| 1 | C13⋊C3×ΓL(1,𝔽8)⋊D7 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | ΓL(1,𝔽8)⋊((C13⋊C3)⋊D7) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C7×ΓL(1,𝔽8)×D13⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | D13⋊C3×C7⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | D13×ΓL(1,𝔽8)⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10587717⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10587716⋊D7 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C7×ΓL(1,𝔽8)×C13⋊C3 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C13⋊C3×C7⋊D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | (C13⋊C3)⋊(C7⋊D7) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | ΓL(1,𝔽8)⋊D91 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16838471 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16838470 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16838469 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | #16838468 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C13×ΓL(1,𝔽8)⋊D7 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C7×ΓL(1,𝔽8)×D13 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C7×#10587717 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C7×#10587716 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C72×D13⋊C3 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C3×D7×D13⋊C3 | — | 7 | 1 | no | maximal |
| 22 | AGL(1,𝔽7)×D13⋊C3 | — | 7 | 1 | no | maximal |
| 23 | D13×C7⋊D7 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 24 | C7×#63270 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C7×#63271 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C7×C13×ΓL(1,𝔽8) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C72×C13⋊C3 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×C3×ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | maximal, Hall |
| 29 | C3×(C13⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 30 | C3×D7×C13⋊C3 | — | 7 | 1 | no | — |
| 31 | C3×C7×D13⋊C3 | — | 7 | 1 | no | — |
| 32 | ΓL(1,𝔽8)⋊(D13⋊C3) | — | 7 | 1 | no | — |
| 33 | C13⋊C3×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 34 | ΓL(1,𝔽8)×D13⋊C3 | D7 | 1 | 1 | yes | characteristic, complemented |
| 35 | C7⋊D91 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 36 | C13×C7⋊D7 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 37 | C72×D13 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 38 | C3×D7×D13 | — | 7 | 1 | no | — |
| 39 | #10587716⋊C2 | — | 7 | 1 | no | — |
| 40 | #10587717⋊C2 | — | 7 | 1 | no | — |
| 41 | D13×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 42 | D7×D13⋊C3 | — | 7 | 1 | no | — |
| 43 | D7×D13⋊C3 | — | 7 | 1 | no | — |
| 44 | D7×D13⋊C3 | — | 7 | 1 | no | — |
| 45 | D7×D13⋊C3 | — | 21 | 1 | no | — |
| 46 | D7×D13⋊C3 | — | 21 | 1 | no | — |
| 47 | D7×D13⋊C3 | — | 21 | 1 | no | — |
| 48 | C2×C3×C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 49 | C3×ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 50 | C3×ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 51 | C3×C7×C13⋊C3 | — | 7 | 1 | no | — |
| 52 | ΓL(1,𝔽8)×C13⋊C3 | C2×D7 | 1 | 1 | yes | characteristic, complemented |
| 53 | C72×C13 | C22×C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 54 | C2×C3×C7⋊D7 | — | 13 | 1 | no | — |
| 55 | C2×ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 56 | C2×ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 57 | C2×ΓL(1,𝔽8)⋊D7 | — | 39 | 1 | no | — |
| 58 | C3×D91 | — | 7 | 1 | no | — |
| 59 | C3×C13×D7 | — | 7 | 1 | no | — |
| 60 | C3×C7×D13 | — | 7 | 1 | no | — |
| 61 | #10587723 | — | 7 | 1 | no | — |
| 62 | #10587722 | — | 7 | 1 | no | — |
| 63 | #10587721 | — | 7 | 1 | no | — |
| 64 | #10587720 | — | 7 | 1 | no | — |
| 65 | ΓL(1,𝔽8)⋊D13 | — | 7 | 1 | no | — |
| 66 | C13×AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 67 | #10587717 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 68 | #10587716 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 69 | ΓL(1,𝔽8)×D13 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 70 | (C13⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 71 | (C13⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 72 | (C13⋊C3)⋊D7 | — | 7 | 1 | no | — |
| 73 | (C13⋊C3)⋊D7 | — | 21 | 1 | no | — |
| 74 | (C13⋊C3)⋊D7 | — | 21 | 1 | no | — |
| 75 | (C13⋊C3)⋊D7 | — | 21 | 1 | no | — |
| 76 | D7×C13⋊C3 | — | 7 | 1 | no | — |
| 77 | D7×C13⋊C3 | — | 7 | 1 | no | — |
| 78 | D7×C13⋊C3 | — | 7 | 1 | no | — |
| 79 | D7×C13⋊C3 | — | 21 | 1 | no | — |
| 80 | D7×C13⋊C3 | — | 21 | 1 | no | — |
| 81 | D7×C13⋊C3 | — | 21 | 1 | no | — |
| 82 | C7×D13⋊C3 | — | 3 | 1 | no | — |
| 83 | C7×D13⋊C3 | — | 3 | 1 | no | — |
| 84 | C7×D13⋊C3 | — | 7 | 1 | no | — |
| 85 | C7×D13⋊C3 | — | 7 | 1 | no | — |
| 86 | C7×D13⋊C3 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 87 | C7×D13⋊C3 | C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 88 | C2×C3×D13⋊C3 | — | 49 | 1 | no | Hall |
| 89 | C3×C7×ΓL(1,𝔽8) | — | 13 | 1 | no | Hall |
| 90 | D7×D13 | — | 7 | 1 | no | — |
| 91 | D7×D13 | — | 21 | 1 | no | — |
| 92 | D7×D13 | — | 21 | 1 | no | — |
| 93 | D7×D13 | — | 21 | 1 | no | — |
| 94 | C2×C3×C72 | — | 13 | 1 | no | — |
| 95 | C3×C7⋊D7 | — | 13 | 1 | no | — |
| 96 | C3×C7⋊D7 | — | 13 | 1 | no | — |
| 97 | C2×C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 98 | C2×C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 99 | C2×C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 100 | ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 101 | ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 102 | ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 103 | ΓL(1,𝔽8)⋊D7 | — | 13 | 1 | no | — |
| 104 | ΓL(1,𝔽8)⋊D7 | — | 39 | 1 | no | — |
| 105 | ΓL(1,𝔽8)⋊D7 | D13⋊C3 | 1 | 1 | yes | characteristic, direct product factor |
| 106 | C3×C7×C13 | — | 7 | 1 | no | — |
| 107 | #63271 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 108 | #63270 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 109 | C7×C13⋊C3 | — | 3 | 1 | no | — |
| 110 | C7×C13⋊C3 | — | 3 | 1 | no | — |
| 111 | C7×C13⋊C3 | — | 7 | 1 | no | — |
| 112 | C7×C13⋊C3 | — | 7 | 1 | no | — |
| 113 | C7×C13⋊C3 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 114 | C7×C13⋊C3 | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 115 | C13×ΓL(1,𝔽8) | C2×C3×D7 | 1 | 1 | yes | characteristic, complemented |
| 116 | C2×C32×D7 | — | 91 | 1 | no | — |
| 117 | C2×C3×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 118 | C2×C3×C13⋊C3 | — | 49 | 1 | no | — |
| 119 | C3×D13⋊C3 | — | 7 | 1 | no | — |
| 120 | C3×D13⋊C3 | — | 49 | 1 | no | — |
| 121 | C2×C7⋊D7 | — | 39 | 1 | no | Hall |
| 122 | D91 | — | 7 | 1 | no | — |
| 123 | D91 | — | 21 | 1 | no | — |
| 124 | D91 | — | 21 | 1 | no | — |
| 125 | D91 | — | 21 | 1 | no | — |
| 126 | C7×D13 | — | 3 | 1 | no | — |
| 127 | C7×D13 | — | 3 | 1 | no | — |
| 128 | C7×D13 | C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 129 | C7×D13 | C32×D7 | 1 | 1 | yes | characteristic, complemented |
| 130 | C13×D7 | — | 7 | 1 | no | — |
| 131 | C13×D7 | — | 21 | 1 | no | — |
| 132 | C13×D7 | — | 21 | 1 | no | — |
| 133 | C13×D7 | — | 21 | 1 | no | — |
| 134 | C2×C3×D13 | — | 49 | 1 | no | — |
| 135 | C2×D13⋊C3 | — | 49 | 1 | no | — |
| 136 | C2×D13⋊C3 | — | 49 | 1 | no | — |
| 137 | C2×D13⋊C3 | — | 147 | 1 | no | — |
| 138 | C3×C72 | — | 13 | 1 | no | — |
| 139 | C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 140 | C7×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 141 | C7×ΓL(1,𝔽8) | C2×D13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 142 | C2×C32×C7 | — | 91 | 1 | no | — |
| 143 | C32×D7 | — | 91 | 1 | no | — |
| 144 | C32×D7 | — | 91 | 1 | no | — |
| 145 | C2×C3×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 146 | C3×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 147 | C3×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 148 | C3×C13⋊C3 | — | 7 | 1 | no | Hall |
| 149 | C2×C72 | — | 13 | 1 | no | — |
| 150 | C7⋊D7 | — | 39 | 1 | no | — |
| 151 | C7⋊D7 | C3×D13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 152 | C7×C13 | — | 3 | 1 | no | — |
| 153 | C7×C13 | — | 3 | 1 | no | — |
| 154 | C7×C13 | C2×C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 155 | C7×C13 | C2×C32×D7 | 1 | 1 | yes | characteristic, complemented |
| 156 | C2×C3×D7 | — | 273 | 1 | no | — |
| 157 | C2×C3×D7 | — | 273 | 1 | no | — |
| 158 | C2×C3×D7 | — | 273 | 1 | no | — |
| 159 | C2×C3×D7 | — | 273 | 1 | no | — |
| 160 | C2×C3×D7 | — | 91 | 1 | no | — |
| 161 | C2×C3×D7 | — | 91 | 1 | no | — |
| 162 | C2×C3×D7 | — | 91 | 1 | no | — |
| 163 | C2×AGL(1,𝔽7) | — | 273 | 1 | no | — |
| 164 | C2×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 165 | C2×AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 166 | C2×C3×C13 | — | 49 | 1 | no | — |
| 167 | C3×D13 | — | 7 | 1 | no | — |
| 168 | C3×D13 | — | 49 | 1 | no | — |
| 169 | C2×C13⋊C3 | — | 49 | 1 | no | — |
| 170 | C2×C13⋊C3 | — | 49 | 1 | no | — |
| 171 | C2×C13⋊C3 | — | 147 | 1 | no | — |
| 172 | D13⋊C3 | — | 7 | 1 | no | — |
| 173 | D13⋊C3 | — | 7 | 1 | no | — |
| 174 | D13⋊C3 | — | 49 | 1 | no | — |
| 175 | D13⋊C3 | — | 49 | 1 | no | — |
| 176 | D13⋊C3 | — | 147 | 1 | no | — |
| 177 | D13⋊C3 | ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, direct product factor |
| 178 | C32×C7 | — | 91 | 1 | no | — |
| 179 | C3×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 180 | C2×D13 | — | 147 | 1 | no | Hall |
| 181 | C72 | C2×C3×D13⋊C3 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 182 | C2×C3×C7 | — | 13 | 1 | no | — |
| 183 | C2×C3×C7 | — | 13 | 1 | no | — |
| 184 | C2×C3×C7 | — | 39 | 1 | no | — |
| 185 | C2×C3×C7 | — | 39 | 1 | no | — |
| 186 | C2×C3×C7 | — | 91 | 1 | no | — |
| 187 | C2×C3×C7 | — | 91 | 1 | no | — |
| 188 | C2×C3×C7 | — | 91 | 1 | no | — |
| 189 | C3×D7 | — | 7 | 1 | no | — |
| 190 | C3×D7 | — | 273 | 1 | no | — |
| 191 | C3×D7 | — | 273 | 1 | no | — |
| 192 | C3×D7 | — | 273 | 1 | no | — |
| 193 | C3×D7 | — | 273 | 1 | no | — |
| 194 | C3×D7 | — | 273 | 1 | no | — |
| 195 | C3×D7 | — | 273 | 1 | no | — |
| 196 | C3×D7 | — | 273 | 1 | no | — |
| 197 | C3×D7 | — | 91 | 1 | no | — |
| 198 | C3×D7 | — | 91 | 1 | no | — |
| 199 | C3×D7 | — | 91 | 1 | no | — |
| 200 | C3×D7 | — | 91 | 1 | no | — |
| 201 | C3×D7 | — | 91 | 1 | no | — |
| 202 | C3×D7 | — | 91 | 1 | no | — |
| 203 | C2×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 204 | C2×ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 205 | C2×ΓL(1,𝔽8) | — | 39 | 1 | no | — |
| 206 | AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 207 | AGL(1,𝔽7) | — | 273 | 1 | no | — |
| 208 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 209 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 210 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 211 | AGL(1,𝔽7) | — | 91 | 1 | no | — |
| 212 | C3×C13 | — | 7 | 1 | no | — |
| 213 | C13⋊C3 | — | 7 | 1 | no | — |
| 214 | C13⋊C3 | — | 7 | 1 | no | — |
| 215 | C13⋊C3 | C2×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 216 | C22×C32 | — | 637 | 1 | no | Hall |
| 217 | C2×D7 | — | 273 | 1 | no | — |
| 218 | C2×D7 | — | 819 | 1 | no | — |
| 219 | C2×D7 | — | 819 | 1 | no | — |
| 220 | C2×D7 | — | 819 | 1 | no | — |
| 221 | C2×C13 | — | 147 | 1 | no | — |
| 222 | D13 | — | 147 | 1 | no | — |
| 223 | D13 | C3×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented |
| 224 | C3×C7 | — | 7 | 1 | no | — |
| 225 | C3×C7 | — | 13 | 1 | no | — |
| 226 | C3×C7 | — | 13 | 1 | no | — |
| 227 | C3×C7 | — | 39 | 1 | no | — |
| 228 | C3×C7 | — | 39 | 1 | no | — |
| 229 | C3×C7 | — | 91 | 1 | no | — |
| 230 | C3×C7 | — | 91 | 1 | no | — |
| 231 | ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 232 | ΓL(1,𝔽8) | — | 13 | 1 | no | — |
| 233 | ΓL(1,𝔽8) | D7×D13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 234 | C2×C32 | — | 91 | 1 | no | — |
| 235 | C2×C32 | — | 637 | 1 | no | — |
| 236 | C2×C32 | — | 637 | 1 | no | — |
| 237 | C2×C7 | — | 13 | 1 | no | — |
| 238 | C2×C7 | — | 39 | 1 | no | — |
| 239 | C2×C7 | — | 117 | 1 | no | — |
| 240 | C2×C7 | — | 117 | 1 | no | — |
| 241 | D7 | — | 7 | 1 | no | — |
| 242 | D7 | — | 273 | 1 | no | — |
| 243 | D7 | — | 273 | 1 | no | — |
| 244 | D7 | — | 273 | 1 | no | — |
| 245 | D7 | — | 21 | 1 | no | — |
| 246 | D7 | — | 21 | 1 | no | — |
| 247 | D7 | — | 21 | 1 | no | — |
| 248 | D7 | — | 819 | 1 | no | — |
| 249 | C13 | C2×C3×ΓL(1,𝔽8)⋊D7 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 250 | C22×C3 | — | 637 | 1 | no | — |
| 251 | C22×C3 | — | 637 | 1 | no | — |
| 252 | C22×C3 | — | 637 | 1 | no | — |
| 253 | C22×C3 | — | 637 | 1 | no | — |
| 254 | C32 | — | 91 | 1 | no | Sylow |
| 255 | C7 | — | 3 | 1 | no | — |
| 256 | C7 | — | 3 | 1 | no | — |
| 257 | C7 | AGL(1,𝔽7)×D13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 258 | C7 | C3×D7×D13⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 259 | C2×C3 | — | 13 | 1 | no | — |
| 260 | C2×C3 | — | 273 | 1 | no | — |
| 261 | C2×C3 | — | 49 | 1 | no | — |
| 262 | C2×C3 | — | 91 | 1 | no | — |
| 263 | C2×C3 | — | 91 | 1 | no | — |
| 264 | C2×C3 | — | 1911 | 1 | no | — |
| 265 | C2×C3 | — | 1911 | 1 | no | — |
| 266 | C2×C3 | — | 637 | 1 | no | — |
| 267 | C2×C3 | — | 637 | 1 | no | — |
| 268 | C2×C3 | — | 637 | 1 | no | — |
| 269 | C2×C3 | — | 637 | 1 | no | — |
| 270 | C2×C3 | — | 637 | 1 | no | — |
| 271 | C22 | — | 637 | 1 | no | Sylow |
| 272 | C3 | — | 7 | 1 | no | — |
| 273 | C3 | — | 13 | 1 | no | — |
| 274 | C3 | — | 91 | 1 | no | — |
| 275 | C3 | — | 91 | 1 | no | — |
| 276 | C2 | — | 39 | 1 | no | — |
| 277 | C2 | — | 49 | 1 | no | — |
| 278 | C2 | — | 5733 | 1 | no | — |
Finite Group Databasebeta