Subgroups — C₃×Dic₃² #88778

Order 432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×Dic₃	C₂	1	2	yes	maximal
3	C₃×C₄×Dic₃	—	3	2	no	maximal
4	Dic₃²	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃³	C₂²	1	1	yes	characteristic
6	C₃×C₃⋊Dic₃	C₄	1	2	yes	complemented
7	C₃²×Dic₃	C₄	1	4	yes	complemented
8	C₂×C₃²×C₄	—	3	2	no	—
9	C₂×C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
10	C₂×C₃×Dic₃	—	2	2	no	—
11	C₂×C₃×Dic₃	—	3	2	no	—
12	C₂×C₃×Dic₃	—	6	1	no	—
13	C₂×C₃×Dic₃	D₃	1	2	yes	—
14	C₂×C₃×Dic₃	C₂×C₃	1	2	yes	—
15	C₂×C₃³	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃³	C₂×C₄	1	2	yes	—
17	C₃×C₄²	—	9	1	no	—
18	C₄×Dic₃	—	3	2	no	—
19	C₂²×C₃²	—	2	1	no	—
20	C₂²×C₃²	—	2	2	no	—
21	C₂²×C₃²	—	4	1	no	—
22	C₂²×C₃²	C₂×D₃	1	2	yes	—
23	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
24	C₃²×C₄	—	3	4	no	—
25	C₃⋊Dic₃	C₃×C₄	1	2	yes	complemented
26	C₃×Dic₃	—	2	4	no	—
27	C₃×Dic₃	—	3	4	no	—
28	C₃×Dic₃	—	6	2	no	—
29	C₃×Dic₃	Dic₃	1	4	yes	direct product factor
30	C₃×Dic₃	C₃×C₄	1	4	yes	complemented
31	C₃³	C₄²	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₄	—	3	2	no	—
33	C₂×C₃×C₄	—	3	2	no	—
34	C₂×C₃×C₄	—	6	2	no	—
35	C₂×C₃×C₄	—	9	1	no	—
36	C₂×Dic₃	—	3	2	no	—
37	C₂×Dic₃	—	6	1	no	—
38	C₂×Dic₃	C₃×D₃	1	2	yes	—
39	C₂×C₃²	—	2	2	no	—
40	C₂×C₃²	—	2	1	no	—
41	C₂×C₃²	—	2	2	no	—
42	C₂×C₃²	—	2	2	no	—
43	C₂×C₃²	—	2	2	no	—
44	C₂×C₃²	—	4	2	no	—
45	C₂×C₃²	—	4	1	no	—
46	C₂×C₃²	C₄×D₃	1	2	yes	—
47	C₂×C₃²	C₄×D₃	1	2	yes	—
48	C₂×C₃²	C₂×Dic₃	1	2	yes	—
49	C₂×C₃²	C₂×C₃×C₄	1	1	yes	characteristic
50	C₂×C₃²	C₂×C₃×C₄	1	2	yes	—
51	C₄²	—	9	1	no	Sylow
52	C₂²×C₃	—	2	1	no	—
53	C₂²×C₃	—	2	2	no	—
54	C₂²×C₃	—	4	1	no	—
55	C₂²×C₃	D₃²	1	1	yes	characteristic
56	C₂²×C₃	C₂×C₃×D₃	1	2	yes	—
57	C₃×C₄	—	3	4	no	—
58	C₃×C₄	—	3	4	no	—
59	C₃×C₄	—	6	4	no	—
60	C₃×C₄	—	9	2	no	—
61	Dic₃	—	3	4	no	—
62	Dic₃	—	6	2	no	—
63	Dic₃	C₃×Dic₃	1	4	yes	direct product factor
64	C₃²	—	2	1	no	—
65	C₃²	—	2	2	no	—
66	C₃²	—	4	1	no	—
67	C₃²	C₄×Dic₃	1	2	yes	complemented
68	C₃²	C₃×C₄²	1	1	yes	characteristic, complemented
69	C₂×C₄	—	3	2	no	—
70	C₂×C₄	—	9	1	no	—
71	C₂×C₃	—	2	2	no	—
72	C₂×C₃	—	2	2	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	2	1	no	—
75	C₂×C₃	—	2	2	no	—
76	C₂×C₃	—	4	2	no	—
77	C₂×C₃	—	4	1	no	—
78	C₂×C₃	D₃×Dic₃	1	2	yes	—
79	C₂×C₃	#624	1	1	yes	characteristic
80	C₂×C₃	C₃×C₄×D₃	1	2	yes	—
81	C₂×C₃	C₃×C₄×D₃	1	2	yes	—
82	C₂×C₃	C₂×C₃×Dic₃	1	2	yes	—
83	C₂²	C₃×D₃²	1	1	yes	characteristic
84	C₄	—	3	4	no	—
85	C₄	—	9	2	no	—
86	C₃	—	2	2	no	—
87	C₃	—	2	1	no	—
88	C₃	—	4	1	no	—
89	C₃	Dic₃²	1	1	yes	characteristic, direct product factor
90	C₃	C₃×C₄×Dic₃	1	2	yes	complemented
91	C₂	C₃×D₃×Dic₃	1	2	yes	—
92	C₂	C₃×#624	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃²
commutator, hypocenter	C₃²	C₃×C₄²
Frattini	C₂²	C₃×D₃²
Fitting, socle, prime radical	C₂²×C₃³	C₂²
cosocle	C₂²×C₃²	C₂²×C₃
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂²×C₃

Complements

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

N	H ≅ G/N	type
4. Dic₃²	C₃	direct (N × H)
6. C₃×C₃⋊Dic₃	C₄	semidirect
7. C₃²×Dic₃	C₄	semidirect
25. C₃⋊Dic₃	C₃×C₄	semidirect
29. C₃×Dic₃	Dic₃	direct (N × H)
30. C₃×Dic₃	C₃×C₄	semidirect
31. C₃³	C₄²	semidirect
63. Dic₃	C₃×Dic₃	direct (N × H)
67. C₃²	C₄×Dic₃	semidirect
68. C₃²	C₃×C₄²	semidirect
89. C₃	Dic₃²	direct (N × H)
90. C₃	C₃×C₄×Dic₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₃⋊Dic₃	2
C₂×C₃²×Dic₃	2
C₃×C₄×Dic₃	3
Dic₃²	3

Subgroups — C3×Dic32 #88778

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃² #88778