Subgroups — C₃×C₄₃×#6860 #44531519

Order 31347.

476 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×3₋¹⁺²×C₄₃	C₃	1	2	yes	maximal
2	C₃×C₄₃×C₃²⋊C₉	C₃	1	2	yes	maximal
3	C₄₃×#6860	C₃	1	9	yes	maximal, direct product factor
4	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
5	C₃×3₋¹⁺²×C₄₃	—	3	4	no	—
6	C₃×3₋¹⁺²×C₄₃	—	3	18	no	—
7	C₃×3₋¹⁺²×C₄₃	C₃²	1	6	yes	—
8	C₃²×C₉×C₄₃	—	3	2	no	—
9	C₃²×C₉×C₄₃	—	3	2	no	—
10	C₄₃×C₃²⋊C₉	—	3	4	no	—
11	C₄₃×C₃²⋊C₉	C₃²	1	6	yes	—
12	C₃³×C₄₃	—	3	6	no	—
13	C₃³×C₄₃	—	3	6	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	2	yes	—
15	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃³×C₄₃	C₃³	1	1	yes	characteristic
17	3₋¹⁺²×C₄₃	—	3	36	no	—
18	3₋¹⁺²×C₄₃	—	3	18	no	—
19	C₃×C₉×C₄₃	—	3	18	no	—
20	C₃×C₉×C₄₃	—	3	6	no	—
21	C₃×C₉×C₄₃	—	3	6	no	—
22	C₃×C₉×C₄₃	—	9	6	no	—
23	C₃×#6860	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
24	C₃²×C₄₃	—	3	4	no	—
25	C₃²×C₄₃	—	3	2	no	—
26	C₃²×C₄₃	—	3	4	no	—
27	C₃²×C₄₃	—	3	2	no	—
28	C₃²×C₄₃	—	9	9	no	—
29	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	6	yes	—
30	C₃²×C₄₃	#733	1	6	yes	—
31	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
32	C₉×C₄₃	—	3	18	no	—
33	C₉×C₄₃	—	9	6	no	—
34	C₃²×3₋¹⁺²	C₃×C₄₃	1	2	yes	—
35	C₃×C₃²⋊C₉	C₃×C₄₃	1	2	yes	—
36	#6860	C₃×C₄₃	1	9	yes	direct product factor
37	C₃×C₄₃	—	9	2	no	—
38	C₃×C₄₃	—	9	1	no	—
39	C₃×C₄₃	#6860	1	9	yes	direct product factor
40	C₃×C₄₃	C₃×AΣL(1,𝔽₂₇)	1	2	yes	—
41	C₃×C₄₃	C₃×#733	1	2	yes	—
42	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
43	C₃×3₋¹⁺²	—	3	4	no	—
44	C₃×3₋¹⁺²	—	3	18	no	—
45	C₃×3₋¹⁺²	C₃²×C₄₃	1	6	yes	—
46	C₃²×C₉	—	3	2	no	—
47	C₃²×C₉	—	3	2	no	—
48	C₃²⋊C₉	—	3	4	no	—
49	C₃²⋊C₉	C₃²×C₄₃	1	6	yes	—
50	C₄₃	C₃×#6860	1	1	yes	characteristic, direct product factor, Sylow
51	C₃³	—	3	6	no	—
52	C₃³	—	3	6	no	—
53	C₃³	H(3,𝔽₃)×C₄₃	1	2	yes	—
54	C₃³	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
55	C₃³	C₃³×C₄₃	1	1	yes	characteristic
56	3₋¹⁺²	—	3	36	no	—
57	3₋¹⁺²	—	3	18	no	—
58	C₃×C₉	—	3	18	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	3	6	no	—
61	C₃×C₉	—	9	6	no	—
62	C₃²	—	3	4	no	—
63	C₃²	—	3	2	no	—
64	C₃²	—	3	4	no	—
65	C₃²	—	3	2	no	—
66	C₃²	—	9	9	no	—
67	C₃²	C₄₃×AΣL(1,𝔽₂₇)	1	6	yes	—
68	C₃²	C₄₃×#733	1	6	yes	—
69	C₃²	C₃×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
70	C₉	—	3	18	no	—
71	C₉	—	9	6	no	—
72	C₃	—	9	2	no	—
73	C₃	—	9	1	no	—
74	C₃	C₄₃×#6860	1	9	yes	direct product factor
75	C₃	C₃×C₄₃×AΣL(1,𝔽₂₇)	1	2	yes	—
76	C₃	C₃×C₄₃×#733	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₃×#6860	C₃	direct (N × H)
23. C₃×#6860	C₄₃	direct (N × H)
36. #6860	C₃×C₄₃	direct (N × H)
39. C₃×C₄₃	#6860	direct (N × H)
50. C₄₃	C₃×#6860	direct (N × H)
74. C₃	C₄₃×#6860	direct (N × H)

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
C₃×C₄₃×C₃²⋊C₉	3
C₄₃×#6860	3
C₃×#6860	43

Subgroups — C3×C43×#6860 #44531519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#6860 #44531519