Subgroups — #44532146

Order 31347.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782716	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃²⋊(C₄₃⋊C₉)	—	3	3	no	—
4	C₃²×C₉×C₄₃	—	3	1	no	—
5	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
6	C₉²×C₄₃	—	3	2	no	—
7	C₉²×C₄₃	C₉	1	3	yes	complemented
8	C₃×C₄₃⋊C₉	—	9	3	no	—
9	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₉×C₄₃	—	3	3	no	—
11	C₃×C₉×C₄₃	—	3	6	no	—
12	C₃×C₉×C₄₃	—	3	3	no	—
13	C₃×C₉×C₄₃	—	3	1	no	—
14	C₃×C₉×C₄₃	—	3	2	no	—
15	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
17	#10624519	—	43	1	no	maximal, Sylow
18	C₃²×C₄₃	—	3	1	no	—
19	C₃²×C₄₃	—	3	2	no	—
20	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
21	C₃²×C₄₃	#732	1	1	yes	characteristic
22	C₃²×C₄₃	#733	1	2	yes	—
23	C₉×C₄₃	—	3	9	no	—
24	C₉×C₄₃	—	3	1	no	—
25	C₉×C₄₃	—	3	2	no	—
26	C₄₃⋊C₉	—	27	3	no	—
27	C₃×C₉²	C₄₃⋊C₃	1	1	yes	characteristic
28	#6868	—	43	3	no	—
29	C₃×C₄₃	—	3	1	no	—
30	C₃×C₄₃	—	3	2	no	—
31	C₃×C₄₃	#6868	1	1	yes	characteristic
32	C₃×C₄₃	#6879	1	1	yes	characteristic
33	C₃×C₄₃	#6880	1	2	yes	—
34	C₃²×C₉	—	3	1	no	—
35	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
36	C₃²⋊C₉	—	129	3	no	—
37	C₉²	—	3	2	no	—
38	C₉²	C₄₃⋊C₉	1	3	yes	complemented
39	C₄₃	#10624519	1	1	yes	characteristic, complemented, Sylow
40	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
41	C₃×C₉	—	3	3	no	—
42	C₃×C₉	—	3	6	no	—
43	C₃×C₉	—	3	3	no	—
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	387	3	no	—
47	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
48	C₃×C₉	#11923958	1	2	yes	—
49	C₃²	—	3	1	no	—
50	C₃²	—	3	2	no	—
51	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
52	C₃²	#16812513	1	1	yes	characteristic
53	C₃²	#16812515	1	2	yes	—
54	C₉	—	3	9	no	—
55	C₉	—	3	1	no	—
56	C₉	—	3	2	no	—
57	C₉	—	1161	3	no	—
58	C₃	—	3	1	no	—
59	C₃	—	3	2	no	—
60	C₃	#23782716	1	1	yes	characteristic
61	C₃	#23782751	1	1	yes	characteristic
62	C₃	#23782754	1	2	yes	—

	subgroup	G/H
center	C₃²	#16812513
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₉²×C₄₃	C₃
socle	C₃²×C₄₃	#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×C₉²	C₄₃⋊C₃
hypocenter	C₄₃	#10624519
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
7. C₉²×C₄₃	C₉	semidirect
38. C₉²	C₄₃⋊C₉	semidirect
39. C₄₃	#10624519	semidirect

Maximal subgroups

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

subgroup	index
#23782716	3
C₃×C₉²×C₄₃	3
#10624519	43