Subgroups — C₃²×D₂₁ #67402

Order 378.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₁	C₃	1	4	yes	maximal, direct product factor
3	C₃²×D₇	—	3	1	no	maximal
4	C₃²×C₇	—	2	4	no	—
5	C₃²×C₇	D₃	1	1	yes	characteristic, complemented
6	C₃²×C₇	C₂×C₃	1	4	yes	complemented
7	C₃²×D₃	—	7	1	no	maximal, Hall
8	D₂₁	C₃²	1	1	yes	characteristic, direct product factor
9	C₃×D₇	—	3	4	no	—
10	C₃³	D₇	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₇	—	2	4	no	—
12	C₃×C₇	C₃×D₃	1	4	yes	complemented
13	C₃×C₇	C₂×C₃²	1	1	yes	characteristic, complemented
14	C₂×C₃²	—	21	1	no	—
15	C₃×D₃	—	7	4	no	—
16	D₇	—	3	1	no	Hall
17	C₃²	—	2	4	no	—
18	C₃²	C₃×D₇	1	4	yes	complemented
19	C₃²	D₂₁	1	1	yes	characteristic, direct product factor
20	C₇	C₃²×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	21	4	no	—
22	D₃	—	7	1	no	—
23	C₃	—	2	4	no	—
24	C₃	C₃²×D₇	1	1	yes	characteristic, complemented
25	C₃	C₃×D₂₁	1	4	yes	direct product factor
26	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃³×C₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ 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.