Finite Group Databasebeta

← #34094624

Subgroups — #34094624

Order 20032.

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×D313C211yesmaximal, characteristic
2C4×D1252C211yesmaximal, characteristic, complemented
3D4×Dic313C211yesmaximal, characteristic, complemented
4#23756459C211yesmaximal, characteristic, complemented
5C4×C22⋊D313C212yesmaximal, complemented
6#23756457C212yesmaximal, complemented
7#23756455C211yesmaximal, characteristic, complemented
8#23756454C211yesmaximal, characteristic, complemented
9C2×#19097538C212yesmaximal, complemented
10C22⋊C4×D313C212yesmaximal, complemented
11C4×D4×C313C211yesmaximal, characteristic, complemented
12C23×D313C2212yes—
13C2×D1252C2211yescharacteristic
14C2×C22⋊D313C2212yes—
15D4×D313C418yescomplemented
16C22×Dic313C2212yescomplemented
17C2×C4×D313C2211yescharacteristic
18C2×C4×D313C2212yescomplemented
19C2×C4×D313C2212yescomplemented
20C4⋊Dic313C2211yescharacteristic, complemented
21#19097540C2211yescharacteristic, complemented
22#19097540C2211yescharacteristic, complemented
23C22⋊Dic313C2212yescomplemented
24#19097538C2211yescharacteristic
25#19097538C2212yes—
26#19097538C2211yescharacteristic
27#19097538C2212yescomplemented
28#19097538C2212yescomplemented
29C4×Dic313C2211yescharacteristic, complemented
30C4×Dic313C2212yescomplemented
31C2×D4×C313C2211yescharacteristic
32C22×C4×C313C2212yescomplemented
33C4⋊C4×C313C2211yescharacteristic, complemented
34C22⋊C4×C313C2212yescomplemented
35C42×C313C2211yescharacteristic, complemented
36C22×D313—42no—
37C22×D313—42no—
38C22×D313C2×C418yescomplemented
39C22×D313C2311yescharacteristic
40C22×D313C2312yes—
41D1252C2×C414yescomplemented
42C22⋊D313C2×C418yescomplemented
43C2×Dic313—42no—
44C2×Dic313C2311yescharacteristic
45C2×Dic313C2312yes—
46C2×Dic313C2311yescharacteristic
47C2×Dic313C2311yescharacteristic
48C4×D313—42no—
49C4×D313—42no—
50C4×D313C2×C414yescomplemented
51C23×C313C2312yes—
52D4×C313C2×C414yescomplemented
53C2×C4×C313—42no—
54C2×C4×C313C2311yescharacteristic
55C2×C4×C313C2311yescharacteristic
56C2×C4×C313C2312yes—
57C2×C4×C313C2311yescharacteristic
58C22×C313—22no—
59C22×C313—22no—
60C22×C313C22×C414yes—
61C22×C313C2411yescharacteristic
62C2×D313—22no—
63C2×D313—22no—
64C2×D313—21no—
65C2×D313—21no—
66C2×D313—48no—
67C2×D313C22×C412yes—
68C2×D313C22×C414yes—
69C4×C313—21no—
70C4×C313—22no—
71C4×C313—21no—
72C4×C313C22×C412yes—
73Dic313—21no—
74Dic313—22no—
75Dic313—21no—
76Dic313C22×C412yes—
77C2×C313—24no—
78C2×C313C23×C411yescharacteristic
79C2×C313H(5,𝔽2)11yescharacteristic
80C2×C313H(5,𝔽2)11yescharacteristic
81D313—22no—
82D313—24no—
83C313#51811yescharacteristic, complemented, Sylow
84#518—3131nomaximal, Sylow
85C22×D4—3131no—
86C4×D4—3131no—
87C4×D4—3132no—
88C4×D4—3131no—
89C4×D4—3132no—
90C4×D4—3131no—
91C4×D4D31311yescharacteristic, complemented
92#117—3131no—
93#117—3131no—
94C2×C22⋊C4—3132no—
95C2×C22⋊C4—3132no—
96C24—3132no—
97C2×D4—3132no—
98C2×D4—3138no—
99C2×D4—3131no—
100C2×D4C2×D31311yescharacteristic
101C22×C4—3131no—
102C22×C4—3132no—
103C22×C4—3132no—
104C22×C4—3132no—
105C22×C4C2×D31312yescomplemented
106C4⋊C4—3131no—
107C4⋊C4—3131no—
108C4⋊C4—3131no—
109C4⋊C4C2×D31311yescharacteristic, complemented
110C22⋊C4—3132no—
111C22⋊C4—3132no—
112C22⋊C4—3131no—
113C22⋊C4—3131no—
114C22⋊C4—3132no—
115C22⋊C4—3132no—
116C22⋊C4C2×D31312yescomplemented
117C42—3132no—
118C42—3131no—
119C42C2×D31311yescharacteristic, complemented
120C23—3131no—
121C23—3132no—
122C23—3138no—
123C23—12522no—
124C23—12522no—
125C23C22×D31312yes—
126D4—3138no—
127D4—3134no—
128D4C4×D31314yescomplemented
129C2×C4—42no—
130C2×C4—3131no—
131C2×C4—3134no—
132C2×C4—3131no—
133C2×C4—3132no—
134C2×C4—3131no—
135C2×C4—12522no—
136C2×C4—12522no—
137C2×C4—12522no—
138C2×C4C22×D31312yes—
139C2×C4C22×D31311yescharacteristic
140C2×C4C22×D31311yescharacteristic
141C2×C4C22×D31311yescharacteristic
142C22—22no—
143C22—22no—
144C22—3132no—
145C22—3134no—
146C22—6262no—
147C22—6261no—
148C22—6262no—
149C22—6261no—
150C22—12528no—
151C22C2×C4×D31314yes—
152C22C23×D31311yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—3132no—
157C4—6261no—
158C4—6262no—
159C4—6261no—
160C4C2×C4×D31312yes—
161C2—24no—
162C2—6262no—
163C2—6264no—
164C2C22×C4×D31311yescharacteristic
165C2#2375654211yescharacteristic
166C2#2375654311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D313
commutatorC2×C313C23×C4
FittingC4×D4×C313C2
socle, cosocleC22×C313C24
prime radicalC2×D4×D313C2
hypercenterC4×D4D313
hypocenterC313#518
LCSG ▷ C2×C313 ▷ C313
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D1252C2semidirect
3. D4×Dic313C2semidirect
4. #23756459C2semidirect
5. C4×C22⋊D313C2semidirect
6. #23756457C2semidirect
7. #23756455C2semidirect
8. #23756454C2semidirect
9. C2×#19097538C2semidirect
10. C22⋊C4×D313C2semidirect
11. C4×D4×C313C2semidirect
15. D4×D313C4semidirect
16. C22×Dic313C22semidirect
18. C2×C4×D313C22semidirect
19. C2×C4×D313C22semidirect
20. C4⋊Dic313C22semidirect
21. #19097540C22semidirect
22. #19097540C22semidirect
23. C22⋊Dic313C22semidirect
27. #19097538C22semidirect
28. #19097538C22semidirect
29. C4×Dic313C22semidirect
30. C4×Dic313C22semidirect
32. C22×C4×C313C22semidirect
33. C4⋊C4×C313C22semidirect
34. C22⋊C4×C313C22semidirect
35. C42×C313C22semidirect
38. C22×D313C2×C4semidirect
41. D1252C2×C4semidirect
42. C22⋊D313C2×C4semidirect
50. C4×D313C2×C4semidirect
52. D4×C313C2×C4semidirect
83. C313#518semidirect
91. C4×D4D313semidirect
105. C22×C4C2×D313semidirect
109. C4⋊C4C2×D313semidirect
116. C22⋊C4C2×D313semidirect
119. C42C2×D313semidirect
128. D4C4×D313semidirect

Maximal subgroups

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

subgroupindex
C2×D4×D3132
C4×D12522
D4×Dic3132
#237564592
C4×C22⋊D3132
#237564572
#237564552
#237564542
C2×#190975382
C22⋊C4×D3132
C4×D4×C3132
#518313