Finite Group DatabasebetaFinite Group DatabasebetaOrder 4032.
876 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 876 conjugacy classes of subgroups — too many to draw. Only its 58 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 | C3×C7⋊#997 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×D7×H(5,𝔽2) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D7⋊#997 | C3 | 1 | 3 | yes | maximal, direct product factor |
| 4 | C2×C3×D7⋊A4 | — | 4 | 1 | no | maximal |
| 5 | C2×C3×D7⋊A4 | — | 4 | 1 | no | maximal |
| 6 | C2×C3×D7⋊A4 | — | 4 | 1 | no | maximal |
| 7 | C3×D7⋊SL(2,𝔽3) | — | 4 | 1 | no | maximal |
| 8 | C3×D7⋊SL(2,𝔽3) | — | 4 | 1 | no | maximal |
| 9 | C3×C7×H(5,𝔽2) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×#6553 | — | 3 | 1 | no | — |
| 11 | C3×#6553 | — | 3 | 1 | no | — |
| 12 | C3×D7×#41 | — | 3 | 1 | no | — |
| 13 | C3×D7×#41 | — | 3 | 1 | no | — |
| 14 | C3×#6548 | — | 3 | 1 | no | — |
| 15 | C3×#6548 | — | 3 | 1 | no | — |
| 16 | C3×#6548 | — | 3 | 1 | no | — |
| 17 | C2×C3×D4×D7 | — | 3 | 1 | no | — |
| 18 | C2×C3×D4×D7 | — | 3 | 1 | no | — |
| 19 | C2×C3×D4×D7 | — | 3 | 1 | no | — |
| 20 | C7⋊#997 | C2×C3 | 1 | 3 | yes | complemented |
| 21 | C2×C3×#997 | — | 7 | 1 | no | maximal, Hall |
| 22 | C2×C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 23 | C2×C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 24 | C2×C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 25 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 26 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 27 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 28 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 29 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 30 | C3×D7⋊A4 | — | 4 | 1 | no | — |
| 31 | C3×C7⋊SL(2,𝔽3) | — | 4 | 1 | no | — |
| 32 | C3×C7⋊SL(2,𝔽3) | — | 4 | 1 | no | — |
| 33 | D7×H(5,𝔽2) | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 34 | C23×C3×D7 | — | 3 | 1 | no | — |
| 35 | C23×C3×D7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C23×C3×D7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 37 | C23×C3×D7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×D7⋊A4 | — | 4 | 3 | no | — |
| 39 | C2×D7⋊A4 | — | 4 | 3 | no | — |
| 40 | C2×D7⋊A4 | — | 4 | 3 | no | — |
| 41 | C3×C7×#41 | — | 3 | 1 | no | — |
| 42 | C3×C7×#41 | — | 3 | 1 | no | — |
| 43 | C2×C3×C7×D4 | — | 3 | 1 | no | — |
| 44 | C2×C3×C7×D4 | — | 3 | 1 | no | — |
| 45 | C2×C3×C7×D4 | — | 3 | 1 | no | — |
| 46 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 47 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 48 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 49 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 50 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 51 | C2×C3×C22⋊D7 | — | 3 | 1 | no | — |
| 52 | C3×#1161 | — | 3 | 1 | no | — |
| 53 | C3×#1161 | — | 3 | 1 | no | — |
| 54 | C3×Q8×D7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 55 | C3×Q8×D7 | A4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C3×#1159 | — | 3 | 1 | no | — |
| 57 | C3×#1159 | — | 3 | 1 | no | — |
| 58 | C3×#1159 | — | 3 | 1 | no | — |
| 59 | C3×#1159 | — | 3 | 1 | no | — |
| 60 | C3×#1159 | — | 3 | 1 | no | — |
| 61 | C3×#1159 | — | 3 | 1 | no | — |
| 62 | C3×D4×D7 | — | 3 | 1 | no | — |
| 63 | C3×D4×D7 | — | 3 | 1 | no | — |
| 64 | C3×D4×D7 | — | 3 | 1 | no | — |
| 65 | C3×D4×D7 | — | 3 | 1 | no | — |
| 66 | C3×D4×D7 | — | 3 | 1 | no | — |
| 67 | C3×D4×D7 | — | 3 | 1 | no | — |
| 68 | C3×D4×D7 | — | 3 | 1 | no | — |
| 69 | C3×D4×D7 | — | 3 | 1 | no | — |
| 70 | C3×D4×D7 | — | 3 | 1 | no | — |
| 71 | C3×D4×D7 | — | 3 | 1 | no | — |
| 72 | C3×D4×D7 | — | 3 | 1 | no | — |
| 73 | C3×D4×D7 | — | 3 | 1 | no | — |
| 74 | C3×D4×D7 | — | 3 | 1 | no | — |
| 75 | C3×D4×D7 | — | 3 | 1 | no | — |
| 76 | C3×D4×D7 | — | 3 | 1 | no | — |
| 77 | C3×D4×D7 | — | 3 | 1 | no | — |
| 78 | C3×D4×D7 | — | 3 | 1 | no | — |
| 79 | C3×D4×D7 | — | 3 | 1 | no | — |
| 80 | C3×#1157 | — | 3 | 1 | no | — |
| 81 | C3×#1157 | — | 3 | 1 | no | — |
| 82 | C3×#1157 | — | 3 | 1 | no | — |
| 83 | C3×#1157 | — | 3 | 1 | no | — |
| 84 | C3×#1157 | — | 3 | 1 | no | — |
| 85 | C3×#1157 | — | 3 | 1 | no | — |
| 86 | C2×C3×D28 | — | 3 | 1 | no | — |
| 87 | C2×C3×D28 | — | 3 | 1 | no | — |
| 88 | C2×C3×D28 | — | 3 | 1 | no | — |
| 89 | C2×C3×C4×D7 | — | 3 | 1 | no | — |
| 90 | C2×C3×C4×D7 | — | 3 | 1 | no | — |
| 91 | C2×C3×C4×D7 | — | 3 | 1 | no | — |
| 92 | D7⋊SL(2,𝔽3) | — | 4 | 3 | no | — |
| 93 | D7⋊SL(2,𝔽3) | — | 4 | 3 | no | — |
| 94 | C3×#997 | — | 7 | 1 | no | — |
| 95 | C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 96 | C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 97 | C3×C22⋊ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 98 | C2×C3×AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 99 | C7×H(5,𝔽2) | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 100 | #6553 | — | 3 | 1 | no | — |
| 101 | #6553 | — | 3 | 1 | no | — |
| 102 | D7×#41 | — | 3 | 1 | no | — |
| 103 | D7×#41 | — | 3 | 1 | no | — |
| 104 | #6548 | — | 3 | 1 | no | — |
| 105 | #6548 | — | 3 | 1 | no | — |
| 106 | #6548 | — | 3 | 1 | no | — |
| 107 | C2×D4×D7 | — | 3 | 1 | no | — |
| 108 | C2×D4×D7 | — | 3 | 1 | no | — |
| 109 | C2×D4×D7 | — | 3 | 1 | no | — |
| 110 | C2×C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 111 | C2×#997 | — | 7 | 3 | no | — |
| 112 | C23×C3×C7 | — | 3 | 1 | no | — |
| 113 | C23×C3×C7 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 114 | C23×C3×C7 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 115 | C23×C3×C7 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 116 | C22×C3×D7 | — | 3 | 1 | no | — |
| 117 | C22×C3×D7 | — | 3 | 1 | no | — |
| 118 | C22×C3×D7 | — | 3 | 1 | no | — |
| 119 | C22×C3×D7 | — | 3 | 1 | no | — |
| 120 | C22×C3×D7 | — | 3 | 1 | no | — |
| 121 | C22×C3×D7 | — | 3 | 1 | no | — |
| 122 | C22×C3×D7 | — | 3 | 1 | no | — |
| 123 | C22×C3×D7 | — | 3 | 1 | no | — |
| 124 | C22×C3×D7 | — | 3 | 1 | no | — |
| 125 | C22×C3×D7 | — | 4 | 1 | no | — |
| 126 | C22×C3×D7 | — | 12 | 1 | no | — |
| 127 | C22×C3×D7 | — | 12 | 1 | no | — |
| 128 | C22×C3×D7 | — | 12 | 1 | no | — |
| 129 | C22×C3×D7 | — | 12 | 1 | no | — |
| 130 | C22×C3×D7 | — | 12 | 1 | no | — |
| 131 | C22×C3×D7 | — | 12 | 1 | no | — |
| 132 | C22×C3×D7 | — | 12 | 1 | no | — |
| 133 | C2×C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 134 | C2×C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 135 | C2×C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 136 | D7⋊A4 | — | 4 | 3 | no | — |
| 137 | D7⋊A4 | — | 4 | 3 | no | — |
| 138 | D7⋊A4 | — | 4 | 3 | no | — |
| 139 | D7⋊A4 | — | 4 | 3 | no | — |
| 140 | D7⋊A4 | — | 4 | 3 | no | — |
| 141 | D7⋊A4 | — | 4 | 3 | no | — |
| 142 | C3×C7×Q8 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 143 | C3×C7×Q8 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 144 | C3×C7×D4 | — | 3 | 1 | no | — |
| 145 | C3×C7×D4 | — | 3 | 1 | no | — |
| 146 | C3×C7×D4 | — | 3 | 1 | no | — |
| 147 | C3×C7×D4 | — | 3 | 1 | no | — |
| 148 | C3×C7×D4 | — | 3 | 1 | no | — |
| 149 | C3×C7×D4 | — | 3 | 1 | no | — |
| 150 | C2×C3×C4×C7 | — | 3 | 1 | no | — |
| 151 | C2×C3×C4×C7 | — | 3 | 1 | no | — |
| 152 | C2×C3×C4×C7 | — | 3 | 1 | no | — |
| 153 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 154 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 155 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 156 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 157 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 158 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 159 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 160 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 161 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 162 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 163 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 164 | C3×C22⋊D7 | — | 3 | 1 | no | — |
| 165 | C2×C3×Dic7 | — | 3 | 1 | no | — |
| 166 | C2×C3×Dic7 | — | 3 | 1 | no | — |
| 167 | C2×C3×Dic7 | — | 3 | 1 | no | — |
| 168 | C3×D28 | — | 3 | 1 | no | — |
| 169 | C3×D28 | — | 3 | 1 | no | — |
| 170 | C3×D28 | — | 3 | 1 | no | — |
| 171 | C3×D28 | — | 3 | 1 | no | — |
| 172 | C3×D28 | — | 3 | 1 | no | — |
| 173 | C3×D28 | — | 3 | 1 | no | — |
| 174 | C3×C4×D7 | — | 3 | 1 | no | — |
| 175 | C3×C4×D7 | — | 3 | 1 | no | — |
| 176 | C3×C4×D7 | — | 3 | 1 | no | — |
| 177 | C3×C4×D7 | — | 3 | 1 | no | — |
| 178 | C3×C4×D7 | — | 3 | 1 | no | — |
| 179 | C3×C4×D7 | — | 3 | 1 | no | — |
| 180 | C3×C4×D7 | — | 3 | 1 | no | — |
| 181 | C3×C4×D7 | — | 3 | 1 | no | — |
| 182 | C3×Dic14 | — | 3 | 1 | no | — |
| 183 | C3×Dic14 | — | 3 | 1 | no | — |
| 184 | C7⋊SL(2,𝔽3) | — | 4 | 3 | no | — |
| 185 | C7⋊SL(2,𝔽3) | — | 4 | 3 | no | — |
| 186 | C22×C3×A4 | — | 28 | 1 | no | — |
| 187 | C22×C3×A4 | — | 28 | 1 | no | — |
| 188 | C22×C3×A4 | — | 28 | 1 | no | — |
| 189 | C2×C3×SL(2,𝔽3) | — | 28 | 1 | no | — |
| 190 | C2×C3×SL(2,𝔽3) | — | 28 | 1 | no | — |
| 191 | C2×C3×ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 192 | C3×AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 193 | C3×AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 194 | C23×D7 | — | 3 | 1 | no | — |
| 195 | C23×D7 | C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 196 | C23×D7 | C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 197 | C23×D7 | C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 198 | C7×#41 | — | 3 | 1 | no | — |
| 199 | C7×#41 | — | 3 | 1 | no | — |
| 200 | C2×C7×D4 | — | 3 | 1 | no | — |
| 201 | C2×C7×D4 | — | 3 | 1 | no | — |
| 202 | C2×C7×D4 | — | 3 | 1 | no | — |
| 203 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 204 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 205 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 206 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 207 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 208 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 209 | #1161 | — | 3 | 1 | no | — |
| 210 | #1161 | — | 3 | 1 | no | — |
| 211 | Q8×D7 | C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 212 | Q8×D7 | C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 213 | #1159 | — | 3 | 1 | no | — |
| 214 | #1159 | — | 3 | 1 | no | — |
| 215 | #1159 | — | 3 | 1 | no | — |
| 216 | #1159 | — | 3 | 1 | no | — |
| 217 | #1159 | — | 3 | 1 | no | — |
| 218 | #1159 | — | 3 | 1 | no | — |
| 219 | D4×D7 | — | 3 | 1 | no | — |
| 220 | D4×D7 | — | 3 | 1 | no | — |
| 221 | D4×D7 | — | 3 | 1 | no | — |
| 222 | D4×D7 | — | 3 | 1 | no | — |
| 223 | D4×D7 | — | 3 | 1 | no | — |
| 224 | D4×D7 | — | 3 | 1 | no | — |
| 225 | D4×D7 | — | 3 | 1 | no | — |
| 226 | D4×D7 | — | 3 | 1 | no | — |
| 227 | D4×D7 | — | 3 | 1 | no | — |
| 228 | D4×D7 | — | 3 | 1 | no | — |
| 229 | D4×D7 | — | 3 | 1 | no | — |
| 230 | D4×D7 | — | 3 | 1 | no | — |
| 231 | D4×D7 | — | 3 | 1 | no | — |
| 232 | D4×D7 | — | 3 | 1 | no | — |
| 233 | D4×D7 | — | 3 | 1 | no | — |
| 234 | D4×D7 | — | 3 | 1 | no | — |
| 235 | D4×D7 | — | 3 | 1 | no | — |
| 236 | D4×D7 | — | 3 | 1 | no | — |
| 237 | #1157 | — | 3 | 1 | no | — |
| 238 | #1157 | — | 3 | 1 | no | — |
| 239 | #1157 | — | 3 | 1 | no | — |
| 240 | #1157 | — | 3 | 1 | no | — |
| 241 | #1157 | — | 3 | 1 | no | — |
| 242 | #1157 | — | 3 | 1 | no | — |
| 243 | C2×D28 | — | 3 | 1 | no | — |
| 244 | C2×D28 | — | 3 | 1 | no | — |
| 245 | C2×D28 | — | 3 | 1 | no | — |
| 246 | C2×C4×D7 | — | 3 | 1 | no | — |
| 247 | C2×C4×D7 | — | 3 | 1 | no | — |
| 248 | C2×C4×D7 | — | 3 | 1 | no | — |
| 249 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 250 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 251 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 252 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 253 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 254 | C3×H(5,𝔽2) | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 255 | C2×C3×#41 | — | 21 | 1 | no | — |
| 256 | C2×C3×#41 | — | 21 | 1 | no | — |
| 257 | C22×C3×D4 | — | 21 | 1 | no | — |
| 258 | C22×C3×D4 | — | 21 | 1 | no | — |
| 259 | C22×C3×D4 | — | 21 | 1 | no | — |
| 260 | #997 | — | 7 | 3 | no | — |
| 261 | C22×C3×C7 | — | 3 | 1 | no | — |
| 262 | C22×C3×C7 | — | 3 | 1 | no | — |
| 263 | C22×C3×C7 | — | 3 | 1 | no | — |
| 264 | C22×C3×C7 | — | 4 | 1 | no | — |
| 265 | C22×C3×C7 | — | 12 | 1 | no | — |
| 266 | C22×C3×C7 | — | 12 | 1 | no | — |
| 267 | C22×C3×C7 | — | 12 | 1 | no | — |
| 268 | C2×C3×D7 | — | 3 | 1 | no | — |
| 269 | C2×C3×D7 | — | 3 | 1 | no | — |
| 270 | C2×C3×D7 | — | 3 | 1 | no | — |
| 271 | C2×C3×D7 | — | 6 | 1 | no | — |
| 272 | C2×C3×D7 | — | 6 | 1 | no | — |
| 273 | C2×C3×D7 | — | 6 | 1 | no | — |
| 274 | C2×C3×D7 | — | 6 | 1 | no | — |
| 275 | C2×C3×D7 | — | 6 | 1 | no | — |
| 276 | C2×C3×D7 | — | 6 | 1 | no | — |
| 277 | C2×C3×D7 | — | 12 | 1 | no | — |
| 278 | C2×C3×D7 | — | 12 | 1 | no | — |
| 279 | C2×C3×D7 | — | 12 | 1 | no | — |
| 280 | C2×C3×D7 | — | 12 | 1 | no | — |
| 281 | C2×C3×D7 | — | 12 | 1 | no | — |
| 282 | C2×C3×D7 | — | 12 | 1 | no | — |
| 283 | C2×C3×D7 | C22⋊A4 | 1 | 1 | yes | characteristic |
| 284 | C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 285 | C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 286 | C22⋊ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 287 | C2×AGL(1,𝔽7) | — | 16 | 3 | no | — |
| 288 | C3×C4×C7 | — | 3 | 1 | no | — |
| 289 | C3×C4×C7 | — | 3 | 1 | no | — |
| 290 | C3×Dic7 | — | 3 | 1 | no | — |
| 291 | C3×Dic7 | — | 3 | 1 | no | — |
| 292 | C2×C3×A4 | — | 28 | 1 | no | — |
| 293 | C2×C3×A4 | — | 28 | 1 | no | — |
| 294 | C2×C3×A4 | — | 28 | 1 | no | — |
| 295 | C2×C3×A4 | — | 28 | 1 | no | — |
| 296 | C2×C3×A4 | — | 28 | 1 | no | — |
| 297 | C2×C3×A4 | — | 28 | 1 | no | — |
| 298 | C2×C3×A4 | — | 28 | 1 | no | — |
| 299 | C2×C3×A4 | — | 28 | 1 | no | — |
| 300 | C2×C3×A4 | — | 28 | 1 | no | — |
| 301 | C3×SL(2,𝔽3) | — | 28 | 1 | no | — |
| 302 | C3×SL(2,𝔽3) | — | 28 | 1 | no | — |
| 303 | C2×H(5,𝔽2) | — | 21 | 1 | no | Sylow |
| 304 | C3×ΓL(1,𝔽8) | — | 16 | 1 | no | Hall |
| 305 | C23×C7 | — | 3 | 1 | no | — |
| 306 | C23×C7 | C2×C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 307 | C23×C7 | C2×C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 308 | C23×C7 | C2×C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 309 | C22×D7 | — | 3 | 1 | no | — |
| 310 | C22×D7 | — | 3 | 1 | no | — |
| 311 | C22×D7 | — | 3 | 1 | no | — |
| 312 | C22×D7 | — | 3 | 1 | no | — |
| 313 | C22×D7 | — | 3 | 1 | no | — |
| 314 | C22×D7 | — | 3 | 1 | no | — |
| 315 | C22×D7 | — | 3 | 1 | no | — |
| 316 | C22×D7 | — | 3 | 1 | no | — |
| 317 | C22×D7 | — | 3 | 1 | no | — |
| 318 | C22×D7 | — | 4 | 1 | no | — |
| 319 | C22×D7 | — | 12 | 1 | no | — |
| 320 | C22×D7 | — | 12 | 1 | no | — |
| 321 | C22×D7 | — | 12 | 1 | no | — |
| 322 | C22×D7 | — | 12 | 1 | no | — |
| 323 | C22×D7 | — | 12 | 1 | no | — |
| 324 | C22×D7 | — | 12 | 1 | no | — |
| 325 | C22×D7 | — | 12 | 1 | no | — |
| 326 | C7×Q8 | C2×C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 327 | C7×Q8 | C2×C3×A4 | 1 | 1 | yes | characteristic, complemented |
| 328 | C7×D4 | — | 3 | 1 | no | — |
| 329 | C7×D4 | — | 3 | 1 | no | — |
| 330 | C7×D4 | — | 3 | 1 | no | — |
| 331 | C7×D4 | — | 3 | 1 | no | — |
| 332 | C7×D4 | — | 3 | 1 | no | — |
| 333 | C7×D4 | — | 3 | 1 | no | — |
| 334 | C2×C4×C7 | — | 3 | 1 | no | — |
| 335 | C2×C4×C7 | — | 3 | 1 | no | — |
| 336 | C2×C4×C7 | — | 3 | 1 | no | — |
| 337 | C22⋊D7 | — | 3 | 1 | no | — |
| 338 | C22⋊D7 | — | 3 | 1 | no | — |
| 339 | C22⋊D7 | — | 3 | 1 | no | — |
| 340 | C22⋊D7 | — | 3 | 1 | no | — |
| 341 | C22⋊D7 | — | 3 | 1 | no | — |
| 342 | C22⋊D7 | — | 3 | 1 | no | — |
| 343 | C22⋊D7 | — | 3 | 1 | no | — |
| 344 | C22⋊D7 | — | 3 | 1 | no | — |
| 345 | C22⋊D7 | — | 3 | 1 | no | — |
| 346 | C22⋊D7 | — | 3 | 1 | no | — |
| 347 | C22⋊D7 | — | 3 | 1 | no | — |
| 348 | C22⋊D7 | — | 3 | 1 | no | — |
| 349 | C2×Dic7 | — | 3 | 1 | no | — |
| 350 | C2×Dic7 | — | 3 | 1 | no | — |
| 351 | C2×Dic7 | — | 3 | 1 | no | — |
| 352 | D28 | — | 3 | 1 | no | — |
| 353 | D28 | — | 3 | 1 | no | — |
| 354 | D28 | — | 3 | 1 | no | — |
| 355 | D28 | — | 3 | 1 | no | — |
| 356 | D28 | — | 3 | 1 | no | — |
| 357 | D28 | — | 3 | 1 | no | — |
| 358 | C4×D7 | — | 3 | 1 | no | — |
| 359 | C4×D7 | — | 3 | 1 | no | — |
| 360 | C4×D7 | — | 3 | 1 | no | — |
| 361 | C4×D7 | — | 3 | 1 | no | — |
| 362 | C4×D7 | — | 3 | 1 | no | — |
| 363 | C4×D7 | — | 3 | 1 | no | — |
| 364 | C4×D7 | — | 3 | 1 | no | — |
| 365 | C4×D7 | — | 3 | 1 | no | — |
| 366 | Dic14 | — | 3 | 1 | no | — |
| 367 | Dic14 | — | 3 | 1 | no | — |
| 368 | C24×C3 | — | 21 | 1 | no | — |
| 369 | C24×C3 | — | 21 | 1 | no | — |
| 370 | C24×C3 | — | 21 | 1 | no | — |
| 371 | C24×C3 | — | 21 | 1 | no | — |
| 372 | C22×A4 | — | 28 | 3 | no | — |
| 373 | C22×A4 | — | 28 | 3 | no | — |
| 374 | C22×A4 | — | 28 | 3 | no | — |
| 375 | C3×#41 | — | 3 | 1 | no | — |
| 376 | C3×#41 | — | 3 | 1 | no | — |
| 377 | C3×#41 | — | 21 | 1 | no | — |
| 378 | C3×#41 | — | 21 | 1 | no | — |
| 379 | C3×#41 | — | 21 | 1 | no | — |
| 380 | C3×#41 | — | 21 | 1 | no | — |
| 381 | C3×#41 | — | 21 | 1 | no | — |
| 382 | C3×#41 | — | 21 | 1 | no | — |
| 383 | C3×#41 | — | 21 | 1 | no | — |
| 384 | C3×#41 | — | 21 | 1 | no | — |
| 385 | C3×#41 | — | 21 | 1 | no | — |
| 386 | C3×#41 | — | 21 | 1 | no | — |
| 387 | C3×#41 | — | 21 | 1 | no | — |
| 388 | C3×#41 | — | 21 | 1 | no | — |
| 389 | C3×#41 | — | 21 | 1 | no | — |
| 390 | C3×#41 | — | 21 | 1 | no | — |
| 391 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 392 | C2×C3×Q8 | — | 21 | 1 | no | — |
| 393 | C2×C3×D4 | — | 3 | 1 | no | — |
| 394 | C2×C3×D4 | — | 3 | 1 | no | — |
| 395 | C2×C3×D4 | — | 3 | 1 | no | — |
| 396 | C2×C3×D4 | — | 21 | 1 | no | — |
| 397 | C2×C3×D4 | — | 21 | 1 | no | — |
| 398 | C2×C3×D4 | — | 21 | 1 | no | — |
| 399 | C2×C3×D4 | — | 21 | 1 | no | — |
| 400 | C2×C3×D4 | — | 21 | 1 | no | — |
| 401 | C2×C3×D4 | — | 21 | 1 | no | — |
| 402 | C2×C3×D4 | — | 21 | 1 | no | — |
| 403 | C2×C3×D4 | — | 21 | 1 | no | — |
| 404 | C2×C3×D4 | — | 21 | 1 | no | — |
| 405 | C2×C3×D4 | — | 21 | 1 | no | — |
| 406 | C2×C3×D4 | — | 21 | 1 | no | — |
| 407 | C2×C3×D4 | — | 21 | 1 | no | — |
| 408 | C2×C3×D4 | — | 21 | 1 | no | — |
| 409 | C2×C3×D4 | — | 21 | 1 | no | — |
| 410 | C2×C3×D4 | — | 21 | 1 | no | — |
| 411 | C2×C3×D4 | — | 21 | 1 | no | — |
| 412 | C2×C3×D4 | — | 21 | 1 | no | — |
| 413 | C2×C3×D4 | — | 21 | 1 | no | — |
| 414 | C2×C3×D4 | — | 21 | 1 | no | — |
| 415 | C2×C3×D4 | — | 21 | 1 | no | — |
| 416 | C2×C3×D4 | — | 21 | 1 | no | — |
| 417 | C2×C3×D4 | — | 21 | 1 | no | — |
| 418 | C2×C3×D4 | — | 21 | 1 | no | — |
| 419 | C2×C3×D4 | — | 21 | 1 | no | — |
| 420 | C2×C3×D4 | — | 21 | 1 | no | — |
| 421 | C2×C3×D4 | — | 21 | 1 | no | — |
| 422 | C2×C3×D4 | — | 21 | 1 | no | — |
| 423 | C22×C3×C4 | — | 21 | 1 | no | — |
| 424 | C22×C3×C4 | — | 21 | 1 | no | — |
| 425 | C22×C3×C4 | — | 21 | 1 | no | — |
| 426 | C2×SL(2,𝔽3) | — | 28 | 3 | no | — |
| 427 | C2×SL(2,𝔽3) | — | 28 | 3 | no | — |
| 428 | C2×C3×C7 | — | 6 | 1 | no | — |
| 429 | C2×C3×C7 | — | 6 | 1 | no | — |
| 430 | C2×C3×C7 | — | 6 | 1 | no | — |
| 431 | C2×C3×C7 | C2×C22⋊A4 | 1 | 1 | yes | characteristic |
| 432 | C3×D7 | — | 6 | 1 | no | — |
| 433 | C3×D7 | — | 6 | 1 | no | — |
| 434 | C3×D7 | — | 6 | 1 | no | — |
| 435 | C3×D7 | #997 | 1 | 1 | yes | characteristic, complemented |
| 436 | C3×D7 | #997 | 1 | 1 | yes | characteristic, complemented |
| 437 | C2×ΓL(1,𝔽8) | — | 16 | 3 | no | — |
| 438 | AGL(1,𝔽7) | — | 16 | 3 | no | — |
| 439 | AGL(1,𝔽7) | — | 16 | 3 | no | — |
| 440 | C22×C32 | — | 112 | 1 | no | — |
| 441 | C3×A4 | — | 28 | 1 | no | — |
| 442 | C3×A4 | — | 28 | 1 | no | — |
| 443 | C3×A4 | — | 28 | 1 | no | — |
| 444 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 445 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 446 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 447 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 448 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 449 | H(5,𝔽2) | C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 450 | C2×#41 | — | 21 | 1 | no | — |
| 451 | C2×#41 | — | 21 | 1 | no | — |
| 452 | C22×D4 | — | 21 | 1 | no | — |
| 453 | C22×D4 | — | 21 | 1 | no | — |
| 454 | C22×D4 | — | 21 | 1 | no | — |
| 455 | C22×C7 | — | 3 | 1 | no | — |
| 456 | C22×C7 | — | 3 | 1 | no | — |
| 457 | C22×C7 | — | 3 | 1 | no | — |
| 458 | C22×C7 | — | 4 | 1 | no | — |
| 459 | C22×C7 | — | 12 | 1 | no | — |
| 460 | C22×C7 | — | 12 | 1 | no | — |
| 461 | C22×C7 | — | 12 | 1 | no | — |
| 462 | C2×D7 | — | 3 | 1 | no | — |
| 463 | C2×D7 | — | 3 | 1 | no | — |
| 464 | C2×D7 | — | 3 | 1 | no | — |
| 465 | C2×D7 | — | 6 | 1 | no | — |
| 466 | C2×D7 | — | 6 | 1 | no | — |
| 467 | C2×D7 | — | 6 | 1 | no | — |
| 468 | C2×D7 | — | 6 | 1 | no | — |
| 469 | C2×D7 | — | 6 | 1 | no | — |
| 470 | C2×D7 | — | 6 | 1 | no | — |
| 471 | C2×D7 | — | 12 | 1 | no | — |
| 472 | C2×D7 | — | 12 | 1 | no | — |
| 473 | C2×D7 | — | 12 | 1 | no | — |
| 474 | C2×D7 | — | 12 | 1 | no | — |
| 475 | C2×D7 | — | 12 | 1 | no | — |
| 476 | C2×D7 | — | 12 | 1 | no | — |
| 477 | C2×D7 | C3×C22⋊A4 | 1 | 1 | yes | characteristic |
| 478 | C4×C7 | — | 3 | 1 | no | — |
| 479 | C4×C7 | — | 3 | 1 | no | — |
| 480 | Dic7 | — | 3 | 1 | no | — |
| 481 | Dic7 | — | 3 | 1 | no | — |
| 482 | C23×C3 | — | 3 | 1 | no | — |
| 483 | C23×C3 | — | 21 | 1 | no | — |
| 484 | C23×C3 | — | 21 | 1 | no | — |
| 485 | C23×C3 | — | 21 | 1 | no | — |
| 486 | C23×C3 | — | 21 | 1 | no | — |
| 487 | C23×C3 | — | 21 | 1 | no | — |
| 488 | C23×C3 | — | 21 | 1 | no | — |
| 489 | C23×C3 | — | 21 | 1 | no | — |
| 490 | C23×C3 | — | 21 | 1 | no | — |
| 491 | C23×C3 | — | 21 | 1 | no | — |
| 492 | C23×C3 | — | 84 | 1 | no | — |
| 493 | C23×C3 | — | 84 | 1 | no | — |
| 494 | C23×C3 | — | 84 | 1 | no | — |
| 495 | C23×C3 | — | 84 | 1 | no | — |
| 496 | C23×C3 | — | 84 | 1 | no | — |
| 497 | C23×C3 | — | 84 | 1 | no | — |
| 498 | C23×C3 | — | 84 | 1 | no | — |
| 499 | C23×C3 | — | 84 | 1 | no | — |
| 500 | C23×C3 | D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 501 | C23×C3 | D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 502 | C23×C3 | D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 503 | C2×A4 | — | 28 | 3 | no | — |
| 504 | C2×A4 | — | 28 | 3 | no | — |
| 505 | C2×A4 | — | 28 | 3 | no | — |
| 506 | C2×A4 | — | 28 | 3 | no | — |
| 507 | C2×A4 | — | 28 | 3 | no | — |
| 508 | C2×A4 | — | 28 | 3 | no | — |
| 509 | C2×A4 | — | 28 | 3 | no | — |
| 510 | C2×A4 | — | 28 | 3 | no | — |
| 511 | C2×A4 | — | 28 | 3 | no | — |
| 512 | C3×Q8 | — | 21 | 1 | no | — |
| 513 | C3×Q8 | — | 21 | 1 | no | — |
| 514 | C3×Q8 | D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 515 | C3×Q8 | D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 516 | C3×D4 | — | 3 | 1 | no | — |
| 517 | C3×D4 | — | 3 | 1 | no | — |
| 518 | C3×D4 | — | 3 | 1 | no | — |
| 519 | C3×D4 | — | 3 | 1 | no | — |
| 520 | C3×D4 | — | 3 | 1 | no | — |
| 521 | C3×D4 | — | 3 | 1 | no | — |
| 522 | C3×D4 | — | 21 | 1 | no | — |
| 523 | C3×D4 | — | 21 | 1 | no | — |
| 524 | C3×D4 | — | 21 | 1 | no | — |
| 525 | C3×D4 | — | 21 | 1 | no | — |
| 526 | C3×D4 | — | 21 | 1 | no | — |
| 527 | C3×D4 | — | 21 | 1 | no | — |
| 528 | C3×D4 | — | 21 | 1 | no | — |
| 529 | C3×D4 | — | 21 | 1 | no | — |
| 530 | C3×D4 | — | 21 | 1 | no | — |
| 531 | C3×D4 | — | 21 | 1 | no | — |
| 532 | C3×D4 | — | 21 | 1 | no | — |
| 533 | C3×D4 | — | 21 | 1 | no | — |
| 534 | C3×D4 | — | 21 | 1 | no | — |
| 535 | C3×D4 | — | 21 | 1 | no | — |
| 536 | C3×D4 | — | 21 | 1 | no | — |
| 537 | C3×D4 | — | 21 | 1 | no | — |
| 538 | C3×D4 | — | 21 | 1 | no | — |
| 539 | C3×D4 | — | 21 | 1 | no | — |
| 540 | C2×C3×C4 | — | 3 | 1 | no | — |
| 541 | C2×C3×C4 | — | 3 | 1 | no | — |
| 542 | C2×C3×C4 | — | 3 | 1 | no | — |
| 543 | C2×C3×C4 | — | 21 | 1 | no | — |
| 544 | C2×C3×C4 | — | 21 | 1 | no | — |
| 545 | C2×C3×C4 | — | 21 | 1 | no | — |
| 546 | C2×C3×C4 | — | 21 | 1 | no | — |
| 547 | C2×C3×C4 | — | 21 | 1 | no | — |
| 548 | C2×C3×C4 | — | 21 | 1 | no | — |
| 549 | C2×C3×C4 | — | 21 | 1 | no | — |
| 550 | C2×C3×C4 | — | 21 | 1 | no | — |
| 551 | C2×C3×C4 | — | 21 | 1 | no | — |
| 552 | C2×C3×C4 | — | 21 | 1 | no | — |
| 553 | C2×C3×C4 | — | 21 | 1 | no | — |
| 554 | SL(2,𝔽3) | — | 28 | 3 | no | — |
| 555 | SL(2,𝔽3) | — | 28 | 3 | no | — |
| 556 | C3×C7 | C2×#997 | 1 | 1 | yes | characteristic, complemented |
| 557 | ΓL(1,𝔽8) | — | 16 | 3 | no | — |
| 558 | C2×C32 | — | 112 | 1 | no | — |
| 559 | C2×C32 | — | 112 | 1 | no | — |
| 560 | C2×C32 | — | 112 | 1 | no | — |
| 561 | C24 | — | 21 | 1 | no | — |
| 562 | C24 | — | 21 | 1 | no | — |
| 563 | C24 | — | 21 | 1 | no | — |
| 564 | C24 | — | 21 | 1 | no | — |
| 565 | #41 | — | 3 | 1 | no | — |
| 566 | #41 | — | 3 | 1 | no | — |
| 567 | #41 | — | 21 | 1 | no | — |
| 568 | #41 | — | 21 | 1 | no | — |
| 569 | #41 | — | 21 | 1 | no | — |
| 570 | #41 | — | 21 | 1 | no | — |
| 571 | #41 | — | 21 | 1 | no | — |
| 572 | #41 | — | 21 | 1 | no | — |
| 573 | #41 | — | 21 | 1 | no | — |
| 574 | #41 | — | 21 | 1 | no | — |
| 575 | #41 | — | 21 | 1 | no | — |
| 576 | #41 | — | 21 | 1 | no | — |
| 577 | #41 | — | 21 | 1 | no | — |
| 578 | #41 | — | 21 | 1 | no | — |
| 579 | #41 | — | 21 | 1 | no | — |
| 580 | #41 | — | 21 | 1 | no | — |
| 581 | C2×Q8 | — | 7 | 1 | no | — |
| 582 | C2×Q8 | — | 21 | 1 | no | — |
| 583 | C2×D4 | — | 3 | 1 | no | — |
| 584 | C2×D4 | — | 3 | 1 | no | — |
| 585 | C2×D4 | — | 3 | 1 | no | — |
| 586 | C2×D4 | — | 21 | 1 | no | — |
| 587 | C2×D4 | — | 21 | 1 | no | — |
| 588 | C2×D4 | — | 21 | 1 | no | — |
| 589 | C2×D4 | — | 21 | 1 | no | — |
| 590 | C2×D4 | — | 21 | 1 | no | — |
| 591 | C2×D4 | — | 21 | 1 | no | — |
| 592 | C2×D4 | — | 21 | 1 | no | — |
| 593 | C2×D4 | — | 21 | 1 | no | — |
| 594 | C2×D4 | — | 21 | 1 | no | — |
| 595 | C2×D4 | — | 21 | 1 | no | — |
| 596 | C2×D4 | — | 21 | 1 | no | — |
| 597 | C2×D4 | — | 21 | 1 | no | — |
| 598 | C2×D4 | — | 21 | 1 | no | — |
| 599 | C2×D4 | — | 21 | 1 | no | — |
| 600 | C2×D4 | — | 21 | 1 | no | — |
| 601 | C2×D4 | — | 21 | 1 | no | — |
| 602 | C2×D4 | — | 21 | 1 | no | — |
| 603 | C2×D4 | — | 21 | 1 | no | — |
| 604 | C2×D4 | — | 21 | 1 | no | — |
| 605 | C2×D4 | — | 21 | 1 | no | — |
| 606 | C2×D4 | — | 21 | 1 | no | — |
| 607 | C2×D4 | — | 21 | 1 | no | — |
| 608 | C2×D4 | — | 21 | 1 | no | — |
| 609 | C2×D4 | — | 21 | 1 | no | — |
| 610 | C2×D4 | — | 21 | 1 | no | — |
| 611 | C2×D4 | — | 21 | 1 | no | — |
| 612 | C2×D4 | — | 21 | 1 | no | — |
| 613 | C22×C4 | — | 21 | 1 | no | — |
| 614 | C22×C4 | — | 21 | 1 | no | — |
| 615 | C22×C4 | — | 21 | 1 | no | — |
| 616 | C2×C7 | — | 6 | 1 | no | — |
| 617 | C2×C7 | — | 6 | 1 | no | — |
| 618 | C2×C7 | — | 6 | 1 | no | — |
| 619 | C2×C7 | C2×C3×C22⋊A4 | 1 | 1 | yes | characteristic |
| 620 | D7 | — | 6 | 1 | no | — |
| 621 | D7 | — | 6 | 1 | no | — |
| 622 | D7 | — | 6 | 1 | no | — |
| 623 | D7 | C3×#997 | 1 | 1 | yes | characteristic, complemented |
| 624 | D7 | C3×#997 | 1 | 1 | yes | characteristic, complemented |
| 625 | C22×C3 | — | 3 | 1 | no | — |
| 626 | C22×C3 | — | 3 | 1 | no | — |
| 627 | C22×C3 | — | 3 | 1 | no | — |
| 628 | C22×C3 | — | 12 | 1 | no | — |
| 629 | C22×C3 | — | 12 | 1 | no | — |
| 630 | C22×C3 | — | 12 | 1 | no | — |
| 631 | C22×C3 | — | 12 | 1 | no | — |
| 632 | C22×C3 | — | 21 | 1 | no | — |
| 633 | C22×C3 | — | 21 | 1 | no | — |
| 634 | C22×C3 | — | 21 | 1 | no | — |
| 635 | C22×C3 | — | 21 | 1 | no | — |
| 636 | C22×C3 | — | 42 | 1 | no | — |
| 637 | C22×C3 | — | 42 | 1 | no | — |
| 638 | C22×C3 | — | 42 | 1 | no | — |
| 639 | C22×C3 | — | 42 | 1 | no | — |
| 640 | C22×C3 | — | 42 | 1 | no | — |
| 641 | C22×C3 | — | 42 | 1 | no | — |
| 642 | C22×C3 | — | 84 | 1 | no | — |
| 643 | C22×C3 | — | 84 | 1 | no | — |
| 644 | C22×C3 | — | 84 | 1 | no | — |
| 645 | C22×C3 | — | 84 | 1 | no | — |
| 646 | C22×C3 | — | 84 | 1 | no | — |
| 647 | C22×C3 | — | 84 | 1 | no | — |
| 648 | C22×C3 | — | 112 | 3 | no | — |
| 649 | A4 | — | 28 | 3 | no | — |
| 650 | A4 | — | 28 | 3 | no | — |
| 651 | A4 | — | 28 | 3 | no | — |
| 652 | C3×C4 | — | 3 | 1 | no | — |
| 653 | C3×C4 | — | 3 | 1 | no | — |
| 654 | C3×C4 | — | 21 | 1 | no | — |
| 655 | C3×C4 | — | 21 | 1 | no | — |
| 656 | C32 | — | 112 | 1 | no | Sylow |
| 657 | C23 | — | 3 | 1 | no | — |
| 658 | C23 | — | 21 | 1 | no | — |
| 659 | C23 | — | 21 | 1 | no | — |
| 660 | C23 | — | 21 | 1 | no | — |
| 661 | C23 | — | 21 | 1 | no | — |
| 662 | C23 | — | 21 | 1 | no | — |
| 663 | C23 | — | 21 | 1 | no | — |
| 664 | C23 | — | 21 | 1 | no | — |
| 665 | C23 | — | 21 | 1 | no | — |
| 666 | C23 | — | 21 | 1 | no | — |
| 667 | C23 | — | 84 | 1 | no | — |
| 668 | C23 | — | 84 | 1 | no | — |
| 669 | C23 | — | 84 | 1 | no | — |
| 670 | C23 | — | 84 | 1 | no | — |
| 671 | C23 | — | 84 | 1 | no | — |
| 672 | C23 | — | 84 | 1 | no | — |
| 673 | C23 | — | 84 | 1 | no | — |
| 674 | C23 | — | 84 | 1 | no | — |
| 675 | C23 | C3×D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 676 | C23 | C3×D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 677 | C23 | C3×D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 678 | Q8 | — | 21 | 1 | no | — |
| 679 | Q8 | — | 21 | 1 | no | — |
| 680 | Q8 | C3×D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 681 | Q8 | C3×D7⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 682 | D4 | — | 3 | 1 | no | — |
| 683 | D4 | — | 3 | 1 | no | — |
| 684 | D4 | — | 3 | 1 | no | — |
| 685 | D4 | — | 3 | 1 | no | — |
| 686 | D4 | — | 3 | 1 | no | — |
| 687 | D4 | — | 3 | 1 | no | — |
| 688 | D4 | — | 21 | 1 | no | — |
| 689 | D4 | — | 21 | 1 | no | — |
| 690 | D4 | — | 21 | 1 | no | — |
| 691 | D4 | — | 21 | 1 | no | — |
| 692 | D4 | — | 21 | 1 | no | — |
| 693 | D4 | — | 21 | 1 | no | — |
| 694 | D4 | — | 21 | 1 | no | — |
| 695 | D4 | — | 21 | 1 | no | — |
| 696 | D4 | — | 21 | 1 | no | — |
| 697 | D4 | — | 21 | 1 | no | — |
| 698 | D4 | — | 21 | 1 | no | — |
| 699 | D4 | — | 21 | 1 | no | — |
| 700 | D4 | — | 21 | 1 | no | — |
| 701 | D4 | — | 21 | 1 | no | — |
| 702 | D4 | — | 21 | 1 | no | — |
| 703 | D4 | — | 21 | 1 | no | — |
| 704 | D4 | — | 21 | 1 | no | — |
| 705 | D4 | — | 21 | 1 | no | — |
| 706 | C2×C4 | — | 3 | 1 | no | — |
| 707 | C2×C4 | — | 3 | 1 | no | — |
| 708 | C2×C4 | — | 3 | 1 | no | — |
| 709 | C2×C4 | — | 21 | 1 | no | — |
| 710 | C2×C4 | — | 21 | 1 | no | — |
| 711 | C2×C4 | — | 21 | 1 | no | — |
| 712 | C2×C4 | — | 21 | 1 | no | — |
| 713 | C2×C4 | — | 21 | 1 | no | — |
| 714 | C2×C4 | — | 21 | 1 | no | — |
| 715 | C2×C4 | — | 21 | 1 | no | — |
| 716 | C2×C4 | — | 21 | 1 | no | — |
| 717 | C2×C4 | — | 21 | 1 | no | — |
| 718 | C2×C4 | — | 21 | 1 | no | — |
| 719 | C2×C4 | — | 21 | 1 | no | — |
| 720 | C7 | C2×C3×#997 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 721 | C2×C3 | — | 6 | 1 | no | — |
| 722 | C2×C3 | — | 6 | 1 | no | — |
| 723 | C2×C3 | — | 6 | 1 | no | — |
| 724 | C2×C3 | — | 21 | 1 | no | — |
| 725 | C2×C3 | — | 21 | 1 | no | — |
| 726 | C2×C3 | — | 42 | 1 | no | — |
| 727 | C2×C3 | — | 42 | 1 | no | — |
| 728 | C2×C3 | — | 42 | 1 | no | — |
| 729 | C2×C3 | — | 112 | 3 | no | — |
| 730 | C2×C3 | — | 112 | 3 | no | — |
| 731 | C2×C3 | — | 112 | 3 | no | — |
| 732 | C2×C3 | D7⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| 733 | C22 | — | 3 | 1 | no | — |
| 734 | C22 | — | 3 | 1 | no | — |
| 735 | C22 | — | 3 | 1 | no | — |
| 736 | C22 | — | 12 | 1 | no | — |
| 737 | C22 | — | 12 | 1 | no | — |
| 738 | C22 | — | 12 | 1 | no | — |
| 739 | C22 | — | 12 | 1 | no | — |
| 740 | C22 | — | 21 | 1 | no | — |
| 741 | C22 | — | 21 | 1 | no | — |
| 742 | C22 | — | 21 | 1 | no | — |
| 743 | C22 | — | 21 | 1 | no | — |
| 744 | C22 | — | 42 | 1 | no | — |
| 745 | C22 | — | 42 | 1 | no | — |
| 746 | C22 | — | 42 | 1 | no | — |
| 747 | C22 | — | 42 | 1 | no | — |
| 748 | C22 | — | 42 | 1 | no | — |
| 749 | C22 | — | 42 | 1 | no | — |
| 750 | C22 | — | 84 | 1 | no | — |
| 751 | C22 | — | 84 | 1 | no | — |
| 752 | C22 | — | 84 | 1 | no | — |
| 753 | C22 | — | 84 | 1 | no | — |
| 754 | C22 | — | 84 | 1 | no | — |
| 755 | C22 | — | 84 | 1 | no | — |
| 756 | C4 | — | 3 | 1 | no | — |
| 757 | C4 | — | 3 | 1 | no | — |
| 758 | C4 | — | 21 | 1 | no | — |
| 759 | C4 | — | 21 | 1 | no | — |
| 760 | C3 | — | 112 | 3 | no | — |
| 761 | C3 | D7⋊#997 | 1 | 1 | yes | characteristic, direct product factor |
| 762 | C2 | — | 6 | 1 | no | — |
| 763 | C2 | — | 6 | 1 | no | — |
| 764 | C2 | — | 6 | 1 | no | — |
| 765 | C2 | — | 21 | 1 | no | — |
| 766 | C2 | — | 21 | 1 | no | — |
| 767 | C2 | — | 42 | 1 | no | — |
| 768 | C2 | — | 42 | 1 | no | — |
| 769 | C2 | — | 42 | 1 | no | — |
| 770 | C2 | C3×D7⋊(C22⋊A4) | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D7⋊(C22⋊A4) |
| commutator, cosocle, hypocenter | C7×H(5,𝔽2) | C2×C32 |
| Frattini | C2 | C3×D7⋊(C22⋊A4) |
| Fitting | C3×C7×H(5,𝔽2) | C2×C3 |
| socle | C2×C3×C7 | C2×C22⋊A4 |
| LCS | G ▷ C7×H(5,𝔽2) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C7⋊#997 | C2 | semidirect |
| 2. C3×D7×H(5,𝔽2) | C3 | semidirect |
| 3. D7⋊#997 | C3 | direct (N × H) |
| 9. C3×C7×H(5,𝔽2) | C2×C3 | semidirect |
| 20. C7⋊#997 | C2×C3 | semidirect |
| 33. D7×H(5,𝔽2) | C32 | semidirect |
| 35. C23×C3×D7 | A4 | semidirect |
| 36. C23×C3×D7 | A4 | semidirect |
| 37. C23×C3×D7 | A4 | semidirect |
| 54. C3×Q8×D7 | A4 | semidirect |
| 55. C3×Q8×D7 | A4 | semidirect |
| 99. C7×H(5,𝔽2) | C2×C32 | semidirect |
| 113. C23×C3×C7 | C2×A4 | semidirect |
| 114. C23×C3×C7 | C2×A4 | semidirect |
| 115. C23×C3×C7 | C2×A4 | semidirect |
| 142. C3×C7×Q8 | C2×A4 | semidirect |
| 143. C3×C7×Q8 | C2×A4 | semidirect |
| 195. C23×D7 | C3×A4 | semidirect |
| 196. C23×D7 | C3×A4 | semidirect |
| 197. C23×D7 | C3×A4 | semidirect |
| 211. Q8×D7 | C3×A4 | semidirect |
| 212. Q8×D7 | C3×A4 | semidirect |
| 254. C3×H(5,𝔽2) | AGL(1,𝔽7) | semidirect |
| 306. C23×C7 | C2×C3×A4 | semidirect |
| 307. C23×C7 | C2×C3×A4 | semidirect |
| 308. C23×C7 | C2×C3×A4 | semidirect |
| 326. C7×Q8 | C2×C3×A4 | semidirect |
| 327. C7×Q8 | C2×C3×A4 | semidirect |
| 435. C3×D7 | #997 | semidirect |
| 436. C3×D7 | #997 | semidirect |
| 449. H(5,𝔽2) | C3×AGL(1,𝔽7) | semidirect |
| 500. C23×C3 | D7⋊A4 | semidirect |
| 501. C23×C3 | D7⋊A4 | semidirect |
| 502. C23×C3 | D7⋊A4 | semidirect |
| 514. C3×Q8 | D7⋊A4 | semidirect |
| 515. C3×Q8 | D7⋊A4 | semidirect |
| 556. C3×C7 | C2×#997 | semidirect |
| 623. D7 | C3×#997 | semidirect |
| 624. D7 | C3×#997 | semidirect |
| 675. C23 | C3×D7⋊A4 | semidirect |
| 676. C23 | C3×D7⋊A4 | semidirect |
| 677. C23 | C3×D7⋊A4 | semidirect |
| 680. Q8 | C3×D7⋊A4 | semidirect |
| 681. Q8 | C3×D7⋊A4 | semidirect |
| 720. C7 | C2×C3×#997 | semidirect |
| 761. C3 | D7⋊#997 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7⋊#997 | 2 |
| C3×D7×H(5,𝔽2) | 3 |
| D7⋊#997 | 3 |
| C2×C3×D7⋊A4 | 4 |
| C3×D7⋊SL(2,𝔽3) | 4 |
| C2×C3×#997 | 7 |