Subgroups — C₉×C₄₇×C₂₇⋊C₃ #46804321

Order 34263.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₉²×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 ◁ C₉²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₇×#6864	C₃	semidirect
4. C₉×C₂₇×C₄₇	C₃	semidirect
7. C₄₇×C₂₇⋊C₃	C₉	direct (N × H)
19. C₂₇×C₄₇	C₃×C₉	semidirect
20. C₉×C₂₇⋊C₃	C₄₇	direct (N × H)
26. C₉×C₄₇	C₂₇⋊C₃	direct (N × H)
30. #6864	C₃×C₄₇	semidirect
31. C₉×C₂₇	C₃×C₄₇	semidirect
37. C₂₇⋊C₃	C₉×C₄₇	direct (N × H)
42. C₄₇	C₉×C₂₇⋊C₃	direct (N × H)
50. C₂₇	C₃×C₉×C₄₇	semidirect
56. C₉	C₄₇×C₂₇⋊C₃	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
C₃×C₉²×C₄₇	3
C₄₇×#6864	3
C₉×C₂₇×C₄₇	3
C₉×C₂₇⋊C₃	47

Subgroups — C9×C47×C27⋊C3 #46804321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₄₇×C₂₇⋊C₃ #46804321