Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1326 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 1326 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 | C2×2−1+4⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10593102 | C2 | 1 | 4 | yes | maximal, complemented |
| 3 | #10593101 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #10593098 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | C2×#63689 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #87287 | — | 3 | 1 | no | maximal |
| 7 | #63710 | — | 4 | 1 | no | maximal |
| 8 | 2−1+4⋊C9 | C22 | 1 | 4 | yes | complemented |
| 9 | C2×#41⋊C9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | C22×Q8⋊C9 | C22 | 1 | 2 | yes | complemented |
| 11 | #63692 | C22 | 1 | 2 | yes | complemented |
| 12 | #63691 | C22 | 1 | 4 | yes | complemented |
| 13 | #63690 | C22 | 1 | 2 | yes | complemented |
| 14 | #63689 | C22 | 1 | 4 | yes | complemented |
| 15 | #63689 | C22 | 1 | 8 | yes | complemented |
| 16 | C2×#3689 | C22 | 1 | 4 | yes | complemented |
| 17 | C2×#3688 | C22 | 1 | 4 | yes | complemented |
| 18 | C2×C3×2−1+4 | D3 | 1 | 1 | yes | characteristic |
| 19 | #5964 | — | 3 | 1 | no | — |
| 20 | #5838 | — | 3 | 4 | no | — |
| 21 | #5838 | — | 3 | 4 | no | — |
| 22 | #5837 | — | 3 | 4 | no | — |
| 23 | #5837 | — | 3 | 4 | no | — |
| 24 | #5822 | — | 3 | 4 | no | — |
| 25 | #5822 | — | 3 | 2 | no | — |
| 26 | #5819 | — | 3 | 1 | no | — |
| 27 | C2×#942 | — | 3 | 2 | no | — |
| 28 | C2×#942 | — | 3 | 4 | no | — |
| 29 | C2×D4×C9 | — | 4 | 1 | no | — |
| 30 | C2×#611 | — | 4 | 4 | no | — |
| 31 | #3699 | — | 4 | 4 | no | — |
| 32 | D4×D9 | — | 4 | 4 | no | — |
| 33 | #3697 | — | 4 | 2 | no | — |
| 34 | #41⋊C9 | C23 | 1 | 2 | yes | — |
| 35 | C2×Q8⋊C9 | C23 | 1 | 4 | yes | — |
| 36 | C2×Q8⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 37 | #3689 | C23 | 1 | 4 | yes | — |
| 38 | #3688 | C23 | 1 | 4 | yes | — |
| 39 | #3586 | — | 9 | 1 | no | Sylow |
| 40 | C3×2−1+4 | — | 3 | 4 | no | — |
| 41 | C3×2−1+4 | C2×D3 | 1 | 4 | yes | — |
| 42 | C2×C3×#41 | — | 3 | 1 | no | — |
| 43 | C2×C3×#41 | — | 3 | 2 | no | — |
| 44 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 45 | C22×C3×Q8 | — | 3 | 1 | no | — |
| 46 | C22×C3×Q8 | C2×D3 | 1 | 2 | yes | — |
| 47 | #1010 | — | 3 | 4 | no | — |
| 48 | #1009 | — | 3 | 4 | no | — |
| 49 | D3×#41 | — | 6 | 4 | no | — |
| 50 | #1007 | — | 6 | 1 | no | — |
| 51 | #1004 | — | 6 | 2 | no | — |
| 52 | #1004 | — | 6 | 1 | no | — |
| 53 | C2×#235 | — | 3 | 4 | no | — |
| 54 | C2×#235 | — | 3 | 2 | no | — |
| 55 | #951 | — | 3 | 2 | no | — |
| 56 | #951 | — | 3 | 8 | no | — |
| 57 | #951 | — | 3 | 2 | no | — |
| 58 | #950 | — | 3 | 4 | no | — |
| 59 | #950 | — | 3 | 8 | no | — |
| 60 | #950 | — | 3 | 8 | no | — |
| 61 | #950 | — | 3 | 4 | no | — |
| 62 | #949 | — | 3 | 2 | no | — |
| 63 | #949 | — | 3 | 8 | no | — |
| 64 | #949 | — | 3 | 2 | no | — |
| 65 | #948 | — | 3 | 4 | no | — |
| 66 | #948 | — | 3 | 4 | no | — |
| 67 | C2×#216 | — | 3 | 4 | no | — |
| 68 | C2×#216 | — | 3 | 4 | no | — |
| 69 | C2×#216 | — | 3 | 4 | no | — |
| 70 | #942 | — | 3 | 8 | no | — |
| 71 | #942 | — | 3 | 8 | no | — |
| 72 | #942 | — | 3 | 4 | no | — |
| 73 | #942 | — | 3 | 4 | no | — |
| 74 | #942 | — | 3 | 4 | no | — |
| 75 | #942 | — | 3 | 8 | no | — |
| 76 | C2×#215 | — | 3 | 4 | no | — |
| 77 | C2×#215 | — | 3 | 4 | no | — |
| 78 | C2×#215 | — | 3 | 4 | no | — |
| 79 | #932 | — | 3 | 4 | no | — |
| 80 | C2×#208 | — | 3 | 4 | no | — |
| 81 | C2×#208 | — | 3 | 2 | no | — |
| 82 | C23×C9 | — | 4 | 2 | no | — |
| 83 | C22×D9 | — | 4 | 4 | no | — |
| 84 | D4×C9 | — | 4 | 4 | no | — |
| 85 | C2×C4×C9 | — | 4 | 1 | no | — |
| 86 | #611 | — | 4 | 4 | no | — |
| 87 | #611 | — | 4 | 8 | no | — |
| 88 | C2×Dic9 | — | 4 | 4 | no | — |
| 89 | D36 | — | 4 | 2 | no | — |
| 90 | C4×D9 | — | 4 | 4 | no | — |
| 91 | Dic18 | — | 4 | 2 | no | — |
| 92 | Q8⋊C9 | C24 | 1 | 1 | yes | characteristic |
| 93 | #585 | — | 9 | 1 | no | — |
| 94 | C2×2−1+4 | D9 | 1 | 1 | yes | characteristic, complemented |
| 95 | #578 | — | 9 | 4 | no | — |
| 96 | #578 | — | 9 | 4 | no | — |
| 97 | #577 | — | 9 | 4 | no | — |
| 98 | #577 | — | 9 | 4 | no | — |
| 99 | #575 | — | 9 | 4 | no | — |
| 100 | #575 | — | 9 | 2 | no | — |
| 101 | C2×#137 | — | 9 | 2 | no | — |
| 102 | C2×#137 | — | 9 | 4 | no | — |
| 103 | #568 | — | 9 | 1 | no | — |
| 104 | C3×#41 | — | 3 | 4 | no | — |
| 105 | C3×#41 | — | 3 | 4 | no | — |
| 106 | C3×#41 | — | 3 | 2 | no | — |
| 107 | C3×#41 | — | 3 | 8 | no | — |
| 108 | C3×#41 | — | 6 | 4 | no | — |
| 109 | C3×#41 | C22×D3 | 1 | 2 | yes | — |
| 110 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 111 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 112 | C2×C3×Q8 | — | 3 | 2 | no | — |
| 113 | C2×C3×Q8 | — | 3 | 4 | no | — |
| 114 | C2×C3×Q8 | — | 6 | 2 | no | — |
| 115 | C2×C3×Q8 | C22×D3 | 1 | 4 | yes | — |
| 116 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 117 | C2×C3×D4 | — | 3 | 2 | no | — |
| 118 | C2×C3×D4 | — | 3 | 1 | no | — |
| 119 | C2×C3×D4 | S4 | 1 | 1 | yes | characteristic |
| 120 | C22×C3×C4 | — | 3 | 2 | no | — |
| 121 | C22×C3×C4 | — | 3 | 1 | no | — |
| 122 | C22×C3×C4 | — | 6 | 1 | no | — |
| 123 | C2×#67 | — | 6 | 2 | no | — |
| 124 | C2×#67 | — | 6 | 4 | no | — |
| 125 | #239 | — | 6 | 4 | no | — |
| 126 | D3×Q8 | — | 6 | 4 | no | — |
| 127 | #237 | — | 6 | 8 | no | — |
| 128 | #237 | — | 6 | 4 | no | — |
| 129 | D3×D4 | — | 6 | 8 | no | — |
| 130 | D3×D4 | — | 6 | 4 | no | — |
| 131 | #235 | — | 3 | 4 | no | — |
| 132 | #235 | — | 3 | 8 | no | — |
| 133 | #235 | — | 3 | 4 | no | — |
| 134 | #235 | — | 6 | 4 | no | — |
| 135 | #235 | — | 6 | 4 | no | — |
| 136 | #235 | — | 6 | 2 | no | — |
| 137 | #235 | — | 6 | 2 | no | — |
| 138 | C2×D12 | — | 3 | 4 | no | — |
| 139 | C2×D12 | — | 3 | 2 | no | — |
| 140 | C2×C4×D3 | — | 6 | 4 | no | — |
| 141 | C2×C4×D3 | — | 6 | 2 | no | — |
| 142 | C2×Dic6 | — | 3 | 4 | no | — |
| 143 | C2×Dic6 | — | 3 | 2 | no | — |
| 144 | #216 | — | 3 | 8 | no | — |
| 145 | #216 | — | 3 | 8 | no | — |
| 146 | #216 | — | 3 | 4 | no | — |
| 147 | #216 | — | 3 | 4 | no | — |
| 148 | #215 | — | 3 | 8 | no | — |
| 149 | #215 | — | 3 | 4 | no | — |
| 150 | #215 | — | 3 | 8 | no | — |
| 151 | #215 | — | 3 | 4 | no | — |
| 152 | #214 | — | 3 | 4 | no | — |
| 153 | #214 | — | 3 | 4 | no | — |
| 154 | #213 | — | 3 | 4 | no | — |
| 155 | #213 | — | 3 | 4 | no | — |
| 156 | #208 | — | 3 | 4 | no | — |
| 157 | #208 | — | 3 | 8 | no | — |
| 158 | #208 | — | 3 | 2 | no | — |
| 159 | #208 | — | 3 | 2 | no | — |
| 160 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 161 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 162 | C2×C3⋊C8 | — | 3 | 4 | no | — |
| 163 | C22×C9 | — | 4 | 4 | no | — |
| 164 | C22×C9 | — | 4 | 1 | no | — |
| 165 | C22×C9 | — | 16 | 2 | no | — |
| 166 | C2×D9 | — | 4 | 4 | no | — |
| 167 | C2×D9 | — | 16 | 4 | no | — |
| 168 | C4×C9 | — | 4 | 2 | no | — |
| 169 | Dic9 | — | 4 | 4 | no | — |
| 170 | 2−1+4 | — | 3 | 4 | no | — |
| 171 | 2−1+4 | — | 9 | 4 | no | — |
| 172 | 2−1+4 | — | 18 | 1 | no | — |
| 173 | 2−1+4 | C2×D9 | 1 | 4 | yes | complemented |
| 174 | H(5,𝔽2) | — | 9 | 4 | no | — |
| 175 | H(5,𝔽2) | — | 18 | 2 | no | — |
| 176 | H(5,𝔽2) | — | 18 | 1 | no | — |
| 177 | C2×#41 | — | 3 | 1 | no | — |
| 178 | C2×#41 | — | 3 | 2 | no | — |
| 179 | C2×#41 | — | 9 | 4 | no | — |
| 180 | C2×#41 | — | 9 | 2 | no | — |
| 181 | C2×#41 | — | 18 | 4 | no | — |
| 182 | C2×#41 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 183 | C22×Q8 | — | 3 | 1 | no | — |
| 184 | C22×Q8 | C2×D9 | 1 | 2 | yes | complemented |
| 185 | #137 | — | 9 | 8 | no | — |
| 186 | #137 | — | 9 | 8 | no | — |
| 187 | #137 | — | 9 | 4 | no | — |
| 188 | #137 | — | 9 | 4 | no | — |
| 189 | #137 | — | 9 | 2 | no | — |
| 190 | #137 | — | 9 | 8 | no | — |
| 191 | #137 | — | 9 | 2 | no | — |
| 192 | #137 | — | 9 | 4 | no | — |
| 193 | #137 | — | 9 | 8 | no | — |
| 194 | AGL(1,ℤ/8) | — | 9 | 4 | no | — |
| 195 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 196 | AGL(1,ℤ/8) | — | 9 | 8 | no | — |
| 197 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 198 | #135 | — | 9 | 4 | no | — |
| 199 | #135 | — | 9 | 8 | no | — |
| 200 | #135 | — | 9 | 8 | no | — |
| 201 | #135 | — | 9 | 4 | no | — |
| 202 | C2×Q16 | — | 9 | 4 | no | — |
| 203 | C2×Q16 | — | 9 | 4 | no | — |
| 204 | C2×Q16 | — | 9 | 4 | no | — |
| 205 | C2×SD16 | — | 9 | 4 | no | — |
| 206 | C2×SD16 | — | 9 | 4 | no | — |
| 207 | C2×SD16 | — | 9 | 4 | no | — |
| 208 | #131 | — | 9 | 4 | no | — |
| 209 | #131 | — | 9 | 4 | no | — |
| 210 | C2×M16 | — | 9 | 4 | no | — |
| 211 | C2×M16 | — | 9 | 2 | no | — |
| 212 | C23×C3 | — | 3 | 1 | no | — |
| 213 | C23×C3 | C2×S4 | 1 | 2 | yes | — |
| 214 | C22×D3 | — | 6 | 2 | no | — |
| 215 | C22×D3 | — | 6 | 4 | no | — |
| 216 | C3×Q8 | — | 3 | 4 | no | — |
| 217 | C3×Q8 | — | 3 | 1 | no | — |
| 218 | C3×Q8 | — | 3 | 4 | no | — |
| 219 | C3×Q8 | — | 6 | 2 | no | — |
| 220 | C3×Q8 | C23×D3 | 1 | 1 | yes | characteristic |
| 221 | C3×D4 | — | 3 | 2 | no | — |
| 222 | C3×D4 | — | 3 | 8 | no | — |
| 223 | C3×D4 | — | 6 | 1 | no | — |
| 224 | C3×D4 | C2×S4 | 1 | 4 | yes | — |
| 225 | C2×C3×C4 | — | 3 | 4 | no | — |
| 226 | C2×C3×C4 | — | 3 | 1 | no | — |
| 227 | C2×C3×C4 | — | 3 | 4 | no | — |
| 228 | C2×C3×C4 | — | 3 | 2 | no | — |
| 229 | C2×C3×C4 | — | 3 | 2 | no | — |
| 230 | C2×C3×C4 | — | 3 | 2 | no | — |
| 231 | C2×C3×C4 | — | 6 | 4 | no | — |
| 232 | C2×C3×C4 | C2×S4 | 1 | 1 | yes | characteristic |
| 233 | #67 | — | 6 | 4 | no | — |
| 234 | #67 | — | 6 | 4 | no | — |
| 235 | #67 | — | 6 | 8 | no | — |
| 236 | C2×Dic3 | — | 6 | 2 | no | — |
| 237 | C2×Dic3 | — | 6 | 4 | no | — |
| 238 | D12 | — | 3 | 4 | no | — |
| 239 | D12 | — | 6 | 4 | no | — |
| 240 | D12 | — | 6 | 2 | no | — |
| 241 | C4×D3 | — | 6 | 4 | no | — |
| 242 | C4×D3 | — | 6 | 8 | no | — |
| 243 | C4×D3 | — | 6 | 4 | no | — |
| 244 | Dic6 | — | 3 | 4 | no | — |
| 245 | Dic6 | — | 6 | 4 | no | — |
| 246 | Dic6 | — | 6 | 2 | no | — |
| 247 | C3⋊C8 | — | 3 | 4 | no | — |
| 248 | C3⋊C8 | — | 3 | 4 | no | — |
| 249 | C2×C9 | — | 4 | 1 | no | — |
| 250 | C2×C9 | — | 8 | 4 | no | — |
| 251 | C2×C9 | — | 8 | 1 | no | — |
| 252 | D9 | — | 8 | 4 | no | — |
| 253 | #41 | — | 3 | 4 | no | — |
| 254 | #41 | — | 3 | 4 | no | — |
| 255 | #41 | — | 3 | 2 | no | — |
| 256 | #41 | — | 3 | 8 | no | — |
| 257 | #41 | — | 6 | 4 | no | — |
| 258 | #41 | — | 9 | 8 | no | — |
| 259 | #41 | — | 9 | 4 | no | — |
| 260 | #41 | — | 9 | 4 | no | — |
| 261 | #41 | — | 18 | 4 | no | — |
| 262 | #41 | — | 18 | 2 | no | — |
| 263 | #41 | — | 18 | 4 | no | — |
| 264 | #41 | — | 18 | 8 | no | — |
| 265 | #41 | — | 18 | 4 | no | — |
| 266 | #41 | — | 18 | 4 | no | — |
| 267 | #41 | — | 18 | 2 | no | — |
| 268 | #41 | C22×D9 | 1 | 2 | yes | — |
| 269 | C2×Q8 | — | 3 | 1 | no | — |
| 270 | C2×Q8 | — | 3 | 4 | no | — |
| 271 | C2×Q8 | — | 3 | 2 | no | — |
| 272 | C2×Q8 | — | 3 | 4 | no | — |
| 273 | C2×Q8 | — | 6 | 2 | no | — |
| 274 | C2×Q8 | — | 9 | 4 | no | — |
| 275 | C2×Q8 | — | 9 | 2 | no | — |
| 276 | C2×Q8 | — | 18 | 4 | no | — |
| 277 | C2×Q8 | C22×D9 | 1 | 4 | yes | — |
| 278 | C2×Q8 | C22×D9 | 1 | 1 | yes | characteristic |
| 279 | C2×D4 | — | 3 | 2 | no | — |
| 280 | C2×D4 | — | 3 | 1 | no | — |
| 281 | C2×D4 | — | 9 | 4 | no | — |
| 282 | C2×D4 | — | 9 | 2 | no | — |
| 283 | C2×D4 | — | 18 | 8 | no | — |
| 284 | C2×D4 | — | 18 | 2 | no | — |
| 285 | C2×D4 | — | 18 | 4 | no | — |
| 286 | C2×D4 | — | 18 | 4 | no | — |
| 287 | C2×D4 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 288 | C22×C4 | — | 3 | 2 | no | — |
| 289 | C22×C4 | — | 3 | 1 | no | — |
| 290 | C22×C4 | — | 6 | 1 | no | — |
| 291 | C22×C4 | — | 18 | 4 | no | — |
| 292 | C22×C4 | — | 18 | 2 | no | — |
| 293 | Q16 | — | 9 | 8 | no | — |
| 294 | Q16 | — | 9 | 4 | no | — |
| 295 | Q16 | — | 9 | 8 | no | — |
| 296 | Q16 | — | 9 | 4 | no | — |
| 297 | SD16 | — | 9 | 4 | no | — |
| 298 | SD16 | — | 9 | 4 | no | — |
| 299 | SD16 | — | 9 | 8 | no | — |
| 300 | SD16 | — | 9 | 4 | no | — |
| 301 | SD16 | — | 9 | 8 | no | — |
| 302 | SD16 | — | 9 | 4 | no | — |
| 303 | D8 | — | 9 | 4 | no | — |
| 304 | D8 | — | 9 | 4 | no | — |
| 305 | M16 | — | 9 | 4 | no | — |
| 306 | M16 | — | 9 | 8 | no | — |
| 307 | M16 | — | 9 | 2 | no | — |
| 308 | M16 | — | 9 | 2 | no | — |
| 309 | C2×C8 | — | 9 | 4 | no | — |
| 310 | C2×C8 | — | 9 | 4 | no | — |
| 311 | C2×C8 | — | 9 | 4 | no | — |
| 312 | C22×C3 | — | 3 | 2 | no | — |
| 313 | C22×C3 | — | 4 | 2 | no | — |
| 314 | C22×C3 | — | 12 | 1 | no | — |
| 315 | C22×C3 | C22×S4 | 1 | 4 | yes | — |
| 316 | C22×C3 | C22×S4 | 1 | 1 | yes | characteristic |
| 317 | C2×D3 | — | 6 | 4 | no | — |
| 318 | C2×D3 | — | 24 | 4 | no | — |
| 319 | C2×D3 | — | 24 | 2 | no | — |
| 320 | C3×C4 | — | 3 | 1 | no | — |
| 321 | C3×C4 | — | 3 | 4 | no | — |
| 322 | C3×C4 | — | 3 | 1 | no | — |
| 323 | C3×C4 | C22×S4 | 1 | 2 | yes | — |
| 324 | Dic3 | — | 6 | 4 | no | — |
| 325 | C9 | — | 4 | 1 | no | Sylow |
| 326 | C23 | — | 3 | 1 | no | — |
| 327 | C23 | — | 18 | 2 | no | — |
| 328 | C23 | — | 18 | 4 | no | — |
| 329 | C23 | C2×(C22⋊C9)⋊C2 | 1 | 2 | yes | — |
| 330 | Q8 | — | 3 | 1 | no | — |
| 331 | Q8 | — | 3 | 4 | no | — |
| 332 | Q8 | — | 3 | 4 | no | — |
| 333 | Q8 | — | 6 | 2 | no | — |
| 334 | Q8 | — | 9 | 4 | no | — |
| 335 | Q8 | — | 18 | 4 | no | — |
| 336 | Q8 | — | 18 | 2 | no | — |
| 337 | Q8 | C23×D9 | 1 | 1 | yes | characteristic |
| 338 | D4 | — | 3 | 2 | no | — |
| 339 | D4 | — | 3 | 8 | no | — |
| 340 | D4 | — | 6 | 1 | no | — |
| 341 | D4 | — | 9 | 4 | no | — |
| 342 | D4 | — | 18 | 4 | no | — |
| 343 | D4 | — | 18 | 4 | no | — |
| 344 | D4 | — | 18 | 4 | no | — |
| 345 | D4 | — | 18 | 8 | no | — |
| 346 | D4 | — | 18 | 2 | no | — |
| 347 | D4 | C2×(C22⋊C9)⋊C2 | 1 | 4 | yes | — |
| 348 | C2×C4 | — | 3 | 4 | no | — |
| 349 | C2×C4 | — | 3 | 1 | no | — |
| 350 | C2×C4 | — | 3 | 2 | no | — |
| 351 | C2×C4 | — | 3 | 4 | no | — |
| 352 | C2×C4 | — | 3 | 2 | no | — |
| 353 | C2×C4 | — | 3 | 2 | no | — |
| 354 | C2×C4 | — | 6 | 4 | no | — |
| 355 | C2×C4 | — | 18 | 4 | no | — |
| 356 | C2×C4 | — | 18 | 8 | no | — |
| 357 | C2×C4 | — | 18 | 2 | no | — |
| 358 | C2×C4 | — | 18 | 4 | no | — |
| 359 | C2×C4 | — | 18 | 4 | no | — |
| 360 | C2×C4 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 361 | C8 | — | 9 | 4 | no | — |
| 362 | C8 | — | 9 | 4 | no | — |
| 363 | C2×C3 | — | 2 | 4 | no | — |
| 364 | C2×C3 | — | 2 | 1 | no | — |
| 365 | C2×C3 | — | 6 | 2 | no | — |
| 366 | C2×C3 | C23×S4 | 1 | 1 | yes | characteristic |
| 367 | D3 | — | 12 | 4 | no | — |
| 368 | C22 | — | 3 | 2 | no | — |
| 369 | C22 | — | 4 | 2 | no | — |
| 370 | C22 | — | 12 | 1 | no | — |
| 371 | C22 | — | 18 | 4 | no | — |
| 372 | C22 | — | 72 | 4 | no | — |
| 373 | C22 | — | 72 | 2 | no | — |
| 374 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 375 | C22 | C22×(C22⋊C9)⋊C2 | 1 | 4 | yes | — |
| 376 | C4 | — | 3 | 1 | no | — |
| 377 | C4 | — | 3 | 1 | no | — |
| 378 | C4 | — | 3 | 4 | no | — |
| 379 | C4 | — | 18 | 4 | no | — |
| 380 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 2 | yes | — |
| 381 | C3 | #87496 | 1 | 1 | yes | characteristic |
| 382 | C2 | — | 2 | 1 | no | — |
| 383 | C2 | — | 2 | 4 | no | — |
| 384 | C2 | — | 6 | 2 | no | — |
| 385 | C2 | — | 36 | 4 | no | — |
| 386 | C2 | C23×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×(C22⋊C9)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C9 | C24 |
| Frattini, socle | C2×C3 | C23×S4 |
| Fitting | C2×C3×2−1+4 | D3 |
| hypercenter | C2×D4 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C9 | |
| UCS | C1 ◁ C2 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×2−1+4⋊C9 | C2 | semidirect |
| 2. #10593102 | C2 | semidirect |
| 3. #10593101 | C2 | semidirect |
| 4. #10593098 | C2 | semidirect |
| 5. C2×#63689 | C2 | semidirect |
| 8. 2−1+4⋊C9 | C22 | semidirect |
| 9. C2×#41⋊C9 | C22 | semidirect |
| 10. C22×Q8⋊C9 | C22 | semidirect |
| 11. #63692 | C22 | semidirect |
| 12. #63691 | C22 | semidirect |
| 13. #63690 | C22 | semidirect |
| 14. #63689 | C22 | semidirect |
| 15. #63689 | C22 | semidirect |
| 16. C2×#3689 | C22 | semidirect |
| 17. C2×#3688 | C22 | semidirect |
| 94. C2×2−1+4 | D9 | semidirect |
| 173. 2−1+4 | C2×D9 | semidirect |
| 182. C2×#41 | C2×D9 | semidirect |
| 184. C22×Q8 | C2×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×2−1+4⋊C9 | 2 |
| #10593102 | 2 |
| #10593101 | 2 |
| #10593098 | 2 |
| C2×#63689 | 2 |
| #87287 | 3 |
| #63710 | 4 |