| 1 | ΓL(1,𝔽8)×#126 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #6461⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6460⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #6459⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #6453⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #6452⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #6451⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #6449⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #6448⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #6446⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #6442⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #6441⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #6441⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #10620712 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #6432⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #90403 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 17 | C2×(C22⋊D7)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 23 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 24 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 25 | C4⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 26 | C22⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 27 | C22⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 28 | C22⋊C4×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 29 | C42×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic |
| 30 | (C22⋊Dic7)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 31 | (C22⋊Dic7)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 32 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 33 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 34 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 35 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 36 | (C2×AGL(1,𝔽7))⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 37 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 38 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 39 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 40 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 41 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 42 | C4⋊(ΓL(1,𝔽8)⋊C4) | C22 | 1 | 1 | yes | characteristic |
| 43 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 44 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 45 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 46 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 47 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 48 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 49 | (ΓL(1,𝔽8)⋊C4)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 51 | C4×ΓL(1,𝔽8)⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 52 | C7×#126 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 53 | #6461 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 54 | #6460 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 55 | #6459 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 56 | #6453 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 57 | #6452 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 58 | #6451 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 59 | #6449 | C2×C3 | 1 | 1 | yes | characteristic |
| 60 | #6448 | C2×C3 | 1 | 1 | yes | characteristic |
| 61 | #6446 | C2×C3 | 1 | 1 | yes | characteristic |
| 62 | #6442 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 63 | #6441 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 64 | #6441 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 65 | #6439 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 66 | #6432 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 67 | C3×#563 | — | 7 | 1 | no | maximal, Hall |
| 68 | C23×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×AGL(1,𝔽7) | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 76 | (C22⋊D7)⋊C3 | — | 4 | 1 | no | — |
| 77 | C2×ΓL(1,𝔽8)⋊C4 | — | 4 | 1 | no | — |
| 78 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4×AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 86 | ΓL(1,𝔽8)⋊Q8 | — | 4 | 1 | no | — |
| 87 | ΓL(1,𝔽8)⋊Q8 | — | 4 | 1 | no | — |
| 88 | ΓL(1,𝔽8)⋊Q8 | — | 4 | 1 | no | — |
| 89 | C2×C22⋊D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 90 | C22×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 91 | C2×C4×D7 | C22×C3 | 1 | 1 | yes | characteristic |
| 92 | C2×Dic14 | C22×C3 | 1 | 1 | yes | characteristic |
| 93 | C2×Dic14 | C22×C3 | 1 | 1 | yes | characteristic |
| 94 | C2×Dic14 | C22×C3 | 1 | 1 | yes | characteristic |
| 95 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 96 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 97 | C7×C4⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 98 | C7×C22⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 99 | C7×C22⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 100 | C7×C22⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 101 | C42×C7 | C22×C3 | 1 | 1 | yes | characteristic |
| 102 | C22⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 103 | C22⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 104 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 105 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 106 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 107 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 108 | (C2×D7)⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 109 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 110 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 111 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 112 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 113 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 114 | C4⋊Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 115 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 116 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 117 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 118 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 119 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 120 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 121 | Dic7⋊C4 | C22×C3 | 1 | 1 | yes | characteristic |
| 122 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 123 | C4×Dic7 | C22×C3 | 1 | 1 | yes | characteristic |
| 124 | C3×C4⋊Q8 | — | 7 | 1 | no | — |
| 125 | C3×C4⋊Q8 | — | 7 | 1 | no | — |
| 126 | C3×#126 | — | 7 | 1 | no | — |
| 127 | C3×#126 | — | 7 | 1 | no | — |
| 128 | C3×#126 | — | 7 | 1 | no | — |
| 129 | C3×#126 | — | 7 | 1 | no | — |
| 130 | C3×#125 | — | 7 | 1 | no | — |
| 131 | C3×#125 | — | 7 | 1 | no | — |
| 132 | C3×#124 | — | 7 | 1 | no | — |
| 133 | C3×#123 | — | 7 | 1 | no | — |
| 134 | C3×#123 | — | 7 | 1 | no | — |
| 135 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 136 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 137 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 138 | C3×C22⋊Q8 | — | 7 | 1 | no | — |
| 139 | C22×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 140 | C22×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 141 | C22×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 142 | C22×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 143 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 144 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 145 | C2×AGL(1,𝔽7) | — | 2 | 1 | no | — |
| 146 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 147 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 148 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 149 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 150 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 151 | C4×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 152 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 153 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 154 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 155 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 156 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 157 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 158 | ΓL(1,𝔽8)⋊C4 | — | 2 | 1 | no | — |
| 159 | #563 | — | 7 | 1 | no | Sylow |
| 160 | C23×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 161 | C22×D7 | C23×C3 | 1 | 1 | yes | characteristic |
| 162 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 163 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 164 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 165 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 166 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 167 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 168 | C22⋊D7 | — | 4 | 1 | no | — |
| 169 | C2×Dic7 | — | 4 | 1 | no | — |
| 170 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 171 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 172 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 173 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 174 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 175 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 176 | C2×Dic7 | C23×C3 | 1 | 1 | yes | characteristic |
| 177 | C4×D7 | — | 4 | 1 | no | — |
| 178 | Dic14 | — | 4 | 1 | no | — |
| 179 | Dic14 | — | 4 | 1 | no | — |
| 180 | Dic14 | — | 4 | 1 | no | — |
| 181 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 182 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 183 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 184 | C2×C3×D4 | — | 7 | 1 | no | — |
| 185 | C22×C3×C4 | — | 7 | 1 | no | — |
| 186 | C22×C3×C4 | — | 7 | 1 | no | — |
| 187 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 188 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 189 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 190 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 191 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 192 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 193 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 194 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 195 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 196 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 197 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 198 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 199 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 200 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 201 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 202 | C3×C4⋊C4 | — | 7 | 1 | no | — |
| 203 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 204 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 205 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 206 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 207 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 208 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 209 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 210 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 211 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 212 | C3×C22⋊C4 | — | 7 | 1 | no | — |
| 213 | C3×C42 | — | 7 | 1 | no | — |
| 214 | C3×C42 | — | 7 | 1 | no | — |
| 215 | C3×C42 | — | 7 | 1 | no | — |
| 216 | C2×ΓL(1,𝔽8) | — | 4 | 1 | no | — |
| 217 | C2×ΓL(1,𝔽8) | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 218 | C2×ΓL(1,𝔽8) | 2−1+4 | 1 | 1 | yes | characteristic |
| 219 | C2×ΓL(1,𝔽8) | 2−1+4 | 1 | 1 | yes | characteristic |
| 220 | AGL(1,𝔽7) | — | 4 | 1 | no | — |
| 221 | C4⋊Q8 | — | 7 | 1 | no | — |
| 222 | C4⋊Q8 | — | 7 | 1 | no | — |
| 223 | #126 | — | 7 | 1 | no | — |
| 224 | #126 | — | 7 | 1 | no | — |
| 225 | #126 | — | 7 | 1 | no | — |
| 226 | #126 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 227 | #125 | — | 7 | 1 | no | — |
| 228 | #125 | — | 7 | 1 | no | — |
| 229 | #124 | — | 7 | 1 | no | — |
| 230 | #123 | — | 7 | 1 | no | — |
| 231 | #123 | — | 7 | 1 | no | — |
| 232 | C22⋊Q8 | — | 7 | 1 | no | — |
| 233 | C22⋊Q8 | — | 7 | 1 | no | — |
| 234 | C22⋊Q8 | — | 7 | 1 | no | — |
| 235 | C22⋊Q8 | — | 7 | 1 | no | — |
| 236 | C22×C7 | — | 2 | 1 | no | — |
| 237 | C22×C7 | — | 2 | 1 | no | — |
| 238 | C22×C7 | — | 2 | 1 | no | — |
| 239 | C22×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 240 | C2×D7 | — | 2 | 1 | no | — |
| 241 | C2×D7 | — | 2 | 1 | no | — |
| 242 | C2×D7 | — | 2 | 1 | no | — |
| 243 | C4×C7 | — | 2 | 1 | no | — |
| 244 | C4×C7 | — | 2 | 1 | no | — |
| 245 | C4×C7 | — | 2 | 1 | no | — |
| 246 | C4×C7 | — | 2 | 1 | no | — |
| 247 | C4×C7 | — | 2 | 1 | no | — |
| 248 | C4×C7 | — | 2 | 1 | no | — |
| 249 | Dic7 | — | 2 | 1 | no | — |
| 250 | Dic7 | — | 2 | 1 | no | — |
| 251 | Dic7 | — | 2 | 1 | no | — |
| 252 | Dic7 | — | 2 | 1 | no | — |
| 253 | Dic7 | — | 2 | 1 | no | — |
| 254 | Dic7 | — | 2 | 1 | no | — |
| 255 | Dic7 | — | 2 | 1 | no | — |
| 256 | C23×C3 | — | 7 | 1 | no | — |
| 257 | C23×C3 | — | 7 | 1 | no | — |
| 258 | C3×Q8 | — | 28 | 1 | no | — |
| 259 | C3×Q8 | — | 28 | 1 | no | — |
| 260 | C3×Q8 | — | 28 | 1 | no | — |
| 261 | C3×D4 | — | 28 | 1 | no | — |
| 262 | C2×C3×C4 | — | 7 | 1 | no | — |
| 263 | C2×C3×C4 | — | 7 | 1 | no | — |
| 264 | C2×C3×C4 | — | 7 | 1 | no | — |
| 265 | C2×C3×C4 | — | 7 | 1 | no | — |
| 266 | C2×C3×C4 | — | 7 | 1 | no | — |
| 267 | C2×C3×C4 | — | 7 | 1 | no | — |
| 268 | C2×C3×C4 | — | 7 | 1 | no | — |
| 269 | C2×C3×C4 | — | 7 | 1 | no | — |
| 270 | C2×C3×C4 | — | 7 | 1 | no | — |
| 271 | C2×C3×C4 | — | 7 | 1 | no | — |
| 272 | C2×C3×C4 | — | 7 | 1 | no | — |
| 273 | C2×C3×C4 | — | 7 | 1 | no | — |
| 274 | C2×C3×C4 | — | 7 | 1 | no | — |
| 275 | C2×C3×C4 | — | 28 | 1 | no | — |
| 276 | C2×C3×C4 | — | 28 | 1 | no | — |
| 277 | ΓL(1,𝔽8) | #563 | 1 | 1 | yes | characteristic, complemented, Hall |
| 278 | C2×Q8 | — | 7 | 1 | no | — |
| 279 | C2×Q8 | — | 7 | 1 | no | — |
| 280 | C2×Q8 | — | 7 | 1 | no | — |
| 281 | C2×D4 | — | 7 | 1 | no | — |
| 282 | C22×C4 | — | 7 | 1 | no | — |
| 283 | C22×C4 | — | 7 | 1 | no | — |
| 284 | C4⋊C4 | — | 7 | 1 | no | — |
| 285 | C4⋊C4 | — | 7 | 1 | no | — |
| 286 | C4⋊C4 | — | 7 | 1 | no | — |
| 287 | C4⋊C4 | — | 7 | 1 | no | — |
| 288 | C4⋊C4 | — | 7 | 1 | no | — |
| 289 | C4⋊C4 | — | 7 | 1 | no | — |
| 290 | C4⋊C4 | — | 7 | 1 | no | — |
| 291 | C4⋊C4 | — | 7 | 1 | no | — |
| 292 | C4⋊C4 | — | 7 | 1 | no | — |
| 293 | C4⋊C4 | — | 7 | 1 | no | — |
| 294 | C4⋊C4 | — | 7 | 1 | no | — |
| 295 | C4⋊C4 | — | 7 | 1 | no | — |
| 296 | C4⋊C4 | — | 7 | 1 | no | — |
| 297 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 298 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 299 | C4⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 300 | C22⋊C4 | — | 7 | 1 | no | — |
| 301 | C22⋊C4 | — | 7 | 1 | no | — |
| 302 | C22⋊C4 | — | 7 | 1 | no | — |
| 303 | C22⋊C4 | — | 7 | 1 | no | — |
| 304 | C22⋊C4 | — | 7 | 1 | no | — |
| 305 | C22⋊C4 | — | 7 | 1 | no | — |
| 306 | C22⋊C4 | — | 7 | 1 | no | — |
| 307 | C22⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 308 | C22⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 309 | C22⋊C4 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 310 | C42 | — | 7 | 1 | no | — |
| 311 | C42 | — | 7 | 1 | no | — |
| 312 | C42 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 313 | C2×C7 | — | 4 | 1 | no | — |
| 314 | C2×C7 | C3×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 315 | C2×C7 | C3×2−1+4 | 1 | 1 | yes | characteristic |
| 316 | C2×C7 | C3×2−1+4 | 1 | 1 | yes | characteristic |
| 317 | D7 | — | 4 | 1 | no | — |
| 318 | C22×C3 | — | 7 | 1 | no | — |
| 319 | C22×C3 | — | 14 | 1 | no | — |
| 320 | C22×C3 | — | 14 | 1 | no | — |
| 321 | C22×C3 | — | 14 | 1 | no | — |
| 322 | C22×C3 | — | 14 | 1 | no | — |
| 323 | C22×C3 | — | 14 | 1 | no | — |
| 324 | C22×C3 | — | 14 | 1 | no | — |
| 325 | C3×C4 | — | 14 | 1 | no | — |
| 326 | C3×C4 | — | 14 | 1 | no | — |
| 327 | C3×C4 | — | 14 | 1 | no | — |
| 328 | C3×C4 | — | 14 | 1 | no | — |
| 329 | C3×C4 | — | 14 | 1 | no | — |
| 330 | C3×C4 | — | 14 | 1 | no | — |
| 331 | C3×C4 | — | 14 | 1 | no | — |
| 332 | C3×C4 | — | 14 | 1 | no | — |
| 333 | C3×C4 | — | 14 | 1 | no | — |
| 334 | C3×C4 | — | 14 | 1 | no | — |
| 335 | C3×C4 | — | 14 | 1 | no | — |
| 336 | C3×C4 | — | 14 | 1 | no | — |
| 337 | C3×C4 | — | 14 | 1 | no | — |
| 338 | C23 | — | 7 | 1 | no | — |
| 339 | C23 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 340 | Q8 | — | 28 | 1 | no | — |
| 341 | Q8 | — | 28 | 1 | no | — |
| 342 | Q8 | — | 28 | 1 | no | — |
| 343 | D4 | — | 28 | 1 | no | — |
| 344 | C2×C4 | — | 7 | 1 | no | — |
| 345 | C2×C4 | — | 7 | 1 | no | — |
| 346 | C2×C4 | — | 7 | 1 | no | — |
| 347 | C2×C4 | — | 7 | 1 | no | — |
| 348 | C2×C4 | — | 7 | 1 | no | — |
| 349 | C2×C4 | — | 7 | 1 | no | — |
| 350 | C2×C4 | — | 7 | 1 | no | — |
| 351 | C2×C4 | — | 28 | 1 | no | — |
| 352 | C2×C4 | — | 28 | 1 | no | — |
| 353 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 354 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 355 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 356 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 357 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 358 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 359 | C7 | C3×#563 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 360 | C2×C3 | — | 7 | 1 | no | — |
| 361 | C2×C3 | — | 7 | 1 | no | — |
| 362 | C2×C3 | — | 7 | 1 | no | — |
| 363 | C2×C3 | — | 28 | 1 | no | — |
| 364 | C2×C3 | — | 28 | 1 | no | — |
| 365 | C22 | — | 2 | 1 | no | — |
| 366 | C22 | — | 2 | 1 | no | — |
| 367 | C22 | — | 2 | 1 | no | — |
| 368 | C22 | — | 14 | 1 | no | — |
| 369 | C22 | — | 14 | 1 | no | — |
| 370 | C22 | — | 14 | 1 | no | — |
| 371 | C22 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 372 | C4 | — | 2 | 1 | no | — |
| 373 | C4 | — | 2 | 1 | no | — |
| 374 | C4 | — | 2 | 1 | no | — |
| 375 | C4 | — | 2 | 1 | no | — |
| 376 | C4 | — | 2 | 1 | no | — |
| 377 | C4 | — | 2 | 1 | no | — |
| 378 | C4 | — | 14 | 1 | no | — |
| 379 | C4 | — | 14 | 1 | no | — |
| 380 | C4 | — | 14 | 1 | no | — |
| 381 | C4 | — | 14 | 1 | no | — |
| 382 | C4 | — | 14 | 1 | no | — |
| 383 | C4 | — | 14 | 1 | no | — |
| 384 | C4 | — | 14 | 1 | no | — |
| 385 | C3 | — | 7 | 1 | no | Sylow |
| 386 | C2 | — | 4 | 1 | no | — |
| 387 | C2 | — | 28 | 1 | no | — |
| 388 | C2 | #10621518 | 1 | 1 | yes | characteristic |
| 389 | C2 | #10621519 | 1 | 1 | yes | characteristic |
| 390 | C2 | #10621519 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta