Subgroups — D₃×C₉×C₂₇ #13090853

Order 1458.

209 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×D₃×C₂₇	C₃	1	3	yes	maximal
3	D₃×C₉²	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₂₇	—	3	1	no	maximal
5	C₃²×C₂₇	C₂×C₃	1	3	yes	—
6	C₃×C₉²	C₂×C₃	1	1	yes	characteristic
7	C₉×C₂₇	—	2	3	no	—
8	C₉×C₂₇	—	2	1	no	—
9	C₉×C₂₇	D₃	1	1	yes	characteristic, direct product factor
10	C₃×D₃×C₉	C₉	1	3	yes	—
11	C₃×D₃×C₉	C₃²	1	1	yes	characteristic
12	C₂×C₃×C₂₇	—	3	3	no	—
13	C₂×C₉²	—	3	1	no	—
14	D₃×C₂₇	C₉	1	9	yes	direct product factor
15	C₃²×C₉	C₂×C₉	1	3	yes	—
16	C₃²×C₉	C₂×C₃²	1	1	yes	characteristic
17	C₃×C₂₇	—	2	3	no	—
18	C₃×C₂₇	—	2	9	no	—
19	C₃×C₂₇	C₂×C₉	1	9	yes	complemented
20	C₃×C₂₇	C₃×D₃	1	3	yes	—
21	C₉²	—	2	3	no	—
22	C₉²	—	2	1	no	—
23	C₉²	C₃×D₃	1	1	yes	characteristic
24	C₃²×D₃	C₃×C₉	1	1	yes	characteristic
25	C₂×C₃×C₉	—	3	3	no	—
26	C₂×C₃×C₉	—	3	1	no	—
27	D₃×C₉	C₂₇	1	9	yes	direct product factor
28	D₃×C₉	C₃×C₉	1	3	yes	—
29	C₂×C₂₇	—	3	9	no	—
30	C₃³	C₂×C₃×C₉	1	1	yes	characteristic
31	C₃×C₉	—	2	3	no	—
32	C₃×C₉	—	2	1	no	—
33	C₃×C₉	—	2	9	no	—
34	C₃×C₉	—	2	3	no	—
35	C₃×C₉	C₂×C₂₇	1	9	yes	complemented
36	C₃×C₉	D₃×C₉	1	3	yes	—
37	C₃×C₉	C₂×C₃×C₉	1	3	yes	—
38	C₃×C₉	C₃²×D₃	1	1	yes	characteristic
39	C₂₇	—	2	9	no	—
40	C₂₇	D₃×C₉	1	9	yes	direct product factor
41	C₂×C₃²	—	3	1	no	—
42	C₃×D₃	C₉²	1	1	yes	characteristic
43	C₃×D₃	C₃×C₂₇	1	3	yes	—
44	C₂×C₉	—	3	9	no	—
45	C₂×C₉	—	3	3	no	—
46	C₃²	—	2	1	no	—
47	C₃²	—	2	3	no	—
48	C₃²	C₂×C₉²	1	1	yes	characteristic
49	C₃²	C₂×C₃×C₂₇	1	3	yes	—
50	C₃²	C₃×D₃×C₉	1	1	yes	characteristic
51	C₉	—	2	3	no	—
52	C₉	—	2	9	no	—
53	C₉	D₃×C₂₇	1	9	yes	direct product factor
54	C₉	C₃×D₃×C₉	1	3	yes	—
55	C₂×C₃	—	3	1	no	—
56	C₂×C₃	—	3	3	no	—
57	D₃	C₉×C₂₇	1	1	yes	characteristic, direct product factor
58	C₃	—	2	1	no	—
59	C₃	—	2	3	no	—
60	C₃	C₂×C₉×C₂₇	1	1	yes	characteristic, complemented
61	C₃	D₃×C₉²	1	1	yes	characteristic
62	C₃	C₃×D₃×C₂₇	1	3	yes	—
63	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉×C₂₇	D₃
commutator, hypocenter	C₃	C₂×C₉×C₂₇
Frattini	C₃×C₉	C₃²×D₃
Fitting	C₃×C₉×C₂₇	C₂
socle	C₃³	C₂×C₃×C₉
prime radical	C₃²×D₃	C₃×C₉
cosocle	C₃²×C₉	C₂×C₃²
LCS	G ▷ C₃
UCS	C₁ ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₂₇	C₂	semidirect
9. C₉×C₂₇	D₃	direct (N × H)
14. D₃×C₂₇	C₉	direct (N × H)
19. C₃×C₂₇	C₂×C₉	semidirect
27. D₃×C₉	C₂₇	direct (N × H)
35. C₃×C₉	C₂×C₂₇	semidirect
40. C₂₇	D₃×C₉	direct (N × H)
53. C₉	D₃×C₂₇	direct (N × H)
57. D₃	C₉×C₂₇	direct (N × H)
60. C₃	C₂×C₉×C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₂₇	2
C₃×D₃×C₂₇	3
D₃×C₉²	3
C₂×C₉×C₂₇	3

Subgroups — D3×C9×C27 #13090853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₉×C₂₇ #13090853