Finite Group Databasebeta

← C2×#23782407 #35228656

Subgroups — C2×#23782407 #35228656

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#23782407C2116yesmaximal, direct product factor
2C2×#19104724C212yesmaximal, complemented
3C2×#19104723C212yesmaximal, complemented
4C2×#19104721C214yesmaximal, complemented
5C2×#19104705C214yesmaximal, complemented
6C2×#19104703C212yesmaximal, complemented
7C2×#124×C163C211yesmaximal, characteristic, complemented
8C24×D163C2212yescomplemented
9C22×Dic326C2212yescomplemented
10C22×D652C2212yes—
11C22×D652C2212yes—
12C22×C22⋊D163C2214yes—
13#19104724C22116yescomplemented
14#19104723C22116yescomplemented
15#19104721C22132yescomplemented
16#19104705C22132yescomplemented
17#19104703C22116yescomplemented
18C2×C22⋊Dic163C2212yescomplemented
19C2×(C2×D163)⋊C4C2214yescomplemented
20C2×(C2×D163)⋊C4C2214yescomplemented
21C2×(C2×D163)⋊C4C2214yescomplemented
22C2×C4×Dic163C2212yescomplemented
23C22×Q8×C163C2211yescharacteristic, complemented
24C22×D4×C163C2211yescharacteristic
25#124×C163C2218yescomplemented
26C2×C22⋊C4×C163C2214yescomplemented
27C2×C42×C163C2211yescharacteristic, complemented
28C23×D163—44no—
29C23×D163—48no—
30C23×D163C2314yes—
31C23×D163C2318yescomplemented
32C2×Dic326—44no—
33C2×Dic326C2318yescomplemented
34C2×D652—44no—
35C2×D652—44no—
36C2×D652C2318yes—
37C2×D652C2318yes—
38C2×C22⋊D163—48no—
39C2×C22⋊D163C23116yes—
40C22×Dic163C2314yes—
41C22⋊Dic163C2318yescomplemented
42(C2×D163)⋊C4C23116yescomplemented
43(C2×D163)⋊C4C23116yescomplemented
44(C2×D163)⋊C4C23116yescomplemented
45C4×Dic163C2318yescomplemented
46C24×C163C2312yes—
47C2×Q8×C163—42no—
48C2×Q8×C163C2314yescomplemented
49C2×D4×C163—42no—
50C2×D4×C163C2314yes—
51C22×C4×C163C2312yes—
52C22×C4×C163C2312yes—
53C22×C4×C163C2311yescharacteristic
54C22⋊C4×C163C23116yescomplemented
55C42×C163C2314yescomplemented
56C22×D163—28no—
57C22×D163—28no—
58C22×D163—28no—
59C22×D163—416no—
60C22×D163—48no—
61C22×D163—432no—
62C22×D163C2418yes—
63Dic326—48no—
64D652—48no—
65D652—48no—
66C22⋊D163—416no—
67C2×Dic163—28no—
68C2×Dic163C2418yes—
69C23×C163—24no—
70C23×C163—28no—
71C23×C163C2414yes—
72C23×C163C2411yescharacteristic
73Q8×C163—44no—
74D4×C163—44no—
75C2×C4×C163—22no—
76C2×C4×C163—24no—
77C2×C4×C163—24no—
78C2×C4×C163C2414yes—
79C2×C4×C163C2412yes—
80C2×C4×C163C2414yes—
81C22×C163—24no—
82C22×C163—28no—
83C22×C163—48no—
84C22×C163H(5,𝔽2)12yes—
85C22×C163H(5,𝔽2)14yes—
86C22×C163C2511yescharacteristic
87C2×D163—28no—
88C2×D163—28no—
89C2×D163—28no—
90C2×D163—432no—
91C2×D163—416no—
92C4×C163—22no—
93C4×C163—24no—
94C4×C163—24no—
95Dic163—28no—
96C2×C163—44no—
97C2×C163H(3,𝔽4)14yescomplemented
98C2×C163C2×H(5,𝔽2)11yescharacteristic
99C2×C163C2×H(5,𝔽2)12yes—
100D163—48no—
101C163C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
102C2×H(3,𝔽4)—1631nomaximal, Sylow
103H(3,𝔽4)—16316no—
104C2×#124—1632no—
105C2×#124—1634no—
106C2×#124—1632no—
107C2×#124D16311yescharacteristic, complemented
108C2×#120—1632no—
109C2×#120—1634no—
110C25—1632no—
111C22×Q8—1632no—
112C22×Q8C2×D16311yescharacteristic, complemented
113C22×D4—1634no—
114C22×D4—1632no—
115C22×D4—1632no—
116C22×D4C2×D16311yescharacteristic
117#124—16316no—
118#124—16332no—
119#124—16316no—
120#124C2×D16318yescomplemented
121#120—16316no—
122#120—16332no—
123C2×C22⋊C4—1632no—
124C2×C22⋊C4—1634no—
125C2×C22⋊C4—1634no—
126C2×C22⋊C4—1634no—
127C2×C22⋊C4C2×D16314yescomplemented
128C2×C42—1632no—
129C2×C42C2×D16311yescharacteristic, complemented
130C24—6524no—
131C24—6528no—
132C24—1634no—
133C24—1638no—
134C24C22×D16312yes—
135C2×Q8—42no—
136C2×Q8—6524no—
137C2×Q8—1638no—
138C2×Q8C22×D16314yescomplemented
139C2×D4—42no—
140C2×D4—6524no—
141C2×D4—6524no—
142C2×D4—6528no—
143C2×D4—16316no—
144C2×D4—1638no—
145C2×D4—1638no—
146C2×D4C22×D16314yes—
147C22×C4—1634no—
148C22×C4C22×D16312yes—
149C22×C4C22×D16311yescharacteristic
150C22×C4C22×D16312yes—
151C22⋊C4—1638no—
152C22⋊C4—16316no—
153C22⋊C4—16316no—
154C22⋊C4—16316no—
155C22⋊C4C22×D163116yescomplemented
156C42—1638no—
157C42C22×D16314yescomplemented
158C23—24no—
159C23—28no—
160C23—3268no—
161C23—3268no—
162C23—3268no—
163C23—6528no—
164C23—65216no—
165C23—65232no—
166C23—1638no—
167C23C23×D16314yes—
168C23C23×D16311yescharacteristic
169Q8—44no—
170Q8—6528no—
171D4—44no—
172D4—6528no—
173D4—6528no—
174D4—65216no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—3268no—
179C2×C4—1638no—
180C2×C4C23×D16314yes—
181C2×C4C23×D16312yes—
182C2×C4C23×D16314yes—
183C22—24no—
184C22—28no—
185C22—48no—
186C22—3268no—
187C22—3268no—
188C22—3268no—
189C22—65232no—
190C22—65216no—
191C22#1910478012yes—
192C22#1910478114yes—
193C22C24×D16311yescharacteristic
194C4—22no—
195C4—24no—
196C4—24no—
197C4—3268no—
198C2—44no—
199C2—6528no—
200C2#2378240714yesdirect product factor
201C2C2×#1910478011yescharacteristic
202C2C2×#1910478112yes—
subgroupG/H
centerC23C23×D163
commutator, cosocleC22×C163C25
FrattiniC22C24×D163
FittingC2×#124×C163C2
socleC23×C163C24
hypercenterC2×#124D163
hypocenterC163C2×H(3,𝔽4)
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. #23782407C2direct (N × H)
2. C2×#19104724C2semidirect
3. C2×#19104723C2semidirect
4. C2×#19104721C2semidirect
5. C2×#19104705C2semidirect
6. C2×#19104703C2semidirect
7. C2×#124×C163C2semidirect
8. C24×D163C22semidirect
9. C22×Dic326C22semidirect
13. #19104724C22semidirect
14. #19104723C22semidirect
15. #19104721C22semidirect
16. #19104705C22semidirect
17. #19104703C22semidirect
18. C2×C22⋊Dic163C22semidirect
19. C2×(C2×D163)⋊C4C22semidirect
20. C2×(C2×D163)⋊C4C22semidirect
21. C2×(C2×D163)⋊C4C22semidirect
22. C2×C4×Dic163C22semidirect
23. C22×Q8×C163C22semidirect
25. #124×C163C22semidirect
26. C2×C22⋊C4×C163C22semidirect
27. C2×C42×C163C22semidirect
31. C23×D163C23semidirect
33. C2×Dic326C23semidirect
41. C22⋊Dic163C23semidirect
42. (C2×D163)⋊C4C23semidirect
43. (C2×D163)⋊C4C23semidirect
44. (C2×D163)⋊C4C23semidirect
45. C4×Dic163C23semidirect
48. C2×Q8×C163C23semidirect
54. C22⋊C4×C163C23semidirect
55. C42×C163C23semidirect
97. C2×C163H(3,𝔽4)semidirect
101. C163C2×H(3,𝔽4)semidirect
107. C2×#124D163semidirect
112. C22×Q8C2×D163semidirect
120. #124C2×D163semidirect
127. C2×C22⋊C4C2×D163semidirect
129. C2×C42C2×D163semidirect
138. C2×Q8C22×D163semidirect
155. C22⋊C4C22×D163semidirect
157. C42C22×D163semidirect
200. C2#23782407direct (N × H)

Maximal subgroups

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

subgroupindex
#237824072
C2×#191047242
C2×#191047232
C2×#191047212
C2×#191047052
C2×#191047032
C2×#124×C1632
C2×H(3,𝔽4)163