Subgroups — #44532143

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	9	no	—
11	C₃×C₉×C₄₃	—	3	3	no	—
12	C₃×C₉×C₄₃	—	3	1	no	—
13	C₃×C₉×C₄₃	—	3	2	no	—
14	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
16	#10624518	—	43	1	no	maximal, Sylow
17	C₃²×C₄₃	—	3	3	no	—
18	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
19	C₃²×C₄₃	#732	1	1	yes	characteristic
20	C₃²×C₄₃	#733	1	2	yes	—
21	C₉×C₄₃	—	3	9	no	—
22	C₉×C₄₃	—	3	1	no	—
23	C₉×C₄₃	—	3	2	no	—
24	C₄₃⋊C₉	—	27	3	no	—
25	C₃×C₉²	C₄₃⋊C₃	1	1	yes	characteristic
26	#6868	—	43	3	no	—
27	C₃×C₄₃	—	3	1	no	—
28	C₃×C₄₃	—	3	2	no	—
29	C₃×C₄₃	#6868	1	1	yes	characteristic
30	C₃×C₄₃	#6878	1	3	yes	—
31	C₃²×C₉	—	3	1	no	—
32	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
33	C₃²⋊C₉	—	129	3	no	—
34	C₉²	—	3	2	no	—
35	C₉²	C₄₃⋊C₉	1	3	yes	complemented
36	C₄₃	#10624518	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	—	3	2	no	—
42	C₃×C₉	—	387	3	no	—
43	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
44	C₃×C₉	#11923958	1	2	yes	—
45	C₃²	—	3	3	no	—
46	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
47	C₃²	#16812513	1	1	yes	characteristic
48	C₃²	#16812515	1	2	yes	—
49	C₉	—	3	9	no	—
50	C₉	—	3	1	no	—
51	C₉	—	3	2	no	—
52	C₉	—	1161	3	no	—
53	C₃	—	3	1	no	—
54	C₃	—	3	2	no	—
55	C₃	#23782716	1	1	yes	characteristic
56	C₃	#23782746	1	3	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	#10624518
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
35. C₉²	C₄₃⋊C₉	semidirect
36. C₄₃	#10624518	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
#10624518	43