Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1327 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 1327 conjugacy classes of subgroups — too many to draw. Only its 133 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 | #10593120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593102 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #10593101 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | #10593100 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10593099 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10593098 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | C2×#63691 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #87297 | — | 3 | 1 | no | maximal |
| 9 | #41×D9 | — | 4 | 1 | no | maximal |
| 10 | 2−1+4⋊C9 | C22 | 1 | 3 | yes | complemented |
| 11 | #63700 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | C2×#41⋊C9 | C22 | 1 | 3 | yes | complemented |
| 13 | #63692 | C22 | 1 | 3 | yes | complemented |
| 14 | #63691 | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | #63691 | C22 | 1 | 3 | yes | complemented |
| 16 | #63691 | C22 | 1 | 3 | yes | complemented |
| 17 | #63691 | C22 | 1 | 3 | yes | complemented |
| 18 | #63690 | C22 | 1 | 3 | yes | complemented |
| 19 | #63689 | C22 | 1 | 6 | yes | complemented |
| 20 | C2×#3689 | C22 | 1 | 3 | yes | complemented |
| 21 | C2×#3688 | C22 | 1 | 3 | yes | complemented |
| 22 | C3×#585 | D3 | 1 | 1 | yes | characteristic |
| 23 | #5964 | — | 3 | 1 | no | — |
| 24 | #5838 | — | 3 | 1 | no | — |
| 25 | #5838 | — | 3 | 3 | no | — |
| 26 | #5837 | — | 3 | 1 | no | — |
| 27 | #5837 | — | 3 | 3 | no | — |
| 28 | #5836 | — | 3 | 3 | no | — |
| 29 | #5836 | — | 3 | 1 | no | — |
| 30 | #5835 | — | 3 | 3 | no | — |
| 31 | #5835 | — | 3 | 1 | no | — |
| 32 | #5822 | — | 3 | 3 | no | — |
| 33 | #5822 | — | 3 | 3 | no | — |
| 34 | C2×#950 | — | 3 | 3 | no | — |
| 35 | C2×#950 | — | 3 | 3 | no | — |
| 36 | C2×#948 | — | 3 | 1 | no | — |
| 37 | C9×#41 | — | 4 | 1 | no | — |
| 38 | #3701 | — | 4 | 1 | no | — |
| 39 | Q8×D9 | — | 4 | 1 | no | — |
| 40 | #3699 | — | 4 | 3 | no | — |
| 41 | D4×D9 | — | 4 | 3 | no | — |
| 42 | #3697 | — | 4 | 3 | no | — |
| 43 | C2×C4×D9 | — | 4 | 3 | no | — |
| 44 | #41⋊C9 | C23 | 1 | 3 | yes | — |
| 45 | #41⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 46 | C2×Q8⋊C9 | C23 | 1 | 3 | yes | — |
| 47 | #3689 | C23 | 1 | 1 | yes | characteristic |
| 48 | #3689 | C23 | 1 | 3 | yes | — |
| 49 | #3688 | C23 | 1 | 1 | yes | characteristic |
| 50 | #3688 | C23 | 1 | 3 | yes | — |
| 51 | #3584 | — | 9 | 1 | no | Sylow |
| 52 | C3×2−1+4 | — | 3 | 1 | no | — |
| 53 | C3×2−1+4 | C2×D3 | 1 | 3 | yes | — |
| 54 | C3×H(5,𝔽2) | — | 3 | 3 | no | — |
| 55 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 56 | C2×C3×#41 | — | 3 | 1 | no | — |
| 57 | C2×C3×#41 | — | 3 | 3 | no | — |
| 58 | C2×C3×#41 | C2×D3 | 1 | 3 | yes | — |
| 59 | #1010 | — | 3 | 1 | no | — |
| 60 | #1010 | — | 3 | 3 | no | — |
| 61 | #1009 | — | 3 | 1 | no | — |
| 62 | #1009 | — | 3 | 3 | no | — |
| 63 | D3×#41 | — | 6 | 3 | no | — |
| 64 | D3×#41 | — | 6 | 1 | no | — |
| 65 | #1007 | — | 6 | 1 | no | — |
| 66 | #1004 | — | 6 | 3 | no | — |
| 67 | C2×#235 | — | 3 | 3 | no | — |
| 68 | C2×#235 | — | 3 | 3 | no | — |
| 69 | #951 | — | 3 | 3 | no | — |
| 70 | #951 | — | 3 | 6 | no | — |
| 71 | #951 | — | 3 | 3 | no | — |
| 72 | #950 | — | 3 | 3 | no | — |
| 73 | #950 | — | 3 | 6 | no | — |
| 74 | #950 | — | 3 | 3 | no | — |
| 75 | #950 | — | 3 | 3 | no | — |
| 76 | #950 | — | 3 | 6 | no | — |
| 77 | #950 | — | 3 | 3 | no | — |
| 78 | #950 | — | 3 | 6 | no | — |
| 79 | #950 | — | 3 | 1 | no | — |
| 80 | #950 | — | 3 | 3 | no | — |
| 81 | #950 | — | 3 | 3 | no | — |
| 82 | #950 | — | 3 | 3 | no | — |
| 83 | #949 | — | 3 | 3 | no | — |
| 84 | #949 | — | 3 | 6 | no | — |
| 85 | #949 | — | 3 | 3 | no | — |
| 86 | #948 | — | 3 | 1 | no | — |
| 87 | #948 | — | 3 | 3 | no | — |
| 88 | #948 | — | 3 | 1 | no | — |
| 89 | #948 | — | 3 | 3 | no | — |
| 90 | C2×#216 | — | 3 | 3 | no | — |
| 91 | C2×#216 | — | 3 | 3 | no | — |
| 92 | #942 | — | 3 | 3 | no | — |
| 93 | #942 | — | 3 | 3 | no | — |
| 94 | #942 | — | 3 | 6 | no | — |
| 95 | C2×#215 | — | 3 | 3 | no | — |
| 96 | C2×#215 | — | 3 | 3 | no | — |
| 97 | C2×#214 | — | 3 | 3 | no | — |
| 98 | C2×#214 | — | 3 | 3 | no | — |
| 99 | #932 | — | 3 | 3 | no | — |
| 100 | #932 | — | 3 | 3 | no | — |
| 101 | #932 | — | 3 | 6 | no | — |
| 102 | C2×#213 | — | 3 | 3 | no | — |
| 103 | C2×#213 | — | 3 | 3 | no | — |
| 104 | C2×#208 | — | 3 | 3 | no | — |
| 105 | C22×C3⋊C8 | — | 3 | 3 | no | — |
| 106 | C22×D9 | — | 4 | 3 | no | — |
| 107 | Q8×C9 | — | 4 | 1 | no | — |
| 108 | D4×C9 | — | 4 | 3 | no | — |
| 109 | C2×C4×C9 | — | 4 | 3 | no | — |
| 110 | #611 | — | 4 | 6 | no | — |
| 111 | C2×Dic9 | — | 4 | 3 | no | — |
| 112 | D36 | — | 4 | 3 | no | — |
| 113 | C4×D9 | — | 4 | 1 | no | — |
| 114 | C4×D9 | — | 4 | 3 | no | — |
| 115 | C4×D9 | — | 4 | 3 | no | — |
| 116 | C4×D9 | — | 4 | 3 | no | — |
| 117 | Dic18 | — | 4 | 3 | no | — |
| 118 | Q8⋊C9 | C24 | 1 | 1 | yes | characteristic |
| 119 | #585 | — | 9 | 1 | no | — |
| 120 | #585 | D9 | 1 | 1 | yes | characteristic, complemented |
| 121 | #578 | — | 9 | 1 | no | — |
| 122 | #578 | — | 9 | 3 | no | — |
| 123 | #577 | — | 9 | 3 | no | — |
| 124 | #577 | — | 9 | 1 | no | — |
| 125 | #577 | — | 9 | 3 | no | — |
| 126 | #577 | — | 9 | 1 | no | — |
| 127 | #576 | — | 9 | 3 | no | — |
| 128 | #576 | — | 9 | 1 | no | — |
| 129 | #575 | — | 9 | 3 | no | — |
| 130 | #575 | — | 9 | 3 | no | — |
| 131 | C2×#135 | — | 9 | 3 | no | — |
| 132 | C2×#135 | — | 9 | 3 | no | — |
| 133 | C2×#131 | — | 9 | 1 | no | — |
| 134 | C3×#41 | — | 3 | 1 | no | — |
| 135 | C3×#41 | — | 3 | 3 | no | — |
| 136 | C3×#41 | — | 3 | 3 | no | — |
| 137 | C3×#41 | — | 3 | 3 | no | — |
| 138 | C3×#41 | — | 3 | 3 | no | — |
| 139 | C3×#41 | — | 3 | 6 | no | — |
| 140 | C3×#41 | — | 6 | 3 | no | — |
| 141 | C3×#41 | S4 | 1 | 1 | yes | characteristic |
| 142 | C3×#41 | C22×D3 | 1 | 3 | yes | — |
| 143 | C3×#41 | C22×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 145 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 146 | C2×C3×Q8 | C22×D3 | 1 | 3 | yes | — |
| 147 | C2×C3×D4 | — | 3 | 3 | no | — |
| 148 | C2×C3×D4 | — | 3 | 3 | no | — |
| 149 | C2×C3×D4 | — | 3 | 3 | no | — |
| 150 | C2×C3×D4 | — | 6 | 3 | no | — |
| 151 | C22×C3×C4 | — | 3 | 3 | no | — |
| 152 | C22×C3×C4 | — | 6 | 1 | no | — |
| 153 | C2×#67 | — | 6 | 3 | no | — |
| 154 | C2×#67 | — | 6 | 3 | no | — |
| 155 | #239 | — | 6 | 3 | no | — |
| 156 | #239 | — | 6 | 1 | no | — |
| 157 | D3×Q8 | — | 6 | 3 | no | — |
| 158 | D3×Q8 | — | 6 | 1 | no | — |
| 159 | #237 | — | 6 | 6 | no | — |
| 160 | #237 | — | 6 | 3 | no | — |
| 161 | #237 | — | 6 | 3 | no | — |
| 162 | D3×D4 | — | 6 | 6 | no | — |
| 163 | D3×D4 | — | 6 | 3 | no | — |
| 164 | D3×D4 | — | 6 | 3 | no | — |
| 165 | #235 | — | 3 | 6 | no | — |
| 166 | #235 | — | 3 | 3 | no | — |
| 167 | #235 | — | 3 | 3 | no | — |
| 168 | #235 | — | 3 | 3 | no | — |
| 169 | #235 | — | 3 | 1 | no | — |
| 170 | #235 | — | 6 | 3 | no | — |
| 171 | #235 | — | 6 | 3 | no | — |
| 172 | #235 | — | 6 | 3 | no | — |
| 173 | #235 | — | 6 | 3 | no | — |
| 174 | C2×D12 | — | 3 | 3 | no | — |
| 175 | C2×D12 | — | 3 | 3 | no | — |
| 176 | C2×C4×D3 | — | 6 | 3 | no | — |
| 177 | C2×C4×D3 | — | 6 | 3 | no | — |
| 178 | C2×Dic6 | — | 3 | 3 | no | — |
| 179 | C2×Dic6 | — | 3 | 3 | no | — |
| 180 | #216 | — | 3 | 3 | no | — |
| 181 | #216 | — | 3 | 6 | no | — |
| 182 | #216 | — | 3 | 3 | no | — |
| 183 | #216 | — | 3 | 3 | no | — |
| 184 | #216 | — | 3 | 1 | no | — |
| 185 | #215 | — | 3 | 3 | no | — |
| 186 | #215 | — | 3 | 6 | no | — |
| 187 | #215 | — | 3 | 3 | no | — |
| 188 | #215 | — | 3 | 1 | no | — |
| 189 | #215 | — | 3 | 3 | no | — |
| 190 | #214 | — | 3 | 6 | no | — |
| 191 | #214 | — | 3 | 3 | no | — |
| 192 | #214 | — | 3 | 3 | no | — |
| 193 | #214 | — | 3 | 3 | no | — |
| 194 | #214 | — | 3 | 1 | no | — |
| 195 | #213 | — | 3 | 3 | no | — |
| 196 | #213 | — | 3 | 1 | no | — |
| 197 | #213 | — | 3 | 3 | no | — |
| 198 | #213 | — | 3 | 3 | no | — |
| 199 | #213 | — | 3 | 6 | no | — |
| 200 | #208 | — | 3 | 6 | no | — |
| 201 | #208 | — | 3 | 3 | no | — |
| 202 | #208 | — | 3 | 3 | no | — |
| 203 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 204 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 205 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 206 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 207 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 208 | C2×C3⋊C8 | — | 3 | 3 | no | — |
| 209 | C22×C9 | — | 4 | 3 | no | — |
| 210 | C2×D9 | — | 4 | 1 | no | — |
| 211 | C2×D9 | — | 4 | 3 | no | — |
| 212 | C2×D9 | — | 8 | 6 | no | — |
| 213 | C4×C9 | — | 4 | 3 | no | — |
| 214 | C4×C9 | — | 4 | 1 | no | — |
| 215 | Dic9 | — | 4 | 3 | no | — |
| 216 | Dic9 | — | 4 | 1 | no | — |
| 217 | 2−1+4 | — | 3 | 1 | no | — |
| 218 | 2−1+4 | — | 9 | 3 | no | — |
| 219 | 2−1+4 | — | 9 | 1 | no | — |
| 220 | 2−1+4 | — | 18 | 1 | no | — |
| 221 | 2−1+4 | C2×D9 | 1 | 3 | yes | complemented |
| 222 | H(5,𝔽2) | — | 3 | 3 | no | — |
| 223 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 224 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 225 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 226 | H(5,𝔽2) | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 227 | C2×#41 | — | 3 | 1 | no | — |
| 228 | C2×#41 | — | 3 | 3 | no | — |
| 229 | C2×#41 | — | 9 | 3 | no | — |
| 230 | C2×#41 | — | 9 | 3 | no | — |
| 231 | C2×#41 | — | 18 | 3 | no | — |
| 232 | C2×#41 | — | 18 | 1 | no | — |
| 233 | C2×#41 | C2×D9 | 1 | 3 | yes | complemented |
| 234 | #137 | — | 9 | 3 | no | — |
| 235 | #137 | — | 9 | 3 | no | — |
| 236 | #137 | — | 9 | 3 | no | — |
| 237 | #137 | — | 9 | 6 | no | — |
| 238 | #137 | — | 9 | 3 | no | — |
| 239 | #137 | — | 9 | 6 | no | — |
| 240 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 241 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 242 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 243 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 244 | AGL(1,ℤ/8) | — | 9 | 6 | no | — |
| 245 | AGL(1,ℤ/8) | — | 9 | 3 | no | — |
| 246 | #135 | — | 9 | 3 | no | — |
| 247 | #135 | — | 9 | 6 | no | — |
| 248 | #135 | — | 9 | 3 | no | — |
| 249 | #135 | — | 9 | 3 | no | — |
| 250 | #135 | — | 9 | 6 | no | — |
| 251 | #135 | — | 9 | 3 | no | — |
| 252 | #135 | — | 9 | 6 | no | — |
| 253 | #135 | — | 9 | 1 | no | — |
| 254 | #135 | — | 9 | 3 | no | — |
| 255 | #135 | — | 9 | 3 | no | — |
| 256 | #135 | — | 9 | 3 | no | — |
| 257 | C2×Q16 | — | 9 | 3 | no | — |
| 258 | C2×Q16 | — | 9 | 3 | no | — |
| 259 | C2×SD16 | — | 9 | 3 | no | — |
| 260 | C2×SD16 | — | 9 | 3 | no | — |
| 261 | C2×SD16 | — | 9 | 3 | no | — |
| 262 | C2×SD16 | — | 9 | 3 | no | — |
| 263 | C2×D8 | — | 9 | 3 | no | — |
| 264 | C2×D8 | — | 9 | 3 | no | — |
| 265 | #131 | — | 9 | 1 | no | — |
| 266 | #131 | — | 9 | 3 | no | — |
| 267 | #131 | — | 9 | 1 | no | — |
| 268 | #131 | — | 9 | 3 | no | — |
| 269 | C2×M16 | — | 9 | 3 | no | — |
| 270 | C22×C8 | — | 9 | 3 | no | — |
| 271 | C23×C3 | — | 3 | 3 | no | — |
| 272 | C23×C3 | — | 6 | 1 | no | — |
| 273 | C22×D3 | — | 6 | 3 | no | — |
| 274 | C22×D3 | — | 6 | 3 | no | — |
| 275 | C3×Q8 | — | 3 | 3 | no | — |
| 276 | C3×Q8 | — | 3 | 3 | no | — |
| 277 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 278 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 279 | C3×D4 | — | 3 | 3 | no | — |
| 280 | C3×D4 | — | 3 | 1 | no | — |
| 281 | C3×D4 | — | 3 | 6 | no | — |
| 282 | C3×D4 | — | 3 | 3 | no | — |
| 283 | C3×D4 | — | 6 | 3 | no | — |
| 284 | C3×D4 | C2×S4 | 1 | 3 | yes | — |
| 285 | C2×C3×C4 | — | 3 | 3 | no | — |
| 286 | C2×C3×C4 | — | 3 | 1 | no | — |
| 287 | C2×C3×C4 | — | 3 | 3 | no | — |
| 288 | C2×C3×C4 | — | 3 | 3 | no | — |
| 289 | C2×C3×C4 | — | 3 | 3 | no | — |
| 290 | C2×C3×C4 | — | 6 | 3 | no | — |
| 291 | C2×C3×C4 | C2×S4 | 1 | 3 | yes | — |
| 292 | #67 | — | 6 | 1 | no | — |
| 293 | #67 | — | 6 | 3 | no | — |
| 294 | #67 | — | 6 | 3 | no | — |
| 295 | #67 | — | 6 | 3 | no | — |
| 296 | #67 | — | 6 | 6 | no | — |
| 297 | C2×Dic3 | — | 6 | 3 | no | — |
| 298 | C2×Dic3 | — | 6 | 3 | no | — |
| 299 | D12 | — | 3 | 3 | no | — |
| 300 | D12 | — | 3 | 1 | no | — |
| 301 | D12 | — | 6 | 3 | no | — |
| 302 | D12 | — | 6 | 3 | no | — |
| 303 | C4×D3 | — | 6 | 6 | no | — |
| 304 | C4×D3 | — | 6 | 1 | no | — |
| 305 | C4×D3 | — | 6 | 3 | no | — |
| 306 | C4×D3 | — | 6 | 3 | no | — |
| 307 | C4×D3 | — | 6 | 3 | no | — |
| 308 | Dic6 | — | 3 | 1 | no | — |
| 309 | Dic6 | — | 3 | 3 | no | — |
| 310 | Dic6 | — | 6 | 3 | no | — |
| 311 | Dic6 | — | 6 | 3 | no | — |
| 312 | C3⋊C8 | — | 3 | 1 | no | — |
| 313 | C3⋊C8 | — | 3 | 1 | no | — |
| 314 | C3⋊C8 | — | 3 | 3 | no | — |
| 315 | C3⋊C8 | — | 3 | 3 | no | — |
| 316 | C2×C9 | — | 4 | 1 | no | — |
| 317 | C2×C9 | — | 8 | 3 | no | — |
| 318 | D9 | — | 4 | 2 | no | — |
| 319 | D9 | — | 8 | 3 | no | — |
| 320 | #41 | — | 3 | 1 | no | — |
| 321 | #41 | — | 3 | 3 | no | — |
| 322 | #41 | — | 3 | 3 | no | — |
| 323 | #41 | — | 3 | 3 | no | — |
| 324 | #41 | — | 3 | 3 | no | — |
| 325 | #41 | — | 3 | 6 | no | — |
| 326 | #41 | — | 6 | 3 | no | — |
| 327 | #41 | — | 9 | 3 | no | — |
| 328 | #41 | — | 9 | 1 | no | — |
| 329 | #41 | — | 9 | 6 | no | — |
| 330 | #41 | — | 9 | 3 | no | — |
| 331 | #41 | — | 9 | 3 | no | — |
| 332 | #41 | — | 18 | 3 | no | — |
| 333 | #41 | — | 18 | 3 | no | — |
| 334 | #41 | — | 18 | 3 | no | — |
| 335 | #41 | — | 18 | 6 | no | — |
| 336 | #41 | — | 18 | 3 | no | — |
| 337 | #41 | — | 18 | 3 | no | — |
| 338 | #41 | — | 18 | 1 | no | — |
| 339 | #41 | — | 18 | 3 | no | — |
| 340 | #41 | — | 18 | 3 | no | — |
| 341 | #41 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 342 | #41 | C22×D9 | 1 | 1 | yes | characteristic |
| 343 | #41 | C22×D9 | 1 | 3 | yes | — |
| 344 | C2×Q8 | — | 3 | 1 | no | — |
| 345 | C2×Q8 | — | 3 | 3 | no | — |
| 346 | C2×Q8 | — | 9 | 3 | no | — |
| 347 | C2×Q8 | — | 9 | 3 | no | — |
| 348 | C2×Q8 | — | 18 | 3 | no | — |
| 349 | C2×Q8 | — | 18 | 1 | no | — |
| 350 | C2×Q8 | C22×D9 | 1 | 3 | yes | — |
| 351 | C2×D4 | — | 3 | 3 | no | — |
| 352 | C2×D4 | — | 3 | 3 | no | — |
| 353 | C2×D4 | — | 3 | 3 | no | — |
| 354 | C2×D4 | — | 6 | 3 | no | — |
| 355 | C2×D4 | — | 9 | 3 | no | — |
| 356 | C2×D4 | — | 9 | 3 | no | — |
| 357 | C2×D4 | — | 18 | 6 | no | — |
| 358 | C2×D4 | — | 18 | 3 | no | — |
| 359 | C2×D4 | — | 18 | 3 | no | — |
| 360 | C2×D4 | — | 18 | 3 | no | — |
| 361 | C2×D4 | — | 18 | 3 | no | — |
| 362 | C22×C4 | — | 3 | 3 | no | — |
| 363 | C22×C4 | — | 6 | 1 | no | — |
| 364 | C22×C4 | — | 18 | 3 | no | — |
| 365 | C22×C4 | — | 18 | 3 | no | — |
| 366 | Q16 | — | 9 | 3 | no | — |
| 367 | Q16 | — | 9 | 6 | no | — |
| 368 | Q16 | — | 9 | 3 | no | — |
| 369 | Q16 | — | 9 | 1 | no | — |
| 370 | Q16 | — | 9 | 3 | no | — |
| 371 | SD16 | — | 9 | 3 | no | — |
| 372 | SD16 | — | 9 | 1 | no | — |
| 373 | SD16 | — | 9 | 6 | no | — |
| 374 | SD16 | — | 9 | 3 | no | — |
| 375 | SD16 | — | 9 | 3 | no | — |
| 376 | SD16 | — | 9 | 3 | no | — |
| 377 | SD16 | — | 9 | 6 | no | — |
| 378 | SD16 | — | 9 | 3 | no | — |
| 379 | SD16 | — | 9 | 1 | no | — |
| 380 | SD16 | — | 9 | 3 | no | — |
| 381 | D8 | — | 9 | 3 | no | — |
| 382 | D8 | — | 9 | 1 | no | — |
| 383 | D8 | — | 9 | 6 | no | — |
| 384 | D8 | — | 9 | 3 | no | — |
| 385 | D8 | — | 9 | 3 | no | — |
| 386 | M16 | — | 9 | 6 | no | — |
| 387 | M16 | — | 9 | 3 | no | — |
| 388 | M16 | — | 9 | 3 | no | — |
| 389 | C2×C8 | — | 9 | 1 | no | — |
| 390 | C2×C8 | — | 9 | 3 | no | — |
| 391 | C2×C8 | — | 9 | 3 | no | — |
| 392 | C2×C8 | — | 9 | 3 | no | — |
| 393 | C2×C8 | — | 9 | 3 | no | — |
| 394 | C2×C8 | — | 9 | 3 | no | — |
| 395 | C22×C3 | — | 3 | 3 | no | — |
| 396 | C22×C3 | — | 3 | 1 | no | — |
| 397 | C22×C3 | — | 12 | 3 | no | — |
| 398 | C22×C3 | — | 24 | 1 | no | — |
| 399 | C22×C3 | C22×S4 | 1 | 3 | yes | — |
| 400 | C2×D3 | — | 6 | 1 | no | — |
| 401 | C2×D3 | — | 6 | 3 | no | — |
| 402 | C2×D3 | — | 24 | 3 | no | — |
| 403 | C2×D3 | — | 24 | 3 | no | — |
| 404 | C3×C4 | — | 3 | 1 | no | — |
| 405 | C3×C4 | — | 3 | 3 | no | — |
| 406 | C3×C4 | C22×S4 | 1 | 3 | yes | — |
| 407 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 408 | Dic3 | — | 6 | 1 | no | — |
| 409 | Dic3 | — | 6 | 3 | no | — |
| 410 | C9 | — | 4 | 1 | no | Sylow |
| 411 | C23 | — | 3 | 3 | no | — |
| 412 | C23 | — | 6 | 1 | no | — |
| 413 | C23 | — | 18 | 3 | no | — |
| 414 | C23 | — | 18 | 3 | no | — |
| 415 | Q8 | — | 3 | 3 | no | — |
| 416 | Q8 | — | 3 | 3 | no | — |
| 417 | Q8 | — | 9 | 3 | no | — |
| 418 | Q8 | — | 9 | 1 | no | — |
| 419 | Q8 | — | 18 | 3 | no | — |
| 420 | Q8 | — | 18 | 3 | no | — |
| 421 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 422 | Q8 | C23×D9 | 1 | 1 | yes | characteristic |
| 423 | D4 | — | 3 | 1 | no | — |
| 424 | D4 | — | 3 | 3 | no | — |
| 425 | D4 | — | 3 | 6 | no | — |
| 426 | D4 | — | 3 | 3 | no | — |
| 427 | D4 | — | 6 | 3 | no | — |
| 428 | D4 | — | 9 | 3 | no | — |
| 429 | D4 | — | 9 | 1 | no | — |
| 430 | D4 | — | 18 | 3 | no | — |
| 431 | D4 | — | 18 | 3 | no | — |
| 432 | D4 | — | 18 | 1 | no | — |
| 433 | D4 | — | 18 | 3 | no | — |
| 434 | D4 | — | 18 | 3 | no | — |
| 435 | D4 | — | 18 | 6 | no | — |
| 436 | D4 | — | 18 | 3 | no | — |
| 437 | D4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 438 | C2×C4 | — | 3 | 3 | no | — |
| 439 | C2×C4 | — | 3 | 3 | no | — |
| 440 | C2×C4 | — | 3 | 3 | no | — |
| 441 | C2×C4 | — | 3 | 1 | no | — |
| 442 | C2×C4 | — | 3 | 3 | no | — |
| 443 | C2×C4 | — | 6 | 3 | no | — |
| 444 | C2×C4 | — | 18 | 6 | no | — |
| 445 | C2×C4 | — | 18 | 3 | no | — |
| 446 | C2×C4 | — | 18 | 3 | no | — |
| 447 | C2×C4 | — | 18 | 3 | no | — |
| 448 | C2×C4 | — | 18 | 3 | no | — |
| 449 | C2×C4 | — | 18 | 3 | no | — |
| 450 | C2×C4 | — | 18 | 1 | no | — |
| 451 | C2×C4 | C2×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 452 | C8 | — | 9 | 1 | no | — |
| 453 | C8 | — | 9 | 1 | no | — |
| 454 | C8 | — | 9 | 3 | no | — |
| 455 | C8 | — | 9 | 3 | no | — |
| 456 | C2×C3 | — | 2 | 3 | no | — |
| 457 | C2×C3 | — | 6 | 3 | no | — |
| 458 | C2×C3 | — | 6 | 1 | no | — |
| 459 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 460 | D3 | — | 12 | 1 | no | — |
| 461 | D3 | — | 12 | 3 | no | — |
| 462 | C22 | — | 3 | 1 | no | — |
| 463 | C22 | — | 3 | 3 | no | — |
| 464 | C22 | — | 12 | 3 | no | — |
| 465 | C22 | — | 18 | 3 | no | — |
| 466 | C22 | — | 18 | 1 | no | — |
| 467 | C22 | — | 24 | 1 | no | — |
| 468 | C22 | — | 72 | 3 | no | — |
| 469 | C22 | — | 72 | 3 | no | — |
| 470 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 471 | C4 | — | 3 | 1 | no | — |
| 472 | C4 | — | 3 | 3 | no | — |
| 473 | C4 | — | 18 | 3 | no | — |
| 474 | C4 | — | 18 | 1 | no | — |
| 475 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 3 | yes | — |
| 476 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 477 | C3 | #87497 | 1 | 1 | yes | characteristic |
| 478 | C2 | — | 2 | 3 | no | — |
| 479 | C2 | — | 6 | 1 | no | — |
| 480 | C2 | — | 6 | 3 | no | — |
| 481 | C2 | — | 36 | 1 | no | — |
| 482 | C2 | — | 36 | 3 | no | — |
| 483 | C2 | C23×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×(C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini, socle | C2×C3 | C23×S4 |
| Fitting | C3×#585 | D3 |
| hypercenter | #41 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C4 ◁ #41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593120 | C2 | semidirect |
| 2. #10593102 | C2 | semidirect |
| 3. #10593101 | C2 | semidirect |
| 4. #10593100 | C2 | semidirect |
| 5. #10593099 | C2 | semidirect |
| 6. #10593098 | C2 | semidirect |
| 7. C2×#63691 | C2 | semidirect |
| 10. 2−1+4⋊C9 | C22 | semidirect |
| 11. #63700 | C22 | semidirect |
| 12. C2×#41⋊C9 | C22 | semidirect |
| 13. #63692 | C22 | semidirect |
| 14. #63691 | C22 | semidirect |
| 15. #63691 | C22 | semidirect |
| 16. #63691 | C22 | semidirect |
| 17. #63691 | C22 | semidirect |
| 18. #63690 | C22 | semidirect |
| 19. #63689 | C22 | semidirect |
| 20. C2×#3689 | C22 | semidirect |
| 21. C2×#3688 | C22 | semidirect |
| 120. #585 | D9 | semidirect |
| 221. 2−1+4 | C2×D9 | semidirect |
| 226. H(5,𝔽2) | C2×D9 | semidirect |
| 233. C2×#41 | C2×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593120 | 2 |
| #10593102 | 2 |
| #10593101 | 2 |
| #10593100 | 2 |
| #10593099 | 2 |
| #10593098 | 2 |
| C2×#63691 | 2 |
| #87297 | 3 |
| #41×D9 | 4 |