Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
528 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 528 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 | #10595439 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#4753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10591646 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10591645 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589343 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C3×#4477 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589182 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #70987 | — | 3 | 1 | no | maximal |
| 9 | #69160 | — | 3 | 1 | no | maximal |
| 10 | C3×#1007 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #64156 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×#947 | C22 | 1 | 1 | yes | characteristic |
| 13 | C3×#947 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×#908 | — | 2 | 1 | no | — |
| 15 | #63923 | — | 2 | 1 | no | — |
| 16 | #63922 | — | 2 | 1 | no | — |
| 17 | #63922 | — | 2 | 1 | no | — |
| 18 | #63915 | — | 2 | 1 | no | — |
| 19 | #63852 | — | 2 | 1 | no | — |
| 20 | #63852 | — | 2 | 1 | no | — |
| 21 | #63825 | — | 2 | 1 | no | — |
| 22 | #63823 | — | 2 | 1 | no | — |
| 23 | C32×#101 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #63663 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C3×#836 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×#825 | — | 2 | 1 | no | — |
| 27 | #63569 | — | 2 | 1 | no | — |
| 28 | #63568 | — | 2 | 1 | no | — |
| 29 | #5683 | — | 3 | 1 | no | — |
| 30 | #5683 | — | 3 | 1 | no | — |
| 31 | C3×#454 | — | 3 | 1 | no | — |
| 32 | #5245 | — | 3 | 1 | no | — |
| 33 | #5245 | — | 3 | 1 | no | — |
| 34 | #5062 | — | 3 | 1 | no | — |
| 35 | #4753 | — | 3 | 1 | no | — |
| 36 | #4753 | D3 | 1 | 1 | yes | characteristic, complemented |
| 37 | C3×#355 | — | 3 | 1 | no | — |
| 38 | #4542 | — | 3 | 1 | no | — |
| 39 | #4477 | — | 3 | 1 | no | — |
| 40 | #4477 | — | 3 | 1 | no | — |
| 41 | #4477 | — | 3 | 1 | no | — |
| 42 | #4477 | — | 6 | 1 | no | — |
| 43 | #4477 | D3 | 1 | 1 | yes | characteristic, complemented |
| 44 | C22×D32 | — | 2 | 1 | no | — |
| 45 | C2×C32×Q8 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 47 | C3×#239 | — | 4 | 1 | no | — |
| 48 | C3×D3×Q8 | — | 4 | 1 | no | — |
| 49 | C3×#235 | — | 2 | 1 | no | — |
| 50 | C3×#235 | — | 2 | 1 | no | — |
| 51 | C3×#235 | — | 2 | 1 | no | — |
| 52 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic |
| 53 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic |
| 54 | C2×#627 | — | 2 | 1 | no | — |
| 55 | C2×#626 | — | 2 | 1 | no | — |
| 56 | C2×#626 | — | 2 | 1 | no | — |
| 57 | C2×#625 | — | 2 | 1 | no | — |
| 58 | C32×M16 | — | 2 | 1 | no | — |
| 59 | #3752 | — | 2 | 1 | no | — |
| 60 | #3752 | — | 2 | 1 | no | — |
| 61 | C4×C3⋊Dic3 | D4 | 1 | 1 | yes | characteristic |
| 62 | #3748 | — | 2 | 1 | no | — |
| 63 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 64 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 65 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 66 | C3×(C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 67 | C3×C4×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 68 | C3×C4×Dic3 | D4 | 1 | 1 | yes | characteristic |
| 69 | C3×#208 | — | 2 | 1 | no | — |
| 70 | C3×D24 | — | 4 | 1 | no | — |
| 71 | C3×#204 | — | 4 | 1 | no | — |
| 72 | #3722 | — | 2 | 1 | no | — |
| 73 | (C2×D3)⋊Dic3 | — | 2 | 1 | no | — |
| 74 | (C2×D3)⋊Dic3 | — | 2 | 1 | no | — |
| 75 | #3717 | — | 4 | 1 | no | — |
| 76 | #3715 | — | 4 | 1 | no | — |
| 77 | #3714 | — | 4 | 1 | no | — |
| 78 | #3713 | — | 4 | 1 | no | — |
| 79 | #2202 | — | 9 | 1 | no | Sylow |
| 80 | C3×2−1+4 | — | 3 | 1 | no | — |
| 81 | #1007 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 82 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 83 | C3×#124 | — | 3 | 1 | no | — |
| 84 | C3×#124 | — | 3 | 1 | no | — |
| 85 | #949 | — | 6 | 1 | no | — |
| 86 | #949 | — | 6 | 1 | no | — |
| 87 | #947 | — | 3 | 1 | no | — |
| 88 | #947 | — | 3 | 1 | no | — |
| 89 | #947 | — | 6 | 1 | no | — |
| 90 | #947 | C2×D3 | 1 | 1 | yes | characteristic |
| 91 | #947 | C2×D3 | 1 | 1 | yes | characteristic |
| 92 | #937 | — | 6 | 1 | no | — |
| 93 | #937 | — | 6 | 1 | no | — |
| 94 | #932 | — | 6 | 1 | no | — |
| 95 | #908 | — | 2 | 1 | no | — |
| 96 | #908 | — | 6 | 1 | no | — |
| 97 | #885 | — | 6 | 1 | no | — |
| 98 | #885 | — | 6 | 1 | no | — |
| 99 | #885 | — | 6 | 1 | no | — |
| 100 | #885 | — | 6 | 1 | no | — |
| 101 | #882 | — | 6 | 1 | no | — |
| 102 | #882 | — | 6 | 1 | no | — |
| 103 | #882 | — | 6 | 1 | no | — |
| 104 | #882 | — | 6 | 1 | no | — |
| 105 | #875 | — | 6 | 1 | no | — |
| 106 | #875 | — | 6 | 1 | no | — |
| 107 | C3×#104 | — | 6 | 1 | no | — |
| 108 | C3×#101 | — | 2 | 1 | no | — |
| 109 | C3×#101 | — | 3 | 1 | no | — |
| 110 | C3×#101 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 111 | C3×#101 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | #837 | — | 6 | 1 | no | — |
| 113 | #837 | — | 6 | 1 | no | — |
| 114 | #836 | — | 3 | 1 | no | — |
| 115 | #836 | — | 3 | 1 | no | — |
| 116 | #836 | — | 6 | 1 | no | — |
| 117 | #836 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 118 | #825 | — | 2 | 1 | no | — |
| 119 | #825 | — | 6 | 1 | no | — |
| 120 | #805 | — | 6 | 1 | no | — |
| 121 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 122 | C22×C3×D3 | — | 2 | 1 | no | — |
| 123 | C22×C3×D3 | — | 2 | 1 | no | — |
| 124 | C2×D32 | — | 8 | 1 | no | — |
| 125 | C2×D32 | — | 8 | 1 | no | — |
| 126 | C2×D32 | — | 8 | 1 | no | — |
| 127 | C32×Q8 | — | 4 | 1 | no | — |
| 128 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 132 | C4⋊(C3⋊D3) | — | 4 | 1 | no | — |
| 133 | C3×#67 | — | 4 | 1 | no | — |
| 134 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 135 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 136 | C3×D12 | — | 2 | 1 | no | — |
| 137 | C3×D12 | — | 2 | 1 | no | — |
| 138 | C3×D12 | — | 2 | 1 | no | — |
| 139 | C3×D12 | — | 4 | 1 | no | — |
| 140 | C3×D12 | — | 4 | 1 | no | — |
| 141 | C3×C4×D3 | — | 4 | 1 | no | — |
| 142 | C3×C4×D3 | — | 4 | 1 | no | — |
| 143 | C3×C4×D3 | — | 4 | 1 | no | — |
| 144 | C3×Dic6 | — | 2 | 1 | no | — |
| 145 | C3×Dic6 | — | 2 | 1 | no | — |
| 146 | C3×Dic6 | — | 2 | 1 | no | — |
| 147 | #627 | — | 8 | 1 | no | — |
| 148 | #626 | — | 8 | 1 | no | — |
| 149 | #626 | — | 8 | 1 | no | — |
| 150 | #625 | — | 8 | 1 | no | — |
| 151 | C32×C8 | — | 4 | 1 | no | — |
| 152 | C3⋊(C3⋊C8) | — | 4 | 1 | no | — |
| 153 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 154 | H(3,𝔽4) | — | 9 | 1 | no | — |
| 155 | #454 | — | 3 | 1 | no | — |
| 156 | #454 | — | 9 | 1 | no | — |
| 157 | #454 | — | 9 | 1 | no | — |
| 158 | #355 | — | 3 | 1 | no | — |
| 159 | #355 | — | 9 | 1 | no | — |
| 160 | #355 | — | 9 | 1 | no | — |
| 161 | C23×D3 | — | 6 | 1 | no | — |
| 162 | C23×D3 | — | 6 | 1 | no | — |
| 163 | C3×#41 | — | 6 | 1 | no | — |
| 164 | C3×#41 | — | 6 | 1 | no | — |
| 165 | C3×#41 | — | 6 | 1 | no | — |
| 166 | C3×#41 | — | 12 | 1 | no | — |
| 167 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 168 | C2×C3×Q8 | — | 12 | 1 | no | — |
| 169 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 170 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 171 | C2×C3×D4 | — | 3 | 1 | no | — |
| 172 | C2×C3×D4 | — | 3 | 1 | no | — |
| 173 | C2×#67 | — | 6 | 1 | no | — |
| 174 | C2×#67 | — | 6 | 1 | no | — |
| 175 | C2×#67 | — | 6 | 1 | no | — |
| 176 | C2×#67 | — | 6 | 1 | no | — |
| 177 | #239 | — | 4 | 1 | no | — |
| 178 | D3×Q8 | — | 4 | 1 | no | — |
| 179 | #235 | — | 2 | 1 | no | — |
| 180 | #235 | — | 2 | 1 | no | — |
| 181 | #235 | — | 2 | 1 | no | — |
| 182 | C2×D12 | — | 3 | 1 | no | — |
| 183 | C2×D12 | — | 3 | 1 | no | — |
| 184 | C2×D12 | — | 6 | 1 | no | — |
| 185 | C2×D12 | — | 6 | 1 | no | — |
| 186 | C2×D12 | — | 6 | 1 | no | — |
| 187 | C2×D12 | D12 | 1 | 1 | yes | characteristic |
| 188 | C2×D12 | #67 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic6 | — | 6 | 1 | no | — |
| 190 | C2×Dic6 | — | 6 | 1 | no | — |
| 191 | C3×SD16 | — | 12 | 1 | no | — |
| 192 | C3×D8 | — | 12 | 1 | no | — |
| 193 | C3×M16 | — | 2 | 1 | no | — |
| 194 | C3×M16 | — | 2 | 1 | no | — |
| 195 | C3×M16 | — | 4 | 1 | no | — |
| 196 | C3×M16 | — | 6 | 1 | no | — |
| 197 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 198 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 199 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 200 | C3×C22⋊C4 | — | 6 | 1 | no | — |
| 201 | C3×C42 | — | 3 | 1 | no | — |
| 202 | C3×C42 | — | 3 | 1 | no | — |
| 203 | #217 | — | 6 | 1 | no | — |
| 204 | #217 | — | 6 | 1 | no | — |
| 205 | #215 | — | 12 | 1 | no | — |
| 206 | #215 | — | 12 | 1 | no | — |
| 207 | #214 | — | 12 | 1 | no | — |
| 208 | #213 | — | 12 | 1 | no | — |
| 209 | #213 | — | 12 | 1 | no | — |
| 210 | #213 | — | 12 | 1 | no | — |
| 211 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 212 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 213 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 214 | (C2×D3)⋊C4 | — | 2 | 1 | no | — |
| 215 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 216 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 217 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 218 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 219 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 220 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 221 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 222 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 223 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 224 | (C2×D3)⋊C4 | — | 12 | 1 | no | — |
| 225 | C4×Dic3 | — | 3 | 1 | no | — |
| 226 | C4×Dic3 | — | 3 | 1 | no | — |
| 227 | C4×Dic3 | — | 6 | 1 | no | — |
| 228 | C4×Dic3 | D12 | 1 | 1 | yes | characteristic |
| 229 | C4×Dic3 | #67 | 1 | 1 | yes | characteristic |
| 230 | #208 | — | 2 | 1 | no | — |
| 231 | #208 | — | 6 | 1 | no | — |
| 232 | #208 | — | 6 | 1 | no | — |
| 233 | #208 | — | 12 | 1 | no | — |
| 234 | D24 | — | 4 | 1 | no | — |
| 235 | D24 | — | 12 | 1 | no | — |
| 236 | #204 | — | 4 | 1 | no | — |
| 237 | #204 | — | 12 | 1 | no | — |
| 238 | C22×C32 | #120 | 1 | 1 | yes | characteristic |
| 239 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 240 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 241 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 242 | C2×C3×D3 | — | 4 | 1 | no | — |
| 243 | C2×C3×D3 | — | 4 | 1 | no | — |
| 244 | C2×C3×D3 | — | 4 | 1 | no | — |
| 245 | C2×C3×D3 | — | 4 | 1 | no | — |
| 246 | C2×C3×D3 | — | 4 | 1 | no | — |
| 247 | C2×C3×D3 | — | 4 | 1 | no | — |
| 248 | C2×C3×D3 | — | 4 | 1 | no | — |
| 249 | D32 | — | 8 | 4 | no | — |
| 250 | C32×C4 | — | 2 | 1 | no | — |
| 251 | C32×C4 | — | 2 | 1 | no | — |
| 252 | C32×C4 | — | 2 | 1 | no | — |
| 253 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 254 | C3×Dic3 | — | 4 | 1 | no | — |
| 255 | C3×Dic3 | — | 4 | 1 | no | — |
| 256 | C3×Dic3 | — | 4 | 1 | no | — |
| 257 | 2−1+4 | — | 3 | 1 | no | — |
| 258 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 259 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 260 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 261 | #124 | — | 3 | 1 | no | — |
| 262 | #124 | — | 3 | 1 | no | — |
| 263 | #124 | — | 9 | 1 | no | — |
| 264 | #124 | — | 18 | 1 | no | — |
| 265 | #124 | — | 18 | 1 | no | — |
| 266 | #124 | — | 18 | 1 | no | — |
| 267 | #120 | — | 18 | 1 | no | — |
| 268 | #120 | — | 18 | 1 | no | — |
| 269 | #120 | — | 18 | 1 | no | — |
| 270 | #104 | — | 6 | 1 | no | — |
| 271 | #104 | — | 18 | 1 | no | — |
| 272 | #104 | — | 18 | 1 | no | — |
| 273 | #101 | — | 3 | 1 | no | — |
| 274 | #101 | — | 9 | 1 | no | — |
| 275 | #101 | D32 | 1 | 1 | yes | characteristic, complemented |
| 276 | C23×C3 | — | 6 | 1 | no | — |
| 277 | C23×C3 | — | 6 | 1 | no | — |
| 278 | C22×D3 | — | 2 | 1 | no | — |
| 279 | C22×D3 | — | 2 | 1 | no | — |
| 280 | C22×D3 | — | 6 | 1 | no | — |
| 281 | C22×D3 | — | 6 | 1 | no | — |
| 282 | C22×D3 | — | 12 | 1 | no | — |
| 283 | C22×D3 | — | 24 | 1 | no | — |
| 284 | C22×D3 | — | 24 | 1 | no | — |
| 285 | C22×D3 | — | 24 | 1 | no | — |
| 286 | C22×D3 | — | 24 | 1 | no | — |
| 287 | C22×D3 | — | 24 | 1 | no | — |
| 288 | C22×D3 | — | 24 | 1 | no | — |
| 289 | C3×Q8 | — | 4 | 1 | no | — |
| 290 | C3×Q8 | — | 4 | 1 | no | — |
| 291 | C3×Q8 | — | 6 | 1 | no | — |
| 292 | C3×Q8 | — | 6 | 1 | no | — |
| 293 | C3×Q8 | — | 6 | 1 | no | — |
| 294 | C3×Q8 | — | 8 | 1 | no | — |
| 295 | C3×D4 | — | 6 | 1 | no | — |
| 296 | C3×D4 | — | 6 | 1 | no | — |
| 297 | C3×D4 | — | 6 | 1 | no | — |
| 298 | C3×D4 | — | 12 | 1 | no | — |
| 299 | C3×D4 | — | 12 | 1 | no | — |
| 300 | C3×D4 | — | 12 | 1 | no | — |
| 301 | C2×C3×C4 | — | 2 | 1 | no | — |
| 302 | C2×C3×C4 | — | 2 | 1 | no | — |
| 303 | C2×C3×C4 | — | 2 | 1 | no | — |
| 304 | C2×C3×C4 | — | 6 | 1 | no | — |
| 305 | C2×C3×C4 | — | 6 | 1 | no | — |
| 306 | C2×C3×C4 | — | 12 | 1 | no | — |
| 307 | C2×C3×C4 | — | 12 | 1 | no | — |
| 308 | C2×C3×C4 | — | 12 | 1 | no | — |
| 309 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 310 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 311 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 312 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 313 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 314 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 315 | #67 | — | 4 | 1 | no | — |
| 316 | #67 | — | 24 | 1 | no | — |
| 317 | #67 | — | 24 | 1 | no | — |
| 318 | #67 | — | 24 | 1 | no | — |
| 319 | #67 | — | 24 | 1 | no | — |
| 320 | C2×Dic3 | — | 2 | 1 | no | — |
| 321 | C2×Dic3 | — | 2 | 1 | no | — |
| 322 | C2×Dic3 | — | 6 | 1 | no | — |
| 323 | C2×Dic3 | — | 6 | 1 | no | — |
| 324 | C2×Dic3 | — | 12 | 1 | no | — |
| 325 | D12 | — | 2 | 1 | no | — |
| 326 | D12 | — | 2 | 1 | no | — |
| 327 | D12 | — | 2 | 1 | no | — |
| 328 | D12 | — | 4 | 1 | no | — |
| 329 | D12 | — | 4 | 1 | no | — |
| 330 | D12 | — | 12 | 1 | no | — |
| 331 | D12 | — | 12 | 1 | no | — |
| 332 | D12 | — | 24 | 1 | no | — |
| 333 | D12 | — | 24 | 1 | no | — |
| 334 | D12 | — | 24 | 1 | no | — |
| 335 | C4×D3 | — | 4 | 1 | no | — |
| 336 | C4×D3 | — | 4 | 1 | no | — |
| 337 | C4×D3 | — | 4 | 1 | no | — |
| 338 | Dic6 | — | 2 | 1 | no | — |
| 339 | Dic6 | — | 2 | 1 | no | — |
| 340 | Dic6 | — | 2 | 1 | no | — |
| 341 | Dic6 | — | 24 | 1 | no | — |
| 342 | Dic6 | — | 24 | 1 | no | — |
| 343 | C3×C8 | — | 4 | 1 | no | — |
| 344 | C3×C8 | — | 4 | 1 | no | — |
| 345 | C3×C8 | — | 8 | 1 | no | — |
| 346 | C3×C8 | — | 12 | 1 | no | — |
| 347 | C3⋊C8 | — | 4 | 1 | no | — |
| 348 | C3⋊C8 | — | 12 | 1 | no | — |
| 349 | C3⋊C8 | — | 12 | 1 | no | — |
| 350 | C3⋊C8 | — | 24 | 1 | no | — |
| 351 | C2×C32 | — | 2 | 1 | no | — |
| 352 | C2×C32 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 353 | C3⋊D3 | — | 8 | 1 | no | — |
| 354 | C3×D3 | — | 8 | 1 | no | — |
| 355 | C3×D3 | — | 8 | 1 | no | — |
| 356 | C3×D3 | — | 8 | 1 | no | — |
| 357 | C24 | — | 18 | 1 | no | — |
| 358 | #41 | — | 6 | 1 | no | — |
| 359 | #41 | — | 6 | 1 | no | — |
| 360 | #41 | — | 6 | 1 | no | — |
| 361 | #41 | — | 12 | 1 | no | — |
| 362 | C2×Q8 | — | 12 | 1 | no | — |
| 363 | C2×Q8 | — | 18 | 1 | no | — |
| 364 | C2×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 365 | C2×D4 | — | 3 | 1 | no | — |
| 366 | C2×D4 | — | 3 | 1 | no | — |
| 367 | C2×D4 | — | 9 | 1 | no | — |
| 368 | C2×D4 | — | 18 | 1 | no | — |
| 369 | C2×D4 | — | 18 | 1 | no | — |
| 370 | C2×D4 | — | 18 | 1 | no | — |
| 371 | SD16 | — | 12 | 1 | no | — |
| 372 | SD16 | — | 36 | 1 | no | — |
| 373 | SD16 | — | 36 | 1 | no | — |
| 374 | D8 | — | 12 | 1 | no | — |
| 375 | D8 | — | 36 | 1 | no | — |
| 376 | D8 | — | 36 | 1 | no | — |
| 377 | M16 | — | 2 | 1 | no | — |
| 378 | M16 | — | 6 | 1 | no | — |
| 379 | M16 | — | 18 | 1 | no | — |
| 380 | C22⋊C4 | — | 6 | 1 | no | — |
| 381 | C22⋊C4 | — | 6 | 1 | no | — |
| 382 | C22⋊C4 | — | 6 | 1 | no | — |
| 383 | C22⋊C4 | — | 6 | 1 | no | — |
| 384 | C22⋊C4 | — | 18 | 1 | no | — |
| 385 | C22⋊C4 | — | 18 | 1 | no | — |
| 386 | C22⋊C4 | — | 18 | 1 | no | — |
| 387 | C22⋊C4 | — | 18 | 1 | no | — |
| 388 | C22⋊C4 | — | 18 | 1 | no | — |
| 389 | C42 | — | 3 | 1 | no | — |
| 390 | C42 | — | 3 | 1 | no | — |
| 391 | C42 | — | 9 | 1 | no | — |
| 392 | C22×C3 | — | 2 | 1 | no | — |
| 393 | C22×C3 | — | 12 | 1 | no | — |
| 394 | C22×C3 | — | 12 | 1 | no | — |
| 395 | C22×C3 | — | 12 | 1 | no | — |
| 396 | C22×C3 | — | 12 | 1 | no | — |
| 397 | C22×C3 | — | 12 | 1 | no | — |
| 398 | C22×C3 | — | 12 | 1 | no | — |
| 399 | C22×C3 | — | 12 | 1 | no | — |
| 400 | C22×C3 | #882 | 1 | 1 | yes | characteristic |
| 401 | C22×C3 | #937 | 1 | 1 | yes | characteristic |
| 402 | C2×D3 | — | 4 | 1 | no | — |
| 403 | C2×D3 | — | 4 | 1 | no | — |
| 404 | C2×D3 | — | 4 | 1 | no | — |
| 405 | C2×D3 | — | 4 | 1 | no | — |
| 406 | C2×D3 | — | 4 | 1 | no | — |
| 407 | C2×D3 | — | 4 | 1 | no | — |
| 408 | C2×D3 | — | 4 | 1 | no | — |
| 409 | C2×D3 | — | 12 | 1 | no | — |
| 410 | C2×D3 | — | 12 | 1 | no | — |
| 411 | C2×D3 | — | 12 | 1 | no | — |
| 412 | C2×D3 | — | 12 | 1 | no | — |
| 413 | C2×D3 | — | 12 | 1 | no | — |
| 414 | C2×D3 | — | 12 | 1 | no | — |
| 415 | C2×D3 | — | 24 | 1 | no | — |
| 416 | C2×D3 | — | 24 | 1 | no | — |
| 417 | C2×D3 | — | 24 | 1 | no | — |
| 418 | C2×D3 | — | 24 | 4 | no | — |
| 419 | C2×D3 | — | 24 | 4 | no | — |
| 420 | C3×C4 | — | 2 | 1 | no | — |
| 421 | C3×C4 | — | 2 | 1 | no | — |
| 422 | C3×C4 | — | 2 | 1 | no | — |
| 423 | C3×C4 | — | 2 | 1 | no | — |
| 424 | C3×C4 | — | 2 | 1 | no | — |
| 425 | C3×C4 | — | 2 | 1 | no | — |
| 426 | C3×C4 | — | 4 | 1 | no | — |
| 427 | C3×C4 | — | 4 | 1 | no | — |
| 428 | C3×C4 | — | 4 | 1 | no | — |
| 429 | C3×C4 | — | 12 | 1 | no | — |
| 430 | C3×C4 | — | 12 | 1 | no | — |
| 431 | C3×C4 | — | 12 | 1 | no | — |
| 432 | Dic3 | — | 4 | 1 | no | — |
| 433 | Dic3 | — | 4 | 1 | no | — |
| 434 | Dic3 | — | 4 | 1 | no | — |
| 435 | Dic3 | — | 12 | 1 | no | — |
| 436 | Dic3 | — | 12 | 1 | no | — |
| 437 | Dic3 | — | 24 | 1 | no | — |
| 438 | C32 | #2202 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 439 | C23 | — | 6 | 1 | no | — |
| 440 | C23 | — | 6 | 1 | no | — |
| 441 | C23 | — | 18 | 1 | no | — |
| 442 | C23 | — | 72 | 1 | no | — |
| 443 | C23 | — | 72 | 1 | no | — |
| 444 | C23 | — | 72 | 1 | no | — |
| 445 | Q8 | — | 4 | 1 | no | — |
| 446 | Q8 | — | 6 | 1 | no | — |
| 447 | Q8 | — | 6 | 1 | no | — |
| 448 | Q8 | — | 6 | 1 | no | — |
| 449 | Q8 | — | 72 | 1 | no | — |
| 450 | D4 | — | 6 | 1 | no | — |
| 451 | D4 | — | 6 | 1 | no | — |
| 452 | D4 | — | 6 | 1 | no | — |
| 453 | D4 | — | 12 | 1 | no | — |
| 454 | D4 | — | 12 | 1 | no | — |
| 455 | D4 | — | 12 | 1 | no | — |
| 456 | D4 | — | 36 | 1 | no | — |
| 457 | D4 | — | 72 | 1 | no | — |
| 458 | D4 | — | 72 | 1 | no | — |
| 459 | D4 | — | 72 | 1 | no | — |
| 460 | C2×C4 | — | 6 | 1 | no | — |
| 461 | C2×C4 | — | 6 | 1 | no | — |
| 462 | C2×C4 | — | 12 | 1 | no | — |
| 463 | C2×C4 | — | 12 | 1 | no | — |
| 464 | C2×C4 | — | 12 | 1 | no | — |
| 465 | C2×C4 | — | 18 | 1 | no | — |
| 466 | C2×C4 | D3×D12 | 1 | 1 | yes | characteristic |
| 467 | C2×C4 | #3802 | 1 | 1 | yes | characteristic |
| 468 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 469 | C8 | — | 4 | 1 | no | — |
| 470 | C8 | — | 12 | 1 | no | — |
| 471 | C8 | — | 36 | 1 | no | — |
| 472 | C2×C3 | — | 2 | 1 | no | — |
| 473 | C2×C3 | — | 2 | 1 | no | — |
| 474 | C2×C3 | — | 2 | 1 | no | — |
| 475 | C2×C3 | — | 4 | 1 | no | — |
| 476 | C2×C3 | — | 24 | 1 | no | — |
| 477 | C2×C3 | — | 24 | 1 | no | — |
| 478 | C2×C3 | — | 24 | 1 | no | — |
| 479 | C2×C3 | #4741 | 1 | 1 | yes | characteristic |
| 480 | C2×C3 | #5032 | 1 | 1 | yes | characteristic |
| 481 | D3 | — | 8 | 1 | no | — |
| 482 | D3 | — | 8 | 1 | no | — |
| 483 | D3 | — | 8 | 1 | no | — |
| 484 | D3 | — | 24 | 1 | no | — |
| 485 | D3 | — | 24 | 1 | no | — |
| 486 | D3 | — | 48 | 1 | no | — |
| 487 | C22 | — | 12 | 1 | no | — |
| 488 | C22 | — | 12 | 1 | no | — |
| 489 | C22 | — | 12 | 1 | no | — |
| 490 | C22 | — | 12 | 1 | no | — |
| 491 | C22 | — | 12 | 1 | no | — |
| 492 | C22 | — | 12 | 1 | no | — |
| 493 | C22 | — | 12 | 1 | no | — |
| 494 | C22 | — | 36 | 1 | no | — |
| 495 | C22 | — | 36 | 1 | no | — |
| 496 | C22 | — | 36 | 1 | no | — |
| 497 | C22 | — | 72 | 4 | no | — |
| 498 | C22 | #63922 | 1 | 1 | yes | characteristic |
| 499 | C4 | — | 2 | 1 | no | — |
| 500 | C4 | — | 2 | 1 | no | — |
| 501 | C4 | — | 2 | 1 | no | — |
| 502 | C4 | — | 12 | 1 | no | — |
| 503 | C4 | — | 12 | 1 | no | — |
| 504 | C4 | — | 12 | 1 | no | — |
| 505 | C4 | — | 36 | 1 | no | — |
| 506 | C3 | — | 2 | 1 | no | — |
| 507 | C3 | #69160 | 1 | 1 | yes | characteristic, complemented |
| 508 | C3 | #70987 | 1 | 1 | yes | characteristic, complemented |
| 509 | C2 | — | 2 | 1 | no | — |
| 510 | C2 | — | 24 | 1 | no | — |
| 511 | C2 | — | 24 | 1 | no | — |
| 512 | C2 | — | 24 | 1 | no | — |
| 513 | C2 | — | 72 | 1 | no | — |
| 514 | C2 | #10590407 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10595439 | C2 | semidirect |
| 2. C3×#4753 | C2 | semidirect |
| 3. #10591646 | C2 | semidirect |
| 4. #10591645 | C2 | semidirect |
| 5. #10589343 | C2 | semidirect |
| 6. C3×#4477 | C2 | semidirect |
| 7. #10589182 | C2 | semidirect |
| 10. C3×#1007 | C22 | semidirect |
| 23. C32×#101 | C22 | semidirect |
| 24. #63663 | C22 | semidirect |
| 25. C3×#836 | C22 | semidirect |
| 36. #4753 | D3 | semidirect |
| 43. #4477 | D3 | semidirect |
| 81. #1007 | C2×D3 | semidirect |
| 110. C3×#101 | C2×D3 | semidirect |
| 111. C3×#101 | C2×D3 | semidirect |
| 117. #836 | C2×D3 | semidirect |
| 275. #101 | D32 | semidirect |
| 438. C32 | #2202 | semidirect |
| 507. C3 | #69160 | semidirect |
| 508. C3 | #70987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595439 | 2 |
| C3×#4753 | 2 |
| #10591646 | 2 |
| #10591645 | 2 |
| #10589343 | 2 |
| C3×#4477 | 2 |
| #10589182 | 2 |
| #70987 | 3 |
| #69160 | 3 |