Subgroups — C₃×#237 #3820

Order 144.

88 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×#67	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#41	—	3	1	no	maximal
7	#237	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃²	C₂²	1	2	yes	—
9	C₂×C₃×D₃	C₂²	1	1	yes	characteristic
10	C₃²×C₄	C₂²	1	1	yes	characteristic
11	C₃×Dic₃	C₂²	1	2	yes	—
12	C₃×Dic₃	C₂²	1	1	yes	characteristic
13	C₃×Q₈	—	3	1	no	—
14	C₃×D₄	—	2	1	no	—
15	C₃×D₄	—	3	2	no	—
16	C₃×D₄	D₃	1	1	yes	characteristic, complemented
17	C₃×D₄	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×C₄	—	3	2	no	—
19	C₂×C₃×C₄	—	3	1	no	—
20	#67	C₂×C₃	1	2	yes	complemented
21	C₂×Dic₃	C₂×C₃	1	2	yes	complemented
22	C₄×D₃	C₂×C₃	1	1	yes	characteristic, complemented
23	Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃²	—	2	2	no	—
25	C₂×C₃²	C₂³	1	1	yes	characteristic
26	C₃×D₃	—	2	1	no	—
27	#41	—	3	1	no	Sylow
28	C₂²×C₃	—	2	2	no	—
29	C₂²×C₃	—	3	1	no	—
30	C₂²×C₃	C₂×D₃	1	2	yes	—
31	C₂²×C₃	C₂²×C₃	1	2	yes	—
32	C₂×D₃	C₂²×C₃	1	1	yes	characteristic
33	C₃×C₄	—	2	1	no	—
34	C₃×C₄	—	3	1	no	—
35	C₃×C₄	—	3	2	no	—
36	C₃×C₄	C₂×D₃	1	1	yes	characteristic
37	C₃×C₄	C₂²×C₃	1	1	yes	characteristic
38	Dic₃	C₂²×C₃	1	2	yes	—
39	Dic₃	C₂²×C₃	1	1	yes	characteristic
40	C₃²	#41	1	1	yes	characteristic, complemented, Sylow
41	Q₈	—	3	1	no	—
42	D₄	—	3	2	no	—
43	D₄	C₃×D₃	1	1	yes	characteristic, complemented
44	C₂×C₄	—	3	2	no	—
45	C₂×C₄	—	3	1	no	—
46	C₂×C₃	—	2	2	no	—
47	C₂×C₃	—	2	2	no	—
48	C₂×C₃	—	2	1	no	—
49	C₂×C₃	—	4	2	no	—
50	C₂×C₃	—	6	1	no	—
51	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
52	C₂×C₃	C₂³×C₃	1	1	yes	characteristic
53	D₃	—	2	1	no	—
54	C₂²	—	3	1	no	—
55	C₂²	C₂×C₃×D₃	1	2	yes	—
56	C₄	—	3	1	no	—
57	C₄	—	3	2	no	—
58	C₄	C₂×C₃×D₃	1	1	yes	characteristic
59	C₃	—	2	1	no	—
60	C₃	#237	1	1	yes	characteristic, direct product factor
61	C₃	C₃×#41	1	1	yes	characteristic, complemented
62	C₂	—	2	2	no	—
63	C₂	—	6	1	no	—
64	C₂	C₂²×C₃×D₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₃
commutator, cosocle	C₂×C₃	C₂³×C₃
Frattini	C₂	C₂²×C₃×D₃
Fitting	C₃²×D₄	C₂
socle	C₂×C₃²	C₂³
hypercenter	C₃×D₄	D₃
hypocenter	C₃	C₃×#41
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ 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×#67	C₂	semidirect
3. C₂×C₃×Dic₃	C₂	semidirect
4. C₃×C₄×D₃	C₂	semidirect
5. C₃×Dic₆	C₂	semidirect
7. #237	C₃	direct (N × H)
16. C₃×D₄	D₃	semidirect
17. C₃×D₄	C₂×C₃	semidirect
20. #67	C₂×C₃	semidirect
21. C₂×Dic₃	C₂×C₃	semidirect
22. C₄×D₃	C₂×C₃	semidirect
23. Dic₆	C₂×C₃	semidirect
40. C₃²	#41	semidirect
43. D₄	C₃×D₃	semidirect
60. C₃	#237	direct (N × H)
61. C₃	C₃×#41	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×#67	2
C₂×C₃×Dic₃	2
C₃×C₄×D₃	2
C₃×Dic₆	2
C₃×#41	3
#237	3

Subgroups — C3×#237 #3820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#237 #3820