Finite Group DatabasebetaFinite Group DatabasebetaOrder 8064.
1104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 40 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 | #72259859 | — | 3 | 1 | no | maximal |
| 2 | #72259855 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | ΓL(1,𝔽8)×#5933 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #72229375 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #72218844 | — | 4 | 2 | no | maximal |
| 6 | #72218843 | — | 4 | 1 | no | maximal |
| 7 | #72214048 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | ΓL(1,𝔽8)×#997 | C22 | 1 | 1 | yes | characteristic |
| 9 | #13062210 | — | 2 | 1 | no | — |
| 10 | #13062205 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | #13062156 | D3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C7⋊#5935 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | C7×#5933 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #90468⋊C3 | — | 3 | 2 | no | — |
| 15 | #90359⋊C3 | — | 3 | 1 | no | — |
| 16 | ΓL(1,𝔽8)×#455 | — | 3 | 1 | no | — |
| 17 | #90013⋊C3 | — | 3 | 1 | no | — |
| 18 | #89977⋊C3 | — | 3 | 2 | no | — |
| 19 | #89833⋊C3 | — | 3 | 1 | no | — |
| 20 | #89599⋊C3 | — | 3 | 2 | no | — |
| 21 | #104×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 22 | #89519⋊C3 | — | 3 | 1 | no | — |
| 23 | #89517⋊C3 | — | 3 | 1 | no | — |
| 24 | C3×#87520 | — | 7 | 1 | no | maximal, Hall |
| 25 | C2×A4⋊AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 26 | A4×ΓL(1,𝔽8)⋊C4 | — | 4 | 1 | no | — |
| 27 | A4×ΓL(1,𝔽8)⋊C4 | — | 8 | 1 | no | — |
| 28 | ΓL(1,𝔽8)⋊(#41⋊C3) | — | 4 | 2 | no | — |
| 29 | ΓL(1,𝔽8)⋊GL(2,𝔽3) | — | 4 | 2 | no | — |
| 30 | ΓL(1,𝔽8)×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 31 | ΓL(1,𝔽8)×#226 | — | 4 | 2 | no | — |
| 32 | #11737736 | — | 3 | 1 | no | Hall |
| 33 | C7⋊#997 | — | 2 | 1 | no | — |
| 34 | C7×#997 | C22×C3 | 1 | 1 | yes | characteristic |
| 35 | ΓL(1,𝔽8)×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 36 | #10621519 | — | 3 | 2 | no | — |
| 37 | #41×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 38 | C2×#66659 | — | 3 | 1 | no | — |
| 39 | #6548⋊C3 | — | 3 | 1 | no | — |
| 40 | #6548⋊C3 | — | 6 | 1 | no | — |
| 41 | C2×#1159⋊C3 | — | 3 | 1 | no | — |
| 42 | C2×#1159⋊C3 | — | 6 | 1 | no | — |
| 43 | (C7⋊S4)⋊C4 | — | 4 | 1 | no | — |
| 44 | #10621471 | — | 4 | 2 | no | — |
| 45 | ΓL(1,𝔽8)×#137 | — | 3 | 2 | no | — |
| 46 | ΓL(1,𝔽8)×#124 | — | 3 | 1 | no | — |
| 47 | #6512⋊C3 | — | 3 | 2 | no | — |
| 48 | #6507⋊C3 | — | 3 | 1 | no | — |
| 49 | #6505⋊C3 | — | 3 | 2 | no | — |
| 50 | #6503⋊C3 | — | 3 | 1 | no | — |
| 51 | #6482⋊C3 | — | 6 | 2 | no | — |
| 52 | #6481⋊C3 | — | 6 | 2 | no | — |
| 53 | #6479⋊C3 | — | 6 | 2 | no | — |
| 54 | #6477⋊C3 | — | 6 | 2 | no | — |
| 55 | #6471⋊C3 | — | 3 | 2 | no | — |
| 56 | M16×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 57 | #6447⋊C3 | — | 6 | 1 | no | — |
| 58 | #6447⋊C3 | — | 6 | 1 | no | — |
| 59 | ((C22⋊D7)⋊C3)⋊C4 | — | 6 | 1 | no | — |
| 60 | ((C22⋊D7)⋊C3)⋊C4 | — | 6 | 1 | no | — |
| 61 | #6438⋊C3 | — | 3 | 1 | no | — |
| 62 | C42×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 63 | ΓL(1,𝔽8)×#104 | — | 3 | 2 | no | — |
| 64 | ΓL(1,𝔽8)×#100 | — | 3 | 1 | no | — |
| 65 | #6411⋊C3 | — | 3 | 2 | no | — |
| 66 | #6407⋊C3 | — | 3 | 1 | no | — |
| 67 | #6399⋊C3 | — | 3 | 2 | no | — |
| 68 | #6398⋊C3 | — | 3 | 2 | no | — |
| 69 | #6379⋊C3 | — | 3 | 2 | no | — |
| 70 | C3×#5950 | — | 7 | 1 | no | — |
| 71 | C3×#5935 | — | 7 | 1 | no | — |
| 72 | C3×#5933 | — | 7 | 1 | no | — |
| 73 | C2×A4×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 74 | C2×A4×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 75 | A4⋊AGL(1,𝔽7) | — | 4 | 2 | no | — |
| 76 | ΓL(1,𝔽8)×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 77 | (C3⋊AGL(1,𝔽7))⋊C4 | — | 16 | 1 | no | — |
| 78 | #90618 | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 79 | #90468 | — | 3 | 2 | no | — |
| 80 | #90359 | — | 3 | 1 | no | — |
| 81 | C7×#455 | — | 3 | 1 | no | — |
| 82 | #90013 | — | 3 | 1 | no | — |
| 83 | #89977 | — | 3 | 2 | no | — |
| 84 | #89833 | — | 3 | 1 | no | — |
| 85 | #89599 | — | 3 | 2 | no | — |
| 86 | D7×#104 | — | 3 | 2 | no | — |
| 87 | #89519 | — | 3 | 1 | no | — |
| 88 | #89517 | — | 3 | 1 | no | — |
| 89 | #87520 | — | 7 | 1 | no | — |
| 90 | C3×#3018 | — | 21 | 1 | no | — |
| 91 | C2×C7⋊S4 | — | 4 | 1 | no | — |
| 92 | #41×ΓL(1,𝔽8) | — | 3 | 2 | no | — |
| 93 | C2×Q8×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 94 | C2×D4×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 95 | C2×D4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 96 | Dic7⋊A4 | — | 8 | 2 | no | — |
| 97 | Dic7⋊A4 | — | 8 | 1 | no | — |
| 98 | #66665 | — | 8 | 2 | no | — |
| 99 | A4×Dic7 | — | 4 | 1 | no | — |
| 100 | A4×Dic7 | — | 8 | 1 | no | — |
| 101 | #66662 | — | 4 | 2 | no | — |
| 102 | C2×(C22⋊D7)⋊C3 | — | 3 | 1 | no | — |
| 103 | C2×(C22⋊D7)⋊C3 | — | 3 | 1 | no | — |
| 104 | C2×(C22⋊D7)⋊C3 | — | 6 | 1 | no | — |
| 105 | C2×(C22⋊D7)⋊C3 | — | 6 | 1 | no | — |
| 106 | C2×(C22⋊D7)⋊C3 | — | 6 | 1 | no | — |
| 107 | C2×(C22⋊D7)⋊C3 | — | 6 | 1 | no | — |
| 108 | C22×ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 109 | C22×ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 110 | C22×ΓL(1,𝔽8)⋊C4 | S4 | 1 | 1 | yes | characteristic |
| 111 | #66659 | — | 6 | 2 | no | — |
| 112 | #66659 | — | 6 | 2 | no | — |
| 113 | #66659 | S4 | 1 | 2 | yes | complemented |
| 114 | Q8×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 115 | #1159⋊C3 | — | 3 | 2 | no | — |
| 116 | #1159⋊C3 | — | 6 | 2 | no | — |
| 117 | #1159⋊C3 | — | 6 | 2 | no | — |
| 118 | #1159⋊C3 | — | 6 | 2 | no | — |
| 119 | #1159⋊C3 | — | 6 | 2 | no | — |
| 120 | D4×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 121 | D4×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 122 | #1157⋊C3 | — | 3 | 2 | no | — |
| 123 | #1157⋊C3 | — | 6 | 2 | no | — |
| 124 | C2×C4⋊AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 125 | C2×C4⋊AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 126 | C2×C4×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 127 | C2×C4×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 128 | C2×C4×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 129 | C2×C4×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 130 | C2×ΓL(1,𝔽8)⋊Q8 | — | 3 | 1 | no | — |
| 131 | C2×ΓL(1,𝔽8)⋊Q8 | — | 6 | 1 | no | — |
| 132 | C7⋊GL(2,𝔽3) | — | 4 | 2 | no | — |
| 133 | C7×SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 134 | C7×#226 | — | 4 | 2 | no | — |
| 135 | Q16×ΓL(1,𝔽8) | — | 6 | 2 | no | — |
| 136 | SD16×ΓL(1,𝔽8) | — | 6 | 2 | no | — |
| 137 | M16×ΓL(1,𝔽8) | — | 3 | 2 | no | — |
| 138 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 139 | C22⋊C4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 140 | C42×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 141 | #1144⋊C3 | — | 6 | 2 | no | — |
| 142 | #1143⋊C3 | — | 6 | 2 | no | — |
| 143 | #1143⋊C3 | — | 6 | 2 | no | — |
| 144 | #1141⋊C3 | — | 6 | 2 | no | — |
| 145 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 1 | no | — |
| 146 | (C2×AGL(1,𝔽7))⋊C4 | — | 6 | 1 | no | — |
| 147 | (ΓL(1,𝔽8)⋊C4)⋊C4 | — | 6 | 1 | no | — |
| 148 | (ΓL(1,𝔽8)⋊C4)⋊C4 | — | 6 | 1 | no | — |
| 149 | C4×ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 150 | C4×ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 151 | #1136⋊C3 | — | 3 | 2 | no | — |
| 152 | D56⋊C3 | — | 6 | 2 | no | — |
| 153 | #1132⋊C3 | — | 6 | 2 | no | — |
| 154 | #1131⋊C3 | — | 6 | 2 | no | — |
| 155 | C8×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 156 | C3×#997 | — | 7 | 1 | no | — |
| 157 | C3×#985 | — | 28 | 2 | no | — |
| 158 | C3×C4×S4 | — | 28 | 1 | no | — |
| 159 | C2×C3⋊AGL(1,𝔽7) | — | 16 | 1 | no | — |
| 160 | A4×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 161 | A4×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 162 | Dic3×ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 163 | C3×ΓL(1,𝔽8)⋊C4 | — | 16 | 1 | no | — |
| 164 | C7×H(5,𝔽2) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 165 | #6554 | — | 3 | 2 | no | — |
| 166 | D7×#41 | — | 3 | 2 | no | — |
| 167 | C2×#1161 | — | 3 | 1 | no | — |
| 168 | #6548 | — | 3 | 1 | no | — |
| 169 | #6548 | — | 6 | 1 | no | — |
| 170 | C2×#1159 | — | 3 | 1 | no | — |
| 171 | C2×#1159 | — | 6 | 1 | no | — |
| 172 | C7×#137 | — | 3 | 2 | no | — |
| 173 | C7×#124 | — | 3 | 1 | no | — |
| 174 | #6512 | — | 3 | 2 | no | — |
| 175 | #6507 | — | 3 | 1 | no | — |
| 176 | #6505 | — | 3 | 2 | no | — |
| 177 | #6503 | — | 3 | 1 | no | — |
| 178 | #6482 | — | 6 | 2 | no | — |
| 179 | #6481 | — | 6 | 2 | no | — |
| 180 | #6479 | — | 6 | 2 | no | — |
| 181 | #6477 | — | 6 | 2 | no | — |
| 182 | #6471 | — | 3 | 2 | no | — |
| 183 | D7×M16 | — | 3 | 2 | no | — |
| 184 | #6447 | — | 6 | 1 | no | — |
| 185 | #6447 | — | 6 | 1 | no | — |
| 186 | (C22⋊D7)⋊C4 | — | 6 | 1 | no | — |
| 187 | (C22⋊D7)⋊C4 | — | 6 | 1 | no | — |
| 188 | #6438 | — | 3 | 1 | no | — |
| 189 | C42×D7 | — | 3 | 1 | no | — |
| 190 | C7×#104 | — | 3 | 2 | no | — |
| 191 | C7×#100 | — | 3 | 1 | no | — |
| 192 | #6411 | — | 3 | 2 | no | — |
| 193 | #6407 | — | 3 | 1 | no | — |
| 194 | #6399 | — | 3 | 2 | no | — |
| 195 | #6398 | — | 3 | 2 | no | — |
| 196 | #6379 | — | 3 | 2 | no | — |
| 197 | C3×#585 | — | 7 | 1 | no | — |
| 198 | #5950 | — | 7 | 1 | no | — |
| 199 | #5950 | — | 14 | 1 | no | — |
| 200 | #5935 | — | 7 | 1 | no | — |
| 201 | #5933 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 202 | C3×#575 | — | 21 | 2 | no | — |
| 203 | C3×#532 | — | 21 | 1 | no | — |
| 204 | C3×#456 | — | 21 | 2 | no | — |
| 205 | C3×#455 | — | 21 | 1 | no | — |
| 206 | C3×#455 | — | 21 | 1 | no | — |
| 207 | C3×#454 | — | 21 | 2 | no | — |
| 208 | C3×#453 | — | 21 | 1 | no | — |
| 209 | C3×#453 | — | 21 | 1 | no | — |
| 210 | C2×C3×#104 | — | 21 | 2 | no | — |
| 211 | C3×#413 | — | 21 | 1 | no | — |
| 212 | C2×C22⋊ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 213 | C2×C22⋊ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 214 | C2×C7×A4 | — | 4 | 1 | no | — |
| 215 | C2×C7×A4 | — | 8 | 1 | no | — |
| 216 | C23×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 217 | C23×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 218 | C23×ΓL(1,𝔽8) | C2×S4 | 1 | 1 | yes | characteristic |
| 219 | C22×AGL(1,𝔽7) | — | 3 | 1 | no | — |
| 220 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 221 | C22×AGL(1,𝔽7) | — | 6 | 1 | no | — |
| 222 | C7⋊S4 | — | 4 | 2 | no | — |
| 223 | C7⋊SL(2,𝔽3) | — | 8 | 2 | no | — |
| 224 | C7×SL(2,𝔽3) | — | 4 | 2 | no | — |
| 225 | Q8×ΓL(1,𝔽8) | — | 6 | 2 | no | — |
| 226 | Q8×ΓL(1,𝔽8) | C2×S4 | 1 | 2 | yes | — |
| 227 | D4×ΓL(1,𝔽8) | — | 3 | 2 | no | — |
| 228 | D4×ΓL(1,𝔽8) | — | 6 | 2 | no | — |
| 229 | C2×C4×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 230 | C2×C4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 231 | C2×C4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 232 | C2×C4×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 233 | D21⋊C4 | — | 16 | 1 | no | — |
| 234 | (C22⋊D7)⋊C3 | — | 6 | 2 | no | — |
| 235 | (C22⋊D7)⋊C3 | — | 6 | 2 | no | — |
| 236 | (C22⋊D7)⋊C3 | — | 6 | 2 | no | — |
| 237 | (C22⋊D7)⋊C3 | — | 12 | 2 | no | — |
| 238 | (C22⋊D7)⋊C3 | — | 12 | 2 | no | — |
| 239 | C2×ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 240 | C2×ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 241 | C2×ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 242 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 243 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 244 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 245 | C2×ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 246 | C4⋊AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 247 | C4⋊AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 248 | C4⋊AGL(1,𝔽7) | — | 12 | 2 | no | — |
| 249 | C4×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 250 | C4×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 251 | C4×AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 252 | C4×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 253 | C4×AGL(1,𝔽7) | — | 12 | 2 | no | — |
| 254 | C4×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 255 | ΓL(1,𝔽8)⋊Q8 | — | 3 | 2 | no | — |
| 256 | ΓL(1,𝔽8)⋊Q8 | — | 6 | 2 | no | — |
| 257 | C8×ΓL(1,𝔽8) | — | 6 | 2 | no | — |
| 258 | ΓL(1,𝔽8)⋊C8 | — | 6 | 2 | no | — |
| 259 | C2×C3×S4 | — | 28 | 1 | no | — |
| 260 | C3×#41⋊C3 | — | 28 | 2 | no | — |
| 261 | C3×C4×A4 | — | 28 | 1 | no | — |
| 262 | C3×C4×A4 | — | 56 | 1 | no | — |
| 263 | C3×SL(2,ℤ/4) | — | 28 | 1 | no | — |
| 264 | C3×GL(2,𝔽3) | — | 28 | 2 | no | — |
| 265 | C3×#226 | — | 28 | 2 | no | — |
| 266 | #3018 | — | 21 | 1 | no | Sylow |
| 267 | C2×C3×ΓL(1,𝔽8) | — | 16 | 1 | no | — |
| 268 | C3⋊AGL(1,𝔽7) | — | 16 | 2 | no | — |
| 269 | C7×#41 | — | 3 | 2 | no | — |
| 270 | C2×C7×Q8 | — | 3 | 1 | no | — |
| 271 | C2×C7×D4 | — | 3 | 1 | no | — |
| 272 | C2×C7×D4 | — | 6 | 1 | no | — |
| 273 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 274 | C2×C22⋊D7 | — | 3 | 1 | no | — |
| 275 | C2×C22⋊D7 | — | 6 | 1 | no | — |
| 276 | C2×C22⋊D7 | — | 6 | 1 | no | — |
| 277 | C2×C22⋊D7 | — | 6 | 1 | no | — |
| 278 | C2×C22⋊D7 | — | 6 | 1 | no | — |
| 279 | C22×Dic7 | — | 2 | 1 | no | — |
| 280 | C22×Dic7 | — | 3 | 1 | no | — |
| 281 | C22×Dic7 | C3×S4 | 1 | 1 | yes | characteristic |
| 282 | #1161 | — | 6 | 2 | no | — |
| 283 | #1161 | — | 6 | 2 | no | — |
| 284 | #1161 | C3×S4 | 1 | 2 | yes | complemented |
| 285 | Q8×D7 | — | 3 | 2 | no | — |
| 286 | #1159 | — | 3 | 2 | no | — |
| 287 | #1159 | — | 6 | 2 | no | — |
| 288 | #1159 | — | 6 | 2 | no | — |
| 289 | #1159 | — | 6 | 2 | no | — |
| 290 | #1159 | — | 6 | 2 | no | — |
| 291 | D4×D7 | — | 3 | 2 | no | — |
| 292 | D4×D7 | — | 6 | 2 | no | — |
| 293 | #1157 | — | 3 | 2 | no | — |
| 294 | #1157 | — | 6 | 2 | no | — |
| 295 | C2×D28 | — | 3 | 1 | no | — |
| 296 | C2×D28 | — | 6 | 1 | no | — |
| 297 | C2×C4×D7 | — | 3 | 1 | no | — |
| 298 | C2×C4×D7 | — | 6 | 1 | no | — |
| 299 | C2×C4×D7 | — | 6 | 1 | no | — |
| 300 | C2×C4×D7 | — | 6 | 1 | no | — |
| 301 | C2×Dic14 | — | 3 | 1 | no | — |
| 302 | C2×Dic14 | — | 6 | 1 | no | — |
| 303 | C7×Q16 | — | 6 | 2 | no | — |
| 304 | C7×SD16 | — | 6 | 2 | no | — |
| 305 | C7×M16 | — | 3 | 2 | no | — |
| 306 | C7×C22⋊C4 | — | 6 | 1 | no | — |
| 307 | C7×C22⋊C4 | — | 6 | 1 | no | — |
| 308 | C42×C7 | — | 3 | 1 | no | — |
| 309 | #1144 | — | 6 | 2 | no | — |
| 310 | #1143 | — | 6 | 2 | no | — |
| 311 | #1143 | — | 6 | 2 | no | — |
| 312 | #1141 | — | 6 | 2 | no | — |
| 313 | (C2×D7)⋊C4 | — | 6 | 1 | no | — |
| 314 | (C2×D7)⋊C4 | — | 6 | 1 | no | — |
| 315 | Dic7⋊C4 | — | 6 | 1 | no | — |
| 316 | Dic7⋊C4 | — | 6 | 1 | no | — |
| 317 | C4×Dic7 | — | 3 | 1 | no | — |
| 318 | C4×Dic7 | — | 6 | 1 | no | — |
| 319 | #1136 | — | 3 | 2 | no | — |
| 320 | D56 | — | 6 | 2 | no | — |
| 321 | #1132 | — | 6 | 2 | no | — |
| 322 | #1131 | — | 6 | 2 | no | — |
| 323 | C8×D7 | — | 6 | 2 | no | — |
| 324 | C3×2−1+4 | — | 21 | 2 | no | — |
| 325 | C3×H(5,𝔽2) | — | 7 | 1 | no | — |
| 326 | C3×H(5,𝔽2) | — | 21 | 1 | no | — |
| 327 | C3×H(5,𝔽2) | — | 42 | 1 | no | — |
| 328 | C2×C3×#41 | — | 21 | 1 | no | — |
| 329 | C2×C3×#41 | — | 21 | 2 | no | — |
| 330 | C2×C3×#41 | — | 21 | 1 | no | — |
| 331 | C2×C3×#41 | — | 42 | 1 | no | — |
| 332 | #997 | — | 14 | 1 | no | — |
| 333 | #997 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 334 | #985 | — | 28 | 2 | no | — |
| 335 | C4×S4 | — | 28 | 1 | no | — |
| 336 | C3×#137 | — | 21 | 2 | no | — |
| 337 | C3×#137 | — | 21 | 2 | no | — |
| 338 | C3×#137 | — | 42 | 2 | no | — |
| 339 | C3×AGL(1,ℤ/8) | — | 21 | 2 | no | — |
| 340 | C3×AGL(1,ℤ/8) | — | 21 | 2 | no | — |
| 341 | C3×AGL(1,ℤ/8) | — | 42 | 2 | no | — |
| 342 | C3×#135 | — | 42 | 2 | no | — |
| 343 | C3×#135 | — | 42 | 2 | no | — |
| 344 | C2×C3×M16 | — | 21 | 2 | no | — |
| 345 | C3×C4⋊Q8 | — | 21 | 1 | no | — |
| 346 | C3×#127 | — | 21 | 1 | no | — |
| 347 | C3×#124 | — | 21 | 1 | no | — |
| 348 | C3×#124 | — | 21 | 1 | no | — |
| 349 | C3×#121 | — | 42 | 1 | no | — |
| 350 | C3×#121 | — | 42 | 1 | no | — |
| 351 | C3×C4×D4 | — | 42 | 1 | no | — |
| 352 | C3×C4×D4 | — | 42 | 1 | no | — |
| 353 | C2×C3×C42 | — | 21 | 1 | no | — |
| 354 | C3×#104 | — | 21 | 2 | no | — |
| 355 | C3×#104 | — | 21 | 2 | no | — |
| 356 | C3×#104 | — | 21 | 2 | no | — |
| 357 | C3×#104 | — | 21 | 2 | no | — |
| 358 | C3×#101 | — | 21 | 2 | no | — |
| 359 | C3×#100 | — | 21 | 1 | no | — |
| 360 | C3×#100 | — | 21 | 1 | no | — |
| 361 | C2×D21 | — | 16 | 1 | no | — |
| 362 | C22⋊ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 363 | C22⋊ΓL(1,𝔽8) | — | 8 | 2 | no | — |
| 364 | C7×A4 | — | 4 | 1 | no | — |
| 365 | C7×A4 | — | 8 | 1 | no | — |
| 366 | C22×ΓL(1,𝔽8) | — | 3 | 1 | no | — |
| 367 | C22×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 368 | C22×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 369 | C22×ΓL(1,𝔽8) | — | 8 | 1 | no | — |
| 370 | C22×ΓL(1,𝔽8) | — | 12 | 1 | no | — |
| 371 | C2×AGL(1,𝔽7) | — | 3 | 2 | no | — |
| 372 | C2×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 373 | C2×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 374 | C2×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 375 | C2×AGL(1,𝔽7) | — | 12 | 1 | no | — |
| 376 | C2×AGL(1,𝔽7) | — | 24 | 1 | no | — |
| 377 | C3×Dic7 | — | 16 | 1 | no | — |
| 378 | C7×Dic3 | — | 16 | 1 | no | — |
| 379 | C4×ΓL(1,𝔽8) | — | 3 | 2 | no | — |
| 380 | C4×ΓL(1,𝔽8) | — | 12 | 1 | no | — |
| 381 | C4×ΓL(1,𝔽8) | — | 12 | 1 | no | — |
| 382 | ΓL(1,𝔽8)⋊C4 | — | 3 | 1 | no | — |
| 383 | ΓL(1,𝔽8)⋊C4 | — | 6 | 2 | no | — |
| 384 | ΓL(1,𝔽8)⋊C4 | — | 6 | 1 | no | — |
| 385 | ΓL(1,𝔽8)⋊C4 | — | 32 | 1 | no | — |
| 386 | ΓL(1,𝔽8)⋊C4 | #1020 | 1 | 1 | yes | characteristic |
| 387 | C2×C3×A4 | — | 28 | 1 | no | — |
| 388 | C2×C3×A4 | — | 56 | 1 | no | — |
| 389 | C3×S4 | — | 28 | 2 | no | — |
| 390 | C3×C4×D3 | — | 112 | 1 | no | — |
| 391 | C3×SL(2,𝔽3) | — | 28 | 2 | no | — |
| 392 | #585 | — | 7 | 1 | no | — |
| 393 | #575 | — | 21 | 2 | no | — |
| 394 | #532 | — | 21 | 1 | no | — |
| 395 | #456 | — | 21 | 2 | no | — |
| 396 | #455 | — | 3 | 1 | no | — |
| 397 | #455 | — | 21 | 1 | no | — |
| 398 | #454 | — | 21 | 2 | no | — |
| 399 | #453 | — | 21 | 1 | no | — |
| 400 | #453 | — | 21 | 1 | no | — |
| 401 | C2×#104 | — | 21 | 2 | no | — |
| 402 | #413 | — | 21 | 1 | no | — |
| 403 | C3×ΓL(1,𝔽8) | — | 16 | 1 | no | Hall |
| 404 | C23×C7 | — | 2 | 1 | no | — |
| 405 | C23×C7 | — | 3 | 1 | no | — |
| 406 | C23×C7 | C2×C3×S4 | 1 | 1 | yes | characteristic |
| 407 | C22×D7 | — | 3 | 1 | no | — |
| 408 | C22×D7 | — | 6 | 1 | no | — |
| 409 | C22×D7 | — | 6 | 1 | no | — |
| 410 | C7×Q8 | — | 6 | 2 | no | — |
| 411 | C7×Q8 | C2×C3×S4 | 1 | 2 | yes | — |
| 412 | C7×D4 | — | 3 | 2 | no | — |
| 413 | C7×D4 | — | 6 | 2 | no | — |
| 414 | C2×C4×C7 | — | 3 | 1 | no | — |
| 415 | C2×C4×C7 | — | 6 | 1 | no | — |
| 416 | C2×C4×C7 | — | 6 | 1 | no | — |
| 417 | C2×C4×C7 | — | 6 | 1 | no | — |
| 418 | C22⋊D7 | — | 6 | 2 | no | — |
| 419 | C22⋊D7 | — | 6 | 2 | no | — |
| 420 | C22⋊D7 | — | 6 | 2 | no | — |
| 421 | C22⋊D7 | — | 12 | 2 | no | — |
| 422 | C22⋊D7 | — | 12 | 2 | no | — |
| 423 | C2×Dic7 | — | 3 | 1 | no | — |
| 424 | C2×Dic7 | — | 3 | 1 | no | — |
| 425 | C2×Dic7 | — | 3 | 1 | no | — |
| 426 | C2×Dic7 | — | 6 | 1 | no | — |
| 427 | C2×Dic7 | — | 6 | 1 | no | — |
| 428 | C2×Dic7 | — | 6 | 1 | no | — |
| 429 | C2×Dic7 | — | 6 | 1 | no | — |
| 430 | D28 | — | 3 | 2 | no | — |
| 431 | D28 | — | 6 | 2 | no | — |
| 432 | D28 | — | 12 | 2 | no | — |
| 433 | C4×D7 | — | 3 | 2 | no | — |
| 434 | C4×D7 | — | 3 | 2 | no | — |
| 435 | C4×D7 | — | 6 | 2 | no | — |
| 436 | C4×D7 | — | 12 | 1 | no | — |
| 437 | C4×D7 | — | 12 | 2 | no | — |
| 438 | C4×D7 | — | 12 | 1 | no | — |
| 439 | Dic14 | — | 3 | 2 | no | — |
| 440 | Dic14 | — | 6 | 2 | no | — |
| 441 | C7×C8 | — | 6 | 2 | no | — |
| 442 | C7⋊C8 | — | 6 | 2 | no | — |
| 443 | C2×S4 | — | 28 | 1 | no | — |
| 444 | C3×#41 | — | 7 | 2 | no | — |
| 445 | C3×#41 | — | 21 | 2 | no | — |
| 446 | C3×#41 | — | 21 | 2 | no | — |
| 447 | C3×#41 | — | 21 | 2 | no | — |
| 448 | C3×#41 | — | 42 | 2 | no | — |
| 449 | C3×#41 | — | 42 | 2 | no | — |
| 450 | C3×#41 | — | 42 | 2 | no | — |
| 451 | C3×#41 | — | 42 | 2 | no | — |
| 452 | C3×#41 | — | 42 | 2 | no | — |
| 453 | C3×#41 | — | 42 | 2 | no | — |
| 454 | C3×#41 | — | 42 | 2 | no | — |
| 455 | C2×C3×Q8 | — | 21 | 1 | no | — |
| 456 | C2×C3×Q8 | — | 21 | 1 | no | — |
| 457 | C2×C3×Q8 | — | 21 | 2 | no | — |
| 458 | C2×C3×Q8 | — | 42 | 1 | no | — |
| 459 | C2×C3×D4 | — | 21 | 1 | no | — |
| 460 | C2×C3×D4 | — | 21 | 2 | no | — |
| 461 | C2×C3×D4 | — | 21 | 1 | no | — |
| 462 | C2×C3×D4 | — | 21 | 1 | no | — |
| 463 | C2×C3×D4 | — | 21 | 1 | no | — |
| 464 | C2×C3×D4 | — | 42 | 1 | no | — |
| 465 | C2×C3×D4 | — | 42 | 2 | no | — |
| 466 | C2×C3×D4 | — | 42 | 1 | no | — |
| 467 | C2×C3×D4 | — | 42 | 1 | no | — |
| 468 | C2×C3×D4 | — | 42 | 1 | no | — |
| 469 | C2×C3×D4 | — | 42 | 1 | no | — |
| 470 | C2×C3×D4 | — | 42 | 1 | no | — |
| 471 | C22×C3×C4 | — | 7 | 1 | no | — |
| 472 | C22×C3×C4 | — | 14 | 1 | no | — |
| 473 | C22×C3×C4 | — | 21 | 1 | no | — |
| 474 | C22×C3×C4 | — | 21 | 1 | no | — |
| 475 | C22×C3×C4 | — | 42 | 1 | no | — |
| 476 | C22×C3×C4 | — | 42 | 1 | no | — |
| 477 | C22×C3×C4 | — | 42 | 1 | no | — |
| 478 | #41⋊C3 | — | 28 | 2 | no | — |
| 479 | #41⋊C3 | — | 56 | 2 | no | — |
| 480 | C4×A4 | — | 28 | 1 | no | — |
| 481 | C4×A4 | — | 56 | 1 | no | — |
| 482 | C4×A4 | — | 56 | 1 | no | — |
| 483 | C4×A4 | — | 56 | 2 | no | — |
| 484 | SL(2,ℤ/4) | — | 4 | 1 | no | — |
| 485 | GL(2,𝔽3) | — | 28 | 2 | no | — |
| 486 | #226 | — | 4 | 2 | no | — |
| 487 | C3×Q16 | — | 42 | 2 | no | — |
| 488 | C3×Q16 | — | 42 | 2 | no | — |
| 489 | C3×SD16 | — | 42 | 2 | no | — |
| 490 | C3×SD16 | — | 42 | 2 | no | — |
| 491 | C3×SD16 | — | 42 | 2 | no | — |
| 492 | C3×SD16 | — | 42 | 2 | no | — |
| 493 | C3×D8 | — | 42 | 2 | no | — |
| 494 | C3×D8 | — | 42 | 2 | no | — |
| 495 | C3×M16 | — | 21 | 2 | no | — |
| 496 | C3×M16 | — | 21 | 2 | no | — |
| 497 | C3×M16 | — | 42 | 2 | no | — |
| 498 | C2×C3×C8 | — | 42 | 2 | no | — |
| 499 | C3×C4⋊C4 | — | 42 | 1 | no | — |
| 500 | C3×C4⋊C4 | — | 42 | 1 | no | — |
| 501 | C3×C22⋊C4 | — | 42 | 1 | no | — |
| 502 | C3×C22⋊C4 | — | 42 | 1 | no | — |
| 503 | C3×C22⋊C4 | — | 42 | 1 | no | — |
| 504 | C3×C22⋊C4 | — | 42 | 1 | no | — |
| 505 | C3×C42 | — | 21 | 1 | no | — |
| 506 | C3×C42 | — | 21 | 1 | no | — |
| 507 | C3×C42 | — | 42 | 1 | no | — |
| 508 | C2×C3×C7 | — | 16 | 1 | no | — |
| 509 | D21 | — | 16 | 2 | no | — |
| 510 | C2×ΓL(1,𝔽8) | — | 6 | 1 | no | — |
| 511 | C2×ΓL(1,𝔽8) | — | 12 | 1 | no | — |
| 512 | C2×ΓL(1,𝔽8) | — | 32 | 1 | no | — |
| 513 | C2×ΓL(1,𝔽8) | C2×#1020 | 1 | 1 | yes | characteristic |
| 514 | AGL(1,𝔽7) | — | 6 | 2 | no | — |
| 515 | AGL(1,𝔽7) | — | 24 | 1 | no | — |
| 516 | C2×C3×D3 | — | 112 | 1 | no | — |
| 517 | C3×A4 | — | 28 | 1 | no | — |
| 518 | C3×A4 | — | 56 | 1 | no | — |
| 519 | C32×C4 | — | 112 | 1 | no | — |
| 520 | C3×Dic3 | — | 112 | 1 | no | — |
| 521 | 2−1+4 | — | 21 | 2 | no | — |
| 522 | H(5,𝔽2) | — | 21 | 1 | no | — |
| 523 | H(5,𝔽2) | — | 42 | 1 | no | — |
| 524 | H(5,𝔽2) | D3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 525 | C2×#41 | — | 21 | 1 | no | — |
| 526 | C2×#41 | — | 21 | 1 | no | — |
| 527 | C2×#41 | — | 21 | 2 | no | — |
| 528 | C2×#41 | — | 42 | 1 | no | — |
| 529 | #137 | — | 3 | 2 | no | — |
| 530 | #137 | — | 21 | 2 | no | — |
| 531 | #137 | — | 42 | 2 | no | — |
| 532 | AGL(1,ℤ/8) | — | 21 | 2 | no | — |
| 533 | AGL(1,ℤ/8) | — | 21 | 2 | no | — |
| 534 | AGL(1,ℤ/8) | — | 42 | 2 | no | — |
| 535 | #135 | — | 42 | 2 | no | — |
| 536 | #135 | — | 42 | 2 | no | — |
| 537 | C2×M16 | — | 21 | 2 | no | — |
| 538 | C4⋊Q8 | — | 21 | 1 | no | — |
| 539 | #127 | — | 21 | 1 | no | — |
| 540 | #124 | — | 3 | 1 | no | — |
| 541 | #124 | — | 21 | 1 | no | — |
| 542 | #121 | — | 42 | 1 | no | — |
| 543 | #121 | — | 42 | 1 | no | — |
| 544 | C4×D4 | — | 42 | 1 | no | — |
| 545 | C4×D4 | — | 42 | 1 | no | — |
| 546 | C2×C42 | — | 21 | 1 | no | — |
| 547 | #104 | — | 3 | 2 | no | — |
| 548 | #104 | — | 21 | 2 | no | — |
| 549 | #104 | — | 21 | 2 | no | — |
| 550 | #104 | — | 21 | 2 | no | — |
| 551 | #101 | — | 21 | 2 | no | — |
| 552 | #100 | — | 3 | 1 | no | — |
| 553 | #100 | — | 21 | 1 | no | — |
| 554 | C22×C7 | — | 3 | 1 | no | — |
| 555 | C22×C7 | — | 4 | 1 | no | — |
| 556 | C22×C7 | — | 6 | 1 | no | — |
| 557 | C22×C7 | — | 8 | 1 | no | — |
| 558 | C22×C7 | — | 12 | 1 | no | — |
| 559 | C2×D7 | — | 3 | 2 | no | — |
| 560 | C2×D7 | — | 12 | 1 | no | — |
| 561 | C2×D7 | — | 12 | 1 | no | — |
| 562 | C2×D7 | — | 12 | 1 | no | — |
| 563 | C2×D7 | — | 12 | 1 | no | — |
| 564 | C2×D7 | — | 24 | 1 | no | — |
| 565 | C4×C7 | — | 3 | 2 | no | — |
| 566 | C4×C7 | — | 12 | 1 | no | — |
| 567 | C4×C7 | — | 12 | 1 | no | — |
| 568 | Dic7 | — | 3 | 1 | no | — |
| 569 | Dic7 | — | 6 | 2 | no | — |
| 570 | Dic7 | — | 6 | 1 | no | — |
| 571 | Dic7 | C3×#1020 | 1 | 1 | yes | characteristic |
| 572 | C23×C3 | — | 7 | 1 | no | — |
| 573 | C23×C3 | — | 14 | 1 | no | — |
| 574 | C23×C3 | — | 21 | 1 | no | — |
| 575 | C23×C3 | — | 21 | 1 | no | — |
| 576 | C23×C3 | — | 42 | 1 | no | — |
| 577 | C23×C3 | — | 42 | 1 | no | — |
| 578 | C2×A4 | — | 4 | 1 | no | — |
| 579 | C2×A4 | — | 8 | 1 | no | — |
| 580 | C2×A4 | — | 56 | 2 | no | — |
| 581 | C2×A4 | — | 56 | 1 | no | — |
| 582 | S4 | — | 28 | 2 | no | — |
| 583 | C3×Q8 | — | 7 | 2 | no | — |
| 584 | C3×Q8 | — | 21 | 2 | no | — |
| 585 | C3×Q8 | — | 42 | 2 | no | — |
| 586 | C3×Q8 | — | 42 | 2 | no | — |
| 587 | C3×D4 | — | 21 | 2 | no | — |
| 588 | C3×D4 | — | 21 | 2 | no | — |
| 589 | C3×D4 | — | 42 | 2 | no | — |
| 590 | C3×D4 | — | 42 | 2 | no | — |
| 591 | C3×D4 | — | 42 | 2 | no | — |
| 592 | C3×D4 | — | 42 | 2 | no | — |
| 593 | C3×D4 | — | 42 | 2 | no | — |
| 594 | C3×D4 | — | 84 | 2 | no | — |
| 595 | C3×D4 | — | 84 | 2 | no | — |
| 596 | C3×D4 | — | 84 | 2 | no | — |
| 597 | C2×C3×C4 | — | 21 | 1 | no | — |
| 598 | C2×C3×C4 | — | 21 | 2 | no | — |
| 599 | C2×C3×C4 | — | 21 | 1 | no | — |
| 600 | C2×C3×C4 | — | 21 | 2 | no | — |
| 601 | C2×C3×C4 | — | 21 | 1 | no | — |
| 602 | C2×C3×C4 | — | 21 | 1 | no | — |
| 603 | C2×C3×C4 | — | 42 | 1 | no | — |
| 604 | C2×C3×C4 | — | 42 | 1 | no | — |
| 605 | C2×C3×C4 | — | 42 | 1 | no | — |
| 606 | C2×C3×C4 | — | 42 | 1 | no | — |
| 607 | C2×C3×C4 | — | 42 | 2 | no | — |
| 608 | C2×C3×C4 | — | 42 | 1 | no | — |
| 609 | C2×C3×C4 | — | 42 | 1 | no | — |
| 610 | C2×C3×C4 | — | 42 | 1 | no | — |
| 611 | C2×C3×C4 | — | 84 | 1 | no | — |
| 612 | C2×C3×C4 | — | 84 | 1 | no | — |
| 613 | C2×C3×C4 | — | 84 | 2 | no | — |
| 614 | C4×D3 | — | 112 | 1 | no | — |
| 615 | SL(2,𝔽3) | — | 4 | 2 | no | — |
| 616 | SL(2,𝔽3) | — | 56 | 2 | no | — |
| 617 | C3×C8 | — | 42 | 2 | no | — |
| 618 | C3×C8 | — | 42 | 2 | no | — |
| 619 | C3×C7 | — | 16 | 1 | no | — |
| 620 | ΓL(1,𝔽8) | — | 32 | 1 | no | — |
| 621 | ΓL(1,𝔽8) | #87520 | 1 | 1 | yes | characteristic, complemented |
| 622 | C2×C32 | — | 112 | 1 | no | — |
| 623 | C3×D3 | — | 112 | 2 | no | — |
| 624 | #41 | — | 3 | 2 | no | — |
| 625 | #41 | — | 7 | 2 | no | — |
| 626 | #41 | — | 21 | 2 | no | — |
| 627 | #41 | — | 21 | 2 | no | — |
| 628 | #41 | — | 42 | 2 | no | — |
| 629 | #41 | — | 42 | 2 | no | — |
| 630 | #41 | — | 42 | 2 | no | — |
| 631 | #41 | — | 42 | 2 | no | — |
| 632 | #41 | — | 42 | 2 | no | — |
| 633 | #41 | — | 42 | 2 | no | — |
| 634 | #41 | — | 42 | 2 | no | — |
| 635 | C2×Q8 | — | 3 | 1 | no | — |
| 636 | C2×Q8 | — | 21 | 1 | no | — |
| 637 | C2×Q8 | — | 21 | 2 | no | — |
| 638 | C2×Q8 | — | 42 | 1 | no | — |
| 639 | C2×D4 | — | 3 | 1 | no | — |
| 640 | C2×D4 | — | 6 | 1 | no | — |
| 641 | C2×D4 | — | 21 | 1 | no | — |
| 642 | C2×D4 | — | 21 | 2 | no | — |
| 643 | C2×D4 | — | 21 | 1 | no | — |
| 644 | C2×D4 | — | 21 | 1 | no | — |
| 645 | C2×D4 | — | 42 | 1 | no | — |
| 646 | C2×D4 | — | 42 | 2 | no | — |
| 647 | C2×D4 | — | 42 | 1 | no | — |
| 648 | C2×D4 | — | 42 | 1 | no | — |
| 649 | C2×D4 | — | 42 | 1 | no | — |
| 650 | C2×D4 | — | 42 | 1 | no | — |
| 651 | C22×C4 | — | 7 | 1 | no | — |
| 652 | C22×C4 | — | 14 | 1 | no | — |
| 653 | C22×C4 | — | 21 | 1 | no | — |
| 654 | C22×C4 | — | 21 | 1 | no | — |
| 655 | C22×C4 | — | 42 | 1 | no | — |
| 656 | C22×C4 | — | 42 | 1 | no | — |
| 657 | C22×C4 | — | 42 | 1 | no | — |
| 658 | Q16 | — | 6 | 2 | no | — |
| 659 | Q16 | — | 42 | 2 | no | — |
| 660 | SD16 | — | 6 | 2 | no | — |
| 661 | SD16 | — | 42 | 2 | no | — |
| 662 | SD16 | — | 42 | 2 | no | — |
| 663 | SD16 | — | 42 | 2 | no | — |
| 664 | D8 | — | 42 | 2 | no | — |
| 665 | D8 | — | 42 | 2 | no | — |
| 666 | M16 | — | 3 | 2 | no | — |
| 667 | M16 | — | 21 | 2 | no | — |
| 668 | M16 | — | 42 | 2 | no | — |
| 669 | C2×C8 | — | 42 | 2 | no | — |
| 670 | C4⋊C4 | — | 42 | 1 | no | — |
| 671 | C4⋊C4 | — | 42 | 1 | no | — |
| 672 | C22⋊C4 | — | 6 | 1 | no | — |
| 673 | C22⋊C4 | — | 6 | 1 | no | — |
| 674 | C22⋊C4 | — | 42 | 1 | no | — |
| 675 | C22⋊C4 | — | 42 | 1 | no | — |
| 676 | C42 | — | 3 | 1 | no | — |
| 677 | C42 | — | 21 | 1 | no | — |
| 678 | C42 | — | 42 | 1 | no | — |
| 679 | C2×C7 | — | 6 | 1 | no | — |
| 680 | C2×C7 | — | 12 | 1 | no | — |
| 681 | C2×C7 | C2×C3×#1020 | 1 | 1 | yes | characteristic |
| 682 | D7 | — | 6 | 2 | no | — |
| 683 | D7 | — | 24 | 1 | no | — |
| 684 | C22×C3 | — | 21 | 1 | no | — |
| 685 | C22×C3 | — | 21 | 2 | no | — |
| 686 | C22×C3 | — | 28 | 1 | no | — |
| 687 | C22×C3 | — | 42 | 1 | no | — |
| 688 | C22×C3 | — | 56 | 1 | no | — |
| 689 | C22×C3 | — | 84 | 1 | no | — |
| 690 | C22×C3 | — | 84 | 1 | no | — |
| 691 | C22×C3 | — | 84 | 1 | no | — |
| 692 | C22×C3 | — | 84 | 1 | no | — |
| 693 | C22×C3 | — | 84 | 1 | no | — |
| 694 | C22×C3 | — | 168 | 1 | no | — |
| 695 | C2×D3 | — | 112 | 1 | no | — |
| 696 | A4 | — | 4 | 1 | no | — |
| 697 | A4 | — | 8 | 1 | no | — |
| 698 | A4 | — | 56 | 1 | no | — |
| 699 | A4 | — | 56 | 2 | no | — |
| 700 | C3×C4 | — | 7 | 1 | no | — |
| 701 | C3×C4 | — | 21 | 2 | no | — |
| 702 | C3×C4 | — | 21 | 1 | no | — |
| 703 | C3×C4 | — | 42 | 1 | no | — |
| 704 | C3×C4 | — | 42 | 2 | no | — |
| 705 | C3×C4 | — | 84 | 1 | no | — |
| 706 | C3×C4 | — | 84 | 1 | no | — |
| 707 | C3×C4 | — | 112 | 1 | no | — |
| 708 | C3×C4 | — | 224 | 1 | no | — |
| 709 | Dic3 | — | 16 | 1 | no | — |
| 710 | C32 | — | 112 | 1 | no | Sylow |
| 711 | C23 | — | 2 | 1 | no | — |
| 712 | C23 | — | 3 | 1 | no | — |
| 713 | C23 | — | 21 | 1 | no | — |
| 714 | C23 | — | 42 | 1 | no | — |
| 715 | C23 | — | 42 | 1 | no | — |
| 716 | C23 | S4×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 717 | Q8 | — | 6 | 2 | no | — |
| 718 | Q8 | — | 21 | 2 | no | — |
| 719 | Q8 | — | 42 | 2 | no | — |
| 720 | Q8 | S4×AGL(1,𝔽7) | 1 | 2 | yes | — |
| 721 | D4 | — | 3 | 2 | no | — |
| 722 | D4 | — | 6 | 2 | no | — |
| 723 | D4 | — | 21 | 2 | no | — |
| 724 | D4 | — | 42 | 2 | no | — |
| 725 | D4 | — | 42 | 2 | no | — |
| 726 | D4 | — | 42 | 2 | no | — |
| 727 | D4 | — | 42 | 2 | no | — |
| 728 | D4 | — | 84 | 2 | no | — |
| 729 | D4 | — | 84 | 2 | no | — |
| 730 | D4 | — | 84 | 2 | no | — |
| 731 | C2×C4 | — | 3 | 1 | no | — |
| 732 | C2×C4 | — | 6 | 1 | no | — |
| 733 | C2×C4 | — | 6 | 1 | no | — |
| 734 | C2×C4 | — | 6 | 1 | no | — |
| 735 | C2×C4 | — | 21 | 2 | no | — |
| 736 | C2×C4 | — | 21 | 2 | no | — |
| 737 | C2×C4 | — | 21 | 1 | no | — |
| 738 | C2×C4 | — | 21 | 1 | no | — |
| 739 | C2×C4 | — | 21 | 1 | no | — |
| 740 | C2×C4 | — | 42 | 2 | no | — |
| 741 | C2×C4 | — | 42 | 1 | no | — |
| 742 | C2×C4 | — | 42 | 1 | no | — |
| 743 | C2×C4 | — | 42 | 1 | no | — |
| 744 | C2×C4 | — | 42 | 1 | no | — |
| 745 | C2×C4 | — | 84 | 1 | no | — |
| 746 | C2×C4 | — | 84 | 1 | no | — |
| 747 | C2×C4 | — | 84 | 2 | no | — |
| 748 | C8 | — | 6 | 2 | no | — |
| 749 | C8 | — | 42 | 2 | no | — |
| 750 | C7 | C3×#87520 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 751 | C2×C3 | — | 7 | 1 | no | — |
| 752 | C2×C3 | — | 16 | 1 | no | — |
| 753 | C2×C3 | — | 42 | 1 | no | — |
| 754 | C2×C3 | — | 42 | 2 | no | — |
| 755 | C2×C3 | — | 84 | 1 | no | — |
| 756 | C2×C3 | — | 168 | 1 | no | — |
| 757 | C2×C3 | — | 224 | 1 | no | — |
| 758 | D3 | — | 112 | 2 | no | — |
| 759 | C22 | — | 3 | 1 | no | — |
| 760 | C22 | — | 4 | 1 | no | — |
| 761 | C22 | — | 6 | 1 | no | — |
| 762 | C22 | — | 8 | 1 | no | — |
| 763 | C22 | — | 12 | 1 | no | — |
| 764 | C22 | — | 21 | 2 | no | — |
| 765 | C22 | — | 84 | 1 | no | — |
| 766 | C22 | — | 84 | 1 | no | — |
| 767 | C22 | — | 84 | 1 | no | — |
| 768 | C22 | — | 84 | 1 | no | — |
| 769 | C22 | — | 168 | 1 | no | — |
| 770 | C4 | — | 3 | 2 | no | — |
| 771 | C4 | — | 7 | 1 | no | — |
| 772 | C4 | — | 12 | 1 | no | — |
| 773 | C4 | — | 12 | 1 | no | — |
| 774 | C4 | — | 21 | 1 | no | — |
| 775 | C4 | — | 42 | 2 | no | — |
| 776 | C4 | — | 42 | 1 | no | — |
| 777 | C3 | — | 7 | 1 | no | — |
| 778 | C3 | — | 16 | 1 | no | — |
| 779 | C3 | — | 224 | 1 | no | — |
| 780 | C2 | — | 6 | 1 | no | — |
| 781 | C2 | — | 12 | 1 | no | — |
| 782 | C2 | — | 42 | 2 | no | — |
| 783 | C2 | — | 168 | 1 | no | — |
| 784 | C2 | AGL(1,𝔽7)×#1020 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽7)×#1020 |
| commutator, cosocle, hypocenter | C7×#997 | C22×C3 |
| Fitting | C7×H(5,𝔽2) | C2×C3×D3 |
| socle | C2×C7 | C2×C3×#1020 |
| LCS | G ▷ C7×#997 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #72259855 | C3 | semidirect |
| 3. ΓL(1,𝔽8)×#5933 | C2 | semidirect |
| 4. #72229375 | C2 | semidirect |
| 7. #72214048 | C2 | semidirect |
| 10. #13062205 | C2×C3 | semidirect |
| 11. #13062156 | D3 | semidirect |
| 12. C7⋊#5935 | C2×C3 | semidirect |
| 13. C7×#5933 | C2×C3 | semidirect |
| 78. #90618 | C3×D3 | semidirect |
| 113. #66659 | S4 | semidirect |
| 201. #5933 | AGL(1,𝔽7) | semidirect |
| 284. #1161 | C3×S4 | semidirect |
| 621. ΓL(1,𝔽8) | #87520 | semidirect |
| 750. C7 | C3×#87520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72259859 | 3 |
| #72259855 | 3 |
| ΓL(1,𝔽8)×#5933 | 2 |
| #72229375 | 2 |
| #72218844 | 4 |
| #72218843 | 4 |
| #72214048 | 2 |
| C3×#87520 | 7 |