Subgroups — C₃²×#16812513 #44535285

Order 31347.

1376 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	1	3	yes	maximal, complemented
2	C₃×#16812513	C₃	1	36	yes	maximal, direct product factor
3	C₃³×C₉×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₄₃⋊C₃	—	3	3	no	—
5	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	24	no	—
6	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	36	yes	complemented
7	#16812513	C₃²	1	81	yes	direct product factor
8	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
9	C₃²×C₉×C₄₃	—	3	8	no	—
10	C₃²×C₉×C₄₃	—	3	1	no	—
11	C₃²×C₉×C₄₃	C₃²	1	12	yes	complemented
12	C₃²×C₄₃⋊C₃	—	3	36	no	—
13	C₃²×C₄₃⋊C₃	—	9	27	no	—
14	C₃²⋊(C₄₃⋊C₃)	—	3	72	no	—
15	C₃²⋊(C₄₃⋊C₃)	C₃³	1	27	yes	complemented
16	C₃³×C₄₃	—	3	9	no	—
17	C₃³×C₄₃	H(3,𝔽₃)	1	8	yes	—
18	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃³×C₄₃	C₃³	1	4	yes	—
20	C₃×C₉×C₄₃	—	3	24	no	—
21	C₃×C₉×C₄₃	—	3	12	no	—
22	C₃×C₉×C₄₃	C₃³	1	9	yes	complemented
23	C₃²×#732	—	43	1	no	maximal, Sylow
24	C₃²×C₄₃	—	3	24	no	—
25	C₃²×C₄₃	—	3	12	no	—
26	C₃²×C₄₃	#732	1	9	yes	complemented
27	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	8	yes	—
28	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	4	yes	—
29	C₃²×C₄₃	C₃⁴	1	1	yes	characteristic
30	C₃×C₄₃⋊C₃	—	3	27	no	—
31	C₃×C₄₃⋊C₃	—	9	108	no	—
32	C₉×C₄₃	—	3	9	no	—
33	C₃²×H(3,𝔽₃)	—	43	3	no	—
34	C₃³×C₉	C₄₃⋊C₃	1	1	yes	characteristic, complemented
35	C₃×#732	—	43	36	no	—
36	C₃×C₄₃	—	3	8	no	—
37	C₃×C₄₃	—	3	1	no	—
38	C₃×C₄₃	C₃×#732	1	12	yes	complemented
39	C₃×C₄₃	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
40	C₄₃⋊C₃	—	9	27	no	—
41	C₃⁴	—	129	3	no	—
42	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
43	C₃×H(3,𝔽₃)	—	43	36	no	—
44	C₃×H(3,𝔽₃)	—	129	24	no	—
45	C₃²×C₉	—	3	8	no	—
46	C₃²×C₉	—	3	1	no	—
47	C₃²×C₉	C₃×C₄₃⋊C₃	1	12	yes	complemented
48	#732	—	43	81	no	—
49	C₄₃	C₃²×#732	1	1	yes	characteristic, complemented, Sylow
50	C₃³	—	3	9	no	—
51	C₃³	—	129	36	no	—
52	C₃³	—	387	27	no	—
53	C₃³	C₃²⋊(C₄₃⋊C₃)	1	8	yes	—
54	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
55	C₃³	C₃²×C₄₃⋊C₃	1	4	yes	—
56	H(3,𝔽₃)	—	43	27	no	—
57	H(3,𝔽₃)	—	129	72	no	—
58	C₃×C₉	—	3	24	no	—
59	C₃×C₉	—	3	12	no	—
60	C₃×C₉	C₃²×C₄₃⋊C₃	1	9	yes	complemented
61	C₃²	—	3	24	no	—
62	C₃²	—	3	12	no	—
63	C₃²	—	129	27	no	—
64	C₃²	—	387	108	no	—
65	C₃²	#16812513	1	9	yes	direct product factor
66	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	8	yes	—
67	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	4	yes	—
68	C₃²	C₃³×C₄₃⋊C₃	1	1	yes	characteristic
69	C₉	—	3	9	no	—
70	C₃	—	3	8	no	—
71	C₃	—	3	1	no	—
72	C₃	—	387	27	no	—
73	C₃	C₃×#16812513	1	12	yes	direct product factor
74	C₃	C₃²×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃²×C₄₃	C₃⁴
Frattini	C₃²	C₃³×C₄₃⋊C₃
Fitting	C₃³×C₉×C₄₃	C₃
socle	C₃³×C₄₃	H(3,𝔽₃)
hypercenter	C₃³×C₉	C₄₃⋊C₃
hypocenter	C₄₃	C₃²×#732
LCS	G ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃⁴ ◁ C₃³×C₉

Complements

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

N	H ≅ G/N	type
1. C₃²×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
2. C₃×#16812513	C₃	direct (N × H)
3. C₃³×C₉×C₄₃	C₃	semidirect
6. C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	semidirect
7. #16812513	C₃²	direct (N × H)
11. C₃²×C₉×C₄₃	C₃²	semidirect
15. C₃²⋊(C₄₃⋊C₃)	C₃³	semidirect
22. C₃×C₉×C₄₃	C₃³	semidirect
26. C₃²×C₄₃	#732	semidirect
34. C₃³×C₉	C₄₃⋊C₃	semidirect
38. C₃×C₄₃	C₃×#732	semidirect
47. C₃²×C₉	C₃×C₄₃⋊C₃	semidirect
49. C₄₃	C₃²×#732	semidirect
60. C₃×C₉	C₃²×C₄₃⋊C₃	semidirect
65. C₃²	#16812513	direct (N × H)
73. C₃	C₃×#16812513	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×C₃²⋊(C₄₃⋊C₃)	3
C₃×#16812513	3
C₃³×C₉×C₄₃	3
C₃²×#732	43

Subgroups — C32×#16812513 #44535285

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#16812513 #44535285