Subgroups — C₄₃×#10624776 #44531713

Order 31347.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
2	C₄₃×#6891	C₃	1	3	yes	maximal
3	C₄₃×#6868	C₃	1	9	yes	maximal, complemented
4	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
5	C₃×3₋¹⁺²×C₄₃	—	3	3	no	—
6	C₃×3₋¹⁺²×C₄₃	—	3	3	no	—
7	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
8	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
9	C₄₃×C₃²⋊C₉	—	3	6	no	—
10	C₄₃×C₃²⋊C₉	C₃²	1	9	yes	—
11	C₃³×C₄₃	—	3	3	no	—
12	C₃³×C₄₃	—	9	2	no	—
13	C₃³×C₄₃	—	9	1	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
15	C₃³×C₄₃	C₃³	1	1	yes	characteristic
16	3₋¹⁺²×C₄₃	—	3	27	no	—
17	3₋¹⁺²×C₄₃	—	9	9	no	—
18	C₃×C₉×C₄₃	—	3	3	no	—
19	C₃×C₉×C₄₃	—	3	6	no	—
20	C₃×C₉×C₄₃	—	3	9	no	—
21	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	complemented
22	#10624776	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₃²×C₄₃	—	3	2	no	—
24	C₃²×C₄₃	—	3	1	no	—
25	C₃²×C₄₃	—	3	6	no	—
26	C₃²×C₄₃	—	3	3	no	—
27	C₃²×C₄₃	—	3	3	no	—
28	C₃²×C₄₃	—	9	9	no	—
29	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
30	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
31	C₉×C₄₃	—	3	9	no	—
32	C₉×C₄₃	—	9	9	no	—
33	C₃²×3₋¹⁺²	C₃×C₄₃	1	1	yes	characteristic
34	#6891	C₃×C₄₃	1	3	yes	—
35	#6868	C₃×C₄₃	1	9	yes	complemented
36	C₃×C₄₃	—	3	3	no	—
37	C₃×C₄₃	—	9	3	no	—
38	C₃×C₄₃	#6891	1	1	yes	characteristic
39	C₃×C₄₃	#6911	1	1	yes	characteristic
40	C₃×C₄₃	#6912	1	2	yes	—
41	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
42	C₃×3₋¹⁺²	—	3	3	no	—
43	C₃×3₋¹⁺²	—	3	3	no	—
44	C₃×3₋¹⁺²	—	3	9	no	—
45	C₃²×C₉	C₃²×C₄₃	1	3	yes	—
46	C₃²⋊C₉	—	3	6	no	—
47	C₃²⋊C₉	C₃²×C₄₃	1	9	yes	—
48	C₄₃	#10624776	1	1	yes	characteristic, direct product factor, Sylow
49	C₃³	—	3	3	no	—
50	C₃³	—	9	1	no	—
51	C₃³	—	9	2	no	—
52	C₃³	H(3,𝔽₃)×C₄₃	1	3	yes	—
53	C₃³	C₃³×C₄₃	1	1	yes	characteristic
54	3₋¹⁺²	—	3	27	no	—
55	3₋¹⁺²	—	9	9	no	—
56	C₃×C₉	—	3	3	no	—
57	C₃×C₉	—	3	6	no	—
58	C₃×C₉	—	3	9	no	—
59	C₃×C₉	3₋¹⁺²×C₄₃	1	9	yes	complemented
60	C₃²	—	3	1	no	—
61	C₃²	—	3	2	no	—
62	C₃²	—	3	3	no	—
63	C₃²	—	3	6	no	—
64	C₃²	—	3	3	no	—
65	C₃²	—	9	9	no	—
66	C₃²	C₃×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
67	C₃²	C₃×3₋¹⁺²×C₄₃	1	3	yes	—
68	C₉	—	3	9	no	—
69	C₉	—	9	9	no	—
70	C₃	—	3	3	no	—
71	C₃	—	9	3	no	—
72	C₃	C₄₃×#6891	1	1	yes	characteristic
73	C₃	C₄₃×#6911	1	1	yes	characteristic
74	C₃	C₄₃×#6912	1	2	yes	—

	subgroup	G/H
center, socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
commutator, Frattini, cosocle	C₃³	C₃³×C₄₃
prime radical	C₃⁴×C₄₃	C₃²
LCS	G ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₃ ◁ C₃⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#6868	C₃	semidirect
21. C₃×C₉×C₄₃	3₋¹⁺²	semidirect
22. #10624776	C₄₃	direct (N × H)
35. #6868	C₃×C₄₃	semidirect
48. C₄₃	#10624776	direct (N × H)
59. C₃×C₉	3₋¹⁺²×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₃²×3₋¹⁺²×C₄₃	3
C₄₃×#6891	3
C₄₃×#6868	3
#10624776	43

Subgroups — C43×#10624776 #44531713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10624776 #44531713