Finite Group Databasebeta

← C22×#19104697 #35227706

Subgroups — C22×#19104697 #35227706

Order 20864.

2528 conjugacy classes of subgroups; only the 941 normal subgroups are shown.

normal subgroups only

This group has 2528 conjugacy classes of subgroups — too many to draw. Only its 941 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
1C23×D652C211yesmaximal, characteristic
2C23×C4×D163C212yesmaximal, complemented
3C2×#19104697C2124yesmaximal, direct product factor
4C22×(C2×D163)⋊C4C212yesmaximal, complemented
5C22×C4×Dic163C211yesmaximal, characteristic, complemented
6C22×C4⋊C4×C163C211yesmaximal, characteristic, complemented
7C24×D163C2212yes—
8C22×D652C4116yescomplemented
9C22×D652C22112yes—
10C23×Dic163C2211yescharacteristic
11C23×Dic163C2211yescharacteristic
12C22×C4×D163—216no—
13C22×C4×D163C22124yescomplemented
14#19104697C22164yesdirect product factor
15C2×(C2×D163)⋊C4C22124yescomplemented
16C2×C4×Dic163C22112yescomplemented
17C23×C4×C163C2212yes—
18C23×C4×C163C2211yescharacteristic
19C2×C4⋊C4×C163C22112yescomplemented
20C23×D163—28no—
21C23×D163—28no—
22C23×D163C2×C4116yescomplemented
23C23×D163C23112yes—
24C2×D652C2×C4196yescomplemented
25C2×D652C23116yes—
26C22×Dic163—24no—
27C22×Dic163D418yescomplemented
28C22×Dic163C2316yes—
29C22×Dic163C2316yes—
30C2×C4×D163—296no—
31C2×C4×D163C23132yescomplemented
32(C2×D163)⋊C4C23132yescomplemented
33C4×Dic163C23116yescomplemented
34C24×C163C2311yescharacteristic
35C22×C4×C163—28no—
36C22×C4×C163C2×C418yescomplemented
37C22×C4×C163C23112yes—
38C22×C4×C163C2316yes—
39C4⋊C4×C163C23116yescomplemented
40C22×D163—264no—
41C22×D163—224no—
42C22×D163—224no—
43C22×D163C22×C4148yescomplemented
44C22×D163C2418yes—
45D652C22×C4164yescomplemented
46C2×Dic163—212no—
47C2×Dic163C2×D4124yescomplemented
48C2×Dic163C2414yes—
49C2×Dic163C2414yes—
50C4×D163—264no—
51C23×C163C22×C414yes—
52C23×C163C2×D414yes—
53C23×C163#4114yes—
54C23×C163C2413yes—
55C2×C4×C163—224no—
56C2×C4×C163C22×C4124yescomplemented
57C2×C4×C163C2418yes—
58C2×C4×C163C2414yes—
59C22×C163C4×D4116yescomplemented
60C22×C163C23×C416yes—
61C22×C163C22×D416yes—
62C22×C163C2×#4116yes—
63C22×C163C2511yescharacteristic
64C2×D163—296no—
65C2×D163—28no—
66C2×D163—28no—
67C2×D163C23×C4116yescomplemented
68C4×C163—28no—
69C4×C163C23×C418yescomplemented
70Dic163—24no—
71Dic163C22×D418yescomplemented
72C2×C163C2×C4×D4112yescomplemented
73C2×C163C24×C411yescharacteristic
74C2×C163C23×D411yescharacteristic
75C2×C163C22×#4111yescharacteristic
76D163—216no—
77C163C22×C4×D411yescharacteristic, complemented, Sylow
78C22×C4×D4—1631nomaximal, Sylow
79C23×D4—1631no—
80C24×C4—1632no—
81C2×C4×D4—16324no—
82C22×C4⋊C4D16311yescharacteristic, complemented
83C22×C22⋊C4—1632no—
84C22×C42—1631no—
85C25—1632no—
86C22×D4—16316no—
87C22×D4—16312no—
88C23×C4—32616no—
89C23×C4—1631no—
90C23×C4—16324no—
91C23×C4—1631no—
92C23×C4C2×D16312yes—
93C23×C4C2×D16311yescharacteristic
94C4×D4—16364no—
95C2×C4⋊C4C2×D163112yescomplemented
96C2×C22⋊C4—16324no—
97C2×C42—16312no—
98C24—3268no—
99C24—3268no—
100C24—16316no—
101C24—16312no—
102C24C22×D16311yescharacteristic
103C2×D4—16396no—
104C2×D4—16316no—
105C22×C4—28no—
106C22×C4—32696no—
107C22×C4—3264no—
108C22×C4—1636no—
109C22×C4—16332no—
110C22×C4—1638no—
111C22×C4—1636no—
112C22×C4C4×D16318yescomplemented
113C22×C4C22×D163112yes—
114C22×C4C22×D16316yes—
115C4⋊C4C22×D163116yescomplemented
116C22⋊C4—16332no—
117C42—16316no—
118C23—32624no—
119C23—32624no—
120C23—32664no—
121C23—16348no—
122C23—1638no—
123C23C2×C4×D16314yes—
124C23D4×D16314yes—
125C23#1457970014yes—
126C23C23×D16313yes—
127D4—16364no—
128C2×C4—224no—
129C2×C4—32664no—
130C2×C4—32612no—
131C2×C4—1634no—
132C2×C4—16324no—
133C2×C4—1634no—
134C2×C4C2×C4×D163124yescomplemented
135C2×C4C23×D16318yes—
136C2×C4C23×D16314yes—
137C22—3268no—
138C22—3268no—
139C22—32696no—
140C22—16316no—
141C22#19104697116yesdirect product factor
142C22C22×C4×D16316yes—
143C22C2×D4×D16316yes—
144C22C2×#1457970016yes—
145C22C24×D16311yescharacteristic
146C4—28no—
147C4—3264no—
148C4—1638no—
149C4C22×C4×D16318yescomplemented
150C2—32616no—
151C2C2×#19104697112yesdirect product factor
152C2C23×C4×D16311yescharacteristic
153C2C22×D4×D16311yescharacteristic
154C2C22×#1457970011yescharacteristic
subgroupG/H
centerC24C22×D163
commutatorC2×C163C24×C4
FrattiniC22C24×D163
FittingC22×C4⋊C4×C163C2
socleC24×C163C23
prime radicalC23×D652C2
cosocleC22×C163C25
hypercenterC22×C4⋊C4D163
hypocenterC163C22×C4×D4
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C24 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C23×C4×D163C2semidirect
3. C2×#19104697C2direct (N × H)
4. C22×(C2×D163)⋊C4C2semidirect
5. C22×C4×Dic163C2semidirect
6. C22×C4⋊C4×C163C2semidirect
8. C22×D652C4semidirect
13. C22×C4×D163C22semidirect
14. #19104697C22direct (N × H)
15. C2×(C2×D163)⋊C4C22semidirect
16. C2×C4×Dic163C22semidirect
19. C2×C4⋊C4×C163C22semidirect
22. C23×D163C2×C4semidirect
24. C2×D652C2×C4semidirect
27. C22×Dic163D4semidirect
31. C2×C4×D163C23semidirect
32. (C2×D163)⋊C4C23semidirect
33. C4×Dic163C23semidirect
36. C22×C4×C163C2×C4semidirect
39. C4⋊C4×C163C23semidirect
43. C22×D163C22×C4semidirect
45. D652C22×C4semidirect
47. C2×Dic163C2×D4semidirect
56. C2×C4×C163C22×C4semidirect
59. C22×C163C4×D4semidirect
67. C2×D163C23×C4semidirect
69. C4×C163C23×C4semidirect
71. Dic163C22×D4semidirect
72. C2×C163C2×C4×D4semidirect
77. C163C22×C4×D4semidirect
82. C22×C4⋊C4D163semidirect
95. C2×C4⋊C4C2×D163semidirect
112. C22×C4C4×D163semidirect
115. C4⋊C4C22×D163semidirect
134. C2×C4C2×C4×D163semidirect
141. C22#19104697direct (N × H)
149. C4C22×C4×D163semidirect
151. C2C2×#19104697direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D6522
C23×C4×D1632
C2×#191046972
C22×(C2×D163)⋊C42
C22×C4×Dic1632
C22×C4⋊C4×C1632
C22×C4×D4163