Subgroups — C₃²×C₇×C₃²⋊C₉ #19100265

Order 5103.

2996 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃³×C₇×C₉	C₃	1	3	yes	maximal, complemented
3	C₃×C₇×C₃²⋊C₉	C₃	1	36	yes	maximal, direct product factor
4	C₃²×C₃²⋊C₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	—	3	9	no	—
6	C₃⁴×C₇	—	3	18	no	—
7	C₃⁴×C₇	C₉	1	27	yes	complemented
8	C₃⁴×C₇	C₃²	1	12	yes	—
9	C₃⁴×C₇	C₃²	1	1	yes	characteristic
10	C₃²×C₇×C₉	—	3	27	no	—
11	C₃²×C₇×C₉	C₃²	1	36	yes	complemented
12	C₇×C₃²⋊C₉	C₃²	1	81	yes	direct product factor
13	C₃⁵	C₃×C₇	1	1	yes	characteristic
14	C₃³×C₉	C₃×C₇	1	3	yes	complemented
15	C₃×C₃²⋊C₉	C₃×C₇	1	36	yes	direct product factor
16	C₃³×C₇	—	3	243	no	—
17	C₃³×C₇	—	3	36	no	—
18	C₃³×C₇	—	3	72	no	—
19	C₃³×C₇	C₃×C₉	1	9	yes	—
20	C₃³×C₇	C₃×C₉	1	108	yes	complemented
21	C₃³×C₇	H(3,𝔽₃)	1	9	yes	—
22	C₃³×C₇	3₋¹⁺²	1	18	yes	—
23	C₃³×C₇	C₃³	1	9	yes	—
24	C₃³×C₇	C₃³	1	4	yes	—
25	C₃×C₇×C₉	—	3	108	no	—
26	C₃×C₇×C₉	C₃³	1	27	yes	complemented
27	C₃⁴	—	3	9	no	—
28	C₃⁴	—	3	18	no	—
29	C₃⁴	C₇×C₉	1	27	yes	complemented
30	C₃⁴	C₃²×C₇	1	12	yes	—
31	C₃⁴	C₃²×C₇	1	1	yes	characteristic
32	C₃²×C₉	—	3	27	no	—
33	C₃²×C₉	C₃²×C₇	1	36	yes	complemented
34	C₃²⋊C₉	C₃²×C₇	1	81	yes	direct product factor
35	C₃²×C₇	—	3	9	no	—
36	C₃²×C₇	—	3	18	no	—
37	C₃²×C₇	—	3	324	no	—
38	C₃²×C₇	C₃²⋊C₉	1	81	yes	direct product factor
39	C₃²×C₇	C₃²×C₉	1	12	yes	—
40	C₃²×C₇	C₃²×C₉	1	27	yes	complemented
41	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
42	C₃²×C₇	C₃×3₋¹⁺²	1	24	yes	—
43	C₃²×C₇	C₃⁴	1	1	yes	characteristic
44	C₇×C₉	—	3	27	no	—
45	C₃³	—	3	243	no	—
46	C₃³	—	3	36	no	—
47	C₃³	—	3	72	no	—
48	C₃³	C₃×C₇×C₉	1	9	yes	—
49	C₃³	C₃×C₇×C₉	1	108	yes	complemented
50	C₃³	C₇×H(3,𝔽₃)	1	9	yes	—
51	C₃³	C₇×3₋¹⁺²	1	18	yes	—
52	C₃³	C₃³×C₇	1	9	yes	—
53	C₃³	C₃³×C₇	1	4	yes	—
54	C₃×C₉	—	3	108	no	—
55	C₃×C₉	C₃³×C₇	1	27	yes	complemented
56	C₃×C₇	—	3	27	no	—
57	C₃×C₇	C₃×C₃²⋊C₉	1	36	yes	direct product factor
58	C₃×C₇	C₃³×C₉	1	1	yes	characteristic
59	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
60	C₃×C₇	C₃²×3₋¹⁺²	1	2	yes	—
61	C₃²	—	3	324	no	—
62	C₃²	—	3	9	no	—
63	C₃²	—	3	18	no	—
64	C₃²	C₇×C₃²⋊C₉	1	81	yes	direct product factor
65	C₃²	C₃²×C₇×C₉	1	12	yes	—
66	C₃²	C₃²×C₇×C₉	1	27	yes	complemented
67	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
68	C₃²	C₃×C₇×3₋¹⁺²	1	24	yes	—
69	C₃²	C₃⁴×C₇	1	1	yes	characteristic
70	C₉	—	3	27	no	—
71	C₇	C₃²×C₃²⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
72	C₃	—	3	27	no	—
73	C₃	C₃×C₇×C₃²⋊C₉	1	36	yes	direct product factor
74	C₃	C₃³×C₇×C₉	1	1	yes	characteristic
75	C₃	C₃²×C₇×H(3,𝔽₃)	1	1	yes	characteristic
76	C₃	C₃²×C₇×3₋¹⁺²	1	2	yes	—

	subgroup	G/H
center, socle	C₃⁴×C₇	C₃²
commutator	C₃	C₃³×C₇×C₉
Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃³×C₇×C₉	C₃	semidirect
3. C₃×C₇×C₃²⋊C₉	C₃	direct (N × H)
4. C₃²×C₃²⋊C₉	C₇	direct (N × H)
7. C₃⁴×C₇	C₉	semidirect
11. C₃²×C₇×C₉	C₃²	semidirect
12. C₇×C₃²⋊C₉	C₃²	direct (N × H)
14. C₃³×C₉	C₃×C₇	semidirect
15. C₃×C₃²⋊C₉	C₃×C₇	direct (N × H)
20. C₃³×C₇	C₃×C₉	semidirect
26. C₃×C₇×C₉	C₃³	semidirect
29. C₃⁴	C₇×C₉	semidirect
33. C₃²×C₉	C₃²×C₇	semidirect
34. C₃²⋊C₉	C₃²×C₇	direct (N × H)
38. C₃²×C₇	C₃²⋊C₉	direct (N × H)
40. C₃²×C₇	C₃²×C₉	semidirect
49. C₃³	C₃×C₇×C₉	semidirect
55. C₃×C₉	C₃³×C₇	semidirect
57. C₃×C₇	C₃×C₃²⋊C₉	direct (N × H)
64. C₃²	C₇×C₃²⋊C₉	direct (N × H)
66. C₃²	C₃²×C₇×C₉	semidirect
71. C₇	C₃²×C₃²⋊C₉	direct (N × H)
73. C₃	C₃×C₇×C₃²⋊C₉	direct (N × H)

Subgroups — C32×C7×C32⋊C9 #19100265

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×C₃²⋊C₉ #19100265