Subgroups — C₂×C₁₁×D₉ #87676

Order 396.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₁	—	3	1	no	maximal
4	C₉×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁	D₃	1	1	yes	characteristic
6	D₃×C₁₁	—	3	2	no	—
7	C₂²×C₁₁	—	9	1	no	Hall
8	C₂×D₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₁₁	C₂×D₃	1	1	yes	characteristic
10	C₂×C₁₁	—	9	2	no	—
11	C₂×C₁₁	D₉	1	1	yes	characteristic, direct product factor
12	C₂×C₉	C₂×C₁₁	1	1	yes	characteristic, complemented
13	D₉	C₂×C₁₁	1	2	yes	direct product factor
14	C₂×D₃	—	3	1	no	—
15	C₁₁	C₂×D₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₉	C₂²×C₁₁	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	D₃×C₁₁	1	1	yes	characteristic
18	D₃	—	3	2	no	—
19	C₂²	—	9	1	no	Sylow
20	C₃	C₂×D₃×C₁₁	1	1	yes	characteristic
21	C₂	—	9	2	no	—
22	C₂	C₁₁×D₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₉
commutator, cosocle, hypocenter	C₉	C₂²×C₁₁
Frattini	C₃	C₂×D₃×C₁₁
Fitting	C₂×C₉×C₁₁	C₂
socle	C₂×C₃×C₁₁	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₁

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.