Subgroups — C₃×C₇×#6903 #19100326

Order 5103.

848 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic
2	C₇×#6903	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₇×C₂₇⋊C₃	C₃	1	8	yes	maximal, complemented
4	C₃²×C₇×C₂₇	C₃	1	4	yes	maximal, complemented
5	C₃×#6903	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₇×#737	C₉	1	18	yes	—
7	C₇×#737	C₃²	1	9	yes	—
8	C₃×C₇×3₋¹⁺²	C₉	1	8	yes	—
9	C₃×C₇×H(3,𝔽₃)	C₉	1	1	yes	characteristic
10	C₃²×C₇×C₉	C₃²	1	4	yes	—
11	C₇×C₂₇⋊C₃	C₃²	1	72	yes	complemented
12	C₃×C₇×C₂₇	C₃²	1	8	yes	—
13	C₃×C₇×C₂₇	C₃²	1	1	yes	characteristic
14	C₃×C₇×C₂₇	C₃²	1	36	yes	complemented
15	C₃×#737	C₃×C₇	1	1	yes	characteristic
16	#6903	C₃×C₇	1	27	yes	direct product factor
17	C₃×C₂₇⋊C₃	C₃×C₇	1	8	yes	complemented
18	C₃²×C₂₇	C₃×C₇	1	4	yes	complemented
19	C₃³×C₇	C₃×C₉	1	4	yes	—
20	C₇×3₋¹⁺²	C₃×C₉	1	72	yes	—
21	C₇×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
22	C₃×C₇×C₉	C₃×C₉	1	8	yes	—
23	C₃×C₇×C₉	C₃×C₉	1	24	yes	—
24	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
25	C₃×C₇×C₉	C₃³	1	12	yes	—
26	C₇×C₂₇	C₃³	1	24	yes	—
27	C₇×C₂₇	C₃³	1	3	yes	—
28	#737	C₇×C₉	1	18	yes	—
29	#737	C₃²×C₇	1	9	yes	—
30	C₃×3₋¹⁺²	C₇×C₉	1	8	yes	—
31	C₃×H(3,𝔽₃)	C₇×C₉	1	1	yes	characteristic
32	C₃²×C₉	C₃²×C₇	1	4	yes	—
33	C₂₇⋊C₃	C₃²×C₇	1	72	yes	complemented
34	C₃×C₂₇	C₃²×C₇	1	8	yes	—
35	C₃×C₂₇	C₃²×C₇	1	1	yes	characteristic
36	C₃×C₂₇	C₃²×C₇	1	36	yes	complemented
37	C₃²×C₇	—	3	12	no	—
38	C₃²×C₇	C₃²×C₉	1	12	yes	—
39	C₃²×C₇	C₃²×C₉	1	1	yes	characteristic
40	C₇×C₉	C₃²×C₉	1	2	yes	—
41	C₇×C₉	C₃²×C₉	1	24	yes	—
42	C₇×C₉	C₃⁴	1	1	yes	characteristic
43	C₃³	C₃×C₇×C₉	1	4	yes	—
44	3₋¹⁺²	C₃×C₇×C₉	1	72	yes	—
45	H(3,𝔽₃)	C₃×C₇×C₉	1	9	yes	—
46	C₃×C₉	C₃×C₇×C₉	1	8	yes	—
47	C₃×C₉	C₃×C₇×C₉	1	24	yes	—
48	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
49	C₃×C₉	C₃³×C₇	1	12	yes	—
50	C₂₇	C₃³×C₇	1	3	yes	—
51	C₂₇	C₃³×C₇	1	24	yes	—
52	C₃×C₇	—	3	12	no	—
53	C₃×C₇	#6903	1	3	yes	direct product factor
54	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
55	C₃²	—	3	12	no	—
56	C₃²	C₃²×C₇×C₉	1	12	yes	—
57	C₃²	C₃²×C₇×C₉	1	1	yes	characteristic
58	C₉	C₃²×C₇×C₉	1	2	yes	—
59	C₉	C₃²×C₇×C₉	1	24	yes	—
60	C₉	C₃⁴×C₇	1	1	yes	characteristic
61	C₇	C₃×#6903	1	1	yes	characteristic, direct product factor, Sylow
62	C₃	—	3	12	no	—
63	C₃	C₇×#6903	1	3	yes	direct product factor
64	C₃	C₃³×C₇×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₇×C₂₇	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₉	C₃⁴×C₇
socle	C₃²×C₇	C₃²×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇×C₂₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇×#6903	C₃	direct (N × H)
3. C₃×C₇×C₂₇⋊C₃	C₃	semidirect
4. C₃²×C₇×C₂₇	C₃	semidirect
5. C₃×#6903	C₇	direct (N × H)
11. C₇×C₂₇⋊C₃	C₃²	semidirect
14. C₃×C₇×C₂₇	C₃²	semidirect
16. #6903	C₃×C₇	direct (N × H)
17. C₃×C₂₇⋊C₃	C₃×C₇	semidirect
18. C₃²×C₂₇	C₃×C₇	semidirect
33. C₂₇⋊C₃	C₃²×C₇	semidirect
36. C₃×C₂₇	C₃²×C₇	semidirect
53. C₃×C₇	#6903	direct (N × H)
61. C₇	C₃×#6903	direct (N × H)
63. C₃	C₇×#6903	direct (N × H)

Subgroups — C3×C7×#6903 #19100326

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6903 #19100326