Subgroups — C₃×#23782782 #44534645

Order 31347.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782782	C₃	1	27	yes	maximal, direct product factor
2	C₃×#16812500	C₃	1	3	yes	maximal, complemented
3	C₃×#16812499	C₃	1	3	yes	maximal, complemented
4	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	3	yes	maximal
5	C₃×C₉×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃³×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic
7	C₃²×C₄₃⋊C₉	C₃²	1	9	yes	—
8	#16812500	C₃²	1	27	yes	complemented
9	#16812499	C₃²	1	27	yes	complemented
10	C₃²⋊(C₄₃⋊C₉)	C₃²	1	27	yes	—
11	C₉×C₄₃⋊C₉	C₃²	1	27	yes	complemented
12	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
13	C₃²×C₉×C₄₃	C₉	1	27	yes	complemented
14	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
15	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
16	C₃²×C₉×C₄₃	C₃²	1	9	yes	—
17	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
18	C₃×C₄₃⋊C₉	—	3	27	no	—
19	C₃×C₄₃⋊C₉	C₃³	1	27	yes	—
20	C₃³×C₄₃	—	3	9	no	—
21	C₃³×C₄₃	C₃×C₉	1	9	yes	—
22	C₃³×C₄₃	C₃³	1	3	yes	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
25	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
26	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
27	C₃×C₉×C₄₃	C₃×C₉	1	81	yes	complemented
28	C₃×C₉×C₄₃	C₃³	1	3	yes	—
29	C₃×C₉×C₄₃	C₃³	1	3	yes	—
30	C₃×C₉×C₄₃	C₃³	1	3	yes	—
31	C₃×#6887	—	43	1	no	maximal, Sylow
32	C₃²×C₄₃	—	3	9	no	—
33	C₃²×C₄₃	—	3	27	no	—
34	C₃²×C₄₃	C₃²×C₉	1	9	yes	—
35	C₃²×C₄₃	C₃²×C₉	1	3	yes	—
36	C₃²×C₄₃	#737	1	9	yes	—
37	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
38	C₉×C₄₃	C₃²×C₉	1	9	yes	—
39	C₉×C₄₃	C₃²×C₉	1	9	yes	—
40	C₉×C₄₃	C₃²×C₉	1	9	yes	—
41	C₄₃⋊C₉	—	3	27	no	—
42	C₃³×C₉	C₄₃⋊C₃	1	1	yes	characteristic
43	#6887	—	43	27	no	—
44	C₃×C₉⋊C₉	—	43	3	no	—
45	C₃×C₉⋊C₉	—	43	3	no	—
46	C₃×C₃²⋊C₉	—	43	3	no	—
47	C₃×C₉²	—	43	3	no	—
48	C₃×C₄₃	—	3	9	no	—
49	C₃×C₄₃	#6887	1	9	yes	complemented
50	C₃×C₄₃	C₃³×C₉	1	1	yes	characteristic
51	C₃×C₄₃	C₃×#737	1	3	yes	—
52	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃²×C₉	—	43	9	no	—
54	C₃²×C₉	C₄₃⋊C₉	1	27	yes	complemented
55	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
56	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
57	C₃²×C₉	C₃×C₄₃⋊C₃	1	9	yes	—
58	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
59	C₉⋊C₉	—	43	27	no	—
60	C₉⋊C₉	—	43	27	no	—
61	C₃²⋊C₉	—	43	27	no	—
62	C₉²	—	43	27	no	—
63	C₄₃	C₃×#6887	1	1	yes	characteristic, complemented, Sylow
64	C₃³	—	3	9	no	—
65	C₃³	C₃×C₄₃⋊C₉	1	9	yes	—
66	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
67	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
68	C₃×C₉	—	43	27	no	—
69	C₃×C₉	—	129	27	no	—
70	C₃×C₉	C₃×C₄₃⋊C₉	1	9	yes	—
71	C₃×C₉	C₃×C₄₃⋊C₉	1	9	yes	—
72	C₃×C₉	C₃×C₄₃⋊C₉	1	9	yes	—
73	C₃×C₉	C₃×C₄₃⋊C₉	1	81	yes	complemented
74	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
75	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
76	C₃×C₉	C₃²×C₄₃⋊C₃	1	3	yes	—
77	C₃²	—	3	9	no	—
78	C₃²	—	3	27	no	—
79	C₃²	C₃²×C₄₃⋊C₉	1	9	yes	—
80	C₃²	C₃²×C₄₃⋊C₉	1	3	yes	—
81	C₃²	#16812525	1	9	yes	—
82	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
83	C₉	—	129	27	no	—
84	C₉	C₃²×C₄₃⋊C₉	1	9	yes	—
85	C₉	C₃²×C₄₃⋊C₉	1	9	yes	—
86	C₉	C₃²×C₄₃⋊C₉	1	9	yes	—
87	C₃	—	3	9	no	—
88	C₃	#23782782	1	9	yes	direct product factor
89	C₃	C₃³×C₄₃⋊C₉	1	1	yes	characteristic
90	C₃	C₃×#16812525	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃³×C₉
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₃³×C₉×C₄₃	C₃
socle	C₃³×C₄₃	C₃³
prime radical	C₃⁴×C₄₃	C₃²
cosocle	C₃²×C₄₃	C₃⁴
hypercenter	C₃³×C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6887
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃²×C₉ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. #23782782	C₃	direct (N × H)
2. C₃×#16812500	C₃	semidirect
3. C₃×#16812499	C₃	semidirect
5. C₃×C₉×C₄₃⋊C₉	C₃	semidirect
8. #16812500	C₃²	semidirect
9. #16812499	C₃²	semidirect
11. C₉×C₄₃⋊C₉	C₃²	semidirect
13. C₃²×C₉×C₄₃	C₉	semidirect
27. C₃×C₉×C₄₃	C₃×C₉	semidirect
49. C₃×C₄₃	#6887	semidirect
54. C₃²×C₉	C₄₃⋊C₉	semidirect
63. C₄₃	C₃×#6887	semidirect
73. C₃×C₉	C₃×C₄₃⋊C₉	semidirect
88. C₃	#23782782	direct (N × H)

Maximal subgroups

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

subgroup	index
#23782782	3
C₃×#16812500	3
C₃×#16812499	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₃×C₉×C₄₃⋊C₉	3
C₃³×C₉×C₄₃	3
C₃×#6887	43

Subgroups — C3×#23782782 #44534645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782782 #44534645