Finite Group Databasebeta

← C4×#19104727 #35217096

Subgroups — C4×#19104727 #35217096

Order 20864.

484 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C2×#19104727C211yesmaximal, characteristic
2#23781563C212yesmaximal
3#23781549C214yesmaximal
4#23781531C211yesmaximal, characteristic
5C4×Dic163⋊C4C214yesmaximal
6C4×C4⋊Dic163C212yesmaximal
7C43×C163C211yesmaximal, characteristic
8#19104727C418yesdirect product factor
9C2×C4⋊Dic163C2212yes—
10C2×C4⋊Dic163C2212yes—
11C2×Dic163⋊C4C2214yes—
12C2×Dic163⋊C4C2214yes—
13C2×C4×Dic163C2214yes—
14C163⋊#95C2214yes—
15C163⋊#95C2214yes—
16C163⋊#95C2214yes—
17C2×C42×C163C2212yes—
18C2×C42×C163C2212yes—
19C2×C42×C163C2211yescharacteristic
20C2×C42×C163C2211yescharacteristic
21C2×C42×C163C2211yescharacteristic
22C22×Dic163C2314yes—
23C22×Dic163C2314yes—
24C4⋊Dic163—24no—
25C4⋊Dic163C2×C418yes—
26Dic163⋊C4—28no—
27Dic163⋊C4C2×C4116yes—
28C4×Dic163—28no—
29C22×C4×C163C2312yes—
30C22×C4×C163C2311yescharacteristic
31C22×C4×C163C2312yes—
32C22×C4×C163C2311yescharacteristic
33C22×C4×C163C2311yescharacteristic
34C42×C163—24no—
35C42×C163—22no—
36C42×C163—24no—
37C42×C163C2×C414yes—
38C42×C163Q814yes—
39C2×Dic163—24no—
40C2×Dic163—24no—
41C2×Dic163—24no—
42C2×Dic163—24no—
43C2×Dic163—24no—
44C2×Dic163C22×C418yes—
45C23×C163C2411yescharacteristic
46C2×C4×C163—22no—
47C2×C4×C163—22no—
48C2×C4×C163—22no—
49C2×C4×C163—22no—
50C2×C4×C163—22no—
51C2×C4×C163C22×C414yes—
52C2×C4×C163C22×C412yes—
53C2×C4×C163C2×Q812yes—
54C2×C4×C163C2×Q812yes—
55C2×C4×C163C2×Q812yes—
56C2×C4×C163#4114yes—
57C2×C4×C163#4112yes—
58C2×C4×C163#4114yes—
59C22×C163C23×C411yescharacteristic
60C22×C163C22×Q811yescharacteristic
61C22×C163C2×#4111yescharacteristic
62C22×C163C2×#4112yes—
63C22×C163C2×#4112yes—
64C4×C163—24no—
65C4×C163—24no—
66C4×C163—22no—
67C4×C163C4×Q814yes—
68C4×C163#12514yescomplemented
69Dic163—28no—
70Dic163—44no—
71C2×C163C2×C4×Q811yescharacteristic
72C2×C163C4×#4112yes—
73C2×C163C2×#12511yescharacteristic
74C2×C163#52912yes—
75C2×C163#53311yescharacteristic
76C163C4×#12511yescharacteristic, complemented, Sylow
77C4×#125—1631nomaximal, Sylow
78C2×#125—1631no—
79#389—1632no—
80#387—1634no—
81#382—1631no—
82C4×C4⋊C4—1632no—
83C4×C4⋊C4—1634no—
84C43D16311yescharacteristic
85#125—1638no—
86C2×C4⋊C4—1632no—
87C2×C4⋊C4—1634no—
88C2×C4⋊C4—1634no—
89C2×C4⋊C4—1632no—
90C2×C42—1634no—
91C2×C42C2×D16312yes—
92C2×C42C2×D16311yescharacteristic
93C2×C42C2×D16312yes—
94C2×C42C2×D16311yescharacteristic
95C2×C42C2×D16311yescharacteristic
96#95—1634no—
97#95—1634no—
98#95—1634no—
99C22×C4—1634no—
100C22×C4—1634no—
101C22×C4C22×D16312yes—
102C22×C4C22×D16311yescharacteristic
103C22×C4C22×D16312yes—
104C22×C4C22×D16311yescharacteristic
105C22×C4C22×D16311yescharacteristic
106C4⋊C4—3268no—
107C4⋊C4—3264no—
108C4⋊C4—16316no—
109C4⋊C4—1638no—
110C42—24no—
111C42—22no—
112C42—24no—
113C42—3268no—
114C42C4×D16314yes—
115C42Dic32614yes—
116C23C23×D16311yescharacteristic
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—22no—
121C2×C4—22no—
122C2×C4—3264no—
123C2×C4—3264no—
124C2×C4—3264no—
125C2×C4—3264no—
126C2×C4—3264no—
127C2×C4—1638no—
128C2×C4C2×C4×D16314yes—
129C2×C4C2×C4×D16312yes—
130C2×C4C2×Dic32612yes—
131C2×C4C2×Dic32612yes—
132C2×C4C2×Dic32612yes—
133C2×C4#1457969914yes—
134C2×C4#1457969912yes—
135C2×C4#1457969914yes—
136C22C22×C4×D16311yescharacteristic
137C22C22×Dic32611yescharacteristic
138C22C2×#1457969912yes—
139C22C2×#1457969911yescharacteristic
140C22C2×#1457969912yes—
141C4—24no—
142C4—22no—
143C4—24no—
144C4—3268no—
145C4—6524no—
146C4C4×Dic32614yes—
147C4#1910472714yesdirect product factor
148C2C2×C4×Dic32611yescharacteristic
149C2C4×#1457969912yes—
150C2C2×#1910472711yescharacteristic
151C2#2378219912yes—
152C2#2378222211yescharacteristic
subgroupG/H
centerC22×C4C22×D163
commutatorC22×C163C23×C4
FrattiniC23C23×D163
FittingC43×C163C2
socle, prime radical, cosocleC23×C163C24
hypercenterC43D163
hypocenterC163C4×#125
LCSG ▷ C22×C163 ▷ C163
UCSC1 ◁ C22×C4 ◁ C43

Complements

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

NH ≅ G/Ntype
8. #19104727C4direct (N × H)
68. C4×C163#125semidirect
76. C163C4×#125semidirect
147. C4#19104727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191047272
#237815632
#237815492
#237815312
C4×Dic163⋊C42
C4×C4⋊Dic1632
C43×C1632
C4×#125163