Subgroups — C₇×#10624918 #19100327

Order 5103.

828 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, complemented
3	C₃×C₇×C₂₇⋊C₃	C₃	1	12	yes	maximal, complemented
4	#10624918	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₇×#737	C₉	1	18	yes	—
6	C₇×#737	C₃²	1	9	yes	—
7	C₃×C₇×3₋¹⁺²	C₉	1	8	yes	—
8	C₃×C₇×H(3,𝔽₃)	C₉	1	1	yes	characteristic
9	C₃²×C₇×C₉	C₃²	1	4	yes	—
10	C₇×C₂₇⋊C₃	C₃²	1	9	yes	—
11	C₇×C₂₇⋊C₃	C₃²	1	72	yes	complemented
12	C₃×C₇×C₂₇	C₃²	1	36	yes	complemented
13	C₃×#737	C₃×C₇	1	1	yes	characteristic
14	#6903	C₃×C₇	1	27	yes	complemented
15	C₃×C₂₇⋊C₃	C₃×C₇	1	12	yes	complemented
16	C₃³×C₇	C₃×C₉	1	4	yes	—
17	C₇×3₋¹⁺²	C₃×C₉	1	72	yes	—
18	C₇×H(3,𝔽₃)	C₃×C₉	1	9	yes	—
19	C₃×C₇×C₉	C₃×C₉	1	8	yes	—
20	C₃×C₇×C₉	C₃×C₉	1	24	yes	—
21	C₃×C₇×C₉	C₃³	1	12	yes	—
22	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
23	C₇×C₂₇	C₃³	1	27	yes	—
24	#737	C₇×C₉	1	18	yes	—
25	#737	C₃²×C₇	1	9	yes	—
26	C₃×3₋¹⁺²	C₇×C₉	1	8	yes	—
27	C₃×H(3,𝔽₃)	C₇×C₉	1	1	yes	characteristic
28	C₃²×C₉	C₃²×C₇	1	4	yes	—
29	C₂₇⋊C₃	C₃²×C₇	1	9	yes	—
30	C₂₇⋊C₃	C₃²×C₇	1	72	yes	complemented
31	C₃×C₂₇	C₃²×C₇	1	36	yes	complemented
32	C₃²×C₇	—	9	4	no	—
33	C₃²×C₇	C₃²×C₉	1	1	yes	characteristic
34	C₃²×C₇	C₃²×C₉	1	12	yes	—
35	C₇×C₉	C₃²×C₉	1	2	yes	—
36	C₇×C₉	C₃²×C₉	1	24	yes	—
37	C₇×C₉	C₃⁴	1	1	yes	characteristic
38	C₃³	C₃×C₇×C₉	1	4	yes	—
39	3₋¹⁺²	C₃×C₇×C₉	1	72	yes	—
40	H(3,𝔽₃)	C₃×C₇×C₉	1	9	yes	—
41	C₃×C₉	C₃×C₇×C₉	1	8	yes	—
42	C₃×C₉	C₃×C₇×C₉	1	24	yes	—
43	C₃×C₉	C₃³×C₇	1	12	yes	—
44	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
45	C₂₇	C₃³×C₇	1	27	yes	—
46	C₃×C₇	—	3	1	no	—
47	C₃×C₇	—	3	12	no	—
48	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
49	C₃²	—	9	4	no	—
50	C₃²	C₃²×C₇×C₉	1	1	yes	characteristic
51	C₃²	C₃²×C₇×C₉	1	12	yes	—
52	C₉	C₃²×C₇×C₉	1	2	yes	—
53	C₉	C₃²×C₇×C₉	1	24	yes	—
54	C₉	C₃⁴×C₇	1	1	yes	characteristic
55	C₇	#10624918	1	1	yes	characteristic, direct product factor, Sylow
56	C₃	—	3	1	no	—
57	C₃	—	3	12	no	—
58	C₃	C₃³×C₇×C₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇×#6903	C₃	semidirect
3. C₃×C₇×C₂₇⋊C₃	C₃	semidirect
4. #10624918	C₇	direct (N × H)
11. C₇×C₂₇⋊C₃	C₃²	semidirect
12. C₃×C₇×C₂₇	C₃²	semidirect
14. #6903	C₃×C₇	semidirect
15. C₃×C₂₇⋊C₃	C₃×C₇	semidirect
30. C₂₇⋊C₃	C₃²×C₇	semidirect
31. C₃×C₂₇	C₃²×C₇	semidirect
55. C₇	#10624918	direct (N × H)

Subgroups — C7×#10624918 #19100327

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624918 #19100327