Subgroups — D₃×D₂₇ #66346

Order 324.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₉	—	3	1	no	maximal
5	C₂×D₂₇	—	3	1	no	maximal
6	C₃×C₂₇	C₂²	1	1	yes	characteristic, complemented, Sylow
7	C₃⋊D₉	—	3	1	no	—
8	D₃×C₉	D₃	1	1	yes	characteristic
9	C₃×D₉	—	3	1	no	—
10	C₂×C₂₇	—	3	1	no	—
11	D₂₇	—	3	1	no	—
12	D₂₇	—	6	1	no	—
13	D₂₇	D₃	1	1	yes	characteristic, direct product factor
14	D₃²	—	9	1	no	—
15	C₂×D₉	—	9	1	no	—
16	C₃×C₉	C₂×D₃	1	1	yes	characteristic
17	C₂₇	—	2	1	no	—
18	C₂₇	C₂×D₃	1	1	yes	characteristic, complemented
19	C₃⋊D₃	—	9	1	no	—
20	C₃×D₃	—	9	1	no	—
21	C₃×D₃	D₉	1	1	yes	characteristic
22	C₂×C₉	—	3	1	no	—
23	D₉	—	3	1	no	—
24	D₉	—	9	1	no	—
25	D₉	—	18	1	no	—
26	C₂×D₃	—	27	1	no	—
27	C₂×D₃	—	27	1	no	—
28	C₃²	C₂×D₉	1	1	yes	characteristic
29	C₉	—	2	1	no	—
30	C₉	D₃²	1	1	yes	characteristic
31	C₂×C₃	—	3	1	no	—
32	C₂×C₃	—	27	1	no	—
33	D₃	—	9	1	no	—
34	D₃	—	27	1	no	—
35	D₃	—	27	1	no	—
36	D₃	—	54	1	no	—
37	D₃	D₂₇	1	1	yes	characteristic, direct product factor
38	C₂²	—	81	1	no	Sylow
39	C₃	—	2	1	no	—
40	C₃	C₂×D₂₇	1	1	yes	characteristic, complemented
41	C₃	D₃×D₉	1	1	yes	characteristic
42	C₂	—	3	1	no	—
43	C₂	—	27	1	no	—
44	C₂	—	81	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₂₇	C₂²
Frattini	C₉	D₃²
socle	C₃²	C₂×D₉
LCS	G ▷ C₃×C₂₇
UCS	C₁

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

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