Subgroups — D₃×#14584195 #30683170

Order 16884.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×#13064105	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊#14584195	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#14584195	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₇×D₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×#14584195	—	3	1	no	maximal
6	C₃×#13064105	C₂²	1	1	yes	characteristic, complemented, Hall
7	#14584195	—	2	1	no	—
8	#14584195	—	3	1	no	—
9	#14584195	D₃	1	1	yes	characteristic, direct product factor
10	C₇×D₂₀₁	C₂×C₃	1	1	yes	characteristic, complemented
11	D₃×C₇×C₆₇	C₂×C₃	1	1	yes	characteristic, complemented
12	C₃×C₇×D₆₇	C₂×C₃	1	1	yes	characteristic, complemented
13	C₂×#13064105	—	3	1	no	—
14	D₃×D₆₇⋊C₃	—	7	1	no	maximal, Hall
15	C₂×C₇×D₆₇	—	3	1	no	Hall
16	C₃×C₇×C₆₇	C₂²×C₃	1	1	yes	characteristic, complemented
17	#13064105	—	2	1	no	—
18	#13064105	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊(D₆₇⋊C₃)	—	7	1	no	—
20	D₃×C₆₇⋊C₃	—	7	1	no	—
21	C₃×D₆₇⋊C₃	—	7	1	no	—
22	C₂×C₇×C₆₇	—	3	1	no	—
23	C₇×D₆₇	—	3	1	no	—
24	C₇×D₆₇	C₃×D₃	1	1	yes	characteristic, complemented
25	D₃×D₆₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
26	C₂×D₆₇⋊C₃	—	21	1	no	—
27	C₃×C₆₇⋊C₃	—	7	1	no	Hall
28	C₇×C₆₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	D₂₀₁	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
30	C₃×D₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
31	D₃×C₆₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
32	C₂×C₆₇⋊C₃	—	21	1	no	—
33	D₆₇⋊C₃	—	7	1	no	—
34	D₆₇⋊C₃	—	14	1	no	—
35	D₆₇⋊C₃	—	21	1	no	—
36	C₂×D₆₇	—	3	1	no	Hall
37	C₂×D₃×ΓL(1,𝔽₈)	—	67	1	no	maximal, Hall
38	C₃×C₆₇	C₂²×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₆₇⋊C₃	—	7	1	no	—
40	C₆₇⋊C₃	—	14	1	no	—
41	C₂×C₆₇	—	3	1	no	—
42	D₆₇	—	3	1	no	—
43	D₆₇	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
44	C₂×C₃×ΓL(1,𝔽₈)	—	67	1	no	—
45	D₃×ΓL(1,𝔽₈)	—	67	1	no	—
46	D₃×ΓL(1,𝔽₈)	—	134	1	no	—
47	C₂×D₃×C₇	—	67	1	no	—
48	C₂²×ΓL(1,𝔽₈)	—	201	1	no	—
49	C₆₇	C₂×D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
50	C₃×ΓL(1,𝔽₈)	—	134	1	no	Hall
51	C₂×C₃×C₇	—	67	1	no	—
52	D₃×C₇	—	67	1	no	—
53	D₃×C₇	D₆₇⋊C₃	1	1	yes	characteristic, complemented
54	C₂×ΓL(1,𝔽₈)	—	67	1	no	—
55	C₂×ΓL(1,𝔽₈)	—	134	1	no	—
56	C₂×ΓL(1,𝔽₈)	—	402	1	no	—
57	C₂×ΓL(1,𝔽₈)	—	201	1	no	—
58	C₂×C₃×D₃	—	469	1	no	Hall
59	C₂²×C₇	—	201	1	no	Hall
60	C₃×C₇	C₂×D₆₇⋊C₃	1	1	yes	characteristic, complemented
61	ΓL(1,𝔽₈)	—	268	1	no	—
62	ΓL(1,𝔽₈)	—	134	1	no	—
63	C₂×C₃²	—	469	1	no	—
64	C₃×D₃	—	938	1	no	—
65	C₃×D₃	—	469	1	no	—
66	C₂×C₇	—	3	1	no	—
67	C₂×C₇	—	67	1	no	—
68	C₂×C₇	—	201	1	no	—
69	C₂²×C₃	—	1407	1	no	—
70	C₂×D₃	—	67	1	no	—
71	C₃²	—	938	1	no	Sylow
72	C₇	D₃×D₆₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	67	1	no	—
74	C₂×C₃	—	1407	1	no	—
75	C₂×C₃	—	938	1	no	—
76	C₂×C₃	—	469	1	no	—
77	C₂×C₃	—	2814	1	no	—
78	D₃	—	67	1	no	—
79	D₃	#14584195	1	1	yes	characteristic, direct product factor
80	C₂²	—	201	1	no	Sylow
81	C₃	—	1876	1	no	—
82	C₃	—	938	1	no	—
83	C₃	C₂×#14584195	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	67	1	no	—
86	C₂	—	201	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₇×C₆₇	C₂²×C₃
LCS	G ▷ C₃×C₇×C₆₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃×#13064105	C₂	semidirect
2. C₃⋊#14584195	C₂	semidirect
3. C₃×#14584195	C₂	semidirect
4. D₃×C₇×D₆₇	C₃	semidirect
6. C₃×#13064105	C₂²	semidirect
9. #14584195	D₃	direct (N × H)
10. C₇×D₂₀₁	C₂×C₃	semidirect
11. D₃×C₇×C₆₇	C₂×C₃	semidirect
12. C₃×C₇×D₆₇	C₂×C₃	semidirect
16. C₃×C₇×C₆₇	C₂²×C₃	semidirect
18. #13064105	C₂×D₃	semidirect
24. C₇×D₆₇	C₃×D₃	semidirect
25. D₃×D₆₇	ΓL(1,𝔽₈)	semidirect
28. C₇×C₆₇	C₂×C₃×D₃	semidirect
29. D₂₀₁	C₂×ΓL(1,𝔽₈)	semidirect
30. C₃×D₆₇	C₂×ΓL(1,𝔽₈)	semidirect
31. D₃×C₆₇	C₂×ΓL(1,𝔽₈)	semidirect
38. C₃×C₆₇	C₂²×ΓL(1,𝔽₈)	semidirect
43. D₆₇	D₃×ΓL(1,𝔽₈)	semidirect
49. C₆₇	C₂×D₃×ΓL(1,𝔽₈)	semidirect
53. D₃×C₇	D₆₇⋊C₃	semidirect
60. C₃×C₇	C₂×D₆₇⋊C₃	semidirect
72. C₇	D₃×D₆₇⋊C₃	semidirect
79. D₃	#14584195	direct (N × H)
83. C₃	C₂×#14584195	semidirect

Maximal subgroups

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

subgroup	index
D₃×#13064105	2
C₃⋊#14584195	2
C₃×#14584195	2
D₃×C₇×D₆₇	3
C₂×#14584195	3
D₃×D₆₇⋊C₃	7
C₂×D₃×ΓL(1,𝔽₈)	67

Subgroups — D3×#14584195 #30683170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#14584195 #30683170