3×C7 | C2×D4 | 1 | 3 | yes | complemented |
| 111 | C23×C3×C7 | C24 | 1 | 1 | yes | characteristic |
| 112 | C22×D21 | — | 2 | 12 | no | — |
| 113 | C22×D21 | — | 2 | 3 | no | — |
| 114 | C22×D21 | — | 2 | 3 | no | — |
| 115 | C22×D21 | — | 2 | 3 | no | — |
| 116 | C22×D21 | — | 2 | 3 | no | — |
| 117 | C22×D21 | — | 4 | 2 | no | — |
| 118 | C22×D21 | — | 4 | 2 | no | — |
| 119 | C22×D21 | — | 4 | 6 | no | — |
| 120 | C22×D21 | — | 4 | 6 | no | — |
| 121 | C22×D21 | — | 4 | 6 | no | — |
| 122 | C22×D21 | — | 4 | 6 | no | — |
| 123 | C22×D21 | — | 4 | 3 | no | — |
| 124 | C22×D21 | — | 4 | 1 | no | — |
| 125 | C22×D21 | — | 8 | 2 | no | — |
| 126 | C22×D21 | C2×D4 | 1 | 3 | yes | — |
| 127 | C22×D21 | C2×D4 | 1 | 3 | yes | — |
| 128 | C22×D21 | C2×D4 | 1 | 3 | yes | complemented |
| 129 | C3×C7×Q8 | — | 2 | 1 | no | — |
| 130 | C3×C7×D4 | — | 2 | 3 | no | — |
| 131 | C3×C7×D4 | — | 2 | 6 | no | — |
| 132 | C3×C7×D4 | — | 4 | 6 | no | — |
| 133 | C2×C3×C4×C7 | — | 2 | 3 | no | — |
| 134 | C2×C3×C4×C7 | — | 2 | 3 | no | — |
| 135 | C2×C3×C4×C7 | C2×D4 | 1 | 3 | yes | complemented |
| 136 | #4268 | — | 2 | 6 | no | — |
| 137 | #4268 | — | 2 | 6 | no | — |
| 138 | #4268 | — | 2 | 6 | no | — |
| 139 | #4268 | — | 4 | 6 | no | — |
| 140 | #4268 | — | 4 | 6 | no | — |
| 141 | C2×Dic21 | — | 2 | 3 | no | — |
| 142 | C2×Dic21 | — | 2 | 3 | no | — |
| 143 | C2×Dic21 | C2×D4 | 1 | 3 | yes | complemented |
| 144 | D84 | — | 2 | 3 | no | — |
| 145 | D84 | — | 2 | 6 | no | — |
| 146 | D84 | — | 4 | 6 | no | — |
| 147 | C4×D21 | — | 2 | 6 | no | — |
| 148 | C4×D21 | — | 2 | 3 | no | — |
| 149 | C4×D21 | — | 2 | 3 | no | — |
| 150 | C4×D21 | — | 4 | 6 | no | — |
| 151 | Dic42 | — | 2 | 3 | no | — |
| 152 | C2×B(4,𝔽2) | — | 21 | 1 | no | Sylow |
| 153 | C24×C7 | C22×D3 | 1 | 1 | yes | characteristic, complemented |
| 154 | C23×D7 | — | 3 | 1 | no | — |
| 155 | C23×D7 | — | 3 | 3 | no | — |
| 156 | C23×D7 | — | 3 | 1 | no | — |
| 157 | C23×D7 | — | 6 | 3 | no | — |
| 158 | C23×D7 | — | 6 | 3 | no | — |
| 159 | C23×D7 | — | 6 | 1 | no | — |
| 160 | C23×D7 | — | 12 | 4 | no | — |
| 161 | C7×#41 | — | 2 | 3 | no | — |
| 162 | C2×C7×D4 | — | 2 | 3 | no | — |
| 163 | C2×C7×D4 | — | 2 | 3 | no | — |
| 164 | C2×C7×D4 | C22×D3 | 1 | 3 | yes | — |
| 165 | C2×C22⋊D7 | — | 3 | 3 | no | — |
| 166 | C2×C22⋊D7 | — | 3 | 3 | no | — |
| 167 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 168 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 169 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 170 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 171 | #1161 | — | 6 | 3 | no | — |
| 172 | Q8×D7 | — | 6 | 1 | no | — |
| 173 | #1159 | — | 6 | 6 | no | — |
| 174 | #1159 | — | 6 | 3 | no | — |
| 175 | D4×D7 | — | 6 | 6 | no | — |
| 176 | D4×D7 | — | 6 | 6 | no | — |
| 177 | D4×D7 | — | 6 | 6 | no | — |
| 178 | D4×D7 | — | 6 | 3 | no | — |
| 179 | D4×D7 | — | 6 | 6 | no | — |
| 180 | D4×D7 | — | 12 | 12 | no | — |
| 181 | #1157 | — | 6 | 6 | no | — |
| 182 | #1157 | — | 6 | 3 | no | — |
| 183 | C2×D28 | — | 3 | 3 | no | — |
| 184 | C2×D28 | — | 6 | 3 | no | — |
| 185 | C2×D28 | — | 6 | 3 | no | — |
| 186 | C2×C4×D7 | — | 3 | 3 | no | — |
| 187 | C2×C4×D7 | — | 6 | 3 | no | — |
| 188 | C2×C4×D7 | — | 6 | 3 | no | — |
| 189 | C7×C22⋊C4 | — | 2 | 3 | no | — |
| 190 | C7×C22⋊C4 | C22×D3 | 1 | 3 | yes | complemented |
| 191 | C22⋊Dic7 | — | 3 | 3 | no | — |
| 192 | C22⋊Dic7 | — | 6 | 3 | no | — |
| 193 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 194 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 195 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 196 | C24×D3 | — | 7 | 1 | no | — |
| 197 | C3×H(5,𝔽2) | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 198 | #1009 | — | 14 | 3 | no | — |
| 199 | D3×#41 | — | 14 | 3 | no | — |
| 200 | #1004 | — | 7 | 3 | no | — |
| 201 | #1004 | — | 14 | 3 | no | — |
| 202 | C2×D3×D4 | — | 7 | 3 | no | — |
| 203 | C2×D3×D4 | — | 14 | 3 | no | — |
| 204 | C2×D3×D4 | — | 14 | 3 | no | — |
| 205 | C3×#120 | C2×D7 | 1 | 3 | yes | complemented |
| 206 | #953 | — | 7 | 3 | no | — |
| 207 | #937 | — | 7 | 3 | no | — |
| 208 | #937 | — | 14 | 3 | no | — |
| 209 | #882 | — | 7 | 3 | no | — |
| 210 | #882 | — | 14 | 3 | no | — |
| 211 | D3×C22⋊C4 | — | 7 | 3 | no | — |
| 212 | D3×C22⋊C4 | — | 14 | 3 | no | — |
| 213 | C3×#99 | C2×D7 | 1 | 3 | yes | complemented |
| 214 | #834 | — | 7 | 3 | no | — |
| 215 | #806 | — | 7 | 6 | no | — |
| 216 | C22×C3×C7 | — | 2 | 6 | no | — |
| 217 | C22×C3×C7 | — | 2 | 3 | no | — |
| 218 | C22×C3×C7 | — | 4 | 1 | no | — |
| 219 | C22×C3×C7 | — | 4 | 3 | no | — |
| 220 | C22×C3×C7 | — | 4 | 3 | no | — |
| 221 | C22×C3×C7 | — | 4 | 1 | no | — |
| 222 | C22×C3×C7 | — | 8 | 1 | no | — |
| 223 | C22×C3×C7 | C22×D4 | 1 | 3 | yes | — |
| 224 | C2×D21 | — | 2 | 6 | no | — |
| 225 | C2×D21 | — | 2 | 6 | no | — |
| 226 | C2×D21 | — | 2 | 3 | no | — |
| 227 | C2×D21 | — | 4 | 3 | no | — |
| 228 | C2×D21 | — | 4 | 12 | no | — |
| 229 | C2×D21 | — | 4 | 3 | no | — |
| 230 | C2×D21 | — | 4 | 1 | no | — |
| 231 | C2×D21 | — | 4 | 4 | no | — |
| 232 | C2×D21 | — | 4 | 6 | no | — |
| 233 | C2×D21 | — | 4 | 3 | no | — |
| 234 | C2×D21 | — | 8 | 3 | no | — |
| 235 | C2×D21 | — | 8 | 3 | no | — |
| 236 | C2×D21 | #120 | 1 | 3 | yes | — |
| 237 | C2×D21 | #120 | 1 | 1 | yes | characteristic |
| 238 | C3×C4×C7 | — | 2 | 3 | no | — |
| 239 | C3×C4×C7 | — | 4 | 3 | no | — |
| 240 | Dic21 | — | 2 | 3 | no | — |
| 241 | Dic21 | — | 4 | 3 | no | — |
| 242 | C2×H(5,𝔽2) | — | 21 | 1 | no | — |
| 243 | C2×#120 | — | 21 | 3 | no | — |
| 244 | B(4,𝔽2) | — | 21 | 1 | no | — |
| 245 | B(4,𝔽2) | — | 21 | 3 | no | — |
| 246 | B(4,𝔽2) | — | 21 | 3 | no | — |
| 247 | B(4,𝔽2) | D21 | 1 | 1 | yes | characteristic, direct product factor |
| 248 | C2×#99 | — | 21 | 3 | no | — |
| 249 | C23×C7 | — | 2 | 1 | no | — |
| 250 | C23×C7 | — | 2 | 3 | no | — |
| 251 | C23×C7 | — | 4 | 2 | no | — |
| 252 | C23×C7 | D3×D4 | 1 | 3 | yes | complemented |
| 253 | C23×C7 | C23×D3 | 1 | 1 | yes | characteristic |
| 254 | C22×D7 | — | 3 | 3 | no | — |
| 255 | C22×D7 | — | 3 | 3 | no | — |
| 256 | C22×D7 | — | 3 | 3 | no | — |
| 257 | C22×D7 | — | 6 | 3 | no | — |
| 258 | C22×D7 | — | 6 | 3 | no | — |
| 259 | C22×D7 | — | 6 | 12 | no | — |
| 260 | C22×D7 | — | 6 | 3 | no | — |
| 261 | C22×D7 | — | 6 | 3 | no | — |
| 262 | C22×D7 | — | 12 | 1 | no | — |
| 263 | C22×D7 | — | 12 | 3 | no | — |
| 264 | C22×D7 | — | 12 | 2 | no | — |
| 265 | C22×D7 | — | 12 | 2 | no | — |
| 266 | C22×D7 | — | 12 | 6 | no | — |
| 267 | C22×D7 | — | 12 | 6 | no | — |
| 268 | C22×D7 | — | 12 | 6 | no | — |
| 269 | C22×D7 | — | 12 | 6 | no | — |
| 270 | C22×D7 | — | 24 | 2 | no | — |
| 271 | C7×Q8 | — | 2 | 1 | no | — |
| 272 | C7×D4 | — | 2 | 3 | no | — |
| 273 | C7×D4 | — | 2 | 6 | no | — |
| 274 | C7×D4 | — | 4 | 6 | no | — |
| 275 | C2×C4×C7 | — | 2 | 3 | no | — |
| 276 | C2×C4×C7 | — | 2 | 3 | no | — |
| 277 | C2×C4×C7 | D3×D4 | 1 | 3 | yes | complemented |
| 278 | C22⋊D7 | — | 6 | 6 | no | — |
| 279 | C22⋊D7 | — | 6 | 6 | no | — |
| 280 | C22⋊D7 | — | 6 | 6 | no | — |
| 281 | C22⋊D7 | — | 12 | 6 | no | — |
| 282 | C22⋊D7 | — | 12 | 6 | no | — |
| 283 | C2×Dic7 | — | 3 | 3 | no | — |
| 284 | C2×Dic7 | — | 6 | 3 | no | — |
| 285 | C2×Dic7 | — | 6 | 3 | no | — |
| 286 | D28 | — | 6 | 6 | no | — |
| 287 | D28 | — | 6 | 3 | no | — |
| 288 | D28 | — | 12 | 6 | no | — |
| 289 | C4×D7 | — | 6 | 3 | no | — |
| 290 | C4×D7 | — | 6 | 3 | no | — |
| 291 | C4×D7 | — | 6 | 6 | no | — |
| 292 | C4×D7 | — | 12 | 6 | no | — |
| 293 | Dic14 | — | 6 | 3 | no | — |
| 294 | C24×C3 | C22×D7 | 1 | 1 | yes | characteristic, complemented |
| 295 | C23×D3 | — | 7 | 1 | no | — |
| 296 | C23×D3 | — | 7 | 3 | no | — |
| 297 | C23×D3 | — | 7 | 1 | no | — |
| 298 | C23×D3 | — | 14 | 3 | no | — |
| 299 | C23×D3 | — | 14 | 3 | no | — |
| 300 | C23×D3 | — | 14 | 1 | no | — |
| 301 | C23×D3 | — | 28 | 4 | no | — |
| 302 | C3×#41 | — | 2 | 3 | no | — |
| 303 | C2×C3×D4 | — | 2 | 3 | no | — |
| 304 | C2×C3×D4 | — | 2 | 3 | no | — |
| 305 | C2×C3×D4 | C22×D7 | 1 | 3 | yes | — |
| 306 | C2×#67 | — | 7 | 3 | no | — |
| 307 | C2×#67 | — | 7 | 3 | no | — |
| 308 | C2×#67 | — | 14 | 3 | no | — |
| 309 | C2×#67 | — | 14 | 3 | no | — |
| 310 | C2×#67 | — | 14 | 3 | no | — |
| 311 | C2×#67 | — | 14 | 3 | no | — |
| 312 | #239 | — | 14 | 3 | no | — |
| 313 | D3×Q8 | — | 14 | 1 | no | — |
| 314 | #237 | — | 14 | 6 | no | — |
| 315 | #237 | — | 14 | 3 | no | — |
| 316 | D3×D4 | — | 14 | 6 | no | — |
| 317 | D3×D4 | — | 14 | 6 | no | — |
| 318 | D3×D4 | — | 14 | 6 | no | — |
| 319 | D3×D4 | — | 14 | 3 | no | — |
| 320 | D3×D4 | — | 14 | 6 | no | — |
| 321 | D3×D4 | — | 28 | 12 | no | — |
| 322 | #235 | — | 14 | 6 | no | — |
| 323 | #235 | — | 14 | 3 | no | — |
| 324 | C2×D12 | — | 7 | 3 | no | — |
| 325 | C2×D12 | — | 14 | 3 | no | — |
| 326 | C2×D12 | — | 14 | 3 | no | — |
| 327 | C2×C4×D3 | — | 7 | 3 | no | — |
| 328 | C2×C4×D3 | — | 14 | 3 | no | — |
| 329 | C2×C4×D3 | — | 14 | 3 | no | — |
| 330 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 331 | C3×C22⋊C4 | C22×D7 | 1 | 3 | yes | complemented |
| 332 | #217 | — | 7 | 3 | no | — |
| 333 | #217 | — | 14 | 3 | no | — |
| 334 | (C2×D3)⋊C4 | — | 14 | 3 | no | — |
| 335 | (C2×D3)⋊C4 | — | 14 | 3 | no | — |
| 336 | (C2×D3)⋊C4 | — | 14 | 3 | no | — |
| 337 | C2×C3×C7 | — | 2 | 3 | no | — |
| 338 | C2×C3×C7 | — | 4 | 2 | no | — |
| 339 | C2×C3×C7 | — | 4 | 3 | no | — |
| 340 | C2×C3×C7 | C2×#120 | 1 | 1 | yes | characteristic |
| 341 | D21 | — | 2 | 3 | no | — |
| 342 | D21 | — | 4 | 2 | no | — |
| 343 | D21 | — | 4 | 3 | no | — |
| 344 | D21 | B(4,𝔽2) | 1 | 2 | yes | direct product factor |
| 345 | C25 | — | 21 | 1 | no | — |
| 346 | H(5,𝔽2) | — | 21 | 3 | no | — |
| 347 | H(5,𝔽2) | — | 42 | 3 | no | — |
| 348 | H(5,𝔽2) | — | 42 | 3 | no | — |
| 349 | H(5,𝔽2) | C2×D21 | 1 | 1 | yes | characteristic, complemented |
| 350 | C2×#41 | — | 42 | 3 | no | — |
| 351 | C22×D4 | — | 21 | 3 | no | — |
| 352 | C22×D4 | — | 42 | 3 | no | — |
| 353 | C22×D4 | — | 42 | 3 | no | — |
| 354 | #120 | — | 21 | 3 | no | — |
| 355 | #120 | — | 21 | 3 | no | — |
| 356 | #120 | — | 21 | 3 | no | — |
| 357 | #120 | — | 42 | 3 | no | — |
| 358 | #120 | — | 42 | 3 | no | — |
| 359 | #120 | C2×D21 | 1 | 3 | yes | complemented |
| 360 | C2×C22⋊C4 | — | 21 | 3 | no | — |
| 361 | C2×C22⋊C4 | — | 42 | 3 | no | — |
| 362 | #99 | — | 21 | 3 | no | — |
| 363 | #99 | — | 21 | 6 | no | — |
| 364 | #99 | C2×D21 | 1 | 3 | yes | complemented |
| 365 | C22×C7 | — | 2 | 6 | no | — |
| 366 | C22×C7 | — | 2 | 3 | no | — |
| 367 | C22×C7 | — | 4 | 1 | no | — |
| 368 | C22×C7 | — | 4 | 3 | no | — |
| 369 | C22×C7 | — | 4 | 3 | no | — |
| 370 | C22×C7 | — | 4 | 1 | no | — |
| 371 | C22×C7 | — | 8 | 1 | no | — |
| 372 | C22×C7 | C2×D3×D4 | 1 | 3 | yes | — |
| 373 | C2×D7 | — | 3 | 1 | no | — |
| 374 | C2×D7 | — | 3 | 3 | no | — |
| 375 | C2×D7 | — | 6 | 6 | no | — |
| 376 | C2×D7 | — | 6 | 6 | no | — |
| 377 | C2×D7 | — | 6 | 3 | no | — |
| 378 | C2×D7 | — | 12 | 4 | no | — |
| 379 | C2×D7 | — | 12 | 6 | no | — |
| 380 | C2×D7 | — | 12 | 3 | no | — |
| 381 | C2×D7 | — | 12 | 12 | no | — |
| 382 | C2×D7 | — | 12 | 3 | no | — |
| 383 | C2×D7 | — | 12 | 1 | no | — |
| 384 | C2×D7 | — | 12 | 3 | no | — |
| 385 | C2×D7 | — | 24 | 3 | no | — |
| 386 | C2×D7 | — | 24 | 3 | no | — |
| 387 | C4×C7 | — | 2 | 3 | no | — |
| 388 | C4×C7 | — | 4 | 3 | no | — |
| 389 | Dic7 | — | 6 | 3 | no | — |
| 390 | Dic7 | — | 12 | 3 | no | — |
| 391 | C23×C3 | — | 2 | 1 | no | — |
| 392 | C23×C3 | — | 2 | 3 | no | — |
| 393 | C23×C3 | — | 4 | 2 | no | — |
| 394 | C23×C3 | D4×D7 | 1 | 3 | yes | complemented |
| 395 | C23×C3 | C23×D7 | 1 | 1 | yes | characteristic |
| 396 | C22×D3 | — | 7 | 3 | no | — |
| 397 | C22×D3 | — | 7 | 3 | no | — |
| 398 | C22×D3 | — | 7 | 3 | no | — |
| 399 | C22×D3 | — | 14 | 3 | no | — |
| 400 | C22×D3 | — | 14 | 3 | no | — |
| 401 | C22×D3 | — | 14 | 12 | no | — |
| 402 | C22×D3 | — | 14 | 3 | no | — |
| 403 | C22×D3 | — | 14 | 3 | no | — |
| 404 | C22×D3 | — | 28 | 1 | no | — |
| 405 | C22×D3 | — | 28 | 3 | no | — |
| 406 | C22×D3 | — | 28 | 2 | no | — |
| 407 | C22×D3 | — | 28 | 2 | no | — |
| 408 | C22×D3 | — | 28 | 6 | no | — |
| 409 | C22×D3 | — | 28 | 6 | no | — |
| 410 | C22×D3 | — | 28 | 6 | no | — |
| 411 | C22×D3 | — | 28 | 6 | no | — |
| 412 | C22×D3 | — | 56 | 2 | no | — |
| 413 | C3×Q8 | — | 2 | 1 | no | — |
| 414 | C3×D4 | — | 2 | 3 | no | — |
| 415 | C3×D4 | — | 2 | 6 | no | — |
| 416 | C3×D4 | — | 4 | 6 | no | — |
| 417 | C2×C3×C4 | — | 2 | 3 | no | — |
| 418 | C2×C3×C4 | — | 2 | 3 | no | — |
| 419 | C2×C3×C4 | D4×D7 | 1 | 3 | yes | complemented |
| 420 | #67 | — | 14 | 6 | no | — |
| 421 | #67 | — | 14 | 6 | no | — |
| 422 | #67 | — | 14 | 6 | no | — |
| 423 | #67 | — | 28 | 6 | no | — |
| 424 | #67 | — | 28 | 6 | no | — |
| 425 | C2×Dic3 | — | 7 | 3 | no | — |
| 426 | C2×Dic3 | — | 14 | 3 | no | — |
| 427 | C2×Dic3 | — | 14 | 3 | no | — |
| 428 | D12 | — | 14 | 6 | no | — |
| 429 | D12 | — | 14 | 3 | no | — |
| 430 | D12 | — | 28 | 6 | no | — |
| 431 | C4×D3 | — | 14 | 3 | no | — |
| 432 | C4×D3 | — | 14 | 3 | no | — |
| 433 | C4×D3 | — | 14 | 6 | no | — |
| 434 | C4×D3 | — | 28 | 6 | no | — |
| 435 | Dic6 | — | 14 | 3 | no | — |
| 436 | C3×C7 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic, complemented, Hall |
| 437 | C24 | — | 21 | 1 | no | — |
| 438 | C24 | — | 21 | 3 | no | — |
| 439 | C24 | — | 21 | 1 | no | — |
| 440 | C24 | — | 42 | 3 | no | — |
| 441 | C24 | — | 42 | 3 | no | — |
| 442 | C24 | — | 42 | 1 | no | — |
| 443 | C24 | — | 84 | 4 | no | — |
| 444 | C24 | C22×D21 | 1 | 1 | yes | characteristic, complemented |
| 445 | #41 | — | 2 | 3 | no | — |
| 446 | #41 | — | 42 | 6 | no | — |
| 447 | #41 | — | 42 | 6 | no | — |
| 448 | #41 | — | 42 | 3 | no | — |
| 449 | #41 | — | 42 | 3 | no | — |
| 450 | #41 | — | 42 | 3 | no | — |
| 451 | C2×Q8 | — | 42 | 1 | no | — |
| 452 | C2×D4 | — | 2 | 3 | no | — |
| 453 | C2×D4 | — | 2 | 3 | no | — |
| 454 | C2×D4 | — | 21 | 3 | no | — |
| 455 | C2×D4 | — | 21 | 3 | no | — |
| 456 | C2×D4 | — | 21 | 3 | no | — |
| 457 | C2×D4 | — | 42 | 3 | no | — |
| 458 | C2×D4 | — | 42 | 3 | no | — |
| 459 | C2×D4 | — | 42 | 6 | no | — |
| 460 | C2×D4 | — | 42 | 6 | no | — |
| 461 | C2×D4 | — | 42 | 6 | no | — |
| 462 | C2×D4 | — | 42 | 3 | no | — |
| 463 | C2×D4 | — | 42 | 6 | no | — |
| 464 | C2×D4 | — | 42 | 3 | no | — |
| 465 | C2×D4 | — | 42 | 3 | no | — |
| 466 | C2×D4 | — | 42 | 3 | no | — |
| 467 | C2×D4 | — | 42 | 3 | no | — |
| 468 | C2×D4 | — | 84 | 12 | no | — |
| 469 | C2×D4 | C22×D21 | 1 | 3 | yes | — |
| 470 | C22×C4 | — | 21 | 3 | no | — |
| 471 | C22×C4 | — | 42 | 3 | no | — |
| 472 | C22×C4 | — | 42 | 3 | no | — |
| 473 | C22⋊C4 | — | 2 | 3 | no | — |
| 474 | C22⋊C4 | — | 21 | 3 | no | — |
| 475 | C22⋊C4 | — | 42 | 3 | no | — |
| 476 | C22⋊C4 | — | 42 | 3 | no | — |
| 477 | C22⋊C4 | — | 42 | 3 | no | — |
| 478 | C22⋊C4 | — | 42 | 3 | no | — |
| 479 | C22⋊C4 | C22×D21 | 1 | 3 | yes | complemented |
| 480 | C2×C7 | — | 2 | 3 | no | — |
| 481 | C2×C7 | — | 4 | 2 | no | — |
| 482 | C2×C7 | — | 4 | 3 | no | — |
| 483 | C2×C7 | D3×#120 | 1 | 1 | yes | characteristic |
| 484 | D7 | — | 3 | 2 | no | — |
| 485 | D7 | — | 6 | 3 | no | — |
| 486 | D7 | — | 12 | 2 | no | — |
| 487 | D7 | — | 12 | 3 | no | — |
| 488 | C22×C3 | — | 2 | 6 | no | — |
| 489 | C22×C3 | — | 2 | 3 | no | — |
| 490 | C22×C3 | — | 4 | 1 | no | — |
| 491 | C22×C3 | — | 4 | 3 | no | — |
| 492 | C22×C3 | — | 4 | 3 | no | — |
| 493 | C22×C3 | — | 4 | 1 | no | — |
| 494 | C22×C3 | — | 8 | 1 | no | — |
| 495 | C22×C3 | C2×D4×D7 | 1 | 3 | yes | — |
| 496 | C2×D3 | — | 7 | 1 | no | — |
| 497 | C2×D3 | — | 7 | 3 | no | — |
| 498 | C2×D3 | — | 14 | 6 | no | — |
| 499 | C2×D3 | — | 14 | 6 | no | — |
| 500 | C2×D3 | — | 14 | 3 | no | — |
| 501 | C2×D3 | — | 28 | 4 | no | — |
| 502 | C2×D3 | — | 28 | 6 | no | — |
| 503 | C2×D3 | — | 28 | 3 | no | — |
| 504 | C2×D3 | — | 28 | 12 | no | — |
| 505 | C2×D3 | — | 28 | 3 | no | — |
| 506 | C2×D3 | — | 28 | 1 | no | — |
| 507 | C2×D3 | — | 28 | 3 | no | — |
| 508 | C2×D3 | — | 56 | 3 | no | — |
| 509 | C2×D3 | — | 56 | 3 | no | — |
| 510 | C3×C4 | — | 2 | 3 | no | — |
| 511 | C3×C4 | — | 4 | 3 | no | — |
| 512 | Dic3 | — | 14 | 3 | no | — |
| 513 | Dic3 | — | 28 | 3 | no | — |
| 514 | C23 | — | 2 | 1 | no | — |
| 515 | C23 | — | 2 | 3 | no | — |
| 516 | C23 | — | 4 | 2 | no | — |
| 517 | C23 | — | 21 | 3 | no | — |
| 518 | C23 | — | 21 | 3 | no | — |
| 519 | C23 | — | 21 | 3 | no | — |
| 520 | C23 | — | 42 | 3 | no | — |
| 521 | C23 | — | 42 | 3 | no | — |
| 522 | C23 | — | 42 | 12 | no | — |
| 523 | C23 | — | 42 | 3 | no | — |
| 524 | C23 | — | 42 | 3 | no | — |
| 525 | C23 | — | 84 | 6 | no | — |
| 526 | C23 | — | 84 | 1 | no | — |
| 527 | C23 | — | 84 | 3 | no | — |
| 528 | C23 | — | 84 | 2 | no | — |
| 529 | C23 | — | 84 | 2 | no | — |
| 530 | C23 | — | 84 | 6 | no | — |
| 531 | C23 | — | 84 | 6 | no | — |
| 532 | C23 | — | 84 | 6 | no | — |
| 533 | C23 | — | 168 | 2 | no | — |
| 534 | C23 | D4×D21 | 1 | 3 | yes | complemented |
| 535 | C23 | C23×D21 | 1 | 1 | yes | characteristic |
| 536 | Q8 | — | 2 | 1 | no | — |
| 537 | Q8 | — | 42 | 3 | no | — |
| 538 | D4 | — | 2 | 3 | no | — |
| 539 | D4 | — | 2 | 6 | no | — |
| 540 | D4 | — | 4 | 6 | no | — |
| 541 | D4 | — | 42 | 6 | no | — |
| 542 | D4 | — | 42 | 3 | no | — |
| 543 | D4 | — | 42 | 6 | no | — |
| 544 | D4 | — | 42 | 6 | no | — |
| 545 | D4 | — | 42 | 6 | no | — |
| 546 | D4 | — | 84 | 6 | no | — |
| 547 | D4 | — | 84 | 6 | no | — |
| 548 | D4 | — | 84 | 6 | no | — |
| 549 | C2×C4 | — | 2 | 3 | no | — |
| 550 | C2×C4 | — | 2 | 3 | no | — |
| 551 | C2×C4 | — | 21 | 3 | no | — |
| 552 | C2×C4 | — | 42 | 3 | no | — |
| 553 | C2×C4 | — | 42 | 3 | no | — |
| 554 | C2×C4 | — | 42 | 6 | no | — |
| 555 | C2×C4 | — | 42 | 3 | no | — |
| 556 | C2×C4 | — | 42 | 3 | no | — |
| 557 | C2×C4 | — | 84 | 6 | no | — |
| 558 | C2×C4 | D4×D21 | 1 | 3 | yes | complemented |
| 559 | C7 | D3×B(4,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 560 | C2×C3 | — | 2 | 3 | no | — |
| 561 | C2×C3 | — | 4 | 2 | no | — |
| 562 | C2×C3 | — | 4 | 3 | no | — |
| 563 | C2×C3 | D7×#120 | 1 | 1 | yes | characteristic |
| 564 | D3 | — | 7 | 2 | no | — |
| 565 | D3 | — | 14 | 3 | no | — |
| 566 | D3 | — | 28 | 2 | no | — |
| 567 | D3 | — | 28 | 3 | no | — |
| 568 | C22 | — | 2 | 6 | no | — |
| 569 | C22 | — | 2 | 3 | no | — |
| 570 | C22 | — | 4 | 1 | no | — |
| 571 | C22 | — | 4 | 3 | no | — |
| 572 | C22 | — | 4 | 3 | no | — |
| 573 | C22 | — | 4 | 1 | no | — |
| 574 | C22 | — | 8 | 1 | no | — |
| 575 | C22 | — | 21 | 1 | no | — |
| 576 | C22 | — | 21 | 3 | no | — |
| 577 | C22 | — | 42 | 6 | no | — |
| 578 | C22 | — | 42 | 6 | no | — |
| 579 | C22 | — | 42 | 3 | no | — |
| 580 | C22 | — | 84 | 3 | no | — |
| 581 | C22 | — | 84 | 3 | no | — |
| 582 | C22 | — | 84 | 3 | no | — |
| 583 | C22 | — | 84 | 4 | no | — |
| 584 | C22 | — | 84 | 6 | no | — |
| 585 | C22 | — | 84 | 12 | no | — |
| 586 | C22 | — | 84 | 1 | no | — |
| 587 | C22 | — | 168 | 3 | no | — |
| 588 | C22 | — | 168 | 3 | no | — |
| 589 | C22 | C2×D4×D21 | 1 | 3 | yes | — |
| 590 | C4 | — | 2 | 3 | no | — |
| 591 | C4 | — | 4 | 3 | no | — |
| 592 | C4 | — | 42 | 3 | no | — |
| 593 | C4 | — | 84 | 3 | no | — |
| 594 | C3 | D7×B(4,𝔽2) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 595 | C2 | — | 2 | 3 | no | — |
| 596 | C2 | — | 4 | 2 | no | — |
| 597 | C2 | — | 4 | 3 | no | — |
| 598 | C2 | — | 21 | 2 | no | — |
| 599 | C2 | — | 42 | 3 | no | — |
| 600 | C2 | — | 84 | 2 | no | — |
| 601 | C2 | — | 84 | 3 | no | — |
| 602 | C2 | #120×D21 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. H(5,𝔽2)×D21 | C2 | semidirect |
| 2. #120×D21 | C2 | semidirect |
| 3. C3×C7×B(4,𝔽2) | C2 | semidirect |
| 4. #13056881 | C2 | semidirect |
| 5. #13056669 | C2 | semidirect |
| 6. #99×D21 | C2 | semidirect |
| 7. #13056378 | C2 | semidirect |
| 9. C24×D21 | C22 | semidirect |
| 10. C3×C7×H(5,𝔽2) | C22 | semidirect |
| 14. #10621657 | C22 | semidirect |
| 18. C3×C7×#120 | C22 | semidirect |
| 19. #10621436 | C22 | semidirect |
| 21. #10621420 | C22 | semidirect |
| 23. #10621365 | C22 | semidirect |
| 25. C22⋊C4×D21 | C22 | semidirect |
| 26. C3×C7×#99 | C22 | semidirect |
| 27. #10620673 | C22 | semidirect |
| 28. #10620645 | C22 | semidirect |
| 31. C7×B(4,𝔽2) | D3 | semidirect |
| 37. C24×C3×C7 | C23 | semidirect |
| 42. C23×D21 | D4 | semidirect |
| 44. C23×D21 | C23 | semidirect |
| 53. C2×#4268 | D4 | semidirect |
| 69. C2×D84 | D4 | semidirect |
| 72. C2×C4×D21 | D4 | semidirect |
| 74. C3×C7×C22⋊C4 | C23 | semidirect |
| 76. #66636 | C23 | semidirect |
| 81. C7×H(5,𝔽2) | C2×D3 | semidirect |
| 89. C7×#120 | C2×D3 | semidirect |
| 97. C7×#99 | C2×D3 | semidirect |
| 102. C3×B(4,𝔽2) | D7 | semidirect |
| 110. C23×C3×C7 | C2×D4 | semidirect |
| 128. C22×D21 | C2×D4 | semidirect |
| 135. C2×C3×C4×C7 | C2×D4 | semidirect |
| 143. C2×Dic21 | C2×D4 | semidirect |
| 153. C24×C7 | C22×D3 | semidirect |
| 190. C7×C22⋊C4 | C22×D3 | semidirect |
| 197. C3×H(5,𝔽2) | C2×D7 | semidirect |
| 205. C3×#120 | C2×D7 | semidirect |
| 213. C3×#99 | C2×D7 | semidirect |
| 247. B(4,𝔽2) | D21 | direct (N × H) |
| 252. C23×C7 | D3×D4 | semidirect |
| 277. C2×C4×C7 | D3×D4 | semidirect |
| 294. C24×C3 | C22×D7 | semidirect |
| 331. C3×C22⋊C4 | C22×D7 | semidirect |
| 344. D21 | B(4,𝔽2) | direct (N × H) |
| 349. H(5,𝔽2) | C2×D21 | semidirect |
| 359. #120 | C2×D21 | semidirect |
| 364. #99 | C2×D21 | semidirect |
| 394. C23×C3 | D4×D7 | semidirect |
| 419. C2×C3×C4 | D4×D7 | semidirect |
| 436. C3×C7 | C2×B(4,𝔽2) | semidirect |
| 444. C24 | C22×D21 | semidirect |
| 479. C22⋊C4 | C22×D21 | semidirect |
| 534. C23 | D4×D21 | semidirect |
| 558. C2×C4 | D4×D21 | semidirect |
| 559. C7 | D3×B(4,𝔽2) | semidirect |
| 594. C3 | D7×B(4,𝔽2) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×D21 | 2 |
| #120×D21 | 2 |
| C3×C7×B(4,𝔽2) | 2 |
| #13056881 | 2 |
| #13056669 | 2 |
| #99×D21 | 2 |
| #13056378 | 2 |
| D7×B(4,𝔽2) | 3 |
| D3×B(4,𝔽2) | 7 |