Finite Group Databasebeta

← C2×#23781907 #35224111

Subgroups — C2×#23781907 #35224111

Order 20864.

512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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×Dic652C211yesmaximal, characteristic, complemented
2C22×C8×D163C211yesmaximal, characteristic
3C2×#19104715C212yesmaximal
4#23781907C218yesmaximal, direct product factor
5C2×#19104658C212yesmaximal, complemented
6C2×#107×C163C211yesmaximal, characteristic, complemented
7C22×Dic326C2212yes—
8C22×C4×D163C2211yescharacteristic
9C2×Dic652—24no—
10C2×Dic652C2214yescomplemented
11C22×C163⋊C8C2211yescharacteristic
12C2×C8×D163—24no—
13C2×C8×D163C2214yes—
14#19104715—24no—
15#19104715C2218yes—
16C2×C4⋊Dic163—22no—
17C2×(C2×D163)⋊C4—22no—
18#19104658C2218yescomplemented
19C22×C8×C163C2211yescharacteristic
20C2×C4⋊C4×C163C2212yes—
21#107×C163C2214yescomplemented
22C23×D163D411yescharacteristic
23C2×Dic326—22no—
24C2×Dic326—24no—
25C2×Dic326—24no—
26C2×Dic326C2314yes—
27C22×Dic163—22no—
28C22×Dic163D411yescharacteristic
29C2×C4×D163—22no—
30C2×C4×D163—22no—
31C2×C4×D163D412yes—
32C2×C4×D163C2312yes—
33Dic652—28no—
34C2×C163⋊C8—22no—
35C2×C163⋊C8C2312yes—
36C8×D163—28no—
37C4⋊Dic163—28no—
38(C2×D163)⋊C4—28no—
39C22×C4×C163—22no—
40C22×C4×C163C2311yescharacteristic
41C2×C8×C163D414yes—
42C2×C8×C163C2312yes—
43C4⋊C4×C163—22no—
44C4⋊C4×C163C2314yes—
45C22×D163—22no—
46C22×D163—22no—
47C22×D163Q1614yescomplemented
48C22×D163C2×D412yes—
49Dic326—24no—
50Dic326—24no—
51Dic326—44no—
52C2×Dic163—22no—
53C2×Dic163—24no—
54C2×Dic163—44no—
55C2×Dic163C2×D412yes—
56C4×D163—24no—
57C4×D163—22no—
58C4×D163—22no—
59C163⋊C8—22no—
60C23×C163C2×D411yescharacteristic
61C2×C4×C163—24no—
62C2×C4×C163—44no—
63C2×C4×C163C2×D411yescharacteristic
64C2×C4×C163C2×D412yes—
65C2×C4×C163#4112yes—
66C2×C4×C163C2411yescharacteristic
67C8×C163C2×D414yes—
68C22×C163#12112yes—
69C22×C163C2×Q1612yes—
70C22×C163#13512yes—
71C22×C163C22×D411yescharacteristic
72C2×D163—22no—
73C2×D163—22no—
74C2×D163—28no—
75C2×D163C2×Q1614yescomplemented
76C4×C163—44no—
77C4×C163#12112yes—
78C4×C163C22×D411yescharacteristic
79C4×C163C2×#4111yescharacteristic
80Dic163—22no—
81Dic163—44no—
82C2×C163#46714yescomplemented
83C2×C163C2×#12111yescharacteristic
84C2×C163C22×Q1611yescharacteristic
85C2×C163C2×#13511yescharacteristic
86D163—24no—
87C163C2×#46711yescharacteristic, complemented, Sylow
88C2×#467—1631nomaximal, Sylow
89C22×Q16—1631no—
90C23×C8—1631no—
91C2×C22⋊Q8—1632no—
92#467—1638no—
93C2×#107D16311yescharacteristic, complemented
94C2×#103—1632no—
95C22×Q8—1632no—
96C23×C4—1631no—
97C2×Q16—3264no—
98C2×Q16—1634no—
99C22×C8—3264no—
100C22×C8—1631no—
101C22×C8—1634no—
102C22×C8C2×D16311yescharacteristic
103C22⋊Q8—3264no—
104C22⋊Q8—1638no—
105C2×C4⋊C4—3262no—
106C2×C4⋊C4C2×D16312yes—
107C2×C22⋊C4—3262no—
108#107C2×D16314yescomplemented
109#103—1638no—
110C24—1631no—
111C2×Q8—3262no—
112C2×Q8—3264no—
113C2×Q8—3264no—
114C2×Q8—1634no—
115C22×C4—22no—
116C22×C4—3262no—
117C22×C4—3262no—
118C22×C4—3262no—
119C22×C4—1631no—
120C22×C4—1632no—
121C22×C4—1632no—
122C22×C4C22×D16311yescharacteristic
123Q16—3268no—
124C2×C8—3262no—
125C2×C8—3268no—
126C2×C8—1632no—
127C2×C8D65214yes—
128C2×C8C22×D16312yes—
129C4⋊C4—22no—
130C4⋊C4—3268no—
131C4⋊C4C22×D16314yes—
132C22⋊C4—3268no—
133C23—3262no—
134C23—3262no—
135C23—1632no—
136C23—1634no—
137C23D4×D16311yescharacteristic
138Q8—3264no—
139Q8—3264no—
140Q8—6524no—
141C2×C4—24no—
142C2×C4—44no—
143C2×C4—3262no—
144C2×C4—3262no—
145C2×C4—3262no—
146C2×C4—3264no—
147C2×C4—3264no—
148C2×C4—6524no—
149C2×C4—1632no—
150C2×C4D4×D16311yescharacteristic
151C2×C4C2×D65212yes—
152C2×C4#1457970012yes—
153C2×C4C23×D16311yescharacteristic
154C8—3262no—
155C8C2×D65214yes—
156C22—3262no—
157C22—3268no—
158C22—3262no—
159C22—1634no—
160C22#1910471012yes—
161C22Q16×D16312yes—
162C22#1910475412yes—
163C22C2×D4×D16311yescharacteristic
164C4—44no—
165C4—3262no—
166C4—6524no—
167C4#1910471012yes—
168C4C22×D65211yescharacteristic
169C4C2×#1457970011yescharacteristic
170C2—3264no—
171C2#2378190714yesdirect product factor
172C2C2×#1910471011yescharacteristic
173C2C2×Q16×D16311yescharacteristic
174C2C2×#1910475411yescharacteristic
subgroupG/H
centerC23D4×D163
commutator, cosocleC2×C4×C163C24
FrattiniC2×C4C23×D163
FittingC2×#107×C163C2
socleC23×C163C2×D4
prime radicalC23×D163D4
hypercenterC2×#107D163
hypocenterC163C2×#467
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×Dic652C2semidirect
4. #23781907C2direct (N × H)
5. C2×#19104658C2semidirect
6. C2×#107×C163C2semidirect
10. C2×Dic652C22semidirect
18. #19104658C22semidirect
21. #107×C163C22semidirect
47. C22×D163Q16semidirect
75. C2×D163C2×Q16semidirect
82. C2×C163#467semidirect
87. C163C2×#467semidirect
93. C2×#107D163semidirect
108. #107C2×D163semidirect
171. C2#23781907direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Dic6522
C22×C8×D1632
C2×#191047152
#237819072
C2×#191046582
C2×#107×C1632
C2×#467163