Finite Group Databasebeta

← C3×#3802 #89003

Subgroups — C3×#3802 #89003

Order 432.

270 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 68 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×C3×D32C212yesmaximal, complemented
2C3×C4×C3⋊D3C211yesmaximal, characteristic, complemented
3C32×D12C212yesmaximal, complemented
4C3×#625C212yesmaximal, complemented
5C3×D3×D4—32nomaximal
6#3802C311yesmaximal, characteristic, direct product factor
7C2×C3×C3⋊D3C2211yescharacteristic
8C2×C32×D3C2214yescomplemented
9C3×D32—24no—
10C33×C4C2211yescharacteristic, complemented
11C3×C3⋊Dic3C2211yescharacteristic, complemented
12C22×C3×D3—34no—
13C2×D32C2×C312yescomplemented
14C32×D4—32no—
15C4×C3⋊D3C2×C311yescharacteristic, complemented
16C3×#67—34no—
17C3×D12—22no—
18C3×D12D312yescomplemented
19C3×D12C2×C312yescomplemented
20C3×C4×D3—32no—
21C3×C4×D3—61no—
22#625C2×C312yescomplemented
23C2×C33C2311yescharacteristic
24C3×C3⋊D3D412yescomplemented
25C32×D3—24no—
26C2×C3×D4—91no—
27D3×D4—32no—
28C22×C32—34no—
29C2×C3⋊D3C22×C311yescharacteristic
30C2×C3×D3—24no—
31C2×C3×D3—32no—
32C2×C3×D3—61no—
33C2×C3×D3—68no—
34C2×C3×D3C2×D314yescomplemented
35C2×C3×D3C22×C314yescomplemented
36D32—24no—
37C32×C4—21no—
38C32×C4—22no—
39C32×C4—41no—
40C32×C4C2×D312yescomplemented
41C32×C4C22×C311yescharacteristic, complemented
42C3⋊Dic3C22×C311yescharacteristic, complemented
43C3×Dic3—32no—
44C3×Dic3—61no—
45C33C2×D411yescharacteristic, complemented, Sylow
46C23×C3—92no—
47C22×D3—34no—
48C3×D4—32no—
49C3×D4—32no—
50C3×D4—62no—
51C3×D4—92no—
52C2×C3×C4—91no—
53#67—34no—
54D12C3×D312yescomplemented
55C4×D3—32no—
56C4×D3—61no—
57C2×C32—21no—
58C2×C32—22no—
59C2×C32—41no—
60C2×C32—64no—
61C2×C32C22×D312yes—
62C2×C32C23×C311yescharacteristic
63C3⋊D3C3×D412yescomplemented
64C3×D3—24no—
65C3×D3—24no—
66C3×D3—34no—
67C3×D3—44no—
68C3×D3—62no—
69C2×D4—91noSylow
70C22×C3—34no—
71C22×C3—34no—
72C22×C3—64no—
73C22×C3—91no—
74C22×C3—184no—
75C2×D3—32no—
76C2×D3—61no—
77C2×D3—68no—
78C2×D3C2×C3×D314yescomplemented
79C3×C4—21no—
80C3×C4—22no—
81C3×C4—41no—
82C3×C4—91no—
83C3×C4D3211yescharacteristic, complemented
84C3×C4C2×C3×D312yescomplemented
85Dic3—32no—
86Dic3—61no—
87C32—21no—
88C32—22no—
89C32—41no—
90C32D3×D412yescomplemented
91C32C2×C3×D411yescharacteristic, complemented
92C23—92no—
93D4—32no—
94D4—92no—
95C2×C4—91no—
96C2×C3—21no—
97C2×C3—22no—
98C2×C3—41no—
99C2×C3—64no—
100C2×C3—64no—
101C2×C3—92no—
102C2×C3—124no—
103C2×C3C2×D3211yescharacteristic
104C2×C3C22×C3×D312yes—
105D3—24no—
106D3—34no—
107D3—62no—
108C22—34no—
109C22—91no—
110C22—184no—
111C4—91no—
112C4C3×D3211yescharacteristic, complemented
113C3—21no—
114C3—22no—
115C3—41no—
116C3#380211yescharacteristic, direct product factor
117C3C3×D3×D412yescomplemented
118C2—64no—
119C2—92no—
120C2C2×C3×D3211yescharacteristic
subgroupG/H
centerC2×C3C2×D32
commutator, cosocleC2×C32C23×C3
FrattiniC2C2×C3×D32
FittingC33×C4C22
socleC2×C33C23
hypercenterC3×C4D32
hypocenterC32C2×C3×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D32C2semidirect
2. C3×C4×C3⋊D3C2semidirect
3. C32×D12C2semidirect
4. C3×#625C2semidirect
6. #3802C3direct (N × H)
8. C2×C32×D3C22semidirect
10. C33×C4C22semidirect
11. C3×C3⋊Dic3C22semidirect
13. C2×D32C2×C3semidirect
15. C4×C3⋊D3C2×C3semidirect
18. C3×D12D3semidirect
19. C3×D12C2×C3semidirect
22. #625C2×C3semidirect
24. C3×C3⋊D3D4semidirect
34. C2×C3×D3C2×D3semidirect
35. C2×C3×D3C22×C3semidirect
40. C32×C4C2×D3semidirect
41. C32×C4C22×C3semidirect
42. C3⋊Dic3C22×C3semidirect
45. C33C2×D4semidirect
54. D12C3×D3semidirect
63. C3⋊D3C3×D4semidirect
78. C2×D3C2×C3×D3semidirect
83. C3×C4D32semidirect
84. C3×C4C2×C3×D3semidirect
90. C32D3×D4semidirect
91. C32C2×C3×D4semidirect
112. C4C3×D32semidirect
116. C3#3802direct (N × H)
117. C3C3×D3×D4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D322
C3×C4×C3⋊D32
C32×D122
C3×#6252
C3×D3×D43
#38023