Subgroups — C₃²×C₃⋊(C₃⋊(C₃⋊D₃)) #13091723

Order 1458.

30224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁶	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₃⋊(C₃⋊D₃)	—	3	40	no	maximal
4	C₃⁵	—	2	160	no	—
5	C₃⁵	D₃	1	40	yes	complemented
6	C₃⁵	C₂×C₃	1	4	yes	complemented
7	C₃⋊(C₃⋊(C₃⋊D₃))	C₃²	1	1	yes	characteristic, direct product factor
8	C₃×C₃⋊(C₃⋊D₃)	—	3	160	no	—
9	C₃²×C₃⋊D₃	—	9	130	no	—
10	C₃⁴	—	2	3120	no	—
11	C₃⁴	—	2	160	no	—
12	C₃⁴	—	2	2080	no	—
13	C₃⁴	C₃×D₃	1	160	yes	complemented
14	C₃⁴	C₃⋊D₃	1	130	yes	complemented
15	C₃⁴	C₂×C₃²	1	1	yes	characteristic, complemented
16	C₃⋊(C₃⋊D₃)	—	3	40	no	—
17	C₃×C₃⋊D₃	—	9	520	no	—
18	C₃²×D₃	—	27	40	no	—
19	C₃³	—	2	12480	no	—
20	C₃³	—	2	2080	no	—
21	C₃³	—	2	2080	no	—
22	C₃³	C₃²×D₃	1	40	yes	complemented
23	C₃³	C₃×C₃⋊D₃	1	520	yes	complemented
24	C₃³	C₃⋊(C₃⋊D₃)	1	40	yes	complemented
25	C₂×C₃²	—	81	1	no	—
26	C₃⋊D₃	—	9	130	no	—
27	C₃×D₃	—	27	160	no	—
28	C₃²	—	2	3120	no	—
29	C₃²	—	2	2080	no	—
30	C₃²	—	2	160	no	—
31	C₃²	C₃²×C₃⋊D₃	1	130	yes	complemented
32	C₃²	C₃×C₃⋊(C₃⋊D₃)	1	160	yes	complemented
33	C₃²	C₃⋊(C₃⋊(C₃⋊D₃))	1	1	yes	characteristic, direct product factor
34	C₂×C₃	—	81	4	no	—
35	D₃	—	27	40	no	—
36	C₃	—	2	160	no	—
37	C₃	C₃²×C₃⋊(C₃⋊D₃)	1	40	yes	complemented
38	C₃	C₃×C₃⋊(C₃⋊(C₃⋊D₃))	1	4	yes	direct product factor
39	C₂	—	81	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃²	C₃⋊(C₃⋊(C₃⋊D₃))
commutator, cosocle, hypocenter	C₃⁴	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃⁶	C₂
LCS	G ▷ C₃⁴
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.