Subgroups — C₃⋊D₃×D₁₁ #87688

Order 396.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₁	—	3	4	no	maximal
5	C₃²×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₃	—	3	4	no	—
7	C₃×D₁₁	D₃	1	4	yes	complemented
8	D₃×C₁₁	—	3	4	no	—
9	C₂×D₁₁	—	9	1	no	Hall
10	C₂×C₃⋊D₃	—	11	1	no	maximal, Hall
11	C₃×C₁₁	C₂×D₃	1	4	yes	complemented
12	C₂×C₁₁	—	9	1	no	—
13	D₁₁	—	9	1	no	—
14	D₁₁	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₃²	—	11	1	no	—
16	C₃⋊D₃	—	11	1	no	—
17	C₃⋊D₃	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×D₃	—	33	4	no	—
19	C₁₁	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
20	C₃²	C₂×D₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	11	4	no	—
22	D₃	—	3	4	no	—
23	D₃	—	33	4	no	—
24	C₂²	—	99	1	no	Sylow
25	C₃	D₃×D₁₁	1	4	yes	complemented
26	C₂	—	9	1	no	—
27	C₂	—	11	1	no	—
28	C₂	—	99	1	no	—

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