Subgroups — C₃×#64602 #11745513

Order 936.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₃₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₂²⋊D₁₃	—	3	1	no	maximal
5	#64602	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂×C₃²×C₁₃	C₂²	1	1	yes	characteristic
7	C₃×D₃×C₁₃	—	2	1	no	—
8	C₃²×D₁₃	—	2	1	no	—
9	C₂²×C₃×C₁₃	—	3	1	no	—
10	C₂×D₃×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
11	C₂×C₃×D₁₃	—	2	1	no	—
12	C₂×C₃×D₁₃	D₃	1	1	yes	characteristic, complemented
13	C₂×C₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	Dic₃₉	C₂×C₃	1	1	yes	characteristic, complemented
15	C₃×Dic₁₃	—	3	1	no	—
16	C₃²×C₁₃	D₄	1	1	yes	characteristic, complemented, Hall
17	C₂²⋊D₁₃	—	3	1	no	Hall
18	C₂×C₃×C₁₃	—	2	1	no	—
19	C₂×C₃×C₁₃	—	6	1	no	—
20	C₂×C₃×C₁₃	C₂×D₃	1	1	yes	characteristic
21	C₂×C₃×C₁₃	C₂²×C₃	1	1	yes	characteristic
22	C₃×D₁₃	—	2	2	no	—
23	C₃×D₁₃	—	2	1	no	—
24	C₃×D₁₃	—	2	1	no	—
25	D₃×C₁₃	—	2	1	no	—
26	C₃×#67	—	13	1	no	maximal, Hall
27	C₂²×C₁₃	—	3	1	no	—
28	C₂×D₁₃	C₃×D₃	1	1	yes	characteristic, complemented
29	Dic₁₃	—	3	1	no	—
30	C₃×C₁₃	—	2	1	no	—
31	C₃×C₁₃	#67	1	1	yes	characteristic, complemented
32	C₃×C₁₃	C₃×D₄	1	1	yes	characteristic, complemented
33	C₂²×C₃²	—	13	1	no	—
34	C₂×C₃×D₃	D₁₃	1	1	yes	characteristic, complemented
35	C₃×Dic₃	—	13	1	no	—
36	C₂×C₁₃	—	6	1	no	—
37	C₂×C₁₃	C₂×C₃×D₃	1	1	yes	characteristic
38	D₁₃	—	2	1	no	—
39	C₃×D₄	—	39	1	no	—
40	#67	—	13	1	no	—
41	C₂×C₃²	—	26	1	no	—
42	C₂×C₃²	C₂×D₁₃	1	1	yes	characteristic
43	C₃×D₃	—	2	1	no	—
44	C₁₃	C₃×#67	1	1	yes	characteristic, complemented, Sylow
45	C₂²×C₃	—	3	1	no	—
46	C₂²×C₃	—	13	1	no	—
47	C₂²×C₃	—	13	1	no	—
48	C₂²×C₃	—	26	1	no	—
49	C₂×D₃	C₃×D₁₃	1	1	yes	characteristic, complemented
50	C₃×C₄	—	39	1	no	—
51	Dic₃	—	13	1	no	—
52	C₃²	C₂²⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
53	D₄	—	39	1	no	Sylow
54	C₂×C₃	—	2	1	no	—
55	C₂×C₃	—	6	1	no	—
56	C₂×C₃	—	26	2	no	—
57	C₂×C₃	—	26	1	no	—
58	C₂×C₃	—	26	1	no	—
59	C₂×C₃	D₃×D₁₃	1	1	yes	characteristic
60	C₂×C₃	C₂×C₃×D₁₃	1	1	yes	characteristic
61	D₃	—	2	1	no	—
62	C₂²	—	3	1	no	—
63	C₂²	—	13	1	no	—
64	C₄	—	39	1	no	—
65	C₃	—	2	1	no	—
66	C₃	#64602	1	1	yes	characteristic, direct product factor
67	C₃	C₃×C₂²⋊D₁₃	1	1	yes	characteristic, complemented
68	C₂	—	6	1	no	—
69	C₂	—	26	1	no	—
70	C₂	C₃×D₃×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×D₁₃
commutator, cosocle	C₂×C₃×C₁₃	C₂²×C₃
Frattini	C₂	C₃×D₃×D₁₃
Fitting, socle	C₂×C₃²×C₁₃	C₂²
hypocenter	C₃×C₁₃	C₃×D₄
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×C₁₃	C₂	semidirect
2. C₂×C₃²×D₁₃	C₂	semidirect
3. C₃×Dic₃₉	C₂	semidirect
5. #64602	C₃	direct (N × H)
10. C₂×D₃×C₁₃	C₂×C₃	semidirect
12. C₂×C₃×D₁₃	D₃	semidirect
13. C₂×C₃×D₁₃	C₂×C₃	semidirect
14. Dic₃₉	C₂×C₃	semidirect
16. C₃²×C₁₃	D₄	semidirect
28. C₂×D₁₃	C₃×D₃	semidirect
31. C₃×C₁₃	#67	semidirect
32. C₃×C₁₃	C₃×D₄	semidirect
34. C₂×C₃×D₃	D₁₃	semidirect
44. C₁₃	C₃×#67	semidirect
49. C₂×D₃	C₃×D₁₃	semidirect
52. C₃²	C₂²⋊D₁₃	semidirect
66. C₃	#64602	direct (N × H)
67. C₃	C₃×C₂²⋊D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×C₁₃	2
C₂×C₃²×D₁₃	2
C₃×Dic₃₉	2
C₃×C₂²⋊D₁₃	3
#64602	3
C₃×#67	13

Subgroups — C3×#64602 #11745513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#64602 #11745513