Subgroups — C₂³×C₃⋊(C₃⋊D₃) #89127

Order 432.

1876 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃³	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃⋊(C₃⋊D₃)	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₃⋊D₃	—	3	13	no	maximal
4	C₂²×C₃³	C₂²	1	7	yes	complemented
5	C₂×C₃⋊(C₃⋊D₃)	C₂²	1	28	yes	direct product factor
6	C₂³×C₃²	D₃	1	13	yes	complemented
7	C₂²×C₃⋊D₃	—	3	182	no	—
8	C₂×C₃³	C₂³	1	7	yes	complemented
9	C₃⋊(C₃⋊D₃)	C₂³	1	8	yes	direct product factor
10	C₂³×D₃	—	9	13	no	—
11	C₂²×C₃²	C₂×D₃	1	91	yes	complemented
12	C₂×C₃⋊D₃	—	3	364	no	—
13	C₃³	C₂⁴	1	1	yes	characteristic, complemented, Sylow
14	C₂³×C₃	C₃⋊D₃	1	13	yes	complemented
15	C₂²×D₃	—	9	182	no	—
16	C₂×C₃²	C₂²×D₃	1	91	yes	complemented
17	C₃⋊D₃	—	3	104	no	—
18	C₂⁴	—	27	1	no	Sylow
19	C₂²×C₃	C₂×C₃⋊D₃	1	91	yes	complemented
20	C₂×D₃	—	9	364	no	—
21	C₃²	C₂³×D₃	1	13	yes	complemented
22	C₂³	—	27	14	no	—
23	C₂³	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
24	C₂×C₃	C₂²×C₃⋊D₃	1	91	yes	complemented
25	D₃	—	9	104	no	—
26	C₂²	—	27	28	no	—
27	C₂²	C₂×C₃⋊(C₃⋊D₃)	1	7	yes	direct product factor
28	C₃	C₂³×C₃⋊D₃	1	13	yes	complemented
29	C₂	—	27	8	no	—
30	C₂	C₂²×C₃⋊(C₃⋊D₃)	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₃³	C₂
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂³

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.