Subgroups — C₇×#10624838 #19100247

Order 5103.

198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#733	C₃	1	2	yes	maximal, complemented
2	C₃×C₇×#732	C₃	1	1	yes	maximal, characteristic
3	C₇×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₇×#6878	C₃	1	9	yes	maximal, complemented
5	#10624838	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃×C₇×3₋¹⁺²	—	3	2	no	—
7	C₃×C₇×H(3,𝔽₃)	—	3	1	no	—
8	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
9	C₇×#733	—	3	4	no	—
10	C₇×#733	C₃²	1	6	yes	complemented
11	C₇×#732	—	3	2	no	—
12	C₇×#732	C₃²	1	3	yes	—
13	C₇×C₉⋊C₉	—	3	2	no	—
14	C₇×C₃²⋊C₉	—	3	1	no	—
15	C₇×C₉²	C₃²	1	3	yes	complemented
16	C₃×#733	C₃×C₇	1	2	yes	complemented
17	C₃×#732	C₃×C₇	1	1	yes	characteristic
18	#6887	C₃×C₇	1	1	yes	characteristic, complemented
19	#6878	C₃×C₇	1	9	yes	complemented
20	C₃³×C₇	—	9	1	no	—
21	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
22	C₇×3₋¹⁺²	—	3	6	no	—
23	C₇×3₋¹⁺²	—	9	2	no	—
24	C₇×3₋¹⁺²	—	9	2	no	—
25	C₇×H(3,𝔽₃)	—	3	3	no	—
26	C₇×H(3,𝔽₃)	—	9	2	no	—
27	C₃×C₇×C₉	—	3	2	no	—
28	C₃×C₇×C₉	—	3	1	no	—
29	C₃×C₇×C₉	—	3	3	no	—
30	C₃×C₇×C₉	—	9	2	no	—
31	C₃×C₇×C₉	H(3,𝔽₃)	1	2	yes	—
32	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
33	C₃×3₋¹⁺²	—	3	2	no	—
34	C₃×H(3,𝔽₃)	—	3	1	no	—
35	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
36	#733	—	3	4	no	—
37	#733	C₃²×C₇	1	6	yes	complemented
38	#732	—	3	2	no	—
39	#732	C₃²×C₇	1	3	yes	—
40	C₉⋊C₉	—	3	2	no	—
41	C₃²⋊C₉	—	3	1	no	—
42	C₉²	C₃²×C₇	1	3	yes	complemented
43	C₃²×C₇	—	9	1	no	—
44	C₃²×C₇	—	9	3	no	—
45	C₃²×C₇	—	27	3	no	—
46	C₃²×C₇	#732	1	2	yes	—
47	C₃²×C₇	#732	1	1	yes	characteristic
48	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
49	C₇×C₉	—	3	2	no	—
50	C₇×C₉	—	3	1	no	—
51	C₇×C₉	—	9	3	no	—
52	C₇×C₉	—	9	6	no	—
53	C₃³	—	9	1	no	—
54	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
55	3₋¹⁺²	—	3	6	no	—
56	3₋¹⁺²	—	9	2	no	—
57	3₋¹⁺²	—	9	2	no	—
58	H(3,𝔽₃)	—	3	3	no	—
59	H(3,𝔽₃)	—	9	2	no	—
60	C₃×C₉	—	3	2	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	9	2	no	—
64	C₃×C₉	C₇×H(3,𝔽₃)	1	2	yes	—
65	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
66	C₃×C₇	—	3	1	no	—
67	C₃×C₇	—	3	1	no	—
68	C₃×C₇	—	3	2	no	—
69	C₃×C₇	—	27	3	no	—
70	C₃×C₇	C₃×#732	1	1	yes	characteristic
71	C₃²	—	9	1	no	—
72	C₃²	—	9	3	no	—
73	C₃²	—	27	3	no	—
74	C₃²	C₇×#732	1	2	yes	—
75	C₃²	C₇×#732	1	1	yes	characteristic
76	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
77	C₉	—	3	2	no	—
78	C₉	—	3	1	no	—
79	C₉	—	9	3	no	—
80	C₉	—	9	6	no	—
81	C₇	#10624838	1	1	yes	characteristic, direct product factor, Sylow
82	C₃	—	3	1	no	—
83	C₃	—	3	1	no	—
84	C₃	—	3	2	no	—
85	C₃	—	27	3	no	—
86	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×#733	C₃	semidirect
3. C₇×#6887	C₃	semidirect
4. C₇×#6878	C₃	semidirect
5. #10624838	C₇	direct (N × H)
10. C₇×#733	C₃²	semidirect
15. C₇×C₉²	C₃²	semidirect
16. C₃×#733	C₃×C₇	semidirect
18. #6887	C₃×C₇	semidirect
19. #6878	C₃×C₇	semidirect
37. #733	C₃²×C₇	semidirect
42. C₉²	C₃²×C₇	semidirect
81. C₇	#10624838	direct (N × H)

Subgroups — C7×#10624838 #19100247

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624838 #19100247