Subgroups — C₄₇×#10624530 #46804171

Order 34263.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#6908	C₃	1	1	yes	maximal, characteristic
2	C₃×C₄₇×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#6869	C₃	1	2	yes	maximal, complemented
4	C₄₇×#737	—	3	1	no	—
5	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
6	C₄₇×#733	C₉	1	2	yes	—
7	C₄₇×#732	C₉	1	1	yes	characteristic
8	C₄₇×#731	—	3	1	no	—
9	C₄₇×AΣL(1,𝔽₂₇)	—	3	1	no	—
10	C₄₇×C₂₇⋊C₃	—	3	3	no	—
11	C₄₇×C₂₇⋊C₃	—	3	2	no	—
12	C₃×C₂₇×C₄₇	—	3	1	no	—
13	C₃³×C₄₇	3₋¹⁺²	1	1	yes	characteristic
14	3₋¹⁺²×C₄₇	—	3	2	no	—
15	3₋¹⁺²×C₄₇	—	9	1	no	—
16	3₋¹⁺²×C₄₇	—	9	1	no	—
17	H(3,𝔽₃)×C₄₇	—	3	1	no	—
18	C₃×C₉×C₄₇	—	3	1	no	—
19	C₃×C₉×C₄₇	—	3	1	no	—
20	C₃×C₉×C₄₇	—	3	1	no	—
21	C₃×C₉×C₄₇	—	9	1	no	—
22	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×C₉×C₄₇	3₋¹⁺²	1	1	yes	characteristic
25	C₂₇×C₄₇	—	3	3	no	—
26	C₂₇×C₄₇	—	9	2	no	—
27	#10624530	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₃²×C₄₇	—	3	1	no	—
29	C₃²×C₄₇	—	9	1	no	—
30	C₃²×C₄₇	—	9	1	no	—
31	C₃²×C₄₇	C₃²⋊C₉	1	1	yes	characteristic
32	C₉×C₄₇	—	3	1	no	—
33	C₉×C₄₇	—	3	1	no	—
34	C₉×C₄₇	—	9	2	no	—
35	C₉×C₄₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
36	C₉×C₄₇	#731	1	1	yes	characteristic
37	C₉×C₄₇	#732	1	1	yes	characteristic
38	#6908	C₃×C₄₇	1	1	yes	characteristic
39	C₃×C₂₇⋊C₃	C₃×C₄₇	1	1	yes	characteristic, complemented
40	#6869	C₃×C₄₇	1	2	yes	complemented
41	C₃×C₄₇	—	3	1	no	—
42	C₃×C₄₇	—	9	1	no	—
43	C₃×C₄₇	—	27	1	no	—
44	C₃×C₄₇	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
45	#737	—	3	1	no	—
46	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
47	#733	C₉×C₄₇	1	2	yes	—
48	#732	C₉×C₄₇	1	1	yes	characteristic
49	#731	—	3	1	no	—
50	AΣL(1,𝔽₂₇)	—	3	1	no	—
51	C₂₇⋊C₃	—	3	3	no	—
52	C₂₇⋊C₃	—	3	2	no	—
53	C₃×C₂₇	—	3	1	no	—
54	C₄₇	#10624530	1	1	yes	characteristic, direct product factor, Sylow
55	C₃³	3₋¹⁺²×C₄₇	1	1	yes	characteristic
56	3₋¹⁺²	—	3	2	no	—
57	3₋¹⁺²	—	9	1	no	—
58	3₋¹⁺²	—	9	1	no	—
59	H(3,𝔽₃)	—	3	1	no	—
60	C₃×C₉	—	3	1	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	3	1	no	—
63	C₃×C₉	—	9	1	no	—
64	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
65	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
66	C₃×C₉	3₋¹⁺²×C₄₇	1	1	yes	characteristic
67	C₂₇	—	3	3	no	—
68	C₂₇	—	9	2	no	—
69	C₃²	—	3	1	no	—
70	C₃²	—	9	1	no	—
71	C₃²	—	9	1	no	—
72	C₃²	C₄₇×C₃²⋊C₉	1	1	yes	characteristic
73	C₉	—	3	1	no	—
74	C₉	—	3	1	no	—
75	C₉	—	9	2	no	—
76	C₉	C₄₇×AΣL(1,𝔽₂₇)	1	1	yes	characteristic
77	C₉	C₄₇×#731	1	1	yes	characteristic
78	C₉	C₄₇×#732	1	1	yes	characteristic
79	C₃	—	3	1	no	—
80	C₃	—	9	1	no	—
81	C₃	—	27	1	no	—
82	C₃	C₄₇×H(3,𝔽₃)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉×C₄₇	#732
commutator	C₃×C₉	C₃×C₉×C₄₇
Frattini, cosocle	C₃²×C₉	C₃²×C₄₇
socle	C₃×C₄₇	H(3,𝔽₃)⋊C₉
prime radical	C₄₇×#6908	C₃
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₉×C₄₇ ◁ C₃×C₉×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₄₇×C₂₇⋊C₃	C₃	semidirect
3. C₄₇×#6869	C₃	semidirect
27. #10624530	C₄₇	direct (N × H)
39. C₃×C₂₇⋊C₃	C₃×C₄₇	semidirect
40. #6869	C₃×C₄₇	semidirect
54. C₄₇	#10624530	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#6908	3
C₃×C₄₇×C₂₇⋊C₃	3
C₄₇×#6869	3
#10624530	47

Subgroups — C47×#10624530 #46804171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624530 #46804171