Subgroups — #44532124

Order 31347.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782714	C₃	1	3	yes	maximal
2	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₄₃⋊C₉)	—	3	3	no	—
4	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
5	C₄₃×C₉⋊C₉	—	3	2	no	—
6	C₄₃×C₃²⋊C₉	—	3	1	no	—
7	C₉²×C₄₃	C₉	1	3	yes	complemented
8	C₃×C₄₃⋊C₉	—	9	3	no	—
9	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₉×C₄₃	—	3	3	no	—
11	C₃×C₉×C₄₃	—	3	3	no	—
12	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
13	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
14	#10624512	—	43	1	no	maximal, Sylow
15	C₃²×C₄₃	—	9	1	no	—
16	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
17	C₃²×C₄₃	#731	1	3	yes	—
18	C₉×C₄₃	—	3	1	no	—
19	C₉×C₄₃	—	3	2	no	—
20	C₉×C₄₃	—	9	3	no	—
21	C₄₃⋊C₉	—	27	3	no	—
22	#6887	C₄₃⋊C₃	1	1	yes	characteristic
23	#6867	—	43	3	no	—
24	C₃×C₄₃	—	3	3	no	—
25	C₃×C₄₃	—	3	1	no	—
26	C₃×C₄₃	#6867	1	1	yes	characteristic
27	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
28	C₉⋊C₉	—	3	2	no	—
29	C₃²⋊C₉	—	3	1	no	—
30	C₃²⋊C₉	—	129	3	no	—
31	C₉²	C₄₃⋊C₉	1	3	yes	complemented
32	C₄₃	#10624512	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	3	3	no	—
36	C₃×C₉	—	387	3	no	—
37	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
38	C₃×C₉	#11923958	1	2	yes	—
39	C₃²	—	9	1	no	—
40	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
41	C₃²	#16812510	1	3	yes	—
42	C₉	—	3	1	no	—
43	C₉	—	3	2	no	—
44	C₉	—	9	3	no	—
45	C₉	—	1161	3	no	—
46	C₃	—	3	1	no	—
47	C₃	—	3	3	no	—
48	C₃	#23782714	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782714
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	#6867
prime radical	C₃³×C₄₃	H(3,𝔽₃)
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624512
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
7. C₉²×C₄₃	C₉	semidirect
31. C₉²	C₄₃⋊C₉	semidirect
32. C₄₃	#10624512	semidirect

Maximal subgroups

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

subgroup	index
#23782714	3
C₄₃×#6887	3
#10624512	43