Subgroups — C₇×#10624847 #19100256

Order 5103.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#733	C₃	1	3	yes	maximal
2	C₇×#6887	C₃	1	1	yes	maximal, characteristic
3	C₇×#6882	C₃	1	9	yes	maximal, complemented
4	#10624847	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₇×3₋¹⁺²	—	3	3	no	—
6	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
7	C₇×#733	—	3	3	no	—
8	C₇×#733	—	3	3	no	—
9	C₇×#733	C₃²	1	9	yes	—
10	C₇×C₉⋊C₉	—	3	1	no	—
11	C₇×C₉⋊C₉	C₃²	1	3	yes	—
12	C₇×C₃²⋊C₉	—	3	1	no	—
13	C₇×C₉²	—	3	1	no	—
14	C₃×#733	C₃×C₇	1	3	yes	—
15	#6887	C₃×C₇	1	1	yes	characteristic
16	#6882	C₃×C₇	1	9	yes	complemented
17	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
18	C₇×3₋¹⁺²	—	3	9	no	—
19	C₇×3₋¹⁺²	—	9	6	no	—
20	C₃×C₇×C₉	—	3	3	no	—
21	C₃×C₇×C₉	—	3	3	no	—
22	C₃×C₇×C₉	—	9	3	no	—
23	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
25	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
26	C₃×3₋¹⁺²	—	3	3	no	—
27	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
28	#733	—	3	3	no	—
29	#733	—	3	3	no	—
30	#733	C₃²×C₇	1	9	yes	—
31	C₉⋊C₉	—	3	1	no	—
32	C₉⋊C₉	C₃²×C₇	1	3	yes	—
33	C₃²⋊C₉	—	3	1	no	—
34	C₉²	—	3	1	no	—
35	C₃²×C₇	—	9	1	no	—
36	C₃²×C₇	#732	1	3	yes	—
37	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₇×C₉	—	3	1	no	—
39	C₇×C₉	—	3	1	no	—
40	C₇×C₉	—	3	1	no	—
41	C₇×C₉	—	9	3	no	—
42	C₇×C₉	—	9	9	no	—
43	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
44	3₋¹⁺²	—	3	9	no	—
45	3₋¹⁺²	—	9	6	no	—
46	C₃×C₉	—	3	3	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	—	9	3	no	—
49	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
50	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
51	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
52	C₃×C₇	—	3	1	no	—
53	C₃×C₇	—	3	3	no	—
54	C₃×C₇	C₃×#732	1	1	yes	characteristic
55	C₃²	—	9	1	no	—
56	C₃²	C₇×#732	1	3	yes	—
57	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
58	C₉	—	3	1	no	—
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	9	3	no	—
62	C₉	—	9	9	no	—
63	C₇	#10624847	1	1	yes	characteristic, direct product factor, Sylow
64	C₃	—	3	1	no	—
65	C₃	—	3	3	no	—
66	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
3. C₇×#6882	C₃	semidirect
4. #10624847	C₇	direct (N × H)
16. #6882	C₃×C₇	semidirect
63. C₇	#10624847	direct (N × H)

Subgroups — C7×#10624847 #19100256

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624847 #19100256