Subgroups — C₃²×C₇×#733 #19100331

Order 5103.

1052 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	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×#733	C₃	1	36	yes	maximal, direct product factor
4	C₃²×#733	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	C₃²	1	1	yes	characteristic
6	C₃×C₇×3₋¹⁺²	—	3	24	no	—
7	C₃×C₇×3₋¹⁺²	C₃²	1	36	yes	—
8	C₃²×C₇×C₉	—	3	8	no	—
9	C₃²×C₇×C₉	—	3	1	no	—
10	C₃²×C₇×C₉	—	3	3	no	—
11	C₃²×C₇×C₉	C₃²	1	12	yes	—
12	C₇×#733	C₃²	1	81	yes	direct product factor
13	C₃²×3₋¹⁺²	C₃×C₇	1	3	yes	—
14	C₃³×C₉	C₃×C₇	1	1	yes	characteristic
15	C₃×#733	C₃×C₇	1	36	yes	direct product factor
16	C₃³×C₇	—	3	9	no	—
17	C₃³×C₇	H(3,𝔽₃)	1	8	yes	—
18	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃³×C₇	C₃³	1	4	yes	—
20	C₇×3₋¹⁺²	—	3	72	no	—
21	C₇×3₋¹⁺²	C₃³	1	27	yes	—
22	C₃×C₇×C₉	—	3	24	no	—
23	C₃×C₇×C₉	—	3	12	no	—
24	C₃×C₇×C₉	—	3	36	no	—
25	C₃×C₇×C₉	C₃³	1	9	yes	—
26	C₃⁴	C₃²×C₇	1	1	yes	characteristic
27	C₃×3₋¹⁺²	—	3	24	no	—
28	C₃×3₋¹⁺²	C₃²×C₇	1	36	yes	—
29	C₃²×C₉	—	3	8	no	—
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	—	3	3	no	—
32	C₃²×C₉	C₃²×C₇	1	12	yes	—
33	#733	C₃²×C₇	1	81	yes	direct product factor
34	C₃²×C₇	—	3	24	no	—
35	C₃²×C₇	—	3	12	no	—
36	C₃²×C₇	#733	1	9	yes	direct product factor
37	C₃²×C₇	C₃×H(3,𝔽₃)	1	8	yes	—
38	C₃²×C₇	C₃×H(3,𝔽₃)	1	4	yes	—
39	C₃²×C₇	C₃⁴	1	1	yes	characteristic
40	C₇×C₉	—	3	9	no	—
41	C₇×C₉	—	3	27	no	—
42	C₃³	—	3	9	no	—
43	C₃³	C₇×H(3,𝔽₃)	1	8	yes	—
44	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
45	C₃³	C₃³×C₇	1	4	yes	—
46	3₋¹⁺²	—	3	72	no	—
47	3₋¹⁺²	C₃³×C₇	1	27	yes	—
48	C₃×C₉	—	3	24	no	—
49	C₃×C₉	—	3	12	no	—
50	C₃×C₉	—	3	36	no	—
51	C₃×C₉	C₃³×C₇	1	9	yes	—
52	C₃×C₇	—	3	8	no	—
53	C₃×C₇	—	3	1	no	—
54	C₃×C₇	C₃×#733	1	12	yes	direct product factor
55	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
56	C₃²	—	3	24	no	—
57	C₃²	—	3	12	no	—
58	C₃²	C₇×#733	1	9	yes	direct product factor
59	C₃²	C₃×C₇×H(3,𝔽₃)	1	8	yes	—
60	C₃²	C₃×C₇×H(3,𝔽₃)	1	4	yes	—
61	C₃²	C₃⁴×C₇	1	1	yes	characteristic
62	C₉	—	3	9	no	—
63	C₉	—	3	27	no	—
64	C₇	C₃²×#733	1	1	yes	characteristic, direct product factor, Sylow
65	C₃	—	3	8	no	—
66	C₃	—	3	1	no	—
67	C₃	C₃×C₇×#733	1	12	yes	direct product factor
68	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
3. C₃×C₇×#733	C₃	direct (N × H)
4. C₃²×#733	C₇	direct (N × H)
12. C₇×#733	C₃²	direct (N × H)
15. C₃×#733	C₃×C₇	direct (N × H)
33. #733	C₃²×C₇	direct (N × H)
36. C₃²×C₇	#733	direct (N × H)
54. C₃×C₇	C₃×#733	direct (N × H)
58. C₃²	C₇×#733	direct (N × H)
64. C₇	C₃²×#733	direct (N × H)
67. C₃	C₃×C₇×#733	direct (N × H)

Subgroups — C32×C7×#733 #19100331

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×#733 #19100331