Subgroups — #44532166

Order 31347.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄₃⋊C₉	C₃	1	1	yes	maximal, characteristic
2	#23782716	C₃	1	2	yes	maximal
3	C₃×C₄₃×#733	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	—	3	1	no	—
5	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
6	C₉×C₄₃⋊C₉	—	3	3	no	—
7	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
8	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
9	C₄₃×#733	—	3	2	no	—
10	C₄₃×#733	C₉	1	3	yes	complemented
11	C₃×C₄₃⋊C₉	—	3	6	no	—
12	C₃×C₄₃⋊C₉	—	3	3	no	—
13	C₃×C₄₃⋊C₉	—	3	3	no	—
14	C₃×C₄₃⋊C₉	—	9	2	no	—
15	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
16	3₋¹⁺²×C₄₃	—	3	3	no	—
17	3₋¹⁺²×C₄₃	—	9	1	no	—
18	3₋¹⁺²×C₄₃	—	9	1	no	—
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	1	no	—
22	C₃×C₉×C₄₃	—	9	1	no	—
23	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
24	C₃×C₉×C₄₃	3₋¹⁺²	1	2	yes	—
25	#10624525	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	—	3	2	no	—
27	C₃²×C₄₃	—	3	1	no	—
28	C₃²×C₄₃	C₃²⋊C₉	1	1	yes	characteristic
29	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
30	C₃²×C₄₃	#731	1	1	yes	characteristic
31	C₃²×C₄₃	#732	1	1	yes	characteristic
32	C₉×C₄₃	—	3	1	no	—
33	C₉×C₄₃	—	3	2	no	—
34	C₉×C₄₃	—	9	3	no	—
35	C₄₃⋊C₉	—	3	9	no	—
36	C₄₃⋊C₉	—	27	2	no	—
37	C₃×#733	C₄₃⋊C₃	1	1	yes	characteristic
38	C₃×C₉²	—	43	1	no	—
39	#6868	—	43	2	no	—
40	C₃×C₄₃	—	3	1	no	—
41	C₃×C₄₃	—	3	1	no	—
42	C₃×C₄₃	—	3	1	no	—
43	C₃×C₄₃	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
44	C₃×C₄₃	#6878	1	2	yes	—
45	C₃×C₄₃	#6880	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	2	no	—
50	#733	C₄₃⋊C₉	1	3	yes	complemented
51	C₃²⋊C₉	—	129	2	no	—
52	C₉²	—	129	3	no	—
53	C₄₃	#10624525	1	1	yes	characteristic, complemented, Sylow
54	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
55	3₋¹⁺²	—	3	3	no	—
56	3₋¹⁺²	—	9	1	no	—
57	3₋¹⁺²	—	9	1	no	—
58	C₃×C₉	—	3	1	no	—
59	C₃×C₉	—	3	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	9	1	no	—
62	C₃×C₉	—	129	6	no	—
63	C₃×C₉	—	129	3	no	—
64	C₃×C₉	—	129	3	no	—
65	C₃×C₉	—	387	2	no	—
66	C₃×C₉	C₃×C₄₃⋊C₉	1	1	yes	characteristic
67	C₃×C₉	#11923958	1	2	yes	—
68	C₃²	—	3	2	no	—
69	C₃²	—	3	1	no	—
70	C₃²	C₃²⋊(C₄₃⋊C₉)	1	1	yes	characteristic
71	C₃²	#16812506	1	1	yes	characteristic
72	C₃²	#16812509	1	1	yes	characteristic
73	C₃²	#16812512	1	1	yes	characteristic
74	C₉	—	3	1	no	—
75	C₉	—	3	2	no	—
76	C₉	—	9	3	no	—
77	C₉	—	129	9	no	—
78	C₉	—	1161	2	no	—
79	C₃	—	3	1	no	—
80	C₃	—	3	1	no	—
81	C₃	—	3	1	no	—
82	C₃	H(3,𝔽₃)⋊(C₄₃⋊C₉)	1	1	yes	characteristic
83	C₃	#23782748	1	2	yes	—
84	C₃	#23782753	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	#16812512
commutator	C₃×C₉×C₄₃	C₃×C₉
Frattini	C₃²×C₉	C₃×C₄₃⋊C₃
Fitting	C₃×C₄₃×#733	C₃
socle	C₃²×C₄₃	#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
cosocle	C₃²×C₉×C₄₃	C₃²
hypercenter	C₃×#733	C₄₃⋊C₃
hypocenter	C₄₃	#10624525
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×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
10. C₄₃×#733	C₉	semidirect
50. #733	C₄₃⋊C₉	semidirect
53. C₄₃	#10624525	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₄₃⋊C₉	3
#23782716	3
C₃×C₄₃×#733	3
#10624525	43