← C67×#60183 #30739434
Subgroups — C67×#60183 #30739434
Order 17152.
2612 conjugacy classes of subgroups.
The subgroup lattice has 346 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C67×#3584 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C67×#3573 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C67×#2957 | C2 | 1 | 6 | yes | maximal, complemented |
| 4 | C67×#2956 | C2 | 1 | 6 | yes | maximal, complemented |
| 5 | C67×#2955 | C2 | 1 | 6 | yes | maximal, complemented |
| 6 | C2×#443×C67 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | C67×#2916 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C67×#2901 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C4×#131×C67 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #585×C67 | C22 | 1 | 2 | yes | — |
| 11 | #578×C67 | C4 | 1 | 4 | yes | complemented |
| 12 | #577×C67 | C4 | 1 | 8 | yes | complemented |
| 13 | #576×C67 | C4 | 1 | 4 | yes | complemented |
| 14 | #575×C67 | C22 | 1 | 6 | yes | — |
| 15 | C2×#135×C67 | C22 | 1 | 6 | yes | — |
| 16 | #568×C67 | — | 2 | 8 | no | — |
| 17 | #568×C67 | C22 | 1 | 2 | yes | — |
| 18 | #568×C67 | C22 | 1 | 12 | yes | complemented |
| 19 | C2×#131×C67 | — | 2 | 8 | no | — |
| 20 | C2×#131×C67 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#131×C67 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#131×C67 | C22 | 1 | 12 | yes | complemented |
| 23 | C4×#41×C67 | C22 | 1 | 1 | yes | characteristic |
| 24 | #444×C67 | C22 | 1 | 24 | yes | complemented |
| 25 | #443×C67 | C22 | 1 | 4 | yes | complemented |
| 26 | #443×C67 | C22 | 1 | 12 | yes | complemented |
| 27 | #443×C67 | C22 | 1 | 12 | yes | complemented |
| 28 | #443×C67 | C22 | 1 | 12 | yes | complemented |
| 29 | #430×C67 | C22 | 1 | 6 | yes | complemented |
| 30 | C2×#108×C67 | C22 | 1 | 6 | yes | complemented |
| 31 | #421×C67 | C22 | 1 | 12 | yes | complemented |
| 32 | C2×#104×C67 | C22 | 1 | 12 | yes | complemented |
| 33 | #405×C67 | C22 | 1 | 3 | yes | complemented |
| 34 | #405×C67 | C22 | 1 | 3 | yes | complemented |
| 35 | C4×M16×C67 | C22 | 1 | 3 | yes | complemented |
| 36 | C2×C4×C8×C67 | C22 | 1 | 3 | yes | complemented |
| 37 | 2−1+4×C67 | — | 2 | 2 | no | — |
| 38 | 2−1+4×C67 | C2×C4 | 1 | 8 | yes | — |
| 39 | H(5,𝔽2)×C67 | — | 2 | 6 | no | — |
| 40 | H(5,𝔽2)×C67 | C2×C4 | 1 | 8 | yes | — |
| 41 | C2×#41×C67 | — | 2 | 8 | no | — |
| 42 | C2×#41×C67 | C23 | 1 | 12 | yes | — |
| 43 | C2×#41×C67 | C23 | 1 | 1 | yes | characteristic |
| 44 | #137×C67 | C2×C4 | 1 | 24 | yes | complemented |
| 45 | AGL(1,ℤ/8)×C67 | C2×C4 | 1 | 24 | yes | complemented |
| 46 | #135×C67 | C2×C4 | 1 | 12 | yes | complemented |
| 47 | #135×C67 | C2×C4 | 1 | 12 | yes | complemented |
| 48 | #135×C67 | C23 | 1 | 4 | yes | — |
| 49 | #135×C67 | C23 | 1 | 12 | yes | — |
| 50 | C2×Q16×C67 | C2×C4 | 1 | 6 | yes | complemented |
| 51 | C2×SD16×C67 | C2×C4 | 1 | 12 | yes | complemented |
| 52 | C2×D8×C67 | C2×C4 | 1 | 6 | yes | complemented |
| 53 | #131×C67 | — | 2 | 8 | no | — |
| 54 | #131×C67 | — | 2 | 24 | no | — |
| 55 | #131×C67 | — | 2 | 12 | no | — |
| 56 | #131×C67 | — | 2 | 12 | no | — |
| 57 | #131×C67 | C2×C4 | 1 | 4 | yes | — |
| 58 | #131×C67 | C2×C4 | 1 | 4 | yes | — |
| 59 | #131×C67 | D4 | 1 | 4 | yes | — |
| 60 | #131×C67 | D4 | 1 | 4 | yes | — |
| 61 | #131×C67 | C23 | 1 | 8 | yes | — |
| 62 | #131×C67 | C23 | 1 | 24 | yes | — |
| 63 | C2×M16×C67 | — | 2 | 24 | no | — |
| 64 | C2×M16×C67 | — | 2 | 12 | no | — |
| 65 | C2×M16×C67 | C23 | 1 | 12 | yes | — |
| 66 | C2×M16×C67 | C23 | 1 | 3 | yes | — |
| 67 | C2×M16×C67 | C23 | 1 | 3 | yes | — |
| 68 | C22×C8×C67 | — | 2 | 12 | no | — |
| 69 | C22×C8×C67 | C23 | 1 | 3 | yes | — |
| 70 | C22×C8×C67 | C23 | 1 | 3 | yes | — |
| 71 | C4×Q8×C67 | — | 2 | 1 | no | — |
| 72 | C4×D4×C67 | — | 2 | 3 | no | — |
| 73 | #117×C67 | C23 | 1 | 3 | yes | — |
| 74 | C2×C42×C67 | C23 | 1 | 3 | yes | — |
| 75 | #108×C67 | C23 | 1 | 4 | yes | — |
| 76 | #108×C67 | C23 | 1 | 12 | yes | — |
| 77 | #104×C67 | C23 | 1 | 8 | yes | — |
| 78 | #104×C67 | C23 | 1 | 24 | yes | — |
| 79 | #97×C67 | C23 | 1 | 6 | yes | — |
| 80 | C4×C8×C67 | C23 | 1 | 1 | yes | characteristic |
| 81 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 82 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 83 | C4×C8×C67 | C23 | 1 | 3 | yes | — |
| 84 | #41×C67 | — | 2 | 8 | no | — |
| 85 | #41×C67 | — | 2 | 24 | no | — |
| 86 | #41×C67 | — | 2 | 12 | no | — |
| 87 | #41×C67 | — | 2 | 12 | no | — |
| 88 | #41×C67 | C22×C4 | 1 | 24 | yes | — |
| 89 | #41×C67 | C22×C4 | 1 | 4 | yes | — |
| 90 | #41×C67 | C2×D4 | 1 | 4 | yes | — |
| 91 | #41×C67 | C24 | 1 | 8 | yes | — |
| 92 | C2×Q8×C67 | — | 2 | 8 | no | — |
| 93 | C2×Q8×C67 | C22×C4 | 1 | 12 | yes | — |
| 94 | C2×Q8×C67 | #41 | 1 | 1 | yes | characteristic |
| 95 | C2×D4×C67 | — | 2 | 12 | no | — |
| 96 | C2×D4×C67 | — | 2 | 24 | no | — |
| 97 | C2×D4×C67 | C22×C4 | 1 | 12 | yes | — |
| 98 | C2×D4×C67 | #41 | 1 | 3 | yes | — |
| 99 | C22×C4×C67 | — | 2 | 12 | no | — |
| 100 | C22×C4×C67 | — | 2 | 3 | no | — |
| 101 | C22×C4×C67 | C24 | 1 | 3 | yes | — |
| 102 | Q16×C67 | C22×C4 | 1 | 4 | yes | — |
| 103 | Q16×C67 | C22×C4 | 1 | 12 | yes | — |
| 104 | SD16×C67 | C22×C4 | 1 | 8 | yes | — |
| 105 | SD16×C67 | C22×C4 | 1 | 24 | yes | — |
| 106 | D8×C67 | C22×C4 | 1 | 4 | yes | — |
| 107 | D8×C67 | C22×C4 | 1 | 12 | yes | — |
| 108 | M16×C67 | — | 2 | 12 | no | — |
| 109 | M16×C67 | — | 2 | 24 | no | — |
| 110 | M16×C67 | — | 2 | 8 | no | — |
| 111 | M16×C67 | C22×C4 | 1 | 12 | yes | — |
| 112 | M16×C67 | C2×D4 | 1 | 12 | yes | — |
| 113 | M16×C67 | C24 | 1 | 8 | yes | — |
| 114 | C2×C8×C67 | — | 2 | 12 | no | — |
| 115 | C2×C8×C67 | — | 2 | 24 | no | — |
| 116 | C2×C8×C67 | — | 2 | 8 | no | — |
| 117 | C2×C8×C67 | C22×C4 | 1 | 6 | yes | — |
| 118 | C2×C8×C67 | C22×C4 | 1 | 6 | yes | — |
| 119 | C2×C8×C67 | C2×D4 | 1 | 6 | yes | — |
| 120 | C2×C8×C67 | C2×D4 | 1 | 6 | yes | — |
| 121 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 122 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 123 | C2×C8×C67 | C24 | 1 | 3 | yes | — |
| 124 | C2×C8×C67 | C24 | 1 | 1 | yes | characteristic |
| 125 | C4⋊C4×C67 | — | 2 | 3 | no | — |
| 126 | C22⋊C4×C67 | — | 2 | 3 | no | — |
| 127 | C42×C67 | — | 2 | 3 | no | — |
| 128 | C42×C67 | C24 | 1 | 1 | yes | characteristic |
| 129 | C42×C67 | C24 | 1 | 3 | yes | — |
| 130 | C23×C67 | — | 2 | 12 | no | — |
| 131 | C23×C67 | C2×#41 | 1 | 3 | yes | — |
| 132 | Q8×C67 | — | 2 | 12 | no | — |
| 133 | Q8×C67 | C4×D4 | 1 | 4 | yes | — |
| 134 | Q8×C67 | C23×C4 | 1 | 8 | yes | — |
| 135 | D4×C67 | — | 2 | 24 | no | — |
| 136 | D4×C67 | — | 2 | 8 | no | — |
| 137 | D4×C67 | — | 2 | 12 | no | — |
| 138 | D4×C67 | C4×D4 | 1 | 12 | yes | — |
| 139 | D4×C67 | C23×C4 | 1 | 8 | yes | — |
| 140 | C2×C4×C67 | — | 2 | 12 | no | — |
| 141 | C2×C4×C67 | — | 2 | 1 | no | — |
| 142 | C2×C4×C67 | — | 2 | 24 | no | — |
| 143 | C2×C4×C67 | — | 2 | 8 | no | — |
| 144 | C2×C4×C67 | — | 2 | 3 | no | — |
| 145 | C2×C4×C67 | — | 4 | 6 | no | — |
| 146 | C2×C4×C67 | C23×C4 | 1 | 6 | yes | — |
| 147 | C2×C4×C67 | C22×D4 | 1 | 6 | yes | — |
| 148 | C2×C4×C67 | C2×#41 | 1 | 3 | yes | — |
| 149 | C2×C4×C67 | C25 | 1 | 1 | yes | characteristic |
| 150 | C8×C67 | — | 2 | 8 | no | — |
| 151 | C8×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 152 | C8×C67 | C23×C4 | 1 | 1 | yes | characteristic |
| 153 | C8×C67 | C23×C4 | 1 | 6 | yes | — |
| 154 | C8×C67 | C22×D4 | 1 | 6 | yes | — |
| 155 | C8×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 156 | C8×C67 | C22×D4 | 1 | 1 | yes | characteristic |
| 157 | C22×C67 | — | 2 | 8 | no | — |
| 158 | C22×C67 | — | 4 | 3 | no | — |
| 159 | C22×C67 | — | 8 | 12 | no | — |
| 160 | C22×C67 | C2×C4×D4 | 1 | 6 | yes | — |
| 161 | C22×C67 | C22×#41 | 1 | 1 | yes | characteristic |
| 162 | C4×C67 | — | 2 | 2 | no | — |
| 163 | C4×C67 | — | 2 | 8 | no | — |
| 164 | C4×C67 | — | 4 | 3 | no | — |
| 165 | C4×C67 | C2×C4×D4 | 1 | 6 | yes | — |
| 166 | C4×C67 | C24×C4 | 1 | 1 | yes | characteristic |
| 167 | C4×C67 | C23×D4 | 1 | 1 | yes | characteristic |
| 168 | #60183 | C67 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 169 | C2×C67 | — | 2 | 1 | no | — |
| 170 | C2×C67 | — | 2 | 6 | no | — |
| 171 | C2×C67 | — | 4 | 8 | no | — |
| 172 | C2×C67 | C22×C4×D4 | 1 | 1 | yes | characteristic |
| 173 | #3584 | C2×C67 | 1 | 1 | yes | characteristic |
| 174 | #3573 | C2×C67 | 1 | 2 | yes | complemented |
| 175 | #2957 | C2×C67 | 1 | 6 | yes | complemented |
| 176 | #2956 | C2×C67 | 1 | 6 | yes | complemented |
| 177 | #2955 | C2×C67 | 1 | 6 | yes | complemented |
| 178 | C2×#443 | C2×C67 | 1 | 6 | yes | complemented |
| 179 | #2916 | C2×C67 | 1 | 1 | yes | characteristic, complemented |
| 180 | #2901 | C2×C67 | 1 | 2 | yes | complemented |
| 181 | C4×#131 | C2×C67 | 1 | 1 | yes | characteristic, complemented |
| 182 | C67 | #60183 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 183 | #585 | C22×C67 | 1 | 2 | yes | — |
| 184 | #578 | C4×C67 | 1 | 4 | yes | complemented |
| 185 | #577 | C4×C67 | 1 | 8 | yes | complemented |
| 186 | #576 | C4×C67 | 1 | 4 | yes | complemented |
| 187 | #575 | C22×C67 | 1 | 6 | yes | — |
| 188 | C2×#135 | C22×C67 | 1 | 6 | yes | — |
| 189 | #568 | — | 2 | 8 | no | — |
| 190 | #568 | C22×C67 | 1 | 2 | yes | — |
| 191 | #568 | C22×C67 | 1 | 12 | yes | complemented |
| 192 | C2×#131 | — | 2 | 8 | no | — |
| 193 | C2×#131 | C22×C67 | 1 | 1 | yes | characteristic |
| 194 | C2×#131 | C22×C67 | 1 | 1 | yes | characteristic |
| 195 | C2×#131 | C22×C67 | 1 | 12 | yes | complemented |
| 196 | C4×#41 | C22×C67 | 1 | 1 | yes | characteristic |
| 197 | #444 | C22×C67 | 1 | 24 | yes | complemented |
| 198 | #443 | C22×C67 | 1 | 4 | yes | complemented |
| 199 | #443 | C22×C67 | 1 | 12 | yes | complemented |
| 200 | #443 | C22×C67 | 1 | 12 | yes | complemented |
| 201 | #443 | C22×C67 | 1 | 12 | yes | complemented |
| 202 | #430 | C22×C67 | 1 | 6 | yes | complemented |
| 203 | C2×#108 | C22×C67 | 1 | 6 | yes | complemented |
| 204 | #421 | C22×C67 | 1 | 12 | yes | complemented |
| 205 | C2×#104 | C22×C67 | 1 | 12 | yes | complemented |
| 206 | #405 | C22×C67 | 1 | 3 | yes | complemented |
| 207 | #405 | C22×C67 | 1 | 3 | yes | complemented |
| 208 | C4×M16 | C22×C67 | 1 | 3 | yes | complemented |
| 209 | C2×C4×C8 | C22×C67 | 1 | 3 | yes | complemented |
| 210 | 2−1+4 | — | 2 | 2 | no | — |
| 211 | 2−1+4 | C2×C4×C67 | 1 | 8 | yes | — |
| 212 | H(5,𝔽2) | — | 2 | 6 | no | — |
| 213 | H(5,𝔽2) | C2×C4×C67 | 1 | 8 | yes | — |
| 214 | C2×#41 | — | 2 | 8 | no | — |
| 215 | C2×#41 | C23×C67 | 1 | 12 | yes | — |
| 216 | C2×#41 | C23×C67 | 1 | 1 | yes | characteristic |
| 217 | #137 | C2×C4×C67 | 1 | 24 | yes | complemented |
| 218 | AGL(1,ℤ/8) | C2×C4×C67 | 1 | 24 | yes | complemented |
| 219 | #135 | C2×C4×C67 | 1 | 12 | yes | complemented |
| 220 | #135 | C2×C4×C67 | 1 | 12 | yes | complemented |
| 221 | #135 | C23×C67 | 1 | 4 | yes | — |
| 222 | #135 | C23×C67 | 1 | 12 | yes | — |
| 223 | C2×Q16 | C2×C4×C67 | 1 | 6 | yes | complemented |
| 224 | C2×SD16 | C2×C4×C67 | 1 | 12 | yes | complemented |
| 225 | C2×D8 | C2×C4×C67 | 1 | 6 | yes | complemented |
| 226 | #131 | — | 2 | 8 | no | — |
| 227 | #131 | — | 2 | 24 | no | — |
| 228 | #131 | — | 2 | 12 | no | — |
| 229 | #131 | — | 2 | 12 | no | — |
| 230 | #131 | C2×C4×C67 | 1 | 4 | yes | — |
| 231 | #131 | C2×C4×C67 | 1 | 4 | yes | — |
| 232 | #131 | D4×C67 | 1 | 4 | yes | — |
| 233 | #131 | D4×C67 | 1 | 4 | yes | — |
| 234 | #131 | C23×C67 | 1 | 8 | yes | — |
| 235 | #131 | C23×C67 | 1 | 24 | yes | — |
| 236 | C2×M16 | — | 2 | 24 | no | — |
| 237 | C2×M16 | — | 2 | 12 | no | — |
| 238 | C2×M16 | C23×C67 | 1 | 12 | yes | — |
| 239 | C2×M16 | C23×C67 | 1 | 3 | yes | — |
| 240 | C2×M16 | C23×C67 | 1 | 3 | yes | — |
| 241 | C22×C8 | — | 2 | 12 | no | — |
| 242 | C22×C8 | C23×C67 | 1 | 3 | yes | — |
| 243 | C22×C8 | C23×C67 | 1 | 3 | yes | — |
| 244 | C4×Q8 | — | 2 | 1 | no | — |
| 245 | C4×D4 | — | 2 | 3 | no | — |
| 246 | #117 | C23×C67 | 1 | 3 | yes | — |
| 247 | C2×C42 | C23×C67 | 1 | 3 | yes | — |
| 248 | #108 | C23×C67 | 1 | 4 | yes | — |
| 249 | #108 | C23×C67 | 1 | 12 | yes | — |
| 250 | #104 | C23×C67 | 1 | 8 | yes | — |
| 251 | #104 | C23×C67 | 1 | 24 | yes | — |
| 252 | #97 | C23×C67 | 1 | 6 | yes | — |
| 253 | C4×C8 | C23×C67 | 1 | 1 | yes | characteristic |
| 254 | C4×C8 | C23×C67 | 1 | 3 | yes | — |
| 255 | C4×C8 | C23×C67 | 1 | 3 | yes | — |
| 256 | C4×C8 | C23×C67 | 1 | 3 | yes | — |
| 257 | #41 | — | 2 | 8 | no | — |
| 258 | #41 | — | 2 | 24 | no | — |
| 259 | #41 | — | 2 | 12 | no | — |
| 260 | #41 | — | 2 | 12 | no | — |
| 261 | #41 | C22×C4×C67 | 1 | 24 | yes | — |
| 262 | #41 | C22×C4×C67 | 1 | 4 | yes | — |
| 263 | #41 | C2×D4×C67 | 1 | 4 | yes | — |
| 264 | #41 | C24×C67 | 1 | 8 | yes | — |
| 265 | C2×Q8 | — | 2 | 8 | no | — |
| 266 | C2×Q8 | C22×C4×C67 | 1 | 12 | yes | — |
| 267 | C2×Q8 | #41×C67 | 1 | 1 | yes | characteristic |
| 268 | C2×D4 | — | 2 | 12 | no | — |
| 269 | C2×D4 | — | 2 | 24 | no | — |
| 270 | C2×D4 | C22×C4×C67 | 1 | 12 | yes | — |
| 271 | C2×D4 | #41×C67 | 1 | 3 | yes | — |
| 272 | C22×C4 | — | 2 | 12 | no | — |
| 273 | C22×C4 | — | 2 | 3 | no | — |
| 274 | C22×C4 | C24×C67 | 1 | 3 | yes | — |
| 275 | Q16 | C22×C4×C67 | 1 | 4 | yes | — |
| 276 | Q16 | C22×C4×C67 | 1 | 12 | yes | — |
| 277 | SD16 | C22×C4×C67 | 1 | 8 | yes | — |
| 278 | SD16 | C22×C4×C67 | 1 | 24 | yes | — |
| 279 | D8 | C22×C4×C67 | 1 | 4 | yes | — |
| 280 | D8 | C22×C4×C67 | 1 | 12 | yes | — |
| 281 | M16 | — | 2 | 12 | no | — |
| 282 | M16 | — | 2 | 24 | no | — |
| 283 | M16 | — | 2 | 8 | no | — |
| 284 | M16 | C22×C4×C67 | 1 | 12 | yes | — |
| 285 | M16 | C2×D4×C67 | 1 | 12 | yes | — |
| 286 | M16 | C24×C67 | 1 | 8 | yes | — |
| 287 | C2×C8 | — | 2 | 12 | no | — |
| 288 | C2×C8 | — | 2 | 8 | no | — |
| 289 | C2×C8 | — | 2 | 24 | no | — |
| 290 | C2×C8 | C22×C4×C67 | 1 | 6 | yes | — |
| 291 | C2×C8 | C22×C4×C67 | 1 | 6 | yes | — |
| 292 | C2×C8 | C2×D4×C67 | 1 | 6 | yes | — |
| 293 | C2×C8 | C2×D4×C67 | 1 | 6 | yes | — |
| 294 | C2×C8 | C24×C67 | 1 | 1 | yes | characteristic |
| 295 | C2×C8 | C24×C67 | 1 | 3 | yes | — |
| 296 | C2×C8 | C24×C67 | 1 | 1 | yes | characteristic |
| 297 | C2×C8 | C24×C67 | 1 | 3 | yes | — |
| 298 | C4⋊C4 | — | 2 | 3 | no | — |
| 299 | C22⋊C4 | — | 2 | 3 | no | — |
| 300 | C42 | — | 2 | 3 | no | — |
| 301 | C42 | C24×C67 | 1 | 1 | yes | characteristic |
| 302 | C42 | C24×C67 | 1 | 3 | yes | — |
| 303 | C23 | — | 2 | 12 | no | — |
| 304 | C23 | C2×#41×C67 | 1 | 3 | yes | — |
| 305 | Q8 | — | 2 | 12 | no | — |
| 306 | Q8 | C4×D4×C67 | 1 | 4 | yes | — |
| 307 | Q8 | C23×C4×C67 | 1 | 8 | yes | — |
| 308 | D4 | — | 2 | 24 | no | — |
| 309 | D4 | — | 2 | 8 | no | — |
| 310 | D4 | — | 2 | 12 | no | — |
| 311 | D4 | C4×D4×C67 | 1 | 12 | yes | — |
| 312 | D4 | C23×C4×C67 | 1 | 8 | yes | — |
| 313 | C2×C4 | — | 2 | 12 | no | — |
| 314 | C2×C4 | — | 2 | 1 | no | — |
| 315 | C2×C4 | — | 2 | 24 | no | — |
| 316 | C2×C4 | — | 2 | 8 | no | — |
| 317 | C2×C4 | — | 2 | 3 | no | — |
| 318 | C2×C4 | — | 4 | 6 | no | — |
| 319 | C2×C4 | C23×C4×C67 | 1 | 6 | yes | — |
| 320 | C2×C4 | C22×D4×C67 | 1 | 6 | yes | — |
| 321 | C2×C4 | C2×#41×C67 | 1 | 3 | yes | — |
| 322 | C2×C4 | C25×C67 | 1 | 1 | yes | characteristic |
| 323 | C8 | — | 2 | 8 | no | — |
| 324 | C8 | C23×C4×C67 | 1 | 1 | yes | characteristic |
| 325 | C8 | C23×C4×C67 | 1 | 1 | yes | characteristic |
| 326 | C8 | C23×C4×C67 | 1 | 6 | yes | — |
| 327 | C8 | C22×D4×C67 | 1 | 1 | yes | characteristic |
| 328 | C8 | C22×D4×C67 | 1 | 6 | yes | — |
| 329 | C8 | C22×D4×C67 | 1 | 1 | yes | characteristic |
| 330 | C22 | — | 2 | 8 | no | — |
| 331 | C22 | — | 4 | 3 | no | — |
| 332 | C22 | — | 8 | 12 | no | — |
| 333 | C22 | C2×C4×D4×C67 | 1 | 6 | yes | — |
| 334 | C22 | C22×#41×C67 | 1 | 1 | yes | characteristic |
| 335 | C4 | — | 2 | 2 | no | — |
| 336 | C4 | — | 2 | 8 | no | — |
| 337 | C4 | — | 4 | 3 | no | — |
| 338 | C4 | C2×C4×D4×C67 | 1 | 6 | yes | — |
| 339 | C4 | C24×C4×C67 | 1 | 1 | yes | characteristic |
| 340 | C4 | C23×D4×C67 | 1 | 1 | yes | characteristic |
| 341 | C2 | — | 2 | 1 | no | — |
| 342 | C2 | — | 2 | 6 | no | — |
| 343 | C2 | — | 4 | 8 | no | — |
| 344 | C2 | C22×C4×D4×C67 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta