Subgroups — C₄₃×#10624943 #44531880

Order 31347.

5490 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×3₋¹⁺⁴	C₃	1	80	yes	maximal, complemented
2	C₄₃×H(5,𝔽₃)	C₃	1	1	yes	maximal, characteristic
3	C₃×C₄₃×#737	C₃	1	40	yes	maximal, complemented
4	C₄₃×#737	C₃²	1	90	yes	complemented
5	C₄₃×#737	C₃²	1	720	yes	complemented
6	C₃×3₋¹⁺²×C₄₃	C₃²	1	320	yes	complemented
7	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	40	yes	—
8	C₃²×C₉×C₄₃	C₃²	1	40	yes	complemented
9	C₃³×C₄₃	C₃³	1	40	yes	—
10	3₋¹⁺²×C₄₃	C₃³	1	720	yes	—
11	H(3,𝔽₃)×C₄₃	C₃³	1	90	yes	—
12	C₃×C₉×C₄₃	C₃³	1	320	yes	—
13	C₃×C₉×C₄₃	C₃³	1	40	yes	—
14	#10624943	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃²×C₄₃	—	9	40	no	—
16	C₃²×C₄₃	C₃⁴	1	40	yes	—
17	C₉×C₄₃	C₃⁴	1	80	yes	—
18	C₉×C₄₃	C₃⁴	1	1	yes	characteristic
19	3₋¹⁺⁴	C₃×C₄₃	1	80	yes	complemented
20	H(5,𝔽₃)	C₃×C₄₃	1	1	yes	characteristic
21	C₃×#737	C₃×C₄₃	1	40	yes	complemented
22	C₃×C₄₃	—	3	40	no	—
23	C₃×C₄₃	C₃⁵	1	1	yes	characteristic
24	#737	C₃²×C₄₃	1	90	yes	complemented
25	#737	C₃²×C₄₃	1	720	yes	complemented
26	C₃×3₋¹⁺²	C₃²×C₄₃	1	320	yes	complemented
27	C₃×H(3,𝔽₃)	C₃²×C₄₃	1	40	yes	—
28	C₃²×C₉	C₃²×C₄₃	1	40	yes	complemented
29	C₄₃	#10624943	1	1	yes	characteristic, direct product factor, Sylow
30	C₃³	C₃³×C₄₃	1	40	yes	—
31	3₋¹⁺²	C₃³×C₄₃	1	720	yes	—
32	H(3,𝔽₃)	C₃³×C₄₃	1	90	yes	—
33	C₃×C₉	C₃³×C₄₃	1	40	yes	—
34	C₃×C₉	C₃³×C₄₃	1	320	yes	—
35	C₃²	—	9	40	no	—
36	C₃²	C₃⁴×C₄₃	1	40	yes	—
37	C₉	C₃⁴×C₄₃	1	80	yes	—
38	C₉	C₃⁴×C₄₃	1	1	yes	characteristic
39	C₃	—	3	40	no	—
40	C₃	C₃⁵×C₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₄₃	C₃⁴
commutator, Frattini, cosocle	C₃	C₃⁵×C₄₃
socle	C₃×C₄₃	C₃⁵
prime radical	C₄₃×H(5,𝔽₃)	C₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×3₋¹⁺⁴	C₃	semidirect
3. C₃×C₄₃×#737	C₃	semidirect
4. C₄₃×#737	C₃²	semidirect
5. C₄₃×#737	C₃²	semidirect
6. C₃×3₋¹⁺²×C₄₃	C₃²	semidirect
8. C₃²×C₉×C₄₃	C₃²	semidirect
14. #10624943	C₄₃	direct (N × H)
19. 3₋¹⁺⁴	C₃×C₄₃	semidirect
21. C₃×#737	C₃×C₄₃	semidirect
24. #737	C₃²×C₄₃	semidirect
25. #737	C₃²×C₄₃	semidirect
26. C₃×3₋¹⁺²	C₃²×C₄₃	semidirect
28. C₃²×C₉	C₃²×C₄₃	semidirect
29. C₄₃	#10624943	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×3₋¹⁺⁴	3
C₄₃×H(5,𝔽₃)	3
C₃×C₄₃×#737	3
#10624943	43

Subgroups — C43×#10624943 #44531880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10624943 #44531880