Finite Group Databasebeta

← #35213112

Subgroups — #35213112

Order 20864.

218 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 61 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#23782201C211yesmaximal, characteristic
2#23781715C211yesmaximal, characteristic, complemented
3#23781532C211yesmaximal, characteristic, complemented
4#23781402C211yesmaximal, characteristic, complemented
5#23781400C211yesmaximal, characteristic
6#23781398C211yesmaximal, characteristic
7#328×C163C211yesmaximal, characteristic, complemented
8#19104730—21no—
9#19104726C411yescharacteristic, complemented
10#19104724C411yescharacteristic, complemented
11#19104719—21no—
12#19104709C2211yescharacteristic
13Q8×Dic163C411yescharacteristic, complemented
14#19104697C411yescharacteristic, complemented
15(C22⋊D163)⋊C4—21no—
16#19104693—21no—
17C2×C4×Dic163C2211yescharacteristic
18Dic163⋊C8—21no—
19C22⋊(C163⋊C8)C2211yescharacteristic
20C8×Dic163—21no—
21C163⋊#95—21no—
22C163⋊#95—21no—
23C163⋊#95C2211yescharacteristic
24C22⋊Q8×C163C2211yescharacteristic
25C22⋊C8×C163C2211yescharacteristic
26#95×C163C2211yescharacteristic
27C2×D652C2×C411yescharacteristic
28C2×C22⋊D163—21no—
29C22×Dic163—21no—
30C22×Dic163D411yescharacteristic
31C22×Dic163D411yescharacteristic
32C2×C4×D163—21no—
33C2×C163⋊C8—21no—
34C4⋊Dic163—21no—
35C4⋊Dic163—21no—
36C4⋊Dic163C2×C411yescharacteristic
37Dic163⋊C4—21no—
38(C2×D163)⋊C4—21no—
39(C2×D163)⋊C4—21no—
40(C2×D163)⋊C4—21no—
41(C2×D163)⋊C4—21no—
42C4×Dic163—21no—
43C4×Dic163C2×C411yescharacteristic
44C4×Dic163C2×C411yescharacteristic
45C4×Dic163D411yescharacteristic
46C4×Dic163D411yescharacteristic
47C2×Q8×C163C2×C411yescharacteristic
48C22×C4×C163—21no—
49C22×C4×C163C2311yescharacteristic
50C2×C8×C163—21no—
51C4⋊C4×C163—21no—
52C4⋊C4×C163C2×C411yescharacteristic
53C22⋊C4×C163—21no—
54C22×D163—21no—
55D652—41no—
56C22⋊D163—41no—
57C22⋊D163—41no—
58C2×Dic163—21no—
59C2×Dic163—21no—
60C2×Dic163—21no—
61C2×Dic163—41no—
62C2×Dic163—41no—
63C2×Dic163—41no—
64C2×Dic163—41no—
65C2×Dic163C22⋊C411yescharacteristic
66C2×Dic163C22⋊C411yescharacteristic
67C2×Dic163C22⋊C411yescharacteristic
68C2×Dic163C22⋊C411yescharacteristic
69C4×D163—42no—
70C163⋊C8—41no—
71C23×C163C2×D411yescharacteristic
72Q8×C163—41no—
73C2×C4×C163—21no—
74C2×C4×C163—21no—
75C2×C4×C163—41no—
76C2×C4×C163—41no—
77C2×C4×C163—41no—
78C2×C4×C163—41no—
79C2×C4×C163C22×C411yescharacteristic
80C2×C4×C163C2×D411yescharacteristic
81C8×C163—41no—
82C22×C163—21no—
83C22×C163—21no—
84C22×C163C2×C22⋊C411yescharacteristic
85C22×C163#13511yescharacteristic
86C22×C163#13511yescharacteristic
87C2×D163—41no—
88C2×D163—41no—
89C2×D163—41no—
90C4×C163—21no—
91C4×C163—21no—
92C4×C163—41no—
93C4×C163—41no—
94C4×C163—81no—
95Dic163—21no—
96Dic163—21no—
97Dic163—21no—
98Dic163—21no—
99Dic163—41no—
100Dic163—81no—
101C2×C163—21no—
102C2×C163—21no—
103C2×C163#41011yescharacteristic
104C2×C163#41611yescharacteristic
105C2×C163#42111yescharacteristic
106D163—81no—
107C163#152111yescharacteristic, complemented, Sylow
108#1521—1631nomaximal, Sylow
109#529—1631no—
110#431—1631no—
111#383—1631no—
112#328—1631no—
113#328D16311yescharacteristic, complemented
114#327—1631no—
115#327—1631no—
116#126—3261no—
117#125—1631no—
118#124—1631no—
119#123—3261no—
120C22⋊Q8C2×D16311yescharacteristic
121#121—1631no—
122C4×Q8—1631no—
123C4×D4—3261no—
124C4×D4—1631no—
125#117—3261no—
126C2×C42—1631no—
127C4⋊C8—3261no—
128C22⋊C8—1631no—
129C22⋊C8C2×D16311yescharacteristic
130C4×C8—3261no—
131#95—3261no—
132#95—3261no—
133#95—1631no—
134#95C2×D16311yescharacteristic
135C2×Q8C4×D16311yescharacteristic
136C2×D4—3261no—
137C2×D4—1631no—
138C22×C4—21no—
139C22×C4—3261no—
140C22×C4—3261no—
141C22×C4—1631no—
142C22×C4—1631no—
143C22×C4C22×D16311yescharacteristic
144C2×C8—21no—
145C2×C8—3261no—
146C4⋊C4—21no—
147C4⋊C4—3261no—
148C4⋊C4—3261no—
149C4⋊C4—3261no—
150C4⋊C4—1631no—
151C4⋊C4C4×D16311yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—3261no—
154C22⋊C4—3261no—
155C22⋊C4—3261no—
156C22⋊C4—3261no—
157C42—3261no—
158C42—1631no—
159C42—1631no—
160C42—1631no—
161C42—1631no—
162C23—3261no—
163C23D4×D16311yescharacteristic
164Q8—41no—
165D4—6521no—
166D4—6521no—
167D4—6521no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—3261no—
175C2×C4—3261no—
176C2×C4—3261no—
177C2×C4—6522no—
178C2×C4—6521no—
179C2×C4—6521no—
180C2×C4—6521no—
181C2×C4—6521no—
182C2×C4—1631no—
183C2×C4—1631no—
184C2×C4—1631no—
185C2×C4—1631no—
186C2×C4C2×C4×D16311yescharacteristic
187C2×C4D4×D16311yescharacteristic
188C8—41no—
189C8—6521no—
190C22—21no—
191C22—21no—
192C22—6521no—
193C22—6521no—
194C22—6521no—
195C22C22⋊C4×D16311yescharacteristic
196C22#1910475611yescharacteristic
197C22#1910475811yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—41no—
202C4—81no—
203C4—13041no—
204C4—3261no—
205C4—3261no—
206C4—3261no—
207C4—3261no—
208C4—6521no—
209C2—21no—
210C2—21no—
211C2—13041no—
212C2#2378163711yescharacteristic
213C2#2378166011yescharacteristic
214C2#2378168011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D163
commutatorC2×C4×C163C22×C4
FrattiniC22×C4C22×D163
Fitting#328×C163C2
socleC22×C163C2×C22⋊C4
prime radical#19104709C22
cosocleC22×C4×C163C23
hypercenter#328D163
hypocenterC163#1521
LCSG ▷ C2×C4×C163 ▷ C22×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #23781715C2semidirect
3. #23781532C2semidirect
4. #23781402C2semidirect
7. #328×C163C2semidirect
9. #19104726C4semidirect
10. #19104724C4semidirect
13. Q8×Dic163C4semidirect
14. #19104697C4semidirect
107. C163#1521semidirect
113. #328D163semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237822012
#237817152
#237815322
#237814022
#237814002
#237813982
#328×C1632
#1521163