Subgroups — C₃⋊D₆₃ #67389

Order 378.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊D₂₁	—	3	1	no	maximal
3	D₆₃	—	3	3	no	maximal
4	C₃²×C₇	D₃	1	1	yes	characteristic
5	C₇×C₉	D₃	1	3	yes	complemented
6	C₃⋊D₉	—	7	1	no	maximal, Hall
7	D₂₁	—	9	3	no	—
8	D₂₁	—	9	1	no	—
9	C₃×C₉	D₇	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₇	D₉	1	3	yes	complemented
11	C₃×C₇	C₃⋊D₃	1	1	yes	characteristic
12	C₃⋊D₃	—	21	1	no	—
13	D₉	—	21	3	no	—
14	D₇	—	27	1	no	Hall
15	C₃²	D₂₁	1	1	yes	characteristic
16	C₉	D₂₁	1	3	yes	complemented
17	C₇	C₃⋊D₉	1	1	yes	characteristic, complemented, Sylow
18	D₃	—	63	3	no	—
19	D₃	—	63	1	no	—
20	C₃	D₆₃	1	3	yes	complemented
21	C₃	C₃⋊D₂₁	1	1	yes	characteristic
22	C₂	—	189	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₇×C₉	C₂
Frattini	C₃	C₃⋊D₂₁
socle	C₃²×C₇	D₃
LCS	G ▷ C₃×C₇×C₉
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.