Subgroups — C₃×#3674 #88509

Order 432.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₁₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₃×#216	—	3	1	no	maximal
5	#3674	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×C₄×C₉	—	2	1	no	—
7	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
8	C₃×Dic₉	—	2	1	no	—
9	C₃²×Q₈	D₃	1	1	yes	characteristic
10	C₃×Dic₆	—	3	1	no	—
11	C₃×C₃⋊C₈	—	3	1	no	—
12	Q₈×C₉	—	2	1	no	—
13	Q₈×C₉	C₂×C₃	1	1	yes	characteristic
14	Dic₁₈	C₂×C₃	1	1	yes	characteristic
15	C₉⋊C₈	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃×C₉	D₄	1	1	yes	characteristic
17	C₃×Q₁₆	—	9	1	no	—
18	#216	—	3	1	no	—
19	C₃²×C₄	—	2	1	no	—
20	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
21	C₃×Dic₃	—	6	1	no	—
22	C₄×C₉	—	2	2	no	—
23	C₄×C₉	—	2	1	no	—
24	C₄×C₉	—	2	1	no	—
25	C₄×C₉	C₂²×C₃	1	1	yes	characteristic
26	Dic₉	—	2	1	no	—
27	C₃×C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₃×Q₈	—	2	1	no	—
29	C₃×Q₈	—	9	1	no	—
30	C₃×Q₈	D₉	1	1	yes	characteristic
31	C₃×Q₈	C₃×D₃	1	1	yes	characteristic
32	Dic₆	—	3	1	no	—
33	C₃×C₈	—	9	1	no	—
34	C₃⋊C₈	—	3	1	no	—
35	C₂×C₃²	#67	1	1	yes	characteristic
36	C₂×C₉	—	2	1	no	—
37	C₂×C₉	C₃×D₄	1	1	yes	characteristic
38	Q₁₆	—	9	1	no	Sylow
39	C₃×C₄	—	2	2	no	—
40	C₃×C₄	—	2	1	no	—
41	C₃×C₄	—	2	1	no	—
42	C₃×C₄	—	2	1	no	—
43	C₃×C₄	—	18	1	no	—
44	C₃×C₄	C₂×D₉	1	1	yes	characteristic
45	C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
46	Dic₃	—	6	1	no	—
47	C₃²	#216	1	1	yes	characteristic
48	C₉	—	2	1	no	—
49	C₉	C₃×Q₁₆	1	1	yes	characteristic, complemented
50	Q₈	—	9	1	no	—
51	Q₈	C₃×D₉	1	1	yes	characteristic
52	C₈	—	9	1	no	—
53	C₂×C₃	—	2	1	no	—
54	C₂×C₃	#611	1	1	yes	characteristic
55	C₂×C₃	C₃×#67	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	18	1	no	—
58	C₄	C₂×C₃×D₉	1	1	yes	characteristic
59	C₃	—	2	1	no	—
60	C₃	#3674	1	1	yes	characteristic, direct product factor
61	C₃	C₃×#216	1	1	yes	characteristic
62	C₂	C₃×#611	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#611
commutator, cosocle	C₄×C₉	C₂²×C₃
Frattini	C₃×C₄	C₂×C₃×D₃
Fitting	C₃×Q₈×C₉	C₂
socle, prime radical	C₂×C₃²	#67
hypercenter	C₃×Q₈	D₉
hypocenter	C₉	C₃×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×Q₈

Complements

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

N	H ≅ G/N	type
5. #3674	C₃	direct (N × H)
27. C₃×C₉	Q₁₆	semidirect
49. C₉	C₃×Q₁₆	semidirect
60. C₃	#3674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₉	2
C₃×Dic₁₈	2
C₃×C₉⋊C₈	2
C₃×#216	3
#3674	3

Subgroups — C3×#3674 #88509

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3674 #88509