Subgroups — C₂×C₃⋊(#41⋊C₃) #64273

Order 288.

105 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(#41⋊C₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×#239	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×#41⋊C₃	—	3	1	no	maximal
5	C₂×C₃×Dic₃	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	C₂²	1	1	yes	characteristic, complemented
7	C₂×C₃×Q₈	C₂×C₃	1	1	yes	characteristic
8	#239	—	3	2	no	—
9	#239	C₂×C₃	1	2	yes	complemented
10	C₂×D₁₂	—	3	1	no	—
11	C₂×C₄×D₃	—	3	1	no	—
12	#41⋊C₃	—	3	2	no	—
13	C₂×SL(2,𝔽₃)	—	2	1	no	—
14	C₂×SL(2,𝔽₃)	D₃	1	1	yes	characteristic, complemented
15	C₂²×C₃²	—	4	1	no	—
16	C₃×Dic₃	—	4	2	no	—
17	C₂×#41	—	3	1	no	Sylow
18	C₂²×D₃	—	3	1	no	—
19	C₃×Q₈	—	3	1	no	—
20	C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
21	C₂×C₃×C₄	—	3	1	no	—
22	C₂×C₃×C₄	—	12	1	no	—
23	C₂×Dic₃	A₄	1	1	yes	characteristic
24	D₁₂	—	3	2	no	—
25	D₁₂	—	3	2	no	—
26	C₄×D₃	—	3	2	no	—
27	C₄×D₃	—	3	2	no	—
28	SL(2,𝔽₃)	—	2	1	no	—
29	SL(2,𝔽₃)	C₂×D₃	1	1	yes	characteristic, complemented
30	C₂×C₃²	—	4	2	no	—
31	C₂×C₃²	—	4	1	no	—
32	#41	—	3	2	no	—
33	#41	—	9	2	no	—
34	C₂×Q₈	C₃×D₃	1	1	yes	characteristic
35	C₂×D₄	—	9	1	no	—
36	C₂²×C₄	—	9	1	no	—
37	C₂²×C₃	—	4	1	no	—
38	C₂²×C₃	—	8	1	no	—
39	C₂²×C₃	C₂×A₄	1	1	yes	characteristic
40	C₂×D₃	—	3	2	no	—
41	C₂×D₃	—	6	2	no	—
42	C₃×C₄	—	3	1	no	—
43	C₃×C₄	—	3	1	no	—
44	C₃×C₄	—	12	2	no	—
45	Dic₃	C₂×A₄	1	2	yes	—
46	C₃²	—	4	1	no	Sylow
47	C₂³	—	9	1	no	—
48	Q₈	—	3	1	no	—
49	Q₈	C₂×C₃×D₃	1	1	yes	characteristic
50	D₄	—	9	2	no	—
51	D₄	—	9	2	no	—
52	C₂×C₄	—	3	1	no	—
53	C₂×C₄	—	3	1	no	—
54	C₂×C₄	—	9	2	no	—
55	C₂×C₄	—	9	2	no	—
56	C₂×C₃	—	4	1	no	—
57	C₂×C₃	—	4	2	no	—
58	C₂×C₃	—	8	1	no	—
59	C₂×C₃	—	8	2	no	—
60	C₂×C₃	#41⋊C₃	1	2	yes	complemented
61	C₂×C₃	C₂²×A₄	1	1	yes	characteristic
62	D₃	—	6	2	no	—
63	C₂²	—	9	2	no	—
64	C₂²	—	18	2	no	—
65	C₂²	D₃×A₄	1	1	yes	characteristic
66	C₄	—	3	1	no	—
67	C₄	—	3	1	no	—
68	C₄	—	3	2	no	—
69	C₃	—	4	1	no	—
70	C₃	—	8	1	no	—
71	C₃	C₂×#41⋊C₃	1	1	yes	characteristic, complemented
72	C₂	—	18	2	no	—
73	C₂	C₃⋊(#41⋊C₃)	1	2	yes	direct product factor
74	C₂	C₂×D₃×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×A₄
commutator, cosocle, hypocenter	C₃×Q₈	C₂²×C₃
Frattini	C₂	C₂×D₃×A₄
Fitting	C₂×C₃×Q₈	C₂×C₃
socle	C₂²×C₃	C₂×A₄
LCS	G ▷ C₃×Q₈
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×SL(2,𝔽₃)	C₂	semidirect
2. C₃⋊(#41⋊C₃)	C₂	direct (N × H)
3. C₂×#239	C₃	semidirect
6. C₃×SL(2,𝔽₃)	C₂²	semidirect
9. #239	C₂×C₃	semidirect
14. C₂×SL(2,𝔽₃)	D₃	semidirect
29. SL(2,𝔽₃)	C₂×D₃	semidirect
60. C₂×C₃	#41⋊C₃	semidirect
71. C₃	C₂×#41⋊C₃	semidirect
73. C₂	C₃⋊(#41⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×SL(2,𝔽₃)	2
C₃⋊(#41⋊C₃)	2
C₂×#239	3
C₂×#41⋊C₃	3
C₂×C₃×Dic₃	4

Subgroups — C2×C3⋊(#41⋊C3) #64273

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊(#41⋊C₃) #64273