Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
672 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 142 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 | #10589868 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #10589864 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | C9×#497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10588872 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #10588857 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #10588775 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #10588742 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #10588741 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #10588397 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #81885 | — | 3 | 1 | no | maximal |
| 11 | #63713 | C22 | 1 | 2 | yes | — |
| 12 | #63713 | C22 | 1 | 1 | yes | characteristic, complemented |
| 13 | #63710 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×C9×Q16 | C22 | 1 | 2 | yes | complemented |
| 15 | C2×C9×SD16 | C22 | 1 | 2 | yes | — |
| 16 | C9×C4⋊Q8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 17 | C9×#124 | C22 | 1 | 1 | yes | characteristic |
| 18 | #63505 | C22 | 1 | 2 | yes | — |
| 19 | #63505 | C22 | 1 | 2 | yes | — |
| 20 | #63505 | C22 | 1 | 2 | yes | complemented |
| 21 | #63495 | C22 | 1 | 2 | yes | — |
| 22 | #63481 | — | 2 | 2 | no | — |
| 23 | #63480 | — | 2 | 2 | no | — |
| 24 | #63480 | — | 2 | 2 | no | — |
| 25 | Q16×D9 | — | 2 | 2 | no | — |
| 26 | #63478 | — | 2 | 2 | no | — |
| 27 | #63477 | — | 2 | 2 | no | — |
| 28 | #63476 | — | 2 | 2 | no | — |
| 29 | SD16×D9 | — | 2 | 2 | no | — |
| 30 | #63467 | C22 | 1 | 2 | yes | — |
| 31 | #63464 | C22 | 1 | 2 | yes | — |
| 32 | #63464 | C22 | 1 | 2 | yes | complemented |
| 33 | C9×#97 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | #63394 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #63394 | C22 | 1 | 2 | yes | complemented |
| 36 | #63391 | C22 | 1 | 1 | yes | characteristic |
| 37 | #63372 | C22 | 1 | 2 | yes | complemented |
| 38 | #63364 | C22 | 1 | 2 | yes | — |
| 39 | #63364 | C22 | 1 | 2 | yes | complemented |
| 40 | #5766 | — | 3 | 2 | no | — |
| 41 | #5762 | — | 3 | 2 | no | — |
| 42 | C3×#497 | D3 | 1 | 1 | yes | characteristic |
| 43 | #5192 | — | 3 | 2 | no | — |
| 44 | #5177 | — | 3 | 2 | no | — |
| 45 | #5095 | — | 3 | 2 | no | — |
| 46 | #5062 | — | 3 | 1 | no | — |
| 47 | #5061 | — | 3 | 1 | no | — |
| 48 | #4717 | — | 3 | 2 | no | — |
| 49 | C2×Q8×C9 | C23 | 1 | 1 | yes | characteristic |
| 50 | C2×Q8×C9 | C23 | 1 | 2 | yes | — |
| 51 | C2×D4×C9 | C23 | 1 | 1 | yes | characteristic |
| 52 | C2×#611 | — | 4 | 1 | no | — |
| 53 | #3701 | — | 2 | 2 | no | — |
| 54 | #3701 | — | 2 | 2 | no | — |
| 55 | #3701 | — | 2 | 2 | no | — |
| 56 | Q8×D9 | — | 2 | 2 | no | — |
| 57 | Q8×D9 | — | 2 | 2 | no | — |
| 58 | Q8×D9 | — | 2 | 2 | no | — |
| 59 | #3699 | — | 2 | 2 | no | — |
| 60 | D4×D9 | — | 2 | 2 | no | — |
| 61 | #3697 | — | 4 | 2 | no | — |
| 62 | #3697 | — | 4 | 1 | no | — |
| 63 | #3697 | C23 | 1 | 2 | yes | — |
| 64 | #3697 | C23 | 1 | 2 | yes | — |
| 65 | C9×Q16 | — | 2 | 2 | no | — |
| 66 | C9×Q16 | — | 2 | 2 | no | — |
| 67 | C9×SD16 | — | 2 | 2 | no | — |
| 68 | C9×SD16 | — | 2 | 2 | no | — |
| 69 | C2×C8×C9 | C23 | 1 | 2 | yes | — |
| 70 | C9×C4⋊C4 | — | 4 | 1 | no | — |
| 71 | C9×C22⋊C4 | — | 4 | 1 | no | — |
| 72 | C42×C9 | C23 | 1 | 1 | yes | characteristic |
| 73 | #3675 | — | 2 | 2 | no | — |
| 74 | #3675 | — | 2 | 2 | no | — |
| 75 | #3675 | — | 2 | 2 | no | — |
| 76 | #3674 | — | 2 | 2 | no | — |
| 77 | #3674 | — | 2 | 2 | no | — |
| 78 | #3674 | — | 2 | 2 | no | — |
| 79 | #3673 | — | 2 | 2 | no | — |
| 80 | #3672 | — | 2 | 2 | no | — |
| 81 | #3667 | C23 | 1 | 2 | yes | — |
| 82 | #3667 | C23 | 1 | 2 | yes | — |
| 83 | D72 | D4 | 1 | 2 | yes | — |
| 84 | #3664 | D4 | 1 | 2 | yes | — |
| 85 | #3664 | D4 | 1 | 2 | yes | — |
| 86 | #3663 | — | 2 | 2 | no | — |
| 87 | #3663 | — | 2 | 2 | no | — |
| 88 | C8×D9 | — | 2 | 2 | no | — |
| 89 | C8×D9 | — | 2 | 2 | no | — |
| 90 | Dic36 | D4 | 1 | 2 | yes | — |
| 91 | #3289 | — | 9 | 1 | no | Sylow |
| 92 | #1007 | — | 3 | 2 | no | — |
| 93 | #1007 | — | 3 | 1 | no | — |
| 94 | #1004 | — | 3 | 1 | no | — |
| 95 | C2×C3×Q16 | C2×D3 | 1 | 2 | yes | — |
| 96 | C2×C3×SD16 | C2×D3 | 1 | 2 | yes | — |
| 97 | C3×C4⋊Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 98 | C3×#124 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | #942 | — | 3 | 2 | no | — |
| 100 | #942 | — | 3 | 2 | no | — |
| 101 | #942 | — | 3 | 2 | no | — |
| 102 | #932 | — | 3 | 2 | no | — |
| 103 | #919 | — | 6 | 2 | no | — |
| 104 | #918 | — | 6 | 2 | no | — |
| 105 | #918 | — | 6 | 2 | no | — |
| 106 | D3×Q16 | — | 6 | 2 | no | — |
| 107 | #916 | — | 6 | 2 | no | — |
| 108 | #915 | — | 6 | 2 | no | — |
| 109 | #914 | — | 6 | 2 | no | — |
| 110 | D3×SD16 | — | 6 | 2 | no | — |
| 111 | #904 | — | 3 | 2 | no | — |
| 112 | #901 | — | 3 | 2 | no | — |
| 113 | #901 | — | 3 | 2 | no | — |
| 114 | C3×#97 | C2×D3 | 1 | 1 | yes | characteristic |
| 115 | #836 | — | 3 | 2 | no | — |
| 116 | #836 | — | 3 | 1 | no | — |
| 117 | #833 | — | 3 | 1 | no | — |
| 118 | #819 | — | 3 | 2 | no | — |
| 119 | #805 | — | 3 | 2 | no | — |
| 120 | #805 | — | 3 | 2 | no | — |
| 121 | C23×C9 | — | 2 | 1 | no | — |
| 122 | C22×D9 | — | 4 | 1 | no | — |
| 123 | Q8×C9 | — | 2 | 2 | no | — |
| 124 | Q8×C9 | — | 2 | 2 | no | — |
| 125 | Q8×C9 | — | 2 | 2 | no | — |
| 126 | D4×C9 | — | 2 | 2 | no | — |
| 127 | C2×C4×C9 | — | 2 | 1 | no | — |
| 128 | C2×C4×C9 | — | 2 | 1 | no | — |
| 129 | C2×C4×C9 | — | 2 | 2 | no | — |
| 130 | C2×C4×C9 | C24 | 1 | 1 | yes | characteristic |
| 131 | #611 | — | 2 | 2 | no | — |
| 132 | #611 | — | 2 | 2 | no | — |
| 133 | #611 | — | 4 | 2 | no | — |
| 134 | C2×Dic9 | — | 4 | 1 | no | — |
| 135 | D36 | — | 4 | 1 | no | — |
| 136 | D36 | — | 4 | 2 | no | — |
| 137 | D36 | C2×D4 | 1 | 2 | yes | — |
| 138 | D36 | C2×D4 | 1 | 2 | yes | — |
| 139 | C4×D9 | — | 2 | 2 | no | — |
| 140 | C4×D9 | — | 2 | 2 | no | — |
| 141 | C4×D9 | — | 4 | 2 | no | — |
| 142 | C4×D9 | — | 4 | 2 | no | — |
| 143 | C4×D9 | — | 4 | 2 | no | — |
| 144 | Dic18 | — | 4 | 1 | no | — |
| 145 | Dic18 | — | 4 | 2 | no | — |
| 146 | Dic18 | C2×D4 | 1 | 2 | yes | — |
| 147 | Dic18 | C2×D4 | 1 | 2 | yes | — |
| 148 | C8×C9 | C2×D4 | 1 | 2 | yes | — |
| 149 | C8×C9 | C2×D4 | 1 | 2 | yes | — |
| 150 | C9⋊C8 | — | 2 | 2 | no | — |
| 151 | C9⋊C8 | — | 2 | 2 | no | — |
| 152 | #578 | — | 9 | 2 | no | — |
| 153 | #577 | — | 9 | 2 | no | — |
| 154 | #497 | D9 | 1 | 1 | yes | characteristic, complemented |
| 155 | #473 | — | 9 | 2 | no | — |
| 156 | #471 | — | 9 | 2 | no | — |
| 157 | #456 | — | 9 | 2 | no | — |
| 158 | #455 | — | 9 | 1 | no | — |
| 159 | #454 | — | 9 | 1 | no | — |
| 160 | #444 | — | 9 | 2 | no | — |
| 161 | C2×C3×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 162 | C2×C3×Q8 | C22×D3 | 1 | 2 | yes | — |
| 163 | C2×C3×D4 | C22×D3 | 1 | 1 | yes | characteristic |
| 164 | C2×#67 | — | 12 | 1 | no | — |
| 165 | #239 | — | 6 | 2 | no | — |
| 166 | #239 | — | 6 | 2 | no | — |
| 167 | #239 | — | 6 | 2 | no | — |
| 168 | D3×Q8 | — | 6 | 2 | no | — |
| 169 | D3×Q8 | — | 6 | 2 | no | — |
| 170 | D3×Q8 | — | 6 | 2 | no | — |
| 171 | #237 | — | 6 | 2 | no | — |
| 172 | D3×D4 | — | 6 | 2 | no | — |
| 173 | #235 | — | 3 | 2 | no | — |
| 174 | #235 | — | 3 | 2 | no | — |
| 175 | #235 | — | 12 | 1 | no | — |
| 176 | #235 | — | 12 | 2 | no | — |
| 177 | C3×Q16 | — | 2 | 2 | no | — |
| 178 | C3×Q16 | — | 2 | 2 | no | — |
| 179 | C3×SD16 | — | 2 | 2 | no | — |
| 180 | C3×SD16 | — | 2 | 2 | no | — |
| 181 | C2×C3×C8 | C22×D3 | 1 | 2 | yes | — |
| 182 | C3×C4⋊C4 | — | 4 | 1 | no | — |
| 183 | C3×C22⋊C4 | — | 4 | 1 | no | — |
| 184 | C3×C42 | C22×D3 | 1 | 1 | yes | characteristic |
| 185 | #216 | — | 6 | 2 | no | — |
| 186 | #216 | — | 6 | 2 | no | — |
| 187 | #216 | — | 6 | 2 | no | — |
| 188 | #215 | — | 6 | 2 | no | — |
| 189 | #215 | — | 6 | 2 | no | — |
| 190 | #215 | — | 6 | 2 | no | — |
| 191 | #214 | — | 6 | 2 | no | — |
| 192 | #213 | — | 6 | 2 | no | — |
| 193 | #208 | — | 3 | 2 | no | — |
| 194 | #208 | — | 3 | 2 | no | — |
| 195 | Dic12 | — | 3 | 2 | no | — |
| 196 | D24 | — | 3 | 2 | no | — |
| 197 | #204 | — | 3 | 2 | no | — |
| 198 | #204 | — | 3 | 2 | no | — |
| 199 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 200 | ΓL(1,𝔽25) | — | 6 | 2 | no | — |
| 201 | D3×C8 | — | 6 | 2 | no | — |
| 202 | D3×C8 | — | 6 | 2 | no | — |
| 203 | C22×C9 | — | 4 | 1 | no | — |
| 204 | C22×C9 | — | 8 | 1 | no | — |
| 205 | C22×C9 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 206 | C2×D9 | — | 2 | 2 | no | — |
| 207 | C2×D9 | — | 2 | 2 | no | — |
| 208 | C2×D9 | — | 16 | 1 | no | — |
| 209 | C4×C9 | — | 4 | 1 | no | — |
| 210 | C4×C9 | — | 4 | 1 | no | — |
| 211 | C4×C9 | — | 4 | 2 | no | — |
| 212 | C4×C9 | C22×D4 | 1 | 2 | yes | — |
| 213 | Dic9 | — | 2 | 2 | no | — |
| 214 | Dic9 | — | 2 | 2 | no | — |
| 215 | 2−1+4 | — | 9 | 2 | no | — |
| 216 | 2−1+4 | — | 9 | 1 | no | — |
| 217 | H(5,𝔽2) | — | 9 | 1 | no | — |
| 218 | #137 | — | 9 | 2 | no | — |
| 219 | #137 | — | 9 | 2 | no | — |
| 220 | #137 | — | 9 | 2 | no | — |
| 221 | #137 | — | 18 | 2 | no | — |
| 222 | #137 | — | 18 | 2 | no | — |
| 223 | #137 | — | 18 | 2 | no | — |
| 224 | AGL(1,ℤ/8) | — | 9 | 2 | no | — |
| 225 | AGL(1,ℤ/8) | — | 18 | 2 | no | — |
| 226 | #135 | — | 9 | 2 | no | — |
| 227 | #135 | — | 18 | 2 | no | — |
| 228 | #135 | — | 18 | 2 | no | — |
| 229 | C2×Q16 | — | 18 | 2 | no | — |
| 230 | C2×Q16 | C2×D9 | 1 | 2 | yes | complemented |
| 231 | C2×SD16 | — | 18 | 2 | no | — |
| 232 | C2×SD16 | C2×D9 | 1 | 2 | yes | — |
| 233 | #131 | — | 9 | 2 | no | — |
| 234 | #131 | — | 9 | 2 | no | — |
| 235 | C4⋊Q8 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 236 | #124 | C2×D9 | 1 | 1 | yes | characteristic |
| 237 | #108 | — | 9 | 2 | no | — |
| 238 | #104 | — | 9 | 2 | no | — |
| 239 | #104 | — | 9 | 2 | no | — |
| 240 | #101 | — | 9 | 1 | no | — |
| 241 | #101 | — | 9 | 2 | no | — |
| 242 | #100 | — | 9 | 1 | no | — |
| 243 | #97 | C2×D9 | 1 | 1 | yes | characteristic, complemented |
| 244 | C23×C3 | — | 2 | 1 | no | — |
| 245 | C22×D3 | — | 12 | 1 | no | — |
| 246 | C3×Q8 | — | 2 | 2 | no | — |
| 247 | C3×Q8 | — | 2 | 2 | no | — |
| 248 | C3×Q8 | — | 2 | 2 | no | — |
| 249 | C3×D4 | — | 2 | 2 | no | — |
| 250 | C2×C3×C4 | — | 2 | 1 | no | — |
| 251 | C2×C3×C4 | — | 2 | 1 | no | — |
| 252 | C2×C3×C4 | — | 2 | 2 | no | — |
| 253 | C2×C3×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 254 | #67 | — | 6 | 2 | no | — |
| 255 | #67 | — | 6 | 2 | no | — |
| 256 | #67 | — | 12 | 2 | no | — |
| 257 | C2×Dic3 | — | 12 | 1 | no | — |
| 258 | D12 | — | 3 | 2 | no | — |
| 259 | D12 | — | 3 | 2 | no | — |
| 260 | D12 | — | 12 | 1 | no | — |
| 261 | D12 | — | 12 | 2 | no | — |
| 262 | C4×D3 | — | 6 | 2 | no | — |
| 263 | C4×D3 | — | 6 | 2 | no | — |
| 264 | C4×D3 | — | 12 | 2 | no | — |
| 265 | C4×D3 | — | 12 | 2 | no | — |
| 266 | C4×D3 | — | 12 | 2 | no | — |
| 267 | Dic6 | — | 3 | 2 | no | — |
| 268 | Dic6 | — | 3 | 2 | no | — |
| 269 | Dic6 | — | 12 | 1 | no | — |
| 270 | Dic6 | — | 12 | 2 | no | — |
| 271 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 272 | C3×C8 | D3×D4 | 1 | 2 | yes | — |
| 273 | C3⋊C8 | — | 6 | 2 | no | — |
| 274 | C3⋊C8 | — | 6 | 2 | no | — |
| 275 | C2×C9 | — | 2 | 1 | no | — |
| 276 | C2×C9 | — | 8 | 1 | no | — |
| 277 | C2×C9 | D42 | 1 | 1 | yes | characteristic |
| 278 | D9 | — | 4 | 2 | no | — |
| 279 | D9 | — | 4 | 2 | no | — |
| 280 | #41 | — | 9 | 2 | no | — |
| 281 | #41 | — | 9 | 2 | no | — |
| 282 | #41 | — | 18 | 2 | no | — |
| 283 | #41 | — | 18 | 2 | no | — |
| 284 | #41 | — | 18 | 2 | no | — |
| 285 | #41 | — | 18 | 2 | no | — |
| 286 | #41 | — | 36 | 1 | no | — |
| 287 | #41 | — | 36 | 2 | no | — |
| 288 | C2×Q8 | — | 18 | 2 | no | — |
| 289 | C2×Q8 | — | 18 | 2 | no | — |
| 290 | C2×Q8 | — | 18 | 2 | no | — |
| 291 | C2×Q8 | C22×D9 | 1 | 1 | yes | characteristic |
| 292 | C2×Q8 | C22×D9 | 1 | 2 | yes | — |
| 293 | C2×D4 | — | 18 | 2 | no | — |
| 294 | C2×D4 | — | 36 | 1 | no | — |
| 295 | C2×D4 | C22×D9 | 1 | 1 | yes | characteristic |
| 296 | Q16 | — | 2 | 2 | no | — |
| 297 | Q16 | — | 2 | 2 | no | — |
| 298 | Q16 | — | 9 | 2 | no | — |
| 299 | Q16 | — | 18 | 2 | no | — |
| 300 | Q16 | — | 18 | 2 | no | — |
| 301 | Q16 | — | 18 | 2 | no | — |
| 302 | SD16 | — | 2 | 2 | no | — |
| 303 | SD16 | — | 2 | 2 | no | — |
| 304 | SD16 | — | 9 | 2 | no | — |
| 305 | SD16 | — | 9 | 2 | no | — |
| 306 | SD16 | — | 18 | 2 | no | — |
| 307 | SD16 | — | 18 | 2 | no | — |
| 308 | SD16 | — | 18 | 2 | no | — |
| 309 | SD16 | — | 18 | 2 | no | — |
| 310 | D8 | — | 9 | 2 | no | — |
| 311 | D8 | — | 18 | 2 | no | — |
| 312 | M16 | — | 9 | 2 | no | — |
| 313 | M16 | — | 9 | 2 | no | — |
| 314 | M16 | — | 18 | 2 | no | — |
| 315 | M16 | — | 18 | 2 | no | — |
| 316 | C2×C8 | — | 18 | 2 | no | — |
| 317 | C2×C8 | — | 18 | 2 | no | — |
| 318 | C2×C8 | C22×D9 | 1 | 2 | yes | — |
| 319 | C4⋊C4 | — | 4 | 1 | no | — |
| 320 | C22⋊C4 | — | 4 | 1 | no | — |
| 321 | C42 | C22×D9 | 1 | 1 | yes | characteristic |
| 322 | C22×C3 | — | 4 | 1 | no | — |
| 323 | C22×C3 | — | 8 | 1 | no | — |
| 324 | C22×C3 | #1004 | 1 | 1 | yes | characteristic |
| 325 | C2×D3 | — | 6 | 2 | no | — |
| 326 | C2×D3 | — | 6 | 2 | no | — |
| 327 | C2×D3 | — | 48 | 1 | no | — |
| 328 | C3×C4 | — | 4 | 1 | no | — |
| 329 | C3×C4 | — | 4 | 1 | no | — |
| 330 | C3×C4 | — | 4 | 2 | no | — |
| 331 | C3×C4 | C2×D3×D4 | 1 | 2 | yes | — |
| 332 | Dic3 | — | 6 | 2 | no | — |
| 333 | Dic3 | — | 6 | 2 | no | — |
| 334 | C9 | #3289 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 335 | C23 | — | 2 | 1 | no | — |
| 336 | C23 | — | 36 | 1 | no | — |
| 337 | Q8 | — | 2 | 2 | no | — |
| 338 | Q8 | — | 2 | 2 | no | — |
| 339 | Q8 | — | 2 | 2 | no | — |
| 340 | Q8 | — | 9 | 2 | no | — |
| 341 | Q8 | — | 9 | 2 | no | — |
| 342 | Q8 | — | 36 | 2 | no | — |
| 343 | Q8 | — | 36 | 1 | no | — |
| 344 | D4 | — | 2 | 2 | no | — |
| 345 | D4 | — | 9 | 2 | no | — |
| 346 | D4 | — | 9 | 2 | no | — |
| 347 | D4 | — | 18 | 2 | no | — |
| 348 | D4 | — | 18 | 2 | no | — |
| 349 | D4 | — | 36 | 1 | no | — |
| 350 | D4 | — | 36 | 2 | no | — |
| 351 | D4 | — | 36 | 2 | no | — |
| 352 | C2×C4 | — | 2 | 1 | no | — |
| 353 | C2×C4 | — | 2 | 1 | no | — |
| 354 | C2×C4 | — | 2 | 2 | no | — |
| 355 | C2×C4 | — | 18 | 2 | no | — |
| 356 | C2×C4 | — | 18 | 2 | no | — |
| 357 | C2×C4 | — | 36 | 2 | no | — |
| 358 | C2×C4 | — | 36 | 2 | no | — |
| 359 | C2×C4 | — | 36 | 2 | no | — |
| 360 | C2×C4 | — | 36 | 1 | no | — |
| 361 | C2×C4 | C23×D9 | 1 | 1 | yes | characteristic |
| 362 | C8 | — | 18 | 2 | no | — |
| 363 | C8 | — | 18 | 2 | no | — |
| 364 | C8 | D4×D9 | 1 | 2 | yes | — |
| 365 | C8 | D4×D9 | 1 | 2 | yes | — |
| 366 | C2×C3 | — | 2 | 1 | no | — |
| 367 | C2×C3 | — | 8 | 1 | no | — |
| 368 | C2×C3 | #5717 | 1 | 1 | yes | characteristic |
| 369 | D3 | — | 12 | 2 | no | — |
| 370 | D3 | — | 12 | 2 | no | — |
| 371 | C22 | — | 4 | 1 | no | — |
| 372 | C22 | — | 8 | 1 | no | — |
| 373 | C22 | — | 18 | 2 | no | — |
| 374 | C22 | — | 18 | 2 | no | — |
| 375 | C22 | — | 144 | 1 | no | — |
| 376 | C22 | #63710 | 1 | 1 | yes | characteristic |
| 377 | C4 | — | 4 | 1 | no | — |
| 378 | C4 | — | 4 | 1 | no | — |
| 379 | C4 | — | 4 | 2 | no | — |
| 380 | C4 | — | 18 | 2 | no | — |
| 381 | C4 | — | 18 | 2 | no | — |
| 382 | C4 | C2×D4×D9 | 1 | 2 | yes | — |
| 383 | C3 | #81885 | 1 | 1 | yes | characteristic |
| 384 | C2 | — | 2 | 1 | no | — |
| 385 | C2 | — | 8 | 1 | no | — |
| 386 | C2 | — | 36 | 2 | no | — |
| 387 | C2 | — | 36 | 2 | no | — |
| 388 | C2 | #10589819 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10589819 |
| commutator, cosocle | C2×C4×C9 | C24 |
| Frattini | C2×C3×C4 | C23×D3 |
| Fitting | C9×#497 | C2 |
| socle | C2×C3 | #5717 |
| hypercenter | #497 | D9 |
| hypocenter | C9 | #3289 |
| LCS | G ▷ C2×C4×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #497 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10589868 | C2 | semidirect |
| 2. #10589864 | C2 | semidirect |
| 3. C9×#497 | C2 | semidirect |
| 4. #10588872 | C2 | semidirect |
| 5. #10588857 | C2 | semidirect |
| 6. #10588775 | C2 | semidirect |
| 7. #10588742 | C2 | semidirect |
| 8. #10588741 | C2 | semidirect |
| 9. #10588397 | C2 | semidirect |
| 12. #63713 | C22 | semidirect |
| 14. C2×C9×Q16 | C22 | semidirect |
| 16. C9×C4⋊Q8 | C22 | semidirect |
| 20. #63505 | C22 | semidirect |
| 32. #63464 | C22 | semidirect |
| 33. C9×#97 | C22 | semidirect |
| 34. #63394 | C22 | semidirect |
| 35. #63394 | C22 | semidirect |
| 37. #63372 | C22 | semidirect |
| 39. #63364 | C22 | semidirect |
| 154. #497 | D9 | semidirect |
| 230. C2×Q16 | C2×D9 | semidirect |
| 235. C4⋊Q8 | C2×D9 | semidirect |
| 243. #97 | C2×D9 | semidirect |
| 334. C9 | #3289 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589868 | 2 |
| #10589864 | 2 |
| C9×#497 | 2 |
| #10588872 | 2 |
| #10588857 | 2 |
| #10588775 | 2 |
| #10588742 | 2 |
| #10588741 | 2 |
| #10588397 | 2 |
| #81885 | 3 |