Finite Group Databasebeta

← #20275846

Subgroups — #20275846

Order 6784.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#16811185C211yesmaximal, characteristic
2C2×#13133200C212yesmaximal, complemented
3C2×#13133131C212yesmaximal, complemented
4#16810390C211yesmaximal, characteristic, complemented
5C53×#381C211yesmaximal, characteristic, complemented
6C22×C22⋊D53C2212yes—
7#13133201—22no—
8#13133200—24no—
9#13133200—24no—
10#13133191—22no—
11#13133187—22no—
12C2×#11719919—22no—
13C2×C22⋊Dic53C2212yes—
14C2×#11719921—22no—
15#13133131—24no—
16C23×C4×C53C2211yescharacteristic
17C2×C22⋊C4×C53C2211yescharacteristic
18C2×C22⋊C4×C53C2211yescharacteristic
19#95×C53—22no—
20C24×C53C2311yescharacteristic
21C23×D53D412yes—
22C22×C4×C53—21no—
23C22×C4×C53—22no—
24C22×C4×C53—22no—
25C22×C4×C53—21no—
26C22×C4×C53—21no—
27C22×C4×C53D412yes—
28C22×C4×C53D412yescomplemented
29C2×C22⋊D53—22no—
30C2×C22⋊D53—22no—
31C2×C22⋊D53—22no—
32C2×C22⋊D53—22no—
33C2×C22⋊D53—22no—
34C2×C22⋊D53—22no—
35C22×Dic53—22no—
36C22×Dic53D412yes—
37C2×D212—22no—
38C22⋊C4×C53—22no—
39C22⋊C4×C53—22no—
40C22⋊Dic53—22no—
41C22⋊Dic53D414yescomplemented
42#11719921—28no—
43#11719921—24no—
44C4⋊Dic53—22no—
45#11719919—28no—
46C23×C53—42no—
47C23×C53C2×D411yescharacteristic
48C23×C53C2×D412yes—
49C23×C53C2×D412yes—
50C23×C53C2×D411yescharacteristic
51C23×C53#4111yescharacteristic
52C22×D53—22no—
53C22×D53—22no—
54C22×D53—22no—
55C22×D53—44no—
56C2×C4×C53—22no—
57C2×C4×C53—24no—
58C2×C4×C53—22no—
59C2×C4×C53—41no—
60C2×C4×C53—42no—
61C2×C4×C53—41no—
62C2×C4×C53—42no—
63C2×C4×C53—42no—
64C2×C4×C53—41no—
65C22⋊D53—42no—
66C22⋊D53—42no—
67C22⋊D53—42no—
68C22⋊D53—42no—
69C2×Dic53—24no—
70C2×Dic53—22no—
71C2×Dic53—22no—
72C2×Dic53—22no—
73C2×Dic53—44no—
74D212—82no—
75C22×C53—24no—
76C22×C53—22no—
77C22×C53—41no—
78C22×C53—42no—
79C22×C53—41no—
80C22×C53#12011yescharacteristic
81C22×C53#12012yes—
82C22×C53#12112yes—
83C22×C53#12111yescharacteristic
84C22×C53#12711yescharacteristic
85C2×D53—44no—
86C2×D53—42no—
87C2×D53—44no—
88C2×D53—82no—
89C4×C53—42no—
90C4×C53—42no—
91C4×C53—81no—
92Dic53—44no—
93Dic53—42no—
94#2022—531nomaximal, Sylow
95C2×C53—22no—
96C2×C53—21no—
97C2×C53—22no—
98C2×C53—21no—
99C2×C53#39211yescharacteristic
100C2×C53#45812yes—
101D53—82no—
102#534—531no—
103C2×#123—532no—
104C2×#99—532no—
105#381D5311yescharacteristic, complemented
106#342—531no—
107C53#202211yescharacteristic, complemented, Sylow
108C22×D4—532no—
109C23×C4C2×D5311yescharacteristic
110#123—1062no—
111#123—1064no—
112#123—1064no—
113#121—1062no—
114#120—1062no—
115C2×C4⋊C4—1062no—
116C2×C22⋊C4—532no—
117C2×C22⋊C4—1062no—
118C2×C22⋊C4C2×D5311yescharacteristic
119C2×C22⋊C4C2×D5311yescharacteristic
120#99—1064no—
121#95—22no—
122C24—532no—
123C24C22×D5311yescharacteristic
124C2×D4—1062no—
125C2×D4—1062no—
126C2×D4—1062no—
127C2×D4—1062no—
128C2×D4—1062no—
129C2×D4—1062no—
130C2×D4—1062no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—532no—
137C22×C4—1062no—
138C22×C4D21212yescomplemented
139C22×C4C22⋊D5312yes—
140C4⋊C4—1068no—
141C4⋊C4—1062no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—534no—
145C22⋊C4—1068no—
146C22⋊C4—1064no—
147C22⋊C4—1062no—
148C23—42no—
149C23—1062no—
150C23—1062no—
151C23—1062no—
152C23—2124no—
153C23C2×D21211yescharacteristic
154C23#1171994511yescharacteristic
155C23D4×D5312yes—
156C23D4×D5312yes—
157C23C2×C22⋊D5311yescharacteristic
158D4—4242no—
159D4—2122no—
160D4—2122no—
161D4—2122no—
162D4—2122no—
163C2×C4—22no—
164C2×C4—24no—
165C2×C4—22no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—1062no—
173C2×C4—1064no—
174C2×C4—1062no—
175C2×C4—1062no—
176C2×C4—2124no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—4242no—
183C22—2124no—
184C22—2122no—
185C22—2124no—
186C22#1313318511yescharacteristic
187C22#1313318712yes—
188C22#1313319012yes—
189C22#1313319111yescharacteristic
190C22#1313321311yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—2124no—
195C4—2122no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—4242no—
201C2#1681053211yescharacteristic
202C2#1681081212yes—
subgroupG/H
centerC22#13133185
commutatorC24×C53C23
FrattiniC24C22×D53
FittingC53×#381C2
socleC22×C53#120
hypercenter#381D53
hypocenterC53#2022
LCSG ▷ C24×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#13133200C2semidirect
3. C2×#13133131C2semidirect
4. #16810390C2semidirect
5. C53×#381C2semidirect
28. C22×C4×C53D4semidirect
41. C22⋊Dic53D4semidirect
105. #381D53semidirect
107. C53#2022semidirect
138. C22×C4D212semidirect