Subgroups — C₃×#23782986 #44535698

Order 31356.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19104947	C₂	1	1	yes	maximal, characteristic
2	C₃×C₆₇⋊#261	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782986	C₃	1	3	yes	maximal, direct product factor
4	C₃×#14579732	C₄	1	1	yes	characteristic, complemented, Hall
5	#19104947	C₂×C₃	1	3	yes	—
6	C₃×D₁₃×C₆₇	C₂×C₃	1	1	yes	characteristic
7	C₆₇⋊#261	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented
9	#14579732	C₃×C₄	1	3	yes	complemented
10	C₃×(C₆₇⋊C₃)⋊C₄	—	13	1	no	maximal, Hall
11	D₁₃×C₆₇	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃×C₆₇⋊C₃	—	13	1	no	—
13	C₁₃×C₆₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×Dic₆₇	—	13	1	no	—
15	(C₆₇⋊C₃)⋊C₄	—	13	3	no	—
16	C₃×C₆₇⋊C₃	—	13	1	no	Hall
17	C₃×AGL(1,𝔽₁₃)	—	67	1	no	maximal, Hall
18	C₂×C₃×C₆₇	—	13	1	no	—
19	C₂×C₆₇⋊C₃	—	13	3	no	—
20	Dic₆₇	—	13	1	no	Hall
21	C₃×D₁₃⋊C₃	—	67	1	no	—
22	C₃×C₆₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
23	C₆₇⋊C₃	—	13	3	no	—
24	C₃×#261	—	67	1	no	—
25	AGL(1,𝔽₁₃)	—	67	3	no	—
26	C₂×C₆₇	—	13	1	no	—
27	C₃×C₁₃⋊C₃	—	67	1	no	Hall
28	C₃×D₁₃	D₆₇⋊C₃	1	1	yes	characteristic
29	D₁₃⋊C₃	—	67	3	no	—
30	C₆₇	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
31	#261	—	67	1	no	Hall
32	C₃×C₁₃	(C₆₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
33	C₁₃⋊C₃	—	67	3	no	—
34	C₃²×C₄	—	871	1	no	Hall
35	D₁₃	C₃×D₆₇⋊C₃	1	1	yes	characteristic
36	C₂×C₃²	—	871	1	no	—
37	C₁₃	C₃×(C₆₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	871	1	no	—
39	C₃×C₄	—	871	3	no	—
40	C₃²	—	871	1	no	Sylow
41	C₂×C₃	—	13	1	no	—
42	C₂×C₃	—	871	3	no	—
43	C₄	—	871	1	no	Sylow
44	C₃	—	871	3	no	—
45	C₃	#23782986	1	1	yes	characteristic, direct product factor
46	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#23782986
commutator, hypocenter	C₁₃×C₆₇	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₆₇	C₃×C₄
prime radical	C₃×#19104947	C₂
cosocle	D₁₃×C₆₇	C₂×C₃²
LCS	G ▷ C₁₃×C₆₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₆₇⋊#261	C₃	semidirect
3. #23782986	C₃	direct (N × H)
4. C₃×#14579732	C₄	semidirect
7. C₆₇⋊#261	C₃²	semidirect
8. C₃×C₁₃×C₆₇	C₃×C₄	semidirect
9. #14579732	C₃×C₄	semidirect
13. C₁₃×C₆₇	C₃²×C₄	semidirect
22. C₃×C₆₇	AGL(1,𝔽₁₃)	semidirect
30. C₆₇	C₃×AGL(1,𝔽₁₃)	semidirect
32. C₃×C₁₃	(C₆₇⋊C₃)⋊C₄	semidirect
37. C₁₃	C₃×(C₆₇⋊C₃)⋊C₄	semidirect
45. C₃	#23782986	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#19104947	2
C₃×C₆₇⋊#261	3
#23782986	3
C₃×(C₆₇⋊C₃)⋊C₄	13
C₃×AGL(1,𝔽₁₃)	67

Subgroups — C3×#23782986 #44535698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782986 #44535698