← #13150948
Subgroups — #13150948
Order 1728.
664 conjugacy classes of subgroups.
The subgroup lattice has 424 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11721836 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C9×#935 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#63497 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #11721253 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11721249 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11721247 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #11721246 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #11720928 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11720905 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #10595275 | — | 3 | 1 | no | maximal |
| 11 | #10589753 | — | 3 | 1 | no | maximal |
| 12 | C2×C3×D4×C9 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#6226 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C9×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 15 | C22×C3×Dic9 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×#6189 | C22 | 1 | 2 | yes | — |
| 17 | #88551 | C22 | 1 | 2 | yes | — |
| 18 | #88551 | C22 | 1 | 2 | yes | — |
| 19 | C4×C3⋊Dic9 | C22 | 1 | 1 | yes | characteristic |
| 20 | C9×#217 | C22 | 1 | 1 | yes | characteristic |
| 21 | C9×#217 | C22 | 1 | 2 | yes | — |
| 22 | C3×#3676 | C22 | 1 | 2 | yes | — |
| 23 | C3×#3676 | C22 | 1 | 1 | yes | characteristic |
| 24 | C9×Dic3⋊C4 | C22 | 1 | 2 | yes | — |
| 25 | C3×Dic9⋊C4 | C22 | 1 | 2 | yes | — |
| 26 | Dic3⋊Dic9 | C22 | 1 | 2 | yes | — |
| 27 | Dic3⋊Dic9 | C22 | 1 | 2 | yes | — |
| 28 | #88442 | C22 | 1 | 2 | yes | — |
| 29 | #88442 | C22 | 1 | 2 | yes | — |
| 30 | Dic9⋊Dic3 | C22 | 1 | 2 | yes | — |
| 31 | Dic9⋊Dic3 | C22 | 1 | 2 | yes | — |
| 32 | Dic3×Dic9 | C22 | 1 | 2 | yes | — |
| 33 | #64145 | — | 3 | 1 | no | — |
| 34 | C3×#935 | — | 3 | 1 | no | — |
| 35 | C3×#935 | D3 | 1 | 1 | yes | characteristic |
| 36 | #63964 | — | 3 | 2 | no | — |
| 37 | #63964 | — | 3 | 2 | no | — |
| 38 | #63956 | — | 3 | 2 | no | — |
| 39 | #63956 | — | 3 | 2 | no | — |
| 40 | #63870 | — | 3 | 2 | no | — |
| 41 | #63840 | — | 3 | 2 | no | — |
| 42 | C9×#123 | — | 3 | 1 | no | — |
| 43 | #63498 | — | 3 | 1 | no | — |
| 44 | #63498 | — | 6 | 1 | no | — |
| 45 | #63497 | D3 | 1 | 1 | yes | characteristic |
| 46 | #63486 | — | 3 | 2 | no | — |
| 47 | #63451 | — | 3 | 2 | no | — |
| 48 | #63450 | — | 3 | 2 | no | — |
| 49 | #63441 | — | 3 | 2 | no | — |
| 50 | #63441 | — | 3 | 2 | no | — |
| 51 | #63440 | — | 3 | 2 | no | — |
| 52 | C23×C3×C9 | C23 | 1 | 1 | yes | characteristic |
| 53 | C23×C3×C9 | C23 | 1 | 1 | yes | characteristic |
| 54 | C3×D4×C9 | — | 4 | 1 | no | — |
| 55 | C2×C3×C4×C9 | C23 | 1 | 1 | yes | characteristic |
| 56 | C2×C3⋊Dic9 | C23 | 1 | 2 | yes | — |
| 57 | C2×C3⋊Dic9 | C23 | 1 | 2 | yes | — |
| 58 | #6226 | — | 4 | 1 | no | — |
| 59 | C2×C9×Dic3 | — | 4 | 1 | no | — |
| 60 | C2×C9×Dic3 | C23 | 1 | 2 | yes | — |
| 61 | C2×C9×Dic3 | C23 | 1 | 2 | yes | — |
| 62 | C2×C3×Dic9 | — | 4 | 1 | no | — |
| 63 | C2×C3×Dic9 | C23 | 1 | 2 | yes | — |
| 64 | C2×C3×Dic9 | C23 | 1 | 2 | yes | — |
| 65 | #6189 | — | 4 | 2 | no | — |
| 66 | #5651 | — | 9 | 1 | no | — |
| 67 | #5651 | — | 9 | 1 | no | — |
| 68 | C2×C32×D4 | C2×D3 | 1 | 1 | yes | characteristic |
| 69 | C2×#634 | — | 3 | 1 | no | — |
| 70 | C22×C3×Dic3 | — | 3 | 1 | no | — |
| 71 | C22×C3×Dic3 | C2×D3 | 1 | 1 | yes | characteristic |
| 72 | C2×#627 | — | 3 | 2 | no | — |
| 73 | #3757 | — | 3 | 2 | no | — |
| 74 | #3757 | — | 3 | 2 | no | — |
| 75 | C4×C3⋊Dic3 | — | 3 | 1 | no | — |
| 76 | C3×#217 | — | 3 | 1 | no | — |
| 77 | C3×#217 | — | 3 | 2 | no | — |
| 78 | C3×#217 | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C3×#217 | C2×D3 | 1 | 2 | yes | — |
| 80 | C3×Dic3⋊C4 | — | 3 | 2 | no | — |
| 81 | C3×Dic3⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 82 | #3724 | — | 3 | 2 | no | — |
| 83 | #3724 | — | 3 | 2 | no | — |
| 84 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 85 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 86 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 87 | Dic3⋊Dic3 | — | 3 | 2 | no | — |
| 88 | Dic32 | — | 3 | 2 | no | — |
| 89 | C2×D4×C9 | — | 2 | 1 | no | — |
| 90 | C2×D4×C9 | C2×D3 | 1 | 1 | yes | characteristic |
| 91 | C22×C4×C9 | — | 3 | 1 | no | — |
| 92 | C22×Dic9 | C2×D3 | 1 | 1 | yes | characteristic |
| 93 | C2×Dic18 | — | 3 | 1 | no | — |
| 94 | C2×Dic18 | — | 3 | 2 | no | — |
| 95 | C2×Dic18 | — | 6 | 1 | no | — |
| 96 | C9×C4⋊C4 | — | 3 | 2 | no | — |
| 97 | C9×C22⋊C4 | — | 3 | 2 | no | — |
| 98 | C9×C22⋊C4 | — | 3 | 1 | no | — |
| 99 | #3676 | — | 3 | 2 | no | — |
| 100 | #3676 | — | 3 | 2 | no | — |
| 101 | #3676 | — | 6 | 2 | no | — |
| 102 | #3676 | — | 6 | 2 | no | — |
| 103 | #3676 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | #3676 | C2×D3 | 1 | 2 | yes | — |
| 105 | C4⋊Dic9 | — | 3 | 2 | no | — |
| 106 | C4⋊Dic9 | — | 3 | 2 | no | — |
| 107 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 108 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 109 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 110 | Dic9⋊C4 | — | 3 | 2 | no | — |
| 111 | Dic9⋊C4 | C2×D3 | 1 | 2 | yes | — |
| 112 | C4×Dic9 | — | 3 | 1 | no | — |
| 113 | C4×Dic9 | — | 3 | 2 | no | — |
| 114 | C4×Dic9 | — | 6 | 1 | no | — |
| 115 | C22×C3×C9 | — | 2 | 1 | no | — |
| 116 | C22×C3×C9 | — | 2 | 1 | no | — |
| 117 | C22×C3×C9 | — | 2 | 2 | no | — |
| 118 | C22×C3×C9 | — | 2 | 2 | no | — |
| 119 | C22×C3×C9 | C24 | 1 | 1 | yes | characteristic |
| 120 | C3×C4×C9 | — | 2 | 1 | no | — |
| 121 | C3⋊Dic9 | — | 2 | 2 | no | — |
| 122 | C3⋊Dic9 | — | 2 | 2 | no | — |
| 123 | C9×Dic3 | — | 2 | 2 | no | — |
| 124 | C9×Dic3 | — | 2 | 2 | no | — |
| 125 | C3×Dic9 | — | 2 | 2 | no | — |
| 126 | C3×Dic9 | — | 2 | 2 | no | — |
| 127 | C3×#123 | — | 3 | 1 | no | — |
| 128 | C3×#123 | — | 9 | 1 | no | — |
| 129 | #936 | — | 9 | 1 | no | — |
| 130 | #936 | — | 9 | 1 | no | — |
| 131 | #936 | — | 18 | 1 | no | — |
| 132 | #935 | — | 3 | 1 | no | — |
| 133 | #935 | D9 | 1 | 1 | yes | characteristic |
| 134 | #924 | — | 9 | 2 | no | — |
| 135 | #924 | — | 9 | 2 | no | — |
| 136 | #889 | — | 9 | 2 | no | — |
| 137 | #889 | — | 9 | 2 | no | — |
| 138 | #888 | — | 9 | 2 | no | — |
| 139 | #888 | — | 9 | 2 | no | — |
| 140 | #879 | — | 9 | 2 | no | — |
| 141 | #879 | — | 9 | 2 | no | — |
| 142 | #879 | — | 9 | 2 | no | — |
| 143 | #879 | — | 9 | 2 | no | — |
| 144 | #878 | — | 9 | 2 | no | — |
| 145 | #878 | — | 9 | 2 | no | — |
| 146 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 147 | C23×C32 | C22×D3 | 1 | 1 | yes | characteristic |
| 148 | C32×D4 | — | 4 | 1 | no | — |
| 149 | C2×C32×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 150 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 151 | C2×C3⋊Dic3 | — | 3 | 2 | no | — |
| 152 | #634 | — | 12 | 1 | no | — |
| 153 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 154 | C2×C3×Dic3 | — | 3 | 2 | no | — |
| 155 | C2×C3×Dic3 | — | 4 | 1 | no | — |
| 156 | C2×C3×Dic3 | — | 12 | 1 | no | — |
| 157 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 158 | C2×C3×Dic3 | C22×D3 | 1 | 2 | yes | — |
| 159 | #627 | — | 12 | 2 | no | — |
| 160 | C23×C9 | — | 2 | 1 | no | — |
| 161 | C23×C9 | — | 2 | 1 | no | — |
| 162 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 163 | C23×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 164 | D4×C9 | — | 4 | 1 | no | — |
| 165 | D4×C9 | — | 4 | 2 | no | — |
| 166 | C2×C4×C9 | — | 2 | 1 | no | — |
| 167 | C2×C4×C9 | — | 3 | 2 | no | — |
| 168 | C2×C4×C9 | — | 3 | 2 | no | — |
| 169 | C2×C4×C9 | — | 12 | 1 | no | — |
| 170 | C2×C4×C9 | C22×D3 | 1 | 1 | yes | characteristic |
| 171 | C2×Dic9 | — | 3 | 2 | no | — |
| 172 | C2×Dic9 | — | 3 | 2 | no | — |
| 173 | C2×Dic9 | — | 4 | 1 | no | — |
| 174 | C2×Dic9 | — | 6 | 2 | no | — |
| 175 | C2×Dic9 | — | 6 | 2 | no | — |
| 176 | C2×Dic9 | C22×D3 | 1 | 2 | yes | — |
| 177 | C2×Dic9 | C22×D3 | 1 | 2 | yes | — |
| 178 | Dic18 | — | 12 | 2 | no | — |
| 179 | Dic18 | — | 12 | 1 | no | — |
| 180 | Dic18 | — | 12 | 2 | no | — |
| 181 | #563 | — | 27 | 1 | no | Sylow |
| 182 | C2×C3×C9 | — | 4 | 1 | no | — |
| 183 | C2×C3×C9 | — | 4 | 1 | no | — |
| 184 | C2×C3×C9 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 185 | C2×C3×C9 | 2−1+4 | 1 | 2 | yes | — |
| 186 | C2×C3×D4 | — | 2 | 1 | no | — |
| 187 | C2×C3×D4 | C2×D9 | 1 | 1 | yes | characteristic |
| 188 | C2×C3×D4 | D32 | 1 | 1 | yes | characteristic |
| 189 | C22×C3×C4 | — | 3 | 1 | no | — |
| 190 | C22×C3×C4 | — | 9 | 1 | no | — |
| 191 | C22×Dic3 | — | 3 | 1 | no | — |
| 192 | C22×Dic3 | C2×D9 | 1 | 1 | yes | characteristic |
| 193 | C2×Dic6 | — | 9 | 2 | no | — |
| 194 | C2×Dic6 | — | 9 | 1 | no | — |
| 195 | C2×Dic6 | — | 9 | 1 | no | — |
| 196 | C2×Dic6 | — | 9 | 2 | no | — |
| 197 | C2×Dic6 | — | 18 | 1 | no | — |
| 198 | C3×C4⋊C4 | — | 3 | 2 | no | — |
| 199 | C3×C4⋊C4 | — | 9 | 2 | no | — |
| 200 | C3×C22⋊C4 | — | 3 | 2 | no | — |
| 201 | C3×C22⋊C4 | — | 3 | 1 | no | — |
| 202 | C3×C22⋊C4 | — | 9 | 2 | no | — |
| 203 | C3×C22⋊C4 | — | 9 | 1 | no | — |
| 204 | #217 | — | 3 | 1 | no | — |
| 205 | #217 | — | 3 | 2 | no | — |
| 206 | #217 | — | 9 | 2 | no | — |
| 207 | #217 | — | 9 | 2 | no | — |
| 208 | #217 | — | 9 | 2 | no | — |
| 209 | #217 | — | 9 | 2 | no | — |
| 210 | #217 | — | 18 | 2 | no | — |
| 211 | #217 | — | 18 | 2 | no | — |
| 212 | #217 | C2×D9 | 1 | 1 | yes | characteristic |
| 213 | #217 | C2×D9 | 1 | 2 | yes | — |
| 214 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 215 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 216 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 217 | C4⋊Dic3 | — | 9 | 2 | no | — |
| 218 | Dic3⋊C4 | — | 3 | 2 | no | — |
| 219 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 220 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 221 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 222 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 223 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 224 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 225 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 226 | Dic3⋊C4 | — | 9 | 2 | no | — |
| 227 | Dic3⋊C4 | C2×D9 | 1 | 2 | yes | — |
| 228 | C4×Dic3 | — | 9 | 2 | no | — |
| 229 | C4×Dic3 | — | 9 | 1 | no | — |
| 230 | C4×Dic3 | — | 9 | 1 | no | — |
| 231 | C4×Dic3 | — | 9 | 2 | no | — |
| 232 | C4×Dic3 | — | 18 | 1 | no | — |
| 233 | C22×C32 | — | 2 | 1 | no | — |
| 234 | C22×C32 | — | 2 | 1 | no | — |
| 235 | C22×C32 | — | 2 | 2 | no | — |
| 236 | C22×C32 | — | 2 | 2 | no | — |
| 237 | C22×C32 | C23×D3 | 1 | 1 | yes | characteristic |
| 238 | C32×C4 | — | 2 | 1 | no | — |
| 239 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 240 | C3⋊Dic3 | — | 6 | 2 | no | — |
| 241 | C3×Dic3 | — | 2 | 2 | no | — |
| 242 | C3×Dic3 | — | 2 | 2 | no | — |
| 243 | C3×Dic3 | — | 6 | 2 | no | — |
| 244 | C3×Dic3 | — | 6 | 2 | no | — |
| 245 | C22×C9 | — | 2 | 1 | no | — |
| 246 | C22×C9 | — | 2 | 1 | no | — |
| 247 | C22×C9 | — | 2 | 2 | no | — |
| 248 | C22×C9 | — | 2 | 2 | no | — |
| 249 | C22×C9 | — | 2 | 1 | no | — |
| 250 | C22×C9 | — | 4 | 1 | no | — |
| 251 | C22×C9 | — | 4 | 1 | no | — |
| 252 | C22×C9 | — | 4 | 2 | no | — |
| 253 | C22×C9 | — | 4 | 2 | no | — |
| 254 | C22×C9 | C23×D3 | 1 | 1 | yes | characteristic |
| 255 | C4×C9 | — | 2 | 2 | no | — |
| 256 | C4×C9 | — | 2 | 1 | no | — |
| 257 | C4×C9 | — | 6 | 2 | no | — |
| 258 | C4×C9 | — | 6 | 2 | no | — |
| 259 | Dic9 | — | 2 | 2 | no | — |
| 260 | Dic9 | — | 2 | 2 | no | — |
| 261 | Dic9 | — | 6 | 2 | no | — |
| 262 | Dic9 | — | 6 | 2 | no | — |
| 263 | Dic9 | — | 12 | 2 | no | — |
| 264 | Dic9 | — | 12 | 2 | no | — |
| 265 | C4⋊Q8 | — | 27 | 2 | no | — |
| 266 | #126 | — | 27 | 2 | no | — |
| 267 | #126 | — | 27 | 2 | no | — |
| 268 | #125 | — | 27 | 2 | no | — |
| 269 | #124 | — | 27 | 1 | no | — |
| 270 | #123 | — | 3 | 1 | no | — |
| 271 | #123 | — | 9 | 1 | no | — |
| 272 | C22⋊Q8 | — | 27 | 2 | no | — |
| 273 | C22⋊Q8 | — | 27 | 2 | no | — |
| 274 | C3×C9 | #563 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 275 | C23×C3 | — | 2 | 1 | no | — |
| 276 | C23×C3 | — | 2 | 1 | no | — |
| 277 | C23×C3 | C22×D9 | 1 | 1 | yes | characteristic |
| 278 | C23×C3 | C22×D9 | 1 | 1 | yes | characteristic |
| 279 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 280 | C23×C3 | C2×D32 | 1 | 1 | yes | characteristic |
| 281 | C3×D4 | — | 4 | 1 | no | — |
| 282 | C3×D4 | — | 4 | 1 | no | — |
| 283 | C3×D4 | — | 4 | 2 | no | — |
| 284 | C2×C3×C4 | — | 2 | 1 | no | — |
| 285 | C2×C3×C4 | — | 3 | 2 | no | — |
| 286 | C2×C3×C4 | — | 3 | 2 | no | — |
| 287 | C2×C3×C4 | — | 9 | 2 | no | — |
| 288 | C2×C3×C4 | — | 9 | 2 | no | — |
| 289 | C2×C3×C4 | — | 12 | 1 | no | — |
| 290 | C2×C3×C4 | — | 36 | 1 | no | — |
| 291 | C2×C3×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 292 | C2×C3×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 293 | C2×Dic3 | — | 3 | 2 | no | — |
| 294 | C2×Dic3 | — | 3 | 2 | no | — |
| 295 | C2×Dic3 | — | 4 | 1 | no | — |
| 296 | C2×Dic3 | — | 9 | 2 | no | — |
| 297 | C2×Dic3 | — | 9 | 2 | no | — |
| 298 | C2×Dic3 | — | 9 | 2 | no | — |
| 299 | C2×Dic3 | — | 9 | 2 | no | — |
| 300 | C2×Dic3 | — | 12 | 1 | no | — |
| 301 | C2×Dic3 | — | 18 | 2 | no | — |
| 302 | C2×Dic3 | — | 18 | 2 | no | — |
| 303 | C2×Dic3 | C22×D9 | 1 | 2 | yes | — |
| 304 | C2×Dic3 | C22×D9 | 1 | 2 | yes | — |
| 305 | Dic6 | — | 36 | 2 | no | — |
| 306 | Dic6 | — | 36 | 2 | no | — |
| 307 | Dic6 | — | 36 | 1 | no | — |
| 308 | Dic6 | — | 36 | 1 | no | — |
| 309 | Dic6 | — | 36 | 2 | no | — |
| 310 | C2×C32 | — | 4 | 1 | no | — |
| 311 | C2×C32 | — | 4 | 1 | no | — |
| 312 | C2×C32 | #1004 | 1 | 1 | yes | characteristic |
| 313 | C2×C32 | #1010 | 1 | 2 | yes | — |
| 314 | C2×C9 | — | 2 | 2 | no | — |
| 315 | C2×C9 | — | 2 | 1 | no | — |
| 316 | C2×C9 | — | 4 | 1 | no | — |
| 317 | C2×C9 | — | 4 | 1 | no | — |
| 318 | C2×C9 | — | 8 | 1 | no | — |
| 319 | C2×C9 | — | 8 | 1 | no | — |
| 320 | C2×C9 | #1004 | 1 | 1 | yes | characteristic |
| 321 | C2×C9 | #1010 | 1 | 2 | yes | — |
| 322 | C2×Q8 | — | 27 | 2 | no | — |
| 323 | C2×Q8 | — | 27 | 1 | no | — |
| 324 | C2×D4 | D3×D9 | 1 | 1 | yes | characteristic |
| 325 | C22×C4 | — | 3 | 1 | no | — |
| 326 | C22×C4 | — | 9 | 1 | no | — |
| 327 | C4⋊C4 | — | 3 | 2 | no | — |
| 328 | C4⋊C4 | — | 9 | 2 | no | — |
| 329 | C4⋊C4 | — | 27 | 2 | no | — |
| 330 | C4⋊C4 | — | 27 | 2 | no | — |
| 331 | C4⋊C4 | — | 27 | 2 | no | — |
| 332 | C4⋊C4 | — | 27 | 2 | no | — |
| 333 | C4⋊C4 | — | 27 | 2 | no | — |
| 334 | C4⋊C4 | — | 27 | 2 | no | — |
| 335 | C22⋊C4 | — | 3 | 2 | no | — |
| 336 | C22⋊C4 | — | 3 | 1 | no | — |
| 337 | C22⋊C4 | — | 9 | 2 | no | — |
| 338 | C22⋊C4 | — | 9 | 1 | no | — |
| 339 | C22⋊C4 | — | 27 | 2 | no | — |
| 340 | C22⋊C4 | — | 27 | 2 | no | — |
| 341 | C42 | — | 27 | 2 | no | — |
| 342 | C42 | — | 27 | 1 | no | — |
| 343 | C22×C3 | — | 2 | 2 | no | — |
| 344 | C22×C3 | — | 2 | 2 | no | — |
| 345 | C22×C3 | — | 2 | 1 | no | — |
| 346 | C22×C3 | — | 2 | 1 | no | — |
| 347 | C22×C3 | — | 2 | 1 | no | — |
| 348 | C22×C3 | — | 2 | 1 | no | — |
| 349 | C22×C3 | — | 2 | 2 | no | — |
| 350 | C22×C3 | — | 2 | 2 | no | — |
| 351 | C22×C3 | — | 2 | 1 | no | — |
| 352 | C22×C3 | — | 4 | 1 | no | — |
| 353 | C22×C3 | — | 4 | 1 | no | — |
| 354 | C22×C3 | — | 4 | 2 | no | — |
| 355 | C22×C3 | — | 4 | 2 | no | — |
| 356 | C22×C3 | C23×D9 | 1 | 1 | yes | characteristic |
| 357 | C22×C3 | C22×D32 | 1 | 1 | yes | characteristic |
| 358 | C3×C4 | — | 2 | 2 | no | — |
| 359 | C3×C4 | — | 2 | 1 | no | — |
| 360 | C3×C4 | — | 2 | 1 | no | — |
| 361 | C3×C4 | — | 6 | 2 | no | — |
| 362 | C3×C4 | — | 6 | 2 | no | — |
| 363 | C3×C4 | — | 18 | 2 | no | — |
| 364 | C3×C4 | — | 18 | 2 | no | — |
| 365 | Dic3 | — | 2 | 2 | no | — |
| 366 | Dic3 | — | 2 | 2 | no | — |
| 367 | Dic3 | — | 6 | 2 | no | — |
| 368 | Dic3 | — | 6 | 2 | no | — |
| 369 | Dic3 | — | 18 | 2 | no | — |
| 370 | Dic3 | — | 18 | 2 | no | — |
| 371 | Dic3 | — | 18 | 2 | no | — |
| 372 | Dic3 | — | 18 | 2 | no | — |
| 373 | Dic3 | — | 36 | 2 | no | — |
| 374 | Dic3 | — | 36 | 2 | no | — |
| 375 | C32 | #5651 | 1 | 1 | yes | characteristic |
| 376 | C9 | — | 2 | 1 | no | — |
| 377 | C9 | #5651 | 1 | 1 | yes | characteristic, complemented |
| 378 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 379 | C23 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 380 | Q8 | — | 108 | 1 | no | — |
| 381 | Q8 | — | 108 | 2 | no | — |
| 382 | D4 | — | 4 | 1 | no | — |
| 383 | C2×C4 | — | 3 | 2 | no | — |
| 384 | C2×C4 | — | 3 | 2 | no | — |
| 385 | C2×C4 | — | 9 | 2 | no | — |
| 386 | C2×C4 | — | 9 | 2 | no | — |
| 387 | C2×C4 | — | 12 | 1 | no | — |
| 388 | C2×C4 | — | 27 | 2 | no | — |
| 389 | C2×C4 | — | 27 | 2 | no | — |
| 390 | C2×C4 | — | 36 | 1 | no | — |
| 391 | C2×C4 | C2×D3×D9 | 1 | 1 | yes | characteristic |
| 392 | C2×C3 | — | 2 | 1 | no | — |
| 393 | C2×C3 | — | 2 | 2 | no | — |
| 394 | C2×C3 | — | 4 | 1 | no | — |
| 395 | C2×C3 | — | 4 | 1 | no | — |
| 396 | C2×C3 | — | 4 | 1 | no | — |
| 397 | C2×C3 | — | 4 | 1 | no | — |
| 398 | C2×C3 | — | 8 | 1 | no | — |
| 399 | C2×C3 | — | 8 | 1 | no | — |
| 400 | C2×C3 | #63710 | 1 | 1 | yes | characteristic |
| 401 | C2×C3 | #63716 | 1 | 2 | yes | — |
| 402 | C2×C3 | #64309 | 1 | 2 | yes | — |
| 403 | C2×C3 | #64330 | 1 | 1 | yes | characteristic |
| 404 | C22 | — | 2 | 1 | no | — |
| 405 | C22 | — | 2 | 1 | no | — |
| 406 | C22 | — | 2 | 2 | no | — |
| 407 | C22 | — | 2 | 2 | no | — |
| 408 | C22 | C22×D3×D9 | 1 | 1 | yes | characteristic |
| 409 | C4 | — | 2 | 1 | no | — |
| 410 | C4 | — | 6 | 2 | no | — |
| 411 | C4 | — | 6 | 2 | no | — |
| 412 | C4 | — | 18 | 2 | no | — |
| 413 | C4 | — | 18 | 2 | no | — |
| 414 | C4 | — | 54 | 2 | no | — |
| 415 | C4 | — | 54 | 2 | no | — |
| 416 | C3 | — | 2 | 1 | no | — |
| 417 | C3 | #10589753 | 1 | 1 | yes | characteristic, complemented |
| 418 | C3 | #10595275 | 1 | 1 | yes | characteristic |
| 419 | C2 | — | 4 | 1 | no | — |
| 420 | C2 | — | 4 | 1 | no | — |
| 421 | C2 | #11722494 | 1 | 2 | yes | — |
| 422 | C2 | #11722535 | 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