Subgroups — C₃²×C₃⋊(C₃⋊D₃) #92413

Order 486.

1584 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁵	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊D₃)	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₃⋊D₃	—	3	13	no	maximal
4	C₃⁴	—	2	52	no	—
5	C₃⁴	D₃	1	13	yes	complemented
6	C₃⁴	C₂×C₃	1	4	yes	complemented
7	C₃⋊(C₃⋊D₃)	C₃²	1	1	yes	characteristic, direct product factor
8	C₃×C₃⋊D₃	—	3	52	no	—
9	C₃²×D₃	—	9	13	no	—
10	C₃³	—	2	312	no	—
11	C₃³	—	2	52	no	—
12	C₃³	—	2	208	no	—
13	C₃³	C₃×D₃	1	52	yes	complemented
14	C₃³	C₃⋊D₃	1	13	yes	complemented
15	C₃³	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₂×C₃²	—	27	1	no	—
17	C₃⋊D₃	—	3	13	no	—
18	C₃×D₃	—	9	52	no	—
19	C₃²	—	2	312	no	—
20	C₃²	—	2	208	no	—
21	C₃²	—	2	52	no	—
22	C₃²	C₃²×D₃	1	13	yes	complemented
23	C₃²	C₃×C₃⋊D₃	1	52	yes	complemented
24	C₃²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
25	C₂×C₃	—	27	4	no	—
26	D₃	—	9	13	no	—
27	C₃	—	2	52	no	—
28	C₃	C₃²×C₃⋊D₃	1	13	yes	complemented
29	C₃	C₃×C₃⋊(C₃⋊D₃)	1	4	yes	direct product factor
30	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₃⋊(C₃⋊D₃)
commutator, cosocle, hypocenter	C₃³	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃⁵	C₂
LCS	G ▷ C₃³
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.