Subgroups — C₇×#10624848 #19100257

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×#6883	C₃	1	9	yes	maximal, complemented
5	#10624848	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	2	no	—
10	C₇×#733	—	3	2	no	—
11	C₇×#733	C₃²	1	6	yes	complemented
12	C₇×#732	—	3	1	no	—
13	C₇×#732	—	3	1	no	—
14	C₇×#732	C₃²	1	3	yes	—
15	C₇×C₉⋊C₉	—	3	1	no	—
16	C₇×C₉⋊C₉	C₃²	1	3	yes	complemented
17	C₇×C₃²⋊C₉	—	3	1	no	—
18	C₇×C₉²	—	3	1	no	—
19	C₃×#733	C₃×C₇	1	2	yes	complemented
20	C₃×#732	C₃×C₇	1	1	yes	characteristic
21	#6887	C₃×C₇	1	1	yes	characteristic, complemented
22	#6883	C₃×C₇	1	9	yes	complemented
23	C₃³×C₇	—	9	1	no	—
24	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
25	C₇×3₋¹⁺²	—	3	6	no	—
26	C₇×3₋¹⁺²	—	9	2	no	—
27	C₇×3₋¹⁺²	—	9	2	no	—
28	C₇×H(3,𝔽₃)	—	3	3	no	—
29	C₇×H(3,𝔽₃)	—	9	2	no	—
30	C₃×C₇×C₉	—	3	2	no	—
31	C₃×C₇×C₉	—	3	1	no	—
32	C₃×C₇×C₉	—	3	3	no	—
33	C₃×C₇×C₉	—	9	2	no	—
34	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
35	C₃×C₇×C₉	H(3,𝔽₃)	1	1	yes	characteristic
36	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	2	no	—
38	C₃×H(3,𝔽₃)	—	3	1	no	—
39	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
40	#733	—	3	2	no	—
41	#733	—	3	2	no	—
42	#733	C₃²×C₇	1	6	yes	complemented
43	#732	—	3	1	no	—
44	#732	—	3	1	no	—
45	#732	C₃²×C₇	1	3	yes	—
46	C₉⋊C₉	—	3	1	no	—
47	C₉⋊C₉	C₃²×C₇	1	3	yes	complemented
48	C₃²⋊C₉	—	3	1	no	—
49	C₉²	—	3	1	no	—
50	C₃²×C₇	—	9	1	no	—
51	C₃²×C₇	—	9	3	no	—
52	C₃²×C₇	—	27	3	no	—
53	C₃²×C₇	#732	1	2	yes	—
54	C₃²×C₇	#732	1	1	yes	characteristic
55	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
56	C₇×C₉	—	3	1	no	—
57	C₇×C₉	—	3	1	no	—
58	C₇×C₉	—	3	1	no	—
59	C₇×C₉	—	9	3	no	—
60	C₇×C₉	—	9	6	no	—
61	C₃³	—	9	1	no	—
62	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
63	3₋¹⁺²	—	3	6	no	—
64	3₋¹⁺²	—	9	2	no	—
65	3₋¹⁺²	—	9	2	no	—
66	H(3,𝔽₃)	—	3	3	no	—
67	H(3,𝔽₃)	—	9	2	no	—
68	C₃×C₉	—	3	2	no	—
69	C₃×C₉	—	3	1	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	—	9	2	no	—
72	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
73	C₃×C₉	C₇×H(3,𝔽₃)	1	1	yes	characteristic
74	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
75	C₃×C₇	—	3	1	no	—
76	C₃×C₇	—	3	1	no	—
77	C₃×C₇	—	3	2	no	—
78	C₃×C₇	—	27	3	no	—
79	C₃×C₇	C₃×#732	1	1	yes	characteristic
80	C₃²	—	9	1	no	—
81	C₃²	—	9	3	no	—
82	C₃²	—	27	3	no	—
83	C₃²	C₇×#732	1	2	yes	—
84	C₃²	C₇×#732	1	1	yes	characteristic
85	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
86	C₉	—	3	1	no	—
87	C₉	—	3	1	no	—
88	C₉	—	3	1	no	—
89	C₉	—	9	3	no	—
90	C₉	—	9	6	no	—
91	C₇	#10624848	1	1	yes	characteristic, direct product factor, Sylow
92	C₃	—	3	1	no	—
93	C₃	—	3	1	no	—
94	C₃	—	3	2	no	—
95	C₃	—	27	3	no	—
96	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×#6883	C₃	semidirect
5. #10624848	C₇	direct (N × H)
11. C₇×#733	C₃²	semidirect
16. C₇×C₉⋊C₉	C₃²	semidirect
19. C₃×#733	C₃×C₇	semidirect
21. #6887	C₃×C₇	semidirect
22. #6883	C₃×C₇	semidirect
42. #733	C₃²×C₇	semidirect
47. C₉⋊C₉	C₃²×C₇	semidirect
91. C₇	#10624848	direct (N × H)

Subgroups — C7×#10624848 #19100257

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624848 #19100257