Finite Group Databasebeta

← #26011963

Subgroups — #26011963

Order 11072.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×D4×D173C211yesmaximal, characteristic
2C4×D692C211yesmaximal, characteristic, complemented
3D4×Dic173C211yesmaximal, characteristic, complemented
4#19149641C211yesmaximal, characteristic, complemented
5C4×C22⋊D173C212yesmaximal, complemented
6#19149639C212yesmaximal, complemented
7#19149637C211yesmaximal, characteristic, complemented
8#19149636C211yesmaximal, characteristic, complemented
9C2×#14583803C212yesmaximal, complemented
10C22⋊C4×D173C212yesmaximal, complemented
11C4×D4×C173C211yesmaximal, characteristic, complemented
12C23×D173C2212yes—
13C2×D692C2211yescharacteristic
14C2×C22⋊D173C2212yes—
15D4×D173C418yescomplemented
16C22×Dic173C2212yescomplemented
17C2×C4×D173C2211yescharacteristic
18C2×C4×D173C2212yescomplemented
19C2×C4×D173C2212yescomplemented
20C4⋊Dic173C2211yescharacteristic, complemented
21#14583805C2211yescharacteristic, complemented
22#14583805C2211yescharacteristic, complemented
23C22⋊Dic173C2212yescomplemented
24#14583803C2211yescharacteristic
25#14583803C2212yes—
26#14583803C2211yescharacteristic
27#14583803C2212yescomplemented
28#14583803C2212yescomplemented
29C4×Dic173C2211yescharacteristic, complemented
30C4×Dic173C2212yescomplemented
31C2×D4×C173C2211yescharacteristic
32C22×C4×C173C2212yescomplemented
33C4⋊C4×C173C2211yescharacteristic, complemented
34C22⋊C4×C173C2212yescomplemented
35C42×C173C2211yescharacteristic, complemented
36C22×D173—42no—
37C22×D173—42no—
38C22×D173C2×C418yescomplemented
39C22×D173C2311yescharacteristic
40C22×D173C2312yes—
41D692C2×C414yescomplemented
42C22⋊D173C2×C418yescomplemented
43C2×Dic173—42no—
44C2×Dic173C2311yescharacteristic
45C2×Dic173C2312yes—
46C2×Dic173C2311yescharacteristic
47C2×Dic173C2311yescharacteristic
48C4×D173—42no—
49C4×D173—42no—
50C4×D173C2×C414yescomplemented
51C23×C173C2312yes—
52D4×C173C2×C414yescomplemented
53C2×C4×C173—42no—
54C2×C4×C173C2311yescharacteristic
55C2×C4×C173C2312yes—
56C2×C4×C173C2311yescharacteristic
57C2×C4×C173C2311yescharacteristic
58C22×C173—22no—
59C22×C173—22no—
60C22×C173C22×C414yes—
61C22×C173C2411yescharacteristic
62C2×D173—22no—
63C2×D173—22no—
64C2×D173—21no—
65C2×D173—21no—
66C2×D173—48no—
67C2×D173C22×C412yes—
68C2×D173C22×C414yes—
69C4×C173—21no—
70C4×C173—22no—
71C4×C173—21no—
72C4×C173C22×C412yes—
73Dic173—21no—
74Dic173—22no—
75Dic173—21no—
76Dic173C22×C412yes—
77C2×C173—24no—
78C2×C173C23×C411yescharacteristic
79C2×C173H(5,𝔽2)11yescharacteristic
80C2×C173H(5,𝔽2)11yescharacteristic
81D173—22no—
82D173—24no—
83C173#51811yescharacteristic, complemented, Sylow
84#518—1731nomaximal, Sylow
85C22×D4—1731no—
86C4×D4—1731no—
87C4×D4—1732no—
88C4×D4—1731no—
89C4×D4—1732no—
90C4×D4—1731no—
91C4×D4D17311yescharacteristic, complemented
92#117—1731no—
93#117—1731no—
94C2×C22⋊C4—1732no—
95C2×C22⋊C4—1732no—
96C24—1732no—
97C2×D4—1732no—
98C2×D4—1738no—
99C2×D4—1731no—
100C2×D4C2×D17311yescharacteristic
101C22×C4—1731no—
102C22×C4—1732no—
103C22×C4—1732no—
104C22×C4—1732no—
105C22×C4C2×D17312yescomplemented
106C4⋊C4—1731no—
107C4⋊C4—1731no—
108C4⋊C4—1731no—
109C4⋊C4C2×D17311yescharacteristic, complemented
110C22⋊C4—1732no—
111C22⋊C4—1732no—
112C22⋊C4—1731no—
113C22⋊C4—1731no—
114C22⋊C4—1732no—
115C22⋊C4—1732no—
116C22⋊C4C2×D17312yescomplemented
117C42—1731no—
118C42—1732no—
119C42C2×D17311yescharacteristic, complemented
120C23—1731no—
121C23—1732no—
122C23—1738no—
123C23—6922no—
124C23—6922no—
125C23C22×D17312yes—
126D4—1738no—
127D4—1734no—
128D4C4×D17314yescomplemented
129C2×C4—42no—
130C2×C4—1731no—
131C2×C4—1732no—
132C2×C4—1731no—
133C2×C4—1731no—
134C2×C4—1734no—
135C2×C4—6922no—
136C2×C4—6922no—
137C2×C4—6922no—
138C2×C4C22×D17312yes—
139C2×C4C22×D17311yescharacteristic
140C2×C4C22×D17311yescharacteristic
141C2×C4C22×D17311yescharacteristic
142C22—22no—
143C22—22no—
144C22—3462no—
145C22—3461no—
146C22—3462no—
147C22—3461no—
148C22—1732no—
149C22—1734no—
150C22—6928no—
151C22C2×C4×D17314yes—
152C22C23×D17311yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—3461no—
157C4—3462no—
158C4—3461no—
159C4—1732no—
160C4C2×C4×D17312yes—
161C2—24no—
162C2—3464no—
163C2—3462no—
164C2C22×C4×D17311yescharacteristic
165C2#1914972411yescharacteristic
166C2#1914972511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D173
commutatorC2×C173C23×C4
FittingC4×D4×C173C2
socle, cosocleC22×C173C24
prime radicalC2×D4×D173C2
hypercenterC4×D4D173
hypocenterC173#518
LCSG ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D692C2semidirect
3. D4×Dic173C2semidirect
4. #19149641C2semidirect
5. C4×C22⋊D173C2semidirect
6. #19149639C2semidirect
7. #19149637C2semidirect
8. #19149636C2semidirect
9. C2×#14583803C2semidirect
10. C22⋊C4×D173C2semidirect
11. C4×D4×C173C2semidirect
15. D4×D173C4semidirect
16. C22×Dic173C22semidirect
18. C2×C4×D173C22semidirect
19. C2×C4×D173C22semidirect
20. C4⋊Dic173C22semidirect
21. #14583805C22semidirect
22. #14583805C22semidirect
23. C22⋊Dic173C22semidirect
27. #14583803C22semidirect
28. #14583803C22semidirect
29. C4×Dic173C22semidirect
30. C4×Dic173C22semidirect
32. C22×C4×C173C22semidirect
33. C4⋊C4×C173C22semidirect
34. C22⋊C4×C173C22semidirect
35. C42×C173C22semidirect
38. C22×D173C2×C4semidirect
41. D692C2×C4semidirect
42. C22⋊D173C2×C4semidirect
50. C4×D173C2×C4semidirect
52. D4×C173C2×C4semidirect
83. C173#518semidirect
91. C4×D4D173semidirect
105. C22×C4C2×D173semidirect
109. C4⋊C4C2×D173semidirect
116. C22⋊C4C2×D173semidirect
119. C42C2×D173semidirect
128. D4C4×D173semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D1732
C4×D6922
D4×Dic1732
#191496412
C4×C22⋊D1732
#191496392
#191496372
#191496362
C2×#145838032
C22⋊C4×D1732
C4×D4×C1732
#518173