Subgroups — #44531987

Order 31347.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812515	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#16812513	C₃	1	1	yes	maximal, characteristic
3	#23782714	C₃	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#6867	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#11923958	—	3	1	no	—
6	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
7	#16812515	—	3	3	no	—
8	#16812513	—	3	3	no	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
10	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₄₃×C₃²⋊C₉	—	3	1	no	—
12	C₃²×C₄₃⋊C₃	—	9	1	no	—
13	#11923958	—	3	3	no	—
14	#11923958	—	9	1	no	—
15	#11923958	—	9	1	no	—
16	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
17	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
18	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
19	C₃×C₄₃⋊C₉	—	9	1	no	—
20	C₃×C₄₃⋊C₉	—	9	1	no	—
21	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
22	C₃×C₉×C₄₃	—	3	1	no	—
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	—	3	1	no	—
25	C₃×C₉×C₄₃	—	3	1	no	—
26	C₃×C₉×C₄₃	—	9	1	no	—
27	#10624478	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	9	1	no	—
29	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
31	C₃²×C₄₃	#732	1	1	yes	characteristic
32	C₃²×C₄₃	#732	1	1	yes	characteristic
33	C₃×C₄₃⋊C₃	—	9	3	no	—
34	C₃×C₄₃⋊C₃	—	27	3	no	—
35	C₉×C₄₃	—	9	1	no	—
36	C₉×C₄₃	—	27	1	no	—
37	C₄₃⋊C₉	—	9	3	no	—
38	C₄₃⋊C₉	—	27	1	no	—
39	C₃×#733	—	43	1	no	—
40	C₃×#732	—	43	1	no	—
41	#6867	—	43	1	no	—
42	#6867	C₄₃⋊C₃	1	1	yes	characteristic, complemented
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	3	1	no	—
46	C₃×C₄₃	—	3	1	no	—
47	C₃×C₄₃	#6856	1	1	yes	characteristic
48	C₄₃⋊C₃	—	27	3	no	—
49	C₃×3₋¹⁺²	—	129	1	no	—
50	C₃×H(3,𝔽₃)	—	129	1	no	—
51	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	#733	—	129	3	no	—
53	#732	—	129	3	no	—
54	C₃²⋊C₉	—	3	1	no	—
55	C₃²⋊C₉	—	129	1	no	—
56	C₄₃	#10624478	1	1	yes	characteristic, complemented, Sylow
57	C₃³	—	387	1	no	—
58	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
59	3₋¹⁺²	—	129	3	no	—
60	3₋¹⁺²	—	387	1	no	—
61	3₋¹⁺²	—	387	1	no	—
62	H(3,𝔽₃)	—	129	3	no	—
63	H(3,𝔽₃)	—	387	1	no	—
64	H(3,𝔽₃)	—	387	1	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	3	1	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	3	1	no	—
69	C₃×C₉	—	9	1	no	—
70	C₃×C₉	—	387	1	no	—
71	C₃×C₉	—	387	1	no	—
72	C₃²	—	9	1	no	—
73	C₃²	—	387	3	no	—
74	C₃²	—	1161	3	no	—
75	C₃²	#16812508	1	1	yes	characteristic
76	C₃²	#16812508	1	1	yes	characteristic
77	C₃²	#16812512	1	1	yes	characteristic
78	C₃²	#16812513	1	1	yes	characteristic
79	C₉	—	9	1	no	—
80	C₉	—	27	1	no	—
81	C₉	—	387	3	no	—
82	C₉	—	1161	1	no	—
83	C₃	—	3	1	no	—
84	C₃	—	3	1	no	—
85	C₃	—	3	1	no	—
86	C₃	—	3	1	no	—
87	C₃	—	1161	3	no	—
88	C₃	#23782687	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782687
commutator, cosocle	C₃²×C₉×C₄₃	C₃²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6867	C₃
socle	C₃×C₄₃	#6856
prime radical	C₃×#16812513	C₃
hypercenter	#6867	C₄₃⋊C₃
hypocenter	C₄₃	#10624478
LCS	G ▷ C₃²×C₉×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6867

Complements

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

N	H ≅ G/N	type
1. C₃×#16812515	C₃	semidirect
3. #23782714	C₃	semidirect
4. C₄₃×#6867	C₃	semidirect
42. #6867	C₄₃⋊C₃	semidirect
56. 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×#16812515	3
C₃×#16812513	3
#23782714	3
C₄₃×#6867	3
#10624478	43