Subgroups — C₃×#3676 #88517

Order 432.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₉	C₂	1	2	yes	maximal, complemented
3	C₃×#217	—	3	1	no	maximal
4	#3676	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃×C₉	—	2	2	no	—
6	C₂²×C₃×C₉	C₄	1	2	yes	complemented
7	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₃×Dic₉	—	2	2	no	—
9	C₂³×C₃²	D₃	1	1	yes	characteristic
10	C₂×C₃×Dic₃	—	3	2	no	—
11	C₂³×C₉	—	2	1	no	—
12	C₂³×C₉	C₂×C₃	1	1	yes	characteristic
13	C₂×Dic₉	C₂×C₃	1	2	yes	complemented
14	C₂×C₃×C₉	—	2	2	no	—
15	C₂×C₃×C₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₉	D₄	1	2	yes	—
17	C₃×C₂²⋊C₄	—	9	1	no	—
18	#217	—	3	1	no	—
19	C₂²×C₃²	—	2	2	no	—
20	C₂²×C₃²	Dic₃	1	2	yes	—
21	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
22	C₃×Dic₃	—	6	2	no	—
23	C₂²×C₉	—	2	4	no	—
24	C₂²×C₉	—	2	2	no	—
25	C₂²×C₉	—	2	2	no	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₃×C₄	1	2	yes	complemented
28	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
29	Dic₉	—	2	2	no	—
30	C₃×C₉	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
31	C₂³×C₃	—	2	1	no	—
32	C₂³×C₃	D₉	1	1	yes	characteristic
33	C₂³×C₃	C₃×D₃	1	1	yes	characteristic
34	C₂×C₃×C₄	—	9	2	no	—
35	C₂×Dic₃	—	3	2	no	—
36	C₂×C₃²	—	2	2	no	—
37	C₂×C₃²	C₂×Dic₃	1	1	yes	characteristic
38	C₂×C₃²	#67	1	2	yes	—
39	C₂×C₉	—	2	4	no	—
40	C₂×C₉	—	2	2	no	—
41	C₂×C₉	—	2	1	no	—
42	C₂×C₉	—	2	2	no	—
43	C₂×C₉	C₂×C₃×C₄	1	1	yes	characteristic
44	C₂×C₉	C₃×D₄	1	2	yes	—
45	C₂²⋊C₄	—	9	1	no	Sylow
46	C₂²×C₃	—	2	4	no	—
47	C₂²×C₃	—	2	2	no	—
48	C₂²×C₃	—	2	2	no	—
49	C₂²×C₃	—	2	2	no	—
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	Dic₉	1	2	yes	complemented
52	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
53	C₂²×C₃	C₃×Dic₃	1	2	yes	—
54	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
55	C₃×C₄	—	18	2	no	—
56	Dic₃	—	6	2	no	—
57	C₃²	#217	1	1	yes	characteristic
58	C₉	—	2	1	no	—
59	C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
60	C₂³	C₃×D₉	1	1	yes	characteristic
61	C₂×C₄	—	9	2	no	—
62	C₂×C₃	—	2	4	no	—
63	C₂×C₃	—	2	2	no	—
64	C₂×C₃	—	2	2	no	—
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	—	2	2	no	—
67	C₂×C₃	C₂×Dic₉	1	1	yes	characteristic
68	C₂×C₃	#611	1	2	yes	—
69	C₂×C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
70	C₂×C₃	C₃×#67	1	2	yes	—
71	C₂²	—	2	2	no	—
72	C₂²	C₃×Dic₉	1	2	yes	complemented
73	C₂²	C₂×C₃×D₉	1	1	yes	characteristic
74	C₄	—	18	2	no	—
75	C₃	—	2	1	no	—
76	C₃	#3676	1	1	yes	characteristic, direct product factor
77	C₃	C₃×#217	1	1	yes	characteristic
78	C₂	—	2	2	no	—
79	C₂	C₂×C₃×Dic₉	1	1	yes	characteristic
80	C₂	C₃×#611	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₉
commutator	C₂×C₉	C₂×C₃×C₄
Frattini	C₂²×C₃	C₂×C₃×D₃
Fitting	C₂³×C₃×C₉	C₂
socle	C₂²×C₃²	C₂×D₃
prime radical	C₂³×C₃²	D₃
cosocle	C₂²×C₉	C₂²×C₃
hypercenter	C₂³×C₃	D₉
hypocenter	C₉	C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×C₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×Dic₉	C₂	semidirect
4. #3676	C₃	direct (N × H)
6. C₂²×C₃×C₉	C₄	semidirect
13. C₂×Dic₉	C₂×C₃	semidirect
27. C₂²×C₉	C₃×C₄	semidirect
30. C₃×C₉	C₂²⋊C₄	semidirect
51. C₂²×C₃	Dic₉	semidirect
59. C₉	C₃×C₂²⋊C₄	semidirect
72. C₂²	C₃×Dic₉	semidirect
76. C₃	#3676	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₉	2
C₂×C₃×Dic₉	2
C₃×#217	3
#3676	3

Subgroups — C3×#3676 #88517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3676 #88517