Finite Group Databasebeta

← #20273724

Subgroups — #20273724

Order 6784.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#16811252C211yesmaximal, characteristic
2#16810954C211yesmaximal, characteristic
3#16810951C211yesmaximal, characteristic
4#16810555C211yesmaximal, characteristic
5#16810359C211yesmaximal, characteristic
6#16810348C211yesmaximal, characteristic
7C53×#328C211yesmaximal, characteristic
8#13133216—21no—
9#13133215—21no—
10#13133207—21no—
11#13133207—21no—
12#13133196C2211yescharacteristic
13#13133194—21no—
14#13133173—21no—
15C2×C4⋊Dic53—21no—
16C2×C4⋊Dic53C2211yescharacteristic
17C2×#11719919C2211yescharacteristic
18#13133149—21no—
19#13133148—21no—
20#13133142—21no—
21#13133141—21no—
22C22⋊#88322C2211yescharacteristic
23#13133124—21no—
24C22⋊Q8×C53C2211yescharacteristic
25C22⋊C8×C53C2211yescharacteristic
26#95×C53C2211yescharacteristic
27C2×Q8×C53D411yescharacteristic
28C22×C4×C53—21no—
29C22×C4×C53C2311yescharacteristic
30C22×Dic53—21no—
31C22×Dic53D411yescharacteristic
32C22×Dic53D411yescharacteristic
33C2×Dic106—21no—
34C2×Dic106D411yescharacteristic
35C2×C8×C53—21no—
36C4⋊C4×C53—21no—
37C4⋊C4×C53D411yescharacteristic
38C22⋊C4×C53—21no—
39C22⋊Dic53—21no—
40C4⋊Dic53—21no—
41C4⋊Dic53—21no—
42C4⋊Dic53—21no—
43C4⋊Dic53—42no—
44C4⋊Dic53D411yescharacteristic
45#11719919—21no—
46#11719919—21no—
47#11719919—21no—
48#11719919—21no—
49#11719919—21no—
50#11719919—21no—
51#11719919—21no—
52C4×Dic53—21no—
53C4×Dic53—21no—
54C2×#88322—21no—
55C23×C53C2×D411yescharacteristic
56Q8×C53—41no—
57C2×C4×C53—22no—
58C2×C4×C53—21no—
59C2×C4×C53—21no—
60C2×C4×C53—41no—
61C2×C4×C53—41no—
62C2×C4×C53—41no—
63C2×C4×C53C2×D411yescharacteristic
64C2×C4×C53C2×D411yescharacteristic
65C2×Dic53—21no—
66C2×Dic53—21no—
67C2×Dic53—21no—
68C2×Dic53—21no—
69C2×Dic53—21no—
70C2×Dic53—41no—
71C2×Dic53—41no—
72C2×Dic53—41no—
73C2×Dic53—41no—
74C2×Dic53SD1612yes—
75Dic106—41no—
76Dic106—81no—
77C8×C53—41no—
78#88322—41no—
79C22×C53—21no—
80C22×C53—21no—
81C22×C53#12011yescharacteristic
82C22×C53C2×SD1611yescharacteristic
83C22×C53#13711yescharacteristic
84C4×C53—21no—
85C4×C53—21no—
86C4×C53—42no—
87C4×C53—41no—
88C4×C53—41no—
89Dic53—22no—
90Dic53—41no—
91Dic53—41no—
92Dic53—41no—
93Dic53—81no—
94#1611—531nomaximal, Sylow
95C2×C53—21no—
96C2×C53—21no—
97C2×C53#44811yescharacteristic
98C2×C53#45611yescharacteristic
99C2×C53#45811yescharacteristic
100#544—531no—
101#483—531no—
102#483—531no—
103#398—531no—
104#328—531no—
105#328D5311yescharacteristic
106#324—531no—
107C53#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—1061no—
109C4⋊Q8—1061no—
110#125—1061no—
111#125—1061no—
112C22⋊Q8—531no—
113C22⋊Q8—1061no—
114C22⋊Q8C2×D5311yescharacteristic
115#117—1061no—
116C2×C4⋊C4—531no—
117C2×C4⋊C4—531no—
118C2×C4⋊C4—1061no—
119#106—1061no—
120#106—1061no—
121#103—1061no—
122#103—1061no—
123C22⋊C8—531no—
124C22⋊C8C2×D5311yescharacteristic
125#95—1061no—
126#95C2×D5311yescharacteristic
127C2×Q8—531no—
128C2×Q8—1061no—
129C2×Q8D21211yescharacteristic
130C22×C4—21no—
131C22×C4—531no—
132C22×C4—531no—
133C22×C4—1061no—
134C22×C4C22×D5311yescharacteristic
135C2×C8—21no—
136C2×C8—1061no—
137C4⋊C4—21no—
138C4⋊C4—531no—
139C4⋊C4—1061no—
140C4⋊C4—1061no—
141C4⋊C4—1061no—
142C4⋊C4—1061no—
143C4⋊C4—1061no—
144C4⋊C4—1061no—
145C4⋊C4—1061no—
146C4⋊C4—1061no—
147C4⋊C4—1061no—
148C4⋊C4—1061no—
149C4⋊C4—2122no—
150C4⋊C4D21211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—1061no—
153C42—1061no—
154C42—1061no—
155C23D4×D5311yescharacteristic
156Q8—41no—
157Q8—4241no—
158Q8—2121no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—532no—
166C2×C4—1061no—
167C2×C4—1061no—
168C2×C4—1061no—
169C2×C4—1061no—
170C2×C4—1061no—
171C2×C4—2121no—
172C2×C4—2121no—
173C2×C4—2121no—
174C2×C4—2121no—
175C2×C4C2×D21211yescharacteristic
176C2×C4D4×D5311yescharacteristic
177C8—41no—
178C8—2121no—
179C22—21no—
180C22—21no—
181C22#1313318711yescharacteristic
182C22SD16×D5311yescharacteristic
183C22#1313324911yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—1062no—
190C4—4241no—
191C4—2121no—
192C4—2121no—
193C4—2121no—
194C2—21no—
195C2—21no—
196C2#1681076311yescharacteristic
197C2#1681080711yescharacteristic
198C2#1681081411yescharacteristic
subgroupG/H
centerC22#13133187
commutatorC22×C4×C53C23
FrattiniC22×C4C22×D53
FittingC53×#328C2
socleC22×C53#120
hypercenter#328D53
hypocenterC53#1611
LCSG ▷ C22×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
107. C53#1611semidirect