Subgroups — #44534498

Order 31347.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812515	C₃	1	3	yes	maximal
2	#23782754	C₃	1	9	yes	maximal, complemented
3	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
4	C₃×#11923958	—	3	3	no	—
5	#16812515	—	3	6	no	—
6	#16812515	C₃²	1	9	yes	—
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₉⋊C₉	—	3	2	no	—
9	C₄₃×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₄₃	C₃²	1	3	yes	—
11	#11923958	—	3	9	no	—
12	#11923958	—	9	6	no	—
13	C₃×C₄₃⋊C₉	—	9	3	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₄₃	—	3	3	no	—
16	C₃×C₉×C₄₃	—	3	3	no	—
17	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
18	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
19	#10624840	—	43	1	no	maximal, Sylow
20	C₃²×C₄₃	—	9	1	no	—
21	C₃²×C₄₃	#732	1	3	yes	—
22	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₉×C₄₃	—	3	2	no	—
24	C₉×C₄₃	—	3	1	no	—
25	C₉×C₄₃	—	9	3	no	—
26	C₄₃⋊C₉	—	9	9	no	—
27	C₃×#733	—	43	3	no	—
28	#6887	C₄₃⋊C₃	1	1	yes	characteristic
29	#6880	—	43	9	no	—
30	C₃×C₄₃	—	3	1	no	—
31	C₃×C₄₃	—	3	3	no	—
32	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
33	C₃×3₋¹⁺²	—	129	3	no	—
34	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
35	#733	—	43	9	no	—
36	#733	—	129	6	no	—
37	C₉⋊C₉	—	3	2	no	—
38	C₃²⋊C₉	—	3	1	no	—
39	C₉²	C₃×C₄₃⋊C₃	1	3	yes	—
40	C₄₃	#10624840	1	1	yes	characteristic, complemented, Sylow
41	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
42	3₋¹⁺²	—	129	9	no	—
43	3₋¹⁺²	—	387	6	no	—
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	3	3	no	—
46	C₃×C₉	—	387	3	no	—
47	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
48	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
49	C₃²	—	9	1	no	—
50	C₃²	#16812513	1	3	yes	—
51	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
52	C₉	—	3	2	no	—
53	C₉	—	3	1	no	—
54	C₉	—	9	3	no	—
55	C₉	—	387	9	no	—
56	C₃	—	3	1	no	—
57	C₃	—	3	3	no	—
58	C₃	C₃×#16812513	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#16812513
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	C₃×#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624840
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
2. #23782754	C₃	semidirect
40. C₄₃	#10624840	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
#23782754	3
C₄₃×#6887	3
#10624840	43