Subgroups — D₃×#19104443 #44527985

Order 31122.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19104443	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×#19104443	—	3	1	no	maximal
4	#19104443	—	2	1	no	—
5	#19104443	D₃	1	1	yes	characteristic, direct product factor
6	C₃×C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×#10625203	—	7	1	no	maximal, Hall
8	C₂×C₇×C₁₃×C₁₉	—	3	1	no	Hall
9	D₃×#87704	—	13	1	no	maximal, Hall
10	C₃×#10625203	—	7	1	no	Hall
11	C₇×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
12	D₃×#63271	—	19	1	no	maximal, Hall
13	D₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₂×#10625203	—	21	1	no	—
15	C₃×#87704	—	13	1	no	Hall
16	C₃×#63271	—	19	1	no	Hall
17	D₃×C₇×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented
18	C₂×#87704	—	39	1	no	—
19	C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
20	#10625203	—	7	1	no	—
21	#10625203	—	14	1	no	—
22	D₃×C₇×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented
23	C₂×#63271	—	57	1	no	—
24	C₂×C₁₃×C₁₉	—	3	1	no	Hall
25	C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
26	#87704	—	13	1	no	—
27	#87704	—	26	1	no	—
28	D₃×C₁₉⋊C₃	—	91	1	no	Hall
29	C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
30	#63271	—	19	1	no	—
31	#63271	—	38	1	no	—
32	C₂×C₇×C₁₉	—	3	1	no	Hall
33	C₁₃×C₁₉	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
34	D₃×C₁₃⋊C₃	—	133	1	no	Hall
35	C₂×C₇×C₁₃	—	3	1	no	Hall
36	C₃×C₁₉⋊C₃	—	91	1	no	Hall
37	C₇×C₁₉	D₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
38	D₃×ΓL(1,𝔽₈)	—	247	1	no	Hall
39	C₃×C₁₃⋊C₃	—	133	1	no	Hall
40	D₃×C₁₉	#63271	1	1	yes	characteristic, complemented
41	C₂×C₁₉⋊C₃	—	273	1	no	—
42	C₇×C₁₃	D₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
43	D₃×C₁₃	#87704	1	1	yes	characteristic, complemented
44	C₂×C₁₃⋊C₃	—	399	1	no	—
45	C₃×ΓL(1,𝔽₈)	—	247	1	no	Hall
46	C₃×C₁₉	C₂×#63271	1	1	yes	characteristic, complemented
47	C₁₉⋊C₃	—	91	1	no	—
48	C₁₉⋊C₃	—	182	1	no	—
49	D₃×C₇	#10625203	1	1	yes	characteristic, complemented
50	C₂×ΓL(1,𝔽₈)	—	741	1	no	—
51	C₃×C₁₃	C₂×#87704	1	1	yes	characteristic, complemented
52	C₁₃⋊C₃	—	266	1	no	—
53	C₁₃⋊C₃	—	133	1	no	—
54	C₂×C₁₉	—	3	1	no	Hall
55	C₂×C₁₃	—	3	1	no	Hall
56	C₃×C₇	C₂×#10625203	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	494	1	no	—
58	ΓL(1,𝔽₈)	—	247	1	no	—
59	C₁₉	D₃×#63271	1	1	yes	characteristic, complemented, Sylow
60	C₃×D₃	—	1729	1	no	Hall
61	C₂×C₇	—	3	1	no	Hall
62	C₁₃	D₃×#87704	1	1	yes	characteristic, complemented, Sylow
63	C₃²	—	1729	1	no	Sylow
64	C₇	D₃×#10625203	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	5187	1	no	—
66	D₃	#19104443	1	1	yes	characteristic, direct product factor
67	C₃	—	3458	1	no	—
68	C₃	—	1729	1	no	—
69	C₃	C₂×#19104443	1	1	yes	characteristic, complemented
70	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#19104443	C₂	semidirect
2. D₃×C₇×C₁₃×C₁₉	C₃	semidirect
5. #19104443	D₃	direct (N × H)
6. C₃×C₇×C₁₃×C₁₉	C₂×C₃	semidirect
11. C₇×C₁₃×C₁₉	C₃×D₃	semidirect
13. D₃×C₁₃×C₁₉	ΓL(1,𝔽₈)	semidirect
17. D₃×C₇×C₁₉	C₁₃⋊C₃	semidirect
19. C₃×C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
22. D₃×C₇×C₁₃	C₁₉⋊C₃	semidirect
25. C₃×C₇×C₁₉	C₂×C₁₃⋊C₃	semidirect
29. C₃×C₇×C₁₃	C₂×C₁₉⋊C₃	semidirect
33. C₁₃×C₁₉	D₃×ΓL(1,𝔽₈)	semidirect
37. C₇×C₁₉	D₃×C₁₃⋊C₃	semidirect
40. D₃×C₁₉	#63271	semidirect
42. C₇×C₁₃	D₃×C₁₉⋊C₃	semidirect
43. D₃×C₁₃	#87704	semidirect
46. C₃×C₁₉	C₂×#63271	semidirect
49. D₃×C₇	#10625203	semidirect
51. C₃×C₁₃	C₂×#87704	semidirect
56. C₃×C₇	C₂×#10625203	semidirect
59. C₁₉	D₃×#63271	semidirect
62. C₁₃	D₃×#87704	semidirect
64. C₇	D₃×#10625203	semidirect
66. D₃	#19104443	direct (N × H)
69. C₃	C₂×#19104443	semidirect

Maximal subgroups

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

subgroup	index
C₃×#19104443	2
D₃×C₇×C₁₃×C₁₉	3
C₂×#19104443	3
D₃×#10625203	7
D₃×#87704	13
D₃×#63271	19

Subgroups — D3×#19104443 #44527985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#19104443 #44527985