Subgroups — C₄₇×#10624516 #46804157

Order 34263.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₄₇×#6869	C₃	1	3	yes	maximal
3	C₃²×C₉×C₄₇	—	3	1	no	—
4	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
5	C₄₇×C₂₇⋊C₃	—	3	3	no	—
6	C₄₇×C₉⋊C₉	—	3	1	no	—
7	C₄₇×C₉⋊C₉	—	3	1	no	—
8	C₄₇×C₉⋊C₉	C₉	1	3	yes	—
9	C₃³×C₄₇	3₋¹⁺²	1	1	yes	characteristic
10	C₃×C₉×C₄₇	—	3	3	no	—
11	C₃×C₉×C₄₇	—	3	3	no	—
12	C₃×C₉×C₄₇	—	9	3	no	—
13	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
14	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₄₇	3₋¹⁺²	1	1	yes	characteristic
16	C₂₇×C₄₇	—	9	3	no	—
17	#10624516	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃²×C₄₇	—	3	3	no	—
19	C₃²×C₄₇	—	3	1	no	—
20	C₃²×C₄₇	C₃²⋊C₉	1	1	yes	characteristic
21	C₉×C₄₇	—	3	1	no	—
22	C₉×C₄₇	—	3	1	no	—
23	C₉×C₄₇	—	9	3	no	—
24	C₉×C₄₇	#731	1	3	yes	—
25	C₃×C₉⋊C₉	C₃×C₄₇	1	1	yes	characteristic
26	#6869	C₃×C₄₇	1	3	yes	—
27	C₃×C₄₇	—	3	1	no	—
28	C₃×C₄₇	—	3	3	no	—
29	C₃×C₄₇	#6867	1	1	yes	characteristic
30	C₃²×C₉	—	3	1	no	—
31	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
32	C₂₇⋊C₃	—	3	3	no	—
33	C₉⋊C₉	—	3	1	no	—
34	C₉⋊C₉	—	3	1	no	—
35	C₉⋊C₉	C₉×C₄₇	1	3	yes	—
36	C₄₇	#10624516	1	1	yes	characteristic, direct product factor, Sylow
37	C₃³	3₋¹⁺²×C₄₇	1	1	yes	characteristic
38	C₃×C₉	—	3	3	no	—
39	C₃×C₉	—	3	3	no	—
40	C₃×C₉	—	9	3	no	—
41	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
42	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
43	C₃×C₉	3₋¹⁺²×C₄₇	1	1	yes	characteristic
44	C₂₇	—	9	3	no	—
45	C₃²	—	3	3	no	—
46	C₃²	—	3	1	no	—
47	C₃²	C₄₇×C₃²⋊C₉	1	1	yes	characteristic
48	C₉	—	3	1	no	—
49	C₉	—	3	1	no	—
50	C₉	—	9	3	no	—
51	C₉	C₄₇×#731	1	3	yes	—
52	C₃	—	3	1	no	—
53	C₃	—	3	3	no	—
54	C₃	C₄₇×#6867	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₄₇	#6867
commutator	C₃×C₉	C₃×C₉×C₄₇
Frattini, cosocle	C₃²×C₉	C₃²×C₄₇
prime radical	C₃³×C₄₇	3₋¹⁺²
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₇ ◁ C₃×C₉×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
17. #10624516	C₄₇	direct (N × H)
36. C₄₇	#10624516	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×C₄₇×C₉⋊C₉	3
C₄₇×#6869	3
#10624516	47

Subgroups — C47×#10624516 #46804157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624516 #46804157