Subgroups — C₄₇×#10624495 #46804136

Order 34263.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#6868	C₃	1	2	yes	maximal
2	C₄₇×#6868	C₃	1	1	yes	maximal, characteristic
3	C₄₇×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉×C₄₇	—	3	1	no	—
5	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
6	C₄₇×C₃²⋊C₉	—	3	2	no	—
7	C₄₇×C₃²⋊C₉	—	3	1	no	—
8	C₃³×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉×C₄₇	—	3	3	no	—
10	C₃×C₉×C₄₇	—	3	1	no	—
11	C₃×C₉×C₄₇	—	3	1	no	—
12	C₃×C₉×C₄₇	—	3	2	no	—
13	C₃×C₉×C₄₇	—	9	1	no	—
14	C₃×C₉×C₄₇	—	9	1	no	—
15	C₃×C₉×C₄₇	—	9	1	no	—
16	C₃×C₉×C₄₇	—	9	2	no	—
17	C₃×C₉×C₄₇	—	9	1	no	—
18	#10624495	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₃²×C₄₇	—	3	1	no	—
20	C₃²×C₄₇	—	3	1	no	—
21	C₃²×C₄₇	—	3	1	no	—
22	C₃²×C₄₇	#731	1	1	yes	characteristic
23	C₃²×C₄₇	#732	1	1	yes	characteristic
24	C₃²×C₄₇	#733	1	2	yes	—
25	C₉×C₄₇	—	9	3	no	—
26	C₉×C₄₇	—	9	1	no	—
27	C₉×C₄₇	—	27	2	no	—
28	C₉×C₄₇	—	27	1	no	—
29	#6868	C₃×C₄₇	1	2	yes	—
30	#6868	C₃×C₄₇	1	1	yes	characteristic
31	#6855	C₃×C₄₇	1	1	yes	characteristic
32	C₃×C₄₇	—	3	1	no	—
33	C₃×C₄₇	—	3	2	no	—
34	C₃×C₄₇	#6861	1	1	yes	characteristic
35	C₃×C₄₇	#6880	1	1	yes	characteristic
36	C₃×C₄₇	#6881	1	1	yes	characteristic
37	C₃×C₄₇	#6883	1	1	yes	characteristic
38	C₃²×C₉	—	3	1	no	—
39	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
40	C₃²⋊C₉	—	3	2	no	—
41	C₃²⋊C₉	—	3	1	no	—
42	C₄₇	#10624495	1	1	yes	characteristic, direct product factor, Sylow
43	C₃³	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
44	C₃×C₉	—	3	3	no	—
45	C₃×C₉	—	3	1	no	—
46	C₃×C₉	—	3	1	no	—
47	C₃×C₉	—	3	2	no	—
48	C₃×C₉	—	9	1	no	—
49	C₃×C₉	—	9	1	no	—
50	C₃×C₉	—	9	1	no	—
51	C₃×C₉	—	9	2	no	—
52	C₃×C₉	—	9	1	no	—
53	C₃²	—	3	1	no	—
54	C₃²	—	3	1	no	—
55	C₃²	—	3	1	no	—
56	C₃²	C₄₇×#731	1	1	yes	characteristic
57	C₃²	C₄₇×#732	1	1	yes	characteristic
58	C₃²	C₄₇×#733	1	2	yes	—
59	C₉	—	9	3	no	—
60	C₉	—	9	1	no	—
61	C₉	—	27	2	no	—
62	C₉	—	27	1	no	—
63	C₃	—	3	1	no	—
64	C₃	—	3	2	no	—
65	C₃	C₄₇×#6861	1	1	yes	characteristic
66	C₃	C₄₇×#6880	1	1	yes	characteristic
67	C₃	C₄₇×#6881	1	1	yes	characteristic
68	C₃	C₄₇×#6883	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₄₇	#732
commutator, Frattini, cosocle	C₃²×C₉	C₃²×C₄₇
prime radical	C₃³×C₄₇	H(3,𝔽₃)
LCS	G ▷ C₃²×C₉ ▷ C₃³ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ C₃³×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
18. #10624495	C₄₇	direct (N × H)
42. C₄₇	#10624495	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×#6868	3
C₄₇×#6855	3
#10624495	47

Subgroups — C47×#10624495 #46804136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624495 #46804136