Subgroups — C₃×C₄₇×#737 #26037726

Order 11421.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#737	C₃	1	27	yes	maximal, direct product factor
2	C₃×3₋¹⁺²×C₄₇	C₃	1	8	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₄₇	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉×C₄₇	C₃	1	4	yes	maximal, complemented
5	C₃³×C₄₇	C₃²	1	4	yes	—
6	3₋¹⁺²×C₄₇	C₃²	1	72	yes	complemented
7	H(3,𝔽₃)×C₄₇	C₃²	1	9	yes	—
8	C₃×C₉×C₄₇	C₃²	1	8	yes	—
9	C₃×C₉×C₄₇	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₄₇	C₃²	1	36	yes	complemented
11	C₃²×C₄₇	—	3	12	no	—
12	C₃²×C₄₇	C₃³	1	12	yes	—
13	C₃²×C₄₇	C₃³	1	1	yes	characteristic
14	C₉×C₄₇	C₃³	1	24	yes	—
15	C₉×C₄₇	C₃³	1	3	yes	—
16	C₃×#737	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃×C₄₇	—	3	12	no	—
18	C₃×C₄₇	#737	1	3	yes	direct product factor
19	C₃×C₄₇	C₃⁴	1	1	yes	characteristic
20	#737	C₃×C₄₇	1	27	yes	direct product factor
21	C₃×3₋¹⁺²	C₃×C₄₇	1	8	yes	complemented
22	C₃×H(3,𝔽₃)	C₃×C₄₇	1	1	yes	characteristic
23	C₃²×C₉	C₃×C₄₇	1	4	yes	complemented
24	C₄₇	C₃×#737	1	1	yes	characteristic, direct product factor, Sylow
25	C₃³	C₃²×C₄₇	1	4	yes	—
26	3₋¹⁺²	C₃²×C₄₇	1	72	yes	complemented
27	H(3,𝔽₃)	C₃²×C₄₇	1	9	yes	—
28	C₃×C₉	C₃²×C₄₇	1	8	yes	—
29	C₃×C₉	C₃²×C₄₇	1	1	yes	characteristic
30	C₃×C₉	C₃²×C₄₇	1	36	yes	complemented
31	C₃²	—	3	12	no	—
32	C₃²	C₃³×C₄₇	1	12	yes	—
33	C₃²	C₃³×C₄₇	1	1	yes	characteristic
34	C₉	C₃³×C₄₇	1	3	yes	—
35	C₉	C₃³×C₄₇	1	24	yes	—
36	C₃	—	3	12	no	—
37	C₃	C₄₇×#737	1	3	yes	direct product factor
38	C₃	C₃⁴×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉×C₄₇	C₃²
commutator, Frattini, cosocle	C₃	C₃⁴×C₄₇
socle	C₃²×C₄₇	C₃³
prime radical	C₃×H(3,𝔽₃)×C₄₇	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#737	C₃	direct (N × H)
2. C₃×3₋¹⁺²×C₄₇	C₃	semidirect
4. C₃²×C₉×C₄₇	C₃	semidirect
6. 3₋¹⁺²×C₄₇	C₃²	semidirect
10. C₃×C₉×C₄₇	C₃²	semidirect
16. C₃×#737	C₄₇	direct (N × H)
18. C₃×C₄₇	#737	direct (N × H)
20. #737	C₃×C₄₇	direct (N × H)
21. C₃×3₋¹⁺²	C₃×C₄₇	semidirect
23. C₃²×C₉	C₃×C₄₇	semidirect
24. C₄₇	C₃×#737	direct (N × H)
26. 3₋¹⁺²	C₃²×C₄₇	semidirect
30. C₃×C₉	C₃²×C₄₇	semidirect
37. C₃	C₄₇×#737	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄₇×#737	3
C₃×3₋¹⁺²×C₄₇	3
C₃×H(3,𝔽₃)×C₄₇	3
C₃²×C₉×C₄₇	3
C₃×#737	47

Subgroups — C3×C47×#737 #26037726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×#737 #26037726