Subgroups — C₄₃×#10624460 #44531397

Order 31347.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
2	C₄₃×C₃²⋊C₂₇	C₃	1	3	yes	maximal
3	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
4	C₃×C₂₇×C₄₃	—	3	3	no	—
5	C₄₃×C₉⋊C₉	—	3	2	no	—
6	C₄₃×C₃²⋊C₉	C₉	1	3	yes	—
7	C₉²×C₄₃	—	3	1	no	—
8	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
9	C₃×C₉×C₄₃	—	3	3	no	—
10	C₃×C₉×C₄₃	—	3	3	no	—
11	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
13	C₂₇×C₄₃	—	9	3	no	—
14	#10624460	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₃²×C₄₃	—	3	1	no	—
16	C₃²×C₄₃	—	3	3	no	—
17	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
18	C₉×C₄₃	—	3	2	no	—
19	C₉×C₄₃	—	9	3	no	—
20	C₉×C₄₃	#731	1	3	yes	—
21	#6887	C₃×C₄₃	1	1	yes	characteristic
22	C₃²⋊C₂₇	C₃×C₄₃	1	3	yes	—
23	C₃×C₄₃	—	9	1	no	—
24	C₃×C₄₃	#6867	1	1	yes	characteristic
25	C₃×C₄₃	#6873	1	3	yes	—
26	C₃²×C₉	C₃²×C₄₃	1	1	yes	characteristic
27	C₃×C₂₇	—	3	3	no	—
28	C₉⋊C₉	—	3	2	no	—
29	C₃²⋊C₉	C₉×C₄₃	1	3	yes	—
30	C₉²	—	3	1	no	—
31	C₄₃	#10624460	1	1	yes	characteristic, direct product factor, Sylow
32	C₃³	C₃×C₉×C₄₃	1	1	yes	characteristic
33	C₃×C₉	—	3	3	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
36	C₃×C₉	3₋¹⁺²×C₄₃	1	2	yes	—
37	C₂₇	—	9	3	no	—
38	C₃²	—	3	1	no	—
39	C₃²	—	3	3	no	—
40	C₃²	C₄₃×C₃²⋊C₉	1	1	yes	characteristic
41	C₉	—	3	2	no	—
42	C₉	—	9	3	no	—
43	C₉	C₄₃×#731	1	3	yes	—
44	C₃	—	9	1	no	—
45	C₃	C₄₃×#6867	1	1	yes	characteristic
46	C₃	C₄₃×#6873	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₄₃	H(3,𝔽₃)
commutator	C₃³	C₃×C₉×C₄₃
Frattini, cosocle	C₃²×C₉	C₃²×C₄₃
socle	C₃²×C₄₃	C₃²⋊C₉
prime radical	C₃³×C₄₃	C₃×C₉
LCS	G ▷ C₃³ ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₃ ◁ C₃²×C₉×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
14. #10624460	C₄₃	direct (N × H)
31. C₄₃	#10624460	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×#6887	3
C₄₃×C₃²⋊C₂₇	3
#10624460	43

Subgroups — C43×#10624460 #44531397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10624460 #44531397