Subgroups — C₃×#213 #3737

Order 144.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₈	—	3	1	no	maximal
5	#213	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃²	—	2	1	no	—
7	C₂×C₃×D₃	—	2	1	no	—
8	C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₃×D₄	—	2	1	no	—
10	C₃×D₄	—	3	1	no	—
11	C₃×D₄	D₃	1	1	yes	characteristic, complemented
12	C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
13	D₁₂	C₂×C₃	1	1	yes	characteristic, complemented
14	C₃×C₈	—	3	1	no	—
15	C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²	—	4	1	no	—
17	C₂×C₃²	D₄	1	1	yes	characteristic
18	C₃×D₃	—	4	1	no	—
19	D₈	—	3	1	no	Sylow
20	C₂²×C₃	—	2	2	no	—
21	C₂²×C₃	—	2	1	no	—
22	C₂²×C₃	—	2	1	no	—
23	C₂²×C₃	—	6	1	no	—
24	C₂×D₃	—	2	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂×D₃	1	1	yes	characteristic
27	C₃×C₄	C₂²×C₃	1	1	yes	characteristic
28	C₃²	D₈	1	1	yes	characteristic, complemented, Sylow
29	D₄	—	3	1	no	—
30	D₄	C₃×D₃	1	1	yes	characteristic, complemented
31	C₈	—	3	1	no	—
32	C₂×C₃	—	2	1	no	—
33	C₂×C₃	—	4	2	no	—
34	C₂×C₃	—	4	1	no	—
35	C₂×C₃	—	4	1	no	—
36	C₂×C₃	—	12	1	no	—
37	C₂×C₃	#67	1	1	yes	characteristic
38	C₂×C₃	C₃×D₄	1	1	yes	characteristic
39	D₃	—	4	1	no	—
40	C₂²	—	2	1	no	—
41	C₂²	—	6	1	no	—
42	C₄	C₂×C₃×D₃	1	1	yes	characteristic
43	C₃	—	2	1	no	—
44	C₃	#213	1	1	yes	characteristic, direct product factor
45	C₃	C₃×D₈	1	1	yes	characteristic, complemented
46	C₂	—	4	1	no	—
47	C₂	—	12	1	no	—
48	C₂	C₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#67
commutator, cosocle	C₃×C₄	C₂²×C₃
Frattini	C₄	C₂×C₃×D₃
Fitting	C₃²×D₄	C₂
socle	C₂×C₃²	D₄
hypercenter	C₃×D₄	D₃
hypocenter	C₃	C₃×D₈
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₃×C₄ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃²×D₄	C₂	semidirect
2. C₃×D₁₂	C₂	semidirect
3. C₃×C₃⋊C₈	C₂	semidirect
5. #213	C₃	direct (N × H)
11. C₃×D₄	D₃	semidirect
12. C₃×D₄	C₂×C₃	semidirect
13. D₁₂	C₂×C₃	semidirect
15. C₃⋊C₈	C₂×C₃	semidirect
28. C₃²	D₈	semidirect
30. D₄	C₃×D₃	semidirect
44. C₃	#213	direct (N × H)
45. C₃	C₃×D₈	semidirect

Maximal subgroups

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

subgroup	index
C₃²×D₄	2
C₃×D₁₂	2
C₃×C₃⋊C₈	2
C₃×D₈	3
#213	3

Subgroups — C3×#213 #3737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#213 #3737