Subgroups — C₂×C₃⋊D₂₁ #7006

Order 252.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₁	—	3	4	no	maximal
4	C₃²×C₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₇	D₃	1	4	yes	complemented
6	D₂₁	—	3	8	no	—
7	C₂×C₃⋊D₃	—	7	1	no	maximal, Hall
8	C₂×D₇	—	9	1	no	Hall
9	C₃×C₇	C₂×D₃	1	4	yes	complemented
10	C₂×C₃²	D₇	1	1	yes	characteristic, complemented
11	C₃⋊D₃	—	7	2	no	—
12	C₂×C₇	C₃⋊D₃	1	1	yes	characteristic, complemented
13	D₇	—	9	2	no	—
14	C₂×D₃	—	21	4	no	—
15	C₃²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
16	C₇	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₃	D₂₁	1	4	yes	complemented
18	D₃	—	21	8	no	—
19	C₂²	—	63	1	no	Sylow
20	C₃	C₂×D₂₁	1	4	yes	complemented
21	C₂	—	63	2	no	—
22	C₂	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂

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.