Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1149 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 1149 conjugacy classes of subgroups — too many to draw. Only its 160 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 | #10593141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #10589688 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C9×B(4,𝔽2) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #10588923 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10588712 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #10588422 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #10588420 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #80304 | — | 3 | 1 | no | maximal |
| 9 | C9×H(5,𝔽2) | C22 | 1 | 1 | yes | characteristic |
| 10 | C23×Dic9 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | #63716 | — | 2 | 3 | no | — |
| 12 | #41×D9 | — | 2 | 3 | no | — |
| 13 | #63710 | — | 2 | 3 | no | — |
| 14 | #63710 | C22 | 1 | 3 | yes | — |
| 15 | C2×#3699 | — | 2 | 3 | no | — |
| 16 | C2×#3699 | C22 | 1 | 3 | yes | — |
| 17 | C9×#120 | C22 | 1 | 3 | yes | complemented |
| 18 | #63515 | C22 | 1 | 3 | yes | complemented |
| 19 | #63501 | — | 2 | 3 | no | — |
| 20 | #63497 | C22 | 1 | 3 | yes | complemented |
| 21 | D4×Dic9 | — | 2 | 3 | no | — |
| 22 | #63448 | C22 | 1 | 3 | yes | complemented |
| 23 | #611⋊C4 | — | 2 | 3 | no | — |
| 24 | #63440 | — | 2 | 3 | no | — |
| 25 | #63439 | C22 | 1 | 3 | yes | complemented |
| 26 | C9×#99 | C22 | 1 | 3 | yes | complemented |
| 27 | #63393 | C22 | 1 | 3 | yes | complemented |
| 28 | #63365 | C22 | 1 | 6 | yes | complemented |
| 29 | #5966 | — | 3 | 1 | no | — |
| 30 | #5586 | — | 3 | 3 | no | — |
| 31 | C3×B(4,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 32 | #5243 | — | 3 | 1 | no | — |
| 33 | #5032 | — | 3 | 3 | no | — |
| 34 | #4742 | — | 3 | 3 | no | — |
| 35 | #4740 | — | 3 | 3 | no | — |
| 36 | C24×C9 | C23 | 1 | 1 | yes | characteristic |
| 37 | C9×#41 | — | 2 | 3 | no | — |
| 38 | C2×D4×C9 | — | 2 | 3 | no | — |
| 39 | C2×D4×C9 | — | 2 | 3 | no | — |
| 40 | C2×D4×C9 | C23 | 1 | 3 | yes | — |
| 41 | C2×#611 | — | 2 | 3 | no | — |
| 42 | C2×#611 | — | 2 | 3 | no | — |
| 43 | C2×#611 | — | 2 | 3 | no | — |
| 44 | C2×#611 | D4 | 1 | 3 | yes | complemented |
| 45 | C2×#611 | C23 | 1 | 3 | yes | — |
| 46 | C22×Dic9 | — | 2 | 1 | no | — |
| 47 | C22×Dic9 | — | 2 | 3 | no | — |
| 48 | C22×Dic9 | — | 2 | 3 | no | — |
| 49 | C22×Dic9 | D4 | 1 | 3 | yes | complemented |
| 50 | C22×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 51 | C22×Dic9 | C23 | 1 | 1 | yes | characteristic |
| 52 | #3701 | — | 2 | 1 | no | — |
| 53 | Q8×D9 | — | 2 | 3 | no | — |
| 54 | #3699 | — | 2 | 3 | no | — |
| 55 | #3699 | — | 2 | 6 | no | — |
| 56 | #3699 | — | 2 | 6 | no | — |
| 57 | #3699 | — | 2 | 6 | no | — |
| 58 | #3699 | — | 2 | 6 | no | — |
| 59 | D4×D9 | — | 2 | 3 | no | — |
| 60 | D4×D9 | — | 2 | 6 | no | — |
| 61 | #3697 | — | 2 | 6 | no | — |
| 62 | #3697 | — | 2 | 3 | no | — |
| 63 | C2×C4×D9 | — | 2 | 3 | no | — |
| 64 | C2×C4×D9 | D4 | 1 | 3 | yes | complemented |
| 65 | C2×Dic18 | — | 2 | 3 | no | — |
| 66 | C2×Dic18 | D4 | 1 | 3 | yes | complemented |
| 67 | C9×C22⋊C4 | — | 2 | 3 | no | — |
| 68 | C9×C22⋊C4 | C23 | 1 | 3 | yes | — |
| 69 | #3676 | — | 2 | 3 | no | — |
| 70 | #3676 | — | 2 | 3 | no | — |
| 71 | #3676 | C23 | 1 | 3 | yes | — |
| 72 | (C2×D9)⋊C4 | — | 2 | 3 | no | — |
| 73 | C4⋊Dic9 | — | 2 | 3 | no | — |
| 74 | Dic9⋊C4 | — | 2 | 3 | no | — |
| 75 | Dic9⋊C4 | — | 2 | 3 | no | — |
| 76 | C4×Dic9 | — | 2 | 3 | no | — |
| 77 | #3025 | — | 9 | 1 | no | Sylow |
| 78 | C3×H(5,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 79 | C23×Dic3 | — | 3 | 1 | no | — |
| 80 | #1010 | — | 6 | 3 | no | — |
| 81 | D3×#41 | — | 6 | 3 | no | — |
| 82 | #1004 | — | 3 | 3 | no | — |
| 83 | #1004 | — | 6 | 3 | no | — |
| 84 | C2×#237 | — | 3 | 3 | no | — |
| 85 | C2×#237 | — | 6 | 3 | no | — |
| 86 | C3×#120 | C2×D3 | 1 | 3 | yes | — |
| 87 | #953 | — | 3 | 3 | no | — |
| 88 | #939 | — | 6 | 3 | no | — |
| 89 | #935 | — | 3 | 3 | no | — |
| 90 | D4×Dic3 | — | 6 | 3 | no | — |
| 91 | #886 | — | 3 | 3 | no | — |
| 92 | #67⋊C4 | — | 6 | 3 | no | — |
| 93 | #878 | — | 6 | 3 | no | — |
| 94 | #877 | — | 3 | 3 | no | — |
| 95 | C3×#99 | C2×D3 | 1 | 3 | yes | — |
| 96 | #834 | — | 3 | 3 | no | — |
| 97 | #806 | — | 3 | 6 | no | — |
| 98 | C23×C9 | — | 2 | 1 | no | — |
| 99 | C23×C9 | — | 2 | 3 | no | — |
| 100 | C23×C9 | — | 4 | 2 | no | — |
| 101 | C23×C9 | C2×D4 | 1 | 3 | yes | — |
| 102 | C23×C9 | C24 | 1 | 1 | yes | characteristic |
| 103 | C22×D9 | — | 2 | 3 | no | — |
| 104 | C22×D9 | C2×D4 | 1 | 3 | yes | — |
| 105 | Q8×C9 | — | 2 | 1 | no | — |
| 106 | D4×C9 | — | 2 | 3 | no | — |
| 107 | D4×C9 | — | 2 | 6 | no | — |
| 108 | D4×C9 | — | 4 | 6 | no | — |
| 109 | C2×C4×C9 | — | 2 | 3 | no | — |
| 110 | C2×C4×C9 | — | 2 | 3 | no | — |
| 111 | C2×C4×C9 | C2×D4 | 1 | 3 | yes | — |
| 112 | #611 | — | 2 | 6 | no | — |
| 113 | #611 | — | 2 | 6 | no | — |
| 114 | #611 | — | 2 | 6 | no | — |
| 115 | #611 | — | 4 | 6 | no | — |
| 116 | C2×Dic9 | — | 2 | 3 | no | — |
| 117 | C2×Dic9 | — | 2 | 3 | no | — |
| 118 | C2×Dic9 | — | 2 | 3 | no | — |
| 119 | C2×Dic9 | — | 2 | 3 | no | — |
| 120 | C2×Dic9 | — | 2 | 3 | no | — |
| 121 | C2×Dic9 | — | 4 | 3 | no | — |
| 122 | C2×Dic9 | — | 4 | 1 | no | — |
| 123 | C2×Dic9 | C2×D4 | 1 | 3 | yes | — |
| 124 | C2×Dic9 | C2×D4 | 1 | 3 | yes | — |
| 125 | C2×Dic9 | C2×D4 | 1 | 3 | yes | — |
| 126 | D36 | — | 2 | 3 | no | — |
| 127 | C4×D9 | — | 2 | 6 | no | — |
| 128 | C4×D9 | — | 2 | 3 | no | — |
| 129 | C4×D9 | — | 2 | 3 | no | — |
| 130 | Dic18 | — | 2 | 3 | no | — |
| 131 | Dic18 | — | 2 | 6 | no | — |
| 132 | #585 | — | 9 | 1 | no | — |
| 133 | #525 | — | 9 | 3 | no | — |
| 134 | #458 | — | 9 | 1 | no | — |
| 135 | #458 | — | 9 | 3 | no | — |
| 136 | B(4,𝔽2) | — | 9 | 3 | no | — |
| 137 | B(4,𝔽2) | D9 | 1 | 1 | yes | characteristic, complemented |
| 138 | #410 | — | 9 | 3 | no | — |
| 139 | C24×C3 | C22×D3 | 1 | 1 | yes | characteristic |
| 140 | C3×#41 | — | 2 | 3 | no | — |
| 141 | C2×C3×D4 | — | 2 | 3 | no | — |
| 142 | C2×C3×D4 | — | 2 | 3 | no | — |
| 143 | C2×C3×D4 | C22×D3 | 1 | 3 | yes | — |
| 144 | C2×#67 | — | 3 | 3 | no | — |
| 145 | C2×#67 | — | 3 | 3 | no | — |
| 146 | C2×#67 | — | 6 | 3 | no | — |
| 147 | C2×#67 | — | 6 | 3 | no | — |
| 148 | C2×#67 | — | 6 | 3 | no | — |
| 149 | C22×Dic3 | — | 3 | 1 | no | — |
| 150 | C22×Dic3 | — | 3 | 3 | no | — |
| 151 | C22×Dic3 | — | 3 | 1 | no | — |
| 152 | C22×Dic3 | — | 6 | 3 | no | — |
| 153 | C22×Dic3 | — | 6 | 3 | no | — |
| 154 | C22×Dic3 | — | 6 | 1 | no | — |
| 155 | #239 | — | 6 | 1 | no | — |
| 156 | D3×Q8 | — | 6 | 3 | no | — |
| 157 | #237 | — | 6 | 6 | no | — |
| 158 | #237 | — | 6 | 6 | no | — |
| 159 | #237 | — | 6 | 6 | no | — |
| 160 | #237 | — | 6 | 3 | no | — |
| 161 | #237 | — | 6 | 6 | no | — |
| 162 | D3×D4 | — | 6 | 6 | no | — |
| 163 | D3×D4 | — | 6 | 3 | no | — |
| 164 | #235 | — | 6 | 6 | no | — |
| 165 | #235 | — | 6 | 3 | no | — |
| 166 | C2×C4×D3 | — | 3 | 3 | no | — |
| 167 | C2×C4×D3 | — | 6 | 3 | no | — |
| 168 | C2×Dic6 | — | 3 | 3 | no | — |
| 169 | C2×Dic6 | — | 6 | 3 | no | — |
| 170 | C3×C22⋊C4 | — | 2 | 3 | no | — |
| 171 | C3×C22⋊C4 | C22×D3 | 1 | 3 | yes | — |
| 172 | #217 | — | 3 | 3 | no | — |
| 173 | #217 | — | 6 | 3 | no | — |
| 174 | #217 | — | 6 | 3 | no | — |
| 175 | (C2×D3)⋊C4 | — | 6 | 3 | no | — |
| 176 | C4⋊Dic3 | — | 6 | 3 | no | — |
| 177 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 178 | Dic3⋊C4 | — | 6 | 3 | no | — |
| 179 | C4×Dic3 | — | 6 | 3 | no | — |
| 180 | C22×C9 | — | 2 | 6 | no | — |
| 181 | C22×C9 | — | 2 | 3 | no | — |
| 182 | C22×C9 | — | 4 | 1 | no | — |
| 183 | C22×C9 | — | 4 | 3 | no | — |
| 184 | C22×C9 | — | 4 | 3 | no | — |
| 185 | C22×C9 | — | 4 | 1 | no | — |
| 186 | C22×C9 | — | 8 | 1 | no | — |
| 187 | C22×C9 | C22×D4 | 1 | 3 | yes | — |
| 188 | C2×D9 | — | 2 | 3 | no | — |
| 189 | C2×D9 | — | 4 | 3 | no | — |
| 190 | C2×D9 | — | 8 | 3 | no | — |
| 191 | C4×C9 | — | 2 | 3 | no | — |
| 192 | C4×C9 | — | 4 | 3 | no | — |
| 193 | Dic9 | — | 2 | 3 | no | — |
| 194 | Dic9 | — | 4 | 3 | no | — |
| 195 | Dic9 | — | 4 | 1 | no | — |
| 196 | Dic9 | #120 | 1 | 3 | yes | — |
| 197 | Dic9 | #120 | 1 | 1 | yes | characteristic |
| 198 | 2−1+4 | — | 18 | 3 | no | — |
| 199 | H(5,𝔽2) | — | 9 | 3 | no | — |
| 200 | H(5,𝔽2) | — | 18 | 3 | no | — |
| 201 | H(5,𝔽2) | C2×D9 | 1 | 1 | yes | characteristic |
| 202 | C2×#41 | — | 9 | 3 | no | — |
| 203 | C2×#41 | — | 18 | 3 | no | — |
| 204 | C2×#41 | — | 18 | 3 | no | — |
| 205 | C23×C4 | — | 9 | 1 | no | — |
| 206 | #123 | — | 9 | 3 | no | — |
| 207 | #123 | — | 9 | 3 | no | — |
| 208 | C22⋊Q8 | — | 18 | 3 | no | — |
| 209 | #121 | — | 18 | 3 | no | — |
| 210 | #120 | — | 9 | 3 | no | — |
| 211 | #120 | C2×D9 | 1 | 3 | yes | complemented |
| 212 | C4×D4 | — | 18 | 3 | no | — |
| 213 | C4×D4 | — | 18 | 3 | no | — |
| 214 | #117 | — | 9 | 3 | no | — |
| 215 | #99 | — | 9 | 3 | no | — |
| 216 | #99 | — | 9 | 6 | no | — |
| 217 | #99 | C2×D9 | 1 | 3 | yes | complemented |
| 218 | C23×C3 | — | 2 | 1 | no | — |
| 219 | C23×C3 | — | 2 | 3 | no | — |
| 220 | C23×C3 | — | 4 | 2 | no | — |
| 221 | C23×C3 | D3×D4 | 1 | 3 | yes | — |
| 222 | C23×C3 | C23×D3 | 1 | 1 | yes | characteristic |
| 223 | C22×D3 | — | 3 | 3 | no | — |
| 224 | C22×D3 | — | 6 | 3 | no | — |
| 225 | C3×Q8 | — | 2 | 1 | no | — |
| 226 | C3×D4 | — | 2 | 3 | no | — |
| 227 | C3×D4 | — | 2 | 6 | no | — |
| 228 | C3×D4 | — | 4 | 6 | no | — |
| 229 | C2×C3×C4 | — | 2 | 3 | no | — |
| 230 | C2×C3×C4 | — | 2 | 3 | no | — |
| 231 | C2×C3×C4 | D3×D4 | 1 | 3 | yes | — |
| 232 | #67 | — | 6 | 6 | no | — |
| 233 | #67 | — | 6 | 6 | no | — |
| 234 | #67 | — | 6 | 6 | no | — |
| 235 | #67 | — | 12 | 6 | no | — |
| 236 | C2×Dic3 | — | 3 | 3 | no | — |
| 237 | C2×Dic3 | — | 3 | 3 | no | — |
| 238 | C2×Dic3 | — | 3 | 3 | no | — |
| 239 | C2×Dic3 | — | 6 | 3 | no | — |
| 240 | C2×Dic3 | — | 6 | 3 | no | — |
| 241 | C2×Dic3 | — | 6 | 3 | no | — |
| 242 | C2×Dic3 | — | 6 | 3 | no | — |
| 243 | C2×Dic3 | — | 6 | 3 | no | — |
| 244 | C2×Dic3 | — | 12 | 3 | no | — |
| 245 | C2×Dic3 | — | 12 | 1 | no | — |
| 246 | D12 | — | 6 | 3 | no | — |
| 247 | C4×D3 | — | 6 | 3 | no | — |
| 248 | C4×D3 | — | 6 | 3 | no | — |
| 249 | C4×D3 | — | 6 | 6 | no | — |
| 250 | Dic6 | — | 6 | 6 | no | — |
| 251 | Dic6 | — | 6 | 3 | no | — |
| 252 | C2×C9 | — | 2 | 3 | no | — |
| 253 | C2×C9 | — | 4 | 3 | no | — |
| 254 | C2×C9 | — | 4 | 2 | no | — |
| 255 | C2×C9 | C2×#120 | 1 | 1 | yes | characteristic |
| 256 | D9 | — | 4 | 3 | no | — |
| 257 | C24 | C22×D9 | 1 | 1 | yes | characteristic |
| 258 | #41 | — | 2 | 3 | no | — |
| 259 | #41 | — | 18 | 6 | no | — |
| 260 | #41 | — | 18 | 6 | no | — |
| 261 | #41 | — | 18 | 6 | no | — |
| 262 | #41 | — | 18 | 6 | no | — |
| 263 | #41 | — | 18 | 3 | no | — |
| 264 | #41 | — | 18 | 6 | no | — |
| 265 | #41 | — | 18 | 1 | no | — |
| 266 | #41 | — | 18 | 3 | no | — |
| 267 | C2×Q8 | — | 9 | 3 | no | — |
| 268 | C2×Q8 | — | 18 | 3 | no | — |
| 269 | C2×Q8 | — | 18 | 3 | no | — |
| 270 | C2×D4 | — | 2 | 3 | no | — |
| 271 | C2×D4 | — | 2 | 3 | no | — |
| 272 | C2×D4 | — | 9 | 3 | no | — |
| 273 | C2×D4 | — | 9 | 3 | no | — |
| 274 | C2×D4 | — | 18 | 6 | no | — |
| 275 | C2×D4 | — | 18 | 3 | no | — |
| 276 | C2×D4 | — | 18 | 3 | no | — |
| 277 | C2×D4 | — | 18 | 3 | no | — |
| 278 | C2×D4 | — | 18 | 3 | no | — |
| 279 | C2×D4 | C22×D9 | 1 | 3 | yes | — |
| 280 | C22×C4 | — | 9 | 1 | no | — |
| 281 | C22×C4 | — | 9 | 3 | no | — |
| 282 | C22×C4 | — | 9 | 3 | no | — |
| 283 | C22×C4 | — | 9 | 1 | no | — |
| 284 | C22×C4 | — | 18 | 3 | no | — |
| 285 | C22×C4 | — | 18 | 3 | no | — |
| 286 | C22×C4 | — | 18 | 3 | no | — |
| 287 | C22×C4 | — | 18 | 1 | no | — |
| 288 | C4⋊C4 | — | 18 | 3 | no | — |
| 289 | C4⋊C4 | — | 18 | 3 | no | — |
| 290 | C4⋊C4 | — | 18 | 3 | no | — |
| 291 | C22⋊C4 | — | 2 | 3 | no | — |
| 292 | C22⋊C4 | — | 9 | 3 | no | — |
| 293 | C22⋊C4 | — | 18 | 3 | no | — |
| 294 | C22⋊C4 | — | 18 | 3 | no | — |
| 295 | C22⋊C4 | — | 18 | 3 | no | — |
| 296 | C22⋊C4 | C22×D9 | 1 | 3 | yes | — |
| 297 | C42 | — | 18 | 3 | no | — |
| 298 | C22×C3 | — | 2 | 6 | no | — |
| 299 | C22×C3 | — | 2 | 3 | no | — |
| 300 | C22×C3 | — | 4 | 1 | no | — |
| 301 | C22×C3 | — | 4 | 3 | no | — |
| 302 | C22×C3 | — | 4 | 3 | no | — |
| 303 | C22×C3 | — | 4 | 1 | no | — |
| 304 | C22×C3 | — | 8 | 1 | no | — |
| 305 | C22×C3 | C2×D3×D4 | 1 | 3 | yes | — |
| 306 | C2×D3 | — | 6 | 3 | no | — |
| 307 | C2×D3 | — | 12 | 3 | no | — |
| 308 | C2×D3 | — | 24 | 3 | no | — |
| 309 | C3×C4 | — | 2 | 3 | no | — |
| 310 | C3×C4 | — | 4 | 3 | no | — |
| 311 | Dic3 | — | 3 | 3 | no | — |
| 312 | Dic3 | — | 3 | 1 | no | — |
| 313 | Dic3 | — | 6 | 3 | no | — |
| 314 | Dic3 | — | 12 | 3 | no | — |
| 315 | Dic3 | — | 12 | 1 | no | — |
| 316 | C9 | #3025 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 317 | C23 | — | 2 | 1 | no | — |
| 318 | C23 | — | 2 | 3 | no | — |
| 319 | C23 | — | 4 | 2 | no | — |
| 320 | C23 | — | 9 | 3 | no | — |
| 321 | C23 | — | 18 | 3 | no | — |
| 322 | C23 | D4×D9 | 1 | 3 | yes | — |
| 323 | C23 | C23×D9 | 1 | 1 | yes | characteristic |
| 324 | Q8 | — | 2 | 1 | no | — |
| 325 | Q8 | — | 18 | 6 | no | — |
| 326 | Q8 | — | 18 | 3 | no | — |
| 327 | D4 | — | 2 | 3 | no | — |
| 328 | D4 | — | 2 | 6 | no | — |
| 329 | D4 | — | 4 | 6 | no | — |
| 330 | D4 | — | 18 | 3 | no | — |
| 331 | D4 | — | 18 | 6 | no | — |
| 332 | D4 | — | 18 | 6 | no | — |
| 333 | D4 | — | 18 | 6 | no | — |
| 334 | D4 | — | 36 | 6 | no | — |
| 335 | C2×C4 | — | 2 | 3 | no | — |
| 336 | C2×C4 | — | 2 | 3 | no | — |
| 337 | C2×C4 | — | 9 | 3 | no | — |
| 338 | C2×C4 | — | 9 | 3 | no | — |
| 339 | C2×C4 | — | 9 | 3 | no | — |
| 340 | C2×C4 | — | 18 | 3 | no | — |
| 341 | C2×C4 | — | 18 | 3 | no | — |
| 342 | C2×C4 | — | 18 | 6 | no | — |
| 343 | C2×C4 | — | 18 | 3 | no | — |
| 344 | C2×C4 | — | 18 | 3 | no | — |
| 345 | C2×C4 | — | 18 | 3 | no | — |
| 346 | C2×C4 | — | 18 | 3 | no | — |
| 347 | C2×C4 | — | 18 | 3 | no | — |
| 348 | C2×C4 | — | 36 | 1 | no | — |
| 349 | C2×C4 | — | 36 | 3 | no | — |
| 350 | C2×C4 | D4×D9 | 1 | 3 | yes | — |
| 351 | C2×C3 | — | 2 | 3 | no | — |
| 352 | C2×C3 | — | 4 | 3 | no | — |
| 353 | C2×C3 | — | 4 | 2 | no | — |
| 354 | C2×C3 | D3×#120 | 1 | 1 | yes | characteristic |
| 355 | D3 | — | 12 | 3 | no | — |
| 356 | C22 | — | 2 | 6 | no | — |
| 357 | C22 | — | 2 | 3 | no | — |
| 358 | C22 | — | 4 | 1 | no | — |
| 359 | C22 | — | 4 | 3 | no | — |
| 360 | C22 | — | 4 | 3 | no | — |
| 361 | C22 | — | 4 | 1 | no | — |
| 362 | C22 | — | 8 | 1 | no | — |
| 363 | C22 | — | 18 | 3 | no | — |
| 364 | C22 | — | 36 | 3 | no | — |
| 365 | C22 | — | 72 | 3 | no | — |
| 366 | C22 | C2×D4×D9 | 1 | 3 | yes | — |
| 367 | C4 | — | 2 | 3 | no | — |
| 368 | C4 | — | 4 | 3 | no | — |
| 369 | C4 | — | 9 | 1 | no | — |
| 370 | C4 | — | 9 | 3 | no | — |
| 371 | C4 | — | 18 | 3 | no | — |
| 372 | C4 | — | 36 | 3 | no | — |
| 373 | C4 | — | 36 | 1 | no | — |
| 374 | C3 | #80304 | 1 | 1 | yes | characteristic |
| 375 | C2 | — | 2 | 3 | no | — |
| 376 | C2 | — | 4 | 2 | no | — |
| 377 | C2 | — | 4 | 3 | no | — |
| 378 | C2 | — | 36 | 3 | no | — |
| 379 | C2 | D9×#120 | 1 | 1 | yes | characteristic |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D9×#120 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini | C23×C3 | C23×D3 |
| Fitting | C9×B(4,𝔽2) | C2 |
| socle | C2×C3 | D3×#120 |
| hypercenter | B(4,𝔽2) | D9 |
| hypocenter | C9 | #3025 |
| LCS | G ▷ C23×C9 ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ B(4,𝔽2) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10593141 | C2 | semidirect |
| 2. #10589688 | C2 | semidirect |
| 3. C9×B(4,𝔽2) | C2 | semidirect |
| 4. #10588923 | C2 | semidirect |
| 5. #10588712 | C2 | semidirect |
| 6. #10588422 | C2 | semidirect |
| 7. #10588420 | C2 | semidirect |
| 10. C23×Dic9 | C22 | semidirect |
| 17. C9×#120 | C22 | semidirect |
| 18. #63515 | C22 | semidirect |
| 20. #63497 | C22 | semidirect |
| 22. #63448 | C22 | semidirect |
| 25. #63439 | C22 | semidirect |
| 26. C9×#99 | C22 | semidirect |
| 27. #63393 | C22 | semidirect |
| 28. #63365 | C22 | semidirect |
| 44. C2×#611 | D4 | semidirect |
| 49. C22×Dic9 | D4 | semidirect |
| 64. C2×C4×D9 | D4 | semidirect |
| 66. C2×Dic18 | D4 | semidirect |
| 137. B(4,𝔽2) | D9 | semidirect |
| 211. #120 | C2×D9 | semidirect |
| 217. #99 | C2×D9 | semidirect |
| 316. C9 | #3025 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593141 | 2 |
| #10589688 | 2 |
| C9×B(4,𝔽2) | 2 |
| #10588923 | 2 |
| #10588712 | 2 |
| #10588422 | 2 |
| #10588420 | 2 |
| #80304 | 3 |