Subgroups — C₃⋊(C₃⋊(#41⋊C₃)) #88978

Order 432.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	#3832	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(#41⋊C₃)	—	3	4	no	maximal
4	C₃×C₃⋊Dic₃	—	4	1	no	maximal
5	C₃²×Q₈	C₂×C₃	1	1	yes	characteristic
6	C₄⋊(C₃⋊D₃)	—	3	1	no	—
7	C₄×C₃⋊D₃	—	3	1	no	—
8	C₃×SL(2,𝔽₃)	—	2	4	no	—
9	C₃×SL(2,𝔽₃)	D₃	1	4	yes	complemented
10	C₂×C₃³	—	4	1	no	—
11	#239	—	3	4	no	—
12	#41⋊C₃	—	9	1	no	—
13	C₂×C₃⋊D₃	—	3	1	no	—
14	C₃²×C₄	—	3	1	no	—
15	C₃⋊Dic₃	A₄	1	1	yes	characteristic
16	C₃×Dic₃	—	12	4	no	—
17	C₃³	—	4	1	no	Sylow
18	C₃×Q₈	C₃×D₃	1	4	yes	—
19	D₁₂	—	9	4	no	—
20	C₄×D₃	—	9	4	no	—
21	SL(2,𝔽₃)	—	2	4	no	—
22	SL(2,𝔽₃)	C₃⋊D₃	1	1	yes	characteristic, complemented
23	C₂×C₃²	—	4	4	no	—
24	C₂×C₃²	—	8	4	no	—
25	C₂×C₃²	C₂×A₄	1	1	yes	characteristic
26	C₃⋊D₃	—	6	1	no	—
27	#41	—	9	1	no	Sylow
28	C₂×D₃	—	9	4	no	—
29	C₃×C₄	—	3	4	no	—
30	C₃×C₄	—	36	1	no	—
31	Dic₃	—	3	4	no	—
32	C₃²	—	4	4	no	—
33	C₃²	—	8	4	no	—
34	C₃²	#41⋊C₃	1	1	yes	characteristic, complemented
35	Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic
36	D₄	—	27	1	no	—
37	C₂×C₄	—	27	1	no	—
38	C₂×C₃	—	4	1	no	—
39	C₂×C₃	—	8	4	no	—
40	C₂×C₃	D₃×A₄	1	4	yes	—
41	D₃	—	18	4	no	—
42	C₂²	—	27	1	no	—
43	C₄	—	3	1	no	—
44	C₄	—	9	1	no	—
45	C₃	—	4	1	no	—
46	C₃	—	8	4	no	—
47	C₃	C₃⋊(#41⋊C₃)	1	4	yes	complemented
48	C₂	—	54	1	no	—
49	C₂	A₄×C₃⋊D₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	A₄×C₃⋊D₃
commutator, Fitting, cosocle, hypocenter	C₃²×Q₈	C₂×C₃
socle	C₂×C₃²	C₂×A₄
LCS	G ▷ C₃²×Q₈
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.