Finite Group Databasebeta

← #19133922

Subgroups — #19133922

Order 5504.

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

normal subgroups only

This group has 172 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
1C43⋊#564C211yesmaximal, characteristic
2#14583305C211yesmaximal, characteristic
3#14583267C211yesmaximal, characteristic
4#14582641C211yesmaximal, characteristic
5#14582640C211yesmaximal, characteristic
6#14582640C211yesmaximal, characteristic
7C43×#501C211yesmaximal, characteristic
8#13063317C2211yescharacteristic
9#13063317C2211yescharacteristic
10#13063316—21no—
11#13063316—21no—
12#13063315—21no—
13#13063315—21no—
14#13063315—21no—
15#13063315—21no—
16#13063258—21no—
17#13063256—21no—
18#13063249—21no—
19#13063249—21no—
20#13063236C2211yescharacteristic
21#13063236C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23#125×C43C2211yescharacteristic
24#107×C43—21no—
25#106×C43—21no—
26#97×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×C8×C43—21no—
29C4⋊C4×C43—21no—
30C4⋊C4×C43—21no—
31C4⋊C4×C43—21no—
32C4⋊C4×C43—21no—
33C4⋊C4×C43D411yescharacteristic
34C4⋊C4×C43D411yescharacteristic
35C42×C43C2311yescharacteristic
36C4⋊Dic43—21no—
37C4⋊Dic43—21no—
38C4⋊Dic43D411yescharacteristic
39C4⋊Dic43D411yescharacteristic
40C4⋊Dic43D411yescharacteristic
41C4⋊Dic43D411yescharacteristic
42Dic43⋊C4—21no—
43Dic43⋊C4—21no—
44Dic43⋊C4—21no—
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50C4×Dic43—21no—
51C4×Dic43—21no—
52C2×C43⋊C8—21no—
53C2×C43⋊C8—21no—
54Q8×C43—42no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—41no—
58C2×C4×C43C2×D411yescharacteristic
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×Dic43—21no—
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65C8×C43—22no—
66C43⋊C8—22no—
67C43⋊C8—41no—
68C22×C43#12011yescharacteristic
69C4×C43—21no—
70C4×C43—21no—
71C4×C43—21no—
72C4×C43—41no—
73C4×C43—41no—
74C4×C43—81no—
75Dic43—41no—
76Dic43—41no—
77Dic43—41no—
78Dic43—41no—
79#1663—431nomaximal, Sylow
80C2×C43#45411yescharacteristic
81C2×C43#45611yescharacteristic
82C2×C43#45611yescharacteristic
83#564—431no—
84#501—431no—
85#501D4311yescharacteristic
86#491—431no—
87#330—431no—
88#330—431no—
89#330—431no—
90C43#166311yescharacteristic, complemented, Sylow
91C4⋊Q8C2×D4311yescharacteristic
92#125—431no—
93#125—431no—
94#125—861no—
95#125—861no—
96#125—861no—
97#125—861no—
98#125—861no—
99#125—861no—
100#125C2×D4311yescharacteristic
101#107—21no—
102#107—861no—
103#106—21no—
104#106—861no—
105#103—861no—
106#103—861no—
107#97—431no—
108#97—431no—
109#97C2×D4311yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—861no—
113C2×C8—861no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—431no—
119C4⋊C4—431no—
120C4⋊C4—431no—
121C4⋊C4—431no—
122C4⋊C4—861no—
123C4⋊C4—861no—
124C4⋊C4—861no—
125C4⋊C4—861no—
126C4⋊C4—861no—
127C4⋊C4—861no—
128C4⋊C4—861no—
129C4⋊C4—861no—
130C4⋊C4—861no—
131C4⋊C4—861no—
132C4⋊C4C22⋊D4311yescharacteristic
133C4⋊C4C22⋊D4311yescharacteristic
134C42—861no—
135C42—861no—
136C42C22×D4311yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—861no—
142C2×C4—861no—
143C2×C4—861no—
144C2×C4—861no—
145C2×C4D4×D4311yescharacteristic
146C2×C4D4×D4311yescharacteristic
147C2×C4C2×C22⋊D4311yescharacteristic
148C8—22no—
149C8—862no—
150C8—1721no—
151C22#1306329311yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—1721no—
159C4—1721no—
160C4—1721no—
161C4—1721no—
162C2#1458307011yescharacteristic
163C2#1458308011yescharacteristic
164C2#1458308111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#501C2
socleC22×C43#120
hypercenter#501D43
hypocenterC43#1663
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
90. C43#1663semidirect