Finite Group Databasebeta

← #20274042

Subgroups — #20274042

Order 6784.

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
1C53⋊#564C211yesmaximal, characteristic
2#16811029C211yesmaximal, characteristic
3#16810991C211yesmaximal, characteristic
4#16810365C211yesmaximal, characteristic
5#16810364C211yesmaximal, characteristic
6#16810364C211yesmaximal, characteristic
7C53×#501C211yesmaximal, characteristic
8#13133209C2211yescharacteristic
9#13133209C2211yescharacteristic
10#13133208—21no—
11#13133208—21no—
12#13133207—21no—
13#13133207—21no—
14#13133207—21no—
15#13133207—21no—
16#13133150—21no—
17#13133148—21no—
18#13133141—21no—
19#13133141—21no—
20#13133128C2211yescharacteristic
21#13133128C2211yescharacteristic
22C4⋊Q8×C53C2211yescharacteristic
23#125×C53C2211yescharacteristic
24#107×C53—21no—
25#106×C53—21no—
26#97×C53C2211yescharacteristic
27C2×Q8×C53—21no—
28C2×C8×C53—21no—
29C4⋊C4×C53—21no—
30C4⋊C4×C53—21no—
31C4⋊C4×C53—21no—
32C4⋊C4×C53—21no—
33C4⋊C4×C53D411yescharacteristic
34C4⋊C4×C53D411yescharacteristic
35C42×C53C2311yescharacteristic
36C4⋊Dic53—21no—
37C4⋊Dic53—21no—
38C4⋊Dic53D411yescharacteristic
39C4⋊Dic53D411yescharacteristic
40C4⋊Dic53D411yescharacteristic
41C4⋊Dic53D411yescharacteristic
42#11719919—21no—
43#11719919—21no—
44#11719919—21no—
45#11719919—21no—
46#11719919—21no—
47#11719919—21no—
48#11719919—21no—
49#11719919—21no—
50C4×Dic53—21no—
51C4×Dic53—21no—
52C2×#88322—21no—
53C2×#88322—21no—
54Q8×C53—42no—
55C2×C4×C53—21no—
56C2×C4×C53—21no—
57C2×C4×C53—41no—
58C2×C4×C53C2×D411yescharacteristic
59C2×C4×C53C2×D411yescharacteristic
60C2×C4×C53C2×D411yescharacteristic
61C2×Dic53—21no—
62C2×Dic53—21no—
63C2×Dic53—21no—
64C2×Dic53—21no—
65C8×C53—22no—
66#88322—22no—
67#88322—41no—
68C22×C53#12011yescharacteristic
69C4×C53—21no—
70C4×C53—21no—
71C4×C53—21no—
72C4×C53—41no—
73C4×C53—41no—
74C4×C53—81no—
75Dic53—41no—
76Dic53—41no—
77Dic53—41no—
78Dic53—41no—
79#1663—531nomaximal, Sylow
80C2×C53#45411yescharacteristic
81C2×C53#45611yescharacteristic
82C2×C53#45611yescharacteristic
83#564—531no—
84#501—531no—
85#501D5311yescharacteristic
86#491—531no—
87#330—531no—
88#330—531no—
89#330—531no—
90C53#166311yescharacteristic, complemented, Sylow
91C4⋊Q8C2×D5311yescharacteristic
92#125—531no—
93#125—531no—
94#125—1061no—
95#125—1061no—
96#125—1061no—
97#125—1061no—
98#125—1061no—
99#125—1061no—
100#125C2×D5311yescharacteristic
101#107—21no—
102#107—1061no—
103#106—21no—
104#106—1061no—
105#103—1061no—
106#103—1061no—
107#97—531no—
108#97—531no—
109#97C2×D5311yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—1061no—
113C2×C8—1061no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—531no—
119C4⋊C4—531no—
120C4⋊C4—531no—
121C4⋊C4—531no—
122C4⋊C4—1061no—
123C4⋊C4—1061no—
124C4⋊C4—1061no—
125C4⋊C4—1061no—
126C4⋊C4—1061no—
127C4⋊C4—1061no—
128C4⋊C4—1061no—
129C4⋊C4—1061no—
130C4⋊C4—1061no—
131C4⋊C4—1061no—
132C4⋊C4C22⋊D5311yescharacteristic
133C4⋊C4C22⋊D5311yescharacteristic
134C42—1061no—
135C42—1061no—
136C42C22×D5311yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—1061no—
142C2×C4—1061no—
143C2×C4—1061no—
144C2×C4—1061no—
145C2×C4D4×D5311yescharacteristic
146C2×C4D4×D5311yescharacteristic
147C2×C4C2×C22⋊D5311yescharacteristic
148C8—22no—
149C8—1062no—
150C8—2121no—
151C22#1313318511yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—2121no—
159C4—2121no—
160C4—2121no—
161C4—2121no—
162C2#1681079411yescharacteristic
163C2#1681080411yescharacteristic
164C2#1681080511yescharacteristic
subgroupG/H
centerC22#13133185
commutatorC42×C53C23
FrattiniC42C22×D53
FittingC53×#501C2
socleC22×C53#120
hypercenter#501D53
hypocenterC53#1663
LCSG ▷ C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
90. C53#1663semidirect