Subgroups — C₃×C₄₃×#6855 #44531480

Order 31347.

1052 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₉×C₄₃	C₃	1	4	yes	maximal
2	C₄₃×#6855	C₃	1	9	yes	maximal, direct product factor
3	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
4	C₃²×C₉×C₄₃	—	3	12	no	—
5	C₃²×C₉×C₄₃	—	3	24	no	—
6	C₃²×C₉×C₄₃	C₉	1	36	yes	complemented
7	C₃²×C₉×C₄₃	C₃²	1	12	yes	—
8	C₃³×C₄₃	C₃×C₉	1	12	yes	—
9	C₃³×C₄₃	H(3,𝔽₃)	1	3	yes	—
10	C₃³×C₄₃	3₋¹⁺²	1	24	yes	—
11	C₃³×C₄₃	C₃³	1	1	yes	characteristic
12	C₃×C₉×C₄₃	—	3	108	no	—
13	C₃×C₉×C₄₃	—	3	12	no	—
14	C₃×C₉×C₄₃	—	3	24	no	—
15	C₃×C₉×C₄₃	C₃×C₉	1	36	yes	complemented
16	C₃×#6855	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₃²×C₄₃	C₉²	1	9	yes	—
18	C₃²×C₄₃	C₃²⋊C₉	1	36	yes	—
19	C₃²×C₄₃	C₉⋊C₉	1	72	yes	—
20	C₃²×C₄₃	C₃²×C₉	1	4	yes	—
21	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
22	C₃²×C₄₃	C₃×3₋¹⁺²	1	8	yes	—
23	C₉×C₄₃	—	3	36	no	—
24	C₃³×C₉	C₃×C₄₃	1	4	yes	—
25	#6855	C₃×C₄₃	1	9	yes	direct product factor
26	C₃×C₄₃	#6855	1	27	yes	direct product factor
27	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
28	C₃×C₄₃	C₃×C₃²⋊C₉	1	4	yes	—
29	C₃×C₄₃	C₃×C₉⋊C₉	1	8	yes	—
30	C₃⁴	C₃²×C₄₃	1	1	yes	characteristic
31	C₃²×C₉	—	3	12	no	—
32	C₃²×C₉	—	3	24	no	—
33	C₃²×C₉	C₉×C₄₃	1	36	yes	complemented
34	C₃²×C₉	C₃²×C₄₃	1	12	yes	—
35	C₄₃	C₃×#6855	1	1	yes	characteristic, direct product factor, Sylow
36	C₃³	C₃×C₉×C₄₃	1	12	yes	—
37	C₃³	H(3,𝔽₃)×C₄₃	1	3	yes	—
38	C₃³	3₋¹⁺²×C₄₃	1	24	yes	—
39	C₃³	C₃³×C₄₃	1	1	yes	characteristic
40	C₃×C₉	—	3	108	no	—
41	C₃×C₉	—	3	12	no	—
42	C₃×C₉	—	3	24	no	—
43	C₃×C₉	C₃×C₉×C₄₃	1	36	yes	complemented
44	C₃²	C₉²×C₄₃	1	9	yes	—
45	C₃²	C₄₃×C₃²⋊C₉	1	36	yes	—
46	C₃²	C₄₃×C₉⋊C₉	1	72	yes	—
47	C₃²	C₃²×C₉×C₄₃	1	4	yes	—
48	C₃²	C₃×H(3,𝔽₃)×C₄₃	1	1	yes	characteristic
49	C₃²	C₃×3₋¹⁺²×C₄₃	1	8	yes	—
50	C₉	—	3	36	no	—
51	C₃	C₄₃×#6855	1	27	yes	direct product factor
52	C₃	C₃×C₉²×C₄₃	1	1	yes	characteristic
53	C₃	C₃×C₄₃×C₃²⋊C₉	1	4	yes	—
54	C₃	C₃×C₄₃×C₉⋊C₉	1	8	yes	—

	subgroup	G/H
center, socle, prime radical	C₃⁴×C₄₃	C₃²
commutator	C₃	C₃×C₉²×C₄₃
Frattini, cosocle	C₃³	C₃³×C₄₃
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#6855	C₃	direct (N × H)
6. C₃²×C₉×C₄₃	C₉	semidirect
15. C₃×C₉×C₄₃	C₃×C₉	semidirect
16. C₃×#6855	C₄₃	direct (N × H)
25. #6855	C₃×C₄₃	direct (N × H)
26. C₃×C₄₃	#6855	direct (N × H)
33. C₃²×C₉	C₉×C₄₃	semidirect
35. C₄₃	C₃×#6855	direct (N × H)
43. C₃×C₉	C₃×C₉×C₄₃	semidirect
51. C₃	C₄₃×#6855	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₉×C₄₃	3
C₄₃×#6855	3
C₃×#6855	43

Subgroups — C3×C43×#6855 #44531480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₃×#6855 #44531480