Subgroups — C₃×C₄₇×#6864 #46804320

Order 34263.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇×C₄₇	C₃	1	3	yes	maximal
2	C₃×C₉²×C₄₇	C₃	1	1	yes	maximal, characteristic
3	C₄₇×#6864	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉×C₄₇	C₉	1	3	yes	—
5	C₃²×C₉×C₄₇	C₃²	1	1	yes	characteristic
6	C₃×C₂₇×C₄₇	C₉	1	27	yes	complemented
7	C₃×C₂₇×C₄₇	C₃²	1	9	yes	—
8	C₉²×C₄₇	C₉	1	6	yes	—
9	C₉²×C₄₇	C₃²	1	3	yes	—
10	C₃³×C₄₇	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₄₇	—	3	9	no	—
12	C₃×C₉×C₄₇	C₃×C₉	1	9	yes	—
13	C₃×C₉×C₄₇	C₃×C₉	1	2	yes	—
14	C₃×C₉×C₄₇	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₄₇	C₃³	1	1	yes	characteristic
16	C₂₇×C₄₇	C₃×C₉	1	27	yes	complemented
17	C₃×#6864	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₃²×C₄₇	C₉²	1	3	yes	—
19	C₃²×C₄₇	C₂₇⋊C₃	1	9	yes	—
20	C₃²×C₄₇	C₃²×C₉	1	1	yes	characteristic
21	C₉×C₄₇	—	3	9	no	—
22	C₉×C₄₇	C₉²	1	6	yes	—
23	C₉×C₄₇	C₃²×C₉	1	3	yes	—
24	C₃²×C₂₇	C₃×C₄₇	1	3	yes	—
25	C₃×C₉²	C₃×C₄₇	1	1	yes	characteristic
26	#6864	C₃×C₄₇	1	9	yes	direct product factor
27	C₃×C₄₇	#6864	1	9	yes	direct product factor
28	C₃×C₄₇	C₃×C₉²	1	1	yes	characteristic
29	C₃×C₄₇	C₃×C₂₇⋊C₃	1	3	yes	—
30	C₃²×C₉	C₉×C₄₇	1	3	yes	—
31	C₃²×C₉	C₃²×C₄₇	1	1	yes	characteristic
32	C₃×C₂₇	C₉×C₄₇	1	27	yes	complemented
33	C₃×C₂₇	C₃²×C₄₇	1	9	yes	—
34	C₉²	C₉×C₄₇	1	6	yes	—
35	C₉²	C₃²×C₄₇	1	3	yes	—
36	C₄₇	C₃×#6864	1	1	yes	characteristic, direct product factor, Sylow
37	C₃³	C₃×C₉×C₄₇	1	1	yes	characteristic
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	C₃×C₉×C₄₇	1	9	yes	—
40	C₃×C₉	C₃×C₉×C₄₇	1	2	yes	—
41	C₃×C₉	C₃×C₉×C₄₇	1	9	yes	—
42	C₃×C₉	C₃³×C₄₇	1	1	yes	characteristic
43	C₂₇	C₃×C₉×C₄₇	1	27	yes	complemented
44	C₃²	C₉²×C₄₇	1	3	yes	—
45	C₃²	C₄₇×C₂₇⋊C₃	1	9	yes	—
46	C₃²	C₃²×C₉×C₄₇	1	1	yes	characteristic
47	C₉	—	3	9	no	—
48	C₉	C₉²×C₄₇	1	6	yes	—
49	C₉	C₃²×C₉×C₄₇	1	3	yes	—
50	C₃	C₄₇×#6864	1	9	yes	direct product factor
51	C₃	C₃×C₉²×C₄₇	1	1	yes	characteristic
52	C₃	C₃×C₄₇×C₂₇⋊C₃	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₄₇×#6864	C₃	direct (N × H)
6. C₃×C₂₇×C₄₇	C₉	semidirect
16. C₂₇×C₄₇	C₃×C₉	semidirect
17. C₃×#6864	C₄₇	direct (N × H)
26. #6864	C₃×C₄₇	direct (N × H)
27. C₃×C₄₇	#6864	direct (N × H)
32. C₃×C₂₇	C₉×C₄₇	semidirect
36. C₄₇	C₃×#6864	direct (N × H)
43. C₂₇	C₃×C₉×C₄₇	semidirect
50. C₃	C₄₇×#6864	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₇×C₄₇	3
C₃×C₉²×C₄₇	3
C₄₇×#6864	3
C₃×#6864	47

Subgroups — C3×C47×#6864 #46804320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₇×#6864 #46804320