Subgroups — #44533670

Order 31347.

446 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11923958	C₃	1	1	yes	maximal, characteristic
2	C₃×#16812514	C₃	1	9	yes	maximal, complemented
3	#23782798	C₃	1	2	yes	maximal
4	C₄₃×#6891	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	9	no	—
6	C₃×#11923958	—	3	3	no	—
7	C₃×#11923958	C₃²	1	6	yes	—
8	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
9	#16812514	—	3	27	no	—
10	C₃²⋊(C₄₃⋊C₉)	—	3	6	no	—
11	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
12	C₃×3₋¹⁺²×C₄₃	C₃²	1	3	yes	—
13	C₄₃×C₃²⋊C₉	—	3	3	no	—
14	#11923958	—	3	27	no	—
15	#11923958	—	3	18	no	—
16	C₃×C₄₃⋊C₉	—	3	6	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	3	6	no	—
19	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	9	yes	—
20	C₃³×C₄₃	—	3	3	no	—
21	C₃³×C₄₃	—	9	3	no	—
22	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	—	3	9	no	—
25	C₃×C₉×C₄₃	—	3	3	no	—
26	#10624738	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	—	3	3	no	—
28	C₃²×C₄₃	—	3	9	no	—
29	C₃²×C₄₃	—	3	3	no	—
30	C₃²×C₄₃	—	9	9	no	—
31	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	—
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₉×C₄₃	—	9	3	no	—
34	C₄₃⋊C₉	—	3	9	no	—
35	C₄₃⋊C₉	—	9	6	no	—
36	C₃²×3₋¹⁺²	—	43	1	no	—
37	C₃×#733	—	43	9	no	—
38	#6891	—	43	2	no	—
39	#6891	C₄₃⋊C₃	1	1	yes	characteristic
40	C₃×C₄₃	—	3	3	no	—
41	C₃×C₄₃	—	9	3	no	—
42	C₃×C₄₃	C₃²⋊H(3,𝔽₃)	1	1	yes	characteristic
43	C₃×C₄₃	#6912	1	3	yes	—
44	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₃×3₋¹⁺²	—	43	6	no	—
46	C₃×3₋¹⁺²	—	129	9	no	—
47	C₃×3₋¹⁺²	—	129	3	no	—
48	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	3	yes	—
49	C₃²×C₉	—	43	3	no	—
50	#733	—	129	27	no	—
51	C₃²⋊C₉	—	3	3	no	—
52	C₃²⋊C₉	—	129	6	no	—
53	C₄₃	#10624738	1	1	yes	characteristic, complemented, Sylow
54	C₃³	—	3	3	no	—
55	C₃³	—	9	3	no	—
56	C₃³	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
57	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
58	3₋¹⁺²	—	3	9	no	—
59	3₋¹⁺²	—	129	27	no	—
60	3₋¹⁺²	—	129	18	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	43	9	no	—
63	C₃×C₉	—	129	6	no	—
64	C₃×C₉	—	129	3	no	—
65	C₃×C₉	—	129	6	no	—
66	C₃²	—	3	3	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	9	no	—
69	C₃²	—	9	9	no	—
70	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	3	yes	—
71	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
72	C₉	—	9	3	no	—
73	C₉	—	129	9	no	—
74	C₉	—	387	6	no	—
75	C₃	—	3	3	no	—
76	C₃	—	9	3	no	—
77	C₃	(C₃×C₄₃⋊C₃)⋊H(3,𝔽₃)	1	1	yes	characteristic
78	C₃	#23782895	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6891	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	#6891	C₄₃⋊C₃
hypocenter	C₄₃	#10624738
LCS	G ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ #6891

Complements

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

N	H ≅ G/N	type
2. C₃×#16812514	C₃	semidirect
53. C₄₃	#10624738	semidirect

Maximal subgroups

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

subgroup	index
C₃²×#11923958	3
C₃×#16812514	3
#23782798	3
C₄₃×#6891	3
#10624738	43