Subgroups — C₃×C₇×#6912 #19100336

Order 5103.

980 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	3	yes	maximal
2	C₃²×C₇×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic
3	C₇×#6912	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₇×#733	C₃	1	9	yes	maximal, complemented
5	C₃×#6912	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×3₋¹⁺²	—	3	18	no	—
8	C₃×C₇×3₋¹⁺²	—	3	6	no	—
9	C₃×C₇×3₋¹⁺²	—	3	6	no	—
10	C₃×C₇×3₋¹⁺²	—	3	3	no	—
11	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
12	C₃×C₇×3₋¹⁺²	C₃²	1	27	yes	—
13	C₃×C₇×3₋¹⁺²	C₃²	1	9	yes	—
14	C₃²×C₇×C₉	—	3	3	no	—
15	C₃²×C₇×C₉	C₃²	1	3	yes	—
16	C₇×#733	C₃²	1	81	yes	complemented
17	C₃²×3₋¹⁺²	C₃×C₇	1	3	yes	—
18	C₃²×3₋¹⁺²	C₃×C₇	1	1	yes	characteristic
19	#6912	C₃×C₇	1	27	yes	direct product factor
20	C₃×#733	C₃×C₇	1	9	yes	complemented
21	C₃³×C₇	—	9	3	no	—
22	C₃³×C₇	H(3,𝔽₃)	1	3	yes	—
23	C₃³×C₇	H(3,𝔽₃)	1	6	yes	—
24	C₃³×C₇	C₃³	1	1	yes	characteristic
25	C₃³×C₇	C₃³	1	3	yes	—
26	C₇×3₋¹⁺²	—	3	18	no	—
27	C₇×3₋¹⁺²	—	3	54	no	—
28	C₇×3₋¹⁺²	—	3	27	no	—
29	C₇×3₋¹⁺²	C₃³	1	27	yes	—
30	C₃×C₇×C₉	—	3	27	no	—
31	C₃×C₇×C₉	—	3	6	no	—
32	C₃×C₇×C₉	—	3	9	no	—
33	C₃×C₇×C₉	—	3	3	no	—
34	C₃×C₇×C₉	C₃³	1	9	yes	—
35	C₃⁴	C₃²×C₇	1	1	yes	characteristic
36	C₃×3₋¹⁺²	—	3	6	no	—
37	C₃×3₋¹⁺²	—	3	18	no	—
38	C₃×3₋¹⁺²	—	3	3	no	—
39	C₃×3₋¹⁺²	—	3	6	no	—
40	C₃×3₋¹⁺²	C₃²×C₇	1	27	yes	—
41	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
42	C₃×3₋¹⁺²	C₃²×C₇	1	9	yes	—
43	C₃²×C₉	—	3	3	no	—
44	C₃²×C₉	C₃²×C₇	1	3	yes	—
45	#733	C₃²×C₇	1	81	yes	complemented
46	C₃²×C₇	—	3	9	no	—
47	C₃²×C₇	—	3	3	no	—
48	C₃²×C₇	—	9	6	no	—
49	C₃²×C₇	—	9	3	no	—
50	C₃²×C₇	C₃×H(3,𝔽₃)	1	9	yes	—
51	C₃²×C₇	C₃×H(3,𝔽₃)	1	2	yes	—
52	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
53	C₃²×C₇	C₃⁴	1	1	yes	characteristic
54	C₇×C₉	—	3	27	no	—
55	C₇×C₉	—	3	9	no	—
56	C₃³	—	9	3	no	—
57	C₃³	C₇×H(3,𝔽₃)	1	3	yes	—
58	C₃³	C₇×H(3,𝔽₃)	1	6	yes	—
59	C₃³	C₃³×C₇	1	1	yes	characteristic
60	C₃³	C₃³×C₇	1	3	yes	—
61	3₋¹⁺²	—	3	54	no	—
62	3₋¹⁺²	—	3	18	no	—
63	3₋¹⁺²	—	3	27	no	—
64	3₋¹⁺²	C₃³×C₇	1	27	yes	—
65	C₃×C₉	—	3	27	no	—
66	C₃×C₉	—	3	9	no	—
67	C₃×C₉	—	3	6	no	—
68	C₃×C₉	—	3	3	no	—
69	C₃×C₉	C₃³×C₇	1	9	yes	—
70	C₃×C₇	—	3	9	no	—
71	C₃×C₇	—	3	2	no	—
72	C₃×C₇	—	3	1	no	—
73	C₃×C₇	#6912	1	3	yes	direct product factor
74	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
75	C₃²	—	3	9	no	—
76	C₃²	—	3	3	no	—
77	C₃²	—	9	6	no	—
78	C₃²	—	9	3	no	—
79	C₃²	C₃×C₇×H(3,𝔽₃)	1	9	yes	—
80	C₃²	C₃×C₇×H(3,𝔽₃)	1	2	yes	—
81	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
82	C₃²	C₃⁴×C₇	1	1	yes	characteristic
83	C₉	—	3	27	no	—
84	C₉	—	3	9	no	—
85	C₇	C₃×#6912	1	1	yes	characteristic, direct product factor, Sylow
86	C₃	—	3	9	no	—
87	C₃	—	3	2	no	—
88	C₃	—	3	1	no	—
89	C₃	C₇×#6912	1	3	yes	direct product factor
90	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₇	C₃×H(3,𝔽₃)
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇ ◁ C₃⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×#6912	C₃	direct (N × H)
4. C₃×C₇×#733	C₃	semidirect
5. C₃×#6912	C₇	direct (N × H)
16. C₇×#733	C₃²	semidirect
19. #6912	C₃×C₇	direct (N × H)
20. C₃×#733	C₃×C₇	semidirect
45. #733	C₃²×C₇	semidirect
73. C₃×C₇	#6912	direct (N × H)
85. C₇	C₃×#6912	direct (N × H)
89. C₃	C₇×#6912	direct (N × H)

Subgroups — C3×C7×#6912 #19100336

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6912 #19100336