Subgroups — D₉×D₁₁ #87673

Order 396.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₉₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×D₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×D₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₁₁	—	3	1	no	maximal
5	C₉×C₁₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃₃	—	3	1	no	—
7	C₃×D₁₁	D₃	1	1	yes	characteristic
8	D₃×C₁₁	—	3	1	no	—
9	C₂×D₁₁	—	9	1	no	Hall
10	C₂×D₉	—	11	1	no	maximal, Hall
11	C₃×C₁₁	C₂×D₃	1	1	yes	characteristic
12	C₂×C₁₁	—	9	1	no	—
13	D₁₁	—	9	1	no	—
14	D₁₁	D₉	1	1	yes	characteristic, direct product factor
15	C₂×C₉	—	11	1	no	—
16	D₉	—	11	1	no	—
17	D₉	D₁₁	1	1	yes	characteristic, direct product factor
18	C₂×D₃	—	33	1	no	—
19	C₁₁	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
20	C₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	11	1	no	—
22	D₃	—	3	1	no	—
23	D₃	—	33	1	no	—
24	C₂²	—	99	1	no	Sylow
25	C₃	D₃×D₁₁	1	1	yes	characteristic
26	C₂	—	9	1	no	—
27	C₂	—	11	1	no	—
28	C₂	—	99	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₁	C₂²
Frattini	C₃	D₃×D₁₁
socle	C₃×C₁₁	C₂×D₃
LCS	G ▷ C₉×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.