Subgroups — C₃³×C₇×H(3,𝔽₃) #19100347

Order 5103.

11744 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵×C₇	C₃	1	4	yes	maximal, complemented
2	C₃²×C₇×H(3,𝔽₃)	C₃	1	117	yes	maximal, direct product factor
3	C₃³×H(3,𝔽₃)	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₃⁴×C₇	—	3	108	no	—
5	C₃⁴×C₇	C₃²	1	1	yes	characteristic
6	C₃⁴×C₇	C₃²	1	156	yes	complemented
7	C₃×C₇×H(3,𝔽₃)	C₃²	1	1053	yes	direct product factor
8	C₃⁵	C₃×C₇	1	4	yes	complemented
9	C₃²×H(3,𝔽₃)	C₃×C₇	1	117	yes	direct product factor
10	C₃³×C₇	—	3	1404	no	—
11	C₃³×C₇	H(3,𝔽₃)	1	27	yes	direct product factor
12	C₃³×C₇	C₃³	1	13	yes	—
13	C₃³×C₇	C₃³	1	468	yes	complemented
14	C₇×H(3,𝔽₃)	C₃³	1	729	yes	direct product factor
15	C₃⁴	—	3	108	no	—
16	C₃⁴	C₃²×C₇	1	1	yes	characteristic
17	C₃⁴	C₃²×C₇	1	156	yes	complemented
18	C₃×H(3,𝔽₃)	C₃²×C₇	1	1053	yes	direct product factor
19	C₃²×C₇	—	3	1404	no	—
20	C₃²×C₇	C₃×H(3,𝔽₃)	1	117	yes	direct product factor
21	C₃²×C₇	C₃⁴	1	13	yes	—
22	C₃²×C₇	C₃⁴	1	108	yes	complemented
23	C₃³	—	3	1404	no	—
24	C₃³	C₇×H(3,𝔽₃)	1	27	yes	direct product factor
25	C₃³	C₃³×C₇	1	13	yes	—
26	C₃³	C₃³×C₇	1	468	yes	complemented
27	H(3,𝔽₃)	C₃³×C₇	1	729	yes	direct product factor
28	C₃×C₇	—	3	108	no	—
29	C₃×C₇	C₃²×H(3,𝔽₃)	1	39	yes	direct product factor
30	C₃×C₇	C₃⁵	1	1	yes	characteristic
31	C₃²	—	3	1404	no	—
32	C₃²	C₃×C₇×H(3,𝔽₃)	1	117	yes	direct product factor
33	C₃²	C₃⁴×C₇	1	13	yes	—
34	C₃²	C₃⁴×C₇	1	108	yes	complemented
35	C₇	C₃³×H(3,𝔽₃)	1	1	yes	characteristic, direct product factor, Sylow
36	C₃	—	3	108	no	—
37	C₃	C₃²×C₇×H(3,𝔽₃)	1	39	yes	direct product factor
38	C₃	C₃⁵×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃⁴×C₇	C₃²
commutator, Frattini	C₃	C₃⁵×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
1. C₃⁵×C₇	C₃	semidirect
2. C₃²×C₇×H(3,𝔽₃)	C₃	direct (N × H)
3. C₃³×H(3,𝔽₃)	C₇	direct (N × H)
6. C₃⁴×C₇	C₃²	semidirect
7. C₃×C₇×H(3,𝔽₃)	C₃²	direct (N × H)
8. C₃⁵	C₃×C₇	semidirect
9. C₃²×H(3,𝔽₃)	C₃×C₇	direct (N × H)
11. C₃³×C₇	H(3,𝔽₃)	direct (N × H)
13. C₃³×C₇	C₃³	semidirect
14. C₇×H(3,𝔽₃)	C₃³	direct (N × H)
17. C₃⁴	C₃²×C₇	semidirect
18. C₃×H(3,𝔽₃)	C₃²×C₇	direct (N × H)
20. C₃²×C₇	C₃×H(3,𝔽₃)	direct (N × H)
22. C₃²×C₇	C₃⁴	semidirect
24. C₃³	C₇×H(3,𝔽₃)	direct (N × H)
26. C₃³	C₃³×C₇	semidirect
27. H(3,𝔽₃)	C₃³×C₇	direct (N × H)
29. C₃×C₇	C₃²×H(3,𝔽₃)	direct (N × H)
32. C₃²	C₃×C₇×H(3,𝔽₃)	direct (N × H)
34. C₃²	C₃⁴×C₇	semidirect
35. C₇	C₃³×H(3,𝔽₃)	direct (N × H)
37. C₃	C₃²×C₇×H(3,𝔽₃)	direct (N × H)

Subgroups — C33×C7×H(3,𝔽3) #19100347

Conjugacy classes of subgroups

Complements

Subgroups — C₃³×C₇×H(3,𝔽₃) #19100347