Subgroups — #44532131

Order 31347.

96 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	#23782714	C₃	1	2	yes	maximal
3	C₄₃×#6867	C₃	1	1	yes	maximal, characteristic
4	#16812500	—	3	1	no	—
5	#16812499	C₉	1	3	yes	complemented
6	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
7	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
8	C₉×C₄₃⋊C₉	—	3	1	no	—
9	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
10	C₄₃×C₃²⋊C₉	—	3	1	no	—
11	C₃×C₄₃⋊C₉	—	3	3	no	—
12	C₃×C₄₃⋊C₉	—	9	2	no	—
13	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃×C₉×C₄₃	—	3	1	no	—
15	C₃×C₉×C₄₃	—	3	2	no	—
16	C₃×C₉×C₄₃	—	9	1	no	—
17	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	#10624515	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	9	1	no	—
22	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
23	C₃²×C₄₃	#731	1	1	yes	characteristic
24	C₃²×C₄₃	#731	1	2	yes	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	—	3	1	no	—
27	C₉×C₄₃	—	3	1	no	—
28	C₉×C₄₃	—	27	1	no	—
29	C₄₃⋊C₉	—	9	3	no	—
30	C₄₃⋊C₉	—	27	2	no	—
31	#6887	—	43	1	no	—
32	#6867	—	43	2	no	—
33	#6867	C₄₃⋊C₃	1	1	yes	characteristic
34	C₃×C₄₃	—	3	1	no	—
35	C₃×C₄₃	—	3	2	no	—
36	C₃×C₄₃	—	3	1	no	—
37	C₃×C₄₃	#6867	1	1	yes	characteristic
38	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
39	C₉⋊C₉	—	43	3	no	—
40	C₉⋊C₉	—	129	1	no	—
41	C₃²⋊C₉	—	3	1	no	—
42	C₃²⋊C₉	—	129	1	no	—
43	C₃²⋊C₉	—	129	2	no	—
44	C₉²	—	129	1	no	—
45	C₄₃	#10624515	1	1	yes	characteristic, complemented, Sylow
46	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	3	2	no	—
49	C₃×C₉	—	9	1	no	—
50	C₃×C₉	—	129	3	no	—
51	C₃×C₉	—	387	2	no	—
52	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃×C₉	#11923956	1	1	yes	characteristic
54	C₃×C₉	#11923957	1	1	yes	characteristic
55	C₃²	—	9	1	no	—
56	C₃²	(C₃×C₄₃⋊C₃)⋊C₉	1	1	yes	characteristic
57	C₃²	#16812509	1	1	yes	characteristic
58	C₃²	#16812511	1	2	yes	—
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	3	1	no	—
62	C₉	—	27	1	no	—
63	C₉	—	387	3	no	—
64	C₉	—	1161	2	no	—
65	C₃	—	3	1	no	—
66	C₃	—	3	1	no	—
67	C₃	—	3	2	no	—
68	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×#6867	C₃
socle	C₃×C₄₃	#6867
prime radical	C₃³×C₄₃	H(3,𝔽₃)
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	#6867	C₄₃⋊C₃
hypocenter	C₄₃	#10624515
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6867

Complements

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

N	H ≅ G/N	type
5. #16812499	C₉	semidirect
45. C₄₃	#10624515	semidirect

Maximal subgroups

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

subgroup	index
#23782782	3
#23782714	3
C₄₃×#6867	3
#10624515	43