Subgroups — #44532129

Order 31347.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782782	C₃	1	1	yes	maximal, characteristic
2	#23782718	C₃	1	2	yes	maximal
3	C₄₃×#6869	C₃	1	1	yes	maximal, characteristic
4	#16812505	—	3	2	no	—
5	#16812500	—	3	1	no	—
6	#16812499	—	3	1	no	—
7	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
8	C₉×C₄₃⋊C₉	C₉	1	3	yes	—
9	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
10	C₄₃×C₂₇⋊C₃	—	3	1	no	—
11	C₃×C₄₃⋊C₉	—	3	3	no	—
12	C₄₃⋊C₂₇	—	9	2	no	—
13	C₃³×C₄₃	3₋¹⁺²	1	1	yes	characteristic
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	—	3	2	no	—
16	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₂₇×C₄₃	—	9	1	no	—
20	#10624514	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	3	1	no	—
22	C₃²×C₄₃	—	9	1	no	—
23	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
24	C₉×C₄₃	—	3	1	no	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	#731	1	1	yes	characteristic
27	C₉×C₄₃	#731	1	2	yes	—
28	C₄₃⋊C₉	—	9	3	no	—
29	#6887	—	43	1	no	—
30	#6869	—	43	2	no	—
31	#6869	C₄₃⋊C₃	1	1	yes	characteristic
32	C₃×C₄₃	—	3	1	no	—
33	C₃×C₄₃	—	9	1	no	—
34	C₃×C₄₃	#6867	1	1	yes	characteristic
35	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
36	C₂₇⋊C₃	—	3	1	no	—
37	C₂₇⋊C₃	—	129	2	no	—
38	C₉⋊C₉	—	129	1	no	—
39	C₉⋊C₉	—	129	1	no	—
40	C₃²⋊C₉	—	129	1	no	—
41	C₉²	—	43	3	no	—
42	C₄₃	#10624514	1	1	yes	characteristic, complemented, Sylow
43	C₃³	#11923957	1	1	yes	characteristic
44	C₃×C₉	—	3	1	no	—
45	C₃×C₉	—	3	2	no	—
46	C₃×C₉	—	129	3	no	—
47	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
48	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
49	C₃×C₉	#11923956	1	1	yes	characteristic
50	C₂₇	—	9	1	no	—
51	C₂₇	—	387	2	no	—
52	C₃²	—	3	1	no	—
53	C₃²	—	9	1	no	—
54	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
55	C₉	—	3	1	no	—
56	C₉	—	3	1	no	—
57	C₉	—	387	3	no	—
58	C₉	#16812509	1	1	yes	characteristic
59	C₉	#16812511	1	2	yes	—
60	C₃	—	3	1	no	—
61	C₃	—	9	1	no	—
62	C₃	#23782713	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782713
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6869	C₃
socle	C₃×C₄₃	#6867
prime radical	C₃³×C₄₃	3₋¹⁺²
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6869	C₄₃⋊C₃
hypocenter	C₄₃	#10624514
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6869

Complements

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

N	H ≅ G/N	type
42. C₄₃	#10624514	semidirect

Maximal subgroups

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

subgroup	index
#23782782	3
#23782718	3
C₄₃×#6869	3
#10624514	43