Subgroups — C₃²×C₇×#732 #19100330

Order 5103.

1376 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×H(3,𝔽₃)	C₃	1	3	yes	maximal, complemented
2	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×#732	C₃	1	36	yes	maximal, direct product factor
4	C₃²×#732	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	—	3	3	no	—
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃×C₇×H(3,𝔽₃)	—	3	24	no	—
8	C₃×C₇×H(3,𝔽₃)	C₃²	1	36	yes	complemented
9	C₃²×C₇×C₉	—	3	8	no	—
10	C₃²×C₇×C₉	—	3	1	no	—
11	C₃²×C₇×C₉	C₃²	1	12	yes	complemented
12	C₇×#732	C₃²	1	81	yes	direct product factor
13	C₃²×H(3,𝔽₃)	C₃×C₇	1	3	yes	complemented
14	C₃³×C₉	C₃×C₇	1	1	yes	characteristic, complemented
15	C₃×#732	C₃×C₇	1	36	yes	direct product factor
16	C₃³×C₇	—	3	9	no	—
17	C₃³×C₇	—	3	36	no	—
18	C₃³×C₇	—	9	27	no	—
19	C₃³×C₇	H(3,𝔽₃)	1	8	yes	—
20	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃³×C₇	C₃³	1	4	yes	—
22	C₇×H(3,𝔽₃)	—	3	72	no	—
23	C₇×H(3,𝔽₃)	C₃³	1	27	yes	complemented
24	C₃×C₇×C₉	—	3	24	no	—
25	C₃×C₇×C₉	—	3	12	no	—
26	C₃×C₇×C₉	C₃³	1	9	yes	complemented
27	C₃⁴	—	3	3	no	—
28	C₃⁴	C₃²×C₇	1	1	yes	characteristic
29	C₃×H(3,𝔽₃)	—	3	24	no	—
30	C₃×H(3,𝔽₃)	C₃²×C₇	1	36	yes	complemented
31	C₃²×C₉	—	3	8	no	—
32	C₃²×C₉	—	3	1	no	—
33	C₃²×C₉	C₃²×C₇	1	12	yes	complemented
34	#732	C₃²×C₇	1	81	yes	direct product factor
35	C₃²×C₇	—	3	24	no	—
36	C₃²×C₇	—	3	12	no	—
37	C₃²×C₇	—	3	27	no	—
38	C₃²×C₇	—	9	108	no	—
39	C₃²×C₇	#732	1	9	yes	direct product factor
40	C₃²×C₇	C₃×H(3,𝔽₃)	1	8	yes	—
41	C₃²×C₇	C₃×H(3,𝔽₃)	1	4	yes	—
42	C₃²×C₇	C₃⁴	1	1	yes	characteristic
43	C₇×C₉	—	3	9	no	—
44	C₃³	—	3	9	no	—
45	C₃³	—	3	36	no	—
46	C₃³	—	9	27	no	—
47	C₃³	C₇×H(3,𝔽₃)	1	8	yes	—
48	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃³	C₃³×C₇	1	4	yes	—
50	H(3,𝔽₃)	—	3	72	no	—
51	H(3,𝔽₃)	C₃³×C₇	1	27	yes	complemented
52	C₃×C₉	—	3	24	no	—
53	C₃×C₉	—	3	12	no	—
54	C₃×C₉	C₃³×C₇	1	9	yes	complemented
55	C₃×C₇	—	3	8	no	—
56	C₃×C₇	—	3	1	no	—
57	C₃×C₇	—	9	27	no	—
58	C₃×C₇	C₃×#732	1	12	yes	direct product factor
59	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
60	C₃²	—	3	24	no	—
61	C₃²	—	3	12	no	—
62	C₃²	—	3	27	no	—
63	C₃²	—	9	108	no	—
64	C₃²	C₇×#732	1	9	yes	direct product factor
65	C₃²	C₃×C₇×H(3,𝔽₃)	1	8	yes	—
66	C₃²	C₃×C₇×H(3,𝔽₃)	1	4	yes	—
67	C₃²	C₃⁴×C₇	1	1	yes	characteristic
68	C₉	—	3	9	no	—
69	C₇	C₃²×#732	1	1	yes	characteristic, direct product factor, Sylow
70	C₃	—	3	8	no	—
71	C₃	—	3	1	no	—
72	C₃	—	9	27	no	—
73	C₃	C₃×C₇×#732	1	12	yes	direct product factor
74	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃³×C₇	H(3,𝔽₃)
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃³×C₇ ◁ C₃⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×H(3,𝔽₃)	C₃	semidirect
2. C₃³×C₇×C₉	C₃	semidirect
3. C₃×C₇×#732	C₃	direct (N × H)
4. C₃²×#732	C₇	direct (N × H)
8. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
11. C₃²×C₇×C₉	C₃²	semidirect
12. C₇×#732	C₃²	direct (N × H)
13. C₃²×H(3,𝔽₃)	C₃×C₇	semidirect
14. C₃³×C₉	C₃×C₇	semidirect
15. C₃×#732	C₃×C₇	direct (N × H)
23. C₇×H(3,𝔽₃)	C₃³	semidirect
26. C₃×C₇×C₉	C₃³	semidirect
30. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
33. C₃²×C₉	C₃²×C₇	semidirect
34. #732	C₃²×C₇	direct (N × H)
39. C₃²×C₇	#732	direct (N × H)
51. H(3,𝔽₃)	C₃³×C₇	semidirect
54. C₃×C₉	C₃³×C₇	semidirect
58. C₃×C₇	C₃×#732	direct (N × H)
64. C₃²	C₇×#732	direct (N × H)
69. C₇	C₃²×#732	direct (N × H)
73. C₃	C₃×C₇×#732	direct (N × H)

Subgroups — C32×C7×#732 #19100330

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×#732 #19100330