Subgroups — C₇×#10624862 #19100271

Order 5103.

1178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉×H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
3	C₃×C₇×C₃²⋊C₉	C₃	1	12	yes	maximal, complemented
4	#10624862	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	C₃²	1	4	yes	—
6	C₃×C₇×H(3,𝔽₃)	C₉	1	27	yes	complemented
7	C₃×C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
8	C₃²×C₇×C₉	C₃²	1	36	yes	complemented
9	C₇×C₃²⋊C₉	C₃²	1	9	yes	—
10	C₇×C₃²⋊C₉	C₃²	1	72	yes	complemented
11	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
12	C₉×H(3,𝔽₃)	C₃×C₇	1	27	yes	complemented
13	C₃×C₃²⋊C₉	C₃×C₇	1	12	yes	complemented
14	C₃³×C₇	—	9	4	no	—
15	C₃³×C₇	—	9	8	no	—
16	C₃³×C₇	C₃×C₉	1	36	yes	complemented
17	C₃³×C₇	C₃³	1	1	yes	characteristic
18	C₃³×C₇	C₃³	1	12	yes	—
19	C₇×H(3,𝔽₃)	C₃×C₉	1	81	yes	complemented
20	C₃×C₇×C₉	—	9	36	no	—
21	C₃×C₇×C₉	C₃³	1	27	yes	—
22	C₃⁴	C₃²×C₇	1	4	yes	—
23	C₃×H(3,𝔽₃)	C₇×C₉	1	27	yes	complemented
24	C₃×H(3,𝔽₃)	C₃²×C₇	1	9	yes	—
25	C₃²×C₉	C₃²×C₇	1	36	yes	complemented
26	C₃²⋊C₉	C₃²×C₇	1	9	yes	—
27	C₃²⋊C₉	C₃²×C₇	1	72	yes	complemented
28	C₃²×C₇	—	3	12	no	—
29	C₃²×C₇	—	3	1	no	—
30	C₃²×C₇	—	3	2	no	—
31	C₃²×C₇	—	3	24	no	—
32	C₃²×C₇	—	9	36	no	—
33	C₃²×C₇	C₃²×C₉	1	36	yes	—
34	C₃²×C₇	C₃²×C₉	1	3	yes	—
35	C₃²×C₇	C₃⁴	1	1	yes	characteristic
36	C₇×C₉	—	3	27	no	—
37	C₃³	—	9	4	no	—
38	C₃³	—	9	8	no	—
39	C₃³	C₃×C₇×C₉	1	36	yes	complemented
40	C₃³	C₃³×C₇	1	1	yes	characteristic
41	C₃³	C₃³×C₇	1	12	yes	—
42	H(3,𝔽₃)	C₃×C₇×C₉	1	81	yes	complemented
43	C₃×C₉	—	9	36	no	—
44	C₃×C₉	C₃³×C₇	1	27	yes	—
45	C₃×C₇	—	3	3	no	—
46	C₃×C₇	—	3	36	no	—
47	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
48	C₃×C₇	H(5,𝔽₃)	1	1	yes	characteristic
49	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
50	C₃²	—	3	12	no	—
51	C₃²	—	3	1	no	—
52	C₃²	—	3	2	no	—
53	C₃²	—	3	24	no	—
54	C₃²	—	9	36	no	—
55	C₃²	C₃²×C₇×C₉	1	36	yes	—
56	C₃²	C₃²×C₇×C₉	1	3	yes	—
57	C₃²	C₃⁴×C₇	1	1	yes	characteristic
58	C₉	—	3	27	no	—
59	C₇	#10624862	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	—	3	3	no	—
61	C₃	—	3	36	no	—
62	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
63	C₃	C₇×H(5,𝔽₃)	1	1	yes	characteristic
64	C₃	C₇×3₋¹⁺⁴	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×C₉×H(3,𝔽₃)	C₃	semidirect
3. C₃×C₇×C₃²⋊C₉	C₃	semidirect
4. #10624862	C₇	direct (N × H)
6. C₃×C₇×H(3,𝔽₃)	C₉	semidirect
8. C₃²×C₇×C₉	C₃²	semidirect
10. C₇×C₃²⋊C₉	C₃²	semidirect
12. C₉×H(3,𝔽₃)	C₃×C₇	semidirect
13. C₃×C₃²⋊C₉	C₃×C₇	semidirect
16. C₃³×C₇	C₃×C₉	semidirect
19. C₇×H(3,𝔽₃)	C₃×C₉	semidirect
23. C₃×H(3,𝔽₃)	C₇×C₉	semidirect
25. C₃²×C₉	C₃²×C₇	semidirect
27. C₃²⋊C₉	C₃²×C₇	semidirect
39. C₃³	C₃×C₇×C₉	semidirect
42. H(3,𝔽₃)	C₃×C₇×C₉	semidirect
59. C₇	#10624862	direct (N × H)

Subgroups — C7×#10624862 #19100271

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624862 #19100271