Finite Group Databasebeta

← #19133904

Subgroups — #19133904

Order 5504.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583649C211yesmaximal, characteristic
2#14583305C212yesmaximal, complemented
3#14582640C212yesmaximal, complemented
4#14582639C211yesmaximal, characteristic
5C43×#497C211yesmaximal, characteristic
6#13063323—21no—
7#13063318—22no—
8#13063317C2212yes—
9#13063306—21no—
10#13063302—22no—
11#13063258—22no—
12#13063256—22no—
13#13063236C2212yes—
14C2×Q16×C43—21no—
15C2×SD16×C43—21no—
16C4⋊Q8×C43C2211yescharacteristic
17#124×C43C2211yescharacteristic
18#97×C43C2211yescharacteristic
19C2×Q8×C43—21no—
20C2×Q8×C43D411yescharacteristic
21C2×D4×C43D411yescharacteristic
22C22×Dic43—21no—
23C2×Dic86—21no—
24Q16×C43—42no—
25SD16×C43—42no—
26C2×C8×C43—21no—
27C4⋊C4×C43—22no—
28C22⋊C4×C43—22no—
29C42×C43C2311yescharacteristic
30C22⋊Dic43—22no—
31C22⋊Dic43—21no—
32C4⋊Dic43D412yes—
33C4⋊Dic43D412yes—
34Dic43⋊C4—22no—
35Dic43⋊C4—22no—
36Dic43⋊C4—22no—
37C4×Dic43—21no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40Q8×C43—41no—
41Q8×C43—41no—
42Q8×C43—41no—
43D4×C43—41no—
44C2×C4×C43—21no—
45C2×C4×C43—41no—
46C2×C4×C43C2×D412yes—
47C2×C4×C43C2×D411yescharacteristic
48C2×Dic43—22no—
49C2×Dic43—22no—
50C2×Dic43—81no—
51Dic86—81no—
52C8×C43—22no—
53C43⋊C8—24no—
54C22×C43—41no—
55C22×C43—42no—
56C22×C43#12011yescharacteristic
57C4×C43—21no—
58C4×C43—22no—
59C4×C43—41no—
60C4×C43—81no—
61Dic43—42no—
62Dic43—42no—
63#1660—431nomaximal, Sylow
64C2×C43—81no—
65C2×C43#45311yescharacteristic
66C2×C43#45612yes—
67#563—431no—
68#501—432no—
69#497D4311yescharacteristic
70#330—432no—
71#329—431no—
72C43#166011yescharacteristic, complemented, Sylow
73C2×Q16—21no—
74C2×SD16—21no—
75C4⋊Q8—861no—
76C4⋊Q8C2×D4311yescharacteristic
77#126—862no—
78#125—432no—
79#124C2×D4311yescharacteristic
80#123—861no—
81C22⋊Q8—862no—
82#107—862no—
83#106—862no—
84#97—432no—
85#97C2×D4311yescharacteristic
86C2×Q8—21no—
87C2×Q8—861no—
88C2×Q8C22⋊D4311yescharacteristic
89C2×D4C22⋊D4311yescharacteristic
90C22×C4—861no—
91Q16—42no—
92SD16—42no—
93C2×C8—21no—
94C2×C8—862no—
95C4⋊C4—22no—
96C4⋊C4—432no—
97C4⋊C4—432no—
98C4⋊C4—862no—
99C4⋊C4—862no—
100C4⋊C4—862no—
101C22⋊C4—22no—
102C22⋊C4—862no—
103C22⋊C4—861no—
104C42—861no—
105C42C22×D4311yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—41no—
109Q8—41no—
110Q8—3441no—
111D4—41no—
112C2×C4—21no—
113C2×C4—41no—
114C2×C4—862no—
115C2×C4—862no—
116C2×C4—3441no—
117C2×C4D4×D4312yes—
118C2×C4C2×C22⋊D4311yescharacteristic
119C8—22no—
120C8—864no—
121C22—41no—
122C22—42no—
123C22#1306329311yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—81no—
128C4—1722no—
129C4—1722no—
130C2—81no—
131C2#1458306611yescharacteristic
132C2#1458308012yes—
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#497C2
socleC22×C43#120
hypercenter#497D43
hypocenterC43#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #14583305C2semidirect
3. #14582640C2semidirect
72. C43#1660semidirect