Subgroups — C₃×#20259485 #32913784

Order 18396.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#13095276	C₂	1	1	yes	maximal, characteristic
2	#20259485	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×Dic₇₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#13095276	C₄	1	1	yes	characteristic, complemented, Hall
5	C₂×#13095276	C₂×C₃	1	3	yes	—
6	C₂×C₃×C₇×C₇₃	C₂×C₃	1	1	yes	characteristic
7	C₃×Dic₇₃⋊C₃	—	7	1	no	maximal, Hall
8	C₇×Dic₇₃	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇×C₇₃	C₃×C₄	1	1	yes	characteristic, complemented
10	#13095276	C₃×C₄	1	3	yes	complemented
11	C₂×C₃×C₇₃⋊C₃	—	7	1	no	—
12	C₂×C₇×C₇₃	C₂×C₃²	1	1	yes	characteristic
13	C₃×Dic₇₃	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	Dic₇₃⋊C₃	—	7	3	no	—
15	C₃×C₇₃⋊C₃	—	7	1	no	Hall
16	C₇×C₇₃	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
18	C₂×C₇₃⋊C₃	—	7	3	no	—
19	Dic₇₃	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×ΓL(1,𝔽₈)	—	73	1	no	maximal, Hall
21	C₃×C₇₃	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
22	C₇₃⋊C₃	—	7	3	no	—
23	C₂×C₇₃	C₂×C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₂×C₃×ΓL(1,𝔽₈)	—	73	1	no	—
25	C₃×C₄×C₇	—	219	1	no	—
26	C₄×ΓL(1,𝔽₈)	—	73	3	no	—
27	C₇₃	C₃×C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
28	C₃×ΓL(1,𝔽₈)	—	73	1	no	Hall
29	C₂×C₃×C₇	D₇₃⋊C₃	1	1	yes	characteristic
30	C₂×ΓL(1,𝔽₈)	—	73	3	no	—
31	C₃²×C₄	—	511	1	no	Hall
32	C₄×C₇	—	219	1	no	Hall
33	C₃×C₇	Dic₇₃⋊C₃	1	1	yes	characteristic, complemented
34	ΓL(1,𝔽₈)	—	73	3	no	—
35	C₂×C₃²	—	511	1	no	—
36	C₂×C₇	C₃×D₇₃⋊C₃	1	1	yes	characteristic
37	C₃×C₄	—	219	1	no	—
38	C₃×C₄	—	511	3	no	—
39	C₃²	—	511	1	no	Sylow
40	C₇	C₃×Dic₇₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₃	—	511	3	no	—
42	C₂×C₃	#15690442	1	1	yes	characteristic
43	C₄	—	219	1	no	Sylow
44	C₃	—	511	3	no	—
45	C₃	#20259485	1	1	yes	characteristic, direct product factor
46	C₂	C₃×#15690442	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	#15690442
commutator, hypocenter	C₇×C₇₃	C₃²×C₄
Frattini	C₂	C₃×#15690442
Fitting, socle	C₂×C₃×C₇×C₇₃	C₂×C₃
prime radical	C₂×C₃×#13095276	C₂
cosocle	C₂×C₇×C₇₃	C₂×C₃²
LCS	G ▷ C₇×C₇₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. #20259485	C₃	direct (N × H)
3. C₃×C₇×Dic₇₃	C₃	semidirect
4. C₃×#13095276	C₄	semidirect
8. C₇×Dic₇₃	C₃²	semidirect
9. C₃×C₇×C₇₃	C₃×C₄	semidirect
10. #13095276	C₃×C₄	semidirect
13. C₃×Dic₇₃	ΓL(1,𝔽₈)	semidirect
16. C₇×C₇₃	C₃²×C₄	semidirect
19. Dic₇₃	C₃×ΓL(1,𝔽₈)	semidirect
21. C₃×C₇₃	C₄×ΓL(1,𝔽₈)	semidirect
27. C₇₃	C₃×C₄×ΓL(1,𝔽₈)	semidirect
33. C₃×C₇	Dic₇₃⋊C₃	semidirect
40. C₇	C₃×Dic₇₃⋊C₃	semidirect
45. C₃	#20259485	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×#13095276	2
#20259485	3
C₃×C₇×Dic₇₃	3
C₃×Dic₇₃⋊C₃	7
C₃×C₄×ΓL(1,𝔽₈)	73

Subgroups — C3×#20259485 #32913784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#20259485 #32913784