Subgroups — C₇×#10624933 #19100342

Order 5103.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×3₋¹⁺⁴	C₃	1	3	yes	maximal
2	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic
3	C₇×#6912	C₃	1	24	yes	maximal, complemented
4	C₃×C₇×#733	C₃	1	12	yes	maximal, complemented
5	#10624933	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₇×#737	—	3	9	no	—
7	C₇×#737	—	3	27	no	—
8	C₃×C₇×3₋¹⁺²	C₃²	1	36	yes	—
9	C₃×C₇×3₋¹⁺²	C₃²	1	8	yes	—
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
11	C₃²×C₇×C₉	C₃²	1	4	yes	—
12	C₇×#733	C₃²	1	9	yes	—
13	C₇×#733	C₃²	1	72	yes	—
14	3₋¹⁺⁴	C₃×C₇	1	3	yes	—
15	C₃×#737	C₃×C₇	1	1	yes	characteristic
16	#6912	C₃×C₇	1	24	yes	complemented
17	C₃×#733	C₃×C₇	1	12	yes	complemented
18	C₃³×C₇	C₃³	1	4	yes	—
19	C₇×3₋¹⁺²	—	3	72	no	—
20	C₇×3₋¹⁺²	—	3	24	no	—
21	C₇×3₋¹⁺²	C₃³	1	27	yes	—
22	C₇×H(3,𝔽₃)	H(3,𝔽₃)	1	9	yes	—
23	C₃×C₇×C₉	—	3	12	no	—
24	C₃×C₇×C₉	—	3	36	no	—
25	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
26	C₃×C₇×C₉	C₃³	1	8	yes	—
27	#737	—	3	9	no	—
28	#737	—	3	27	no	—
29	C₃×3₋¹⁺²	C₃²×C₇	1	36	yes	—
30	C₃×3₋¹⁺²	C₃²×C₇	1	8	yes	—
31	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
32	C₃²×C₉	C₃²×C₇	1	4	yes	—
33	#733	C₃²×C₇	1	72	yes	—
34	#733	C₃²×C₇	1	9	yes	—
35	C₃²×C₇	—	9	4	no	—
36	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
37	C₃²×C₇	C₃⁴	1	1	yes	characteristic
38	C₇×C₉	—	3	1	no	—
39	C₇×C₉	—	3	27	no	—
40	C₇×C₉	—	3	8	no	—
41	C₃³	C₃³×C₇	1	4	yes	—
42	3₋¹⁺²	—	3	72	no	—
43	3₋¹⁺²	—	3	24	no	—
44	3₋¹⁺²	C₃³×C₇	1	27	yes	—
45	H(3,𝔽₃)	C₇×H(3,𝔽₃)	1	9	yes	—
46	C₃×C₉	—	3	12	no	—
47	C₃×C₉	—	3	36	no	—
48	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
49	C₃×C₉	C₃³×C₇	1	8	yes	—
50	C₃×C₇	—	3	1	no	—
51	C₃×C₇	—	3	12	no	—
52	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
53	C₃²	—	9	4	no	—
54	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
55	C₃²	C₃⁴×C₇	1	1	yes	characteristic
56	C₉	—	3	1	no	—
57	C₉	—	3	27	no	—
58	C₉	—	3	8	no	—
59	C₇	#10624933	1	1	yes	characteristic, direct product factor, Sylow
60	C₃	—	3	1	no	—
61	C₃	—	3	12	no	—
62	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	C₃²×H(3,𝔽₃)
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃×C₇×H(3,𝔽₃) ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#6912	C₃	semidirect
4. C₃×C₇×#733	C₃	semidirect
5. #10624933	C₇	direct (N × H)
16. #6912	C₃×C₇	semidirect
17. C₃×#733	C₃×C₇	semidirect
59. C₇	#10624933	direct (N × H)

Subgroups — C7×#10624933 #19100342

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624933 #19100342