| 1 | C2×C17×ΓL(1,𝔽8)2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | ΓL(1,𝔽8)×C17⋊AGL(1,𝔽7) | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 3 | ΓL(1,𝔽8)×C17⋊AGL(1,𝔽7) | C2 | 1 | 1 | yes | maximal, characteristic, direct product factor |
| 4 | C2×ΓL(1,𝔽8)×D119 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C17⋊#64422 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C2×C17⋊#64423 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C7×C17⋊AGL(1,𝔽7) | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C17×ΓL(1,𝔽8)2 | C22 | 1 | 1 | yes | characteristic, complemented, Hall |
| 9 | C2×C17×#3862 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C2×C17×#3861 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×C7×C17×ΓL(1,𝔽8) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×C7×C17×ΓL(1,𝔽8) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 13 | ΓL(1,𝔽8)×D119 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 14 | ΓL(1,𝔽8)×D119 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 15 | C17⋊#64422 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 16 | C17⋊#64422 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | C17⋊#64423 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 18 | C17⋊#64423 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 19 | C7×C17⋊AGL(1,𝔽7) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 20 | C7×C17⋊AGL(1,𝔽7) | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×C3×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | maximal |
| 22 | C2×C3×C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | maximal |
| 23 | C2×C7×D119 | C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 24 | C17×#3862 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 25 | C17×#3861 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C7×C17×ΓL(1,𝔽8) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | C7×C17×ΓL(1,𝔽8) | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 28 | C2×C3×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 29 | C2×C3×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 30 | C3×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 31 | C3×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 32 | C3×C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 33 | C3×C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 34 | C2×ΓL(1,𝔽8)×AGL(1,𝔽7) | — | 17 | 1 | no | maximal, Hall |
| 35 | C2×C72×C17 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 36 | C7×D119 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 37 | C7×D119 | C2×C32 | 1 | 1 | yes | characteristic, complemented |
| 38 | C2×C3×D119 | — | 7 | 1 | no | — |
| 39 | C2×C3×C7×D17 | — | 7 | 1 | no | — |
| 40 | C2×C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 41 | C2×C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 42 | C2×C17⋊AGL(1,𝔽7) | ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 43 | C2×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 44 | C2×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 45 | C2×ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 46 | C3×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 47 | C3×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 48 | C2×ΓL(1,𝔽8)2 | D17 | 1 | 1 | yes | characteristic, complemented |
| 49 | ΓL(1,𝔽8)×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 50 | ΓL(1,𝔽8)×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 51 | C72×C17 | C22×C32 | 1 | 1 | yes | characteristic, complemented, Hall |
| 52 | C2×C3×C7×C17 | — | 7 | 1 | no | — |
| 53 | C2×C3×C7×C17 | — | 7 | 1 | no | — |
| 54 | C3×D119 | — | 7 | 1 | no | — |
| 55 | C3×D119 | — | 7 | 1 | no | — |
| 56 | C3×C7×D17 | — | 7 | 1 | no | — |
| 57 | C3×C7×D17 | — | 7 | 1 | no | — |
| 58 | C2×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 59 | C2×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 60 | C2×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 61 | C2×C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 62 | C2×C17×ΓL(1,𝔽8) | — | 42 | 1 | no | — |
| 63 | C2×C17×ΓL(1,𝔽8) | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×C17×ΓL(1,𝔽8) | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 65 | C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 66 | C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 67 | C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 68 | C17⋊AGL(1,𝔽7) | — | 7 | 1 | no | — |
| 69 | C17⋊AGL(1,𝔽7) | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 70 | C17⋊AGL(1,𝔽7) | C2×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, direct product factor |
| 71 | ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 72 | ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 73 | ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 74 | ΓL(1,𝔽8)×D17 | — | 7 | 1 | no | — |
| 75 | ΓL(1,𝔽8)×D17 | — | 21 | 1 | no | — |
| 76 | ΓL(1,𝔽8)×D17 | — | 21 | 1 | no | — |
| 77 | C2×C32×D17 | — | 49 | 1 | no | Hall |
| 78 | C2×#64422 | — | 17 | 1 | no | — |
| 79 | C2×#64423 | — | 17 | 1 | no | — |
| 80 | C2×D7×ΓL(1,𝔽8) | — | 17 | 1 | no | — |
| 81 | C2×C7×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 82 | C2×D119 | C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 83 | C2×C7×D17 | — | 7 | 1 | no | — |
| 84 | ΓL(1,𝔽8)2 | C2×D17 | 1 | 1 | yes | characteristic, complemented, Hall |
| 85 | C3×C7×C17 | — | 7 | 1 | no | — |
| 86 | C3×C7×C17 | — | 7 | 1 | no | — |
| 87 | C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 88 | C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 89 | C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 90 | C17×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 91 | C17×ΓL(1,𝔽8) | — | 42 | 1 | no | — |
| 92 | C17×ΓL(1,𝔽8) | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 93 | C17×ΓL(1,𝔽8) | C22×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 94 | C2×C32×C17 | — | 49 | 1 | no | — |
| 95 | C32×D17 | — | 49 | 1 | no | — |
| 96 | C32×D17 | — | 49 | 1 | no | — |
| 97 | C2×#3862 | C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 98 | C2×#3861 | C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 99 | C2×C7×ΓL(1,𝔽8) | C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 100 | C2×C7×ΓL(1,𝔽8) | C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 101 | #64423 | — | 17 | 1 | no | — |
| 102 | #64423 | — | 17 | 1 | no | — |
| 103 | #64422 | — | 17 | 1 | no | — |
| 104 | #64422 | — | 17 | 1 | no | — |
| 105 | D7×ΓL(1,𝔽8) | — | 17 | 1 | no | — |
| 106 | D7×ΓL(1,𝔽8) | — | 17 | 1 | no | — |
| 107 | C7×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 108 | C7×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 109 | C22×C3×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 110 | C2×C3×AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 111 | C2×C7×C17 | — | 6 | 1 | no | — |
| 112 | C2×C7×C17 | C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 113 | C2×C7×C17 | C2×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 114 | D119 | C2×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 115 | D119 | C2×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 116 | C7×D17 | — | 21 | 1 | no | — |
| 117 | C7×D17 | — | 21 | 1 | no | — |
| 118 | C2×C3×D17 | — | 7 | 1 | no | — |
| 119 | C2×C3×D17 | — | 49 | 1 | no | — |
| 120 | C2×C3×D17 | — | 49 | 1 | no | — |
| 121 | C2×C3×D17 | — | 147 | 1 | no | — |
| 122 | C2×C7×D7 | — | 17 | 1 | no | Hall |
| 123 | C32×C17 | — | 49 | 1 | no | Hall |
| 124 | #3862 | C2×C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 125 | #3861 | C2×C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 126 | C7×ΓL(1,𝔽8) | C2×C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 127 | C7×ΓL(1,𝔽8) | C2×C3×D17 | 1 | 1 | yes | characteristic, complemented |
| 128 | C2×C3×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 129 | C2×C3×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 130 | C2×C3×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 131 | C2×C3×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 132 | C3×AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 133 | C3×AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 134 | C7×C17 | — | 6 | 1 | no | — |
| 135 | C7×C17 | C2×C3×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 136 | C7×C17 | C22×C3×ΓL(1,𝔽8) | 1 | 1 | yes | characteristic, complemented |
| 137 | C2×C3×C17 | — | 7 | 1 | no | — |
| 138 | C2×C3×C17 | — | 7 | 1 | no | — |
| 139 | C2×C3×C17 | — | 49 | 1 | no | — |
| 140 | C2×C3×C17 | — | 49 | 1 | no | — |
| 141 | C3×D17 | — | 7 | 1 | no | — |
| 142 | C3×D17 | — | 7 | 1 | no | — |
| 143 | C3×D17 | — | 49 | 1 | no | — |
| 144 | C3×D17 | — | 49 | 1 | no | — |
| 145 | C3×D17 | — | 49 | 1 | no | — |
| 146 | C3×D17 | — | 49 | 1 | no | — |
| 147 | C3×D17 | — | 49 | 1 | no | — |
| 148 | C3×D17 | — | 147 | 1 | no | — |
| 149 | C2×C72 | C32×D17 | 1 | 1 | yes | characteristic, complemented |
| 150 | C7×D7 | — | 17 | 1 | no | — |
| 151 | C7×D7 | — | 17 | 1 | no | — |
| 152 | C22×C3×C7 | — | 119 | 1 | no | — |
| 153 | C2×C3×D7 | — | 119 | 1 | no | — |
| 154 | C22×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 155 | C22×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 156 | C22×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 157 | C2×AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 158 | C2×AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 159 | C2×AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 160 | C2×D17 | — | 21 | 1 | no | Hall |
| 161 | C3×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 162 | C3×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 163 | C3×C17 | — | 7 | 1 | no | — |
| 164 | C3×C17 | — | 7 | 1 | no | — |
| 165 | C3×C17 | — | 49 | 1 | no | — |
| 166 | C3×C17 | — | 49 | 1 | no | — |
| 167 | C72 | C2×C32×D17 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 168 | C2×C3×C7 | — | 7 | 1 | no | — |
| 169 | C2×C3×C7 | — | 7 | 1 | no | — |
| 170 | C2×C3×C7 | — | 119 | 1 | no | — |
| 171 | C2×C3×C7 | — | 119 | 1 | no | — |
| 172 | C3×D7 | — | 119 | 1 | no | — |
| 173 | C3×D7 | — | 119 | 1 | no | — |
| 174 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 175 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 176 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 177 | C2×ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 178 | C2×ΓL(1,𝔽8) | — | 42 | 1 | no | — |
| 179 | C2×ΓL(1,𝔽8) | — | 357 | 1 | no | — |
| 180 | C2×ΓL(1,𝔽8) | — | 357 | 1 | no | — |
| 181 | C2×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 182 | C2×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 183 | C2×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 184 | C2×ΓL(1,𝔽8) | — | 119 | 1 | no | — |
| 185 | C2×ΓL(1,𝔽8) | ΓL(1,𝔽8)×D17 | 1 | 1 | yes | characteristic, complemented |
| 186 | C2×ΓL(1,𝔽8) | C17⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 187 | AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 188 | AGL(1,𝔽7) | — | 17 | 1 | no | — |
| 189 | AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 190 | AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 191 | AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 192 | AGL(1,𝔽7) | — | 119 | 1 | no | — |
| 193 | C22×C32 | — | 833 | 1 | no | Hall |
| 194 | C2×C17 | ΓL(1,𝔽8)×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 195 | D17 | — | 7 | 1 | no | — |
| 196 | D17 | — | 21 | 1 | no | — |
| 197 | C22×C7 | — | 119 | 1 | no | — |
| 198 | C2×D7 | — | 17 | 1 | no | — |
| 199 | C3×C7 | — | 7 | 1 | no | — |
| 200 | C3×C7 | — | 7 | 1 | no | — |
| 201 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 202 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 203 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 204 | ΓL(1,𝔽8) | — | 7 | 1 | no | — |
| 205 | ΓL(1,𝔽8) | — | 42 | 1 | no | — |
| 206 | ΓL(1,𝔽8) | C2×ΓL(1,𝔽8)×D17 | 1 | 1 | yes | characteristic, complemented |
| 207 | ΓL(1,𝔽8) | C2×C17⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
| 208 | C2×C32 | — | 49 | 1 | no | — |
| 209 | C2×C32 | — | 833 | 1 | no | — |
| 210 | C2×C32 | — | 833 | 1 | no | — |
| 211 | C17 | C2×ΓL(1,𝔽8)×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented, Sylow |
| 212 | C2×C7 | — | 6 | 1 | no | — |
| 213 | C2×C7 | — | 357 | 1 | no | — |
| 214 | C2×C7 | — | 357 | 1 | no | — |
| 215 | C2×C7 | C3×C17⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 216 | C2×C7 | C3×ΓL(1,𝔽8)×D17 | 1 | 1 | yes | characteristic, complemented |
| 217 | D7 | — | 17 | 1 | no | — |
| 218 | D7 | — | 17 | 1 | no | — |
| 219 | C22×C3 | — | 833 | 1 | no | — |
| 220 | C22×C3 | — | 833 | 1 | no | — |
| 221 | C22×C3 | — | 119 | 1 | no | — |
| 222 | C22×C3 | — | 2499 | 1 | no | — |
| 223 | C32 | — | 49 | 1 | no | Sylow |
| 224 | C7 | — | 6 | 1 | no | — |
| 225 | C7 | C2×C3×C17⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 226 | C7 | C2×C3×ΓL(1,𝔽8)×D17 | 1 | 1 | yes | characteristic, complemented |
| 227 | C2×C3 | — | 7 | 1 | no | — |
| 228 | C2×C3 | — | 7 | 1 | no | — |
| 229 | C2×C3 | — | 49 | 1 | no | — |
| 230 | C2×C3 | — | 49 | 1 | no | — |
| 231 | C2×C3 | — | 833 | 1 | no | — |
| 232 | C2×C3 | — | 833 | 1 | no | — |
| 233 | C2×C3 | — | 833 | 1 | no | — |
| 234 | C2×C3 | — | 833 | 1 | no | — |
| 235 | C2×C3 | — | 833 | 1 | no | — |
| 236 | C2×C3 | — | 119 | 1 | no | — |
| 237 | C2×C3 | — | 119 | 1 | no | — |
| 238 | C2×C3 | — | 2499 | 1 | no | — |
| 239 | C22 | — | 357 | 1 | no | Sylow |
| 240 | C3 | — | 7 | 1 | no | — |
| 241 | C3 | — | 7 | 1 | no | — |
| 242 | C3 | — | 49 | 1 | no | — |
| 243 | C3 | — | 49 | 1 | no | — |
| 244 | C2 | — | 357 | 1 | no | — |
| 245 | C2 | — | 119 | 1 | no | — |
| 246 | C2 | ΓL(1,𝔽8)×C17⋊AGL(1,𝔽7) | 1 | 1 | yes | characteristic, direct product factor |
Finite Group Databasebeta