Subgroups — #44532138

Order 31347.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782718	C₃	1	3	yes	maximal
2	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
3	#16812505	—	3	3	no	—
4	C₃²×C₉×C₄₃	—	3	1	no	—
5	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
6	C₄₃×C₉⋊C₉	—	3	1	no	—
7	C₄₃×C₉⋊C₉	—	3	1	no	—
8	C₄₃×C₉⋊C₉	C₉	1	3	yes	—
9	C₄₃⋊C₂₇	—	9	3	no	—
10	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
11	C₃×C₉×C₄₃	—	3	3	no	—
12	C₃×C₉×C₄₃	—	3	3	no	—
13	C₃×C₉×C₄₃	—	9	3	no	—
14	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
17	#10624516	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	3	no	—
20	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
21	C₉×C₄₃	—	3	1	no	—
22	C₉×C₄₃	—	3	1	no	—
23	C₉×C₄₃	—	9	3	no	—
24	C₉×C₄₃	#731	1	3	yes	—
25	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
26	#6869	—	43	3	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	—	3	3	no	—
29	C₃×C₄₃	#6867	1	1	yes	characteristic
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
32	C₂₇⋊C₃	—	129	3	no	—
33	C₉⋊C₉	—	3	1	no	—
34	C₉⋊C₉	—	3	1	no	—
35	C₉⋊C₉	C₄₃⋊C₉	1	3	yes	—
36	C₄₃	#10624516	1	1	yes	characteristic, complemented, Sylow
37	C₃³	#11923958	1	1	yes	characteristic
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	9	3	no	—
41	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
42	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
43	C₃×C₉	#11923958	1	1	yes	characteristic
44	C₂₇	—	387	3	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	#16812510	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	3	3	no	—
54	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	C₃×C₄₃×C₉⋊C₉	C₃
socle	C₃×C₄₃	#6867
prime radical	C₃³×C₄₃	3₋¹⁺²
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624516
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
36. C₄₃	#10624516	semidirect

Maximal subgroups

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

subgroup	index
#23782718	3
C₃×C₄₃×C₉⋊C₉	3
#10624516	43