Subgroups — #44531909

Order 31347.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	3	yes	maximal
2	C₃²×3₋¹⁺²×C₄₃	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₄₃⋊C₉	—	3	3	no	—
4	C₃²⋊(C₄₃⋊C₉)	—	3	9	no	—
5	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
6	C₃×3₋¹⁺²×C₄₃	—	3	2	no	—
7	C₃×3₋¹⁺²×C₄₃	—	3	9	no	—
8	C₃×3₋¹⁺²×C₄₃	C₉	1	3	yes	complemented
9	C₃²×C₉×C₄₃	—	3	1	no	—
10	C₃×C₄₃⋊C₉	—	3	9	no	—
11	C₃×C₄₃⋊C₉	—	9	3	no	—
12	C₃×C₄₃⋊C₉	—	9	3	no	—
13	C₃×C₄₃⋊C₉	—	9	3	no	—
14	C₃³×C₄₃	—	3	3	no	—
15	C₃³×C₄₃	—	3	3	no	—
16	C₃³×C₄₃	—	3	3	no	—
17	C₃³×C₄₃	—	3	3	no	—
18	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
19	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	C₃³×C₄₃	3₋¹⁺²	1	2	yes	—
21	3₋¹⁺²×C₄₃	—	3	18	no	—
22	3₋¹⁺²×C₄₃	—	3	9	no	—
23	C₃×C₉×C₄₃	—	3	3	no	—
24	C₃×C₉×C₄₃	—	3	9	no	—
25	#10624452	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	—	3	2	no	—
28	C₃²×C₄₃	—	3	3	no	—
29	C₃²×C₄₃	—	3	6	no	—
30	C₃²×C₄₃	—	9	3	no	—
31	C₃²×C₄₃	—	9	3	no	—
32	C₃²×C₄₃	—	9	3	no	—
33	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
34	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	—
35	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	3	yes	—
36	C₃²×C₄₃	#731	1	3	yes	—
37	C₃²×C₄₃	#733	1	3	yes	—
38	C₉×C₄₃	—	3	9	no	—
39	C₄₃⋊C₉	—	9	9	no	—
40	C₃²×3₋¹⁺²	C₄₃⋊C₃	1	1	yes	characteristic
41	C₃×C₃²⋊C₉	—	43	3	no	—
42	C₃×C₄₃	—	9	1	no	—
43	C₃×C₄₃	—	9	2	no	—
44	C₃×C₄₃	#6857	1	3	yes	—
45	C₃×C₄₃	#6858	1	3	yes	—
46	C₃×C₄₃	#6860	1	3	yes	—
47	C₃×C₄₃	#6866	1	1	yes	characteristic
48	C₃×C₄₃	3₋¹⁺²⋊C₉	1	3	yes	—
49	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
50	C₃×3₋¹⁺²	—	3	2	no	—
51	C₃×3₋¹⁺²	—	3	9	no	—
52	C₃×3₋¹⁺²	C₄₃⋊C₉	1	3	yes	complemented
53	C₃²×C₉	—	3	1	no	—
54	C₃²×C₉	—	129	3	no	—
55	C₃²⋊C₉	—	129	9	no	—
56	C₄₃	#10624452	1	1	yes	characteristic, complemented, Sylow
57	C₃³	—	3	3	no	—
58	C₃³	—	3	3	no	—
59	C₃³	—	3	3	no	—
60	C₃³	—	3	3	no	—
61	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
62	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
63	C₃³	#11923958	1	2	yes	—
64	3₋¹⁺²	—	3	18	no	—
65	3₋¹⁺²	—	3	9	no	—
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	3	9	no	—
68	C₃×C₉	—	129	9	no	—
69	C₃×C₉	—	387	3	no	—
70	C₃×C₉	—	387	3	no	—
71	C₃×C₉	—	387	3	no	—
72	C₃²	—	3	1	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	6	no	—
76	C₃²	—	9	3	no	—
77	C₃²	—	9	3	no	—
78	C₃²	—	9	3	no	—
79	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
80	C₃²	#16812507	1	3	yes	—
81	C₃²	#16812508	1	3	yes	—
82	C₃²	#16812511	1	3	yes	—
83	C₃²	#16812514	1	3	yes	—
84	C₉	—	3	9	no	—
85	C₉	—	387	9	no	—
86	C₃	—	9	1	no	—
87	C₃	—	9	2	no	—
88	C₃	#23782688	1	3	yes	—
89	C₃	#23782691	1	3	yes	—
90	C₃	#23782698	1	3	yes	—
91	C₃	#23782712	1	1	yes	characteristic
92	C₃	3₋¹⁺²⋊(C₄₃⋊C₉)	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²⋊(C₄₃⋊C₃)
commutator	C₃³×C₄₃	C₃×C₉
Frattini	C₃⁴	C₃×C₄₃⋊C₃
Fitting	C₃²×3₋¹⁺²×C₄₃	C₃
socle	C₃³×C₄₃	H(3,𝔽₃)
prime radical, cosocle	C₃⁴×C₄₃	C₃²
hypercenter	C₃²×3₋¹⁺²	C₄₃⋊C₃
hypocenter	C₄₃	#10624452
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃²×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
8. C₃×3₋¹⁺²×C₄₃	C₉	semidirect
52. C₃×3₋¹⁺²	C₄₃⋊C₉	semidirect
56. C₄₃	#10624452	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₃²×3₋¹⁺²×C₄₃	3
#10624452	43