Finite Group Databasebeta

← #19133907

Subgroups — #19133907

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#14583308C212yesmaximal, complemented
3#14583294C211yesmaximal, characteristic
4#14582640C212yesmaximal, complemented
5C43×#329C211yesmaximal, characteristic
6C2×#10621885—21no—
7C2×#10621883—21no—
8#13063325C2211yescharacteristic
9#13063323—21no—
10#13063318—22no—
11#13063317C2212yes—
12#13063306—21no—
13#13063302—22no—
14#13063259—22no—
15#13063257—22no—
16#13063236C2211yescharacteristic
17#124×C43C2211yescharacteristic
18#97×C43C2212yes—
19C2×Q8×C43D411yescharacteristic
20C2×D4×C43D411yescharacteristic
21C22×Dic43—21no—
22C2×Dic86—21no—
23C2×Dic86—21no—
24C2×C8×C43—22no—
25C22⋊C4×C43—22no—
26C42×C43C2311yescharacteristic
27C22⋊Dic43—22no—
28C22⋊Dic43—21no—
29#10621885—42no—
30#10621883—42no—
31C4⋊Dic43—22no—
32C4⋊Dic43D412yes—
33C4⋊Dic43D412yes—
34Dic43⋊C4—22no—
35Dic43⋊C4—22no—
36Dic43⋊C4—22no—
37C4×Dic43—21no—
38C2×C43⋊C8—21no—
39C23×C43—21no—
40Q8×C43—41no—
41D4×C43—41no—
42C2×C4×C43—21no—
43C2×C4×C43C2×D411yescharacteristic
44C2×C4×C43C2×D412yes—
45C2×Dic43—22no—
46C2×Dic43—22no—
47C2×Dic43—41no—
48C2×Dic43—81no—
49Dic86—41no—
50Dic86—41no—
51Dic86—81no—
52C8×C43—24no—
53C43⋊C8—22no—
54C22×C43—41no—
55C22×C43—42no—
56C22×C43#12011yescharacteristic
57C4×C43—21no—
58C4×C43—22no—
59C4×C43—41no—
60Dic43—42no—
61Dic43—42no—
62Dic43—81no—
63#1660—431nomaximal, Sylow
64C2×C43—81no—
65C2×C43#45311yescharacteristic
66C2×C43#45612yes—
67#563—431no—
68#501—432no—
69#497—431no—
70#330—432no—
71#329D4311yescharacteristic
72C43#166011yescharacteristic, complemented, Sylow
73C2×Q16—861no—
74C2×SD16—861no—
75C4⋊Q8—431no—
76C4⋊Q8—861no—
77#126—862no—
78#125—432no—
79#124C2×D4311yescharacteristic
80#123—861no—
81C22⋊Q8—862no—
82#107—862no—
83#106—862no—
84#97—431no—
85#97C2×D4312yes—
86C2×Q8—861no—
87C2×Q8—861no—
88C2×Q8D17211yescharacteristic
89C2×D4D17211yescharacteristic
90C22×C4—861no—
91Q16—1722no—
92SD16—1722no—
93C2×C8—22no—
94C2×C8—861no—
95C4⋊C4—432no—
96C4⋊C4—432no—
97C4⋊C4—862no—
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—3441no—
109Q8—1721no—
110Q8—1721no—
111D4—41no—
112C2×C4—21no—
113C2×C4—862no—
114C2×C4—862no—
115C2×C4—3441no—
116C2×C4—1721no—
117C2×C4C2×D17211yescharacteristic
118C2×C4D4×D4312yes—
119C8—24no—
120C8—862no—
121C22—41no—
122C22—42no—
123C22#1306329511yescharacteristic
124C4—21no—
125C4—22no—
126C4—41no—
127C4—3441no—
128C4—1722no—
129C4—1722no—
130C2—81no—
131C2#1458306911yescharacteristic
132C2#1458308312yes—
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#329C2
socleC22×C43#120
hypercenter#329D43
hypocenterC43#1660
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14583308C2semidirect
4. #14582640C2semidirect
72. C43#1660semidirect