Subgroups — C₄₃⋊#10624497 #44532083

Order 31347.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782712	C₃	1	1	yes	maximal, characteristic
2	#23782712	C₃	1	2	yes	maximal
3	C₄₃×#6866	C₃	1	1	yes	maximal, characteristic
4	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
5	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
6	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
7	C₄₃×C₃²⋊C₉	—	3	1	no	—
8	C₃×C₄₃⋊C₉	—	9	1	no	—
9	C₃×C₄₃⋊C₉	—	9	2	no	—
10	C₃³×C₄₃	—	3	1	no	—
11	C₃³×C₄₃	—	3	1	no	—
12	C₃³×C₄₃	—	3	2	no	—
13	C₃³×C₄₃	—	9	3	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₄₃	—	9	1	no	—
16	#10624497	—	43	1	no	maximal, Sylow
17	C₃²×C₄₃	—	9	1	no	—
18	C₃²×C₄₃	—	9	3	no	—
19	C₃²×C₄₃	—	9	6	no	—
20	C₃²×C₄₃	—	9	3	no	—
21	C₃²×C₄₃	—	9	1	no	—
22	C₃²×C₄₃	#731	1	1	yes	characteristic
23	C₃²×C₄₃	#731	1	1	yes	characteristic
24	C₃²×C₄₃	#731	1	2	yes	—
25	C₉×C₄₃	—	27	1	no	—
26	C₄₃⋊C₉	—	27	1	no	—
27	C₄₃⋊C₉	—	27	2	no	—
28	#6866	—	43	1	no	—
29	#6866	—	43	2	no	—
30	#6866	C₄₃⋊C₃	1	1	yes	characteristic
31	C₃×C₄₃	—	3	1	no	—
32	C₃×C₄₃	—	3	2	no	—
33	C₃×C₄₃	—	3	1	no	—
34	C₃×C₄₃	—	9	3	no	—
35	C₃×C₄₃	#6862	1	1	yes	characteristic
36	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	C₃²⋊C₉	—	3	1	no	—
38	C₃²⋊C₉	—	129	1	no	—
39	C₃²⋊C₉	—	129	2	no	—
40	C₄₃	#10624497	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	3	1	no	—
42	C₃³	—	3	1	no	—
43	C₃³	—	3	2	no	—
44	C₃³	—	9	3	no	—
45	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
46	C₃×C₉	—	9	1	no	—
47	C₃×C₉	—	387	1	no	—
48	C₃×C₉	—	387	2	no	—
49	C₃²	—	9	1	no	—
50	C₃²	—	9	3	no	—
51	C₃²	—	9	3	no	—
52	C₃²	—	9	6	no	—
53	C₃²	—	9	1	no	—
54	C₃²	#16812509	1	1	yes	characteristic
55	C₃²	#16812510	1	1	yes	characteristic
56	C₃²	#16812511	1	2	yes	—
57	C₉	—	27	1	no	—
58	C₉	—	1161	1	no	—
59	C₉	—	1161	2	no	—
60	C₃	—	3	1	no	—
61	C₃	—	3	1	no	—
62	C₃	—	3	2	no	—
63	C₃	—	9	3	no	—
64	C₃	C₄₃⋊#6862	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₄₃⋊#6862
commutator, prime radical, cosocle	C₃⁴×C₄₃	C₃²
Frattini	C₃⁴	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6866	C₃
socle	C₃×C₄₃	#6862
hypercenter	#6866	C₄₃⋊C₃
hypocenter	C₄₃	#10624497
LCS	G ▷ C₃⁴×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6866

Complements

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

N	H ≅ G/N	type
40. C₄₃	#10624497	semidirect

Maximal subgroups

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

subgroup	index
#23782712	3
C₄₃×#6866	3
#10624497	43

Subgroups — C43⋊#10624497 #44532083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃⋊#10624497 #44532083