Subgroups — C₃×#23782798 #44534685

Order 31347.

2636 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11923958	C₃	1	3	yes	maximal, complemented
2	#23782798	C₃	1	27	yes	maximal, direct product factor
3	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	9	yes	maximal, complemented
4	C₃⁵×C₄₃	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	27	no	—
6	C₃×#11923958	C₃²	1	27	yes	complemented
7	C₃²×C₄₃⋊C₉	C₃²	1	9	yes	complemented
8	C₃²⋊(C₄₃⋊C₉)	C₃²	1	81	yes	complemented
9	C₃⁴×C₄₃	—	3	9	no	—
10	C₃⁴×C₄₃	—	3	27	no	—
11	C₃⁴×C₄₃	C₃²	1	9	yes	—
12	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
13	C₃⁴×C₄₃	C₃²	1	3	yes	—
14	#11923958	—	3	81	no	—
15	C₃×C₄₃⋊C₉	—	3	27	no	—
16	C₃×C₄₃⋊C₉	C₃³	1	27	yes	complemented
17	C₃³×C₄₃	—	3	243	no	—
18	C₃³×C₄₃	—	3	27	no	—
19	C₃³×C₄₃	—	3	9	no	—
20	C₃³×C₄₃	—	3	9	no	—
21	C₃³×C₄₃	—	3	18	no	—
22	C₃³×C₄₃	—	3	81	no	—
23	C₃³×C₄₃	H(3,𝔽₃)	1	9	yes	—
24	C₃³×C₄₃	3₋¹⁺²	1	27	yes	complemented
25	C₃³×C₄₃	C₃³	1	3	yes	—
26	C₃³×C₄₃	C₃³	1	9	yes	—
27	C₃³×C₄₃	C₃³	1	1	yes	characteristic
28	C₃×#6891	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	3	243	no	—
30	C₃²×C₄₃	—	3	9	no	—
31	C₃²×C₄₃	—	3	9	no	—
32	C₃²×C₄₃	—	3	18	no	—
33	C₃²×C₄₃	—	3	27	no	—
34	C₃²×C₄₃	—	3	81	no	—
35	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	9	yes	—
36	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	3	yes	—
37	C₃²×C₄₃	C₃×3₋¹⁺²	1	9	yes	—
38	C₃²×C₄₃	C₃×3₋¹⁺²	1	27	yes	complemented
39	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
40	C₄₃⋊C₉	—	3	27	no	—
41	C₃⁵	C₄₃⋊C₃	1	1	yes	characteristic
42	C₃²×3₋¹⁺²	—	43	3	no	—
43	#6891	—	43	27	no	—
44	C₃×C₃²⋊C₉	—	43	9	no	—
45	C₃×C₄₃	—	3	9	no	—
46	C₃×C₄₃	—	3	27	no	—
47	C₃×C₄₃	#6891	1	9	yes	complemented
48	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
49	C₃×C₄₃	C₃²×3₋¹⁺²	1	3	yes	—
50	C₃⁴	—	3	9	no	—
51	C₃⁴	—	3	27	no	—
52	C₃⁴	C₃×C₄₃⋊C₃	1	9	yes	—
53	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
54	C₃⁴	C₃×C₄₃⋊C₃	1	3	yes	—
55	C₃×3₋¹⁺²	—	43	27	no	—
56	C₃×3₋¹⁺²	—	129	27	no	—
57	C₃²×C₉	—	43	9	no	—
58	C₃²⋊C₉	—	43	81	no	—
59	C₄₃	C₃×#6891	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	3	243	no	—
61	C₃³	—	3	27	no	—
62	C₃³	—	3	9	no	—
63	C₃³	—	3	9	no	—
64	C₃³	—	3	18	no	—
65	C₃³	—	3	81	no	—
66	C₃³	C₃²⋊(C₄₃⋊C₃)	1	9	yes	—
67	C₃³	#11923958	1	27	yes	complemented
68	C₃³	C₃²×C₄₃⋊C₃	1	3	yes	—
69	C₃³	C₃²×C₄₃⋊C₃	1	9	yes	—
70	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
71	3₋¹⁺²	—	129	81	no	—
72	C₃×C₉	—	43	27	no	—
73	C₃×C₉	—	129	27	no	—
74	C₃²	—	3	243	no	—
75	C₃²	—	3	9	no	—
76	C₃²	—	3	18	no	—
77	C₃²	—	3	27	no	—
78	C₃²	—	3	81	no	—
79	C₃²	—	3	9	no	—
80	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	9	yes	—
81	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
82	C₃²	C₃×#11923958	1	9	yes	—
83	C₃²	C₃×#11923958	1	27	yes	complemented
84	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
85	C₉	—	129	27	no	—
86	C₃	—	3	9	no	—
87	C₃	—	3	27	no	—
88	C₃	#23782798	1	9	yes	direct product factor
89	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
90	C₃	C₃²×#11923958	1	3	yes	—

	subgroup	G/H
center	C₃³	C₃²×C₄₃⋊C₃
commutator, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting, prime radical	C₃⁵×C₄₃	C₃
socle	C₃³×C₄₃	C₃³
hypercenter	C₃⁵	C₄₃⋊C₃
hypocenter	C₄₃	C₃×#6891
LCS	G ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃⁵

Complements

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

N	H ≅ G/N	type
1. C₃²×#11923958	C₃	semidirect
2. #23782798	C₃	direct (N × H)
3. C₃×C₃²⋊(C₄₃⋊C₉)	C₃	semidirect
6. C₃×#11923958	C₃²	semidirect
7. C₃²×C₄₃⋊C₉	C₃²	semidirect
8. C₃²⋊(C₄₃⋊C₉)	C₃²	semidirect
16. C₃×C₄₃⋊C₉	C₃³	semidirect
24. C₃³×C₄₃	3₋¹⁺²	semidirect
38. C₃²×C₄₃	C₃×3₋¹⁺²	semidirect
47. C₃×C₄₃	#6891	semidirect
59. C₄₃	C₃×#6891	semidirect
67. C₃³	#11923958	semidirect
83. C₃²	C₃×#11923958	semidirect
88. C₃	#23782798	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×#11923958	3
#23782798	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
C₃⁵×C₄₃	3
C₃×#6891	43

Subgroups — C3×#23782798 #44534685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#23782798 #44534685