Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
458 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 48 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 | #10593094 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×(C22⋊C9)⋊C2 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | Q16×C22⋊C9 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10589519 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10589518 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10589503 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589502 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #83888 | — | 3 | 1 | no | maximal |
| 9 | Q8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 10 | Q8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 11 | C4⋊((C22⋊C9)⋊C2) | — | 2 | 1 | no | — |
| 12 | C4⋊((C22⋊C9)⋊C2) | C22 | 1 | 1 | yes | characteristic |
| 13 | C4×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 14 | C4×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 15 | C4×(C22⋊C9)⋊C2 | C22 | 1 | 1 | yes | characteristic |
| 16 | (C22⋊C9)⋊Q8 | — | 2 | 1 | no | — |
| 17 | (C22⋊C9)⋊Q8 | C22 | 1 | 1 | yes | characteristic |
| 18 | #63480 | — | 4 | 1 | no | maximal |
| 19 | C8×C22⋊C9 | C22 | 1 | 1 | yes | characteristic |
| 20 | (C22⋊C9)⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 21 | C22×C3×Q16 | D3 | 1 | 1 | yes | characteristic |
| 22 | #5817 | — | 3 | 1 | no | — |
| 23 | Q8×#67 | — | 3 | 1 | no | — |
| 24 | C2×#918 | — | 3 | 1 | no | — |
| 25 | #5228 | — | 3 | 1 | no | — |
| 26 | #5227 | — | 3 | 1 | no | — |
| 27 | #5190 | — | 3 | 1 | no | — |
| 28 | #5189 | — | 3 | 1 | no | — |
| 29 | #5187 | — | 3 | 1 | no | — |
| 30 | #5186 | — | 3 | 1 | no | — |
| 31 | #5185 | — | 3 | 1 | no | — |
| 32 | #5184 | — | 3 | 1 | no | — |
| 33 | #5182 | — | 3 | 1 | no | — |
| 34 | #5114 | — | 3 | 1 | no | — |
| 35 | #5111 | — | 3 | 1 | no | — |
| 36 | C2×(C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 37 | C2×(C22⋊C9)⋊C2 | D4 | 1 | 1 | yes | characteristic |
| 38 | #3701 | — | 4 | 1 | no | — |
| 39 | Q8×D9 | — | 4 | 1 | no | — |
| 40 | C4×C22⋊C9 | — | 2 | 1 | no | — |
| 41 | C4×C22⋊C9 | — | 2 | 1 | no | — |
| 42 | C4×C22⋊C9 | C23 | 1 | 1 | yes | characteristic |
| 43 | (C22⋊C9)⋊C4 | — | 2 | 1 | no | — |
| 44 | (C22⋊C9)⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 45 | C9×Q16 | — | 4 | 1 | no | — |
| 46 | #3675 | — | 4 | 1 | no | — |
| 47 | #3674 | — | 4 | 1 | no | — |
| 48 | #3664 | — | 4 | 1 | no | — |
| 49 | #3663 | — | 4 | 1 | no | — |
| 50 | #3270 | — | 9 | 1 | no | Sylow |
| 51 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 52 | C22×C3×Q8 | C2×D3 | 1 | 1 | yes | characteristic |
| 53 | C2×#239 | — | 3 | 1 | no | — |
| 54 | C2×D3×Q8 | — | 3 | 1 | no | — |
| 55 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 56 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 57 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 58 | C2×C3×Q16 | — | 3 | 1 | no | — |
| 59 | C22×C3×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 60 | #947 | — | 3 | 1 | no | — |
| 61 | #947 | — | 6 | 1 | no | — |
| 62 | #946 | — | 3 | 1 | no | — |
| 63 | #946 | — | 3 | 1 | no | — |
| 64 | #946 | — | 6 | 1 | no | — |
| 65 | #946 | — | 6 | 1 | no | — |
| 66 | Q8×Dic3 | — | 3 | 1 | no | — |
| 67 | Q8×Dic3 | — | 3 | 1 | no | — |
| 68 | #944 | — | 3 | 1 | no | — |
| 69 | #944 | — | 6 | 1 | no | — |
| 70 | C2×#216 | — | 3 | 1 | no | — |
| 71 | C2×#216 | — | 3 | 1 | no | — |
| 72 | C2×#215 | — | 3 | 1 | no | — |
| 73 | C2×#215 | — | 3 | 1 | no | — |
| 74 | #930 | — | 3 | 1 | no | — |
| 75 | #930 | — | 6 | 1 | no | — |
| 76 | C4×#67 | — | 3 | 1 | no | — |
| 77 | C4×#67 | — | 6 | 1 | no | — |
| 78 | C4×#67 | — | 6 | 1 | no | — |
| 79 | #924 | — | 3 | 1 | no | — |
| 80 | #924 | — | 6 | 1 | no | — |
| 81 | #918 | — | 6 | 1 | no | — |
| 82 | #918 | — | 6 | 1 | no | — |
| 83 | #918 | — | 6 | 1 | no | — |
| 84 | #918 | — | 6 | 1 | no | — |
| 85 | C2×#204 | — | 3 | 1 | no | — |
| 86 | C2×ΓL(1,𝔽25) | — | 3 | 1 | no | — |
| 87 | #835 | — | 3 | 1 | no | — |
| 88 | #835 | — | 3 | 1 | no | — |
| 89 | #835 | — | 3 | 1 | no | — |
| 90 | #835 | — | 3 | 1 | no | — |
| 91 | #830 | — | 3 | 1 | no | — |
| 92 | #821 | — | 3 | 1 | no | — |
| 93 | (C2×D3)⋊C8 | — | 3 | 1 | no | — |
| 94 | #817 | — | 3 | 1 | no | — |
| 95 | #816 | — | 3 | 1 | no | — |
| 96 | #815 | — | 3 | 1 | no | — |
| 97 | Dic3⋊C8 | — | 3 | 1 | no | — |
| 98 | C2×C22⋊C9 | C2×D4 | 1 | 1 | yes | characteristic |
| 99 | (C22⋊C9)⋊C2 | — | 2 | 1 | no | — |
| 100 | (C22⋊C9)⋊C2 | — | 4 | 1 | no | — |
| 101 | Q8×C9 | — | 4 | 1 | no | — |
| 102 | Q8×C9 | — | 4 | 1 | no | — |
| 103 | D36 | — | 4 | 1 | no | — |
| 104 | D36 | — | 8 | 1 | no | — |
| 105 | C4×D9 | — | 4 | 1 | no | — |
| 106 | C4×D9 | — | 8 | 1 | no | — |
| 107 | C4×D9 | — | 8 | 1 | no | — |
| 108 | Dic18 | — | 4 | 1 | no | — |
| 109 | Dic18 | — | 8 | 1 | no | — |
| 110 | C8×C9 | — | 4 | 1 | no | — |
| 111 | C9⋊C8 | — | 4 | 1 | no | — |
| 112 | C2×#137 | — | 9 | 1 | no | — |
| 113 | C22×Q16 | D9 | 1 | 1 | yes | characteristic, complemented |
| 114 | D4×Q8 | — | 9 | 1 | no | — |
| 115 | #548 | — | 9 | 1 | no | — |
| 116 | #497 | — | 9 | 1 | no | — |
| 117 | #470 | — | 9 | 1 | no | — |
| 118 | #465 | — | 9 | 1 | no | — |
| 119 | #464 | — | 9 | 1 | no | — |
| 120 | #462 | — | 9 | 1 | no | — |
| 121 | #452 | — | 9 | 1 | no | — |
| 122 | #451 | — | 9 | 1 | no | — |
| 123 | #451 | — | 9 | 1 | no | — |
| 124 | #448 | — | 9 | 1 | no | — |
| 125 | #441 | — | 9 | 1 | no | — |
| 126 | #435 | — | 9 | 1 | no | — |
| 127 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 128 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 129 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 130 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 131 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 132 | C2×C3×Q8 | — | 6 | 1 | no | — |
| 133 | C22×C3×C4 | — | 2 | 1 | no | — |
| 134 | C22×C3×C4 | — | 2 | 1 | no | — |
| 135 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 136 | C2×#67 | — | 3 | 1 | no | — |
| 137 | C2×#67 | — | 6 | 1 | no | — |
| 138 | #239 | — | 6 | 1 | no | — |
| 139 | #239 | — | 6 | 1 | no | — |
| 140 | #239 | — | 12 | 1 | no | — |
| 141 | D3×Q8 | — | 6 | 1 | no | — |
| 142 | D3×Q8 | — | 6 | 1 | no | — |
| 143 | D3×Q8 | — | 12 | 1 | no | — |
| 144 | C2×D12 | — | 3 | 1 | no | — |
| 145 | C2×D12 | — | 6 | 1 | no | — |
| 146 | C2×C4×D3 | — | 3 | 1 | no | — |
| 147 | C2×C4×D3 | — | 6 | 1 | no | — |
| 148 | C2×C4×D3 | — | 6 | 1 | no | — |
| 149 | C2×Dic6 | — | 3 | 1 | no | — |
| 150 | C2×Dic6 | — | 6 | 1 | no | — |
| 151 | C3×Q16 | — | 3 | 1 | no | — |
| 152 | C3×Q16 | — | 3 | 1 | no | — |
| 153 | C3×Q16 | — | 3 | 1 | no | — |
| 154 | C3×Q16 | — | 6 | 1 | no | — |
| 155 | C3×Q16 | S4 | 1 | 1 | yes | characteristic |
| 156 | C2×C3×C8 | — | 3 | 1 | no | — |
| 157 | C2×C3×C8 | — | 3 | 1 | no | — |
| 158 | #217 | — | 3 | 1 | no | — |
| 159 | #217 | — | 6 | 1 | no | — |
| 160 | #216 | — | 6 | 1 | no | — |
| 161 | #216 | — | 6 | 1 | no | — |
| 162 | #216 | — | 12 | 1 | no | — |
| 163 | #215 | — | 6 | 1 | no | — |
| 164 | #215 | — | 6 | 1 | no | — |
| 165 | #215 | — | 12 | 1 | no | — |
| 166 | (C2×D3)⋊C4 | — | 3 | 1 | no | — |
| 167 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 168 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 169 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 170 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 171 | (C2×D3)⋊C4 | — | 6 | 1 | no | — |
| 172 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 173 | C4⋊Dic3 | — | 3 | 1 | no | — |
| 174 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 175 | C4⋊Dic3 | — | 6 | 1 | no | — |
| 176 | Dic3⋊C4 | — | 3 | 1 | no | — |
| 177 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 178 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 179 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 180 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 181 | Dic3⋊C4 | — | 6 | 1 | no | — |
| 182 | C4×Dic3 | — | 3 | 1 | no | — |
| 183 | C4×Dic3 | — | 6 | 1 | no | — |
| 184 | C4×Dic3 | — | 6 | 1 | no | — |
| 185 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 186 | C2×C3⋊C8 | — | 3 | 1 | no | — |
| 187 | #204 | — | 6 | 1 | no | — |
| 188 | #204 | — | 6 | 1 | no | — |
| 189 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 190 | ΓL(1,𝔽25) | — | 6 | 1 | no | — |
| 191 | C2×D9 | — | 4 | 1 | no | — |
| 192 | C2×D9 | — | 8 | 1 | no | — |
| 193 | C22⋊C9 | #137 | 1 | 1 | yes | characteristic, complemented |
| 194 | C4×C9 | — | 4 | 1 | no | — |
| 195 | C4×C9 | — | 8 | 1 | no | — |
| 196 | C4×C9 | — | 8 | 1 | no | — |
| 197 | Dic9 | — | 4 | 1 | no | — |
| 198 | Dic9 | — | 8 | 1 | no | — |
| 199 | C2×#41 | — | 9 | 1 | no | — |
| 200 | C22×Q8 | — | 9 | 1 | no | — |
| 201 | C22×Q8 | C2×D9 | 1 | 1 | yes | characteristic |
| 202 | C22×Q8 | C2×D9 | 1 | 1 | yes | characteristic |
| 203 | #137 | — | 18 | 1 | no | — |
| 204 | #137 | — | 18 | 1 | no | — |
| 205 | #137 | — | 18 | 1 | no | — |
| 206 | #137 | — | 18 | 1 | no | — |
| 207 | C2×Q16 | — | 3 | 1 | no | — |
| 208 | C2×Q16 | — | 3 | 1 | no | — |
| 209 | C2×Q16 | — | 3 | 1 | no | — |
| 210 | C2×Q16 | — | 3 | 1 | no | — |
| 211 | C2×Q16 | — | 9 | 1 | no | — |
| 212 | C2×Q16 | — | 9 | 1 | no | — |
| 213 | C2×SD16 | — | 9 | 1 | no | — |
| 214 | C2×SD16 | — | 9 | 1 | no | — |
| 215 | C2×SD16 | — | 9 | 1 | no | — |
| 216 | C2×M16 | — | 9 | 1 | no | — |
| 217 | C22×C8 | C2×D9 | 1 | 1 | yes | characteristic |
| 218 | C4⋊Q8 | — | 9 | 1 | no | — |
| 219 | C4⋊Q8 | — | 18 | 1 | no | — |
| 220 | #124 | — | 9 | 1 | no | — |
| 221 | #124 | — | 18 | 1 | no | — |
| 222 | C22⋊Q8 | — | 9 | 1 | no | — |
| 223 | C22⋊Q8 | — | 9 | 1 | no | — |
| 224 | C22⋊Q8 | — | 9 | 1 | no | — |
| 225 | C22⋊Q8 | — | 18 | 1 | no | — |
| 226 | C22⋊Q8 | — | 18 | 1 | no | — |
| 227 | C22⋊Q8 | — | 18 | 1 | no | — |
| 228 | #121 | — | 9 | 1 | no | — |
| 229 | #121 | — | 18 | 1 | no | — |
| 230 | C4×Q8 | — | 9 | 1 | no | — |
| 231 | C4×Q8 | — | 9 | 1 | no | — |
| 232 | C4×D4 | — | 9 | 1 | no | — |
| 233 | C4×D4 | — | 18 | 1 | no | — |
| 234 | C4×D4 | — | 18 | 1 | no | — |
| 235 | #106 | — | 9 | 1 | no | — |
| 236 | C4⋊C8 | — | 9 | 1 | no | — |
| 237 | #103 | — | 9 | 1 | no | — |
| 238 | #103 | — | 9 | 1 | no | — |
| 239 | #103 | — | 9 | 1 | no | — |
| 240 | #103 | — | 9 | 1 | no | — |
| 241 | #103 | — | 9 | 1 | no | — |
| 242 | #102 | — | 9 | 1 | no | — |
| 243 | C22⋊C8 | — | 9 | 1 | no | — |
| 244 | C22⋊C8 | — | 9 | 1 | no | — |
| 245 | #97 | — | 9 | 1 | no | — |
| 246 | C23×C3 | D3×D4 | 1 | 1 | yes | characteristic |
| 247 | C22×D3 | — | 3 | 1 | no | — |
| 248 | C22×D3 | — | 6 | 1 | no | — |
| 249 | C3×Q8 | — | 3 | 1 | no | — |
| 250 | C3×Q8 | — | 3 | 1 | no | — |
| 251 | C3×Q8 | — | 6 | 1 | no | — |
| 252 | C3×Q8 | — | 6 | 1 | no | — |
| 253 | C3×Q8 | — | 6 | 1 | no | — |
| 254 | C3×Q8 | — | 6 | 1 | no | — |
| 255 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 256 | C3×Q8 | C2×S4 | 1 | 1 | yes | characteristic |
| 257 | C2×C3×C4 | — | 3 | 1 | no | — |
| 258 | C2×C3×C4 | — | 3 | 1 | no | — |
| 259 | C2×C3×C4 | — | 6 | 1 | no | — |
| 260 | C2×C3×C4 | — | 6 | 1 | no | — |
| 261 | C2×C3×C4 | — | 6 | 1 | no | — |
| 262 | C2×C3×C4 | — | 6 | 1 | no | — |
| 263 | #67 | — | 6 | 1 | no | — |
| 264 | #67 | — | 6 | 1 | no | — |
| 265 | #67 | — | 12 | 1 | no | — |
| 266 | #67 | — | 12 | 1 | no | — |
| 267 | C2×Dic3 | — | 3 | 1 | no | — |
| 268 | C2×Dic3 | — | 3 | 1 | no | — |
| 269 | C2×Dic3 | — | 3 | 1 | no | — |
| 270 | C2×Dic3 | — | 6 | 1 | no | — |
| 271 | C2×Dic3 | — | 6 | 1 | no | — |
| 272 | C2×Dic3 | — | 6 | 1 | no | — |
| 273 | D12 | — | 6 | 1 | no | — |
| 274 | D12 | — | 6 | 1 | no | — |
| 275 | D12 | — | 12 | 1 | no | — |
| 276 | D12 | — | 12 | 1 | no | — |
| 277 | C4×D3 | — | 6 | 1 | no | — |
| 278 | C4×D3 | — | 6 | 1 | no | — |
| 279 | C4×D3 | — | 12 | 1 | no | — |
| 280 | C4×D3 | — | 12 | 1 | no | — |
| 281 | C4×D3 | — | 12 | 1 | no | — |
| 282 | C4×D3 | — | 12 | 1 | no | — |
| 283 | Dic6 | — | 6 | 1 | no | — |
| 284 | Dic6 | — | 6 | 1 | no | — |
| 285 | Dic6 | — | 12 | 1 | no | — |
| 286 | Dic6 | — | 12 | 1 | no | — |
| 287 | C3×C8 | — | 3 | 1 | no | — |
| 288 | C3×C8 | C2×S4 | 1 | 1 | yes | characteristic |
| 289 | C3⋊C8 | — | 6 | 1 | no | — |
| 290 | C3⋊C8 | — | 6 | 1 | no | — |
| 291 | C2×C9 | — | 4 | 1 | no | — |
| 292 | D9 | — | 8 | 1 | no | — |
| 293 | D9 | — | 16 | 1 | no | — |
| 294 | #41 | — | 18 | 1 | no | — |
| 295 | #41 | — | 18 | 1 | no | — |
| 296 | #41 | — | 36 | 1 | no | — |
| 297 | C2×Q8 | — | 3 | 1 | no | — |
| 298 | C2×Q8 | — | 3 | 1 | no | — |
| 299 | C2×Q8 | — | 3 | 1 | no | — |
| 300 | C2×Q8 | — | 3 | 1 | no | — |
| 301 | C2×Q8 | — | 6 | 1 | no | — |
| 302 | C2×Q8 | — | 6 | 1 | no | — |
| 303 | C2×Q8 | — | 9 | 1 | no | — |
| 304 | C2×Q8 | — | 18 | 1 | no | — |
| 305 | C2×Q8 | — | 18 | 1 | no | — |
| 306 | C2×Q8 | — | 18 | 1 | no | — |
| 307 | C2×Q8 | — | 36 | 1 | no | — |
| 308 | C2×D4 | — | 9 | 1 | no | — |
| 309 | C2×D4 | — | 9 | 1 | no | — |
| 310 | C2×D4 | — | 18 | 1 | no | — |
| 311 | C2×D4 | — | 18 | 1 | no | — |
| 312 | C22×C4 | — | 2 | 1 | no | — |
| 313 | C22×C4 | — | 2 | 1 | no | — |
| 314 | C22×C4 | — | 9 | 1 | no | — |
| 315 | C22×C4 | — | 18 | 1 | no | — |
| 316 | C22×C4 | — | 18 | 1 | no | — |
| 317 | C22×C4 | C22×D9 | 1 | 1 | yes | characteristic |
| 318 | Q16 | — | 3 | 1 | no | — |
| 319 | Q16 | — | 3 | 1 | no | — |
| 320 | Q16 | — | 3 | 1 | no | — |
| 321 | Q16 | — | 6 | 1 | no | — |
| 322 | Q16 | — | 18 | 1 | no | — |
| 323 | Q16 | — | 18 | 1 | no | — |
| 324 | Q16 | — | 36 | 1 | no | — |
| 325 | Q16 | (C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 326 | SD16 | — | 18 | 1 | no | — |
| 327 | SD16 | — | 18 | 1 | no | — |
| 328 | SD16 | — | 18 | 1 | no | — |
| 329 | SD16 | — | 18 | 1 | no | — |
| 330 | SD16 | — | 36 | 1 | no | — |
| 331 | M16 | — | 18 | 1 | no | — |
| 332 | M16 | — | 18 | 1 | no | — |
| 333 | C2×C8 | — | 3 | 1 | no | — |
| 334 | C2×C8 | — | 3 | 1 | no | — |
| 335 | C2×C8 | — | 9 | 1 | no | — |
| 336 | C2×C8 | — | 9 | 1 | no | — |
| 337 | C4⋊C4 | — | 9 | 1 | no | — |
| 338 | C4⋊C4 | — | 9 | 1 | no | — |
| 339 | C4⋊C4 | — | 9 | 1 | no | — |
| 340 | C4⋊C4 | — | 18 | 1 | no | — |
| 341 | C4⋊C4 | — | 18 | 1 | no | — |
| 342 | C4⋊C4 | — | 18 | 1 | no | — |
| 343 | C4⋊C4 | — | 18 | 1 | no | — |
| 344 | C4⋊C4 | — | 18 | 1 | no | — |
| 345 | C4⋊C4 | — | 18 | 1 | no | — |
| 346 | C4⋊C4 | — | 18 | 1 | no | — |
| 347 | C22⋊C4 | — | 9 | 1 | no | — |
| 348 | C22⋊C4 | — | 9 | 1 | no | — |
| 349 | C22⋊C4 | — | 18 | 1 | no | — |
| 350 | C22⋊C4 | — | 18 | 1 | no | — |
| 351 | C22⋊C4 | — | 18 | 1 | no | — |
| 352 | C22⋊C4 | — | 18 | 1 | no | — |
| 353 | C22⋊C4 | — | 18 | 1 | no | — |
| 354 | C22⋊C4 | — | 18 | 1 | no | — |
| 355 | C42 | — | 9 | 1 | no | — |
| 356 | C42 | — | 18 | 1 | no | — |
| 357 | C42 | — | 18 | 1 | no | — |
| 358 | C22×C3 | — | 3 | 1 | no | — |
| 359 | C22×C3 | — | 3 | 1 | no | — |
| 360 | C22×C3 | #918 | 1 | 1 | yes | characteristic |
| 361 | C2×D3 | — | 6 | 1 | no | — |
| 362 | C2×D3 | — | 6 | 1 | no | — |
| 363 | C2×D3 | — | 6 | 1 | no | — |
| 364 | C2×D3 | — | 12 | 1 | no | — |
| 365 | C2×D3 | — | 12 | 1 | no | — |
| 366 | C2×D3 | — | 12 | 1 | no | — |
| 367 | C3×C4 | — | 2 | 1 | no | — |
| 368 | C3×C4 | — | 2 | 1 | no | — |
| 369 | C3×C4 | — | 3 | 1 | no | — |
| 370 | C3×C4 | — | 6 | 1 | no | — |
| 371 | C3×C4 | — | 6 | 1 | no | — |
| 372 | C3×C4 | C22×S4 | 1 | 1 | yes | characteristic |
| 373 | Dic3 | — | 6 | 1 | no | — |
| 374 | Dic3 | — | 6 | 1 | no | — |
| 375 | Dic3 | — | 6 | 1 | no | — |
| 376 | Dic3 | — | 12 | 1 | no | — |
| 377 | Dic3 | — | 12 | 1 | no | — |
| 378 | Dic3 | — | 12 | 1 | no | — |
| 379 | C9 | — | 4 | 1 | no | Sylow |
| 380 | C23 | — | 9 | 1 | no | — |
| 381 | C23 | — | 18 | 1 | no | — |
| 382 | C23 | D4×D9 | 1 | 1 | yes | characteristic |
| 383 | Q8 | — | 3 | 1 | no | — |
| 384 | Q8 | — | 3 | 1 | no | — |
| 385 | Q8 | — | 6 | 1 | no | — |
| 386 | Q8 | — | 6 | 1 | no | — |
| 387 | Q8 | — | 6 | 1 | no | — |
| 388 | Q8 | — | 6 | 1 | no | — |
| 389 | Q8 | — | 18 | 1 | no | — |
| 390 | Q8 | — | 18 | 1 | no | — |
| 391 | Q8 | — | 36 | 1 | no | — |
| 392 | Q8 | — | 36 | 1 | no | — |
| 393 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 394 | Q8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 395 | D4 | — | 18 | 1 | no | — |
| 396 | D4 | — | 18 | 1 | no | — |
| 397 | D4 | — | 18 | 1 | no | — |
| 398 | D4 | — | 18 | 1 | no | — |
| 399 | D4 | — | 36 | 1 | no | — |
| 400 | D4 | — | 36 | 1 | no | — |
| 401 | D4 | — | 36 | 1 | no | — |
| 402 | D4 | — | 36 | 1 | no | — |
| 403 | C2×C4 | — | 3 | 1 | no | — |
| 404 | C2×C4 | — | 3 | 1 | no | — |
| 405 | C2×C4 | — | 6 | 1 | no | — |
| 406 | C2×C4 | — | 6 | 1 | no | — |
| 407 | C2×C4 | — | 6 | 1 | no | — |
| 408 | C2×C4 | — | 6 | 1 | no | — |
| 409 | C2×C4 | — | 9 | 1 | no | — |
| 410 | C2×C4 | — | 9 | 1 | no | — |
| 411 | C2×C4 | — | 9 | 1 | no | — |
| 412 | C2×C4 | — | 18 | 1 | no | — |
| 413 | C2×C4 | — | 18 | 1 | no | — |
| 414 | C2×C4 | — | 18 | 1 | no | — |
| 415 | C2×C4 | — | 18 | 1 | no | — |
| 416 | C2×C4 | — | 18 | 1 | no | — |
| 417 | C2×C4 | — | 36 | 1 | no | — |
| 418 | C2×C4 | — | 36 | 1 | no | — |
| 419 | C2×C4 | — | 36 | 1 | no | — |
| 420 | C2×C4 | — | 36 | 1 | no | — |
| 421 | C8 | — | 3 | 1 | no | — |
| 422 | C8 | — | 18 | 1 | no | — |
| 423 | C8 | — | 18 | 1 | no | — |
| 424 | C8 | C2×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 425 | C2×C3 | — | 3 | 1 | no | — |
| 426 | C2×C3 | — | 3 | 1 | no | — |
| 427 | C2×C3 | D4×S4 | 1 | 1 | yes | characteristic |
| 428 | D3 | — | 12 | 1 | no | — |
| 429 | D3 | — | 24 | 1 | no | — |
| 430 | C22 | — | 3 | 1 | no | — |
| 431 | C22 | — | 3 | 1 | no | — |
| 432 | C22 | — | 18 | 1 | no | — |
| 433 | C22 | — | 18 | 1 | no | — |
| 434 | C22 | — | 18 | 1 | no | — |
| 435 | C22 | — | 36 | 1 | no | — |
| 436 | C22 | — | 36 | 1 | no | — |
| 437 | C22 | — | 36 | 1 | no | — |
| 438 | C22 | #63480 | 1 | 1 | yes | characteristic, complemented |
| 439 | C4 | — | 2 | 1 | no | — |
| 440 | C4 | — | 2 | 1 | no | — |
| 441 | C4 | — | 3 | 1 | no | — |
| 442 | C4 | — | 6 | 1 | no | — |
| 443 | C4 | — | 6 | 1 | no | — |
| 444 | C4 | — | 18 | 1 | no | — |
| 445 | C4 | — | 18 | 1 | no | — |
| 446 | C4 | — | 18 | 1 | no | — |
| 447 | C4 | — | 36 | 1 | no | — |
| 448 | C4 | — | 36 | 1 | no | — |
| 449 | C4 | — | 36 | 1 | no | — |
| 450 | C4 | C22×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
| 451 | C3 | #85464 | 1 | 1 | yes | characteristic |
| 452 | C2 | — | 3 | 1 | no | — |
| 453 | C2 | — | 3 | 1 | no | — |
| 454 | C2 | — | 36 | 1 | no | — |
| 455 | C2 | — | 72 | 1 | no | — |
| 456 | C2 | D4×(C22⋊C9)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. Q8×(C22⋊C9)⋊C2 | C2 | semidirect |
| 3. Q16×C22⋊C9 | C2 | semidirect |
| 4. #10589519 | C2 | semidirect |
| 5. #10589518 | C2 | semidirect |
| 6. #10589503 | C2 | semidirect |
| 7. #10589502 | C2 | semidirect |
| 113. C22×Q16 | D9 | semidirect |
| 193. C22⋊C9 | #137 | semidirect |
| 325. Q16 | (C22⋊C9)⋊C2 | semidirect |
| 438. C22 | #63480 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593094 | 2 |
| Q8×(C22⋊C9)⋊C2 | 2 |
| Q16×C22⋊C9 | 2 |
| #10589519 | 2 |
| #10589518 | 2 |
| #10589503 | 2 |
| #10589502 | 2 |
| #83888 | 3 |
| #63480 | 4 |