Subgroups — D₃×#16813064 #36318656

Order 21294.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16813064	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₆₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813064	—	3	1	no	maximal
4	#16813064	—	2	1	no	—
5	#16813064	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇×C₁₆₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₁₆₉⋊C₃	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₆₉	—	3	1	no	Hall
9	D₃×#63271	—	13	1	no	maximal
10	C₃×C₁₆₉⋊C₃	—	7	1	no	Hall
11	C₇×C₁₆₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃×C₁₆₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₂×C₁₆₉⋊C₃	—	21	1	no	—
14	C₃×#63271	—	13	1	no	—
15	D₃×C₇×C₁₃	C₁₃⋊C₃	1	1	yes	characteristic
16	C₂×#63271	—	39	1	no	—
17	C₃×C₁₆₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
18	C₁₆₉⋊C₃	—	7	1	no	—
19	C₁₆₉⋊C₃	—	14	1	no	—
20	C₂×C₁₆₉	—	3	1	no	Hall
21	C₃×C₇×C₁₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic
22	#63271	—	13	1	no	—
23	#63271	—	26	1	no	—
24	D₃×C₁₃⋊C₃	—	91	1	no	—
25	C₂×C₇×C₁₃	—	3	1	no	—
26	C₁₆₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
27	D₃×ΓL(1,𝔽₈)	—	169	1	no	Hall
28	C₃×C₁₃⋊C₃	—	91	1	no	—
29	C₇×C₁₃	D₃×C₁₃⋊C₃	1	1	yes	characteristic
30	D₃×C₁₃	#63271	1	1	yes	characteristic
31	C₂×C₁₃⋊C₃	—	273	1	no	—
32	C₃×ΓL(1,𝔽₈)	—	169	1	no	Hall
33	D₃×C₇	C₁₆₉⋊C₃	1	1	yes	characteristic, complemented
34	C₂×ΓL(1,𝔽₈)	—	507	1	no	—
35	C₃×C₁₃	C₂×#63271	1	1	yes	characteristic
36	C₁₃⋊C₃	—	91	1	no	—
37	C₁₃⋊C₃	—	182	1	no	—
38	C₂×C₁₃	—	3	1	no	—
39	C₃×C₇	C₂×C₁₆₉⋊C₃	1	1	yes	characteristic, complemented
40	ΓL(1,𝔽₈)	—	338	1	no	—
41	ΓL(1,𝔽₈)	—	169	1	no	—
42	C₃×D₃	—	1183	1	no	Hall
43	C₂×C₇	—	3	1	no	Hall
44	C₁₃	D₃×#63271	1	1	yes	characteristic
45	C₃²	—	1183	1	no	Sylow
46	C₇	D₃×C₁₆₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	3549	1	no	—
48	D₃	#16813064	1	1	yes	characteristic, direct product factor
49	C₃	—	2366	1	no	—
50	C₃	—	1183	1	no	—
51	C₃	C₂×#16813064	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₇×C₁₆₉	C₂×C₃
Frattini	C₁₃	D₃×#63271
socle	C₃×C₇×C₁₃	C₂×C₁₃⋊C₃
LCS	G ▷ C₃×C₇×C₁₆₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#16813064	C₂	semidirect
2. D₃×C₇×C₁₆₉	C₃	semidirect
5. #16813064	D₃	direct (N × H)
6. C₃×C₇×C₁₆₉	C₂×C₃	semidirect
11. C₇×C₁₆₉	C₃×D₃	semidirect
12. D₃×C₁₆₉	ΓL(1,𝔽₈)	semidirect
17. C₃×C₁₆₉	C₂×ΓL(1,𝔽₈)	semidirect
26. C₁₆₉	D₃×ΓL(1,𝔽₈)	semidirect
33. D₃×C₇	C₁₆₉⋊C₃	semidirect
39. C₃×C₇	C₂×C₁₆₉⋊C₃	semidirect
46. C₇	D₃×C₁₆₉⋊C₃	semidirect
48. D₃	#16813064	direct (N × H)
51. C₃	C₂×#16813064	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16813064	2
D₃×C₇×C₁₆₉	3
C₂×#16813064	3
D₃×C₁₆₉⋊C₃	7
D₃×#63271	13

Subgroups — D3×#16813064 #36318656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#16813064 #36318656