Subgroups — C₇×#10624840 #19100249

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×#6880	C₃	1	9	yes	maximal, complemented
4	#10624840	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	6	no	—
8	C₇×#733	C₃²	1	9	yes	—
9	C₇×C₉⋊C₉	—	3	2	no	—
10	C₇×C₃²⋊C₉	—	3	1	no	—
11	C₇×C₉²	C₃²	1	3	yes	—
12	C₃×#733	C₃×C₇	1	3	yes	—
13	#6887	C₃×C₇	1	1	yes	characteristic
14	#6880	C₃×C₇	1	9	yes	complemented
15	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
16	C₇×3₋¹⁺²	—	3	9	no	—
17	C₇×3₋¹⁺²	—	9	6	no	—
18	C₃×C₇×C₉	—	3	3	no	—
19	C₃×C₇×C₉	—	3	3	no	—
20	C₃×C₇×C₉	—	9	3	no	—
21	C₃×C₇×C₉	H(3,𝔽₃)	1	2	yes	—
22	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
23	C₃×3₋¹⁺²	—	3	3	no	—
24	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
25	#733	—	3	6	no	—
26	#733	C₃²×C₇	1	9	yes	—
27	C₉⋊C₉	—	3	2	no	—
28	C₃²⋊C₉	—	3	1	no	—
29	C₉²	C₃²×C₇	1	3	yes	—
30	C₃²×C₇	—	9	1	no	—
31	C₃²×C₇	#732	1	3	yes	—
32	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₇×C₉	—	3	2	no	—
34	C₇×C₉	—	3	1	no	—
35	C₇×C₉	—	9	3	no	—
36	C₇×C₉	—	9	9	no	—
37	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
38	3₋¹⁺²	—	3	9	no	—
39	3₋¹⁺²	—	9	6	no	—
40	C₃×C₉	—	3	3	no	—
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	9	3	no	—
43	C₃×C₉	C₇×H(3,𝔽₃)	1	2	yes	—
44	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
45	C₃×C₇	—	3	1	no	—
46	C₃×C₇	—	3	3	no	—
47	C₃×C₇	C₃×#732	1	1	yes	characteristic
48	C₃²	—	9	1	no	—
49	C₃²	C₇×#732	1	3	yes	—
50	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
51	C₉	—	3	2	no	—
52	C₉	—	3	1	no	—
53	C₉	—	9	3	no	—
54	C₉	—	9	9	no	—
55	C₇	#10624840	1	1	yes	characteristic, direct product factor, Sylow
56	C₃	—	3	1	no	—
57	C₃	—	3	3	no	—
58	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×#6880	C₃	semidirect
4. #10624840	C₇	direct (N × H)
14. #6880	C₃×C₇	semidirect
55. C₇	#10624840	direct (N × H)

Subgroups — C7×#10624840 #19100249

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624840 #19100249