Finite Group Databasebeta

← C2×#23782408 #35228657

Subgroups — C2×#23782408 #35228657

Order 20864.

1408 conjugacy classes of subgroups; only the 469 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 469 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#23782408C2116yesmaximal, direct product factor
2C2×#19104722C213yesmaximal, complemented
3C2×#19104721C216yesmaximal, complemented
4C2×#19104704C212yesmaximal, complemented
5C2×#19104703C213yesmaximal, complemented
6C2×#120×C163C211yesmaximal, characteristic, complemented
7C24×D163C2211yescharacteristic, complemented
8C22×Dic326C2213yescomplemented
9C22×C22⋊D163C2216yes—
10#19104722C22124yescomplemented
11#19104721C22148yescomplemented
12#19104704C22116yescomplemented
13#19104703C22124yescomplemented
14C2×C22⋊Dic163C2213yescomplemented
15C2×C22⋊Dic163C2216yescomplemented
16C2×(C2×D163)⋊C4C2216yescomplemented
17C2×C4×Dic163C2213yescomplemented
18C25×C163C2211yescharacteristic, complemented
19C22×D4×C163C2213yes—
20#120×C163C2218yescomplemented
21C2×C22⋊C4×C163C2213yescomplemented
22C23×D163—46no—
23C23×D163C2312yes—
24C23×D163C2314yescomplemented
25C2×Dic326—46no—
26C2×Dic326C23112yescomplemented
27C2×C22⋊D163—412no—
28C2×C22⋊D163C23124yes—
29C22×Dic163C2316yes—
30C22⋊Dic163C23112yescomplemented
31C22⋊Dic163C23124yescomplemented
32(C2×D163)⋊C4C23124yescomplemented
33C4×Dic163C23112yescomplemented
34C24×C163—46no—
35C24×C163C2313yes—
36C24×C163C2311yescharacteristic
37C24×C163C2314yescomplemented
38C2×D4×C163—46no—
39C2×D4×C163C23112yes—
40C22×C4×C163C2313yes—
41C22⋊C4×C163C23112yescomplemented
42C22×D163—212no—
43C22×D163—412no—
44C22×D163—416no—
45C22×D163C2414yes—
46Dic326—412no—
47C22⋊D163—424no—
48C2×Dic163—212no—
49C2×Dic163C24112yes—
50C23×C163—26no—
51C23×C163—26no—
52C23×C163—212no—
53C23×C163—412no—
54C23×C163—416no—
55C23×C163C2416yes—
56C23×C163C2412yes—
57C23×C163C2411yescharacteristic
58D4×C163—412no—
59C2×C4×C163—26no—
60C2×C4×C163C2416yes—
61C22×C163—26no—
62C22×C163—26no—
63C22×C163—212no—
64C22×C163—416no—
65C22×C163—412no—
66C22×C163—44no—
67C22×C163H(5,𝔽2)16yes—
68C22×C163C2511yescharacteristic
69C2×D163—212no—
70C2×D163—416no—
71C2×D163—48no—
72C4×C163—26no—
73Dic163—212no—
74C2×C163—42no—
75C2×C163—46no—
76C2×C163H(3,𝔽4)14yescomplemented
77C2×C163C2×H(5,𝔽2)13yes—
78D163—44no—
79C163C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
80C2×H(3,𝔽4)—1631nomaximal, Sylow
81H(3,𝔽4)—16316no—
82C2×#124—1633no—
83C2×#124—1636no—
84C2×#120—1632no—
85C2×#120—1633no—
86C2×#120D16311yescharacteristic, complemented
87C25—1631no—
88C25C2×D16311yescharacteristic, complemented
89C22×Q8—1633no—
90C22×D4—1636no—
91C22×D4C2×D16313yes—
92#124—16324no—
93#124—16348no—
94#120—16316no—
95#120—16324no—
96#120C2×D16318yescomplemented
97C2×C22⋊C4—1633no—
98C2×C22⋊C4—1636no—
99C2×C22⋊C4—1636no—
100C2×C22⋊C4C2×D16313yescomplemented
101C2×C42—1633no—
102C24—46no—
103C24—6526no—
104C24—1632no—
105C24—1634no—
106C24C22×D16311yescharacteristic
107C24C22×D16313yes—
108C24C22×D16314yescomplemented
109C2×Q8—6526no—
110C2×Q8—16312no—
111C2×D4—46no—
112C2×D4—65212no—
113C2×D4—16324no—
114C2×D4C22×D163112yes—
115C22×C4—1636no—
116C22×C4C22×D16313yes—
117C22⋊C4—16312no—
118C22⋊C4—16324no—
119C22⋊C4—16324no—
120C22⋊C4C22×D163112yescomplemented
121C42—16312no—
122C23—26no—
123C23—26no—
124C23—212no—
125C23—412no—
126C23—416no—
127C23—32612no—
128C23—65212no—
129C23—65216no—
130C23—1634no—
131C23C23×D16312yes—
132C23C23×D16316yes—
133C23C23×D16311yescharacteristic
134Q8—65212no—
135D4—412no—
136D4—65224no—
137C2×C4—26no—
138C2×C4—32612no—
139C2×C4—16312no—
140C2×C4C23×D16316yes—
141C22—26no—
142C22—26no—
143C22—212no—
144C22—416no—
145C22—412no—
146C22—44no—
147C22—32612no—
148C22—65216no—
149C22—6528no—
150C22#1910478016yes—
151C22C24×D16311yescharacteristic
152C4—26no—
153C4—32612no—
154C2—46no—
155C2—42no—
156C2—6524no—
157C2#2378240814yesdirect product factor
158C2C2×#1910478013yes—
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#120×C163C2
socleC23×C163C24
hypercenterC2×#120D163
hypocenterC163C2×H(3,𝔽4)
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. #23782408C2direct (N × H)
2. C2×#19104722C2semidirect
3. C2×#19104721C2semidirect
4. C2×#19104704C2semidirect
5. C2×#19104703C2semidirect
6. C2×#120×C163C2semidirect
7. C24×D163C22semidirect
8. C22×Dic326C22semidirect
10. #19104722C22semidirect
11. #19104721C22semidirect
12. #19104704C22semidirect
13. #19104703C22semidirect
14. C2×C22⋊Dic163C22semidirect
15. C2×C22⋊Dic163C22semidirect
16. C2×(C2×D163)⋊C4C22semidirect
17. C2×C4×Dic163C22semidirect
18. C25×C163C22semidirect
20. #120×C163C22semidirect
21. C2×C22⋊C4×C163C22semidirect
24. C23×D163C23semidirect
26. C2×Dic326C23semidirect
30. C22⋊Dic163C23semidirect
31. C22⋊Dic163C23semidirect
32. (C2×D163)⋊C4C23semidirect
33. C4×Dic163C23semidirect
37. C24×C163C23semidirect
41. C22⋊C4×C163C23semidirect
76. C2×C163H(3,𝔽4)semidirect
79. C163C2×H(3,𝔽4)semidirect
86. C2×#120D163semidirect
88. C25C2×D163semidirect
96. #120C2×D163semidirect
100. C2×C22⋊C4C2×D163semidirect
108. C24C22×D163semidirect
120. C22⋊C4C22×D163semidirect
157. C2#23782408direct (N × H)

Maximal subgroups

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

subgroupindex
#237824082
C2×#191047222
C2×#191047212
C2×#191047042
C2×#191047032
C2×#120×C1632
C2×H(3,𝔽4)163