Subgroups — D₃×#14584115 #30660849

Order 16758.

180 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	D₃×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#14584115	—	3	1	no	maximal
4	#14584115	—	2	1	no	—
5	#14584115	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×#87704	—	7	8	no	maximal
8	C₂×C₇²×C₁₉	—	3	1	no	Hall
9	C₃×#87704	—	7	8	no	—
10	C₇²×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×#3861	—	19	1	no	maximal, Hall
12	D₃×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
13	C₂×#87704	—	21	8	no	—
14	C₃×#3861	—	19	1	no	Hall
15	C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	#87704	—	7	8	no	—
17	#87704	—	14	8	no	—
18	D₃×C₁₉⋊C₃	—	49	1	no	Hall
19	D₃×C₇²	C₁₉⋊C₃	1	1	yes	characteristic, complemented
20	C₂×#3861	—	57	1	no	—
21	C₂×C₇×C₁₉	—	3	8	no	—
22	C₃×C₁₉⋊C₃	—	49	1	no	Hall
23	C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
24	#3861	—	19	1	no	—
25	#3861	—	38	1	no	—
26	C₇×C₁₉	D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
27	D₃×ΓL(1,𝔽₈)	—	133	8	no	—
28	D₃×C₁₉	#3861	1	1	yes	characteristic, complemented
29	C₂×C₁₉⋊C₃	—	147	1	no	—
30	C₂×C₇²	—	3	1	no	Hall
31	C₃×ΓL(1,𝔽₈)	—	133	8	no	—
32	C₃×C₁₉	C₂×#3861	1	1	yes	characteristic, complemented
33	C₁₉⋊C₃	—	49	1	no	—
34	C₁₉⋊C₃	—	98	1	no	—
35	C₇²	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	D₃×C₇	#87704	1	8	yes	complemented
37	C₂×ΓL(1,𝔽₈)	—	399	8	no	—
38	C₂×C₁₉	—	3	1	no	Hall
39	C₃×C₇	C₂×#87704	1	8	yes	complemented
40	ΓL(1,𝔽₈)	—	266	8	no	—
41	ΓL(1,𝔽₈)	—	133	8	no	—
42	C₁₉	D₃×#3861	1	1	yes	characteristic, complemented, Sylow
43	C₃×D₃	—	931	1	no	Hall
44	C₂×C₇	—	3	8	no	—
45	C₃²	—	931	1	no	Sylow
46	C₇	D₃×#87704	1	8	yes	complemented
47	C₂×C₃	—	2793	1	no	—
48	D₃	#14584115	1	1	yes	characteristic, direct product factor
49	C₃	—	1862	1	no	—
50	C₃	—	931	1	no	—
51	C₃	C₂×#14584115	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

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

Complements

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

N	H ≅ G/N	type
1. C₃×#14584115	C₂	semidirect
2. D₃×C₇²×C₁₉	C₃	semidirect
5. #14584115	D₃	direct (N × H)
6. C₃×C₇²×C₁₉	C₂×C₃	semidirect
10. C₇²×C₁₉	C₃×D₃	semidirect
12. D₃×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
15. C₃×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
19. D₃×C₇²	C₁₉⋊C₃	semidirect
23. C₃×C₇²	C₂×C₁₉⋊C₃	semidirect
26. C₇×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
28. D₃×C₁₉	#3861	semidirect
32. C₃×C₁₉	C₂×#3861	semidirect
35. C₇²	D₃×C₁₉⋊C₃	semidirect
36. D₃×C₇	#87704	semidirect
39. C₃×C₇	C₂×#87704	semidirect
42. C₁₉	D₃×#3861	semidirect
46. C₇	D₃×#87704	semidirect
48. D₃	#14584115	direct (N × H)
51. C₃	C₂×#14584115	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14584115	2
D₃×C₇²×C₁₉	3
C₂×#14584115	3
D₃×#87704	7
D₃×#3861	19

Subgroups — D3×#14584115 #30660849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#14584115 #30660849