Finite Group Databasebeta

← D3×D36 #88644

Subgroups — D3×D36 #88644

Order 432.

178 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 47 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×D3×D9C212yesmaximal, complemented
2C4⋊(C3⋊D9)C211yesmaximal, characteristic, complemented
3C4×D3×C9C211yesmaximal, characteristic, complemented
4C3×D36C211yesmaximal, characteristic, complemented
5#6192C212yesmaximal, complemented
6D3×D12—31nomaximal
7C2×D36—31nomaximal
8C2×C3⋊D9C2212yescomplemented
9C2×D3×C9C2211yescharacteristic
10C2×C3×D9C2212yescomplemented
11D3×D9—24no—
12C3×C4×C9C2211yescharacteristic, complemented
13C9×Dic3C2211yescharacteristic, complemented
14C2×D32—32no—
15C4⋊(C3⋊D3)—31no—
16C3×D12—31no—
17C3×C4×D3D311yescharacteristic
18#626—32no—
19C22×D9—32no—
20C2×C4×C9—31no—
21D36—32no—
22D36—31no—
23D36—61no—
24D36D311yescharacteristic, direct product factor
25C2×C3×C9C2311yescharacteristic
26C3⋊D9—22no—
27D3×C9D412yescomplemented
28C3×D9—22no—
29D3×D4—91no—
30C2×D12—91no—
31C2×C3⋊D3—32no—
32C2×C3×D3—32no—
33C2×C3×D3C2×D311yescharacteristic
34D32—64no—
35C32×C4C2×D311yescharacteristic
36C3×Dic3C2×D311yescharacteristic
37C22×C9—31no—
38C2×D9—32no—
39C2×D9—62no—
40C2×D9—64no—
41C2×D9C2×D312yescomplemented
42C4×C9—21no—
43C4×C9—31no—
44C4×C9C2×D311yescharacteristic, complemented
45C3×C9C2×D411yescharacteristic, complemented, Sylow
46C22×D3—92no—
47C22×D3—92no—
48C3×D4—91no—
49C2×C3×C4—31no—
50#67—92no—
51D12—31no—
52D12—92no—
53D12—91no—
54D12—91no—
55D12—181no—
56C4×D3D911yescharacteristic, complemented
57C2×C32C22×D311yescharacteristic
58C3⋊D3—62no—
59C3×D3—62no—
60C3×D3D1212yes—
61C2×C9—21no—
62C2×C9—32no—
63C2×C9C22×D311yescharacteristic
64D9—22no—
65D9—62no—
66D9—122no—
67C2×D4—271noSylow
68C22×C3—31no—
69C22×C3—92no—
70C2×D3—32no—
71C2×D3—92no—
72C2×D3—92no—
73C2×D3—182no—
74C2×D3—184no—
75C2×D3—184no—
76C2×D3C2×D911yescharacteristic
77C3×C4—21no—
78C3×C4—31no—
79C3×C4C2×D911yescharacteristic, complemented
80C3×C4D3211yescharacteristic
81Dic3C2×D911yescharacteristic, complemented
82C32C2×D1211yescharacteristic
83C9—21no—
84C9D3×D411yescharacteristic, complemented
85C23—272no—
86D4—91no—
87D4—272no—
88D4—271no—
89C2×C4—31no—
90C2×C3—21no—
91C2×C3—32no—
92C2×C3—182no—
93C2×C3C22×D911yescharacteristic
94C2×C3C2×D3211yescharacteristic
95D3—62no—
96D3—182no—
97D3—182no—
98D3—362no—
99D3D3612yesdirect product factor
100C22—31no—
101C22—92no—
102C22—272no—
103C22—544no—
104C4—31no—
105C4D3×D911yescharacteristic, complemented
106C3—21no—
107C3C2×D3611yescharacteristic, complemented
108C3D3×D1211yescharacteristic
109C2—32no—
110C2—182no—
111C2—542no—
112C2C2×D3×D911yescharacteristic
subgroupG/H
centerC2C2×D3×D9
commutator, cosocleC2×C3×C9C23
FrattiniC2×C3C2×D32
FittingC3×C4×C9C22
socleC2×C32C22×D3
hypercenterC4D3×D9
hypocenterC3×C9C2×D4
LCSG ▷ C2×C3×C9 ▷ C3×C9
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×D9C2semidirect
2. C4⋊(C3⋊D9)C2semidirect
3. C4×D3×C9C2semidirect
4. C3×D36C2semidirect
5. #6192C2semidirect
8. C2×C3⋊D9C22semidirect
10. C2×C3×D9C22semidirect
12. C3×C4×C9C22semidirect
13. C9×Dic3C22semidirect
24. D36D3direct (N × H)
27. D3×C9D4semidirect
41. C2×D9C2×D3semidirect
44. C4×C9C2×D3semidirect
45. C3×C9C2×D4semidirect
56. C4×D3D9semidirect
79. C3×C4C2×D9semidirect
81. Dic3C2×D9semidirect
84. C9D3×D4semidirect
99. D3D36direct (N × H)
105. C4D3×D9semidirect
107. C3C2×D36semidirect

Maximal subgroups

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

subgroupindex
C2×D3×D92
C4⋊(C3⋊D9)2
C4×D3×C92
C3×D362
#61922
D3×D123
C2×D363