Subgroups — C₄₇×#10624681 #46804322

Order 34263.

290 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	C₄₇×#6864	C₃	1	6	yes	maximal, complemented
5	C₉×C₂₇×C₄₇	C₃	1	3	yes	maximal, complemented
6	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
7	C₄₇×C₂₇⋊C₃	C₉	1	18	yes	complemented
8	C₃×C₂₇×C₄₇	C₉	1	9	yes	complemented
9	C₃×C₂₇×C₄₇	C₃²	1	6	yes	—
10	C₃×C₂₇×C₄₇	C₃²	1	2	yes	—
11	C₃×C₂₇×C₄₇	C₃²	1	1	yes	characteristic
12	C₄₇×C₉⋊C₉	C₉	1	6	yes	—
13	C₄₇×C₃²⋊C₉	C₉	1	3	yes	—
14	C₉²×C₄₇	C₃²	1	3	yes	—
15	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₄₇	C₃×C₉	1	9	yes	—
17	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
18	C₃×C₉×C₄₇	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₄₇	C₃×C₉	1	6	yes	—
20	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
21	C₂₇×C₄₇	C₃×C₉	1	6	yes	—
22	C₂₇×C₄₇	C₃×C₉	1	3	yes	—
23	C₂₇×C₄₇	C₃×C₉	1	18	yes	—
24	#10624681	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₃²×C₄₇	—	3	3	no	—
26	C₃²×C₄₇	C₉²	1	3	yes	—
27	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₄₇	—	3	9	no	—
29	C₉×C₄₇	C₉²	1	6	yes	—
30	C₉×C₄₇	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₄₇	C₃²×C₉	1	2	yes	—
32	C₃×C₂₇⋊C₃	C₃×C₄₇	1	2	yes	—
33	C₃²×C₂₇	C₃×C₄₇	1	1	yes	characteristic
34	#6887	C₃×C₄₇	1	1	yes	characteristic
35	#6864	C₃×C₄₇	1	6	yes	complemented
36	C₉×C₂₇	C₃×C₄₇	1	3	yes	complemented
37	C₃×C₄₇	—	3	3	no	—
38	C₃×C₄₇	C₃×C₉²	1	1	yes	characteristic
39	C₃×C₄₇	#6903	1	3	yes	—
40	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
41	C₂₇⋊C₃	C₉×C₄₇	1	18	yes	complemented
42	C₃×C₂₇	C₉×C₄₇	1	9	yes	complemented
43	C₃×C₂₇	C₃²×C₄₇	1	6	yes	—
44	C₃×C₂₇	C₃²×C₄₇	1	2	yes	—
45	C₃×C₂₇	C₃²×C₄₇	1	1	yes	characteristic
46	C₉⋊C₉	C₉×C₄₇	1	6	yes	—
47	C₃²⋊C₉	C₉×C₄₇	1	3	yes	—
48	C₉²	C₃²×C₄₇	1	3	yes	—
49	C₄₇	#10624681	1	1	yes	characteristic, direct product factor, Sylow
50	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
51	C₃×C₉	C₃×C₉×C₄₇	1	9	yes	—
52	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
53	C₃×C₉	C₃×C₉×C₄₇	1	3	yes	—
54	C₃×C₉	C₃×C₉×C₄₇	1	6	yes	—
55	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
56	C₂₇	C₃×C₉×C₄₇	1	6	yes	—
57	C₂₇	C₃×C₉×C₄₇	1	3	yes	—
58	C₂₇	C₃×C₉×C₄₇	1	18	yes	—
59	C₃²	—	3	3	no	—
60	C₃²	C₉²×C₄₇	1	3	yes	—
61	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
62	C₉	—	3	9	no	—
63	C₉	C₉²×C₄₇	1	6	yes	—
64	C₉	C₃²×C₉×C₄₇	1	1	yes	characteristic
65	C₉	C₃²×C₉×C₄₇	1	2	yes	—
66	C₃	—	3	3	no	—
67	C₃	C₃×C₉²×C₄₇	1	1	yes	characteristic
68	C₃	C₄₇×#6903	1	3	yes	—

	subgroup	G/H
center	C₃×C₂₇×C₄₇	C₃²
commutator	C₃	C₃×C₉²×C₄₇
Frattini, cosocle	C₃×C₉	C₃³×C₄₇
socle	C₃²×C₄₇	C₃²×C₉
prime radical	C₃³×C₄₇	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₂₇×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₇×#6864	C₃	semidirect
5. C₉×C₂₇×C₄₇	C₃	semidirect
7. C₄₇×C₂₇⋊C₃	C₉	semidirect
8. C₃×C₂₇×C₄₇	C₉	semidirect
24. #10624681	C₄₇	direct (N × H)
35. #6864	C₃×C₄₇	semidirect
36. C₉×C₂₇	C₃×C₄₇	semidirect
41. C₂₇⋊C₃	C₉×C₄₇	semidirect
42. C₃×C₂₇	C₉×C₄₇	semidirect
49. C₄₇	#10624681	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
C₄₇×#6864	3
C₉×C₂₇×C₄₇	3
#10624681	47

Subgroups — C47×#10624681 #46804322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10624681 #46804322