Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
639 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 639 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10595262 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10592440 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10591532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10591514 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C3×#4473 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589174 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #69154 | — | 3 | 1 | no | maximal |
| 9 | #69131 | — | 3 | 1 | no | maximal |
| 10 | #64361 | C22 | 1 | 1 | yes | characteristic |
| 11 | #64146 | C22 | 1 | 1 | yes | characteristic |
| 12 | #64091 | — | 2 | 1 | no | — |
| 13 | C3×#937 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#936 | C22 | 1 | 1 | yes | characteristic |
| 15 | #63981 | — | 2 | 1 | no | — |
| 16 | #63977 | — | 2 | 1 | no | — |
| 17 | #63977 | — | 2 | 1 | no | — |
| 18 | #63959 | — | 2 | 1 | no | — |
| 19 | #63953 | — | 2 | 1 | no | — |
| 20 | #63907 | — | 2 | 1 | no | — |
| 21 | #63852 | — | 2 | 1 | no | — |
| 22 | #63833 | — | 2 | 1 | no | — |
| 23 | C32×#99 | C22 | 1 | 1 | yes | characteristic |
| 24 | #63633 | — | 2 | 1 | no | — |
| 25 | C3×#834 | C22 | 1 | 1 | yes | characteristic |
| 26 | C3×#833 | C22 | 1 | 1 | yes | characteristic |
| 27 | #63581 | — | 2 | 1 | no | — |
| 28 | #63570 | — | 2 | 1 | no | — |
| 29 | #5683 | — | 3 | 1 | no | — |
| 30 | #5594 | — | 3 | 1 | no | — |
| 31 | #5061 | — | 3 | 1 | no | — |
| 32 | #5032 | — | 3 | 1 | no | — |
| 33 | #4746 | — | 3 | 1 | no | — |
| 34 | #4741 | — | 3 | 1 | no | — |
| 35 | #4741 | — | 3 | 1 | no | — |
| 36 | #4741 | — | 3 | 1 | no | — |
| 37 | #4741 | — | 6 | 1 | no | — |
| 38 | C3×#354 | — | 3 | 1 | no | — |
| 39 | C3×AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 40 | #4475 | — | 3 | 1 | no | — |
| 41 | #4473 | D3 | 1 | 1 | yes | characteristic, complemented |
| 42 | #4471 | — | 3 | 1 | no | — |
| 43 | #4471 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | C23×C3⋊D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 45 | C23×C3×D3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 46 | C2×C32×D4 | C23 | 1 | 1 | yes | characteristic |
| 47 | C2×#638 | — | 2 | 1 | no | — |
| 48 | C2×#638 | — | 2 | 1 | no | — |
| 49 | C2×#638 | — | 2 | 1 | no | — |
| 50 | #3830 | — | 4 | 1 | no | — |
| 51 | D4×C3⋊D3 | — | 4 | 1 | no | — |
| 52 | #3828 | — | 2 | 1 | no | — |
| 53 | C2×C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 54 | C2×C3×#67 | — | 2 | 1 | no | — |
| 55 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#627 | — | 2 | 1 | no | — |
| 57 | C2×#626 | — | 2 | 1 | no | — |
| 58 | C2×#626 | — | 2 | 1 | no | — |
| 59 | C2×#626 | — | 4 | 1 | no | — |
| 60 | C32×C22⋊C4 | — | 2 | 1 | no | — |
| 61 | #3757 | D4 | 1 | 1 | yes | characteristic, complemented |
| 62 | #3752 | — | 2 | 1 | no | — |
| 63 | #3752 | — | 4 | 1 | no | — |
| 64 | C3×#217 | — | 2 | 1 | no | — |
| 65 | C3×#217 | — | 2 | 1 | no | — |
| 66 | C3×#217 | — | 2 | 1 | no | — |
| 67 | C3×#217 | D4 | 1 | 1 | yes | characteristic, complemented |
| 68 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 69 | C3×C4×Dic3 | D4 | 1 | 1 | yes | characteristic, complemented |
| 70 | C3×#208 | — | 2 | 1 | no | — |
| 71 | #3722 | — | 2 | 1 | no | — |
| 72 | #3722 | — | 2 | 1 | no | — |
| 73 | (C2×D3)⋊Dic3 | — | 2 | 1 | no | — |
| 74 | (C2×D3)⋊Dic3 | — | 2 | 1 | no | — |
| 75 | (C2×D3)⋊Dic3 | — | 4 | 1 | no | — |
| 76 | Dic32 | — | 2 | 1 | no | — |
| 77 | #3719 | — | 4 | 1 | no | — |
| 78 | #3717 | — | 4 | 1 | no | — |
| 79 | #2199 | — | 9 | 1 | no | Sylow |
| 80 | #1004 | — | 3 | 1 | no | — |
| 81 | #1004 | — | 3 | 1 | no | — |
| 82 | #1004 | — | 6 | 1 | no | — |
| 83 | C3×#124 | — | 3 | 1 | no | — |
| 84 | C3×#120 | — | 3 | 1 | no | — |
| 85 | #953 | — | 6 | 1 | no | — |
| 86 | #953 | — | 6 | 1 | no | — |
| 87 | #947 | — | 6 | 1 | no | — |
| 88 | #942 | — | 6 | 1 | no | — |
| 89 | #937 | — | 3 | 1 | no | — |
| 90 | #937 | — | 3 | 1 | no | — |
| 91 | #937 | — | 6 | 1 | no | — |
| 92 | #937 | — | 6 | 1 | no | — |
| 93 | #937 | C2×D3 | 1 | 1 | yes | characteristic |
| 94 | #936 | — | 6 | 1 | no | — |
| 95 | #936 | C2×D3 | 1 | 1 | yes | characteristic |
| 96 | #909 | — | 6 | 1 | no | — |
| 97 | #885 | — | 6 | 1 | no | — |
| 98 | #885 | — | 6 | 1 | no | — |
| 99 | #885 | — | 6 | 1 | no | — |
| 100 | #885 | — | 6 | 1 | no | — |
| 101 | #885 | — | 6 | 1 | no | — |
| 102 | #882 | — | 6 | 1 | no | — |
| 103 | #882 | — | 6 | 1 | no | — |
| 104 | #882 | — | 6 | 1 | no | — |
| 105 | #882 | — | 6 | 1 | no | — |
| 106 | #882 | — | 6 | 2 | no | — |
| 107 | #882 | — | 6 | 1 | no | — |
| 108 | #875 | — | 6 | 1 | no | — |
| 109 | C3×#100 | — | 3 | 1 | no | — |
| 110 | C3×#99 | — | 2 | 1 | no | — |
| 111 | C3×#99 | — | 3 | 1 | no | — |
| 112 | C3×#99 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | C3×#99 | C2×D3 | 1 | 1 | yes | characteristic |
| 114 | #834 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | #833 | C2×D3 | 1 | 1 | yes | characteristic |
| 116 | #825 | — | 6 | 1 | no | — |
| 117 | #806 | — | 6 | 1 | no | — |
| 118 | #806 | — | 6 | 1 | no | — |
| 119 | #806 | — | 6 | 1 | no | — |
| 120 | #806 | — | 6 | 2 | no | — |
| 121 | #806 | — | 6 | 1 | no | — |
| 122 | #805 | — | 6 | 1 | no | — |
| 123 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C23×C32 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 126 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 127 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 128 | C22×C3⋊D3 | — | 4 | 1 | no | — |
| 129 | C22×C3⋊D3 | — | 8 | 1 | no | — |
| 130 | C22×C3×D3 | — | 2 | 1 | no | — |
| 131 | C22×C3×D3 | — | 4 | 1 | no | — |
| 132 | C22×C3×D3 | — | 8 | 1 | no | — |
| 133 | C32×D4 | — | 4 | 1 | no | — |
| 134 | C2×C32×C4 | — | 4 | 1 | no | — |
| 135 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | #638 | — | 4 | 1 | no | — |
| 137 | #638 | — | 4 | 1 | no | — |
| 138 | #638 | — | 4 | 1 | no | — |
| 139 | #638 | — | 8 | 1 | no | — |
| 140 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 141 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 142 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 143 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 144 | C4⋊(C3⋊D3) | — | 8 | 2 | no | — |
| 145 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 146 | #634 | — | 2 | 1 | no | — |
| 147 | C3×#67 | — | 8 | 1 | no | — |
| 148 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 149 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 150 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 151 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 152 | C3×Dic6 | — | 4 | 1 | no | — |
| 153 | #627 | — | 8 | 1 | no | — |
| 154 | #626 | — | 8 | 1 | no | — |
| 155 | #626 | — | 8 | 1 | no | — |
| 156 | #626 | — | 8 | 2 | no | — |
| 157 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 158 | H(3,𝔽4) | — | 9 | 1 | no | — |
| 159 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 160 | B(4,𝔽2) | — | 9 | 1 | no | — |
| 161 | #455 | — | 9 | 1 | no | — |
| 162 | #354 | — | 3 | 1 | no | — |
| 163 | AΣL(1,𝔽16) | — | 3 | 1 | no | — |
| 164 | AΣL(1,𝔽16) | — | 9 | 1 | no | — |
| 165 | C24×C3 | — | 3 | 1 | no | — |
| 166 | C23×D3 | — | 3 | 1 | no | — |
| 167 | C23×D3 | — | 3 | 1 | no | — |
| 168 | C23×D3 | — | 6 | 1 | no | — |
| 169 | C23×D3 | D12 | 1 | 1 | yes | characteristic, complemented |
| 170 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 171 | C2×C3×D4 | — | 2 | 1 | no | — |
| 172 | C2×C3×D4 | — | 6 | 1 | no | — |
| 173 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 174 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 175 | C2×#67 | — | 2 | 1 | no | — |
| 176 | C2×#67 | — | 6 | 1 | no | — |
| 177 | C2×#67 | — | 6 | 1 | no | — |
| 178 | C2×#67 | — | 6 | 2 | no | — |
| 179 | C2×#67 | — | 6 | 1 | no | — |
| 180 | C2×#67 | — | 6 | 1 | no | — |
| 181 | C2×#67 | — | 6 | 1 | no | — |
| 182 | C2×#67 | — | 6 | 1 | no | — |
| 183 | C2×#67 | — | 6 | 1 | no | — |
| 184 | C2×#67 | — | 6 | 1 | no | — |
| 185 | C2×#67 | — | 12 | 1 | no | — |
| 186 | C2×#67 | — | 12 | 1 | no | — |
| 187 | C2×#67 | — | 12 | 1 | no | — |
| 188 | #237 | — | 12 | 1 | no | — |
| 189 | #237 | — | 12 | 1 | no | — |
| 190 | #237 | — | 12 | 2 | no | — |
| 191 | D3×D4 | — | 12 | 1 | no | — |
| 192 | D3×D4 | — | 12 | 1 | no | — |
| 193 | D3×D4 | — | 12 | 2 | no | — |
| 194 | #235 | — | 6 | 1 | no | — |
| 195 | #235 | — | 6 | 1 | no | — |
| 196 | #235 | — | 12 | 1 | no | — |
| 197 | C2×D12 | — | 6 | 1 | no | — |
| 198 | C2×D12 | — | 6 | 1 | no | — |
| 199 | C2×D12 | — | 12 | 1 | no | — |
| 200 | C2×D12 | — | 12 | 1 | no | — |
| 201 | C2×D12 | — | 12 | 2 | no | — |
| 202 | C2×D12 | — | 12 | 1 | no | — |
| 203 | C2×Dic6 | — | 6 | 1 | no | — |
| 204 | C2×Dic6 | — | 6 | 1 | no | — |
| 205 | C2×Dic6 | D12 | 1 | 1 | yes | characteristic, complemented |
| 206 | C3×M16 | — | 6 | 1 | no | — |
| 207 | C3×C22⋊C4 | — | 2 | 2 | no | — |
| 208 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 209 | C3×C22⋊C4 | — | 2 | 1 | no | — |
| 210 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 211 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 212 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 213 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 214 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 215 | C3×C42 | — | 3 | 1 | no | — |
| 216 | #217 | — | 2 | 1 | no | — |
| 217 | #217 | — | 2 | 1 | no | — |
| 218 | #217 | — | 2 | 1 | no | — |
| 219 | #217 | — | 3 | 1 | no | — |
| 220 | #217 | — | 3 | 1 | no | — |
| 221 | #217 | — | 6 | 1 | no | — |
| 222 | #217 | — | 6 | 1 | no | — |
| 223 | #217 | — | 6 | 1 | no | — |
| 224 | #217 | — | 12 | 1 | no | — |
| 225 | #217 | D12 | 1 | 1 | yes | characteristic, complemented |
| 226 | #216 | — | 12 | 1 | no | — |
| 227 | #215 | — | 12 | 1 | no | — |
| 228 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 229 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 230 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 231 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 232 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 233 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 234 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 235 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 236 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 237 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 238 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 239 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 240 | (C2×D3)⋊C4 | — | 12 | 2 | no | — |
| 241 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 242 | C4×Dic3 | — | 6 | 1 | no | — |
| 243 | C4×Dic3 | — | 6 | 1 | no | — |
| 244 | C4×Dic3 | D12 | 1 | 1 | yes | characteristic, complemented |
| 245 | #208 | — | 2 | 1 | no | — |
| 246 | Dic12 | — | 12 | 1 | no | — |
| 247 | #204 | — | 12 | 1 | no | — |
| 248 | C22×C32 | — | 2 | 1 | no | — |
| 249 | C22×C32 | — | 2 | 1 | no | — |
| 250 | C22×C32 | — | 4 | 1 | no | — |
| 251 | C22×C32 | — | 4 | 1 | no | — |
| 252 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 253 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 254 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 255 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 256 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 257 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 258 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 259 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 260 | C2×C3⋊D3 | — | 8 | 1 | no | — |
| 261 | C2×C3×D3 | — | 4 | 1 | no | — |
| 262 | C2×C3×D3 | — | 4 | 1 | no | — |
| 263 | C2×C3×D3 | — | 4 | 2 | no | — |
| 264 | C2×C3×D3 | — | 4 | 1 | no | — |
| 265 | C2×C3×D3 | — | 8 | 1 | no | — |
| 266 | C32×C4 | — | 2 | 1 | no | — |
| 267 | C32×C4 | — | 8 | 1 | no | — |
| 268 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 269 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 270 | C3×Dic3 | — | 4 | 1 | no | — |
| 271 | C3×Dic3 | — | 4 | 1 | no | — |
| 272 | C3×Dic3 | — | 4 | 1 | no | — |
| 273 | C3×Dic3 | — | 8 | 1 | no | — |
| 274 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 275 | #137 | — | 18 | 1 | no | — |
| 276 | #124 | — | 3 | 1 | no | — |
| 277 | #124 | — | 18 | 1 | no | — |
| 278 | #124 | — | 18 | 1 | no | — |
| 279 | #124 | — | 18 | 1 | no | — |
| 280 | #124 | — | 18 | 1 | no | — |
| 281 | #120 | — | 3 | 1 | no | — |
| 282 | #120 | — | 9 | 1 | no | — |
| 283 | #120 | — | 18 | 1 | no | — |
| 284 | #120 | — | 18 | 1 | no | — |
| 285 | #120 | — | 18 | 1 | no | — |
| 286 | #120 | — | 18 | 1 | no | — |
| 287 | #104 | — | 18 | 1 | no | — |
| 288 | #100 | — | 3 | 1 | no | — |
| 289 | #99 | — | 3 | 1 | no | — |
| 290 | #99 | — | 18 | 1 | no | — |
| 291 | #99 | — | 18 | 1 | no | — |
| 292 | #99 | D32 | 1 | 1 | yes | characteristic |
| 293 | C23×C3 | — | 2 | 1 | no | — |
| 294 | C23×C3 | — | 2 | 1 | no | — |
| 295 | C23×C3 | — | 6 | 1 | no | — |
| 296 | C23×C3 | — | 12 | 1 | no | — |
| 297 | C23×C3 | — | 24 | 1 | no | — |
| 298 | C23×C3 | C2×D12 | 1 | 1 | yes | characteristic |
| 299 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 300 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 301 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 302 | C22×D3 | — | 2 | 1 | no | — |
| 303 | C22×D3 | — | 4 | 1 | no | — |
| 304 | C22×D3 | — | 6 | 1 | no | — |
| 305 | C22×D3 | — | 6 | 1 | no | — |
| 306 | C22×D3 | — | 6 | 2 | no | — |
| 307 | C22×D3 | — | 6 | 1 | no | — |
| 308 | C22×D3 | — | 6 | 1 | no | — |
| 309 | C22×D3 | — | 6 | 1 | no | — |
| 310 | C22×D3 | — | 6 | 1 | no | — |
| 311 | C22×D3 | — | 8 | 1 | no | — |
| 312 | C22×D3 | — | 12 | 1 | no | — |
| 313 | C22×D3 | — | 12 | 1 | no | — |
| 314 | C22×D3 | — | 12 | 1 | no | — |
| 315 | C22×D3 | — | 12 | 1 | no | — |
| 316 | C22×D3 | — | 12 | 2 | no | — |
| 317 | C22×D3 | — | 24 | 1 | no | — |
| 318 | C22×D3 | — | 24 | 1 | no | — |
| 319 | C22×D3 | — | 24 | 2 | no | — |
| 320 | C3×Q8 | — | 12 | 1 | no | — |
| 321 | C3×D4 | — | 4 | 1 | no | — |
| 322 | C3×D4 | — | 4 | 1 | no | — |
| 323 | C3×D4 | — | 4 | 2 | no | — |
| 324 | C3×D4 | — | 24 | 1 | no | — |
| 325 | C2×C3×C4 | — | 2 | 1 | no | — |
| 326 | C2×C3×C4 | — | 4 | 2 | no | — |
| 327 | C2×C3×C4 | — | 4 | 1 | no | — |
| 328 | C2×C3×C4 | — | 4 | 1 | no | — |
| 329 | C2×C3×C4 | — | 6 | 1 | no | — |
| 330 | C2×C3×C4 | — | 6 | 1 | no | — |
| 331 | C2×C3×C4 | — | 6 | 1 | no | — |
| 332 | C2×C3×C4 | — | 12 | 1 | no | — |
| 333 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 334 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 335 | #67 | — | 8 | 1 | no | — |
| 336 | #67 | — | 12 | 2 | no | — |
| 337 | #67 | — | 12 | 2 | no | — |
| 338 | #67 | — | 12 | 1 | no | — |
| 339 | #67 | — | 12 | 1 | no | — |
| 340 | #67 | — | 12 | 1 | no | — |
| 341 | #67 | — | 12 | 1 | no | — |
| 342 | #67 | — | 12 | 2 | no | — |
| 343 | #67 | — | 12 | 1 | no | — |
| 344 | #67 | — | 12 | 1 | no | — |
| 345 | #67 | — | 24 | 1 | no | — |
| 346 | #67 | — | 24 | 1 | no | — |
| 347 | #67 | — | 24 | 2 | no | — |
| 348 | #67 | — | 24 | 1 | no | — |
| 349 | #67 | — | 24 | 1 | no | — |
| 350 | #67 | — | 24 | 2 | no | — |
| 351 | C2×Dic3 | — | 2 | 1 | no | — |
| 352 | C2×Dic3 | — | 2 | 1 | no | — |
| 353 | C2×Dic3 | — | 2 | 1 | no | — |
| 354 | C2×Dic3 | — | 4 | 1 | no | — |
| 355 | C2×Dic3 | — | 6 | 2 | no | — |
| 356 | C2×Dic3 | — | 6 | 1 | no | — |
| 357 | C2×Dic3 | — | 6 | 1 | no | — |
| 358 | C2×Dic3 | — | 6 | 1 | no | — |
| 359 | C2×Dic3 | — | 6 | 1 | no | — |
| 360 | C2×Dic3 | — | 6 | 1 | no | — |
| 361 | C2×Dic3 | — | 6 | 1 | no | — |
| 362 | C2×Dic3 | — | 12 | 1 | no | — |
| 363 | C2×Dic3 | — | 12 | 1 | no | — |
| 364 | D12 | — | 6 | 1 | no | — |
| 365 | D12 | — | 6 | 1 | no | — |
| 366 | D12 | — | 12 | 1 | no | — |
| 367 | D12 | — | 24 | 4 | no | — |
| 368 | D12 | — | 24 | 2 | no | — |
| 369 | D12 | — | 24 | 2 | no | — |
| 370 | D12 | — | 24 | 1 | no | — |
| 371 | D12 | — | 24 | 1 | no | — |
| 372 | D12 | — | 24 | 2 | no | — |
| 373 | C4×D3 | — | 12 | 1 | no | — |
| 374 | C4×D3 | — | 12 | 1 | no | — |
| 375 | C4×D3 | — | 12 | 2 | no | — |
| 376 | Dic6 | — | 4 | 1 | no | — |
| 377 | Dic6 | — | 6 | 1 | no | — |
| 378 | Dic6 | — | 6 | 1 | no | — |
| 379 | Dic6 | — | 12 | 1 | no | — |
| 380 | Dic6 | — | 24 | 1 | no | — |
| 381 | Dic6 | — | 24 | 1 | no | — |
| 382 | C3×C8 | — | 12 | 1 | no | — |
| 383 | C3⋊C8 | — | 4 | 1 | no | — |
| 384 | C2×C32 | — | 2 | 1 | no | — |
| 385 | C2×C32 | — | 4 | 1 | no | — |
| 386 | C2×C32 | — | 4 | 1 | no | — |
| 387 | C2×C32 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 388 | C3⋊D3 | — | 8 | 1 | no | — |
| 389 | C3⋊D3 | — | 8 | 1 | no | — |
| 390 | C3×D3 | — | 8 | 1 | no | — |
| 391 | C24 | — | 3 | 1 | no | — |
| 392 | C24 | — | 9 | 1 | no | — |
| 393 | #41 | — | 18 | 1 | no | — |
| 394 | #41 | — | 36 | 1 | no | — |
| 395 | C2×Q8 | — | 3 | 1 | no | — |
| 396 | C2×Q8 | — | 18 | 1 | no | — |
| 397 | C2×D4 | — | 6 | 1 | no | — |
| 398 | C2×D4 | — | 18 | 1 | no | — |
| 399 | C2×D4 | — | 18 | 1 | no | — |
| 400 | C2×D4 | — | 18 | 1 | no | — |
| 401 | C2×D4 | — | 18 | 1 | no | — |
| 402 | C2×D4 | — | 18 | 1 | no | — |
| 403 | C2×D4 | — | 36 | 1 | no | — |
| 404 | C2×D4 | — | 36 | 1 | no | — |
| 405 | C2×D4 | — | 36 | 1 | no | — |
| 406 | C2×D4 | C2×D32 | 1 | 1 | yes | characteristic |
| 407 | Q16 | — | 36 | 1 | no | — |
| 408 | SD16 | — | 36 | 1 | no | — |
| 409 | M16 | — | 6 | 1 | no | — |
| 410 | C22⋊C4 | — | 2 | 1 | no | — |
| 411 | C22⋊C4 | — | 3 | 1 | no | — |
| 412 | C22⋊C4 | — | 6 | 1 | no | — |
| 413 | C22⋊C4 | — | 6 | 1 | no | — |
| 414 | C22⋊C4 | — | 6 | 1 | no | — |
| 415 | C22⋊C4 | — | 6 | 1 | no | — |
| 416 | C22⋊C4 | — | 9 | 1 | no | — |
| 417 | C22⋊C4 | — | 18 | 1 | no | — |
| 418 | C22⋊C4 | — | 18 | 1 | no | — |
| 419 | C22⋊C4 | — | 18 | 1 | no | — |
| 420 | C22⋊C4 | — | 18 | 1 | no | — |
| 421 | C22⋊C4 | — | 18 | 1 | no | — |
| 422 | C22⋊C4 | — | 36 | 1 | no | — |
| 423 | C22⋊C4 | — | 36 | 1 | no | — |
| 424 | C42 | — | 3 | 1 | no | — |
| 425 | C42 | — | 18 | 1 | no | — |
| 426 | C22×C3 | — | 2 | 2 | no | — |
| 427 | C22×C3 | — | 2 | 1 | no | — |
| 428 | C22×C3 | — | 2 | 1 | no | — |
| 429 | C22×C3 | — | 2 | 1 | no | — |
| 430 | C22×C3 | — | 2 | 1 | no | — |
| 431 | C22×C3 | — | 2 | 1 | no | — |
| 432 | C22×C3 | — | 4 | 1 | no | — |
| 433 | C22×C3 | — | 4 | 1 | no | — |
| 434 | C22×C3 | — | 4 | 1 | no | — |
| 435 | C22×C3 | — | 4 | 1 | no | — |
| 436 | C22×C3 | — | 4 | 1 | no | — |
| 437 | C22×C3 | — | 8 | 1 | no | — |
| 438 | C22×C3 | — | 8 | 1 | no | — |
| 439 | C22×C3 | — | 12 | 1 | no | — |
| 440 | C22×C3 | — | 12 | 1 | no | — |
| 441 | C22×C3 | — | 12 | 2 | no | — |
| 442 | C22×C3 | — | 12 | 1 | no | — |
| 443 | C22×C3 | — | 24 | 1 | no | — |
| 444 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 445 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 446 | C2×D3 | — | 4 | 1 | no | — |
| 447 | C2×D3 | — | 4 | 1 | no | — |
| 448 | C2×D3 | — | 4 | 2 | no | — |
| 449 | C2×D3 | — | 4 | 1 | no | — |
| 450 | C2×D3 | — | 8 | 1 | no | — |
| 451 | C2×D3 | — | 12 | 2 | no | — |
| 452 | C2×D3 | — | 12 | 1 | no | — |
| 453 | C2×D3 | — | 12 | 1 | no | — |
| 454 | C2×D3 | — | 12 | 1 | no | — |
| 455 | C2×D3 | — | 12 | 1 | no | — |
| 456 | C2×D3 | — | 12 | 4 | no | — |
| 457 | C2×D3 | — | 12 | 2 | no | — |
| 458 | C2×D3 | — | 12 | 2 | no | — |
| 459 | C2×D3 | — | 12 | 2 | no | — |
| 460 | C2×D3 | — | 12 | 1 | no | — |
| 461 | C2×D3 | — | 12 | 1 | no | — |
| 462 | C2×D3 | — | 12 | 1 | no | — |
| 463 | C2×D3 | — | 12 | 1 | no | — |
| 464 | C2×D3 | — | 24 | 1 | no | — |
| 465 | C2×D3 | — | 24 | 1 | no | — |
| 466 | C2×D3 | — | 24 | 2 | no | — |
| 467 | C2×D3 | — | 24 | 2 | no | — |
| 468 | C2×D3 | — | 24 | 1 | no | — |
| 469 | C2×D3 | — | 24 | 1 | no | — |
| 470 | C2×D3 | — | 24 | 1 | no | — |
| 471 | C2×D3 | — | 24 | 1 | no | — |
| 472 | C2×D3 | — | 24 | 1 | no | — |
| 473 | C2×D3 | — | 24 | 1 | no | — |
| 474 | C2×D3 | — | 48 | 1 | no | — |
| 475 | C3×C4 | — | 2 | 1 | no | — |
| 476 | C3×C4 | — | 2 | 1 | no | — |
| 477 | C3×C4 | — | 4 | 1 | no | — |
| 478 | C3×C4 | — | 8 | 2 | no | — |
| 479 | C3×C4 | — | 8 | 1 | no | — |
| 480 | C3×C4 | — | 8 | 1 | no | — |
| 481 | C3×C4 | — | 12 | 1 | no | — |
| 482 | C3×C4 | — | 12 | 1 | no | — |
| 483 | C3×C4 | — | 12 | 1 | no | — |
| 484 | C3×C4 | — | 24 | 1 | no | — |
| 485 | Dic3 | — | 4 | 1 | no | — |
| 486 | Dic3 | — | 4 | 1 | no | — |
| 487 | Dic3 | — | 4 | 1 | no | — |
| 488 | Dic3 | — | 8 | 1 | no | — |
| 489 | Dic3 | — | 12 | 2 | no | — |
| 490 | Dic3 | — | 12 | 1 | no | — |
| 491 | Dic3 | — | 12 | 1 | no | — |
| 492 | Dic3 | — | 12 | 1 | no | — |
| 493 | Dic3 | — | 12 | 1 | no | — |
| 494 | Dic3 | — | 24 | 1 | no | — |
| 495 | C32 | #2199 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 496 | C23 | — | 6 | 1 | no | — |
| 497 | C23 | — | 12 | 1 | no | — |
| 498 | C23 | — | 18 | 1 | no | — |
| 499 | C23 | — | 18 | 1 | no | — |
| 500 | C23 | — | 18 | 1 | no | — |
| 501 | C23 | — | 24 | 1 | no | — |
| 502 | C23 | — | 36 | 1 | no | — |
| 503 | C23 | — | 72 | 1 | no | — |
| 504 | C23 | D3×D12 | 1 | 1 | yes | characteristic |
| 505 | C23 | #3811 | 1 | 1 | yes | characteristic |
| 506 | Q8 | — | 12 | 1 | no | — |
| 507 | Q8 | — | 18 | 1 | no | — |
| 508 | Q8 | — | 72 | 1 | no | — |
| 509 | D4 | — | 4 | 1 | no | — |
| 510 | D4 | — | 18 | 1 | no | — |
| 511 | D4 | — | 24 | 1 | no | — |
| 512 | D4 | — | 36 | 1 | no | — |
| 513 | D4 | — | 36 | 1 | no | — |
| 514 | D4 | — | 36 | 1 | no | — |
| 515 | D4 | — | 72 | 2 | no | — |
| 516 | D4 | — | 72 | 1 | no | — |
| 517 | D4 | — | 72 | 1 | no | — |
| 518 | D4 | — | 72 | 2 | no | — |
| 519 | D4 | — | 72 | 1 | no | — |
| 520 | C2×C4 | — | 4 | 1 | no | — |
| 521 | C2×C4 | — | 6 | 1 | no | — |
| 522 | C2×C4 | — | 6 | 1 | no | — |
| 523 | C2×C4 | — | 6 | 1 | no | — |
| 524 | C2×C4 | — | 12 | 1 | no | — |
| 525 | C2×C4 | — | 18 | 1 | no | — |
| 526 | C2×C4 | — | 18 | 1 | no | — |
| 527 | C2×C4 | — | 18 | 1 | no | — |
| 528 | C2×C4 | — | 36 | 1 | no | — |
| 529 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 530 | C8 | — | 12 | 1 | no | — |
| 531 | C2×C3 | — | 2 | 1 | no | — |
| 532 | C2×C3 | — | 2 | 1 | no | — |
| 533 | C2×C3 | — | 2 | 1 | no | — |
| 534 | C2×C3 | — | 4 | 1 | no | — |
| 535 | C2×C3 | — | 4 | 2 | no | — |
| 536 | C2×C3 | — | 4 | 1 | no | — |
| 537 | C2×C3 | — | 4 | 1 | no | — |
| 538 | C2×C3 | — | 4 | 1 | no | — |
| 539 | C2×C3 | — | 4 | 1 | no | — |
| 540 | C2×C3 | — | 8 | 1 | no | — |
| 541 | C2×C3 | — | 24 | 1 | no | — |
| 542 | C2×C3 | #4741 | 1 | 1 | yes | characteristic |
| 543 | C2×C3 | #4741 | 1 | 1 | yes | characteristic |
| 544 | D3 | — | 8 | 1 | no | — |
| 545 | D3 | — | 24 | 2 | no | — |
| 546 | D3 | — | 24 | 2 | no | — |
| 547 | D3 | — | 24 | 1 | no | — |
| 548 | D3 | — | 24 | 1 | no | — |
| 549 | D3 | — | 24 | 1 | no | — |
| 550 | D3 | — | 24 | 1 | no | — |
| 551 | C22 | — | 2 | 1 | no | — |
| 552 | C22 | — | 2 | 1 | no | — |
| 553 | C22 | — | 4 | 1 | no | — |
| 554 | C22 | — | 4 | 1 | no | — |
| 555 | C22 | — | 12 | 1 | no | — |
| 556 | C22 | — | 12 | 1 | no | — |
| 557 | C22 | — | 12 | 2 | no | — |
| 558 | C22 | — | 12 | 1 | no | — |
| 559 | C22 | — | 24 | 1 | no | — |
| 560 | C22 | — | 36 | 1 | no | — |
| 561 | C22 | — | 36 | 1 | no | — |
| 562 | C22 | — | 36 | 2 | no | — |
| 563 | C22 | — | 36 | 1 | no | — |
| 564 | C22 | — | 36 | 1 | no | — |
| 565 | C22 | — | 72 | 1 | no | — |
| 566 | C22 | — | 72 | 1 | no | — |
| 567 | C22 | — | 72 | 1 | no | — |
| 568 | C22 | #63923 | 1 | 1 | yes | characteristic |
| 569 | C4 | — | 2 | 1 | no | — |
| 570 | C4 | — | 8 | 1 | no | — |
| 571 | C4 | — | 12 | 1 | no | — |
| 572 | C4 | — | 12 | 1 | no | — |
| 573 | C4 | — | 12 | 1 | no | — |
| 574 | C4 | — | 24 | 1 | no | — |
| 575 | C4 | — | 36 | 1 | no | — |
| 576 | C4 | — | 36 | 1 | no | — |
| 577 | C3 | — | 2 | 1 | no | — |
| 578 | C3 | #69131 | 1 | 1 | yes | characteristic, complemented |
| 579 | C3 | #69154 | 1 | 1 | yes | characteristic, complemented |
| 580 | C2 | — | 2 | 1 | no | — |
| 581 | C2 | — | 4 | 1 | no | — |
| 582 | C2 | — | 4 | 1 | no | — |
| 583 | C2 | — | 24 | 1 | no | — |
| 584 | C2 | — | 72 | 1 | no | — |
| 585 | C2 | — | 72 | 1 | no | — |
| 586 | C2 | #10590410 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10595262 | C2 | semidirect |
| 2. #10592440 | C2 | semidirect |
| 3. #10591532 | C2 | semidirect |
| 4. #10591514 | C2 | semidirect |
| 5. C3×#4473 | C2 | semidirect |
| 6. C3×#4471 | C2 | semidirect |
| 7. #10589174 | C2 | semidirect |
| 41. #4473 | D3 | semidirect |
| 43. #4471 | D3 | semidirect |
| 44. C23×C3⋊D3 | D4 | semidirect |
| 45. C23×C3×D3 | D4 | semidirect |
| 55. C2×C3×Dic6 | D4 | semidirect |
| 61. #3757 | D4 | semidirect |
| 67. C3×#217 | D4 | semidirect |
| 69. C3×C4×Dic3 | D4 | semidirect |
| 169. C23×D3 | D12 | semidirect |
| 205. C2×Dic6 | D12 | semidirect |
| 225. #217 | D12 | semidirect |
| 244. C4×Dic3 | D12 | semidirect |
| 495. C32 | #2199 | semidirect |
| 578. C3 | #69131 | semidirect |
| 579. C3 | #69154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595262 | 2 |
| #10592440 | 2 |
| #10591532 | 2 |
| #10591514 | 2 |
| C3×#4473 | 2 |
| C3×#4471 | 2 |
| #10589174 | 2 |
| #69154 | 3 |
| #69131 | 3 |