Subgroups — C₇×#10624880 #19100289

Order 5103.

1718 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×H(3,𝔽₃)	C₃	1	4	yes	maximal, complemented
2	C₇×C₃²⋊H(3,𝔽₃)	C₃	1	36	yes	maximal, complemented
3	#10624880	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃⁴×C₇	C₃²	1	1	yes	characteristic
5	C₃⁴×C₇	C₃²	1	12	yes	complemented
6	C₃×C₇×H(3,𝔽₃)	—	3	36	no	—
7	C₃×C₇×H(3,𝔽₃)	C₃²	1	36	yes	complemented
8	C₃×C₇×H(3,𝔽₃)	C₃²	1	81	yes	complemented
9	C₃²×H(3,𝔽₃)	C₃×C₇	1	4	yes	complemented
10	C₃²⋊H(3,𝔽₃)	C₃×C₇	1	36	yes	complemented
11	C₃³×C₇	—	3	36	no	—
12	C₃³×C₇	—	9	3	no	—
13	C₃³×C₇	—	9	36	no	—
14	C₃³×C₇	H(3,𝔽₃)	1	9	yes	complemented
15	C₃³×C₇	C₃³	1	36	yes	—
16	C₃³×C₇	C₃³	1	4	yes	—
17	C₇×H(3,𝔽₃)	—	3	108	no	—
18	C₇×H(3,𝔽₃)	—	9	81	no	—
19	C₃⁴	C₃²×C₇	1	1	yes	characteristic
20	C₃⁴	C₃²×C₇	1	12	yes	complemented
21	C₃×H(3,𝔽₃)	—	3	36	no	—
22	C₃×H(3,𝔽₃)	C₃²×C₇	1	36	yes	complemented
23	C₃×H(3,𝔽₃)	C₃²×C₇	1	81	yes	complemented
24	C₃²×C₇	—	3	12	no	—
25	C₃²×C₇	—	3	36	no	—
26	C₃²×C₇	—	3	108	no	—
27	C₃²×C₇	—	9	9	no	—
28	C₃²×C₇	—	9	108	no	—
29	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
30	C₃²×C₇	C₃⁴	1	1	yes	characteristic
31	C₃³	—	3	36	no	—
32	C₃³	—	9	3	no	—
33	C₃³	—	9	36	no	—
34	C₃³	C₇×H(3,𝔽₃)	1	9	yes	complemented
35	C₃³	C₃³×C₇	1	36	yes	—
36	C₃³	C₃³×C₇	1	4	yes	—
37	H(3,𝔽₃)	—	3	108	no	—
38	H(3,𝔽₃)	—	9	81	no	—
39	C₃×C₇	—	3	12	no	—
40	C₃×C₇	—	9	36	no	—
41	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃×C₇	H(5,𝔽₃)	1	3	yes	—
43	C₃²	—	3	12	no	—
44	C₃²	—	3	36	no	—
45	C₃²	—	3	108	no	—
46	C₃²	—	9	9	no	—
47	C₃²	—	9	108	no	—
48	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
49	C₃²	C₃⁴×C₇	1	1	yes	characteristic
50	C₇	#10624880	1	1	yes	characteristic, direct product factor, Sylow
51	C₃	—	3	12	no	—
52	C₃	—	9	36	no	—
53	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic
54	C₃	C₇×H(5,𝔽₃)	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×H(3,𝔽₃)	C₃	semidirect
2. C₇×C₃²⋊H(3,𝔽₃)	C₃	semidirect
3. #10624880	C₇	direct (N × H)
5. C₃⁴×C₇	C₃²	semidirect
7. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
8. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
9. C₃²×H(3,𝔽₃)	C₃×C₇	semidirect
10. C₃²⋊H(3,𝔽₃)	C₃×C₇	semidirect
14. C₃³×C₇	H(3,𝔽₃)	semidirect
20. C₃⁴	C₃²×C₇	semidirect
22. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
23. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
34. C₃³	C₇×H(3,𝔽₃)	semidirect
50. C₇	#10624880	direct (N × H)

Subgroups — C7×#10624880 #19100289

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624880 #19100289