Finite Group DatabasebetaFinite Group DatabasebetaOrder 8064.
3374 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 3374 conjugacy classes of subgroups — too many to draw. Only its 55 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 | #72276689 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | ΓL(1,𝔽8)×#5936 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #72276489 | — | 3 | 1 | no | maximal |
| 4 | C2×#72214032 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×AGL(1,𝔽7)×C22⋊A4 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×ΓL(1,𝔽8)×C22⋊A4 | C22 | 1 | 1 | yes | characteristic |
| 7 | #72222255 | — | 4 | 3 | no | maximal |
| 8 | #72214032 | — | 2 | 1 | no | — |
| 9 | AGL(1,𝔽7)×C22⋊A4 | — | 2 | 1 | no | — |
| 10 | C2×D7⋊(C22⋊A4) | — | 2 | 1 | no | — |
| 11 | C2×D7×C22⋊A4 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C25×AGL(1,𝔽7) | D3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C2×C7⋊#1020 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | C7×#5936 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C2×#10620789 | — | 3 | 1 | no | — |
| 16 | C2×#6445⋊C3 | — | 3 | 3 | no | — |
| 17 | C2×#6445⋊C3 | — | 3 | 3 | no | — |
| 18 | ΓL(1,𝔽8)×#379 | — | 3 | 1 | no | — |
| 19 | #89727⋊C3 | — | 3 | 3 | no | — |
| 20 | #89727⋊C3 | — | 3 | 3 | no | — |
| 21 | C3×#87524 | — | 7 | 1 | no | maximal, Hall |
| 22 | ΓL(1,𝔽8)×C22⋊A4 | D4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×A4×AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 24 | C2×A4×AGL(1,𝔽7) | — | 8 | 1 | no | — |
| 25 | C2×A4⋊AGL(1,𝔽7) | — | 4 | 3 | no | — |
| 26 | ΓL(1,𝔽8)×SL(2,ℤ/4) | — | 4 | 3 | no | — |
| 27 | #11731306 | — | 3 | 1 | no | Hall |
| 28 | C2×C22⋊(C22⋊ΓL(1,𝔽8)) | — | 2 | 1 | no | — |
| 29 | C2×C7×C22⋊A4 | C22×C3 | 1 | 1 | yes | characteristic |
| 30 | C25×ΓL(1,𝔽8) | C2×D3 | 1 | 1 | yes | characteristic |
| 31 | D7⋊(C22⋊A4) | — | 2 | 2 | no | — |
| 32 | D7×C22⋊A4 | — | 2 | 1 | no | — |
| 33 | C24×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 34 | C24×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 35 | C24×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 36 | C24×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 37 | C24×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 38 | C24×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 39 | C24×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 40 | C7⋊#1020 | — | 2 | 1 | no | — |
| 41 | C22×(C22⋊D7)⋊C3 | — | 3 | 3 | no | — |
| 42 | C22×C4⋊AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 43 | C22×C4⋊AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 44 | #10621483 | — | 4 | 3 | no | — |
| 45 | C2×C22⋊C4×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 46 | C2×C22⋊C4×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 47 | #10620789 | — | 6 | 3 | no | — |
| 48 | #10620789 | — | 6 | 1 | no | — |
| 49 | C2×(C22⋊Dic7)⋊C3 | — | 3 | 3 | no | — |
| 50 | C2×(C2×AGL(1,𝔽7))⋊C4 | — | 3 | 3 | no | — |
| 51 | C2×(C2×AGL(1,𝔽7))⋊C4 | — | 3 | 6 | no | — |
| 52 | C2×(C2×AGL(1,𝔽7))⋊C4 | — | 3 | 3 | no | — |
| 53 | #6445⋊C3 | — | 6 | 3 | no | — |
| 54 | #6445⋊C3 | — | 6 | 6 | no | — |
| 55 | #6445⋊C3 | — | 6 | 3 | no | — |
| 56 | #6445⋊C3 | — | 6 | 6 | no | — |
| 57 | #6445⋊C3 | — | 6 | 3 | no | — |
| 58 | #6445⋊C3 | — | 6 | 3 | no | — |
| 59 | C22×C3×C22⋊A4 | — | 7 | 1 | no | — |
| 60 | C2×C3×#1020 | — | 7 | 1 | no | — |
| 61 | C3×#5936 | — | 7 | 1 | no | — |
| 62 | C2×A4×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 63 | C2×A4×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 64 | A4×AGL(1,𝔽7) | — | 8 | 3 | no | — |
| 65 | A4×AGL(1,𝔽7) | — | 8 | 2 | no | — |
| 66 | A4⋊AGL(1,𝔽7) | — | 8 | 3 | no | — |
| 67 | #4246⋊C3 | — | 16 | 1 | no | — |
| 68 | C25×D7 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×#6516 | — | 3 | 1 | no | — |
| 70 | C2×#6445 | — | 3 | 3 | no | — |
| 71 | C2×#6445 | — | 3 | 3 | no | — |
| 72 | C7×#379 | — | 3 | 1 | no | — |
| 73 | #89727 | — | 3 | 3 | no | — |
| 74 | #89727 | — | 3 | 3 | no | — |
| 75 | #87524 | — | 7 | 1 | no | — |
| 76 | C3×#2846 | — | 21 | 1 | no | — |
| 77 | C22⋊(C22⋊ΓL(1,𝔽8)) | — | 2 | 1 | no | — |
| 78 | C7×C22⋊A4 | C3×D4 | 1 | 1 | yes | characteristic, complemented |
| 79 | C24×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 80 | C24×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 81 | C24×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 82 | C24×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 83 | C24×ΓL(1,𝔽8) | #67 | 1 | 1 | yes | characteristic, complemented |
| 84 | C2×D7⋊A4 | — | 8 | 2 | no | — |
| 85 | C2×D7⋊A4 | — | 8 | 3 | no | — |
| 86 | C2×A4×D7 | — | 4 | 3 | no | — |
| 87 | C2×A4×D7 | — | 8 | 1 | no | — |
| 88 | C23×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 89 | C23×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 90 | C23×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 91 | C23×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 92 | C23×AGL(1,𝔽7) | — | 3 | 6 | no | — |
| 93 | C23×AGL(1,𝔽7) | — | 3 | 6 | no | — |
| 94 | C23×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 95 | C23×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 96 | C23×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 97 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 98 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 99 | C23×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 100 | C23×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 101 | C23×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 102 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 103 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 104 | C23×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 105 | C23×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 106 | C23×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 107 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 108 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 109 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 110 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 111 | C23×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 112 | C23×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 113 | C23×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 114 | C23×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 115 | C23×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 116 | C23×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 117 | C23×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 118 | C23×AGL(1,𝔽7) | S4 | 1 | 3 | yes | complemented |
| 119 | C2×C7⋊S4 | — | 4 | 3 | no | — |
| 120 | C22×C4×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 121 | C22×C4×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 122 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 123 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 124 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 125 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 126 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 127 | C2×(C22⋊D7)⋊C3 | — | 6 | 3 | no | — |
| 128 | C22×ΓL(1,𝔽8)⋊C4 | — | 3 | 3 | no | — |
| 129 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 130 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 131 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 132 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 133 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 134 | C7×SL(2,ℤ/4) | — | 4 | 3 | no | — |
| 135 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 136 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 137 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 138 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 139 | (C22⋊Dic7)⋊C3 | — | 6 | 3 | no | — |
| 140 | (C22⋊Dic7)⋊C3 | — | 6 | 3 | no | — |
| 141 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 3 | no | — |
| 142 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 12 | no | — |
| 143 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 3 | no | — |
| 144 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 3 | no | — |
| 145 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 3 | no | — |
| 146 | C2×C3×C22⋊A4 | — | 7 | 1 | no | — |
| 147 | C2×C3×C22⋊A4 | — | 14 | 1 | no | — |
| 148 | C3×#1020 | — | 14 | 1 | no | — |
| 149 | C3×GL(2,ℤ/4) | — | 28 | 3 | no | — |
| 150 | C2×C3⋊AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 151 | C2×C3×AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 152 | A4×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 153 | A4×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 154 | Dic3×ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 155 | C25×C7 | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 156 | C24×D7 | — | 2 | 1 | no | — |
| 157 | C24×D7 | — | 3 | 3 | no | — |
| 158 | C24×D7 | — | 3 | 3 | no | — |
| 159 | C24×D7 | — | 6 | 1 | no | — |
| 160 | C24×D7 | — | 6 | 2 | no | — |
| 161 | C24×D7 | — | 6 | 1 | no | — |
| 162 | C24×D7 | — | 6 | 3 | no | — |
| 163 | C22×C22⋊D7 | — | 3 | 3 | no | — |
| 164 | C22×D28 | — | 3 | 3 | no | — |
| 165 | C22×D28 | — | 3 | 1 | no | — |
| 166 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 167 | C2×C7×C22⋊C4 | — | 3 | 3 | no | — |
| 168 | #6516 | — | 6 | 3 | no | — |
| 169 | #6516 | — | 6 | 1 | no | — |
| 170 | C2×C22⋊Dic7 | — | 3 | 3 | no | — |
| 171 | C2×(C2×D7)⋊C4 | — | 3 | 3 | no | — |
| 172 | C2×(C2×D7)⋊C4 | — | 3 | 6 | no | — |
| 173 | C2×(C2×D7)⋊C4 | — | 3 | 3 | no | — |
| 174 | #6445 | — | 6 | 3 | no | — |
| 175 | #6445 | — | 6 | 6 | no | — |
| 176 | #6445 | — | 6 | 6 | no | — |
| 177 | #6445 | — | 6 | 3 | no | — |
| 178 | #6445 | — | 6 | 3 | no | — |
| 179 | #6445 | — | 6 | 3 | no | — |
| 180 | C26×C3 | — | 7 | 1 | no | — |
| 181 | C22×C22⋊A4 | — | 7 | 1 | no | — |
| 182 | C22×C22⋊A4 | — | 14 | 1 | no | — |
| 183 | C2×#1020 | — | 7 | 1 | no | — |
| 184 | #5936 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 185 | C2×C3×#120 | — | 21 | 1 | no | — |
| 186 | C2×C3×#120 | — | 21 | 3 | no | — |
| 187 | C2×C3×#120 | — | 21 | 3 | no | — |
| 188 | C3×#379 | — | 21 | 1 | no | — |
| 189 | C3×#379 | — | 21 | 3 | no | — |
| 190 | C3×#379 | — | 21 | 3 | no | — |
| 191 | C2×C22⋊ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 192 | C2×C22⋊ΓL(1,𝔽8) | — | 8 | 3 | no | — |
| 193 | C2×C7×A4 | — | 4 | 3 | no | — |
| 194 | C2×C7×A4 | — | 8 | 1 | no | — |
| 195 | C23×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 196 | C23×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 197 | C23×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 198 | C23×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 199 | C23×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 200 | C23×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 201 | C23×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 202 | C23×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 203 | C23×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 204 | C23×ΓL(1,𝔽8) | — | 6 | 6 | no | — |
| 205 | C23×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 206 | C23×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 207 | C23×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 208 | C23×ΓL(1,𝔽8) | C2×S4 | 1 | 3 | yes | — |
| 209 | D7⋊A4 | — | 8 | 4 | no | — |
| 210 | D7⋊A4 | — | 8 | 6 | no | — |
| 211 | A4×D7 | — | 8 | 3 | no | — |
| 212 | A4×D7 | — | 8 | 2 | no | — |
| 213 | C22×AGL(1,𝔽7) | — | 2 | 2 | no | — |
| 214 | C22×AGL(1,𝔽7) | — | 2 | 3 | no | — |
| 215 | C22×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 216 | C22×AGL(1,𝔽7) | — | 3 | 12 | no | — |
| 217 | C22×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 218 | C22×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 219 | C22×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 220 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 221 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 222 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 223 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 224 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 225 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 226 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 227 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 228 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 229 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 230 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 231 | C22×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 232 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 233 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 234 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 235 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 236 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 237 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 238 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 239 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 240 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 241 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 242 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 243 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 244 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 245 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 246 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 247 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 248 | C22×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 249 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 250 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 251 | C22×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 252 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 253 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 254 | C22×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 255 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 256 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 257 | C22×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 258 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 259 | C7⋊S4 | — | 8 | 3 | no | — |
| 260 | C2×C4×ΓL(1,𝔽8) | — | 6 | 6 | no | — |
| 261 | C2×C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 262 | C2×C4×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 263 | #4246 | — | 16 | 1 | no | — |
| 264 | (C22⋊D7)⋊C3 | — | 12 | 3 | no | — |
| 265 | (C22⋊D7)⋊C3 | — | 12 | 3 | no | — |
| 266 | (C22⋊D7)⋊C3 | — | 12 | 3 | no | — |
| 267 | (C22⋊D7)⋊C3 | — | 12 | 3 | no | — |
| 268 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 3 | no | — |
| 269 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 3 | no | — |
| 270 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 3 | no | — |
| 271 | C4⋊AGL(1,𝔽7) | — | 12 | 6 | no | — |
| 272 | C4⋊AGL(1,𝔽7) | — | 12 | 6 | no | — |
| 273 | C4⋊AGL(1,𝔽7) | — | 12 | 3 | no | — |
| 274 | C4⋊AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 275 | C3×C22⋊A4 | — | 7 | 1 | no | — |
| 276 | C22×C3×A4 | — | 28 | 3 | no | — |
| 277 | C22×C3×A4 | — | 56 | 1 | no | — |
| 278 | C2×C3×S4 | — | 28 | 3 | no | — |
| 279 | C3×SL(2,ℤ/4) | — | 28 | 3 | no | — |
| 280 | #2846 | — | 21 | 1 | no | Sylow |
| 281 | C2×C3×ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 282 | C3⋊AGL(1,𝔽7) | — | 32 | 1 | no | — |
| 283 | C3×AGL(1,𝔽7) | — | 32 | 1 | no | — |
| 284 | C24×C7 | — | 3 | 3 | no | — |
| 285 | C24×C7 | — | 3 | 3 | no | — |
| 286 | C24×C7 | — | 6 | 1 | no | — |
| 287 | C24×C7 | — | 6 | 1 | no | — |
| 288 | C24×C7 | C3×#67 | 1 | 1 | yes | characteristic, complemented |
| 289 | C23×D7 | — | 2 | 1 | no | — |
| 290 | C23×D7 | — | 3 | 3 | no | — |
| 291 | C23×D7 | — | 3 | 1 | no | — |
| 292 | C23×D7 | — | 3 | 3 | no | — |
| 293 | C23×D7 | — | 3 | 6 | no | — |
| 294 | C23×D7 | — | 3 | 6 | no | — |
| 295 | C23×D7 | — | 3 | 3 | no | — |
| 296 | C23×D7 | — | 3 | 3 | no | — |
| 297 | C23×D7 | — | 3 | 1 | no | — |
| 298 | C23×D7 | — | 6 | 3 | no | — |
| 299 | C23×D7 | — | 6 | 3 | no | — |
| 300 | C23×D7 | — | 6 | 2 | no | — |
| 301 | C23×D7 | — | 6 | 2 | no | — |
| 302 | C23×D7 | — | 6 | 6 | no | — |
| 303 | C23×D7 | — | 6 | 3 | no | — |
| 304 | C23×D7 | — | 6 | 3 | no | — |
| 305 | C23×D7 | — | 6 | 12 | no | — |
| 306 | C23×D7 | — | 6 | 12 | no | — |
| 307 | C23×D7 | — | 6 | 1 | no | — |
| 308 | C23×D7 | — | 6 | 3 | no | — |
| 309 | C23×D7 | — | 6 | 3 | no | — |
| 310 | C23×D7 | — | 6 | 3 | no | — |
| 311 | C23×D7 | — | 6 | 3 | no | — |
| 312 | C23×D7 | — | 6 | 6 | no | — |
| 313 | C23×D7 | — | 6 | 2 | no | — |
| 314 | C23×D7 | — | 6 | 6 | no | — |
| 315 | C23×D7 | — | 6 | 6 | no | — |
| 316 | C23×D7 | — | 6 | 6 | no | — |
| 317 | C23×D7 | — | 6 | 3 | no | — |
| 318 | C23×D7 | — | 6 | 2 | no | — |
| 319 | C23×D7 | C3×S4 | 1 | 3 | yes | complemented |
| 320 | C22×C4×C7 | — | 3 | 3 | no | — |
| 321 | C22×C4×C7 | — | 3 | 1 | no | — |
| 322 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 323 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 324 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 325 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 326 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 327 | C2×C22⋊D7 | — | 6 | 3 | no | — |
| 328 | C22×Dic7 | — | 3 | 3 | no | — |
| 329 | C2×D28 | — | 6 | 3 | no | — |
| 330 | C2×D28 | — | 6 | 12 | no | — |
| 331 | C2×D28 | — | 6 | 3 | no | — |
| 332 | C2×D28 | — | 6 | 3 | no | — |
| 333 | C2×D28 | — | 6 | 3 | no | — |
| 334 | C7×C22⋊C4 | — | 6 | 3 | no | — |
| 335 | C7×C22⋊C4 | — | 6 | 3 | no | — |
| 336 | C7×C22⋊C4 | — | 6 | 3 | no | — |
| 337 | C7×C22⋊C4 | — | 6 | 3 | no | — |
| 338 | C22⋊Dic7 | — | 6 | 3 | no | — |
| 339 | C22⋊Dic7 | — | 6 | 3 | no | — |
| 340 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 341 | (C2×D7)⋊C4 | — | 6 | 12 | no | — |
| 342 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 343 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 344 | (C2×D7)⋊C4 | — | 6 | 3 | no | — |
| 345 | C25×C3 | — | 7 | 1 | no | — |
| 346 | C25×C3 | — | 14 | 1 | no | — |
| 347 | C25×C3 | — | 21 | 3 | no | — |
| 348 | C25×C3 | — | 21 | 3 | no | — |
| 349 | C25×C3 | — | 42 | 1 | no | — |
| 350 | C25×C3 | — | 42 | 3 | no | — |
| 351 | C25×C3 | — | 42 | 1 | no | — |
| 352 | C25×C3 | — | 42 | 2 | no | — |
| 353 | C2×C22⋊A4 | — | 14 | 2 | no | — |
| 354 | C2×C22⋊A4 | — | 14 | 1 | no | — |
| 355 | C2×C22⋊A4 | — | 14 | 1 | no | — |
| 356 | C2×C22⋊A4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 357 | #1020 | — | 14 | 1 | no | — |
| 358 | C22×C3×D4 | — | 21 | 1 | no | — |
| 359 | C22×C3×D4 | — | 21 | 3 | no | — |
| 360 | C22×C3×D4 | — | 21 | 3 | no | — |
| 361 | GL(2,ℤ/4) | — | 28 | 3 | no | — |
| 362 | C3×#120 | — | 42 | 3 | no | — |
| 363 | C3×#120 | — | 42 | 1 | no | — |
| 364 | C3×#120 | — | 42 | 3 | no | — |
| 365 | C3×#120 | — | 42 | 6 | no | — |
| 366 | C3×#120 | — | 42 | 3 | no | — |
| 367 | C3×#120 | — | 42 | 3 | no | — |
| 368 | C3×#120 | — | 42 | 6 | no | — |
| 369 | C3×#120 | — | 42 | 3 | no | — |
| 370 | C2×C3×C22⋊C4 | — | 21 | 3 | no | — |
| 371 | C2×C3×C22⋊C4 | — | 21 | 3 | no | — |
| 372 | C2×C3×C22⋊C4 | — | 21 | 3 | no | — |
| 373 | C2×C3×C22⋊C4 | — | 21 | 3 | no | — |
| 374 | C2×C3×C22⋊C4 | — | 21 | 6 | no | — |
| 375 | C2×C3×C22⋊C4 | — | 21 | 3 | no | — |
| 376 | C2×D21 | — | 16 | 1 | no | — |
| 377 | C2×C3×D7 | — | 16 | 1 | no | — |
| 378 | C22⋊ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 379 | C22⋊ΓL(1,𝔽8) | — | 8 | 3 | no | — |
| 380 | C7×A4 | — | 4 | 3 | no | — |
| 381 | C7×A4 | — | 8 | 1 | no | — |
| 382 | C22×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 383 | C22×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 384 | C22×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 385 | C22×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 386 | C22×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 387 | C22×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 388 | C22×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 389 | C22×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 390 | C22×ΓL(1,𝔽8) | — | 6 | 6 | no | — |
| 391 | C22×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 392 | C22×ΓL(1,𝔽8) | — | 6 | 3 | no | — |
| 393 | C22×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 394 | C22×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 395 | C22×ΓL(1,𝔽8) | GL(2,ℤ/4) | 1 | 3 | yes | complemented |
| 396 | C2×AGL(1,𝔽7) | — | 3 | 6 | no | — |
| 397 | C2×AGL(1,𝔽7) | — | 3 | 6 | no | — |
| 398 | C2×AGL(1,𝔽7) | — | 3 | 3 | no | — |
| 399 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 400 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 401 | C2×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 402 | C2×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 403 | C2×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 404 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 405 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 406 | C2×AGL(1,𝔽7) | — | 6 | 12 | no | — |
| 407 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 408 | C2×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 409 | C2×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 410 | C2×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 411 | C2×AGL(1,𝔽7) | — | 6 | 6 | no | — |
| 412 | C2×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 413 | C2×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 414 | C2×AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 415 | C2×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 416 | C2×AGL(1,𝔽7) | — | 12 | 3 | no | — |
| 417 | C2×AGL(1,𝔽7) | — | 12 | 3 | no | — |
| 418 | C2×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 419 | C2×AGL(1,𝔽7) | — | 32 | 1 | no | — |
| 420 | C2×AGL(1,𝔽7) | #1020 | 1 | 1 | yes | characteristic, complemented |
| 421 | C7×Dic3 | — | 16 | 1 | no | — |
| 422 | C4×ΓL(1,𝔽8) | — | 12 | 3 | no | — |
| 423 | C4×ΓL(1,𝔽8) | — | 12 | 1 | no | — |
| 424 | ΓL(1,𝔽8)⋊C4 | — | 12 | 3 | no | — |
| 425 | C2×C3×A4 | — | 28 | 3 | no | — |
| 426 | C2×C3×A4 | — | 56 | 1 | no | — |
| 427 | C2×C3×A4 | — | 56 | 3 | no | — |
| 428 | C2×C3×A4 | — | 56 | 2 | no | — |
| 429 | C3×S4 | — | 56 | 3 | no | — |
| 430 | C3×#67 | — | 112 | 1 | no | — |
| 431 | C26 | — | 7 | 1 | no | — |
| 432 | C2×#120 | — | 21 | 3 | no | — |
| 433 | C2×#120 | — | 21 | 3 | no | — |
| 434 | C2×#120 | — | 21 | 1 | no | — |
| 435 | #379 | — | 3 | 1 | no | — |
| 436 | #379 | — | 21 | 3 | no | — |
| 437 | #379 | — | 21 | 3 | no | — |
| 438 | C3×ΓL(1,𝔽8) | — | 16 | 1 | no | Hall |
| 439 | C23×C7 | — | 2 | 1 | no | — |
| 440 | C23×C7 | — | 3 | 1 | no | — |
| 441 | C23×C7 | — | 3 | 3 | no | — |
| 442 | C23×C7 | — | 3 | 3 | no | — |
| 443 | C23×C7 | — | 3 | 3 | no | — |
| 444 | C23×C7 | — | 3 | 3 | no | — |
| 445 | C23×C7 | — | 3 | 3 | no | — |
| 446 | C23×C7 | — | 6 | 1 | no | — |
| 447 | C23×C7 | — | 6 | 1 | no | — |
| 448 | C23×C7 | — | 6 | 6 | no | — |
| 449 | C23×C7 | — | 6 | 3 | no | — |
| 450 | C23×C7 | — | 6 | 3 | no | — |
| 451 | C23×C7 | — | 6 | 3 | no | — |
| 452 | C23×C7 | C2×C3×S4 | 1 | 3 | yes | — |
| 453 | C22×D7 | — | 2 | 2 | no | — |
| 454 | C22×D7 | — | 2 | 3 | no | — |
| 455 | C22×D7 | — | 3 | 3 | no | — |
| 456 | C22×D7 | — | 3 | 12 | no | — |
| 457 | C22×D7 | — | 3 | 3 | no | — |
| 458 | C22×D7 | — | 3 | 3 | no | — |
| 459 | C22×D7 | — | 3 | 3 | no | — |
| 460 | C22×D7 | — | 6 | 6 | no | — |
| 461 | C22×D7 | — | 6 | 3 | no | — |
| 462 | C22×D7 | — | 6 | 3 | no | — |
| 463 | C22×D7 | — | 6 | 6 | no | — |
| 464 | C22×D7 | — | 6 | 6 | no | — |
| 465 | C22×D7 | — | 6 | 6 | no | — |
| 466 | C22×D7 | — | 6 | 12 | no | — |
| 467 | C22×D7 | — | 6 | 12 | no | — |
| 468 | C22×D7 | — | 6 | 12 | no | — |
| 469 | C22×D7 | — | 6 | 6 | no | — |
| 470 | C22×D7 | — | 6 | 3 | no | — |
| 471 | C22×D7 | — | 6 | 2 | no | — |
| 472 | C22×D7 | — | 6 | 1 | no | — |
| 473 | C22×D7 | — | 6 | 3 | no | — |
| 474 | C22×D7 | — | 6 | 3 | no | — |
| 475 | C22×D7 | — | 6 | 3 | no | — |
| 476 | C22×D7 | — | 6 | 3 | no | — |
| 477 | C22×D7 | — | 6 | 3 | no | — |
| 478 | C22×D7 | — | 6 | 3 | no | — |
| 479 | C22×D7 | — | 6 | 6 | no | — |
| 480 | C22×D7 | — | 6 | 6 | no | — |
| 481 | C22×D7 | — | 6 | 3 | no | — |
| 482 | C22×D7 | — | 6 | 3 | no | — |
| 483 | C22×D7 | — | 6 | 6 | no | — |
| 484 | C22×D7 | — | 6 | 12 | no | — |
| 485 | C22×D7 | — | 6 | 6 | no | — |
| 486 | C22×D7 | — | 6 | 6 | no | — |
| 487 | C22×D7 | — | 6 | 12 | no | — |
| 488 | C22×D7 | — | 6 | 12 | no | — |
| 489 | C22×D7 | — | 6 | 6 | no | — |
| 490 | C22×D7 | — | 6 | 6 | no | — |
| 491 | C22×D7 | — | 6 | 6 | no | — |
| 492 | C22×D7 | — | 6 | 3 | no | — |
| 493 | C22×D7 | — | 6 | 1 | no | — |
| 494 | C22×D7 | — | 6 | 2 | no | — |
| 495 | C22×D7 | — | 6 | 1 | no | — |
| 496 | C22×D7 | — | 6 | 3 | no | — |
| 497 | C22×D7 | — | 6 | 3 | no | — |
| 498 | C22×D7 | — | 6 | 1 | no | — |
| 499 | C2×C4×C7 | — | 6 | 6 | no | — |
| 500 | C2×C4×C7 | — | 6 | 3 | no | — |
| 501 | C2×C4×C7 | — | 6 | 3 | no | — |
| 502 | C22⋊D7 | — | 12 | 3 | no | — |
| 503 | C22⋊D7 | — | 12 | 3 | no | — |
| 504 | C22⋊D7 | — | 12 | 3 | no | — |
| 505 | C22⋊D7 | — | 12 | 3 | no | — |
| 506 | C2×Dic7 | — | 6 | 3 | no | — |
| 507 | C2×Dic7 | — | 6 | 3 | no | — |
| 508 | C2×Dic7 | — | 6 | 3 | no | — |
| 509 | D28 | — | 12 | 6 | no | — |
| 510 | D28 | — | 12 | 6 | no | — |
| 511 | D28 | — | 12 | 3 | no | — |
| 512 | D28 | — | 12 | 1 | no | — |
| 513 | C24×C3 | — | 7 | 3 | no | — |
| 514 | C24×C3 | — | 7 | 1 | no | — |
| 515 | C24×C3 | — | 14 | 1 | no | — |
| 516 | C24×C3 | — | 21 | 3 | no | — |
| 517 | C24×C3 | — | 21 | 3 | no | — |
| 518 | C24×C3 | — | 21 | 3 | no | — |
| 519 | C24×C3 | — | 21 | 1 | no | — |
| 520 | C24×C3 | — | 21 | 3 | no | — |
| 521 | C24×C3 | — | 21 | 6 | no | — |
| 522 | C24×C3 | — | 21 | 3 | no | — |
| 523 | C24×C3 | — | 21 | 3 | no | — |
| 524 | C24×C3 | — | 21 | 6 | no | — |
| 525 | C24×C3 | — | 21 | 1 | no | — |
| 526 | C24×C3 | — | 42 | 1 | no | — |
| 527 | C24×C3 | — | 42 | 1 | no | — |
| 528 | C24×C3 | — | 42 | 3 | no | — |
| 529 | C24×C3 | — | 42 | 3 | no | — |
| 530 | C24×C3 | — | 42 | 2 | no | — |
| 531 | C24×C3 | — | 42 | 1 | no | — |
| 532 | C24×C3 | — | 42 | 2 | no | — |
| 533 | C24×C3 | — | 42 | 3 | no | — |
| 534 | C24×C3 | — | 42 | 6 | no | — |
| 535 | C24×C3 | — | 42 | 3 | no | — |
| 536 | C24×C3 | — | 42 | 3 | no | — |
| 537 | C24×C3 | — | 42 | 3 | no | — |
| 538 | C24×C3 | — | 42 | 3 | no | — |
| 539 | C24×C3 | — | 42 | 3 | no | — |
| 540 | C24×C3 | — | 42 | 3 | no | — |
| 541 | C24×C3 | — | 42 | 12 | no | — |
| 542 | C24×C3 | — | 42 | 12 | no | — |
| 543 | C24×C3 | — | 42 | 2 | no | — |
| 544 | C24×C3 | — | 42 | 2 | no | — |
| 545 | C24×C3 | — | 42 | 6 | no | — |
| 546 | C24×C3 | — | 42 | 6 | no | — |
| 547 | C24×C3 | — | 42 | 6 | no | — |
| 548 | C24×C3 | — | 42 | 6 | no | — |
| 549 | C22⋊A4 | — | 14 | 1 | no | — |
| 550 | C22⋊A4 | C4⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 551 | C22×A4 | — | 28 | 3 | no | — |
| 552 | C22×A4 | — | 56 | 1 | no | — |
| 553 | C22×A4 | — | 56 | 3 | no | — |
| 554 | C22×A4 | — | 56 | 2 | no | — |
| 555 | C2×S4 | — | 28 | 3 | no | — |
| 556 | C2×C3×D4 | — | 42 | 3 | no | — |
| 557 | C2×C3×D4 | — | 42 | 3 | no | — |
| 558 | C2×C3×D4 | — | 42 | 3 | no | — |
| 559 | C2×C3×D4 | — | 42 | 3 | no | — |
| 560 | C2×C3×D4 | — | 42 | 3 | no | — |
| 561 | C2×C3×D4 | — | 42 | 12 | no | — |
| 562 | C2×C3×D4 | — | 42 | 3 | no | — |
| 563 | C2×C3×D4 | — | 42 | 3 | no | — |
| 564 | C2×C3×D4 | — | 42 | 3 | no | — |
| 565 | C2×C3×D4 | — | 42 | 3 | no | — |
| 566 | C2×C3×D4 | — | 42 | 3 | no | — |
| 567 | C22×C3×C4 | — | 21 | 1 | no | — |
| 568 | C22×C3×C4 | — | 21 | 3 | no | — |
| 569 | C22×C3×C4 | — | 21 | 3 | no | — |
| 570 | SL(2,ℤ/4) | — | 4 | 3 | no | — |
| 571 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 572 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 573 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 574 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 575 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 576 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 577 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 578 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 579 | C3×C22⋊C4 | — | 42 | 12 | no | — |
| 580 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 581 | C3×C22⋊C4 | — | 42 | 3 | no | — |
| 582 | C2×C3×C7 | — | 16 | 1 | no | — |
| 583 | D21 | — | 32 | 1 | no | — |
| 584 | C3×D7 | — | 32 | 1 | no | — |
| 585 | C2×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 586 | C2×ΓL(1,𝔽8) | — | 3 | 3 | no | — |
| 587 | C2×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 588 | C2×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 589 | C2×ΓL(1,𝔽8) | — | 32 | 1 | no | — |
| 590 | C2×ΓL(1,𝔽8) | C2×#1020 | 1 | 1 | yes | characteristic |
| 591 | AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 592 | AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 593 | AGL(1,𝔽7) | — | 6 | 3 | no | — |
| 594 | AGL(1,𝔽7) | — | 24 | 1 | no | — |
| 595 | AGL(1,𝔽7) | — | 32 | 2 | no | — |
| 596 | C22×C32 | — | 112 | 1 | no | — |
| 597 | C2×C3×D3 | — | 112 | 1 | no | — |
| 598 | C3×A4 | — | 28 | 3 | no | — |
| 599 | C3×A4 | — | 56 | 1 | no | — |
| 600 | C3×Dic3 | — | 112 | 1 | no | — |
| 601 | C25 | — | 14 | 1 | no | — |
| 602 | C25 | — | 21 | 3 | no | — |
| 603 | C25 | — | 21 | 3 | no | — |
| 604 | C25 | — | 42 | 3 | no | — |
| 605 | C25 | — | 42 | 1 | no | — |
| 606 | C25 | — | 42 | 1 | no | — |
| 607 | C25 | — | 42 | 2 | no | — |
| 608 | C25 | D3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 609 | C22×D4 | — | 21 | 1 | no | — |
| 610 | C22×D4 | — | 21 | 3 | no | — |
| 611 | C22×D4 | — | 21 | 3 | no | — |
| 612 | #120 | — | 42 | 3 | no | — |
| 613 | #120 | — | 42 | 3 | no | — |
| 614 | #120 | — | 42 | 3 | no | — |
| 615 | #120 | — | 42 | 6 | no | — |
| 616 | #120 | — | 42 | 6 | no | — |
| 617 | #120 | — | 42 | 3 | no | — |
| 618 | #120 | — | 42 | 3 | no | — |
| 619 | #120 | — | 42 | 1 | no | — |
| 620 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 621 | C2×C22⋊C4 | — | 3 | 3 | no | — |
| 622 | C2×C22⋊C4 | — | 21 | 3 | no | — |
| 623 | C2×C22⋊C4 | — | 21 | 3 | no | — |
| 624 | C2×C22⋊C4 | — | 21 | 6 | no | — |
| 625 | C2×C22⋊C4 | — | 21 | 3 | no | — |
| 626 | C22×C7 | — | 2 | 1 | no | — |
| 627 | C22×C7 | — | 3 | 3 | no | — |
| 628 | C22×C7 | — | 3 | 1 | no | — |
| 629 | C22×C7 | — | 3 | 3 | no | — |
| 630 | C22×C7 | — | 3 | 3 | no | — |
| 631 | C22×C7 | — | 3 | 3 | no | — |
| 632 | C22×C7 | — | 3 | 3 | no | — |
| 633 | C22×C7 | — | 6 | 3 | no | — |
| 634 | C22×C7 | — | 6 | 6 | no | — |
| 635 | C22×C7 | — | 6 | 3 | no | — |
| 636 | C22×C7 | — | 6 | 3 | no | — |
| 637 | C22×C7 | — | 6 | 1 | no | — |
| 638 | C22×C7 | — | 6 | 1 | no | — |
| 639 | C22×C7 | C3×GL(2,ℤ/4) | 1 | 3 | yes | complemented |
| 640 | C2×D7 | — | 3 | 6 | no | — |
| 641 | C2×D7 | — | 3 | 6 | no | — |
| 642 | C2×D7 | — | 3 | 3 | no | — |
| 643 | C2×D7 | — | 6 | 3 | no | — |
| 644 | C2×D7 | — | 6 | 3 | no | — |
| 645 | C2×D7 | — | 6 | 2 | no | — |
| 646 | C2×D7 | — | 6 | 2 | no | — |
| 647 | C2×D7 | — | 6 | 12 | no | — |
| 648 | C2×D7 | — | 6 | 3 | no | — |
| 649 | C2×D7 | — | 6 | 3 | no | — |
| 650 | C2×D7 | — | 6 | 12 | no | — |
| 651 | C2×D7 | — | 6 | 3 | no | — |
| 652 | C2×D7 | — | 6 | 6 | no | — |
| 653 | C2×D7 | — | 6 | 6 | no | — |
| 654 | C2×D7 | — | 6 | 6 | no | — |
| 655 | C2×D7 | — | 6 | 6 | no | — |
| 656 | C2×D7 | — | 6 | 2 | no | — |
| 657 | C2×D7 | — | 6 | 1 | no | — |
| 658 | C2×D7 | — | 6 | 3 | no | — |
| 659 | C2×D7 | — | 6 | 2 | no | — |
| 660 | C2×D7 | — | 12 | 3 | no | — |
| 661 | C2×D7 | — | 12 | 3 | no | — |
| 662 | C2×D7 | — | 12 | 1 | no | — |
| 663 | C2×D7 | C3×#1020 | 1 | 1 | yes | characteristic, complemented |
| 664 | C4×C7 | — | 12 | 3 | no | — |
| 665 | C4×C7 | — | 12 | 1 | no | — |
| 666 | Dic7 | — | 12 | 3 | no | — |
| 667 | C23×C3 | — | 7 | 3 | no | — |
| 668 | C23×C3 | — | 14 | 1 | no | — |
| 669 | C23×C3 | — | 14 | 3 | no | — |
| 670 | C23×C3 | — | 14 | 2 | no | — |
| 671 | C23×C3 | — | 21 | 3 | no | — |
| 672 | C23×C3 | — | 21 | 3 | no | — |
| 673 | C23×C3 | — | 21 | 1 | no | — |
| 674 | C23×C3 | — | 21 | 3 | no | — |
| 675 | C23×C3 | — | 21 | 3 | no | — |
| 676 | C23×C3 | — | 21 | 3 | no | — |
| 677 | C23×C3 | — | 21 | 3 | no | — |
| 678 | C23×C3 | — | 21 | 3 | no | — |
| 679 | C23×C3 | — | 21 | 3 | no | — |
| 680 | C23×C3 | — | 21 | 3 | no | — |
| 681 | C23×C3 | — | 21 | 12 | no | — |
| 682 | C23×C3 | — | 42 | 1 | no | — |
| 683 | C23×C3 | — | 42 | 1 | no | — |
| 684 | C23×C3 | — | 42 | 3 | no | — |
| 685 | C23×C3 | — | 42 | 6 | no | — |
| 686 | C23×C3 | — | 42 | 3 | no | — |
| 687 | C23×C3 | — | 42 | 3 | no | — |
| 688 | C23×C3 | — | 42 | 1 | no | — |
| 689 | C23×C3 | — | 42 | 3 | no | — |
| 690 | C23×C3 | — | 42 | 2 | no | — |
| 691 | C23×C3 | — | 42 | 3 | no | — |
| 692 | C23×C3 | — | 42 | 6 | no | — |
| 693 | C23×C3 | — | 42 | 6 | no | — |
| 694 | C23×C3 | — | 42 | 3 | no | — |
| 695 | C23×C3 | — | 42 | 6 | no | — |
| 696 | C23×C3 | — | 42 | 3 | no | — |
| 697 | C23×C3 | — | 42 | 1 | no | — |
| 698 | C23×C3 | — | 42 | 3 | no | — |
| 699 | C23×C3 | — | 42 | 3 | no | — |
| 700 | C23×C3 | — | 42 | 3 | no | — |
| 701 | C23×C3 | — | 42 | 3 | no | — |
| 702 | C23×C3 | — | 42 | 3 | no | — |
| 703 | C23×C3 | — | 42 | 3 | no | — |
| 704 | C23×C3 | — | 42 | 3 | no | — |
| 705 | C23×C3 | — | 42 | 6 | no | — |
| 706 | C23×C3 | — | 42 | 6 | no | — |
| 707 | C23×C3 | — | 42 | 3 | no | — |
| 708 | C23×C3 | — | 42 | 12 | no | — |
| 709 | C23×C3 | — | 42 | 12 | no | — |
| 710 | C23×C3 | — | 42 | 12 | no | — |
| 711 | C23×C3 | — | 42 | 6 | no | — |
| 712 | C23×C3 | — | 42 | 6 | no | — |
| 713 | C23×C3 | — | 42 | 3 | no | — |
| 714 | C23×C3 | — | 42 | 3 | no | — |
| 715 | C23×C3 | — | 42 | 1 | no | — |
| 716 | C23×C3 | — | 42 | 1 | no | — |
| 717 | C23×C3 | — | 42 | 2 | no | — |
| 718 | C23×C3 | — | 42 | 6 | no | — |
| 719 | C23×C3 | — | 42 | 12 | no | — |
| 720 | C23×C3 | — | 42 | 6 | no | — |
| 721 | C23×C3 | — | 42 | 12 | no | — |
| 722 | C23×C3 | — | 42 | 12 | no | — |
| 723 | C23×C3 | — | 42 | 6 | no | — |
| 724 | C23×C3 | — | 42 | 6 | no | — |
| 725 | C23×C3 | — | 42 | 6 | no | — |
| 726 | C23×C3 | — | 42 | 6 | no | — |
| 727 | C2×A4 | — | 4 | 3 | no | — |
| 728 | C2×A4 | — | 8 | 1 | no | — |
| 729 | C2×A4 | — | 56 | 2 | no | — |
| 730 | C2×A4 | — | 56 | 3 | no | — |
| 731 | C2×A4 | — | 56 | 2 | no | — |
| 732 | C2×A4 | — | 56 | 4 | no | — |
| 733 | C2×A4 | — | 56 | 6 | no | — |
| 734 | C2×A4 | — | 56 | 3 | no | — |
| 735 | S4 | — | 56 | 3 | no | — |
| 736 | C3×D4 | — | 84 | 1 | no | — |
| 737 | C3×D4 | — | 84 | 3 | no | — |
| 738 | C3×D4 | — | 84 | 3 | no | — |
| 739 | C3×D4 | — | 84 | 6 | no | — |
| 740 | C3×D4 | — | 84 | 6 | no | — |
| 741 | C3×D4 | — | 84 | 3 | no | — |
| 742 | C3×D4 | — | 84 | 3 | no | — |
| 743 | C3×D4 | — | 84 | 3 | no | — |
| 744 | C2×C3×C4 | — | 42 | 3 | no | — |
| 745 | C2×C3×C4 | — | 42 | 3 | no | — |
| 746 | C2×C3×C4 | — | 42 | 6 | no | — |
| 747 | C2×C3×C4 | — | 42 | 3 | no | — |
| 748 | C2×C3×C4 | — | 42 | 3 | no | — |
| 749 | C2×C3×C4 | — | 42 | 3 | no | — |
| 750 | #67 | — | 112 | 1 | no | — |
| 751 | C3×C7 | — | 16 | 1 | no | — |
| 752 | ΓL(1,𝔽8) | — | 32 | 1 | no | — |
| 753 | ΓL(1,𝔽8) | #87524 | 1 | 1 | yes | characteristic, complemented |
| 754 | C2×C32 | — | 112 | 1 | no | — |
| 755 | C2×C32 | — | 224 | 1 | no | — |
| 756 | C3×D3 | — | 224 | 1 | no | — |
| 757 | C24 | — | 3 | 3 | no | — |
| 758 | C24 | — | 3 | 3 | no | — |
| 759 | C24 | — | 6 | 1 | no | — |
| 760 | C24 | — | 6 | 1 | no | — |
| 761 | C24 | — | 7 | 3 | no | — |
| 762 | C24 | — | 14 | 1 | no | — |
| 763 | C24 | — | 21 | 1 | no | — |
| 764 | C24 | — | 21 | 3 | no | — |
| 765 | C24 | — | 21 | 3 | no | — |
| 766 | C24 | — | 21 | 3 | no | — |
| 767 | C24 | — | 21 | 6 | no | — |
| 768 | C24 | — | 21 | 6 | no | — |
| 769 | C24 | — | 21 | 1 | no | — |
| 770 | C24 | — | 21 | 3 | no | — |
| 771 | C24 | — | 42 | 1 | no | — |
| 772 | C24 | — | 42 | 3 | no | — |
| 773 | C24 | — | 42 | 3 | no | — |
| 774 | C24 | — | 42 | 3 | no | — |
| 775 | C24 | — | 42 | 3 | no | — |
| 776 | C24 | — | 42 | 3 | no | — |
| 777 | C24 | — | 42 | 3 | no | — |
| 778 | C24 | — | 42 | 3 | no | — |
| 779 | C24 | — | 42 | 2 | no | — |
| 780 | C24 | — | 42 | 2 | no | — |
| 781 | C24 | — | 42 | 3 | no | — |
| 782 | C24 | — | 42 | 6 | no | — |
| 783 | C24 | — | 42 | 3 | no | — |
| 784 | C24 | — | 42 | 12 | no | — |
| 785 | C24 | — | 42 | 12 | no | — |
| 786 | C24 | — | 42 | 2 | no | — |
| 787 | C24 | — | 42 | 2 | no | — |
| 788 | C24 | — | 42 | 6 | no | — |
| 789 | C24 | — | 42 | 6 | no | — |
| 790 | C24 | — | 42 | 6 | no | — |
| 791 | C24 | — | 42 | 6 | no | — |
| 792 | C24 | #4246⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 793 | C2×D4 | — | 42 | 3 | no | — |
| 794 | C2×D4 | — | 42 | 3 | no | — |
| 795 | C2×D4 | — | 42 | 12 | no | — |
| 796 | C2×D4 | — | 42 | 3 | no | — |
| 797 | C2×D4 | — | 42 | 3 | no | — |
| 798 | C2×D4 | — | 42 | 3 | no | — |
| 799 | C2×D4 | — | 42 | 3 | no | — |
| 800 | C2×D4 | — | 42 | 3 | no | — |
| 801 | C2×D4 | — | 42 | 3 | no | — |
| 802 | C2×D4 | — | 42 | 3 | no | — |
| 803 | C2×D4 | — | 42 | 3 | no | — |
| 804 | C22×C4 | — | 3 | 3 | no | — |
| 805 | C22×C4 | — | 3 | 1 | no | — |
| 806 | C22×C4 | — | 21 | 3 | no | — |
| 807 | C22⋊C4 | — | 6 | 3 | no | — |
| 808 | C22⋊C4 | — | 6 | 3 | no | — |
| 809 | C22⋊C4 | — | 6 | 3 | no | — |
| 810 | C22⋊C4 | — | 6 | 3 | no | — |
| 811 | C22⋊C4 | — | 42 | 3 | no | — |
| 812 | C22⋊C4 | — | 42 | 3 | no | — |
| 813 | C22⋊C4 | — | 42 | 12 | no | — |
| 814 | C22⋊C4 | — | 42 | 3 | no | — |
| 815 | C22⋊C4 | — | 42 | 3 | no | — |
| 816 | C22⋊C4 | — | 42 | 3 | no | — |
| 817 | C22⋊C4 | — | 42 | 3 | no | — |
| 818 | C2×C7 | — | 3 | 3 | no | — |
| 819 | C2×C7 | — | 3 | 3 | no | — |
| 820 | C2×C7 | — | 6 | 1 | no | — |
| 821 | C2×C7 | — | 6 | 1 | no | — |
| 822 | C2×C7 | C2×C3×#1020 | 1 | 1 | yes | characteristic |
| 823 | D7 | — | 2 | 1 | no | — |
| 824 | D7 | — | 6 | 2 | no | — |
| 825 | D7 | — | 6 | 3 | no | — |
| 826 | D7 | — | 24 | 1 | no | — |
| 827 | C22×C3 | — | 7 | 1 | no | — |
| 828 | C22×C3 | — | 7 | 3 | no | — |
| 829 | C22×C3 | — | 14 | 1 | no | — |
| 830 | C22×C3 | — | 21 | 3 | no | — |
| 831 | C22×C3 | — | 21 | 3 | no | — |
| 832 | C22×C3 | — | 21 | 3 | no | — |
| 833 | C22×C3 | — | 21 | 1 | no | — |
| 834 | C22×C3 | — | 21 | 3 | no | — |
| 835 | C22×C3 | — | 21 | 3 | no | — |
| 836 | C22×C3 | — | 21 | 3 | no | — |
| 837 | C22×C3 | — | 21 | 6 | no | — |
| 838 | C22×C3 | — | 21 | 6 | no | — |
| 839 | C22×C3 | — | 42 | 1 | no | — |
| 840 | C22×C3 | — | 42 | 3 | no | — |
| 841 | C22×C3 | — | 42 | 6 | no | — |
| 842 | C22×C3 | — | 42 | 3 | no | — |
| 843 | C22×C3 | — | 42 | 3 | no | — |
| 844 | C22×C3 | — | 42 | 1 | no | — |
| 845 | C22×C3 | — | 42 | 1 | no | — |
| 846 | C22×C3 | — | 42 | 3 | no | — |
| 847 | C22×C3 | — | 42 | 3 | no | — |
| 848 | C22×C3 | — | 42 | 2 | no | — |
| 849 | C22×C3 | — | 42 | 2 | no | — |
| 850 | C22×C3 | — | 42 | 3 | no | — |
| 851 | C22×C3 | — | 42 | 12 | no | — |
| 852 | C22×C3 | — | 42 | 3 | no | — |
| 853 | C22×C3 | — | 42 | 3 | no | — |
| 854 | C22×C3 | — | 42 | 12 | no | — |
| 855 | C22×C3 | — | 42 | 3 | no | — |
| 856 | C22×C3 | — | 42 | 2 | no | — |
| 857 | C22×C3 | — | 42 | 6 | no | — |
| 858 | C22×C3 | — | 42 | 6 | no | — |
| 859 | C22×C3 | — | 42 | 6 | no | — |
| 860 | C22×C3 | — | 42 | 2 | no | — |
| 861 | C22×C3 | — | 42 | 6 | no | — |
| 862 | C22×C3 | — | 84 | 1 | no | — |
| 863 | C22×C3 | — | 84 | 3 | no | — |
| 864 | C22×C3 | — | 84 | 3 | no | — |
| 865 | C22×C3 | — | 112 | 1 | no | — |
| 866 | C22×C3 | — | 224 | 1 | no | — |
| 867 | C2×D3 | — | 112 | 1 | no | — |
| 868 | A4 | — | 4 | 3 | no | — |
| 869 | A4 | — | 8 | 1 | no | — |
| 870 | A4 | — | 56 | 2 | no | — |
| 871 | A4 | — | 56 | 3 | no | — |
| 872 | C3×C4 | — | 84 | 1 | no | — |
| 873 | C3×C4 | — | 84 | 3 | no | — |
| 874 | C3×C4 | — | 84 | 3 | no | — |
| 875 | Dic3 | — | 16 | 1 | no | — |
| 876 | C32 | — | 112 | 1 | no | Sylow |
| 877 | C23 | — | 2 | 1 | no | — |
| 878 | C23 | — | 3 | 1 | no | — |
| 879 | C23 | — | 3 | 3 | no | — |
| 880 | C23 | — | 3 | 3 | no | — |
| 881 | C23 | — | 3 | 3 | no | — |
| 882 | C23 | — | 3 | 3 | no | — |
| 883 | C23 | — | 3 | 3 | no | — |
| 884 | C23 | — | 6 | 1 | no | — |
| 885 | C23 | — | 6 | 1 | no | — |
| 886 | C23 | — | 6 | 6 | no | — |
| 887 | C23 | — | 6 | 3 | no | — |
| 888 | C23 | — | 6 | 3 | no | — |
| 889 | C23 | — | 6 | 3 | no | — |
| 890 | C23 | — | 14 | 2 | no | — |
| 891 | C23 | — | 14 | 3 | no | — |
| 892 | C23 | — | 21 | 3 | no | — |
| 893 | C23 | — | 21 | 3 | no | — |
| 894 | C23 | — | 21 | 12 | no | — |
| 895 | C23 | — | 21 | 3 | no | — |
| 896 | C23 | — | 21 | 3 | no | — |
| 897 | C23 | — | 42 | 2 | no | — |
| 898 | C23 | — | 42 | 3 | no | — |
| 899 | C23 | — | 42 | 6 | no | — |
| 900 | C23 | — | 42 | 6 | no | — |
| 901 | C23 | — | 42 | 3 | no | — |
| 902 | C23 | — | 42 | 3 | no | — |
| 903 | C23 | — | 42 | 3 | no | — |
| 904 | C23 | — | 42 | 1 | no | — |
| 905 | C23 | — | 42 | 3 | no | — |
| 906 | C23 | — | 42 | 3 | no | — |
| 907 | C23 | — | 42 | 3 | no | — |
| 908 | C23 | — | 42 | 3 | no | — |
| 909 | C23 | — | 42 | 3 | no | — |
| 910 | C23 | — | 42 | 6 | no | — |
| 911 | C23 | — | 42 | 6 | no | — |
| 912 | C23 | — | 42 | 3 | no | — |
| 913 | C23 | — | 42 | 1 | no | — |
| 914 | C23 | — | 42 | 3 | no | — |
| 915 | C23 | — | 42 | 1 | no | — |
| 916 | C23 | — | 42 | 6 | no | — |
| 917 | C23 | — | 42 | 3 | no | — |
| 918 | C23 | — | 42 | 12 | no | — |
| 919 | C23 | — | 42 | 12 | no | — |
| 920 | C23 | — | 42 | 12 | no | — |
| 921 | C23 | — | 42 | 6 | no | — |
| 922 | C23 | — | 42 | 6 | no | — |
| 923 | C23 | — | 42 | 3 | no | — |
| 924 | C23 | — | 42 | 2 | no | — |
| 925 | C23 | — | 42 | 1 | no | — |
| 926 | C23 | — | 42 | 6 | no | — |
| 927 | C23 | — | 42 | 12 | no | — |
| 928 | C23 | — | 42 | 6 | no | — |
| 929 | C23 | — | 42 | 12 | no | — |
| 930 | C23 | — | 42 | 12 | no | — |
| 931 | C23 | — | 42 | 6 | no | — |
| 932 | C23 | — | 42 | 6 | no | — |
| 933 | C23 | — | 42 | 6 | no | — |
| 934 | C23 | — | 42 | 6 | no | — |
| 935 | C23 | — | 42 | 3 | no | — |
| 936 | C23 | S4×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 937 | D4 | — | 84 | 1 | no | — |
| 938 | D4 | — | 84 | 6 | no | — |
| 939 | D4 | — | 84 | 6 | no | — |
| 940 | D4 | — | 84 | 3 | no | — |
| 941 | D4 | — | 84 | 3 | no | — |
| 942 | D4 | — | 84 | 3 | no | — |
| 943 | D4 | — | 84 | 3 | no | — |
| 944 | D4 | — | 84 | 3 | no | — |
| 945 | C2×C4 | — | 6 | 6 | no | — |
| 946 | C2×C4 | — | 6 | 3 | no | — |
| 947 | C2×C4 | — | 6 | 3 | no | — |
| 948 | C2×C4 | — | 42 | 3 | no | — |
| 949 | C2×C4 | — | 42 | 3 | no | — |
| 950 | C2×C4 | — | 42 | 3 | no | — |
| 951 | C7 | C3×#87524 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 952 | C2×C3 | — | 7 | 1 | no | — |
| 953 | C2×C3 | — | 14 | 1 | no | — |
| 954 | C2×C3 | — | 16 | 1 | no | — |
| 955 | C2×C3 | — | 21 | 3 | no | — |
| 956 | C2×C3 | — | 21 | 3 | no | — |
| 957 | C2×C3 | — | 42 | 1 | no | — |
| 958 | C2×C3 | — | 42 | 1 | no | — |
| 959 | C2×C3 | — | 42 | 3 | no | — |
| 960 | C2×C3 | — | 42 | 2 | no | — |
| 961 | C2×C3 | — | 168 | 1 | no | — |
| 962 | C2×C3 | — | 224 | 1 | no | — |
| 963 | C2×C3 | — | 224 | 2 | no | — |
| 964 | C2×C3 | — | 224 | 1 | no | — |
| 965 | D3 | — | 224 | 1 | no | — |
| 966 | C22 | — | 2 | 1 | no | — |
| 967 | C22 | — | 3 | 3 | no | — |
| 968 | C22 | — | 3 | 3 | no | — |
| 969 | C22 | — | 3 | 1 | no | — |
| 970 | C22 | — | 3 | 3 | no | — |
| 971 | C22 | — | 3 | 3 | no | — |
| 972 | C22 | — | 3 | 3 | no | — |
| 973 | C22 | — | 6 | 3 | no | — |
| 974 | C22 | — | 6 | 6 | no | — |
| 975 | C22 | — | 6 | 3 | no | — |
| 976 | C22 | — | 6 | 3 | no | — |
| 977 | C22 | — | 6 | 1 | no | — |
| 978 | C22 | — | 6 | 1 | no | — |
| 979 | C22 | — | 7 | 1 | no | — |
| 980 | C22 | — | 21 | 6 | no | — |
| 981 | C22 | — | 21 | 6 | no | — |
| 982 | C22 | — | 21 | 3 | no | — |
| 983 | C22 | — | 42 | 3 | no | — |
| 984 | C22 | — | 42 | 3 | no | — |
| 985 | C22 | — | 42 | 3 | no | — |
| 986 | C22 | — | 42 | 12 | no | — |
| 987 | C22 | — | 42 | 3 | no | — |
| 988 | C22 | — | 42 | 12 | no | — |
| 989 | C22 | — | 42 | 3 | no | — |
| 990 | C22 | — | 42 | 3 | no | — |
| 991 | C22 | — | 42 | 2 | no | — |
| 992 | C22 | — | 42 | 2 | no | — |
| 993 | C22 | — | 42 | 2 | no | — |
| 994 | C22 | — | 42 | 6 | no | — |
| 995 | C22 | — | 42 | 6 | no | — |
| 996 | C22 | — | 42 | 6 | no | — |
| 997 | C22 | — | 42 | 2 | no | — |
| 998 | C22 | — | 42 | 6 | no | — |
| 999 | C22 | — | 42 | 1 | no | — |
| 1000 | C22 | — | 84 | 3 | no | — |
| 1001 | C22 | — | 84 | 3 | no | — |
| 1002 | C22 | — | 84 | 1 | no | — |
| 1003 | C22 | #72222255 | 1 | 3 | yes | complemented |
| 1004 | C4 | — | 12 | 3 | no | — |
| 1005 | C4 | — | 12 | 1 | no | — |
| 1006 | C4 | — | 84 | 3 | no | — |
| 1007 | C3 | — | 7 | 1 | no | — |
| 1008 | C3 | — | 16 | 1 | no | — |
| 1009 | C3 | — | 224 | 1 | no | — |
| 1010 | C2 | — | 3 | 3 | no | — |
| 1011 | C2 | — | 3 | 3 | no | — |
| 1012 | C2 | — | 6 | 1 | no | — |
| 1013 | C2 | — | 6 | 1 | no | — |
| 1014 | C2 | — | 14 | 1 | no | — |
| 1015 | C2 | — | 42 | 2 | no | — |
| 1016 | C2 | — | 42 | 3 | no | — |
| 1017 | C2 | — | 168 | 1 | no | — |
| 1018 | C2 | AGL(1,𝔽7)×#1020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽7)×#1020 |
| commutator, cosocle | C2×C7×C22⋊A4 | C22×C3 |
| Fitting, socle | C25×C7 | C2×C3×D3 |
| hypocenter | C7×C22⋊A4 | C3×D4 |
| LCS | G ▷ C2×C7×C22⋊A4 ▷ C7×C22⋊A4 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #72276689 | C3 | semidirect |
| 2. ΓL(1,𝔽8)×#5936 | C2 | semidirect |
| 4. C2×#72214032 | C2 | semidirect |
| 5. C2×AGL(1,𝔽7)×C22⋊A4 | C2 | semidirect |
| 11. C2×D7×C22⋊A4 | C2×C3 | semidirect |
| 12. C25×AGL(1,𝔽7) | D3 | semidirect |
| 13. C2×C7⋊#1020 | C2×C3 | semidirect |
| 14. C7×#5936 | C2×C3 | semidirect |
| 22. ΓL(1,𝔽8)×C22⋊A4 | D4 | semidirect |
| 68. C25×D7 | C3×D3 | semidirect |
| 78. C7×C22⋊A4 | C3×D4 | semidirect |
| 83. C24×ΓL(1,𝔽8) | #67 | semidirect |
| 118. C23×AGL(1,𝔽7) | S4 | semidirect |
| 184. #5936 | AGL(1,𝔽7) | semidirect |
| 288. C24×C7 | C3×#67 | semidirect |
| 319. C23×D7 | C3×S4 | semidirect |
| 395. C22×ΓL(1,𝔽8) | GL(2,ℤ/4) | semidirect |
| 420. C2×AGL(1,𝔽7) | #1020 | semidirect |
| 550. C22⋊A4 | C4⋊AGL(1,𝔽7) | semidirect |
| 639. C22×C7 | C3×GL(2,ℤ/4) | semidirect |
| 663. C2×D7 | C3×#1020 | semidirect |
| 753. ΓL(1,𝔽8) | #87524 | semidirect |
| 792. C24 | #4246⋊C3 | semidirect |
| 951. C7 | C3×#87524 | semidirect |
| 1003. C22 | #72222255 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72276689 | 3 |
| ΓL(1,𝔽8)×#5936 | 2 |
| #72276489 | 3 |
| C2×#72214032 | 2 |
| C2×AGL(1,𝔽7)×C22⋊A4 | 2 |
| #72222255 | 4 |
| C3×#87524 | 7 |