Subgroups — C₃×#19150311 #30660787

Order 16758.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14584115	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#19150311	C₃	1	3	yes	maximal, direct product factor
4	#14584115	C₂×C₃	1	3	yes	complemented
5	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	C₃×#11716321	—	7	8	no	maximal
7	C₇²×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×#87704	—	7	8	no	—
9	C₇²×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×#3861	—	19	1	no	maximal, Hall
11	C₃×C₇×D₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
12	#11716321	—	7	24	no	—
13	C₃×#3861	—	19	1	no	Hall
14	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
15	#87704	—	7	24	no	—
16	C₃×D₁₉⋊C₃	—	49	1	no	Hall
17	C₂×C₃×C₇²	—	57	1	no	—
18	C₂×#3861	—	19	3	no	—
19	C₇×D₁₉	C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
20	C₃×C₁₉⋊C₃	—	49	1	no	Hall
21	C₃×C₇²	D₁₉⋊C₃	1	1	yes	characteristic, complemented
22	#3861	—	19	3	no	—
23	C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	1	8	yes	complemented
24	C₂×C₃×ΓL(1,𝔽₈)	—	133	8	no	—
25	C₃×D₁₉	#3861	1	1	yes	characteristic, complemented
26	D₁₉⋊C₃	—	49	3	no	—
27	C₂×C₇²	—	57	1	no	Hall
28	C₃×ΓL(1,𝔽₈)	—	133	8	no	—
29	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
30	C₁₉⋊C₃	—	49	3	no	—
31	C₇²	C₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₃×C₇	—	57	8	no	—
33	C₂×ΓL(1,𝔽₈)	—	133	24	no	—
34	D₁₉	C₃×#3861	1	1	yes	characteristic, complemented, Hall
35	C₃×C₇	#11716321	1	8	yes	complemented
36	ΓL(1,𝔽₈)	—	133	24	no	—
37	C₁₉	C₂×C₃×#3861	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃²	—	931	1	no	Hall
39	C₂×C₇	—	57	8	no	—
40	C₃²	—	931	1	no	Sylow
41	C₇	C₃×#11716321	1	8	yes	complemented
42	C₂×C₃	—	57	1	no	—
43	C₂×C₃	—	931	3	no	—
44	C₃	—	931	3	no	—
45	C₃	#19150311	1	1	yes	characteristic, direct product factor
46	C₂	—	57	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#19150311
commutator, cosocle, hypocenter	C₇²×C₁₉	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#14584115	C₂	semidirect
2. C₃×C₇²×D₁₉	C₃	semidirect
3. #19150311	C₃	direct (N × H)
4. #14584115	C₂×C₃	semidirect
5. C₃×C₇²×C₁₉	C₂×C₃	semidirect
7. C₇²×D₁₉	C₃²	semidirect
9. C₇²×C₁₉	C₂×C₃²	semidirect
11. C₃×C₇×D₁₉	ΓL(1,𝔽₈)	semidirect
14. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. C₇×D₁₉	C₃×ΓL(1,𝔽₈)	semidirect
21. C₃×C₇²	D₁₉⋊C₃	semidirect
23. C₇×C₁₉	C₂×C₃×ΓL(1,𝔽₈)	semidirect
25. C₃×D₁₉	#3861	semidirect
29. C₃×C₁₉	C₂×#3861	semidirect
31. C₇²	C₃×D₁₉⋊C₃	semidirect
34. D₁₉	C₃×#3861	semidirect
35. C₃×C₇	#11716321	semidirect
37. C₁₉	C₂×C₃×#3861	semidirect
41. C₇	C₃×#11716321	semidirect
45. C₃	#19150311	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×#14584115	2
C₃×C₇²×D₁₉	3
#19150311	3
C₃×#11716321	7
C₂×C₃×#3861	19

Subgroups — C3×#19150311 #30660787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#19150311 #30660787