Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1648 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 1648 conjugacy classes of subgroups — too many to draw. Only its 136 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 | C2×D4×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#63694 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #10593089 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | D4×(C22⋊C9)⋊C2 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #10593087 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #87239 | — | 3 | 1 | no | maximal |
| 7 | C23×C22⋊C9 | C22 | 1 | 2 | yes | complemented |
| 8 | C22×(C22⋊C9)⋊C2 | C22 | 1 | 4 | yes | complemented |
| 9 | #63710 | — | 4 | 1 | no | maximal |
| 10 | D4×C22⋊C9 | C22 | 1 | 4 | yes | complemented |
| 11 | C2×C4×C22⋊C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #63694 | C22 | 1 | 4 | yes | complemented |
| 13 | #63694 | C22 | 1 | 8 | yes | complemented |
| 14 | C2×(C22⋊C9)⋊C4 | C22 | 1 | 4 | yes | complemented |
| 15 | C4⋊((C22⋊C9)⋊C2) | C22 | 1 | 2 | yes | complemented |
| 16 | C4×(C22⋊C9)⋊C2 | C22 | 1 | 4 | yes | complemented |
| 17 | (C22⋊C9)⋊Q8 | C22 | 1 | 2 | yes | complemented |
| 18 | C23×C3×D4 | D3 | 1 | 1 | yes | characteristic |
| 19 | C2×#1004 | — | 3 | 1 | no | — |
| 20 | C2×#953 | — | 3 | 4 | no | — |
| 21 | #5806 | — | 3 | 4 | no | — |
| 22 | #5806 | — | 3 | 4 | no | — |
| 23 | #5805 | — | 3 | 2 | no | — |
| 24 | #5804 | — | 3 | 4 | no | — |
| 25 | D4×#67 | — | 3 | 4 | no | — |
| 26 | D4×#67 | — | 3 | 4 | no | — |
| 27 | #5798 | — | 3 | 1 | no | — |
| 28 | #5791 | — | 3 | 2 | no | — |
| 29 | C22×C22⋊C9 | — | 4 | 2 | no | — |
| 30 | C22×C22⋊C9 | C23 | 1 | 4 | yes | — |
| 31 | C22×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 32 | C2×(C22⋊C9)⋊C2 | — | 4 | 4 | no | — |
| 33 | C2×(C22⋊C9)⋊C2 | C23 | 1 | 4 | yes | — |
| 34 | C2×D4×C9 | — | 4 | 1 | no | — |
| 35 | C2×#611 | — | 4 | 4 | no | — |
| 36 | #3699 | — | 4 | 4 | no | — |
| 37 | D4×D9 | — | 4 | 4 | no | — |
| 38 | #3697 | — | 4 | 2 | no | — |
| 39 | C4×C22⋊C9 | C23 | 1 | 2 | yes | — |
| 40 | (C22⋊C9)⋊C4 | C23 | 1 | 4 | yes | — |
| 41 | #3484 | — | 9 | 1 | no | Sylow |
| 42 | C25×C3 | C2×D3 | 1 | 2 | yes | — |
| 43 | C22×C3×D4 | — | 3 | 1 | no | — |
| 44 | C22×C3×D4 | — | 3 | 4 | no | — |
| 45 | C22×C3×D4 | — | 3 | 2 | no | — |
| 46 | C22×C3×D4 | — | 3 | 1 | no | — |
| 47 | C22×C3×D4 | C2×D3 | 1 | 4 | yes | — |
| 48 | C23×C3×C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 49 | C22×#67 | — | 3 | 4 | no | — |
| 50 | C22×#67 | — | 3 | 4 | no | — |
| 51 | C22×#67 | — | 3 | 4 | no | — |
| 52 | #1004 | — | 6 | 2 | no | — |
| 53 | #1004 | — | 6 | 4 | no | — |
| 54 | #1004 | — | 6 | 1 | no | — |
| 55 | #1004 | — | 6 | 1 | no | — |
| 56 | C2×#237 | — | 3 | 4 | no | — |
| 57 | C2×D3×D4 | — | 3 | 4 | no | — |
| 58 | C2×#235 | — | 3 | 2 | no | — |
| 59 | #953 | — | 3 | 8 | no | — |
| 60 | #953 | — | 3 | 8 | no | — |
| 61 | #953 | — | 3 | 4 | no | — |
| 62 | #953 | — | 3 | 8 | no | — |
| 63 | C2×#217 | — | 3 | 4 | no | — |
| 64 | C2×#217 | — | 3 | 4 | no | — |
| 65 | C2×#217 | — | 3 | 4 | no | — |
| 66 | #940 | — | 3 | 4 | no | — |
| 67 | #939 | — | 3 | 8 | no | — |
| 68 | #939 | — | 3 | 8 | no | — |
| 69 | #938 | — | 3 | 4 | no | — |
| 70 | #938 | — | 3 | 4 | no | — |
| 71 | #937 | — | 3 | 8 | no | — |
| 72 | #936 | — | 3 | 4 | no | — |
| 73 | #935 | — | 3 | 8 | no | — |
| 74 | D4×Dic3 | — | 3 | 4 | no | — |
| 75 | D4×Dic3 | — | 3 | 4 | no | — |
| 76 | #930 | — | 3 | 2 | no | — |
| 77 | #930 | — | 3 | 2 | no | — |
| 78 | #929 | — | 3 | 4 | no | — |
| 79 | C4×#67 | — | 3 | 4 | no | — |
| 80 | C4×#67 | — | 3 | 4 | no | — |
| 81 | #926 | — | 3 | 2 | no | — |
| 82 | #924 | — | 3 | 2 | no | — |
| 83 | #924 | — | 3 | 2 | no | — |
| 84 | C23×C9 | — | 4 | 2 | no | — |
| 85 | C22×D9 | — | 4 | 4 | no | — |
| 86 | C2×C22⋊C9 | — | 2 | 4 | no | — |
| 87 | C2×C22⋊C9 | — | 2 | 1 | no | — |
| 88 | C2×C22⋊C9 | C24 | 1 | 1 | yes | characteristic |
| 89 | (C22⋊C9)⋊C2 | — | 2 | 4 | no | — |
| 90 | D4×C9 | — | 4 | 4 | no | — |
| 91 | C2×C4×C9 | — | 4 | 1 | no | — |
| 92 | #611 | — | 4 | 4 | no | — |
| 93 | #611 | — | 4 | 8 | no | — |
| 94 | C2×Dic9 | — | 4 | 4 | no | — |
| 95 | D36 | — | 4 | 2 | no | — |
| 96 | C4×D9 | — | 4 | 4 | no | — |
| 97 | Dic18 | — | 4 | 2 | no | — |
| 98 | C2×H(5,𝔽2) | — | 9 | 1 | no | — |
| 99 | C23×D4 | D9 | 1 | 1 | yes | characteristic, complemented |
| 100 | #546 | — | 9 | 4 | no | — |
| 101 | #546 | — | 9 | 4 | no | — |
| 102 | D42 | — | 9 | 4 | no | — |
| 103 | D42 | — | 9 | 4 | no | — |
| 104 | #535 | — | 9 | 2 | no | — |
| 105 | #534 | — | 9 | 4 | no | — |
| 106 | #525 | — | 9 | 2 | no | — |
| 107 | C2×#120 | — | 9 | 4 | no | — |
| 108 | #518 | — | 9 | 1 | no | — |
| 109 | C24×C3 | — | 3 | 2 | no | — |
| 110 | C24×C3 | — | 3 | 4 | no | — |
| 111 | C24×C3 | — | 3 | 2 | no | — |
| 112 | C24×C3 | — | 4 | 2 | no | — |
| 113 | C24×C3 | — | 12 | 2 | no | — |
| 114 | C24×C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 115 | C24×C3 | C22×D3 | 1 | 4 | yes | — |
| 116 | C23×D3 | — | 3 | 4 | no | — |
| 117 | C2×C3×D4 | — | 3 | 2 | no | — |
| 118 | C2×C3×D4 | — | 3 | 4 | no | — |
| 119 | C2×C3×D4 | — | 3 | 4 | no | — |
| 120 | C2×C3×D4 | — | 3 | 8 | no | — |
| 121 | C2×C3×D4 | — | 3 | 4 | no | — |
| 122 | C2×C3×D4 | — | 3 | 1 | no | — |
| 123 | C2×C3×D4 | — | 6 | 2 | no | — |
| 124 | C2×C3×D4 | — | 6 | 1 | no | — |
| 125 | C2×C3×D4 | — | 6 | 4 | no | — |
| 126 | C2×C3×D4 | S4 | 1 | 1 | yes | characteristic |
| 127 | C22×C3×C4 | — | 3 | 1 | no | — |
| 128 | C22×C3×C4 | — | 3 | 2 | no | — |
| 129 | C22×C3×C4 | — | 3 | 1 | no | — |
| 130 | C22×C3×C4 | C22×D3 | 1 | 2 | yes | — |
| 131 | C2×#67 | — | 3 | 4 | no | — |
| 132 | C2×#67 | — | 3 | 4 | no | — |
| 133 | C2×#67 | — | 3 | 8 | no | — |
| 134 | C2×#67 | — | 3 | 4 | no | — |
| 135 | C2×#67 | — | 3 | 8 | no | — |
| 136 | C2×#67 | — | 3 | 8 | no | — |
| 137 | C2×#67 | — | 6 | 4 | no | — |
| 138 | C2×#67 | — | 6 | 4 | no | — |
| 139 | C2×#67 | — | 6 | 4 | no | — |
| 140 | C2×#67 | — | 6 | 4 | no | — |
| 141 | C2×#67 | — | 12 | 4 | no | — |
| 142 | C2×#67 | — | 12 | 4 | no | — |
| 143 | C2×#67 | — | 12 | 8 | no | — |
| 144 | C22×Dic3 | — | 3 | 4 | no | — |
| 145 | C22×Dic3 | — | 3 | 4 | no | — |
| 146 | C22×Dic3 | — | 3 | 4 | no | — |
| 147 | #237 | — | 6 | 8 | no | — |
| 148 | #237 | — | 6 | 4 | no | — |
| 149 | #237 | — | 6 | 4 | no | — |
| 150 | D3×D4 | — | 6 | 8 | no | — |
| 151 | D3×D4 | — | 6 | 4 | no | — |
| 152 | D3×D4 | — | 6 | 4 | no | — |
| 153 | #235 | — | 6 | 2 | no | — |
| 154 | #235 | — | 6 | 2 | no | — |
| 155 | #235 | — | 6 | 2 | no | — |
| 156 | #235 | — | 6 | 2 | no | — |
| 157 | C2×D12 | — | 3 | 2 | no | — |
| 158 | C2×C4×D3 | — | 3 | 4 | no | — |
| 159 | C2×Dic6 | — | 3 | 2 | no | — |
| 160 | #217 | — | 3 | 4 | no | — |
| 161 | #217 | — | 3 | 4 | no | — |
| 162 | #217 | — | 3 | 8 | no | — |
| 163 | #217 | — | 3 | 8 | no | — |
| 164 | #217 | — | 3 | 8 | no | — |
| 165 | #217 | — | 3 | 4 | no | — |
| 166 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 167 | (C2×D3)⋊C4 | — | 3 | 4 | no | — |
| 168 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 169 | C4⋊Dic3 | — | 3 | 2 | no | — |
| 170 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 171 | Dic3⋊C4 | — | 3 | 4 | no | — |
| 172 | C4×Dic3 | — | 3 | 4 | no | — |
| 173 | C22×C9 | — | 4 | 4 | no | — |
| 174 | C22×C9 | — | 4 | 1 | no | — |
| 175 | C22×C9 | — | 16 | 2 | no | — |
| 176 | C2×D9 | — | 4 | 4 | no | — |
| 177 | C2×D9 | — | 16 | 4 | no | — |
| 178 | C22⋊C9 | H(5,𝔽2) | 1 | 1 | yes | characteristic, complemented |
| 179 | C4×C9 | — | 4 | 2 | no | — |
| 180 | Dic9 | — | 4 | 4 | no | — |
| 181 | C25 | C2×D9 | 1 | 2 | yes | complemented |
| 182 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 183 | H(5,𝔽2) | — | 18 | 4 | no | — |
| 184 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 185 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 186 | C2×#41 | — | 9 | 2 | no | — |
| 187 | C2×#41 | — | 9 | 4 | no | — |
| 188 | C22×D4 | — | 3 | 1 | no | — |
| 189 | C22×D4 | — | 3 | 2 | no | — |
| 190 | C22×D4 | — | 3 | 1 | no | — |
| 191 | C22×D4 | — | 3 | 4 | no | — |
| 192 | C22×D4 | — | 9 | 4 | no | — |
| 193 | C22×D4 | — | 9 | 4 | no | — |
| 194 | C22×D4 | — | 9 | 4 | no | — |
| 195 | C22×D4 | — | 9 | 4 | no | — |
| 196 | C22×D4 | C2×D9 | 1 | 4 | yes | complemented |
| 197 | C23×C4 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 198 | #127 | — | 9 | 4 | no | — |
| 199 | #124 | — | 9 | 4 | no | — |
| 200 | #123 | — | 9 | 4 | no | — |
| 201 | #123 | — | 9 | 8 | no | — |
| 202 | C22⋊Q8 | — | 9 | 2 | no | — |
| 203 | C22⋊Q8 | — | 9 | 2 | no | — |
| 204 | #121 | — | 9 | 2 | no | — |
| 205 | #121 | — | 9 | 8 | no | — |
| 206 | #121 | — | 9 | 8 | no | — |
| 207 | #121 | — | 9 | 4 | no | — |
| 208 | #121 | — | 9 | 4 | no | — |
| 209 | #121 | — | 9 | 2 | no | — |
| 210 | #120 | — | 9 | 8 | no | — |
| 211 | #120 | — | 9 | 8 | no | — |
| 212 | #120 | — | 9 | 8 | no | — |
| 213 | #120 | — | 9 | 4 | no | — |
| 214 | #120 | — | 9 | 8 | no | — |
| 215 | C4×D4 | — | 9 | 4 | no | — |
| 216 | C4×D4 | — | 9 | 4 | no | — |
| 217 | C4×D4 | — | 9 | 4 | no | — |
| 218 | C4×D4 | — | 9 | 4 | no | — |
| 219 | #117 | — | 9 | 2 | no | — |
| 220 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 221 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 222 | C2×C22⋊C4 | — | 9 | 4 | no | — |
| 223 | C23×C3 | — | 2 | 4 | no | — |
| 224 | C23×C3 | — | 2 | 1 | no | — |
| 225 | C23×C3 | — | 3 | 1 | no | — |
| 226 | C23×C3 | — | 3 | 4 | no | — |
| 227 | C23×C3 | — | 3 | 1 | no | — |
| 228 | C23×C3 | — | 3 | 4 | no | — |
| 229 | C23×C3 | — | 3 | 2 | no | — |
| 230 | C23×C3 | — | 3 | 4 | no | — |
| 231 | C23×C3 | — | 6 | 1 | no | — |
| 232 | C23×C3 | — | 6 | 2 | no | — |
| 233 | C23×C3 | — | 6 | 4 | no | — |
| 234 | C23×C3 | — | 6 | 8 | no | — |
| 235 | C23×C3 | — | 12 | 2 | no | — |
| 236 | C23×C3 | — | 12 | 2 | no | — |
| 237 | C23×C3 | — | 12 | 4 | no | — |
| 238 | C23×C3 | — | 12 | 2 | no | — |
| 239 | C23×C3 | — | 12 | 2 | no | — |
| 240 | C23×C3 | C2×S4 | 1 | 2 | yes | — |
| 241 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 242 | C22×D3 | — | 3 | 4 | no | — |
| 243 | C22×D3 | — | 6 | 4 | no | — |
| 244 | C22×D3 | — | 6 | 4 | no | — |
| 245 | C22×D3 | — | 12 | 4 | no | — |
| 246 | C22×D3 | — | 12 | 4 | no | — |
| 247 | C3×D4 | — | 3 | 8 | no | — |
| 248 | C3×D4 | — | 3 | 4 | no | — |
| 249 | C3×D4 | — | 6 | 4 | no | — |
| 250 | C3×D4 | C2×S4 | 1 | 4 | yes | — |
| 251 | C2×C3×C4 | — | 3 | 1 | no | — |
| 252 | C2×C3×C4 | — | 3 | 2 | no | — |
| 253 | C2×C3×C4 | — | 3 | 2 | no | — |
| 254 | C2×C3×C4 | — | 3 | 2 | no | — |
| 255 | C2×C3×C4 | — | 6 | 1 | no | — |
| 256 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 257 | #67 | — | 6 | 4 | no | — |
| 258 | #67 | — | 6 | 8 | no | — |
| 259 | #67 | — | 6 | 4 | no | — |
| 260 | #67 | — | 6 | 8 | no | — |
| 261 | #67 | — | 6 | 4 | no | — |
| 262 | #67 | — | 6 | 4 | no | — |
| 263 | #67 | — | 6 | 8 | no | — |
| 264 | #67 | — | 12 | 8 | no | — |
| 265 | #67 | — | 12 | 8 | no | — |
| 266 | C2×Dic3 | — | 3 | 4 | no | — |
| 267 | C2×Dic3 | — | 3 | 4 | no | — |
| 268 | C2×Dic3 | — | 3 | 4 | no | — |
| 269 | C2×Dic3 | — | 6 | 4 | no | — |
| 270 | C2×Dic3 | — | 6 | 4 | no | — |
| 271 | C2×Dic3 | — | 12 | 4 | no | — |
| 272 | C2×Dic3 | — | 12 | 4 | no | — |
| 273 | D12 | — | 6 | 2 | no | — |
| 274 | D12 | — | 6 | 2 | no | — |
| 275 | C4×D3 | — | 6 | 4 | no | — |
| 276 | C4×D3 | — | 6 | 4 | no | — |
| 277 | Dic6 | — | 6 | 2 | no | — |
| 278 | Dic6 | — | 6 | 2 | no | — |
| 279 | C2×C9 | — | 4 | 1 | no | — |
| 280 | C2×C9 | — | 8 | 4 | no | — |
| 281 | C2×C9 | — | 8 | 1 | no | — |
| 282 | D9 | — | 8 | 4 | no | — |
| 283 | C24 | — | 3 | 2 | no | — |
| 284 | C24 | — | 3 | 4 | no | — |
| 285 | C24 | — | 3 | 2 | no | — |
| 286 | C24 | — | 4 | 2 | no | — |
| 287 | C24 | — | 9 | 4 | no | — |
| 288 | C24 | — | 12 | 2 | no | — |
| 289 | C24 | C22×D9 | 1 | 4 | yes | — |
| 290 | C24 | C22×D9 | 1 | 1 | yes | characteristic |
| 291 | #41 | — | 18 | 2 | no | — |
| 292 | #41 | — | 18 | 2 | no | — |
| 293 | #41 | — | 18 | 2 | no | — |
| 294 | #41 | — | 18 | 8 | no | — |
| 295 | #41 | — | 18 | 4 | no | — |
| 296 | #41 | — | 18 | 4 | no | — |
| 297 | #41 | — | 18 | 2 | no | — |
| 298 | C2×Q8 | — | 9 | 2 | no | — |
| 299 | C2×D4 | — | 3 | 2 | no | — |
| 300 | C2×D4 | — | 3 | 4 | no | — |
| 301 | C2×D4 | — | 3 | 4 | no | — |
| 302 | C2×D4 | — | 3 | 8 | no | — |
| 303 | C2×D4 | — | 3 | 4 | no | — |
| 304 | C2×D4 | — | 3 | 1 | no | — |
| 305 | C2×D4 | — | 6 | 2 | no | — |
| 306 | C2×D4 | — | 6 | 1 | no | — |
| 307 | C2×D4 | — | 6 | 4 | no | — |
| 308 | C2×D4 | — | 9 | 2 | no | — |
| 309 | C2×D4 | — | 9 | 4 | no | — |
| 310 | C2×D4 | — | 9 | 4 | no | — |
| 311 | C2×D4 | — | 9 | 8 | no | — |
| 312 | C2×D4 | — | 9 | 4 | no | — |
| 313 | C2×D4 | — | 9 | 8 | no | — |
| 314 | C2×D4 | — | 9 | 8 | no | — |
| 315 | C2×D4 | — | 18 | 8 | no | — |
| 316 | C2×D4 | — | 18 | 4 | no | — |
| 317 | C2×D4 | — | 18 | 4 | no | — |
| 318 | C2×D4 | — | 18 | 4 | no | — |
| 319 | C2×D4 | — | 18 | 4 | no | — |
| 320 | C2×D4 | — | 18 | 4 | no | — |
| 321 | C2×D4 | — | 18 | 4 | no | — |
| 322 | C2×D4 | — | 36 | 4 | no | — |
| 323 | C2×D4 | — | 36 | 4 | no | — |
| 324 | C2×D4 | — | 36 | 8 | no | — |
| 325 | C2×D4 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 326 | C22×C4 | — | 3 | 1 | no | — |
| 327 | C22×C4 | — | 3 | 2 | no | — |
| 328 | C22×C4 | — | 3 | 1 | no | — |
| 329 | C22×C4 | — | 9 | 4 | no | — |
| 330 | C22×C4 | — | 9 | 4 | no | — |
| 331 | C22×C4 | — | 9 | 4 | no | — |
| 332 | C22×C4 | — | 9 | 4 | no | — |
| 333 | C22×C4 | C22×D9 | 1 | 2 | yes | — |
| 334 | C4⋊C4 | — | 9 | 2 | no | — |
| 335 | C4⋊C4 | — | 9 | 2 | no | — |
| 336 | C4⋊C4 | — | 9 | 4 | no | — |
| 337 | C4⋊C4 | — | 9 | 4 | no | — |
| 338 | C22⋊C4 | — | 9 | 4 | no | — |
| 339 | C22⋊C4 | — | 9 | 4 | no | — |
| 340 | C22⋊C4 | — | 9 | 4 | no | — |
| 341 | C22⋊C4 | — | 9 | 4 | no | — |
| 342 | C22⋊C4 | — | 9 | 8 | no | — |
| 343 | C22⋊C4 | — | 9 | 8 | no | — |
| 344 | C22⋊C4 | — | 9 | 8 | no | — |
| 345 | C22⋊C4 | — | 9 | 4 | no | — |
| 346 | C42 | — | 9 | 4 | no | — |
| 347 | C22×C3 | — | 3 | 1 | no | — |
| 348 | C22×C3 | — | 3 | 1 | no | — |
| 349 | C22×C3 | — | 3 | 2 | no | — |
| 350 | C22×C3 | — | 3 | 4 | no | — |
| 351 | C22×C3 | — | 3 | 1 | no | — |
| 352 | C22×C3 | — | 4 | 2 | no | — |
| 353 | C22×C3 | — | 6 | 4 | no | — |
| 354 | C22×C3 | — | 6 | 4 | no | — |
| 355 | C22×C3 | — | 6 | 1 | no | — |
| 356 | C22×C3 | — | 6 | 1 | no | — |
| 357 | C22×C3 | — | 6 | 4 | no | — |
| 358 | C22×C3 | — | 6 | 4 | no | — |
| 359 | C22×C3 | — | 6 | 1 | no | — |
| 360 | C22×C3 | — | 12 | 4 | no | — |
| 361 | C22×C3 | — | 12 | 2 | no | — |
| 362 | C22×C3 | — | 12 | 4 | no | — |
| 363 | C22×C3 | #1004 | 1 | 1 | yes | characteristic |
| 364 | C22×C3 | C22×S4 | 1 | 4 | yes | — |
| 365 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 366 | C2×D3 | — | 6 | 4 | no | — |
| 367 | C2×D3 | — | 6 | 4 | no | — |
| 368 | C2×D3 | — | 6 | 4 | no | — |
| 369 | C2×D3 | — | 24 | 4 | no | — |
| 370 | C2×D3 | — | 24 | 4 | no | — |
| 371 | C3×C4 | — | 3 | 2 | no | — |
| 372 | C3×C4 | C22×S4 | 1 | 2 | yes | — |
| 373 | Dic3 | — | 6 | 4 | no | — |
| 374 | Dic3 | — | 6 | 4 | no | — |
| 375 | Dic3 | — | 6 | 4 | no | — |
| 376 | C9 | — | 4 | 1 | no | Sylow |
| 377 | C23 | — | 2 | 4 | no | — |
| 378 | C23 | — | 2 | 1 | no | — |
| 379 | C23 | — | 3 | 1 | no | — |
| 380 | C23 | — | 3 | 4 | no | — |
| 381 | C23 | — | 3 | 1 | no | — |
| 382 | C23 | — | 3 | 4 | no | — |
| 383 | C23 | — | 3 | 4 | no | — |
| 384 | C23 | — | 3 | 2 | no | — |
| 385 | C23 | — | 6 | 1 | no | — |
| 386 | C23 | — | 6 | 2 | no | — |
| 387 | C23 | — | 6 | 4 | no | — |
| 388 | C23 | — | 6 | 8 | no | — |
| 389 | C23 | — | 9 | 4 | no | — |
| 390 | C23 | — | 12 | 2 | no | — |
| 391 | C23 | — | 12 | 2 | no | — |
| 392 | C23 | — | 12 | 4 | no | — |
| 393 | C23 | — | 12 | 2 | no | — |
| 394 | C23 | — | 12 | 2 | no | — |
| 395 | C23 | — | 18 | 4 | no | — |
| 396 | C23 | — | 18 | 4 | no | — |
| 397 | C23 | — | 36 | 4 | no | — |
| 398 | C23 | — | 36 | 4 | no | — |
| 399 | C23 | C2×(C22⋊C9)⋊C2 | 1 | 2 | yes | complemented |
| 400 | C23 | C23×D9 | 1 | 1 | yes | characteristic |
| 401 | Q8 | — | 18 | 2 | no | — |
| 402 | Q8 | — | 18 | 2 | no | — |
| 403 | D4 | — | 3 | 8 | no | — |
| 404 | D4 | — | 3 | 4 | no | — |
| 405 | D4 | — | 6 | 4 | no | — |
| 406 | D4 | — | 18 | 2 | no | — |
| 407 | D4 | — | 18 | 4 | no | — |
| 408 | D4 | — | 18 | 8 | no | — |
| 409 | D4 | — | 18 | 4 | no | — |
| 410 | D4 | — | 18 | 8 | no | — |
| 411 | D4 | — | 18 | 4 | no | — |
| 412 | D4 | — | 18 | 8 | no | — |
| 413 | D4 | — | 18 | 4 | no | — |
| 414 | D4 | — | 18 | 2 | no | — |
| 415 | D4 | — | 36 | 8 | no | — |
| 416 | D4 | — | 36 | 8 | no | — |
| 417 | D4 | C2×(C22⋊C9)⋊C2 | 1 | 4 | yes | complemented |
| 418 | C2×C4 | — | 3 | 1 | no | — |
| 419 | C2×C4 | — | 3 | 2 | no | — |
| 420 | C2×C4 | — | 3 | 2 | no | — |
| 421 | C2×C4 | — | 3 | 2 | no | — |
| 422 | C2×C4 | — | 6 | 1 | no | — |
| 423 | C2×C4 | — | 9 | 4 | no | — |
| 424 | C2×C4 | — | 9 | 4 | no | — |
| 425 | C2×C4 | — | 9 | 4 | no | — |
| 426 | C2×C4 | — | 18 | 4 | no | — |
| 427 | C2×C4 | — | 18 | 4 | no | — |
| 428 | C2×C4 | — | 18 | 4 | no | — |
| 429 | C2×C4 | — | 18 | 4 | no | — |
| 430 | C2×C4 | — | 36 | 4 | no | — |
| 431 | C2×C4 | — | 36 | 4 | no | — |
| 432 | C2×C4 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 433 | C2×C3 | — | 2 | 4 | no | — |
| 434 | C2×C3 | — | 2 | 1 | no | — |
| 435 | C2×C3 | — | 3 | 1 | no | — |
| 436 | C2×C3 | — | 3 | 1 | no | — |
| 437 | C2×C3 | — | 6 | 4 | no | — |
| 438 | C2×C3 | — | 6 | 1 | no | — |
| 439 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 440 | D3 | — | 12 | 4 | no | — |
| 441 | C22 | — | 3 | 1 | no | — |
| 442 | C22 | — | 3 | 1 | no | — |
| 443 | C22 | — | 3 | 2 | no | — |
| 444 | C22 | — | 3 | 1 | no | — |
| 445 | C22 | — | 3 | 4 | no | — |
| 446 | C22 | — | 4 | 2 | no | — |
| 447 | C22 | — | 6 | 4 | no | — |
| 448 | C22 | — | 6 | 4 | no | — |
| 449 | C22 | — | 6 | 1 | no | — |
| 450 | C22 | — | 6 | 1 | no | — |
| 451 | C22 | — | 6 | 4 | no | — |
| 452 | C22 | — | 6 | 4 | no | — |
| 453 | C22 | — | 6 | 1 | no | — |
| 454 | C22 | — | 12 | 4 | no | — |
| 455 | C22 | — | 12 | 2 | no | — |
| 456 | C22 | — | 12 | 4 | no | — |
| 457 | C22 | — | 18 | 4 | no | — |
| 458 | C22 | — | 18 | 4 | no | — |
| 459 | C22 | — | 18 | 4 | no | — |
| 460 | C22 | — | 72 | 4 | no | — |
| 461 | C22 | — | 72 | 4 | no | — |
| 462 | C22 | #63710 | 1 | 1 | yes | characteristic, complemented |
| 463 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 464 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 4 | yes | — |
| 465 | C4 | — | 3 | 2 | no | — |
| 466 | C4 | — | 18 | 4 | no | — |
| 467 | C4 | — | 18 | 4 | no | — |
| 468 | C4 | — | 18 | 4 | no | — |
| 469 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 2 | yes | — |
| 470 | C3 | #87477 | 1 | 1 | yes | characteristic |
| 471 | C2 | — | 2 | 1 | no | — |
| 472 | C2 | — | 2 | 4 | no | — |
| 473 | C2 | — | 3 | 1 | no | — |
| 474 | C2 | — | 3 | 1 | no | — |
| 475 | C2 | — | 6 | 1 | no | — |
| 476 | C2 | — | 6 | 4 | no | — |
| 477 | C2 | — | 36 | 4 | no | — |
| 478 | C2 | C23×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×C22⋊C9 | C2 | semidirect |
| 2. C2×#63694 | C2 | semidirect |
| 3. #10593089 | C2 | semidirect |
| 4. D4×(C22⋊C9)⋊C2 | C2 | semidirect |
| 5. #10593087 | C2 | semidirect |
| 7. C23×C22⋊C9 | C22 | semidirect |
| 8. C22×(C22⋊C9)⋊C2 | C22 | semidirect |
| 10. D4×C22⋊C9 | C22 | semidirect |
| 11. C2×C4×C22⋊C9 | C22 | semidirect |
| 12. #63694 | C22 | semidirect |
| 13. #63694 | C22 | semidirect |
| 14. C2×(C22⋊C9)⋊C4 | C22 | semidirect |
| 15. C4⋊((C22⋊C9)⋊C2) | C22 | semidirect |
| 16. C4×(C22⋊C9)⋊C2 | C22 | semidirect |
| 17. (C22⋊C9)⋊Q8 | C22 | semidirect |
| 99. C23×D4 | D9 | semidirect |
| 178. C22⋊C9 | H(5,𝔽2) | semidirect |
| 181. C25 | C2×D9 | semidirect |
| 196. C22×D4 | C2×D9 | semidirect |
| 197. C23×C4 | C2×D9 | semidirect |
| 325. C2×D4 | (C22⋊C9)⋊C2 | semidirect |
| 399. C23 | C2×(C22⋊C9)⋊C2 | semidirect |
| 417. D4 | C2×(C22⋊C9)⋊C2 | semidirect |
| 432. C2×C4 | C2×(C22⋊C9)⋊C2 | semidirect |
| 462. C22 | #63710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C22⋊C9 | 2 |
| C2×#63694 | 2 |
| #10593089 | 2 |
| D4×(C22⋊C9)⋊C2 | 2 |
| #10593087 | 2 |
| #87239 | 3 |
| #63710 | 4 |