Subgroups — C₃²×#16812524 #44535397

Order 31347.

5804 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812524	C₃	1	108	yes	maximal, direct product factor
2	C₃²×#11923958	C₃	1	8	yes	maximal, complemented
3	C₃³×C₄₃⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₃²×H(3,𝔽₃)×C₄₃	C₃	1	1	yes	maximal, characteristic
5	#16812524	C₃²	1	729	yes	direct product factor
6	C₃×#11923958	C₃²	1	288	yes	complemented
7	C₃²×C₄₃⋊C₉	C₃²	1	8	yes	—
8	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
9	C₃²×C₄₃⋊C₉	C₃²	1	144	yes	complemented
10	C₃⁴×C₄₃	C₃²	1	4	yes	—
11	C₃×H(3,𝔽₃)×C₄₃	C₃²	1	36	yes	—
12	#11923958	C₃³	1	648	yes	complemented
13	C₃×C₄₃⋊C₉	C₃³	1	12	yes	—
14	C₃×C₄₃⋊C₉	C₃³	1	96	yes	—
15	C₃×C₄₃⋊C₉	C₃³	1	324	yes	complemented
16	C₃³×C₄₃	—	3	36	no	—
17	C₃³×C₄₃	C₃³	1	48	yes	—
18	C₃³×C₄₃	C₃³	1	1	yes	characteristic
19	H(3,𝔽₃)×C₄₃	C₃³	1	81	yes	—
20	C₃²×#737	—	43	1	no	maximal, Sylow
21	C₃²×C₄₃	—	3	144	no	—
22	C₃²×C₄₃	#737	1	9	yes	complemented
23	C₃²×C₄₃	C₃⁴	1	36	yes	—
24	C₃²×C₄₃	C₃⁴	1	4	yes	—
25	C₄₃⋊C₉	C₃⁴	1	9	yes	—
26	C₄₃⋊C₉	C₃⁴	1	72	yes	—
27	C₃×#737	—	43	108	no	—
28	C₃²×3₋¹⁺²	—	43	8	no	—
29	C₃²×H(3,𝔽₃)	C₄₃⋊C₃	1	1	yes	characteristic
30	C₃³×C₉	—	43	4	no	—
31	C₃×C₄₃	—	3	36	no	—
32	C₃×C₄₃	C₃×#737	1	12	yes	complemented
33	C₃×C₄₃	C₃⁵	1	1	yes	characteristic
34	C₃⁴	C₃×C₄₃⋊C₃	1	4	yes	—
35	#737	—	43	729	no	—
36	C₃×3₋¹⁺²	—	43	288	no	—
37	C₃×H(3,𝔽₃)	C₃×C₄₃⋊C₃	1	36	yes	—
38	C₃²×C₉	—	43	144	no	—
39	C₃²×C₉	—	43	1	no	—
40	C₃²×C₉	—	43	8	no	—
41	C₄₃	C₃²×#737	1	1	yes	characteristic, complemented, Sylow
42	C₃³	—	3	36	no	—
43	C₃³	C₃²×C₄₃⋊C₃	1	48	yes	—
44	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
45	3₋¹⁺²	—	43	648	no	—
46	H(3,𝔽₃)	C₃²×C₄₃⋊C₃	1	81	yes	—
47	C₃×C₉	—	43	12	no	—
48	C₃×C₉	—	43	96	no	—
49	C₃×C₉	—	43	324	no	—
50	C₃²	—	3	144	no	—
51	C₃²	#16812524	1	9	yes	direct product factor
52	C₃²	C₃³×C₄₃⋊C₃	1	36	yes	—
53	C₃²	C₃³×C₄₃⋊C₃	1	4	yes	—
54	C₉	—	43	9	no	—
55	C₉	—	43	72	no	—
56	C₃	—	3	36	no	—
57	C₃	C₃×#16812524	1	12	yes	direct product factor
58	C₃	C₃⁴×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃³	C₃²×C₄₃⋊C₃
commutator, cosocle	C₃×C₄₃	C₃⁵
Frattini	C₃	C₃⁴×C₄₃⋊C₃
Fitting, prime radical	C₃²×H(3,𝔽₃)×C₄₃	C₃
socle	C₃³×C₄₃	C₃³
hypercenter	C₃²×H(3,𝔽₃)	C₄₃⋊C₃
hypocenter	C₄₃	C₃²×#737
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃²×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#16812524	C₃	direct (N × H)
2. C₃²×#11923958	C₃	semidirect
3. C₃³×C₄₃⋊C₉	C₃	semidirect
5. #16812524	C₃²	direct (N × H)
6. C₃×#11923958	C₃²	semidirect
9. C₃²×C₄₃⋊C₉	C₃²	semidirect
12. #11923958	C₃³	semidirect
15. C₃×C₄₃⋊C₉	C₃³	semidirect
22. C₃²×C₄₃	#737	semidirect
32. C₃×C₄₃	C₃×#737	semidirect
41. C₄₃	C₃²×#737	semidirect
51. C₃²	#16812524	direct (N × H)
57. C₃	C₃×#16812524	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16812524	3
C₃²×#11923958	3
C₃³×C₄₃⋊C₉	3
C₃²×H(3,𝔽₃)×C₄₃	3
C₃²×#737	43

Subgroups — C32×#16812524 #44535397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#16812524 #44535397