Subgroups — C₄₃×#10624485 #44531422

Order 31347.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₃×#732	C₃	1	1	yes	maximal, characteristic
2	C₄₃×#6895	C₃	1	2	yes	maximal, complemented
3	C₄₃×#6867	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×H(3,𝔽₃)×C₄₃	—	3	1	no	—
5	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
6	C₄₃×#732	—	3	3	no	—
7	C₄₃×C₉⋊C₉	—	3	6	no	—
8	C₄₃×C₃²⋊C₉	—	3	2	no	—
9	C₄₃×C₃²⋊C₉	—	3	1	no	—
10	C₃³×C₄₃	—	9	1	no	—
11	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
12	H(3,𝔽₃)×C₄₃	—	3	3	no	—
13	H(3,𝔽₃)×C₄₃	—	9	2	no	—
14	C₃×C₉×C₄₃	—	3	6	no	—
15	C₃×C₉×C₄₃	—	3	2	no	—
16	C₃×C₉×C₄₃	—	3	1	no	—
17	C₃×C₉×C₄₃	—	3	1	no	—
18	C₃×C₉×C₄₃	—	9	1	no	—
19	#10624485	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃²×C₄₃	—	9	1	no	—
21	C₃²×C₄₃	—	9	3	no	—
22	C₃²×C₄₃	—	27	3	no	—
23	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	2	yes	—
24	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
25	C₃²×C₄₃	#731	1	1	yes	characteristic
26	C₉×C₄₃	—	9	6	no	—
27	C₉×C₄₃	—	9	1	no	—
28	C₉×C₄₃	—	27	1	no	—
29	C₃×#732	C₃×C₄₃	1	1	yes	characteristic
30	#6895	C₃×C₄₃	1	2	yes	complemented
31	#6867	C₃×C₄₃	1	1	yes	characteristic, complemented
32	C₃×C₄₃	—	3	2	no	—
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	—	3	1	no	—
35	C₃×C₄₃	—	27	3	no	—
36	C₃×C₄₃	#6857	1	1	yes	characteristic
37	C₃×H(3,𝔽₃)	—	3	1	no	—
38	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
39	#732	—	3	3	no	—
40	C₉⋊C₉	—	3	6	no	—
41	C₃²⋊C₉	—	3	2	no	—
42	C₃²⋊C₉	—	3	1	no	—
43	C₄₃	#10624485	1	1	yes	characteristic, direct product factor, Sylow
44	C₃³	—	9	1	no	—
45	C₃³	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
46	H(3,𝔽₃)	—	3	3	no	—
47	H(3,𝔽₃)	—	9	2	no	—
48	C₃×C₉	—	3	6	no	—
49	C₃×C₉	—	3	2	no	—
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	3	1	no	—
52	C₃×C₉	—	9	1	no	—
53	C₃²	—	9	1	no	—
54	C₃²	—	9	3	no	—
55	C₃²	—	27	3	no	—
56	C₃²	C₄₃×AΣL(1,𝔽₂₇)	1	2	yes	—
57	C₃²	C₄₃×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
58	C₃²	C₄₃×#731	1	1	yes	characteristic
59	C₉	—	9	6	no	—
60	C₉	—	9	1	no	—
61	C₉	—	27	1	no	—
62	C₃	—	3	2	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	1	no	—
65	C₃	—	27	3	no	—
66	C₃	C₄₃×#6857	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₄₃	#6857
commutator, Frattini, cosocle	C₃²×C₉	C₃²×C₄₃
prime radical	C₃×C₄₃×#732	C₃
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₃ ◁ C₃³×C₄₃ ◁ C₃²×C₉×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#6895	C₃	semidirect
3. C₄₃×#6867	C₃	semidirect
19. #10624485	C₄₃	direct (N × H)
30. #6895	C₃×C₄₃	semidirect
31. #6867	C₃×C₄₃	semidirect
43. C₄₃	#10624485	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄₃×#732	3
C₄₃×#6895	3
C₄₃×#6867	3
#10624485	43

Subgroups — C43×#10624485 #44531422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10624485 #44531422