Subgroups — C₉⋊GL(2,𝔽₃) #88606

Order 432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊GL(2,𝔽₃)	—	3	1	no	maximal
3	#3689	—	3	2	no	maximal
4	#3675	—	3	1	no	maximal
5	C₂×C₃⋊D₉	—	4	1	no	maximal
6	C₃×SL(2,𝔽₃)	D₃	1	1	yes	characteristic
7	Q₈×C₉	D₃	1	1	yes	characteristic, complemented
8	D₃₆	—	3	1	no	—
9	Q₈⋊C₉	D₃	1	2	yes	complemented
10	C₉⋊C₈	—	3	1	no	—
11	C₂×C₃×C₉	—	4	1	no	—
12	C₃⋊D₉	—	4	2	no	—
13	GL(2,𝔽₃)	—	9	3	no	—
14	#215	—	9	1	no	—
15	C₂×C₃⋊D₃	—	12	1	no	—
16	C₂×D₉	—	6	1	no	—
17	C₂×D₉	—	12	2	no	—
18	C₄×C₉	—	3	1	no	—
19	C₃×C₉	—	4	1	no	Sylow
20	C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
21	D₁₂	—	9	1	no	—
22	SL(2,𝔽₃)	D₉	1	3	yes	complemented
23	C₃⋊C₈	—	9	1	no	—
24	C₂×C₃²	—	4	1	no	—
25	C₃⋊D₃	—	12	2	no	—
26	C₂×C₉	—	4	2	no	—
27	C₂×C₉	S₄	1	1	yes	characteristic
28	D₉	—	12	4	no	—
29	D₉	—	12	1	no	—
30	SD₁₆	—	27	1	no	Sylow
31	C₂×D₃	—	18	1	no	—
32	C₂×D₃	—	36	3	no	—
33	C₃×C₄	—	3	1	no	—
34	C₃²	—	4	1	no	—
35	C₉	—	4	2	no	—
36	C₉	GL(2,𝔽₃)	1	1	yes	characteristic, complemented
37	Q₈	C₃⋊D₉	1	1	yes	characteristic, complemented
38	D₄	—	27	1	no	—
39	C₈	—	27	1	no	—
40	C₂×C₃	—	4	3	no	—
41	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
42	D₃	—	36	6	no	—
43	D₃	—	36	1	no	—
44	C₂²	—	54	1	no	—
45	C₄	—	3	1	no	—
46	C₃	—	4	3	no	—
47	C₃	C₃⋊GL(2,𝔽₃)	1	1	yes	characteristic
48	C₂	—	108	1	no	—
49	C₂	C₉⋊S₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	C₉⋊S₄
commutator, cosocle, hypocenter	C₉×SL(2,𝔽₃)	C₂
Frattini, socle	C₂×C₃	C₃⋊S₄
Fitting	Q₈×C₉	D₃
LCS	G ▷ C₉×SL(2,𝔽₃)
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.