Subgroups — C₉⋊S₄ #6256

Order 216.

49 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊S₄	—	3	1	no	maximal
3	(C₂²⋊C₉)⋊C₂	—	3	2	no	maximal
4	#611	—	3	1	no	maximal
5	C₃⋊D₉	—	4	1	no	maximal
6	C₃×A₄	D₃	1	1	yes	characteristic
7	C₂²×C₉	D₃	1	1	yes	characteristic, complemented
8	C₂×D₉	—	3	1	no	—
9	C₂²⋊C₉	D₃	1	2	yes	complemented
10	Dic₉	—	3	1	no	—
11	C₃×C₉	—	4	1	no	Sylow
12	S₄	—	9	3	no	—
13	#67	—	9	1	no	—
14	C₃⋊D₃	—	12	1	no	—
15	C₂×C₉	—	3	1	no	—
16	D₉	—	6	1	no	—
17	D₉	—	12	2	no	—
18	C₂²×C₃	C₃⋊D₃	1	1	yes	characteristic
19	C₂×D₃	—	9	1	no	—
20	A₄	D₉	1	3	yes	complemented
21	Dic₃	—	9	1	no	—
22	C₃²	—	4	1	no	—
23	C₉	—	4	2	no	—
24	C₉	S₄	1	1	yes	characteristic, complemented
25	D₄	—	27	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	D₃	—	18	1	no	—
28	D₃	—	36	3	no	—
29	C₂²	—	27	1	no	—
30	C₂²	C₃⋊D₉	1	1	yes	characteristic, complemented
31	C₄	—	27	1	no	—
32	C₃	—	4	3	no	—
33	C₃	C₃⋊S₄	1	1	yes	characteristic
34	C₂	—	3	1	no	—
35	C₂	—	54	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×A₄	C₂
Frattini	C₃	C₃⋊S₄
Fitting	C₂²×C₉	D₃
socle	C₂²×C₃	C₃⋊D₃
LCS	G ▷ C₉×A₄
UCS	C₁

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.