Subgroups — #44531985

Order 31347.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812513	C₃	1	1	yes	maximal, characteristic
2	#23782714	C₃	1	2	yes	maximal, complemented
3	C₃×C₄₃×#733	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
5	#16812513	—	3	3	no	—
6	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
7	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₄₃×#733	—	3	3	no	—
10	C₃²×C₄₃⋊C₃	—	9	1	no	—
11	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
12	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
13	C₃×C₄₃⋊C₉	—	9	2	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
15	3₋¹⁺²×C₄₃	—	3	3	no	—
16	3₋¹⁺²×C₄₃	—	9	2	no	—
17	C₃×C₉×C₄₃	—	3	1	no	—
18	C₃×C₉×C₄₃	—	3	1	no	—
19	C₃×C₉×C₄₃	—	3	2	no	—
20	C₃×C₉×C₄₃	—	9	1	no	—
21	#10624478	—	43	1	no	maximal, Sylow
22	C₃²×C₄₃	—	9	1	no	—
23	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
24	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
25	C₃²×C₄₃	#732	1	2	yes	—
26	C₃×C₄₃⋊C₃	—	9	3	no	—
27	C₃×C₄₃⋊C₃	—	27	3	no	—
28	C₉×C₄₃	—	9	1	no	—
29	C₉×C₄₃	—	9	3	no	—
30	C₄₃⋊C₉	—	27	2	no	—
31	C₃×#733	C₄₃⋊C₃	1	1	yes	characteristic, complemented
32	C₃×#732	—	43	1	no	—
33	#6867	—	43	2	no	—
34	C₃×C₄₃	—	3	2	no	—
35	C₃×C₄₃	—	3	1	no	—
36	C₃×C₄₃	—	3	1	no	—
37	C₃×C₄₃	#6856	1	1	yes	characteristic
38	C₄₃⋊C₃	—	27	3	no	—
39	C₃×3₋¹⁺²	—	3	1	no	—
40	C₃×H(3,𝔽₃)	—	129	1	no	—
41	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
42	#733	—	3	3	no	—
43	#732	—	129	3	no	—
44	C₃²⋊C₉	—	129	2	no	—
45	C₄₃	#10624478	1	1	yes	characteristic, complemented, Sylow
46	C₃³	—	387	1	no	—
47	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
48	3₋¹⁺²	—	3	3	no	—
49	3₋¹⁺²	—	9	2	no	—
50	H(3,𝔽₃)	—	129	3	no	—
51	H(3,𝔽₃)	—	387	2	no	—
52	C₃×C₉	—	3	1	no	—
53	C₃×C₉	—	3	1	no	—
54	C₃×C₉	—	3	2	no	—
55	C₃×C₉	—	9	1	no	—
56	C₃×C₉	—	387	2	no	—
57	C₃²	—	9	1	no	—
58	C₃²	—	387	3	no	—
59	C₃²	—	1161	3	no	—
60	C₃²	#16812506	1	1	yes	characteristic
61	C₃²	#16812507	1	1	yes	characteristic
62	C₃²	#16812512	1	2	yes	—
63	C₉	—	9	1	no	—
64	C₉	—	9	3	no	—
65	C₉	—	1161	2	no	—
66	C₃	—	3	2	no	—
67	C₃	—	3	1	no	—
68	C₃	—	3	1	no	—
69	C₃	—	1161	3	no	—
70	C₃	#23782686	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782686
commutator, cosocle	C₃²×C₉×C₄₃	C₃²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×#733	C₃
socle	C₃×C₄₃	#6856
prime radical	C₃×#16812513	C₃
hypercenter	C₃×#733	C₄₃⋊C₃
hypocenter	C₄₃	#10624478
LCS	G ▷ C₃²×C₉×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
2. #23782714	C₃	semidirect
3. C₃×C₄₃×#733	C₃	semidirect
31. C₃×#733	C₄₃⋊C₃	semidirect
45. C₄₃	#10624478	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812513	3
#23782714	3
C₃×C₄₃×#733	3
#10624478	43