Subgroups — C₃×C₇×C₃²⋊H(3,𝔽₃) #19100274

Order 5103.

3824 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, complemented
2	C₃²×C₇×H(3,𝔽₃)	C₃	1	12	yes	maximal, complemented
3	C₇×C₃²⋊H(3,𝔽₃)	C₃	1	27	yes	maximal, direct product factor
4	C₃×C₃²⋊H(3,𝔽₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃⁴×C₇	—	3	36	no	—
6	C₃⁴×C₇	C₃²	1	4	yes	—
7	C₃⁴×C₇	C₃²	1	9	yes	complemented
8	C₃⁴×C₇	C₃²	1	9	yes	complemented
9	C₃×C₇×H(3,𝔽₃)	—	3	108	no	—
10	C₃×C₇×H(3,𝔽₃)	C₃²	1	108	yes	complemented
11	C₃⁵	C₃×C₇	1	1	yes	characteristic, complemented
12	C₃²×H(3,𝔽₃)	C₃×C₇	1	12	yes	complemented
13	C₃²⋊H(3,𝔽₃)	C₃×C₇	1	27	yes	direct product factor
14	C₃³×C₇	—	3	243	no	—
15	C₃³×C₇	—	3	36	no	—
16	C₃³×C₇	—	3	108	no	—
17	C₃³×C₇	—	3	108	no	—
18	C₃³×C₇	H(3,𝔽₃)	1	36	yes	complemented
19	C₃³×C₇	C₃³	1	12	yes	—
20	C₃³×C₇	C₃³	1	1	yes	characteristic
21	C₃³×C₇	C₃³	1	27	yes	complemented
22	C₇×H(3,𝔽₃)	—	3	324	no	—
23	C₃⁴	—	3	36	no	—
24	C₃⁴	C₃²×C₇	1	4	yes	—
25	C₃⁴	C₃²×C₇	1	9	yes	complemented
26	C₃⁴	C₃²×C₇	1	9	yes	complemented
27	C₃×H(3,𝔽₃)	—	3	108	no	—
28	C₃×H(3,𝔽₃)	C₃²×C₇	1	108	yes	complemented
29	C₃²×C₇	—	3	243	no	—
30	C₃²×C₇	—	3	36	no	—
31	C₃²×C₇	—	3	108	no	—
32	C₃²×C₇	—	3	108	no	—
33	C₃²×C₇	—	9	81	no	—
34	C₃²×C₇	C₃×H(3,𝔽₃)	1	12	yes	—
35	C₃²×C₇	C₃×H(3,𝔽₃)	1	36	yes	complemented
36	C₃²×C₇	C₃⁴	1	1	yes	characteristic
37	C₃³	—	3	243	no	—
38	C₃³	—	3	36	no	—
39	C₃³	—	3	108	no	—
40	C₃³	—	3	108	no	—
41	C₃³	C₇×H(3,𝔽₃)	1	36	yes	complemented
42	C₃³	C₃³×C₇	1	12	yes	—
43	C₃³	C₃³×C₇	1	1	yes	characteristic
44	C₃³	C₃³×C₇	1	27	yes	complemented
45	H(3,𝔽₃)	—	3	324	no	—
46	C₃×C₇	—	3	36	no	—
47	C₃×C₇	—	9	27	no	—
48	C₃×C₇	C₃²⋊H(3,𝔽₃)	1	9	yes	direct product factor
49	C₃×C₇	C₃²×H(3,𝔽₃)	1	4	yes	—
50	C₃²	—	3	243	no	—
51	C₃²	—	3	108	no	—
52	C₃²	—	3	36	no	—
53	C₃²	—	3	108	no	—
54	C₃²	—	9	81	no	—
55	C₃²	C₃×C₇×H(3,𝔽₃)	1	12	yes	—
56	C₃²	C₃×C₇×H(3,𝔽₃)	1	36	yes	complemented
57	C₃²	C₃⁴×C₇	1	1	yes	characteristic
58	C₇	C₃×C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
59	C₃	—	3	36	no	—
60	C₃	—	9	27	no	—
61	C₃	C₇×C₃²⋊H(3,𝔽₃)	1	9	yes	direct product factor
62	C₃	C₃²×C₇×H(3,𝔽₃)	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₃⁵×C₇	C₃	semidirect
2. C₃²×C₇×H(3,𝔽₃)	C₃	semidirect
3. C₇×C₃²⋊H(3,𝔽₃)	C₃	direct (N × H)
4. C₃×C₃²⋊H(3,𝔽₃)	C₇	direct (N × H)
7. C₃⁴×C₇	C₃²	semidirect
8. C₃⁴×C₇	C₃²	semidirect
10. C₃×C₇×H(3,𝔽₃)	C₃²	semidirect
11. C₃⁵	C₃×C₇	semidirect
12. C₃²×H(3,𝔽₃)	C₃×C₇	semidirect
13. C₃²⋊H(3,𝔽₃)	C₃×C₇	direct (N × H)
18. C₃³×C₇	H(3,𝔽₃)	semidirect
21. C₃³×C₇	C₃³	semidirect
25. C₃⁴	C₃²×C₇	semidirect
26. C₃⁴	C₃²×C₇	semidirect
28. C₃×H(3,𝔽₃)	C₃²×C₇	semidirect
35. C₃²×C₇	C₃×H(3,𝔽₃)	semidirect
41. C₃³	C₇×H(3,𝔽₃)	semidirect
44. C₃³	C₃³×C₇	semidirect
48. C₃×C₇	C₃²⋊H(3,𝔽₃)	direct (N × H)
56. C₃²	C₃×C₇×H(3,𝔽₃)	semidirect
58. C₇	C₃×C₃²⋊H(3,𝔽₃)	direct (N × H)
61. C₃	C₇×C₃²⋊H(3,𝔽₃)	direct (N × H)

Subgroups — C3×C7×C32⋊H(3,𝔽3) #19100274

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×C₃²⋊H(3,𝔽₃) #19100274