Subgroups — C₄₇×#10624468 #46804109

Order 34263.

164 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₇×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₃²×C₂₇×C₄₇	C₃	1	1	yes	maximal, characteristic
3	C₄₇×#6887	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
5	C₄₇×C₂₇⋊C₃	—	3	4	no	—
6	C₄₇×C₂₇⋊C₃	C₉	1	6	yes	complemented
7	C₃×C₂₇×C₄₇	—	3	1	no	—
8	C₃×C₂₇×C₄₇	—	3	2	no	—
9	C₃×C₂₇×C₄₇	—	3	2	no	—
10	C₃×C₂₇×C₄₇	C₉	1	3	yes	complemented
11	C₄₇×C₉⋊C₉	—	3	2	no	—
12	C₄₇×C₃²⋊C₉	C₉	1	3	yes	—
13	C₉²×C₄₇	—	3	1	no	—
14	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
15	C₃×C₉×C₄₇	—	3	3	no	—
16	C₃×C₉×C₄₇	C₃×C₉	1	1	yes	characteristic
17	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×C₉×C₄₇	3₋¹⁺²	1	2	yes	—
20	C₃×C₉×C₄₇	3₋¹⁺²	1	4	yes	—
21	C₃×C₉×C₄₇	3₋¹⁺²	1	2	yes	—
22	C₂₇×C₄₇	—	3	3	no	—
23	C₂₇×C₄₇	—	3	6	no	—
24	#10624468	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃²×C₄₇	—	3	3	no	—
26	C₃²×C₄₇	C₉²	1	1	yes	characteristic
27	C₃²×C₄₇	C₃²⋊C₉	1	1	yes	characteristic
28	C₃²×C₄₇	C₉⋊C₉	1	2	yes	—
29	C₉×C₄₇	—	9	3	no	—
30	C₉×C₄₇	C₃²⋊C₉	1	1	yes	characteristic
31	C₉×C₄₇	C₃²⋊C₉	1	2	yes	—
32	C₉×C₄₇	C₉⋊C₉	1	2	yes	—
33	C₉×C₄₇	C₉⋊C₉	1	4	yes	—
34	C₃×C₂₇⋊C₃	C₃×C₄₇	1	2	yes	—
35	C₃²×C₂₇	C₃×C₄₇	1	1	yes	characteristic
36	#6887	C₃×C₄₇	1	1	yes	characteristic
37	C₃×C₄₇	—	3	1	no	—
38	C₃×C₄₇	—	3	2	no	—
39	C₃×C₄₇	#6855	1	1	yes	characteristic
40	C₃×C₄₇	#6873	1	3	yes	—
41	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
42	C₂₇⋊C₃	—	3	4	no	—
43	C₂₇⋊C₃	C₉×C₄₇	1	6	yes	complemented
44	C₃×C₂₇	—	3	1	no	—
45	C₃×C₂₇	—	3	2	no	—
46	C₃×C₂₇	—	3	2	no	—
47	C₃×C₂₇	C₉×C₄₇	1	3	yes	complemented
48	C₉⋊C₉	—	3	2	no	—
49	C₃²⋊C₉	C₉×C₄₇	1	3	yes	—
50	C₉²	—	3	1	no	—
51	C₄₇	#10624468	1	1	yes	characteristic, direct product factor, Sylow
52	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
53	C₃×C₉	—	3	3	no	—
54	C₃×C₉	C₃×C₉×C₄₇	1	1	yes	characteristic
55	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
56	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
57	C₃×C₉	3₋¹⁺²×C₄₇	1	2	yes	—
58	C₃×C₉	3₋¹⁺²×C₄₇	1	4	yes	—
59	C₃×C₉	3₋¹⁺²×C₄₇	1	2	yes	—
60	C₂₇	—	3	3	no	—
61	C₂₇	—	3	6	no	—
62	C₃²	—	3	3	no	—
63	C₃²	C₉²×C₄₇	1	1	yes	characteristic
64	C₃²	C₄₇×C₃²⋊C₉	1	1	yes	characteristic
65	C₃²	C₄₇×C₉⋊C₉	1	2	yes	—
66	C₉	—	9	3	no	—
67	C₉	C₄₇×C₃²⋊C₉	1	1	yes	characteristic
68	C₉	C₄₇×C₃²⋊C₉	1	2	yes	—
69	C₉	C₄₇×C₉⋊C₉	1	2	yes	—
70	C₉	C₄₇×C₉⋊C₉	1	4	yes	—
71	C₃	—	3	1	no	—
72	C₃	—	3	2	no	—
73	C₃	C₄₇×#6855	1	1	yes	characteristic
74	C₃	C₄₇×#6873	1	3	yes	—

	subgroup	G/H
center	C₃×C₉×C₄₇	H(3,𝔽₃)
commutator	C₃²	C₉²×C₄₇
Frattini, cosocle	C₃²×C₉	C₃²×C₄₇
socle	C₃²×C₄₇	C₃²⋊C₉
prime radical	C₃³×C₄₇	C₃×C₉
LCS	G ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₉×C₄₇ ◁ C₃²×C₉×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄₇×C₂₇⋊C₃	C₉	semidirect
10. C₃×C₂₇×C₄₇	C₉	semidirect
24. #10624468	C₄₇	direct (N × H)
43. C₂₇⋊C₃	C₉×C₄₇	semidirect
47. C₃×C₂₇	C₉×C₄₇	semidirect
51. C₄₇	#10624468	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×C₂₇⋊C₃	3
C₃²×C₂₇×C₄₇	3
C₄₇×#6887	3
#10624468	47

Subgroups — C47×#10624468 #46804109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624468 #46804109