Subgroups — D₃×C₂₇⋊C₃ #92269

Order 486.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₇⋊C₃	C₂	semidirect
4. D₃×C₂₇	C₃	semidirect
8. C₂₇⋊C₃	D₃	direct (N × H)
9. C₃×C₂₇	C₂×C₃	semidirect
23. C₂₇	C₃×D₃	semidirect
40. D₃	C₂₇⋊C₃	direct (N × H)
44. C₃	C₂×C₂₇⋊C₃	semidirect

Maximal subgroups

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

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

Subgroups — D3×C27⋊C3 #92269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₂₇⋊C₃ #92269