Subgroups — #44533907

Order 31347.

356 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782798	C₃	1	3	yes	maximal
2	#23782714	C₃	1	9	yes	maximal, complemented
3	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
4	C₃×#11923958	—	3	3	no	—
5	C₃²⋊(C₄₃⋊C₉)	—	3	6	no	—
6	C₃²⋊(C₄₃⋊C₉)	C₃²	1	9	yes	—
7	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
8	C₃×3₋¹⁺²×C₄₃	—	3	3	no	—
9	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
10	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
11	#11923958	—	9	9	no	—
12	C₃×C₄₃⋊C₉	—	3	9	no	—
13	C₃³×C₄₃	—	3	3	no	—
14	C₃³×C₄₃	—	9	3	no	—
15	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
16	C₃³×C₄₃	C₃³	1	1	yes	characteristic
17	3₋¹⁺²×C₄₃	—	3	27	no	—
18	C₃×C₉×C₄₃	—	3	3	no	—
19	C₃×C₉×C₄₃	—	3	6	no	—
20	C₃×C₉×C₄₃	3₋¹⁺²	1	9	yes	complemented
21	#10624775	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	—	3	3	no	—
23	C₃²×C₄₃	—	3	3	no	—
24	C₃²×C₄₃	—	3	6	no	—
25	C₃²×C₄₃	—	3	3	no	—
26	C₃²×C₄₃	—	9	9	no	—
27	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
29	C₉×C₄₃	—	3	9	no	—
30	C₄₃⋊C₉	—	9	9	no	—
31	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
32	#6891	—	43	3	no	—
33	#6867	—	43	9	no	—
34	C₃×C₄₃	—	3	3	no	—
35	C₃×C₄₃	—	9	3	no	—
36	C₃×C₄₃	#6891	1	1	yes	characteristic
37	C₃×C₄₃	#6910	1	3	yes	—
38	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
39	C₃×3₋¹⁺²	—	3	3	no	—
40	C₃×3₋¹⁺²	—	3	9	no	—
41	C₃×3₋¹⁺²	—	129	3	no	—
42	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
43	C₃²⋊C₉	—	43	9	no	—
44	C₃²⋊C₉	—	129	6	no	—
45	C₄₃	#10624775	1	1	yes	characteristic, complemented, Sylow
46	C₃³	—	3	3	no	—
47	C₃³	—	9	3	no	—
48	C₃³	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
49	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
50	3₋¹⁺²	—	3	27	no	—
51	3₋¹⁺²	—	387	9	no	—
52	C₃×C₉	—	3	3	no	—
53	C₃×C₉	—	3	6	no	—
54	C₃×C₉	—	129	9	no	—
55	C₃×C₉	#11923958	1	9	yes	complemented
56	C₃²	—	3	3	no	—
57	C₃²	—	3	3	no	—
58	C₃²	—	3	3	no	—
59	C₃²	—	3	6	no	—
60	C₃²	—	9	9	no	—
61	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
62	C₃²	C₃×#11923958	1	3	yes	—
63	C₉	—	3	9	no	—
64	C₉	—	387	9	no	—
65	C₃	—	3	3	no	—
66	C₃	—	9	3	no	—
67	C₃	#23782798	1	1	yes	characteristic
68	C₃	#23782887	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624775
LCS	G ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #23782714	C₃	semidirect
20. C₃×C₉×C₄₃	3₋¹⁺²	semidirect
45. C₄₃	#10624775	semidirect
55. C₃×C₉	#11923958	semidirect

Maximal subgroups

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

subgroup	index
#23782798	3
#23782714	3
C₃²×3₋¹⁺²×C₄₃	3
#10624775	43