Subgroups — #44534496

Order 31347.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812515	C₃	1	2	yes	maximal
2	#23782782	C₃	1	1	yes	maximal, characteristic
3	#23782752	C₃	1	9	yes	maximal, complemented
4	C₃×C₄₃×#733	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	2	no	—
6	#16812515	—	3	2	no	—
7	#16812515	—	3	2	no	—
8	#16812515	C₃²	1	6	yes	—
9	#16812500	—	3	1	no	—
10	#16812499	—	3	1	no	—
11	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
12	C₉×C₄₃⋊C₉	C₃²	1	3	yes	—
13	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
14	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
15	C₄₃×#733	—	3	1	no	—
16	C₄₃×#733	—	3	1	no	—
17	C₄₃×#733	C₃²	1	3	yes	—
18	#11923958	—	3	6	no	—
19	#11923958	—	9	2	no	—
20	#11923958	—	9	2	no	—
21	C₃×C₄₃⋊C₉	—	3	3	no	—
22	C₃×C₄₃⋊C₉	—	9	2	no	—
23	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	—	3	3	no	—
25	3₋¹⁺²×C₄₃	—	9	2	no	—
26	C₃×C₉×C₄₃	—	3	1	no	—
27	C₃×C₉×C₄₃	—	3	2	no	—
28	C₃×C₉×C₄₃	—	9	1	no	—
29	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
30	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
32	#10624840	—	43	1	no	maximal, Sylow
33	C₃²×C₄₃	—	9	1	no	—
34	C₃²×C₄₃	#732	1	1	yes	characteristic
35	C₃²×C₄₃	#732	1	2	yes	—
36	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
37	C₉×C₄₃	—	3	1	no	—
38	C₉×C₄₃	—	3	1	no	—
39	C₉×C₄₃	—	3	1	no	—
40	C₉×C₄₃	—	9	3	no	—
41	C₄₃⋊C₉	—	9	3	no	—
42	C₄₃⋊C₉	—	9	6	no	—
43	C₃×#733	—	43	2	no	—
44	C₃×#733	C₄₃⋊C₃	1	1	yes	characteristic
45	#6887	—	43	1	no	—
46	#6880	—	43	9	no	—
47	C₃×C₄₃	—	3	1	no	—
48	C₃×C₄₃	—	3	1	no	—
49	C₃×C₄₃	—	3	2	no	—
50	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
51	C₃×3₋¹⁺²	—	3	1	no	—
52	C₃×3₋¹⁺²	—	129	2	no	—
53	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
54	#733	—	3	1	no	—
55	#733	—	3	1	no	—
56	#733	—	43	6	no	—
57	#733	—	129	2	no	—
58	#733	—	129	2	no	—
59	#733	C₃×C₄₃⋊C₃	1	3	yes	—
60	C₉⋊C₉	—	129	1	no	—
61	C₉⋊C₉	—	129	1	no	—
62	C₃²⋊C₉	—	129	1	no	—
63	C₉²	—	43	3	no	—
64	C₄₃	#10624840	1	1	yes	characteristic, complemented, Sylow
65	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
66	3₋¹⁺²	—	3	3	no	—
67	3₋¹⁺²	—	9	2	no	—
68	3₋¹⁺²	—	129	6	no	—
69	3₋¹⁺²	—	387	2	no	—
70	3₋¹⁺²	—	387	2	no	—
71	C₃×C₉	—	3	1	no	—
72	C₃×C₉	—	3	2	no	—
73	C₃×C₉	—	9	1	no	—
74	C₃×C₉	—	129	3	no	—
75	C₃×C₉	—	387	2	no	—
76	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
77	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
78	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
79	C₃²	—	9	1	no	—
80	C₃²	#16812512	1	1	yes	characteristic
81	C₃²	#16812512	1	2	yes	—
82	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
83	C₉	—	3	1	no	—
84	C₉	—	3	1	no	—
85	C₉	—	3	1	no	—
86	C₉	—	9	3	no	—
87	C₉	—	387	3	no	—
88	C₉	—	387	6	no	—
89	C₃	—	3	1	no	—
90	C₃	—	3	1	no	—
91	C₃	—	3	2	no	—
92	C₃	C₃×#16812512	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#16812512
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×#733	C₃
socle	C₃×C₄₃	C₃×#732
prime radical	C₃³×C₄₃	H(3,𝔽₃)
hypercenter	C₃×#733	C₄₃⋊C₃
hypocenter	C₄₃	#10624840
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ C₃×#733

Complements

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

N	H ≅ G/N	type
3. #23782752	C₃	semidirect
64. C₄₃	#10624840	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812515	3
#23782782	3
#23782752	3
C₃×C₄₃×#733	3
#10624840	43