Subgroups — C₃×#26015661 #46802839

Order 34164.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19151048	C₂	1	1	yes	maximal, characteristic
2	C₃×#16838291	C₃	1	1	yes	maximal, characteristic, complemented
3	#26015661	C₃	1	3	yes	maximal, direct product factor
4	C₃×#15667865	C₄	1	1	yes	characteristic, complemented, Hall
5	#19151048	C₂×C₃	1	3	yes	—
6	C₃×D₉₄₉	C₂×C₃	1	1	yes	characteristic
7	#16838291	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₃×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented
9	#15667865	C₃×C₄	1	3	yes	complemented
10	C₃×#64408⋊C₃	—	13	1	no	maximal, Hall
11	D₉₄₉	C₂×C₃²	1	1	yes	characteristic
12	C₃×D₇₃⋊C₃	—	13	1	no	—
13	C₁₃×C₇₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃×#64408	—	13	1	no	—
15	#64408⋊C₃	—	13	3	no	—
16	C₃×C₇₃⋊C₃	—	13	1	no	Hall
17	C₃×AGL(1,𝔽₁₃)	—	73	1	no	maximal, Hall
18	C₃×D₇₃	—	13	1	no	—
19	D₇₃⋊C₃	—	13	3	no	—
20	#64408	—	13	1	no	Hall
21	C₃×D₁₃⋊C₃	—	73	1	no	—
22	C₃×C₇₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
23	C₇₃⋊C₃	—	13	3	no	—
24	C₃×#261	—	73	1	no	—
25	AGL(1,𝔽₁₃)	—	73	3	no	—
26	D₇₃	—	13	1	no	—
27	C₃×C₁₃⋊C₃	—	73	1	no	Hall
28	C₃×D₁₃	—	73	1	no	—
29	D₁₃⋊C₃	—	73	3	no	—
30	C₇₃	C₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
31	#261	—	73	1	no	Hall
32	C₃×C₁₃	#64408⋊C₃	1	1	yes	characteristic, complemented
33	C₁₃⋊C₃	—	73	3	no	—
34	C₃²×C₄	—	949	1	no	Hall
35	D₁₃	—	73	1	no	—
36	C₂×C₃²	—	949	1	no	—
37	C₁₃	C₃×#64408⋊C₃	1	1	yes	characteristic, complemented, Sylow
38	C₃×C₄	—	949	3	no	—
39	C₃×C₄	—	949	1	no	—
40	C₃²	—	949	1	no	Sylow
41	C₂×C₃	—	949	3	no	—
42	C₂×C₃	—	949	1	no	—
43	C₄	—	949	1	no	Sylow
44	C₃	—	949	3	no	—
45	C₃	#26015661	1	1	yes	characteristic, direct product factor
46	C₂	—	949	1	no	—

	subgroup	G/H
center, hypercenter	C₃	#26015661
commutator, hypocenter	C₁₃×C₇₃	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₇₃	C₃×C₄
prime radical	C₃×#19151048	C₂
cosocle	D₉₄₉	C₂×C₃²
LCS	G ▷ C₁₃×C₇₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×#16838291	C₃	semidirect
3. #26015661	C₃	direct (N × H)
4. C₃×#15667865	C₄	semidirect
7. #16838291	C₃²	semidirect
8. C₃×C₁₃×C₇₃	C₃×C₄	semidirect
9. #15667865	C₃×C₄	semidirect
13. C₁₃×C₇₃	C₃²×C₄	semidirect
22. C₃×C₇₃	AGL(1,𝔽₁₃)	semidirect
30. C₇₃	C₃×AGL(1,𝔽₁₃)	semidirect
32. C₃×C₁₃	#64408⋊C₃	semidirect
37. C₁₃	C₃×#64408⋊C₃	semidirect
45. C₃	#26015661	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×#19151048	2
C₃×#16838291	3
#26015661	3
C₃×#64408⋊C₃	13
C₃×AGL(1,𝔽₁₃)	73

Subgroups — C3×#26015661 #46802839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#26015661 #46802839