Subgroups — C₃×D₂₇⋊C₃ #92268

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	C₃²×D₉	—	3	1	no	maximal
3	D₂₇⋊C₃	C₃	1	3	yes	maximal, direct product factor
4	C₃×D₂₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₉	D₃	1	1	yes	characteristic
6	C₂₇⋊C₃	—	2	3	no	—
7	C₂₇⋊C₃	C₂×C₃	1	3	yes	complemented
8	C₃×C₂₇	—	2	1	no	—
9	C₃×C₂₇	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃²×D₃	—	9	1	no	—
11	C₃×D₉	—	3	1	no	—
12	C₃×D₉	—	3	3	no	—
13	D₂₇	C₃²	1	1	yes	characteristic, complemented
14	C₃³	D₉	1	1	yes	characteristic
15	C₃×C₉	—	2	1	no	—
16	C₃×C₉	—	2	3	no	—
17	C₃×C₉	C₃×D₃	1	1	yes	characteristic
18	C₃×C₉	C₃×D₃	1	3	yes	—
19	C₂₇	—	2	3	no	—
20	C₂₇	—	2	1	no	—
21	C₂₇	C₂×C₃²	1	1	yes	characteristic, complemented
22	C₂×C₃²	—	27	1	no	—
23	C₃×D₃	—	9	3	no	—
24	C₃×D₃	—	9	1	no	—
25	D₉	—	3	1	no	—
26	C₃²	—	3	1	no	—
27	C₃²	—	6	1	no	—
28	C₃²	C₃×D₉	1	1	yes	characteristic
29	C₃²	C₃×D₉	1	3	yes	—
30	C₉	—	2	1	no	—
31	C₉	—	2	3	no	—
32	C₉	C₃²×D₃	1	1	yes	characteristic
33	C₂×C₃	—	27	3	no	—
34	C₂×C₃	—	27	1	no	—
35	D₃	—	9	1	no	—
36	C₃	—	2	1	no	—
37	C₃	—	3	3	no	—
38	C₃	D₂₇⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃	C₃²×D₉	1	1	yes	characteristic
40	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₂₇⋊C₃
commutator, cosocle, hypocenter	C₂₇	C₂×C₃²
Frattini	C₉	C₃²×D₃
Fitting	C₃×C₂₇⋊C₃	C₂
socle	C₃²	C₃×D₉
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₃

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.