Subgroups — C₇×#10624839 #19100248

Order 5103.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#732	C₃	1	3	yes	maximal, complemented
2	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6879	C₃	1	9	yes	maximal, complemented
4	#10624839	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₇×H(3,𝔽₃)	—	3	3	no	—
6	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
7	C₇×#732	—	3	6	no	—
8	C₇×#732	C₃²	1	9	yes	complemented
9	C₇×C₉⋊C₉	—	3	2	no	—
10	C₇×C₃²⋊C₉	—	3	1	no	—
11	C₇×C₉²	C₃²	1	3	yes	complemented
12	C₃×#732	C₃×C₇	1	3	yes	complemented
13	#6887	C₃×C₇	1	1	yes	characteristic, complemented
14	#6879	C₃×C₇	1	9	yes	complemented
15	C₃³×C₇	—	9	3	no	—
16	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
17	C₇×H(3,𝔽₃)	—	3	9	no	—
18	C₇×H(3,𝔽₃)	—	9	6	no	—
19	C₃×C₇×C₉	—	3	3	no	—
20	C₃×C₇×C₉	—	3	3	no	—
21	C₃×C₇×C₉	H(3,𝔽₃)	1	2	yes	—
22	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
23	C₃×H(3,𝔽₃)	—	3	3	no	—
24	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
25	#732	—	3	6	no	—
26	#732	C₃²×C₇	1	9	yes	complemented
27	C₉⋊C₉	—	3	2	no	—
28	C₃²⋊C₉	—	3	1	no	—
29	C₉²	C₃²×C₇	1	3	yes	complemented
30	C₃²×C₇	—	9	1	no	—
31	C₃²×C₇	—	9	9	no	—
32	C₃²×C₇	—	27	9	no	—
33	C₃²×C₇	#732	1	3	yes	—
34	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₇×C₉	—	3	2	no	—
36	C₇×C₉	—	3	1	no	—
37	C₇×C₉	—	9	3	no	—
38	C₃³	—	9	3	no	—
39	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
40	H(3,𝔽₃)	—	3	9	no	—
41	H(3,𝔽₃)	—	9	6	no	—
42	C₃×C₉	—	3	3	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	C₇×H(3,𝔽₃)	1	2	yes	—
45	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
46	C₃×C₇	—	3	1	no	—
47	C₃×C₇	—	3	3	no	—
48	C₃×C₇	—	27	9	no	—
49	C₃×C₇	C₃×#732	1	1	yes	characteristic
50	C₃²	—	9	1	no	—
51	C₃²	—	9	9	no	—
52	C₃²	—	27	9	no	—
53	C₃²	C₇×#732	1	3	yes	—
54	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
55	C₉	—	3	2	no	—
56	C₉	—	3	1	no	—
57	C₉	—	9	3	no	—
58	C₇	#10624839	1	1	yes	characteristic, direct product factor, Sylow
59	C₃	—	3	1	no	—
60	C₃	—	3	3	no	—
61	C₃	—	27	9	no	—
62	C₃	C₃×C₇×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₇	C₃×#732
commutator, Frattini	C₃×C₉	C₃³×C₇
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₇ ◁ C₃³×C₇ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#732	C₃	semidirect
2. C₇×#6887	C₃	semidirect
3. C₇×#6879	C₃	semidirect
4. #10624839	C₇	direct (N × H)
8. C₇×#732	C₃²	semidirect
11. C₇×C₉²	C₃²	semidirect
12. C₃×#732	C₃×C₇	semidirect
13. #6887	C₃×C₇	semidirect
14. #6879	C₃×C₇	semidirect
26. #732	C₃²×C₇	semidirect
29. C₉²	C₃²×C₇	semidirect
58. C₇	#10624839	direct (N × H)

Subgroups — C7×#10624839 #19100248

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624839 #19100248