Finite Group Databasebeta

← C2×#23781912 #35224125

Subgroups — C2×#23781912 #35224125

Order 20864.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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
1C22×#14579688C211yesmaximal, characteristic, complemented
2C22×#14579682C211yesmaximal, characteristic, complemented
3C2×#19104715C211yesmaximal, characteristic, complemented
4C2×#19104710C211yesmaximal, characteristic
5#23781912C218yesmaximal, direct product factor
6C2×#19104658C211yesmaximal, characteristic, complemented
7C2×#19104655C211yesmaximal, characteristic, complemented
8C2×#107×C163C211yesmaximal, characteristic, complemented
9C22×Dic326C2211yescharacteristic
10C22×D652—21no—
11C22×D652C2211yescharacteristic
12C22×C4×D163C2211yescharacteristic
13C2×#14579688—24no—
14C2×#14579688C2214yescomplemented
15C2×#14579682—24no—
16C2×#14579682C2214yescomplemented
17C22×C163⋊C8C2211yescharacteristic
18#19104715—22no—
19#19104715C2214yescomplemented
20#19104710—22no—
21#19104710C2214yes—
22C2×C4⋊Dic163—21no—
23C2×(C2×D163)⋊C4—21no—
24C2×(C2×D163)⋊C4—21no—
25#19104658C2214yescomplemented
26#19104655C2214yescomplemented
27C22×C8×C163C2211yescharacteristic
28C2×C4⋊C4×C163C2211yescharacteristic
29C2×C4⋊C4×C163C2211yescharacteristic
30#107×C163C2214yescomplemented
31C23×D163—21no—
32C23×D163D411yescharacteristic
33C2×Dic326—21no—
34C2×Dic326—22no—
35C2×Dic326—22no—
36C2×Dic326C2312yes—
37C2×D652—24no—
38C2×D652—22no—
39C2×D652—21no—
40C2×D652—22no—
41C2×D652—44no—
42C2×D652C2312yes—
43C22×Dic163—21no—
44C22×Dic163D411yescharacteristic
45C2×C4×D163—22no—
46C2×C4×D163—22no—
47C2×C4×D163D412yes—
48C2×C4×D163C2312yes—
49#14579688—28no—
50#14579682—28no—
51C2×C163⋊C8—22no—
52C2×C163⋊C8C2312yes—
53C4⋊Dic163—24no—
54(C2×D163)⋊C4—24no—
55(C2×D163)⋊C4—24no—
56C22×C4×C163—21no—
57C22×C4×C163—21no—
58C22×C4×C163C2311yescharacteristic
59C2×C8×C163D414yescomplemented
60C2×C8×C163C2312yes—
61C4⋊C4×C163—21no—
62C4⋊C4×C163—21no—
63C4⋊C4×C163C2312yes—
64C4⋊C4×C163C2312yes—
65C22×D163—22no—
66C22×D163—22no—
67C22×D163—22no—
68C22×D163—22no—
69C22×D163—42no—
70C22×D163—42no—
71C22×D163—42no—
72C22×D163C2×D412yes—
73Dic326—22no—
74Dic326—22no—
75Dic326—42no—
76D652—22no—
77D652—22no—
78D652—48no—
79D652—42no—
80C2×Dic163—22no—
81C2×Dic163—22no—
82C2×Dic163—42no—
83C2×Dic163C2×D412yes—
84C4×D163—24no—
85C4×D163—22no—
86C4×D163—22no—
87C163⋊C8—22no—
88C23×C163C2×D411yescharacteristic
89C2×C4×C163—22no—
90C2×C4×C163—22no—
91C2×C4×C163—42no—
92C2×C4×C163—42no—
93C2×C4×C163C2×D411yescharacteristic
94C2×C4×C163C2×D412yes—
95C2×C4×C163#4112yes—
96C2×C4×C163C2411yescharacteristic
97C8×C163C2×D414yescomplemented
98C22×C163#12112yes—
99C22×C163AGL(1,ℤ/8)12yes—
100C22×C163#13712yes—
101C22×C163C22×D411yescharacteristic
102C2×D163—22no—
103C2×D163—22no—
104C2×D163—22no—
105C2×D163—44no—
106C2×D163—42no—
107C2×D163—42no—
108C2×D163—42no—
109C2×D163—84no—
110C4×C163—42no—
111C4×C163—42no—
112C4×C163#12112yes—
113C4×C163C22×D411yescharacteristic
114C4×C163C2×#4111yescharacteristic
115Dic163—22no—
116Dic163—42no—
117C2×C163#46814yescomplemented
118C2×C163C2×#12111yescharacteristic
119C2×C163C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C163C2×#13711yescharacteristic
121D163—42no—
122D163—82no—
123C163C2×#46811yescharacteristic, complemented, Sylow
124C2×#468—1631nomaximal, Sylow
125C22×SD16—1631no—
126C22×M16—1631no—
127C2×C22⋊Q8—1631no—
128C2×#121—1631no—
129#468—1638no—
130C2×#107D16311yescharacteristic, complemented
131C2×#103—1631no—
132C2×#102—1631no—
133C22×Q8—1631no—
134C22×D4—3261no—
135C22×D4—1631no—
136C23×C4—1631no—
137C2×SD16—3264no—
138C2×SD16—1634no—
139C2×M16—3264no—
140C2×M16—1634no—
141C22×C8—1631no—
142C22×C8C2×D16311yescharacteristic
143C22⋊Q8—3262no—
144C22⋊Q8—1634no—
145#121—3262no—
146#121—1634no—
147C2×C4⋊C4—3261no—
148C2×C4⋊C4C2×D16311yescharacteristic
149C2×C4⋊C4C2×D16311yescharacteristic
150C2×C22⋊C4—3261no—
151C2×C22⋊C4—3261no—
152#107C2×D16314yescomplemented
153#103—1634no—
154#102—1634no—
155C24—3261no—
156C24—1631no—
157C2×Q8—3261no—
158C2×Q8—3262no—
159C2×Q8—3262no—
160C2×Q8—1632no—
161C2×D4—3264no—
162C2×D4—3261no—
163C2×D4—3262no—
164C2×D4—3262no—
165C2×D4—6524no—
166C2×D4—1632no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—3262no—
170C22×C4—3262no—
171C22×C4—3261no—
172C22×C4—1631no—
173C22×C4—1632no—
174C22×C4—1632no—
175C22×C4C22×D16311yescharacteristic
176SD16—3268no—
177M16—3268no—
178C2×C8—3262no—
179C2×C8—1632no—
180C2×C8D65214yescomplemented
181C2×C8C22×D16312yes—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—3264no—
185C4⋊C4C22×D16312yes—
186C4⋊C4C22×D16312yes—
187C22⋊C4—3264no—
188C22⋊C4—3264no—
189C23—3262no—
190C23—3262no—
191C23—3262no—
192C23—3262no—
193C23—6522no—
194C23—6522no—
195C23—6522no—
196C23—1632no—
197C23D4×D16311yescharacteristic
198Q8—3262no—
199Q8—3262no—
200Q8—6522no—
201D4—3262no—
202D4—3262no—
203D4—6528no—
204D4—6522no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—3262no—
210C2×C4—3262no—
211C2×C4—3262no—
212C2×C4—3264no—
213C2×C4—3262no—
214C2×C4—6522no—
215C2×C4—1632no—
216C2×C4D4×D16311yescharacteristic
217C2×C4C2×D65212yes—
218C2×C4#1457970012yes—
219C2×C4C23×D16311yescharacteristic
220C8—3262no—
221C8C2×D65214yescomplemented
222C22—13044no—
223C22—3262no—
224C22—3262no—
225C22—3262no—
226C22—6522no—
227C22—6522no—
228C22—6522no—
229C22—6524no—
230C22#1910471012yes—
231C22#1910475912yes—
232C22#1910476712yes—
233C22C2×D4×D16311yescharacteristic
234C4—42no—
235C4—42no—
236C4—3262no—
237C4—6522no—
238C4#1910471012yes—
239C4C22×D65211yescharacteristic
240C4C2×#1457970011yescharacteristic
241C2—13042no—
242C2—6522no—
243C2#2378191214yesdirect product factor
244C2C2×#1910471011yescharacteristic
245C2C2×#1910475911yescharacteristic
246C2C2×#1910476711yescharacteristic
subgroupG/H
centerC23D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC2×#107×C163C2
socleC23×C163C2×D4
prime radicalC2×#19104710C2
hypercenterC2×#107D163
hypocenterC163C2×#468
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C22×#14579688C2semidirect
2. C22×#14579682C2semidirect
3. C2×#19104715C2semidirect
5. #23781912C2direct (N × H)
6. C2×#19104658C2semidirect
7. C2×#19104655C2semidirect
8. C2×#107×C163C2semidirect
14. C2×#14579688C22semidirect
16. C2×#14579682C22semidirect
19. #19104715C22semidirect
25. #19104658C22semidirect
26. #19104655C22semidirect
30. #107×C163C22semidirect
59. C2×C8×C163D4semidirect
97. C8×C163C2×D4semidirect
117. C2×C163#468semidirect
123. C163C2×#468semidirect
130. C2×#107D163semidirect
152. #107C2×D163semidirect
180. C2×C8D652semidirect
221. C8C2×D652semidirect
243. C2#23781912direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145796882
C22×#145796822
C2×#191047152
C2×#191047102
#237819122
C2×#191046582
C2×#191046552
C2×#107×C1632
C2×#468163