Subgroups — C₄₃×#10624496 #44531433

Order 31347.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#6866	C₃	1	4	yes	maximal
2	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
3	C₄₃×C₃²⋊C₉	—	3	4	no	—
4	C₃³×C₄₃	—	3	4	no	—
5	C₃³×C₄₃	—	9	3	no	—
6	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
7	C₃×C₉×C₄₃	—	9	4	no	—
8	#10624496	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃²×C₄₃	—	9	1	no	—
10	C₃²×C₄₃	—	9	12	no	—
11	C₃²×C₄₃	—	9	1	no	—
12	C₃²×C₄₃	#731	1	4	yes	—
13	C₉×C₄₃	—	27	4	no	—
14	#6866	C₃×C₄₃	1	4	yes	—
15	C₃×C₄₃	—	3	4	no	—
16	C₃×C₄₃	—	9	3	no	—
17	C₃×C₄₃	#6862	1	1	yes	characteristic
18	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
19	C₃²⋊C₉	—	3	4	no	—
20	C₄₃	#10624496	1	1	yes	characteristic, direct product factor, Sylow
21	C₃³	—	3	4	no	—
22	C₃³	—	9	3	no	—
23	C₃³	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
24	C₃×C₉	—	9	4	no	—
25	C₃²	—	9	1	no	—
26	C₃²	—	9	12	no	—
27	C₃²	—	9	1	no	—
28	C₃²	C₄₃×#731	1	4	yes	—
29	C₉	—	27	4	no	—
30	C₃	—	3	4	no	—
31	C₃	—	9	3	no	—
32	C₃	C₄₃×#6862	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₄₃	#6862
commutator, Frattini, cosocle	C₃⁴	C₃²×C₄₃
prime radical	C₃⁴×C₄₃	C₃²
LCS	G ▷ C₃⁴ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₃ ◁ C₃³×C₄₃ ◁ C₃⁴×C₄₃ ◁ G

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

N	H ≅ G/N	type
8. #10624496	C₄₃	direct (N × H)
20. C₄₃	#10624496	direct (N × H)

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

subgroup	index
C₄₃×#6866	3
#10624496	43