Subgroups — C₃×#217 #3741

Order 144.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₃	C₂	1	2	yes	maximal, complemented
3	C₃×C₂²⋊C₄	—	3	1	no	maximal
4	#217	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂²×C₃²	—	2	2	no	—
6	C₂²×C₃²	C₄	1	2	yes	complemented
7	C₂²×C₃²	C₂²	1	1	yes	characteristic
8	C₃×Dic₃	—	2	2	no	—
9	C₂³×C₃	—	2	1	no	—
10	C₂³×C₃	D₃	1	1	yes	characteristic
11	C₂³×C₃	C₂×C₃	1	1	yes	characteristic
12	C₂×C₃×C₄	—	3	2	no	—
13	C₂×Dic₃	C₂×C₃	1	2	yes	complemented
14	C₂×C₃²	—	2	2	no	—
15	C₂×C₃²	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃²	D₄	1	2	yes	—
17	C₂²⋊C₄	—	3	1	no	Sylow
18	C₂²×C₃	—	2	4	no	—
19	C₂²×C₃	—	2	2	no	—
20	C₂²×C₃	—	2	2	no	—
21	C₂²×C₃	—	2	2	no	—
22	C₂²×C₃	—	2	1	no	—
23	C₂²×C₃	Dic₃	1	2	yes	complemented
24	C₂²×C₃	C₃×C₄	1	2	yes	complemented
25	C₂²×C₃	C₂×D₃	1	1	yes	characteristic
26	C₂²×C₃	C₂²×C₃	1	1	yes	characteristic
27	C₃×C₄	—	6	2	no	—
28	Dic₃	—	2	2	no	—
29	C₃²	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
30	C₂³	C₃×D₃	1	1	yes	characteristic
31	C₂×C₄	—	3	2	no	—
32	C₂×C₃	—	2	4	no	—
33	C₂×C₃	—	2	2	no	—
34	C₂×C₃	—	2	2	no	—
35	C₂×C₃	—	2	1	no	—
36	C₂×C₃	—	2	2	no	—
37	C₂×C₃	C₂×Dic₃	1	1	yes	characteristic
38	C₂×C₃	#67	1	2	yes	—
39	C₂×C₃	C₂×C₃×C₄	1	1	yes	characteristic
40	C₂×C₃	C₃×D₄	1	2	yes	—
41	C₂²	—	2	2	no	—
42	C₂²	C₃×Dic₃	1	2	yes	complemented
43	C₂²	C₂×C₃×D₃	1	1	yes	characteristic
44	C₄	—	6	2	no	—
45	C₃	—	2	1	no	—
46	C₃	#217	1	1	yes	characteristic, direct product factor
47	C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic, complemented
48	C₂	—	2	2	no	—
49	C₂	C₂×C₃×Dic₃	1	1	yes	characteristic
50	C₂	C₃×#67	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₃
commutator	C₂×C₃	C₂×C₃×C₄
Frattini	C₂²	C₂×C₃×D₃
Fitting, prime radical	C₂³×C₃²	C₂
socle	C₂²×C₃²	C₂²
cosocle	C₂²×C₃	C₂²×C₃
hypercenter	C₂³×C₃	D₃
hypocenter	C₃	C₃×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
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×Dic₃	C₂	semidirect
4. #217	C₃	direct (N × H)
6. C₂²×C₃²	C₄	semidirect
13. C₂×Dic₃	C₂×C₃	semidirect
23. C₂²×C₃	Dic₃	semidirect
24. C₂²×C₃	C₃×C₄	semidirect
29. C₃²	C₂²⋊C₄	semidirect
42. C₂²	C₃×Dic₃	semidirect
46. C₃	#217	direct (N × H)
47. C₃	C₃×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃²	2
C₂×C₃×Dic₃	2
C₃×C₂²⋊C₄	3
#217	3

Subgroups — C3×#217 #3741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#217 #3741