Subgroups — #44532044

Order 31347.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782716	C₃	1	1	yes	maximal, characteristic
2	#23782716	C₃	1	1	yes	maximal, characteristic
3	C₄₃⋊#6855	C₃	1	1	yes	maximal, characteristic
4	C₃×C₄₃×#733	C₃	1	1	yes	maximal, characteristic
5	C₃²×C₄₃⋊C₉	—	3	1	no	—
6	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
7	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
8	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
9	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
10	C₄₃×#733	—	3	3	no	—
11	C₃×C₄₃⋊C₉	—	3	3	no	—
12	C₃×C₄₃⋊C₉	—	9	1	no	—
13	C₃×C₄₃⋊C₉	—	9	1	no	—
14	C₃×C₄₃⋊C₉	—	9	1	no	—
15	C₃×C₄₃⋊C₉	—	9	1	no	—
16	C₃×C₄₃⋊C₉	—	9	1	no	—
17	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
18	3₋¹⁺²×C₄₃	—	3	3	no	—
19	3₋¹⁺²×C₄₃	—	9	2	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	2	no	—
22	C₃×C₉×C₄₃	—	3	1	no	—
23	C₃×C₉×C₄₃	—	9	1	no	—
24	#10624490	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	1	no	—
26	C₃²×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
29	C₃²×C₄₃	#731	1	2	yes	—
30	C₃²×C₄₃	#732	1	1	yes	characteristic
31	C₉×C₄₃	—	9	1	no	—
32	C₉×C₄₃	—	9	3	no	—
33	C₄₃⋊C₉	—	9	3	no	—
34	C₄₃⋊C₉	—	27	1	no	—
35	C₄₃⋊C₉	—	27	1	no	—
36	C₃×#733	C₄₃⋊C₃	1	1	yes	characteristic
37	#6868	—	43	1	no	—
38	#6868	—	43	1	no	—
39	#6855	—	43	1	no	—
40	C₃×C₄₃	—	3	1	no	—
41	C₃×C₄₃	—	3	2	no	—
42	C₃×C₄₃	#6859	1	1	yes	characteristic
43	C₃×C₄₃	#6878	1	1	yes	characteristic
44	C₃×C₄₃	#6882	1	1	yes	characteristic
45	C₃×C₄₃	#6883	1	1	yes	characteristic
46	C₃×3₋¹⁺²	—	3	1	no	—
47	C₃²×C₉	—	129	1	no	—
48	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	#733	—	3	3	no	—
50	C₃²⋊C₉	—	129	1	no	—
51	C₃²⋊C₉	—	129	1	no	—
52	C₄₃	#10624490	1	1	yes	characteristic, complemented, Sylow
53	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
54	3₋¹⁺²	—	3	3	no	—
55	3₋¹⁺²	—	9	2	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	2	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	9	1	no	—
60	C₃×C₉	—	129	3	no	—
61	C₃×C₉	—	387	1	no	—
62	C₃×C₉	—	387	1	no	—
63	C₃×C₉	—	387	1	no	—
64	C₃×C₉	—	387	1	no	—
65	C₃×C₉	—	387	1	no	—
66	C₃²	—	3	1	no	—
67	C₃²	—	3	1	no	—
68	C₃²	—	3	1	no	—
69	C₃²	#16812507	1	1	yes	characteristic
70	C₃²	#16812509	1	2	yes	—
71	C₃²	#16812512	1	1	yes	characteristic
72	C₉	—	9	1	no	—
73	C₉	—	9	3	no	—
74	C₉	—	387	3	no	—
75	C₉	—	1161	1	no	—
76	C₉	—	1161	1	no	—
77	C₃	—	3	1	no	—
78	C₃	—	3	2	no	—
79	C₃	#23782695	1	1	yes	characteristic
80	C₃	#23782749	1	1	yes	characteristic
81	C₃	#23782760	1	1	yes	characteristic
82	C₃	#23782766	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812512
commutator, cosocle	C₃²×C₉×C₄₃	C₃²
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×#733	C₃
socle	C₃²×C₄₃	#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
hypercenter	C₃×#733	C₄₃⋊C₃
hypocenter	C₄₃	#10624490
LCS	G ▷ C₃²×C₉×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
52. C₄₃	#10624490	semidirect

Maximal subgroups

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

subgroup	index
#23782716	3
C₄₃⋊#6855	3
C₃×C₄₃×#733	3
#10624490	43