Finite Group Databasebeta

← D4×D1304 #35226213

Subgroups — D4×D1304 #35226213

Order 20864.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×D1304C212yesmaximal, complemented
2D4×D652C212yesmaximal, complemented
3#23782042C211yesmaximal, characteristic, complemented
4#23781901C212yesmaximal, complemented
5#23781861C212yesmaximal, complemented
6#23781801C214yesmaximal, complemented
7C4×D1304C211yesmaximal, characteristic, complemented
8C8×D4×C163C211yesmaximal, characteristic, complemented
9C22×D652C2214yescomplemented
10C2×D4×D163—22no—
11C2×D1304—28no—
12C2×D1304C2211yescharacteristic
13C2×D1304C2212yescomplemented
14C2×D1304C2214yescomplemented
15C2×D1304C2212yescomplemented
16#19104732C2212yescomplemented
17#19104710—22no—
18#19104709C2214yescomplemented
19#19104705—24no—
20C4×D652C2212yescomplemented
21#19104669C2211yescharacteristic, complemented
22#19104657C2214yescomplemented
23#19104657C2212yescomplemented
24C22×C8×C163C2212yescomplemented
25C4×D4×C163C2211yescharacteristic
26C4⋊C8×C163C2211yescharacteristic, complemented
27C22⋊C8×C163C2212yescomplemented
28C4×C8×C163C2211yescharacteristic, complemented
29C23×D163—24no—
30C2×D652—28no—
31C2×D652—22no—
32C2×D652—24no—
33C2×D652—22no—
34C2×D652—44no—
35C2×D652C2314yes—
36C2×D652C2312yes—
37C2×C22⋊D163—24no—
38D4×D163—48no—
39C2×C4×D163—22no—
40D1304—28no—
41D1304—24no—
42D1304—42no—
43D1304D414yesdirect product factor
44C4⋊Dic163C2312yes—
45(C2×D163)⋊C4—22no—
46(C2×D163)⋊C4—24no—
47C2×D4×C163D411yescharacteristic
48C22×C4×C163C2312yes—
49C2×C8×C163—24no—
50C2×C8×C163C2311yescharacteristic
51C2×C8×C163C2312yes—
52C2×C8×C163C2311yescharacteristic
53C4⋊C4×C163D411yescharacteristic
54C22⋊C4×C163D412yes—
55C42×C163C2311yescharacteristic
56C22×D163—22no—
57C22×D163—24no—
58C22×D163—48no—
59C22×D163—48no—
60C22×D163—84no—
61D652—24no—
62D652—22no—
63D652—24no—
64D652—48no—
65D652—44no—
66D652—82no—
67D652C2×D414yescomplemented
68C22⋊D163—48no—
69C2×Dic163—22no—
70C4×D163—44no—
71C23×C163C2×D412yes—
72D4×C163D814yescomplemented
73C2×C4×C163—22no—
74C2×C4×C163—22no—
75C2×C4×C163C2×D411yescharacteristic
76C2×C4×C163C2×D412yes—
77C2×C4×C163C2×D411yescharacteristic
78C2×C4×C163C2411yescharacteristic
79C8×C163—22no—
80C8×C163—21no—
81C8×C163C2×D412yescomplemented
82C22×C163—22no—
83C22×C163—22no—
84C22×C163C2×D814yescomplemented
85C22×C163C22×D411yescharacteristic
86C2×D163—24no—
87C2×D163—42no—
88C2×D163—42no—
89C2×D163—44no—
90C2×D163—44no—
91C2×D163—44no—
92C2×D163—816no—
93C4×C163—22no—
94C4×C163—21no—
95C4×C163C2×D812yescomplemented
96C4×C163C22×D411yescharacteristic
97C4×C163H(5,𝔽2)11yescharacteristic
98Dic163—42no—
99C2×C163—24no—
100C2×C163D4211yescharacteristic
101C2×C163C22×D811yescharacteristic
102C2×C163#57611yescharacteristic
103D163—44no—
104D163—84no—
105C163D4×D811yescharacteristic, complemented, Sylow
106D4×D8—1631nomaximal, Sylow
107C22×D8—1632no—
108D42—1632no—
109#493—1631no—
110#466—1632no—
111#459—1632no—
112#447—1634no—
113C4×D8—1631no—
114C8×D4D16311yescharacteristic, complemented
115C22×D4—3262no—
116C22×D4—1634no—
117C2×D8—3268no—
118C2×D8—1634no—
119C2×D8—1632no—
120C2×D8—1632no—
121C2×D8—1631no—
122C22×C8C2×D16312yescomplemented
123#127—1632no—
124#121—3262no—
125#121—1634no—
126#120—3264no—
127C4×D4—1632no—
128C4×D4C2×D16311yescharacteristic
129#107—1631no—
130C4⋊C8C2×D16311yescharacteristic, complemented
131#102—1632no—
132#102—1634no—
133C22⋊C8C2×D16312yescomplemented
134C4×C8C2×D16311yescharacteristic, complemented
135C24—3264no—
136C2×D4—3268no—
137C2×D4—3264no—
138C2×D4—3262no—
139C2×D4—3264no—
140C2×D4—3262no—
141C2×D4—6524no—
142C2×D4—6528no—
143C2×D4—1634no—
144C2×D4—1632no—
145C2×D4D65211yescharacteristic
146C22×C4—3262no—
147C22×C4C22×D16312yes—
148D8—3268no—
149D8—3264no—
150D8—6522no—
151D8—1634no—
152C2×C8—24no—
153C2×C8C22×D16311yescharacteristic
154C2×C8C22×D16312yes—
155C2×C8C22×D16311yescharacteristic
156C4⋊C4—1632no—
157C4⋊C4D65211yescharacteristic
158C22⋊C4—3262no—
159C22⋊C4—3264no—
160C22⋊C4D65212yes—
161C42C22×D16311yescharacteristic
162C23—13044no—
163C23—3262no—
164C23—3264no—
165C23—6528no—
166C23—6528no—
167C23C2×D65212yes—
168D4—13042no—
169D4—3264no—
170D4—3262no—
171D4—3264no—
172D4—6528no—
173D4—6528no—
174D4—6524no—
175D4—1634no—
176D4D130414yesdirect product factor
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3262no—
180C2×C4—6524no—
181C2×C4C2×D65211yescharacteristic
182C2×C4C2×D65212yes—
183C2×C4C2×D65211yescharacteristic
184C2×C4C23×D16311yescharacteristic
185C8—22no—
186C8—21no—
187C8D4×D16312yescomplemented
188C22—22no—
189C22—22no—
190C22—130416no—
191C22—3264no—
192C22—6524no—
193C22—6524no—
194C22—6524no—
195C22—6522no—
196C22—6522no—
197C22C2×D130414yescomplemented
198C22C22×D65211yescharacteristic
199C4—21no—
200C4—22no—
201C4—6522no—
202C4C2×D130412yescomplemented
203C4C2×D4×D16311yescharacteristic
204C4#1910478111yescharacteristic
205C2—24no—
206C2—13044no—
207C2—6524no—
208C2D4×D65211yescharacteristic
209C2C22×D130411yescharacteristic
210C2#2378247011yescharacteristic
subgroupG/H
centerC22C22×D652
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC8×D4×C163C2
socleC22×C163C22×D4
hypercenterC8×D4D163
hypocenterC163D4×D8
LCSG ▷ C2×C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×D1304C2semidirect
2. D4×D652C2semidirect
3. #23782042C2semidirect
4. #23781901C2semidirect
5. #23781861C2semidirect
6. #23781801C2semidirect
7. C4×D1304C2semidirect
8. C8×D4×C163C2semidirect
9. C22×D652C22semidirect
13. C2×D1304C22semidirect
14. C2×D1304C22semidirect
15. C2×D1304C22semidirect
16. #19104732C22semidirect
18. #19104709C22semidirect
20. C4×D652C22semidirect
21. #19104669C22semidirect
22. #19104657C22semidirect
23. #19104657C22semidirect
24. C22×C8×C163C22semidirect
26. C4⋊C8×C163C22semidirect
27. C22⋊C8×C163C22semidirect
28. C4×C8×C163C22semidirect
43. D1304D4direct (N × H)
67. D652C2×D4semidirect
72. D4×C163D8semidirect
81. C8×C163C2×D4semidirect
84. C22×C163C2×D8semidirect
95. C4×C163C2×D8semidirect
105. C163D4×D8semidirect
114. C8×D4D163semidirect
122. C22×C8C2×D163semidirect
130. C4⋊C8C2×D163semidirect
133. C22⋊C8C2×D163semidirect
134. C4×C8C2×D163semidirect
176. D4D1304direct (N × H)
187. C8D4×D163semidirect
197. C22C2×D1304semidirect
202. C4C2×D1304semidirect

Maximal subgroups

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

subgroupindex
C22×D13042
D4×D6522
#237820422
#237819012
#237818612
#237818012
C4×D13042
C8×D4×C1632
D4×D8163