Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
930 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 930 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #22626253 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | #22626240 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22626168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22625813 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#17989389 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #17989643 | C22 | 1 | 2 | yes | complemented |
| 7 | #17989597 | C22 | 1 | 2 | yes | complemented |
| 8 | #17989566 | — | 2 | 1 | no | — |
| 9 | #17989504 | — | 2 | 4 | no | — |
| 10 | #17989499 | — | 2 | 4 | no | — |
| 11 | #17989484 | — | 2 | 1 | no | — |
| 12 | #17989483 | — | 2 | 1 | no | — |
| 13 | #17989455 | — | 2 | 1 | no | — |
| 14 | C2×#14556637 | — | 2 | 1 | no | — |
| 15 | #17989389 | — | 2 | 4 | no | — |
| 16 | #17989389 | — | 2 | 4 | no | — |
| 17 | C2×#14556618 | — | 2 | 1 | no | — |
| 18 | C2×#14556618 | — | 2 | 1 | no | — |
| 19 | C2×#14556616 | — | 2 | 1 | no | — |
| 20 | C2×#14556614 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#14556614 | C22 | 1 | 1 | yes | characteristic |
| 22 | C22×D584 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×D8×D73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C2×D8×D73 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#14556597 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#135×C73 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | #14556670 | — | 2 | 2 | no | — |
| 28 | #14556666 | — | 2 | 2 | no | — |
| 29 | #14556665 | — | 2 | 2 | no | — |
| 30 | #14556664 | — | 2 | 2 | no | — |
| 31 | #14556660 | — | 2 | 2 | no | — |
| 32 | #14556659 | — | 2 | 2 | no | — |
| 33 | #14556650 | — | 4 | 1 | no | — |
| 34 | #14556649 | — | 4 | 1 | no | — |
| 35 | #14556637 | — | 2 | 8 | no | — |
| 36 | #14556637 | — | 4 | 4 | no | — |
| 37 | C2×#11924029 | — | 2 | 1 | no | — |
| 38 | C2×#11924029 | — | 2 | 1 | no | — |
| 39 | C2×#11924028 | — | 4 | 1 | no | — |
| 40 | C2×#11924028 | D4 | 1 | 1 | yes | characteristic |
| 41 | C22×D292 | — | 2 | 1 | no | — |
| 42 | C22×D292 | — | 4 | 1 | no | — |
| 43 | C2×D4×D73 | — | 2 | 1 | no | — |
| 44 | C2×D4×D73 | — | 2 | 1 | no | — |
| 45 | C2×D4×D73 | — | 4 | 1 | no | — |
| 46 | C2×D4×D73 | — | 4 | 1 | no | — |
| 47 | #14556618 | — | 2 | 8 | no | — |
| 48 | #14556618 | — | 2 | 8 | no | — |
| 49 | #14556616 | — | 2 | 8 | no | — |
| 50 | #14556614 | — | 2 | 2 | no | — |
| 51 | #14556614 | — | 2 | 2 | no | — |
| 52 | #14556614 | — | 2 | 2 | no | — |
| 53 | #14556614 | D4 | 1 | 4 | yes | — |
| 54 | C2×#11924015 | — | 2 | 1 | no | — |
| 55 | C2×#11924015 | — | 2 | 1 | no | — |
| 56 | C2×D584 | — | 2 | 2 | no | — |
| 57 | C2×D584 | — | 2 | 2 | no | — |
| 58 | C2×D584 | — | 2 | 1 | no | — |
| 59 | C2×D584 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×D584 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | C2×#11924013 | — | 2 | 1 | no | — |
| 62 | C2×#11924013 | — | 2 | 1 | no | — |
| 63 | D8×D73 | — | 2 | 2 | no | — |
| 64 | D8×D73 | — | 2 | 2 | no | — |
| 65 | D8×D73 | — | 2 | 2 | no | — |
| 66 | D8×D73 | D4 | 1 | 4 | yes | — |
| 67 | #14556597 | — | 2 | 2 | no | — |
| 68 | #14556597 | — | 2 | 2 | no | — |
| 69 | C2×#11924012 | D4 | 1 | 1 | yes | characteristic |
| 70 | C2×#11924011 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×#11924011 | D4 | 1 | 1 | yes | characteristic |
| 72 | C2×C8×D73 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×D73 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#41×C73 | — | 2 | 1 | no | — |
| 75 | #135×C73 | — | 2 | 2 | no | — |
| 76 | #135×C73 | — | 2 | 2 | no | — |
| 77 | C2×Q16×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C2×SD16×C73 | — | 2 | 1 | no | — |
| 79 | C2×D8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C22×C8×C73 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | C4⋊#64408 | — | 4 | 2 | no | — |
| 82 | C22⋊#64408 | — | 4 | 2 | no | — |
| 83 | C4×#64408 | — | 4 | 2 | no | — |
| 84 | #11924031 | — | 4 | 2 | no | — |
| 85 | C23×D73 | — | 4 | 1 | no | — |
| 86 | C23×D73 | — | 4 | 1 | no | — |
| 87 | C23×D73 | — | 4 | 1 | no | — |
| 88 | #11924029 | — | 2 | 4 | no | — |
| 89 | #11924029 | — | 2 | 4 | no | — |
| 90 | #11924029 | — | 4 | 2 | no | — |
| 91 | #11924029 | — | 4 | 2 | no | — |
| 92 | #11924028 | — | 2 | 2 | no | — |
| 93 | #11924028 | — | 2 | 2 | no | — |
| 94 | #11924028 | — | 4 | 8 | no | — |
| 95 | C2×Dic146 | SD16 | 1 | 1 | yes | characteristic |
| 96 | C2×D292 | — | 2 | 4 | no | — |
| 97 | C2×D292 | — | 2 | 1 | no | — |
| 98 | C2×D292 | — | 2 | 1 | no | — |
| 99 | C2×D292 | — | 4 | 8 | no | — |
| 100 | C2×D292 | — | 4 | 2 | no | — |
| 101 | C2×D292 | — | 4 | 1 | no | — |
| 102 | C2×D292 | — | 4 | 1 | no | — |
| 103 | C2×D292 | — | 4 | 1 | no | — |
| 104 | C2×D292 | D8 | 1 | 1 | yes | characteristic |
| 105 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 106 | C2×C22⋊D73 | — | 4 | 1 | no | — |
| 107 | C2×C22⋊D73 | D8 | 1 | 1 | yes | characteristic |
| 108 | C2×C22⋊D73 | SD16 | 1 | 1 | yes | characteristic |
| 109 | D4×D73 | — | 2 | 4 | no | — |
| 110 | D4×D73 | — | 2 | 4 | no | — |
| 111 | D4×D73 | — | 4 | 2 | no | — |
| 112 | D4×D73 | — | 4 | 8 | no | — |
| 113 | D4×D73 | — | 4 | 8 | no | — |
| 114 | D4×D73 | — | 4 | 2 | no | — |
| 115 | C2×C4×D73 | — | 4 | 1 | no | — |
| 116 | C2×C4×D73 | — | 4 | 1 | no | — |
| 117 | C2×C4×D73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×D73 | C2×D4 | 1 | 1 | yes | characteristic |
| 119 | #11924015 | — | 2 | 4 | no | — |
| 120 | #11924015 | — | 2 | 4 | no | — |
| 121 | D584 | — | 2 | 4 | no | — |
| 122 | D584 | — | 2 | 1 | no | — |
| 123 | D584 | — | 2 | 1 | no | — |
| 124 | D584 | C22⋊C4 | 1 | 2 | yes | — |
| 125 | D584 | C22⋊C4 | 1 | 2 | yes | — |
| 126 | #11924013 | — | 2 | 4 | no | — |
| 127 | #11924013 | — | 2 | 4 | no | — |
| 128 | #11924012 | — | 2 | 2 | no | — |
| 129 | #11924011 | — | 2 | 2 | no | — |
| 130 | #11924011 | — | 2 | 2 | no | — |
| 131 | C2×#10596831 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 132 | C2×#10596831 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C8×D73 | — | 2 | 1 | no | — |
| 134 | C8×D73 | — | 2 | 1 | no | — |
| 135 | C8×D73 | C2×D4 | 1 | 2 | yes | — |
| 136 | C8×D73 | C2×D4 | 1 | 2 | yes | — |
| 137 | #41×C73 | — | 2 | 4 | no | — |
| 138 | #41×C73 | — | 4 | 2 | no | — |
| 139 | C2×Q8×C73 | — | 2 | 1 | no | — |
| 140 | C2×D4×C73 | — | 2 | 1 | no | — |
| 141 | C2×D4×C73 | — | 4 | 1 | no | — |
| 142 | C22×C4×C73 | — | 4 | 1 | no | — |
| 143 | C22×C4×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 144 | Q16×C73 | — | 2 | 1 | no | — |
| 145 | Q16×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 146 | SD16×C73 | — | 2 | 4 | no | — |
| 147 | D8×C73 | — | 2 | 1 | no | — |
| 148 | D8×C73 | C22⋊C4 | 1 | 2 | yes | — |
| 149 | C2×C8×C73 | — | 2 | 1 | no | — |
| 150 | C2×C8×C73 | — | 2 | 1 | no | — |
| 151 | C2×C8×C73 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 152 | C2×C8×C73 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C23×C73 | — | 4 | 1 | no | — |
| 154 | C23×C73 | #102 | 1 | 1 | yes | characteristic |
| 155 | C22×D73 | — | 4 | 4 | no | — |
| 156 | C22×D73 | — | 4 | 1 | no | — |
| 157 | C22×D73 | — | 4 | 1 | no | — |
| 158 | C22×D73 | — | 4 | 4 | no | — |
| 159 | C22×D73 | — | 4 | 4 | no | — |
| 160 | C22×D73 | — | 16 | 2 | no | — |
| 161 | C22×D73 | — | 16 | 2 | no | — |
| 162 | C22×D73 | — | 16 | 2 | no | — |
| 163 | C22×D73 | #102 | 1 | 1 | yes | characteristic |
| 164 | C22×D73 | C2×D8 | 1 | 1 | yes | characteristic |
| 165 | C2×#64408 | — | 8 | 2 | no | — |
| 166 | Q8×C73 | — | 2 | 2 | no | — |
| 167 | Q8×C73 | — | 4 | 1 | no | — |
| 168 | D4×C73 | — | 2 | 2 | no | — |
| 169 | D4×C73 | — | 4 | 4 | no | — |
| 170 | D4×C73 | — | 4 | 1 | no | — |
| 171 | C2×C4×C73 | — | 2 | 1 | no | — |
| 172 | C2×C4×C73 | — | 2 | 1 | no | — |
| 173 | C2×C4×C73 | — | 4 | 4 | no | — |
| 174 | C2×C4×C73 | — | 4 | 1 | no | — |
| 175 | C2×C4×C73 | #102 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 177 | C22⋊D73 | — | 2 | 2 | no | — |
| 178 | C22⋊D73 | — | 2 | 2 | no | — |
| 179 | C22⋊D73 | — | 4 | 4 | no | — |
| 180 | C22⋊D73 | — | 4 | 4 | no | — |
| 181 | C2×Dic73 | #102 | 1 | 1 | yes | characteristic |
| 182 | C2×Dic73 | C2×SD16 | 1 | 1 | yes | characteristic |
| 183 | D292 | — | 2 | 2 | no | — |
| 184 | D292 | — | 2 | 2 | no | — |
| 185 | D292 | — | 2 | 2 | no | — |
| 186 | D292 | — | 4 | 4 | no | — |
| 187 | D292 | — | 4 | 4 | no | — |
| 188 | D292 | — | 4 | 4 | no | — |
| 189 | D292 | — | 4 | 1 | no | — |
| 190 | D292 | — | 4 | 1 | no | — |
| 191 | C4×D73 | — | 2 | 1 | no | — |
| 192 | C4×D73 | — | 2 | 1 | no | — |
| 193 | C4×D73 | — | 4 | 4 | no | — |
| 194 | C4×D73 | — | 4 | 4 | no | — |
| 195 | C4×D73 | #120 | 1 | 2 | yes | — |
| 196 | C4×D73 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 197 | Dic146 | — | 2 | 2 | no | — |
| 198 | C8×C73 | — | 2 | 1 | no | — |
| 199 | C8×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 200 | C8×C73 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | #10596831 | — | 2 | 1 | no | — |
| 202 | #10596831 | #120 | 1 | 2 | yes | — |
| 203 | C22×C73 | — | 2 | 1 | no | — |
| 204 | C22×C73 | — | 4 | 1 | no | — |
| 205 | C22×C73 | — | 4 | 2 | no | — |
| 206 | C22×C73 | — | 8 | 2 | no | — |
| 207 | C22×C73 | C2×#102 | 1 | 1 | yes | characteristic |
| 208 | C2×D73 | — | 2 | 1 | no | — |
| 209 | C2×D73 | — | 4 | 1 | no | — |
| 210 | C2×D73 | — | 4 | 1 | no | — |
| 211 | C2×D73 | — | 4 | 2 | no | — |
| 212 | C2×D73 | — | 4 | 2 | no | — |
| 213 | C2×D73 | — | 8 | 2 | no | — |
| 214 | C2×D73 | — | 8 | 2 | no | — |
| 215 | C2×D73 | — | 16 | 4 | no | — |
| 216 | C2×D73 | — | 16 | 4 | no | — |
| 217 | C2×D73 | — | 16 | 4 | no | — |
| 218 | C2×D73 | #447 | 1 | 2 | yes | — |
| 219 | #64408 | — | 16 | 2 | no | — |
| 220 | C4×C73 | — | 2 | 1 | no | — |
| 221 | C4×C73 | — | 4 | 2 | no | — |
| 222 | C4×C73 | #379 | 1 | 1 | yes | characteristic |
| 223 | C4×C73 | #418 | 1 | 1 | yes | characteristic |
| 224 | Dic73 | — | 2 | 1 | no | — |
| 225 | Dic73 | #450 | 1 | 2 | yes | — |
| 226 | #12741 | — | 73 | 1 | no | maximal, Sylow |
| 227 | C2×C73 | — | 2 | 1 | no | — |
| 228 | C2×C73 | — | 4 | 1 | no | — |
| 229 | C2×C73 | — | 8 | 2 | no | — |
| 230 | C2×C73 | #1786 | 1 | 1 | yes | characteristic |
| 231 | D73 | — | 2 | 2 | no | — |
| 232 | D73 | — | 4 | 1 | no | — |
| 233 | D73 | — | 8 | 2 | no | — |
| 234 | D73 | — | 8 | 2 | no | — |
| 235 | C2×#576 | — | 73 | 1 | no | — |
| 236 | #2145 | — | 73 | 2 | no | — |
| 237 | #2140 | — | 73 | 2 | no | — |
| 238 | #2115 | — | 73 | 1 | no | — |
| 239 | #1812 | — | 73 | 1 | no | — |
| 240 | C73 | #12741 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 241 | C2×H(5,𝔽2) | — | 146 | 1 | no | — |
| 242 | #576 | — | 146 | 4 | no | — |
| 243 | #576 | — | 146 | 4 | no | — |
| 244 | C2×AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 245 | C2×AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 246 | C2×AGL(1,ℤ/8) | — | 146 | 1 | no | — |
| 247 | C2×#135 | — | 73 | 1 | no | — |
| 248 | C2×#135 | — | 73 | 1 | no | — |
| 249 | C2×#135 | #64408 | 1 | 1 | yes | characteristic, complemented |
| 250 | C22×D8 | — | 73 | 1 | no | — |
| 251 | C22×D8 | — | 73 | 1 | no | — |
| 252 | C22×D8 | — | 73 | 1 | no | — |
| 253 | C2×#131 | — | 73 | 1 | no | — |
| 254 | C2×M32 | — | 73 | 2 | no | — |
| 255 | #427 | — | 73 | 2 | no | — |
| 256 | #410 | — | 146 | 1 | no | — |
| 257 | #360 | — | 146 | 4 | no | — |
| 258 | #357 | — | 146 | 4 | no | — |
| 259 | #349 | — | 146 | 1 | no | — |
| 260 | #349 | — | 146 | 1 | no | — |
| 261 | H(3,ℤ/4) | — | 146 | 1 | no | — |
| 262 | H(5,𝔽2) | — | 292 | 4 | no | — |
| 263 | H(5,𝔽2) | — | 146 | 8 | no | — |
| 264 | C2×#41 | — | 2 | 1 | no | — |
| 265 | C2×#41 | — | 292 | 1 | no | — |
| 266 | C2×#41 | — | 73 | 1 | no | — |
| 267 | C2×#41 | — | 146 | 1 | no | — |
| 268 | C2×#41 | — | 146 | 1 | no | — |
| 269 | C22×D4 | — | 292 | 1 | no | — |
| 270 | C22×D4 | — | 292 | 1 | no | — |
| 271 | C22×D4 | — | 292 | 1 | no | — |
| 272 | C22×D4 | — | 146 | 1 | no | — |
| 273 | C22×D4 | — | 146 | 1 | no | — |
| 274 | C22×D4 | — | 146 | 1 | no | — |
| 275 | AGL(1,ℤ/8) | — | 146 | 8 | no | — |
| 276 | AGL(1,ℤ/8) | — | 146 | 8 | no | — |
| 277 | AGL(1,ℤ/8) | — | 146 | 8 | no | — |
| 278 | #135 | — | 2 | 2 | no | — |
| 279 | #135 | — | 2 | 2 | no | — |
| 280 | #135 | — | 73 | 4 | no | — |
| 281 | #135 | — | 146 | 2 | no | — |
| 282 | #135 | — | 146 | 2 | no | — |
| 283 | #135 | — | 146 | 2 | no | — |
| 284 | C2×Q16 | C2×#64408 | 1 | 1 | yes | characteristic |
| 285 | C2×SD16 | — | 2 | 1 | no | — |
| 286 | C2×SD16 | — | 146 | 1 | no | — |
| 287 | C2×SD16 | — | 146 | 1 | no | — |
| 288 | C2×D8 | — | 73 | 4 | no | — |
| 289 | C2×D8 | — | 73 | 1 | no | — |
| 290 | C2×D8 | — | 73 | 1 | no | — |
| 291 | C2×D8 | — | 146 | 2 | no | — |
| 292 | C2×D8 | — | 146 | 2 | no | — |
| 293 | C2×D8 | — | 146 | 2 | no | — |
| 294 | C2×D8 | — | 146 | 1 | no | — |
| 295 | C2×D8 | — | 146 | 1 | no | — |
| 296 | C2×D8 | — | 146 | 2 | no | — |
| 297 | C2×D8 | — | 146 | 2 | no | — |
| 298 | C2×D8 | — | 146 | 1 | no | — |
| 299 | C2×D8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 300 | #131 | — | 146 | 2 | no | — |
| 301 | #131 | — | 146 | 2 | no | — |
| 302 | C2×M16 | — | 73 | 1 | no | — |
| 303 | C2×M16 | — | 73 | 1 | no | — |
| 304 | C2×M16 | — | 73 | 1 | no | — |
| 305 | C22×C8 | — | 73 | 1 | no | — |
| 306 | C22×C8 | — | 73 | 1 | no | — |
| 307 | C22×C8 | C2×#64408 | 1 | 1 | yes | characteristic |
| 308 | #117 | — | 146 | 2 | no | — |
| 309 | M32 | — | 146 | 2 | no | — |
| 310 | M32 | — | 146 | 2 | no | — |
| 311 | C2×C16 | — | 146 | 2 | no | — |
| 312 | #107 | — | 146 | 2 | no | — |
| 313 | #106 | — | 146 | 2 | no | — |
| 314 | #99 | — | 292 | 1 | no | — |
| 315 | #99 | — | 292 | 1 | no | — |
| 316 | C24 | — | 292 | 1 | no | — |
| 317 | C24 | — | 292 | 1 | no | — |
| 318 | C24 | — | 292 | 1 | no | — |
| 319 | #41 | — | 2 | 4 | no | — |
| 320 | #41 | — | 4 | 2 | no | — |
| 321 | #41 | — | 292 | 8 | no | — |
| 322 | #41 | — | 292 | 2 | no | — |
| 323 | #41 | — | 292 | 2 | no | — |
| 324 | #41 | — | 146 | 2 | no | — |
| 325 | #41 | — | 146 | 2 | no | — |
| 326 | #41 | — | 146 | 4 | no | — |
| 327 | #41 | — | 146 | 4 | no | — |
| 328 | C2×Q8 | — | 2 | 1 | no | — |
| 329 | C2×Q8 | — | 73 | 1 | no | — |
| 330 | C2×D4 | — | 2 | 1 | no | — |
| 331 | C2×D4 | — | 4 | 1 | no | — |
| 332 | C2×D4 | — | 292 | 2 | no | — |
| 333 | C2×D4 | — | 292 | 1 | no | — |
| 334 | C2×D4 | — | 292 | 1 | no | — |
| 335 | C2×D4 | — | 292 | 8 | no | — |
| 336 | C2×D4 | — | 292 | 8 | no | — |
| 337 | C2×D4 | — | 292 | 8 | no | — |
| 338 | C2×D4 | — | 292 | 2 | no | — |
| 339 | C2×D4 | — | 292 | 1 | no | — |
| 340 | C2×D4 | — | 292 | 1 | no | — |
| 341 | C2×D4 | — | 292 | 2 | no | — |
| 342 | C2×D4 | — | 292 | 1 | no | — |
| 343 | C2×D4 | — | 73 | 1 | no | — |
| 344 | C2×D4 | — | 73 | 1 | no | — |
| 345 | C2×D4 | — | 73 | 1 | no | — |
| 346 | C2×D4 | — | 146 | 4 | no | — |
| 347 | C2×D4 | — | 146 | 4 | no | — |
| 348 | C2×D4 | — | 146 | 4 | no | — |
| 349 | C2×D4 | — | 146 | 1 | no | — |
| 350 | C2×D4 | — | 146 | 1 | no | — |
| 351 | C22×C4 | — | 4 | 1 | no | — |
| 352 | C22×C4 | — | 292 | 1 | no | — |
| 353 | C22×C4 | — | 292 | 1 | no | — |
| 354 | C22×C4 | — | 73 | 1 | no | — |
| 355 | C22×C4 | — | 73 | 1 | no | — |
| 356 | C22×C4 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 357 | Q16 | — | 2 | 1 | no | — |
| 358 | Q16 | C22⋊#64408 | 1 | 2 | yes | — |
| 359 | SD16 | — | 2 | 4 | no | — |
| 360 | SD16 | — | 146 | 4 | no | — |
| 361 | SD16 | — | 146 | 4 | no | — |
| 362 | D8 | — | 2 | 1 | no | — |
| 363 | D8 | — | 73 | 2 | no | — |
| 364 | D8 | — | 73 | 2 | no | — |
| 365 | D8 | — | 146 | 4 | no | — |
| 366 | D8 | — | 146 | 4 | no | — |
| 367 | D8 | — | 146 | 4 | no | — |
| 368 | D8 | — | 146 | 1 | no | — |
| 369 | D8 | — | 146 | 1 | no | — |
| 370 | D8 | C22⋊#64408 | 1 | 2 | yes | — |
| 371 | M16 | — | 146 | 2 | no | — |
| 372 | M16 | — | 146 | 2 | no | — |
| 373 | M16 | — | 146 | 2 | no | — |
| 374 | C2×C8 | — | 2 | 1 | no | — |
| 375 | C2×C8 | — | 2 | 1 | no | — |
| 376 | C2×C8 | — | 73 | 1 | no | — |
| 377 | C2×C8 | — | 73 | 2 | no | — |
| 378 | C2×C8 | — | 73 | 2 | no | — |
| 379 | C2×C8 | — | 73 | 1 | no | — |
| 380 | C2×C8 | — | 146 | 1 | no | — |
| 381 | C2×C8 | — | 146 | 1 | no | — |
| 382 | C2×C8 | C22⋊#64408 | 1 | 1 | yes | characteristic |
| 383 | C2×C8 | C22×#64408 | 1 | 1 | yes | characteristic |
| 384 | C4⋊C4 | — | 292 | 2 | no | — |
| 385 | C22⋊C4 | — | 292 | 2 | no | — |
| 386 | C42 | — | 292 | 2 | no | — |
| 387 | C16 | — | 292 | 2 | no | — |
| 388 | C23 | — | 4 | 1 | no | — |
| 389 | C23 | — | 292 | 4 | no | — |
| 390 | C23 | — | 292 | 4 | no | — |
| 391 | C23 | — | 292 | 4 | no | — |
| 392 | C23 | — | 292 | 1 | no | — |
| 393 | C23 | — | 292 | 1 | no | — |
| 394 | C23 | — | 73 | 1 | no | — |
| 395 | C23 | — | 73 | 1 | no | — |
| 396 | C23 | — | 1168 | 2 | no | — |
| 397 | C23 | — | 1168 | 2 | no | — |
| 398 | C23 | — | 1168 | 2 | no | — |
| 399 | C23 | #14556653 | 1 | 1 | yes | characteristic |
| 400 | Q8 | — | 2 | 2 | no | — |
| 401 | Q8 | — | 4 | 1 | no | — |
| 402 | Q8 | — | 146 | 2 | no | — |
| 403 | D4 | — | 2 | 2 | no | — |
| 404 | D4 | — | 4 | 4 | no | — |
| 405 | D4 | — | 4 | 1 | no | — |
| 406 | D4 | — | 292 | 4 | no | — |
| 407 | D4 | — | 292 | 4 | no | — |
| 408 | D4 | — | 292 | 4 | no | — |
| 409 | D4 | — | 292 | 4 | no | — |
| 410 | D4 | — | 292 | 4 | no | — |
| 411 | D4 | — | 292 | 1 | no | — |
| 412 | D4 | — | 292 | 1 | no | — |
| 413 | D4 | — | 146 | 2 | no | — |
| 414 | D4 | — | 146 | 2 | no | — |
| 415 | D4 | — | 146 | 2 | no | — |
| 416 | D4 | — | 146 | 2 | no | — |
| 417 | D4 | — | 146 | 2 | no | — |
| 418 | C2×C4 | — | 2 | 1 | no | — |
| 419 | C2×C4 | — | 2 | 1 | no | — |
| 420 | C2×C4 | — | 4 | 4 | no | — |
| 421 | C2×C4 | — | 4 | 1 | no | — |
| 422 | C2×C4 | — | 292 | 4 | no | — |
| 423 | C2×C4 | — | 292 | 4 | no | — |
| 424 | C2×C4 | — | 584 | 2 | no | — |
| 425 | C2×C4 | — | 73 | 1 | no | — |
| 426 | C2×C4 | — | 73 | 2 | no | — |
| 427 | C2×C4 | — | 73 | 2 | no | — |
| 428 | C2×C4 | — | 73 | 1 | no | — |
| 429 | C2×C4 | — | 146 | 1 | no | — |
| 430 | C2×C4 | — | 146 | 1 | no | — |
| 431 | C2×C4 | #14556653 | 1 | 1 | yes | characteristic |
| 432 | C2×C4 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 433 | C8 | — | 2 | 1 | no | — |
| 434 | C8 | — | 73 | 2 | no | — |
| 435 | C8 | — | 146 | 1 | no | — |
| 436 | C8 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 437 | C8 | C2×C22⋊#64408 | 1 | 1 | yes | characteristic |
| 438 | C22 | — | 2 | 1 | no | — |
| 439 | C22 | — | 4 | 1 | no | — |
| 440 | C22 | — | 4 | 2 | no | — |
| 441 | C22 | — | 8 | 2 | no | — |
| 442 | C22 | — | 292 | 1 | no | — |
| 443 | C22 | — | 292 | 1 | no | — |
| 444 | C22 | — | 292 | 2 | no | — |
| 445 | C22 | — | 292 | 2 | no | — |
| 446 | C22 | — | 584 | 2 | no | — |
| 447 | C22 | — | 584 | 2 | no | — |
| 448 | C22 | — | 73 | 2 | no | — |
| 449 | C22 | — | 1168 | 4 | no | — |
| 450 | C22 | — | 1168 | 4 | no | — |
| 451 | C22 | — | 1168 | 4 | no | — |
| 452 | C22 | — | 146 | 1 | no | — |
| 453 | C22 | C2×#14556653 | 1 | 1 | yes | characteristic |
| 454 | C4 | — | 2 | 1 | no | — |
| 455 | C4 | — | 4 | 2 | no | — |
| 456 | C4 | — | 73 | 2 | no | — |
| 457 | C4 | — | 1168 | 2 | no | — |
| 458 | C4 | — | 146 | 1 | no | — |
| 459 | C4 | #17989528 | 1 | 1 | yes | characteristic |
| 460 | C4 | #17989579 | 1 | 1 | yes | characteristic |
| 461 | C2 | — | 2 | 1 | no | — |
| 462 | C2 | — | 4 | 1 | no | — |
| 463 | C2 | — | 8 | 2 | no | — |
| 464 | C2 | — | 292 | 1 | no | — |
| 465 | C2 | — | 584 | 2 | no | — |
| 466 | C2 | — | 584 | 2 | no | — |
| 467 | C2 | — | 146 | 2 | no | — |
| 468 | C2 | #22625769 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626253 | C2 | semidirect |
| 2. #22626240 | C2 | semidirect |
| 3. #22626168 | C2 | semidirect |
| 4. #22625813 | C2 | semidirect |
| 6. #17989643 | C22 | semidirect |
| 7. #17989597 | C22 | semidirect |
| 20. C2×#14556614 | C4 | semidirect |
| 22. C22×D584 | C4 | semidirect |
| 23. C2×D8×D73 | C4 | semidirect |
| 26. C2×#135×C73 | C4 | semidirect |
| 240. C73 | #12741 | semidirect |
| 249. C2×#135 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626253 | 2 |
| #22626240 | 2 |
| #22626168 | 2 |
| #22625813 | 2 |
| C2×#17989389 | 2 |
| #12741 | 73 |