Subgroups — C₃×#23748907 #43269727

Order 28548.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#14558651	C₂	1	1	yes	maximal, characteristic
2	#23748907	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₃×Dic₆₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#14558651	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#14558651	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic
7	C₁₃×Dic₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented
9	#14558651	C₃×C₄	1	3	yes	complemented
10	C₃×Dic₆₁⋊C₃	—	13	1	no	maximal, Hall
11	C₂×C₁₃×C₆₁	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃×C₆₁⋊C₃	—	13	1	no	—
13	C₁₃×C₆₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×Dic₆₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented
15	Dic₆₁⋊C₃	—	13	3	no	—
16	C₃×C₆₁⋊C₃	—	13	1	no	Hall
17	C₃×C₄×C₁₃⋊C₃	—	61	1	no	maximal, Hall
18	C₂×C₃×C₆₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₂×C₆₁⋊C₃	—	13	3	no	—
20	Dic₆₁	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃×C₁₃⋊C₃	—	61	1	no	—
22	C₃×C₆₁	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented
23	C₆₁⋊C₃	—	13	3	no	—
24	C₃×C₄×C₁₃	—	183	1	no	—
25	C₄×C₁₃⋊C₃	—	61	3	no	—
26	C₂×C₆₁	C₂×C₃×C₁₃⋊C₃	1	1	yes	characteristic
27	C₃×C₁₃⋊C₃	—	61	1	no	Hall
28	C₂×C₃×C₁₃	D₆₁⋊C₃	1	1	yes	characteristic
29	C₂×C₁₃⋊C₃	—	61	3	no	—
30	C₆₁	C₃×C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₃	—	183	1	no	Hall
32	C₃×C₁₃	Dic₆₁⋊C₃	1	1	yes	characteristic, complemented
33	C₁₃⋊C₃	—	61	3	no	—
34	C₃²×C₄	—	793	1	no	Hall
35	C₂×C₁₃	C₃×D₆₁⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	793	1	no	—
37	C₁₃	C₃×Dic₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	793	3	no	—
39	C₃×C₄	—	183	1	no	—
40	C₃²	—	793	1	no	Sylow
41	C₂×C₃	—	793	3	no	—
42	C₂×C₃	#18011724	1	1	yes	characteristic
43	C₄	—	183	1	no	Sylow
44	C₃	—	793	3	no	—
45	C₃	#23748907	1	1	yes	characteristic, direct product factor
46	C₂	C₃×#18011724	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#18011724
commutator, hypocenter	C₁₃×C₆₁	C₃²×C₄
Frattini	C₂	C₃×#18011724
Fitting, socle	C₂×C₃×C₁₃×C₆₁	C₂×C₃
prime radical	C₂×C₃×#14558651	C₂
cosocle	C₂×C₁₃×C₆₁	C₂×C₃²
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #23748907	C₃	direct (N × H)
3. C₃×C₁₃×Dic₆₁	C₃	semidirect
4. C₃×#14558651	C₄	semidirect
7. C₁₃×Dic₆₁	C₃²	semidirect
8. C₃×C₁₃×C₆₁	C₃×C₄	semidirect
9. #14558651	C₃×C₄	semidirect
13. C₁₃×C₆₁	C₃²×C₄	semidirect
14. C₃×Dic₆₁	C₁₃⋊C₃	semidirect
20. Dic₆₁	C₃×C₁₃⋊C₃	semidirect
22. C₃×C₆₁	C₄×C₁₃⋊C₃	semidirect
30. C₆₁	C₃×C₄×C₁₃⋊C₃	semidirect
32. C₃×C₁₃	Dic₆₁⋊C₃	semidirect
37. C₁₃	C₃×Dic₆₁⋊C₃	semidirect
45. C₃	#23748907	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×#14558651	2
#23748907	3
C₃×C₁₃×Dic₆₁	3
C₃×Dic₆₁⋊C₃	13
C₃×C₄×C₁₃⋊C₃	61

Subgroups — C3×#23748907 #43269727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23748907 #43269727