Finite Group Databasebeta

← #120×D313 #34094636

Subgroups — #120×D313 #34094636

Order 20032.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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
1C24×D313C211yesmaximal, characteristic, complemented
2C2×D4×D313C213yesmaximal, complemented
3#23756467C213yesmaximal, complemented
4#23756466C211yesmaximal, characteristic, complemented
5#23756465C213yesmaximal, complemented
6C22⋊C4×D313C213yesmaximal, complemented
7#120×C313C211yesmaximal, characteristic, complemented
8C23×D313—212no—
9C23×D313C2213yes—
10C23×D313C2213yescomplemented
11C23×D313C2211yescharacteristic, complemented
12C2×D1252C2213yescomplemented
13C2×C22⋊D313C2213yescomplemented
14C2×C22⋊D313C2213yescomplemented
15D4×D313—212no—
16C2×C4×D313C2213yescomplemented
17C22⋊Dic313C2213yescomplemented
18#19097538C2216yescomplemented
19C24×C313C2211yescharacteristic, complemented
20C2×D4×C313C2213yescomplemented
21C22⋊C4×C313C2213yescomplemented
22C22×D313—232no—
23C22×D313—26no—
24C22×D313—212no—
25C22×D313—212no—
26C22×D313—26no—
27C22×D313D4112yescomplemented
28C22×D313C2313yes—
29C22×D313C2311yescharacteristic
30C22×D313C2311yescharacteristic, complemented
31D1252—26no—
32C22⋊D313—26no—
33C22⋊D313—26no—
34C2×Dic313C2313yescomplemented
35C4×D313—26no—
36C23×C313—26no—
37C23×C313C2313yes—
38C23×C313C2311yescharacteristic, complemented
39D4×C313—26no—
40C2×C4×C313C2313yescomplemented
41C22×C313—28no—
42C22×C313—26no—
43C22×C313—23no—
44C22×C313C2×D416yescomplemented
45C22×C313C2411yescharacteristic
46C2×D313—224no—
47C2×D313—26no—
48C2×D313—224no—
49C2×D313—23no—
50C2×D313—44no—
51C2×D313C2×D416yes—
52C2×D313C2×D416yescomplemented
53C4×C313—23no—
54Dic313—23no—
55C2×C313—26no—
56C2×C313—41no—
57C2×C313C22×D413yes—
58D313—26no—
59D313—41no—
60D313#12014yesdirect product factor
61C313C2×#12011yescharacteristic, complemented, Sylow
62C2×#120—3131nomaximal, Sylow
63C25—3131no—
64C22×D4—3133no—
65#120—3131no—
66#120—3133no—
67#120—3133no—
68#120D31311yescharacteristic, direct product factor
69C2×C22⋊C4—3133no—
70C24—3133no—
71C24—3133no—
72C24—3131no—
73C24—62612no—
74C24C2×D31311yescharacteristic, complemented
75C2×D4—3133no—
76C2×D4—3133no—
77C2×D4—3133no—
78C2×D4—62612no—
79C2×D4C2×D31313yescomplemented
80C22×C4—3133no—
81C22⋊C4—3133no—
82C22⋊C4—3136no—
83C22⋊C4C2×D31313yescomplemented
84C23—26no—
85C23—3131no—
86C23—31312no—
87C23—3133no—
88C23—3131no—
89C23—62612no—
90C23—62612no—
91C23—6266no—
92C23—62632no—
93C23—6266no—
94C23C22×D31313yes—
95C23C22×D31311yescharacteristic, complemented
96D4—26no—
97D4—6266no—
98D4—6266no—
99D4—6266no—
100C2×C4—3133no—
101C2×C4—6266no—
102C2×C4C22×D31313yescomplemented
103C22—28no—
104C22—26no—
105C22—23no—
106C22—3136no—
107C22—3136no—
108C22—62624no—
109C22—62624no—
110C22—6266no—
111C22—6263no—
112C22—12524no—
113C22D4×D31316yescomplemented
114C22C23×D31311yescharacteristic
115C4—23no—
116C4—6263no—
117C2—26no—
118C2—41no—
119C2—3134no—
120C2—6266no—
121C2—12521no—
122C2C2×D4×D31313yes—
subgroupG/H
center, FrattiniC22C23×D313
commutator, socle, cosocleC22×C313C24
Fitting#120×C313C2
hypercenter#120D313
hypocenterC313C2×#120
LCSG ▷ C22×C313 ▷ C313
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D313C2semidirect
2. C2×D4×D313C2semidirect
3. #23756467C2semidirect
4. #23756466C2semidirect
5. #23756465C2semidirect
6. C22⋊C4×D313C2semidirect
7. #120×C313C2semidirect
10. C23×D313C22semidirect
11. C23×D313C22semidirect
12. C2×D1252C22semidirect
13. C2×C22⋊D313C22semidirect
14. C2×C22⋊D313C22semidirect
16. C2×C4×D313C22semidirect
17. C22⋊Dic313C22semidirect
18. #19097538C22semidirect
19. C24×C313C22semidirect
20. C2×D4×C313C22semidirect
21. C22⋊C4×C313C22semidirect
27. C22×D313D4semidirect
30. C22×D313C23semidirect
34. C2×Dic313C23semidirect
38. C23×C313C23semidirect
40. C2×C4×C313C23semidirect
44. C22×C313C2×D4semidirect
52. C2×D313C2×D4semidirect
60. D313#120direct (N × H)
61. C313C2×#120semidirect
68. #120D313direct (N × H)
74. C24C2×D313semidirect
79. C2×D4C2×D313semidirect
83. C22⋊C4C2×D313semidirect
95. C23C22×D313semidirect
102. C2×C4C22×D313semidirect
113. C22D4×D313semidirect

Maximal subgroups

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

subgroupindex
C24×D3132
C2×D4×D3132
#237564672
#237564662
#237564652
C22⋊C4×D3132
#120×C3132
C2×#120313