| 1 | C2×#41×ΓL(1,𝔽8) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10621519 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #10621518 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #41×AGL(1,𝔽7) | C2 | 1 | 8 | yes | maximal, complemented |
| 5 | #10621516 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #6548⋊C3 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C2×#1157⋊C3 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #90616 | C3 | 1 | 1 | yes | maximal, characteristic, complemented, Hall |
| 9 | #41×ΓL(1,𝔽8) | C22 | 1 | 4 | yes | complemented |
| 10 | #41×ΓL(1,𝔽8) | C22 | 1 | 4 | yes | complemented |
| 11 | C2×Q8×ΓL(1,𝔽8) | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×D4×ΓL(1,𝔽8) | C22 | 1 | 3 | yes | complemented |
| 13 | C22×C4×ΓL(1,𝔽8) | C22 | 1 | 3 | yes | complemented |
| 14 | C2×(C22⋊D7)⋊C3 | C22 | 1 | 12 | yes | complemented |
| 15 | #66659 | C22 | 1 | 8 | yes | complemented |
| 16 | Q8×AGL(1,𝔽7) | C22 | 1 | 8 | yes | complemented |
| 17 | #1159⋊C3 | C22 | 1 | 24 | yes | complemented |
| 18 | D4×AGL(1,𝔽7) | C22 | 1 | 24 | yes | complemented |
| 19 | #1157⋊C3 | C22 | 1 | 4 | yes | complemented |
| 20 | #1157⋊C3 | C22 | 1 | 12 | yes | complemented |
| 21 | #1157⋊C3 | C22 | 1 | 12 | yes | complemented |
| 22 | #1157⋊C3 | C22 | 1 | 12 | yes | complemented |
| 23 | C2×C4⋊AGL(1,𝔽7) | C22 | 1 | 6 | yes | complemented |
| 24 | C2×C4×AGL(1,𝔽7) | C22 | 1 | 12 | yes | complemented |
| 25 | C2×ΓL(1,𝔽8)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 26 | C2×C7×#41 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 27 | #6554 | C2×C3 | 1 | 4 | yes | complemented |
| 28 | #6553 | C2×C3 | 1 | 4 | yes | complemented |
| 29 | D7×#41 | C2×C3 | 1 | 8 | yes | complemented |
| 30 | #6551 | C2×C3 | 1 | 2 | yes | complemented |
| 31 | #6548 | C2×C3 | 1 | 6 | yes | complemented |
| 32 | C2×#1157 | C2×C3 | 1 | 6 | yes | complemented |
| 33 | C3×#585 | — | 7 | 1 | no | maximal, Hall |
| 34 | C23×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | — |
| 35 | C22×AGL(1,𝔽7) | C23 | 1 | 12 | yes | — |
| 36 | Q8×ΓL(1,𝔽8) | C23 | 1 | 4 | yes | — |
| 37 | D4×ΓL(1,𝔽8) | C23 | 1 | 12 | yes | — |
| 38 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | — |
| 39 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 6 | yes | — |
| 40 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 1 | yes | characteristic |
| 41 | C2×C4×ΓL(1,𝔽8) | C23 | 1 | 3 | yes | — |
| 42 | (C22⋊D7)⋊C3 | C23 | 1 | 8 | yes | — |
| 43 | (C22⋊D7)⋊C3 | C23 | 1 | 24 | yes | — |
| 44 | C2×ΓL(1,𝔽8)⋊C4 | C23 | 1 | 12 | yes | — |
| 45 | C4⋊AGL(1,𝔽7) | C23 | 1 | 4 | yes | — |
| 46 | C4⋊AGL(1,𝔽7) | C23 | 1 | 12 | yes | — |
| 47 | C4×AGL(1,𝔽7) | C23 | 1 | 8 | yes | — |
| 48 | C4×AGL(1,𝔽7) | C23 | 1 | 24 | yes | — |
| 49 | ΓL(1,𝔽8)⋊Q8 | C23 | 1 | 4 | yes | — |
| 50 | ΓL(1,𝔽8)⋊Q8 | C23 | 1 | 12 | yes | — |
| 51 | C7×#41 | C22×C3 | 1 | 4 | yes | complemented |
| 52 | C7×#41 | C22×C3 | 1 | 4 | yes | complemented |
| 53 | C2×C7×Q8 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 54 | C2×C7×D4 | C22×C3 | 1 | 3 | yes | complemented |
| 55 | C22×C4×C7 | C22×C3 | 1 | 3 | yes | complemented |
| 56 | C2×C22⋊D7 | C22×C3 | 1 | 12 | yes | complemented |
| 57 | #1161 | C22×C3 | 1 | 8 | yes | complemented |
| 58 | Q8×D7 | C22×C3 | 1 | 8 | yes | complemented |
| 59 | #1159 | C22×C3 | 1 | 24 | yes | complemented |
| 60 | D4×D7 | C22×C3 | 1 | 24 | yes | complemented |
| 61 | #1157 | C22×C3 | 1 | 4 | yes | complemented |
| 62 | #1157 | C22×C3 | 1 | 12 | yes | complemented |
| 63 | #1157 | C22×C3 | 1 | 12 | yes | complemented |
| 64 | #1157 | C22×C3 | 1 | 12 | yes | complemented |
| 65 | C2×D28 | C22×C3 | 1 | 6 | yes | complemented |
| 66 | C2×C4×D7 | C22×C3 | 1 | 12 | yes | complemented |
| 67 | C2×Dic14 | C22×C3 | 1 | 6 | yes | complemented |
| 68 | C3×2−1+4 | — | 7 | 2 | no | — |
| 69 | C3×2−1+4 | — | 7 | 4 | no | — |
| 70 | C3×H(5,𝔽2) | — | 7 | 6 | no | — |
| 71 | C3×H(5,𝔽2) | — | 7 | 4 | no | — |
| 72 | C2×C3×#41 | — | 7 | 6 | no | — |
| 73 | C2×C3×#41 | — | 7 | 8 | no | — |
| 74 | C2×C3×#41 | — | 7 | 1 | no | — |
| 75 | C22×ΓL(1,𝔽8) | — | 4 | 3 | no | — |
| 76 | C22×ΓL(1,𝔽8) | C24 | 1 | 6 | yes | — |
| 77 | C22×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 78 | C2×AGL(1,𝔽7) | — | 4 | 12 | no | — |
| 79 | C2×AGL(1,𝔽7) | C24 | 1 | 8 | yes | — |
| 80 | C4×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 81 | C4×ΓL(1,𝔽8) | C24 | 1 | 6 | yes | — |
| 82 | C4×ΓL(1,𝔽8) | C24 | 1 | 1 | yes | characteristic |
| 83 | ΓL(1,𝔽8)⋊C4 | C24 | 1 | 8 | yes | — |
| 84 | #585 | — | 7 | 1 | no | Sylow |
| 85 | C23×C7 | C23×C3 | 1 | 3 | yes | — |
| 86 | C22×D7 | C23×C3 | 1 | 12 | yes | — |
| 87 | C7×Q8 | C23×C3 | 1 | 4 | yes | — |
| 88 | C7×D4 | C23×C3 | 1 | 12 | yes | — |
| 89 | C2×C4×C7 | C23×C3 | 1 | 6 | yes | — |
| 90 | C2×C4×C7 | C23×C3 | 1 | 6 | yes | — |
| 91 | C2×C4×C7 | C23×C3 | 1 | 1 | yes | characteristic |
| 92 | C2×C4×C7 | C23×C3 | 1 | 3 | yes | — |
| 93 | C22⋊D7 | C23×C3 | 1 | 8 | yes | — |
| 94 | C22⋊D7 | C23×C3 | 1 | 24 | yes | — |
| 95 | C2×Dic7 | C23×C3 | 1 | 12 | yes | — |
| 96 | D28 | C23×C3 | 1 | 4 | yes | — |
| 97 | D28 | C23×C3 | 1 | 12 | yes | — |
| 98 | C4×D7 | C23×C3 | 1 | 8 | yes | — |
| 99 | C4×D7 | C23×C3 | 1 | 24 | yes | — |
| 100 | Dic14 | C23×C3 | 1 | 4 | yes | — |
| 101 | Dic14 | C23×C3 | 1 | 12 | yes | — |
| 102 | C3×#41 | — | 7 | 4 | no | — |
| 103 | C3×#41 | — | 7 | 12 | no | — |
| 104 | C3×#41 | — | 7 | 12 | no | — |
| 105 | C3×#41 | — | 7 | 12 | no | — |
| 106 | C3×#41 | — | 7 | 24 | no | — |
| 107 | C3×#41 | — | 7 | 8 | no | — |
| 108 | C3×#41 | — | 7 | 4 | no | — |
| 109 | C3×#41 | — | 7 | 4 | no | — |
| 110 | C2×C3×Q8 | — | 7 | 6 | no | — |
| 111 | C2×C3×Q8 | — | 7 | 8 | no | — |
| 112 | C2×C3×Q8 | — | 7 | 1 | no | — |
| 113 | C2×C3×D4 | — | 7 | 6 | no | — |
| 114 | C2×C3×D4 | — | 7 | 24 | no | — |
| 115 | C2×C3×D4 | — | 7 | 12 | no | — |
| 116 | C2×C3×D4 | — | 7 | 3 | no | — |
| 117 | C22×C3×C4 | — | 7 | 12 | no | — |
| 118 | C22×C3×C4 | — | 7 | 3 | no | — |
| 119 | C2×ΓL(1,𝔽8) | — | 2 | 6 | no | — |
| 120 | C2×ΓL(1,𝔽8) | — | 2 | 1 | no | — |
| 121 | C2×ΓL(1,𝔽8) | C25 | 1 | 1 | yes | characteristic |
| 122 | AGL(1,𝔽7) | — | 2 | 8 | no | — |
| 123 | 2−1+4 | — | 7 | 4 | no | — |
| 124 | 2−1+4 | — | 7 | 2 | no | — |
| 125 | H(5,𝔽2) | — | 7 | 4 | no | — |
| 126 | H(5,𝔽2) | — | 7 | 6 | no | — |
| 127 | C2×#41 | — | 7 | 8 | no | — |
| 128 | C2×#41 | — | 7 | 6 | no | — |
| 129 | C2×#41 | AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 130 | C22×C7 | — | 4 | 3 | no | — |
| 131 | C22×C7 | C24×C3 | 1 | 6 | yes | — |
| 132 | C22×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 133 | C2×D7 | — | 4 | 12 | no | — |
| 134 | C2×D7 | C24×C3 | 1 | 8 | yes | — |
| 135 | C4×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 136 | C4×C7 | C24×C3 | 1 | 6 | yes | — |
| 137 | C4×C7 | C24×C3 | 1 | 1 | yes | characteristic |
| 138 | Dic7 | C24×C3 | 1 | 8 | yes | — |
| 139 | C23×C3 | — | 7 | 12 | no | — |
| 140 | C23×C3 | — | 7 | 3 | no | — |
| 141 | C3×Q8 | — | 7 | 4 | no | — |
| 142 | C3×Q8 | — | 7 | 12 | no | — |
| 143 | C3×Q8 | — | 7 | 4 | no | — |
| 144 | C3×D4 | — | 7 | 4 | no | — |
| 145 | C3×D4 | — | 7 | 12 | no | — |
| 146 | C3×D4 | — | 7 | 8 | no | — |
| 147 | C3×D4 | — | 7 | 24 | no | — |
| 148 | C3×D4 | — | 7 | 12 | no | — |
| 149 | C2×C3×C4 | — | 7 | 8 | no | — |
| 150 | C2×C3×C4 | — | 7 | 24 | no | — |
| 151 | C2×C3×C4 | — | 7 | 12 | no | — |
| 152 | C2×C3×C4 | — | 7 | 6 | no | — |
| 153 | C2×C3×C4 | — | 7 | 1 | no | — |
| 154 | C2×C3×C4 | — | 7 | 6 | no | — |
| 155 | C2×C3×C4 | — | 7 | 3 | no | — |
| 156 | ΓL(1,𝔽8) | #585 | 1 | 1 | yes | characteristic, complemented, Hall |
| 157 | #41 | — | 7 | 8 | no | — |
| 158 | #41 | — | 7 | 24 | no | — |
| 159 | #41 | — | 7 | 12 | no | — |
| 160 | #41 | — | 7 | 4 | no | — |
| 161 | #41 | — | 7 | 12 | no | — |
| 162 | #41 | — | 7 | 12 | no | — |
| 163 | #41 | C2×AGL(1,𝔽7) | 1 | 4 | yes | complemented |
| 164 | #41 | C2×AGL(1,𝔽7) | 1 | 4 | yes | complemented |
| 165 | C2×Q8 | — | 7 | 8 | no | — |
| 166 | C2×Q8 | — | 7 | 6 | no | — |
| 167 | C2×Q8 | C2×AGL(1,𝔽7) | 1 | 1 | yes | characteristic, complemented |
| 168 | C2×D4 | — | 7 | 12 | no | — |
| 169 | C2×D4 | — | 7 | 24 | no | — |
| 170 | C2×D4 | — | 7 | 6 | no | — |
| 171 | C2×D4 | C2×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 172 | C22×C4 | — | 7 | 12 | no | — |
| 173 | C22×C4 | C2×AGL(1,𝔽7) | 1 | 3 | yes | complemented |
| 174 | C2×C7 | — | 2 | 6 | no | — |
| 175 | C2×C7 | — | 2 | 1 | no | — |
| 176 | C2×C7 | C25×C3 | 1 | 1 | yes | characteristic |
| 177 | D7 | — | 2 | 8 | no | — |
| 178 | C22×C3 | — | 7 | 8 | no | — |
| 179 | C22×C3 | — | 7 | 6 | no | — |
| 180 | C22×C3 | — | 7 | 1 | no | — |
| 181 | C22×C3 | — | 28 | 3 | no | — |
| 182 | C22×C3 | — | 28 | 12 | no | — |
| 183 | C3×C4 | — | 7 | 8 | no | — |
| 184 | C3×C4 | — | 7 | 6 | no | — |
| 185 | C3×C4 | — | 7 | 1 | no | — |
| 186 | C3×C4 | — | 7 | 1 | no | — |
| 187 | C23 | — | 7 | 12 | no | — |
| 188 | C23 | C22×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 189 | Q8 | — | 7 | 12 | no | — |
| 190 | Q8 | — | 7 | 4 | no | — |
| 191 | Q8 | C22×AGL(1,𝔽7) | 1 | 4 | yes | — |
| 192 | D4 | — | 7 | 24 | no | — |
| 193 | D4 | — | 7 | 8 | no | — |
| 194 | D4 | — | 7 | 12 | no | — |
| 195 | D4 | — | 7 | 4 | no | — |
| 196 | D4 | C22×AGL(1,𝔽7) | 1 | 12 | yes | — |
| 197 | C2×C4 | — | 7 | 12 | no | — |
| 198 | C2×C4 | — | 7 | 24 | no | — |
| 199 | C2×C4 | — | 7 | 8 | no | — |
| 200 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 201 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 3 | yes | — |
| 202 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 203 | C2×C4 | C22×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 204 | C7 | C3×#585 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 205 | C2×C3 | — | 7 | 1 | no | — |
| 206 | C2×C3 | — | 14 | 1 | no | — |
| 207 | C2×C3 | — | 14 | 6 | no | — |
| 208 | C2×C3 | — | 14 | 8 | no | — |
| 209 | C22 | — | 4 | 3 | no | — |
| 210 | C22 | — | 7 | 8 | no | — |
| 211 | C22 | — | 28 | 12 | no | — |
| 212 | C22 | C23×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 213 | C22 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 214 | C4 | — | 7 | 8 | no | — |
| 215 | C4 | C23×AGL(1,𝔽7) | 1 | 6 | yes | — |
| 216 | C4 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 217 | C4 | C23×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
| 218 | C3 | — | 7 | 1 | no | Sylow |
| 219 | C2 | — | 2 | 1 | no | — |
| 220 | C2 | — | 2 | 6 | no | — |
| 221 | C2 | — | 14 | 8 | no | — |
| 222 | C2 | C24×AGL(1,𝔽7) | 1 | 1 | yes | characteristic |
Finite Group Databasebeta