Finite Group Databasebeta

← #20273069

Subgroups — #20273069

Order 6784.

204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C2×#13133207C211yesmaximal, characteristic
2#16810677C211yesmaximal, characteristic
3#16810673C211yesmaximal, characteristic
4#16810349C211yesmaximal, characteristic
5#16810348C211yesmaximal, characteristic
6#16810348C211yesmaximal, characteristic
7C53×#324C211yesmaximal, characteristic
8#13133207—21no—
9#13133207—21no—
10#13133207—21no—
11#13133207—21no—
12C2×C4⋊Dic53C411yescharacteristic
13C2×#11719919C411yescharacteristic
14C2×#11719919C411yescharacteristic
15C2×#11719919C411yescharacteristic
16C2×#11719919C2211yescharacteristic
17C2×C4×Dic53C2211yescharacteristic
18#13133146—21no—
19#13133146—21no—
20C22⋊#88322C2211yescharacteristic
21C22⋊#88322C2211yescharacteristic
22#13133127—21no—
23C8×Dic53—21no—
24C2×C4⋊C4×C53C2211yescharacteristic
25C22⋊C8×C53C2211yescharacteristic
26C22⋊C8×C53C2211yescharacteristic
27C22×C4×C53C2×C411yescharacteristic
28C22×C4×C53C2×C411yescharacteristic
29C22×C4×C53C2311yescharacteristic
30C22×Dic53C2×C411yescharacteristic
31C22×Dic53C2×C411yescharacteristic
32C22×Dic53C2×C411yescharacteristic
33C22×Dic53C2×C411yescharacteristic
34C2×C8×C53—21no—
35C2×C8×C53—21no—
36C4⋊C4×C53—21no—
37C4⋊C4×C53—21no—
38C4⋊Dic53—21no—
39C4⋊Dic53—21no—
40#11719919—21no—
41#11719919—21no—
42#11719919—21no—
43#11719919—21no—
44#11719919—21no—
45#11719919—21no—
46#11719919—21no—
47#11719919—21no—
48C4×Dic53D411yescharacteristic
49C4×Dic53D411yescharacteristic
50C4×Dic53D411yescharacteristic
51C4×Dic53D411yescharacteristic
52C2×#88322—21no—
53C2×#88322—21no—
54C23×C53C22×C411yescharacteristic
55C2×C4×C53—21no—
56C2×C4×C53—21no—
57C2×C4×C53—21no—
58C2×C4×C53—21no—
59C2×C4×C53—41no—
60C2×C4×C53—41no—
61C2×C4×C53C2×D411yescharacteristic
62C2×C4×C53C2×D411yescharacteristic
63C2×Dic53—21no—
64C2×Dic53—21no—
65C2×Dic53—22no—
66C2×Dic53—21no—
67C2×Dic53—21no—
68C2×Dic53—21no—
69C2×Dic53—21no—
70C2×Dic53—41no—
71C2×Dic53C22⋊C411yescharacteristic
72C2×Dic53C22⋊C411yescharacteristic
73C2×Dic53C22⋊C411yescharacteristic
74C2×Dic53C22⋊C411yescharacteristic
75C8×C53—41no—
76C8×C53—41no—
77#88322—41no—
78#88322—41no—
79C22×C53—21no—
80C22×C53—21no—
81C22×C53C2×C22⋊C411yescharacteristic
82C22×C53#13111yescharacteristic
83C22×C53#13111yescharacteristic
84C4×C53—21no—
85C4×C53—21no—
86C4×C53—41no—
87C4×C53—41no—
88Dic53—21no—
89Dic53—21no—
90Dic53—21no—
91Dic53—41no—
92Dic53—41no—
93Dic53#10112yes—
94#1470—531nomaximal, Sylow
95C2×C53—21no—
96C2×C53—21no—
97C2×C53#40811yescharacteristic
98C2×C53#41011yescharacteristic
99C2×C53C2×#10111yescharacteristic
100C2×#125—531no—
101#432—531no—
102#431—531no—
103#324—531no—
104#324—531no—
105#324—531no—
106#324D5311yescharacteristic
107C53#147011yescharacteristic, complemented, Sylow
108#125—1061no—
109#125—1061no—
110#125—1061no—
111#125—1061no—
112C2×C4⋊C4—531no—
113C2×C4⋊C4—531no—
114C2×C4⋊C4—531no—
115C2×C4⋊C4—531no—
116C2×C4⋊C4—531no—
117C2×C4⋊C4C2×D5311yescharacteristic
118C2×C42—531no—
119C4⋊C8—1061no—
120C4⋊C8—1061no—
121C22⋊C8—531no—
122C22⋊C8—531no—
123C22⋊C8C2×D5311yescharacteristic
124C22⋊C8C2×D5311yescharacteristic
125#97—1061no—
126C4×C8—1061no—
127C22×C4—531no—
128C22×C4—531no—
129C22×C4—531no—
130C22×C4—531no—
131C22×C4C4×D5311yescharacteristic
132C22×C4C4×D5311yescharacteristic
133C22×C4C22×D5311yescharacteristic
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—1061no—
137C2×C8—1061no—
138C4⋊C4—21no—
139C4⋊C4—21no—
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—1061no—
150C42—531no—
151C42—531no—
152C42—531no—
153C42—531no—
154C23C2×C4×D5311yescharacteristic
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—531no—
162C2×C4—531no—
163C2×C4—531no—
164C2×C4—531no—
165C2×C4—1062no—
166C2×C4—1061no—
167C2×C4—1061no—
168C2×C4—1061no—
169C2×C4—1061no—
170C2×C4—1061no—
171C2×C4—1061no—
172C2×C4—2121no—
173C2×C4D4×D5311yescharacteristic
174C2×C4D4×D5311yescharacteristic
175C8—41no—
176C8—41no—
177C8—2121no—
178C8—2121no—
179C22—21no—
180C22—21no—
181C22C22⋊C4×D5311yescharacteristic
182C22#1313322311yescharacteristic
183C22#1313322511yescharacteristic
184C4—21no—
185C4—21no—
186C4—41no—
187C4—41no—
188C4—532no—
189C4—1061no—
190C4—1061no—
191C4—1061no—
192C4—2121no—
193C4—2121no—
194C2—21no—
195C2—21no—
196C2#1681058811yescharacteristic
197C2#1681059511yescharacteristic
198C2#101×D5311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D53
commutatorC23×C53C22×C4
FrattiniC22×C4C22×D53
FittingC53×#324C2
socleC22×C53C2×C22⋊C4
hypercenter#324D53
hypocenterC53#1470
LCSG ▷ C23×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
107. C53#1470semidirect