Subgroups — C₃×#3745 #88836

Order 432.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
2	C₃³×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#3745	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×D₂₄	—	3	4	no	maximal
5	C₂×C₃×C₃⋊D₃	—	2	2	no	—
6	C₃³×C₄	C₂²	1	1	yes	characteristic
7	C₄⋊(C₃⋊D₃)	C₂×C₃	1	2	yes	complemented
8	C₃×D₁₂	—	3	8	no	—
9	C₃²×C₈	—	2	4	no	—
10	C₃²×C₈	D₃	1	4	yes	complemented
11	C₃²×C₈	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×C₃³	D₄	1	1	yes	characteristic
13	C₃×C₃⋊D₃	—	4	2	no	—
14	C₃×D₈	—	9	1	no	—
15	D₂₄	—	3	4	no	—
16	C₂×C₃⋊D₃	—	2	2	no	—
17	C₂×C₃×D₃	—	6	8	no	—
18	C₃²×C₄	—	2	4	no	—
19	C₃²×C₄	C₂×D₃	1	4	yes	—
20	C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
21	C₃³	D₈	1	1	yes	characteristic, complemented, Sylow
22	C₃×D₄	—	9	2	no	—
23	D₁₂	—	3	8	no	—
24	C₃×C₈	—	2	4	no	—
25	C₃×C₈	C₃×D₃	1	4	yes	complemented
26	C₃×C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
27	C₂×C₃²	—	2	4	no	—
28	C₂×C₃²	D₁₂	1	4	yes	—
29	C₂×C₃²	C₃×D₄	1	1	yes	characteristic
30	C₃⋊D₃	—	4	2	no	—
31	C₃×D₃	—	12	8	no	—
32	D₈	—	9	1	no	Sylow
33	C₂²×C₃	—	18	2	no	—
34	C₂×D₃	—	6	8	no	—
35	C₃×C₄	—	2	4	no	—
36	C₃×C₄	C₂×C₃×D₃	1	4	yes	—
37	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
38	C₃²	—	2	4	no	—
39	C₃²	D₂₄	1	4	yes	complemented
40	C₃²	C₃×D₈	1	1	yes	characteristic, complemented
41	D₄	—	9	2	no	—
42	C₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
43	C₂×C₃	—	2	4	no	—
44	C₂×C₃	—	36	2	no	—
45	C₂×C₃	C₃×D₁₂	1	4	yes	—
46	C₂×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
47	D₃	—	12	8	no	—
48	C₂²	—	18	2	no	—
49	C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
50	C₃	—	2	4	no	—
51	C₃	C₃×D₂₄	1	4	yes	complemented
52	C₃	#3745	1	1	yes	characteristic, direct product factor
53	C₂	—	36	2	no	—
54	C₂	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₄⋊(C₃⋊D₃)
commutator, cosocle	C₃²×C₄	C₂²×C₃
Frattini	C₄	C₂×C₃×C₃⋊D₃
Fitting	C₃³×C₈	C₂
socle	C₂×C₃³	D₄
hypercenter	C₃×C₈	C₃⋊D₃
hypocenter	C₃²	C₃×D₈
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×C₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₄⋊(C₃⋊D₃)	C₂	semidirect
2. C₃³×C₈	C₂	semidirect
3. #3745	C₃	direct (N × H)
7. C₄⋊(C₃⋊D₃)	C₂×C₃	semidirect
10. C₃²×C₈	D₃	semidirect
11. C₃²×C₈	C₂×C₃	semidirect
21. C₃³	D₈	semidirect
25. C₃×C₈	C₃×D₃	semidirect
26. C₃×C₈	C₃⋊D₃	semidirect
39. C₃²	D₂₄	semidirect
40. C₃²	C₃×D₈	semidirect
42. C₈	C₃×C₃⋊D₃	semidirect
51. C₃	C₃×D₂₄	semidirect
52. C₃	#3745	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×C₄⋊(C₃⋊D₃)	2
C₃³×C₈	2
#3745	3
C₃×D₂₄	3

Subgroups — C3×#3745 #88836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#3745 #88836