Finite Group Databasebeta

← D4×D692 #26012127

Subgroups — D4×D692 #26012127

Order 11072.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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×D692C212yesmaximal, complemented
2C2×D4×D173C212yesmaximal, complemented
3#19149676C211yesmaximal, characteristic, complemented
4#19149654C212yesmaximal, complemented
5#19149653C212yesmaximal, complemented
6#19149649C214yesmaximal, complemented
7C4×D692C211yesmaximal, characteristic, complemented
8C4×D4×C173C211yesmaximal, characteristic, complemented
9C23×D173C2214yescomplemented
10C2×D692—28no—
11C2×D692C2211yescharacteristic
12C2×D692C2214yescomplemented
13C2×D692C2212yescomplemented
14C2×D692C2212yescomplemented
15C2×D692C2212yescomplemented
16C2×C22⋊D173C2214yescomplemented
17D4×D173—28no—
18C2×C4×D173C2212yescomplemented
19C4⋊Dic173C2211yescharacteristic, complemented
20#14583803C2212yescomplemented
21#14583803C2214yescomplemented
22C2×D4×C173C2211yescharacteristic
23C22×C4×C173C2212yescomplemented
24C4⋊C4×C173C2211yescharacteristic, complemented
25C22⋊C4×C173C2212yescomplemented
26C42×C173C2211yescharacteristic, complemented
27C22×D173—28no—
28C22×D173—28no—
29C22×D173—44no—
30C22×D173C2314yes—
31C22×D173C2312yes—
32D692—28no—
33D692—24no—
34D692—24no—
35D692—42no—
36D692D414yesdirect product factor
37C22⋊D173—28no—
38C2×Dic173C2312yes—
39C4×D173—24no—
40C23×C173C2312yes—
41D4×C173D414yescomplemented
42C2×C4×C173—24no—
43C2×C4×C173C2311yescharacteristic
44C2×C4×C173C2312yes—
45C2×C4×C173C2311yescharacteristic
46C2×C4×C173C2311yescharacteristic
47C22×C173—22no—
48C22×C173—22no—
49C22×C173C2×D414yescomplemented
50C22×C173C2411yescharacteristic
51C2×D173—22no—
52C2×D173—22no—
53C2×D173—24no—
54C2×D173—24no—
55C2×D173—24no—
56C2×D173—416no—
57C2×D173C2×D414yescomplemented
58C4×C173—22no—
59C4×C173—21no—
60C4×C173C2×D412yescomplemented
61C4×C173C2×D412yescomplemented
62Dic173—22no—
63C2×C173—24no—
64C2×C173C22×D411yescharacteristic
65C2×C173C22×D411yescharacteristic
66C2×C173H(5,𝔽2)11yescharacteristic
67D173—24no—
68D173—44no—
69C173D4211yescharacteristic, complemented, Sylow
70D42—1731nomaximal, Sylow
71C22×D4—1732no—
72C22×D4—1732no—
73#127—1731no—
74#121—1732no—
75#121—1732no—
76#120—1734no—
77C4×D4—1731no—
78C4×D4D17311yescharacteristic, complemented
79C24—1734no—
80C2×D4—3468no—
81C2×D4—3468no—
82C2×D4—1734no—
83C2×D4—1734no—
84C2×D4—1732no—
85C2×D4—1732no—
86C2×D4—1731no—
87C2×D4—1732no—
88C2×D4C2×D17311yescharacteristic
89C22×C4—1732no—
90C22×C4C2×D17312yescomplemented
91C4⋊C4—1731no—
92C4⋊C4C2×D17311yescharacteristic, complemented
93C22⋊C4—1732no—
94C22⋊C4—1734no—
95C22⋊C4C2×D17312yescomplemented
96C42C2×D17311yescharacteristic, complemented
97C23—3468no—
98C23—3468no—
99C23—1734no—
100C23—1732no—
101C23—6924no—
102C23C22×D17312yes—
103D4—3468no—
104D4—3468no—
105D4—3464no—
106D4—3464no—
107D4—1734no—
108D4—6922no—
109D4D69214yesdirect product factor
110C2×C4—24no—
111C2×C4—3464no—
112C2×C4—1732no—
113C2×C4C22×D17311yescharacteristic
114C2×C4C22×D17312yes—
115C2×C4C22×D17311yescharacteristic
116C2×C4C22×D17311yescharacteristic
117C22—22no—
118C22—22no—
119C22—3462no—
120C22—3462no—
121C22—3464no—
122C22—3464no—
123C22—3464no—
124C22—1734no—
125C22—69216no—
126C22C2×D69214yescomplemented
127C22C23×D17311yescharacteristic
128C4—22no—
129C4—21no—
130C4—3462no—
131C4D4×D17312yescomplemented
132C4C2×D69212yescomplemented
133C2—24no—
134C2—3464no—
135C2—6924no—
136C2C2×D4×D17311yescharacteristic
137C2C22×D69211yescharacteristic
138C2#1914972511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutator, socle, cosocleC22×C173C24
FittingC4×D4×C173C2
hypercenterC4×D4D173
hypocenterC173D42
LCSG ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×D692C2semidirect
2. C2×D4×D173C2semidirect
3. #19149676C2semidirect
4. #19149654C2semidirect
5. #19149653C2semidirect
6. #19149649C2semidirect
7. C4×D692C2semidirect
8. C4×D4×C173C2semidirect
9. C23×D173C22semidirect
12. C2×D692C22semidirect
13. C2×D692C22semidirect
14. C2×D692C22semidirect
15. C2×D692C22semidirect
16. C2×C22⋊D173C22semidirect
18. C2×C4×D173C22semidirect
19. C4⋊Dic173C22semidirect
20. #14583803C22semidirect
21. #14583803C22semidirect
23. C22×C4×C173C22semidirect
24. C4⋊C4×C173C22semidirect
25. C22⋊C4×C173C22semidirect
26. C42×C173C22semidirect
36. D692D4direct (N × H)
41. D4×C173D4semidirect
49. C22×C173C2×D4semidirect
57. C2×D173C2×D4semidirect
60. C4×C173C2×D4semidirect
61. C4×C173C2×D4semidirect
69. C173D42semidirect
78. C4×D4D173semidirect
90. C22×C4C2×D173semidirect
92. C4⋊C4C2×D173semidirect
95. C22⋊C4C2×D173semidirect
96. C42C2×D173semidirect
109. D4D692direct (N × H)
126. C22C2×D692semidirect
131. C4D4×D173semidirect
132. C4C2×D692semidirect

Maximal subgroups

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

subgroupindex
C22×D6922
C2×D4×D1732
#191496762
#191496542
#191496532
#191496492
C4×D6922
C4×D4×C1732
D42173