Subgroups — #44535357

Order 31347.

936 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782924	C₃	1	3	yes	maximal
2	#23782896	C₃	1	24	yes	maximal, complemented
3	C₃×#16812515	C₃	1	12	yes	maximal, complemented
4	C₃×C₄₃×#737	C₃	1	1	yes	maximal, characteristic
5	#16812524	—	3	27	no	—
6	C₃×#11923958	C₃²	1	36	yes	—
7	#16812515	C₃²	1	9	yes	—
8	#16812515	C₃²	1	72	yes	—
9	C₄₃×#737	—	3	9	no	—
10	C₃×3₋¹⁺²×C₄₃	C₃²	1	8	yes	—
11	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₄₃	C₃²	1	4	yes	—
13	#11923958	—	3	72	no	—
14	#11923958	C₃³	1	27	yes	—
15	C₃×C₄₃⋊C₉	—	3	36	no	—
16	C₃³×C₄₃	C₃³	1	4	yes	—
17	3₋¹⁺²×C₄₃	—	3	24	no	—
18	H(3,𝔽₃)×C₄₃	H(3,𝔽₃)	1	9	yes	—
19	C₃×C₉×C₄₃	—	3	12	no	—
20	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
21	C₃×C₉×C₄₃	C₃³	1	8	yes	—
22	#10624933	—	43	1	no	maximal, Sylow
23	C₃²×C₄₃	—	9	4	no	—
24	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	12	yes	—
25	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
26	C₉×C₄₃	—	3	1	no	—
27	C₉×C₄₃	—	3	8	no	—
28	C₄₃⋊C₉	—	3	27	no	—
29	3₋¹⁺⁴	—	43	3	no	—
30	C₃×#737	C₄₃⋊C₃	1	1	yes	characteristic
31	#6912	—	43	24	no	—
32	C₃×#733	—	43	12	no	—
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	—	3	12	no	—
35	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
36	#737	—	3	9	no	—
37	#737	—	129	27	no	—
38	C₃×3₋¹⁺²	—	43	36	no	—
39	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	8	yes	—
40	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	1	yes	characteristic
41	C₃²×C₉	C₃×C₄₃⋊C₃	1	4	yes	—
42	#733	—	43	72	no	—
43	#733	—	43	9	no	—
44	C₄₃	#10624933	1	1	yes	characteristic, complemented, Sylow
45	C₃³	C₃²×C₄₃⋊C₃	1	4	yes	—
46	3₋¹⁺²	—	3	24	no	—
47	3₋¹⁺²	—	43	27	no	—
48	3₋¹⁺²	—	129	72	no	—
49	H(3,𝔽₃)	C₃²⋊(C₄₃⋊C₃)	1	9	yes	—
50	C₃×C₉	—	3	12	no	—
51	C₃×C₉	—	129	36	no	—
52	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃²×C₄₃⋊C₃	1	8	yes	—
54	C₃²	—	9	4	no	—
55	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	12	yes	—
56	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	8	no	—
59	C₉	—	129	27	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	12	no	—
62	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₃×C₄₃×#737	C₃
socle	C₃×C₄₃	C₃²×H(3,𝔽₃)
prime radical	C₃×H(3,𝔽₃)×C₄₃	C₃²
hypercenter	C₃×#737	C₄₃⋊C₃
hypocenter	C₄₃	#10624933
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×H(3,𝔽₃) ◁ C₃×#737

Complements

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

N	H ≅ G/N	type
2. #23782896	C₃	semidirect
3. C₃×#16812515	C₃	semidirect
44. C₄₃	#10624933	semidirect

Maximal subgroups

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

subgroup	index
#23782924	3
#23782896	3
C₃×#16812515	3
C₃×C₄₃×#737	3
#10624933	43