Subgroups — #44532467

Order 31347.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11923958	C₃	1	3	yes	maximal
2	#23782702	C₃	1	3	yes	maximal
3	#23782699	C₃	1	3	yes	maximal
4	#23782693	C₃	1	3	yes	maximal
5	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
6	C₃×#11923958	C₃²	1	3	yes	—
7	(C₄₃⋊C₉)⋊C₉	—	3	6	no	—
8	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
9	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
10	C₉×C₄₃⋊C₉	—	3	3	no	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	—	3	2	no	—
13	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₄₃	—	3	1	no	—
15	#11923958	—	3	9	no	—
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	3	3	no	—
19	C₃³×C₄₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	3	3	no	—
21	C₃×C₉×C₄₃	—	3	3	no	—
22	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
23	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
24	#10624588	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	—	3	3	no	—
27	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₉×C₄₃	—	3	2	no	—
29	C₉×C₄₃	—	9	3	no	—
30	C₉×C₄₃	#733	1	3	yes	—
31	C₄₃⋊C₉	—	3	9	no	—
32	C₄₃⋊C₉	—	9	3	no	—
33	C₄₃⋊C₉	—	9	3	no	—
34	C₉×3₋¹⁺²	—	43	3	no	—
35	#6887	C₄₃⋊C₃	1	1	yes	characteristic
36	#6861	—	43	3	no	—
37	#6860	—	43	3	no	—
38	#6858	—	43	3	no	—
39	C₃×C₄₃	—	9	1	no	—
40	C₃×C₄₃	C₃×#733	1	1	yes	characteristic
41	C₃×C₄₃	#6908	1	3	yes	—
42	C₃×3₋¹⁺²	—	43	3	no	—
43	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
44	C₉⋊C₉	—	3	2	no	—
45	C₉⋊C₉	—	129	6	no	—
46	C₃²⋊C₉	—	43	3	no	—
47	C₃²⋊C₉	—	43	3	no	—
48	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
49	C₉²	—	3	1	no	—
50	C₉²	—	129	3	no	—
51	C₄₃	#10624588	1	1	yes	characteristic, complemented, Sylow
52	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
53	3₋¹⁺²	—	129	9	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	—	3	3	no	—
56	C₃×C₉	—	129	3	no	—
57	C₃×C₉	—	129	3	no	—
58	C₃×C₉	—	129	3	no	—
59	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
60	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
61	C₃²	—	3	1	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
64	C₉	—	3	2	no	—
65	C₉	—	9	3	no	—
66	C₉	—	129	9	no	—
67	C₉	—	387	3	no	—
68	C₉	—	387	3	no	—
69	C₉	#16812515	1	3	yes	—
70	C₃	—	9	1	no	—
71	C₃	C₃×#16812515	1	1	yes	characteristic
72	C₃	#23782874	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator, prime radical, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624588
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
51. C₄₃	#10624588	semidirect

Maximal subgroups

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

subgroup	index
C₉×#11923958	3
#23782702	3
#23782699	3
#23782693	3
C₄₃×#6887	3
#10624588	43