| 1 | C19⋊C3×ΓL(1,𝔽8)⋊D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | ΓL(1,𝔽8)⋊((C19⋊C3)⋊D7) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×ΓL(1,𝔽8)×D19⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C7⋊D7×D19⋊C3 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D19×ΓL(1,𝔽8)⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11716322⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11716321⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×ΓL(1,𝔽8)×C19⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C19⋊C3×C7⋊D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | (C19⋊C3)⋊(C7⋊D7) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | ΓL(1,𝔽8)⋊D133 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | #19150309 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | #19150308 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #19150307 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #19150306 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C19×ΓL(1,𝔽8)⋊D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C7×ΓL(1,𝔽8)×D19 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C7×#11716322 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C7×#11716321 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C72×D19⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×D7×D19⋊C3 | — | 7 | 1 | no | maximal |
| 22 | AGL(1,𝔽7)×D19⋊C3 | — | 7 | 1 | no | maximal |
| 23 | D19×C7⋊D7 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 24 | C7×#87705 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C7×#87704 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C7×C19×ΓL(1,𝔽8) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C72×C19⋊C3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C3×D7×C19⋊C3 | — | 7 | 1 | no | — |
| 29 | C3×(C19⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 30 | C3×C7×D19⋊C3 | — | 7 | 1 | no | — |
| 31 | ΓL(1,𝔽8)×D19⋊C3 | D7 | 1 | 1 | yes | characteristic, complemented |
| 32 | AGL(1,𝔽7)×C19⋊C3 | — | 7 | 1 | no | — |
| 33 | ΓL(1,𝔽8)⋊(D19⋊C3) | — | 7 | 1 | no | — |
| 34 | C7⋊D133 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 35 | C19×C7⋊D7 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 36 | C72×D19 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×C3×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | maximal, Hall |
| 38 | C3×D7×D19 | — | 7 | 1 | no | — |
| 39 | #11716322⋊C2 | — | 7 | 1 | no | — |
| 40 | #11716321⋊C2 | — | 7 | 1 | no | — |
| 41 | D19×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 42 | D7×D19⋊C3 | — | 7 | 1 | no | — |
| 43 | D7×D19⋊C3 | — | 7 | 1 | no | — |
| 44 | D7×D19⋊C3 | — | 7 | 1 | no | — |
| 45 | D7×D19⋊C3 | — | 7 | 1 | no | — |
| 46 | D7×D19⋊C3 | — | 21 | 2 | no | — |
| 47 | C3×C7×C19⋊C3 | — | 7 | 1 | no | — |
| 48 | ΓL(1,𝔽8)×C19⋊C3 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 49 | C72×C19 | C22×C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 50 | C2×C3×C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 51 | C3×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 52 | C3×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 53 | C3×D133 | — | 7 | 1 | no | — |
| 54 | C3×D7×C19 | — | 7 | 1 | no | — |
| 55 | C3×C7×D19 | — | 7 | 1 | no | — |
| 56 | #11716328 | — | 7 | 1 | no | — |
| 57 | #11716327 | — | 7 | 1 | no | — |
| 58 | #11716326 | — | 7 | 1 | no | — |
| 59 | #11716325 | — | 7 | 1 | no | — |
| 60 | ΓL(1,𝔽8)⋊D19 | — | 7 | 1 | no | — |
| 61 | C19×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 62 | #11716322 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 63 | #11716321 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 64 | ΓL(1,𝔽8)×D19 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 65 | (C19⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 66 | (C19⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 67 | (C19⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 68 | (C19⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 69 | (C19⋊C3)⋊D7 | — | 21 | 2 | no | — |
| 70 | D7×C19⋊C3 | — | 7 | 1 | no | — |
| 71 | D7×C19⋊C3 | — | 7 | 1 | no | — |
| 72 | D7×C19⋊C3 | — | 7 | 1 | no | — |
| 73 | D7×C19⋊C3 | — | 7 | 1 | no | — |
| 74 | D7×C19⋊C3 | — | 21 | 2 | no | — |
| 75 | C7×D19⋊C3 | — | 3 | 2 | no | — |
| 76 | C7×D19⋊C3 | — | 7 | 1 | no | — |
| 77 | C7×D19⋊C3 | — | 7 | 1 | no | — |
| 78 | C7×D19⋊C3 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 79 | C7×D19⋊C3 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 80 | C2×C3×D19⋊C3 | — | 49 | 1 | no | Hall |
| 81 | C2×C3×C7⋊D7 | — | 19 | 1 | no | — |
| 82 | C2×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 83 | C2×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 84 | C2×ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 85 | D7×D19 | — | 7 | 1 | no | — |
| 86 | D7×D19 | — | 7 | 1 | no | — |
| 87 | D7×D19 | — | 21 | 2 | no | — |
| 88 | C3×C7×ΓL(1,𝔽8) | — | 19 | 1 | no | Hall |
| 89 | C3×C7×C19 | — | 7 | 1 | no | — |
| 90 | #87705 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 91 | #87704 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 92 | C7×C19⋊C3 | — | 3 | 2 | no | — |
| 93 | C7×C19⋊C3 | — | 7 | 1 | no | — |
| 94 | C7×C19⋊C3 | — | 7 | 1 | no | — |
| 95 | C7×C19⋊C3 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 96 | C7×C19⋊C3 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 97 | C19×ΓL(1,𝔽8) | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 98 | C2×C3×C19⋊C3 | — | 49 | 1 | no | — |
| 99 | C3×D19⋊C3 | — | 7 | 1 | no | — |
| 100 | C3×D19⋊C3 | — | 49 | 1 | no | — |
| 101 | C2×C3×C72 | — | 19 | 1 | no | — |
| 102 | C3×C7⋊D7 | — | 19 | 1 | no | — |
| 103 | C3×C7⋊D7 | — | 19 | 1 | no | — |
| 104 | C2×C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 105 | C2×C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 106 | C2×C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 107 | ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 108 | ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 109 | ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 110 | ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 111 | ΓL(1,𝔽8)⋊D7 | — | 19 | 1 | no | — |
| 112 | ΓL(1,𝔽8)⋊D7 | D19⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 113 | D133 | — | 7 | 1 | no | — |
| 114 | D133 | — | 7 | 1 | no | — |
| 115 | D133 | — | 21 | 2 | no | — |
| 116 | C7×D19 | — | 3 | 2 | no | — |
| 117 | C7×D19 | C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 118 | C7×D19 | C32×D7 | 1 | 1 | yes | characteristic, complemented |
| 119 | D7×C19 | — | 7 | 1 | no | — |
| 120 | D7×C19 | — | 7 | 1 | no | — |
| 121 | D7×C19 | — | 21 | 2 | no | — |
| 122 | C2×C32×D7 | — | 133 | 1 | no | — |
| 123 | C2×C3×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 124 | C2×C3×D19 | — | 49 | 1 | no | — |
| 125 | C2×D19⋊C3 | — | 49 | 1 | no | — |
| 126 | C2×D19⋊C3 | — | 49 | 1 | no | — |
| 127 | C2×D19⋊C3 | — | 49 | 1 | no | — |
| 128 | C2×C7⋊D7 | — | 19 | 1 | no | Hall |
| 129 | C3×C19⋊C3 | — | 7 | 1 | no | Hall |
| 130 | C3×C72 | — | 19 | 1 | no | — |
| 131 | C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 132 | C7×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 133 | C7×ΓL(1,𝔽8) | C2×D19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 134 | C7×C19 | — | 3 | 2 | no | — |
| 135 | C7×C19 | C2×C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 136 | C7×C19 | C2×C32×D7 | 1 | 1 | yes | characteristic, complemented |
| 137 | C2×C32×C7 | — | 133 | 1 | no | — |
| 138 | C32×D7 | — | 133 | 1 | no | — |
| 139 | C32×D7 | — | 133 | 1 | no | — |
| 140 | C2×C3×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 141 | C3×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 142 | C3×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 143 | C2×C3×C19 | — | 49 | 1 | no | — |
| 144 | C3×D19 | — | 7 | 1 | no | — |
| 145 | C3×D19 | — | 49 | 1 | no | — |
| 146 | C2×C19⋊C3 | — | 49 | 1 | no | — |
| 147 | C2×C19⋊C3 | — | 49 | 1 | no | — |
| 148 | C2×C19⋊C3 | — | 49 | 1 | no | — |
| 149 | D19⋊C3 | — | 7 | 1 | no | — |
| 150 | D19⋊C3 | — | 7 | 1 | no | — |
| 151 | D19⋊C3 | — | 49 | 1 | no | — |
| 152 | D19⋊C3 | — | 49 | 1 | no | — |
| 153 | D19⋊C3 | — | 49 | 1 | no | — |
| 154 | D19⋊C3 | ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, direct product factor |
| 155 | C2×C72 | — | 19 | 1 | no | — |
| 156 | C7⋊D7 | — | 19 | 1 | no | — |
| 157 | C7⋊D7 | C3×D19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 158 | C2×C3×D7 | — | 133 | 1 | no | — |
| 159 | C2×C3×D7 | — | 133 | 1 | no | — |
| 160 | C2×C3×D7 | — | 133 | 1 | no | — |
| 161 | C2×C3×D7 | — | 133 | 1 | no | — |
| 162 | C2×C3×D7 | — | 133 | 1 | no | — |
| 163 | C2×C3×D7 | — | 399 | 2 | no | — |
| 164 | C2×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 165 | C2×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 166 | C2×AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 167 | C2×D19 | — | 49 | 1 | no | Hall |
| 168 | C32×C7 | — | 133 | 1 | no | — |
| 169 | C3×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 170 | C3×C19 | — | 7 | 1 | no | — |
| 171 | C19⋊C3 | — | 7 | 1 | no | — |
| 172 | C19⋊C3 | — | 7 | 1 | no | — |
| 173 | C19⋊C3 | C2×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 174 | C72 | C2×C3×D19⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 175 | C2×C3×C7 | — | 19 | 1 | no | — |
| 176 | C2×C3×C7 | — | 19 | 1 | no | — |
| 177 | C2×C3×C7 | — | 57 | 2 | no | — |
| 178 | C2×C3×C7 | — | 133 | 1 | no | — |
| 179 | C2×C3×C7 | — | 133 | 1 | no | — |
| 180 | C2×C3×C7 | — | 133 | 1 | no | — |
| 181 | C3×D7 | — | 7 | 1 | no | — |
| 182 | C3×D7 | — | 133 | 1 | no | — |
| 183 | C3×D7 | — | 133 | 1 | no | — |
| 184 | C3×D7 | — | 133 | 1 | no | — |
| 185 | C3×D7 | — | 133 | 1 | no | — |
| 186 | C3×D7 | — | 133 | 1 | no | — |
| 187 | C3×D7 | — | 133 | 1 | no | — |
| 188 | C3×D7 | — | 133 | 1 | no | — |
| 189 | C3×D7 | — | 133 | 1 | no | — |
| 190 | C3×D7 | — | 133 | 1 | no | — |
| 191 | C3×D7 | — | 399 | 2 | no | — |
| 192 | C3×D7 | — | 399 | 2 | no | — |
| 193 | C2×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 194 | C2×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 195 | C2×ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 196 | AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 197 | AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 198 | AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 199 | AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 200 | AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 201 | AGL(1,𝔽7) | — | 133 | 1 | no | — |
| 202 | C2×C19 | — | 49 | 1 | no | — |
| 203 | D19 | — | 49 | 1 | no | — |
| 204 | D19 | C3×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 205 | C22×C32 | — | 931 | 1 | no | Hall |
| 206 | C2×D7 | — | 133 | 1 | no | — |
| 207 | C2×D7 | — | 133 | 1 | no | — |
| 208 | C2×D7 | — | 399 | 2 | no | — |
| 209 | C3×C7 | — | 7 | 1 | no | — |
| 210 | C3×C7 | — | 19 | 1 | no | — |
| 211 | C3×C7 | — | 19 | 1 | no | — |
| 212 | C3×C7 | — | 57 | 2 | no | — |
| 213 | C3×C7 | — | 133 | 1 | no | — |
| 214 | C3×C7 | — | 133 | 1 | no | — |
| 215 | ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 216 | ΓL(1,𝔽8) | — | 19 | 1 | no | — |
| 217 | ΓL(1,𝔽8) | D7×D19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 218 | C19 | C2×C3×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 219 | C2×C32 | — | 133 | 1 | no | — |
| 220 | C2×C32 | — | 931 | 1 | no | — |
| 221 | C2×C32 | — | 931 | 1 | no | — |
| 222 | C2×C7 | — | 19 | 1 | no | — |
| 223 | C2×C7 | — | 19 | 1 | no | — |
| 224 | C2×C7 | — | 57 | 2 | no | — |
| 225 | D7 | — | 7 | 1 | no | — |
| 226 | D7 | — | 7 | 1 | no | — |
| 227 | D7 | — | 21 | 2 | no | — |
| 228 | D7 | — | 133 | 1 | no | — |
| 229 | D7 | — | 133 | 1 | no | — |
| 230 | D7 | — | 399 | 2 | no | — |
| 231 | C22×C3 | — | 931 | 1 | no | — |
| 232 | C22×C3 | — | 931 | 1 | no | — |
| 233 | C22×C3 | — | 931 | 1 | no | — |
| 234 | C22×C3 | — | 931 | 1 | no | — |
| 235 | C32 | — | 133 | 1 | no | Sylow |
| 236 | C7 | — | 3 | 2 | no | — |
| 237 | C7 | AGL(1,𝔽7)×D19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 238 | C7 | C3×D7×D19⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 239 | C2×C3 | — | 19 | 1 | no | — |
| 240 | C2×C3 | — | 49 | 1 | no | — |
| 241 | C2×C3 | — | 133 | 1 | no | — |
| 242 | C2×C3 | — | 133 | 1 | no | — |
| 243 | C2×C3 | — | 133 | 1 | no | — |
| 244 | C2×C3 | — | 931 | 1 | no | — |
| 245 | C2×C3 | — | 931 | 1 | no | — |
| 246 | C2×C3 | — | 931 | 1 | no | — |
| 247 | C2×C3 | — | 931 | 1 | no | — |
| 248 | C2×C3 | — | 931 | 1 | no | — |
| 249 | C2×C3 | — | 931 | 1 | no | — |
| 250 | C2×C3 | — | 931 | 1 | no | — |
| 251 | C22 | — | 931 | 1 | no | Sylow |
| 252 | C3 | — | 7 | 1 | no | — |
| 253 | C3 | — | 19 | 1 | no | — |
| 254 | C3 | — | 133 | 1 | no | — |
| 255 | C3 | — | 133 | 1 | no | — |
| 256 | C2 | — | 19 | 1 | no | — |
| 257 | C2 | — | 49 | 1 | no | — |
| 258 | C2 | — | 931 | 1 | no | — |
Finite Group Databasebeta