Subgroups — C₃²×C₇×#731 #19100329

Order 5103.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×3₋¹⁺²	C₃	1	2	yes	maximal, complemented
2	C₃²×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃³×C₇×C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₇×#731	C₃	1	36	yes	maximal, direct product factor
5	C₃²×#731	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	—	3	1	no	—
7	C₃⁴×C₇	C₃²	1	1	yes	characteristic
8	C₃×C₇×3₋¹⁺²	—	3	16	no	—
9	C₃×C₇×3₋¹⁺²	C₃²	1	24	yes	complemented
10	C₃×C₇×H(3,𝔽₃)	—	3	8	no	—
11	C₃×C₇×H(3,𝔽₃)	C₃²	1	12	yes	—
12	C₃²×C₇×C₉	—	3	8	no	—
13	C₃²×C₇×C₉	—	3	1	no	—
14	C₃²×C₇×C₉	—	3	2	no	—
15	C₃²×C₇×C₉	C₃²	1	12	yes	complemented
16	C₇×#731	C₃²	1	81	yes	direct product factor
17	C₃²×3₋¹⁺²	C₃×C₇	1	2	yes	complemented
18	C₃²×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
19	C₃³×C₉	C₃×C₇	1	1	yes	characteristic, complemented
20	C₃×#731	C₃×C₇	1	36	yes	direct product factor
21	C₃³×C₇	—	3	9	no	—
22	C₃³×C₇	—	3	12	no	—
23	C₃³×C₇	—	9	9	no	—
24	C₃³×C₇	H(3,𝔽₃)	1	8	yes	—
25	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
26	C₃³×C₇	C₃³	1	4	yes	—
27	C₇×3₋¹⁺²	—	3	48	no	—
28	C₇×3₋¹⁺²	C₃³	1	18	yes	complemented
29	C₇×H(3,𝔽₃)	—	3	24	no	—
30	C₇×H(3,𝔽₃)	C₃³	1	9	yes	—
31	C₃×C₇×C₉	—	3	24	no	—
32	C₃×C₇×C₉	—	3	12	no	—
33	C₃×C₇×C₉	—	3	24	no	—
34	C₃×C₇×C₉	C₃³	1	9	yes	complemented
35	C₃⁴	—	3	1	no	—
36	C₃⁴	C₃²×C₇	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	3	16	no	—
38	C₃×3₋¹⁺²	C₃²×C₇	1	24	yes	complemented
39	C₃×H(3,𝔽₃)	—	3	8	no	—
40	C₃×H(3,𝔽₃)	C₃²×C₇	1	12	yes	—
41	C₃²×C₉	—	3	8	no	—
42	C₃²×C₉	—	3	1	no	—
43	C₃²×C₉	—	3	2	no	—
44	C₃²×C₉	C₃²×C₇	1	12	yes	complemented
45	#731	C₃²×C₇	1	81	yes	direct product factor
46	C₃²×C₇	—	3	24	no	—
47	C₃²×C₇	—	3	12	no	—
48	C₃²×C₇	—	3	9	no	—
49	C₃²×C₇	—	9	36	no	—
50	C₃²×C₇	#731	1	9	yes	direct product factor
51	C₃²×C₇	C₃×H(3,𝔽₃)	1	8	yes	—
52	C₃²×C₇	C₃×H(3,𝔽₃)	1	4	yes	—
53	C₃²×C₇	C₃⁴	1	1	yes	characteristic
54	C₇×C₉	—	3	9	no	—
55	C₇×C₉	—	3	18	no	—
56	C₃³	—	3	9	no	—
57	C₃³	—	3	12	no	—
58	C₃³	—	9	9	no	—
59	C₃³	C₇×H(3,𝔽₃)	1	8	yes	—
60	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
61	C₃³	C₃³×C₇	1	4	yes	—
62	3₋¹⁺²	—	3	48	no	—
63	3₋¹⁺²	C₃³×C₇	1	18	yes	complemented
64	H(3,𝔽₃)	—	3	24	no	—
65	H(3,𝔽₃)	C₃³×C₇	1	9	yes	—
66	C₃×C₉	—	3	24	no	—
67	C₃×C₉	—	3	12	no	—
68	C₃×C₉	—	3	24	no	—
69	C₃×C₉	C₃³×C₇	1	9	yes	complemented
70	C₃×C₇	—	3	8	no	—
71	C₃×C₇	—	3	1	no	—
72	C₃×C₇	—	9	9	no	—
73	C₃×C₇	C₃×#731	1	12	yes	direct product factor
74	C₃×C₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
75	C₃²	—	3	24	no	—
76	C₃²	—	3	12	no	—
77	C₃²	—	3	9	no	—
78	C₃²	—	9	36	no	—
79	C₃²	C₇×#731	1	9	yes	direct product factor
80	C₃²	C₃×C₇×H(3,𝔽₃)	1	8	yes	—
81	C₃²	C₃×C₇×H(3,𝔽₃)	1	4	yes	—
82	C₃²	C₃⁴×C₇	1	1	yes	characteristic
83	C₉	—	3	9	no	—
84	C₉	—	3	18	no	—
85	C₇	C₃²×#731	1	1	yes	characteristic, direct product factor, Sylow
86	C₃	—	3	8	no	—
87	C₃	—	3	1	no	—
88	C₃	—	9	9	no	—
89	C₃	C₃×C₇×#731	1	12	yes	direct product factor
90	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×C₇×3₋¹⁺²	C₃	semidirect
3. C₃³×C₇×C₉	C₃	semidirect
4. C₃×C₇×#731	C₃	direct (N × H)
5. C₃²×#731	C₇	direct (N × H)
9. C₃×C₇×3₋¹⁺²	C₃²	semidirect
15. C₃²×C₇×C₉	C₃²	semidirect
16. C₇×#731	C₃²	direct (N × H)
17. C₃²×3₋¹⁺²	C₃×C₇	semidirect
19. C₃³×C₉	C₃×C₇	semidirect
20. C₃×#731	C₃×C₇	direct (N × H)
28. C₇×3₋¹⁺²	C₃³	semidirect
34. C₃×C₇×C₉	C₃³	semidirect
38. C₃×3₋¹⁺²	C₃²×C₇	semidirect
44. C₃²×C₉	C₃²×C₇	semidirect
45. #731	C₃²×C₇	direct (N × H)
50. C₃²×C₇	#731	direct (N × H)
63. 3₋¹⁺²	C₃³×C₇	semidirect
69. C₃×C₉	C₃³×C₇	semidirect
73. C₃×C₇	C₃×#731	direct (N × H)
79. C₃²	C₇×#731	direct (N × H)
85. C₇	C₃²×#731	direct (N × H)
89. C₃	C₃×C₇×#731	direct (N × H)

Subgroups — C32×C7×#731 #19100329

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×C₇×#731 #19100329