Subgroups — C₂×C₃²×D₁₁ #87693

Order 396.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×D₁₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₁₁	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₁	C₂×C₃	1	4	yes	complemented
6	C₃×D₁₁	C₂×C₃	1	8	yes	direct product factor
7	C₂×D₁₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₃²	—	11	1	no	maximal, Hall
9	C₃×C₁₁	C₂²×C₃	1	4	yes	complemented
10	C₂×C₁₁	C₂×C₃²	1	1	yes	characteristic, complemented
11	D₁₁	C₂×C₃²	1	2	yes	direct product factor
12	C₂×C₃²	—	11	2	no	—
13	C₂×C₃²	D₁₁	1	1	yes	characteristic, direct product factor
14	C₂²×C₃	—	11	4	no	—
15	C₁₁	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
16	C₃²	C₂×D₁₁	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₃	—	11	8	no	—
18	C₂×C₃	C₃×D₁₁	1	4	yes	direct product factor
19	C₂²	—	11	1	no	Sylow
20	C₃	C₂×C₃×D₁₁	1	4	yes	direct product factor
21	C₂	—	11	2	no	—
22	C₂	C₃²×D₁₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃²

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.