Subgroups — C₄₃×#10624502 #44531439

Order 31347.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
2	C₄₃×C₈₁⋊C₃	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₄₃	C₉	1	1	yes	characteristic
4	C₃×C₂₇×C₄₃	—	3	1	no	—
5	C₃×C₂₇×C₄₃	—	3	2	no	—
6	C₃×C₂₇×C₄₃	C₉	1	2	yes	—
7	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₈₁	—	3	3	no	—
9	C₃³×C₄₃	C₂₇	1	1	yes	characteristic
10	C₃×C₉×C₄₃	—	3	1	no	—
11	C₃×C₉×C₄₃	—	3	2	no	—
12	C₃×C₉×C₄₃	C₂₇	1	2	yes	—
13	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
14	C₂₇×C₄₃	—	3	2	no	—
15	C₂₇×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₂₇×C₄₃	3₋¹⁺²	1	2	yes	—
17	#10624502	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	3	no	—
20	C₃²×C₄₃	C₃×C₂₇	1	1	yes	characteristic
21	C₉×C₄₃	—	3	2	no	—
22	C₉×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
23	C₉×C₄₃	C₂₇⋊C₃	1	2	yes	—
24	C₃²×C₂₇	C₃×C₄₃	1	1	yes	characteristic
25	C₈₁⋊C₃	C₃×C₄₃	1	3	yes	complemented
26	C₃×C₄₃	—	3	3	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	C₃²⋊C₂₇	1	1	yes	characteristic
29	C₃²×C₉	C₉×C₄₃	1	1	yes	characteristic
30	C₃×C₂₇	—	3	1	no	—
31	C₃×C₂₇	—	3	2	no	—
32	C₃×C₂₇	C₉×C₄₃	1	2	yes	—
33	C₃×C₂₇	C₃²×C₄₃	1	1	yes	characteristic
34	C₈₁	—	3	3	no	—
35	C₄₃	#10624502	1	1	yes	characteristic, direct product factor, Sylow
36	C₃³	C₂₇×C₄₃	1	1	yes	characteristic
37	C₃×C₉	—	3	1	no	—
38	C₃×C₉	—	3	2	no	—
39	C₃×C₉	C₂₇×C₄₃	1	2	yes	—
40	C₃×C₉	C₃×C₉×C₄₃	1	1	yes	characteristic
41	C₂₇	—	3	2	no	—
42	C₂₇	H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
43	C₂₇	3₋¹⁺²×C₄₃	1	2	yes	—
44	C₃²	—	3	3	no	—
45	C₃²	—	3	1	no	—
46	C₃²	C₃×C₂₇×C₄₃	1	1	yes	characteristic
47	C₉	—	3	2	no	—
48	C₉	C₄₃×C₃²⋊C₉	1	1	yes	characteristic
49	C₉	C₄₃×C₂₇⋊C₃	1	2	yes	—
50	C₃	—	3	3	no	—
51	C₃	—	3	1	no	—
52	C₃	C₄₃×C₃²⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂₇×C₄₃	H(3,𝔽₃)
commutator	C₃²	C₃×C₂₇×C₄₃
Frattini, cosocle	C₃×C₂₇	C₃²×C₄₃
socle	C₃×C₄₃	C₃²⋊C₂₇
prime radical	C₃³×C₄₃	C₂₇
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂₇×C₄₃ ◁ C₃×C₂₇×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×C₈₁⋊C₃	C₃	semidirect
17. #10624502	C₄₃	direct (N × H)
25. C₈₁⋊C₃	C₃×C₄₃	semidirect
35. C₄₃	#10624502	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×C₂₇×C₄₃	3
C₄₃×C₈₁⋊C₃	3
#10624502	43

Subgroups — C43×#10624502 #44531439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#10624502 #44531439