Subgroups — C₉⋊(C₉⋊S₄) #14518095

Order 1944.

573 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉²×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(C₉⋊S₄)	—	3	4	no	maximal
3	C₉⋊((C₂²⋊C₉)⋊C₂)	—	3	8	no	maximal
4	#10619673	—	3	1	no	maximal
5	C₃⋊(C₉⋊D₉)	—	4	1	no	maximal
6	C₃×C₉×A₄	D₃	1	4	yes	—
7	C₂²×C₉²	D₃	1	1	yes	characteristic, complemented
8	C₂×C₉⋊D₉	—	3	1	no	—
9	C₉×C₂²⋊C₉	D₃	1	8	yes	complemented
10	C₉⋊Dic₉	—	3	1	no	—
11	C₃×C₉²	—	4	1	no	Sylow
12	C₃⋊(C₃⋊S₄)	—	9	1	no	—
13	C₃⋊((C₂²⋊C₉)⋊C₂)	—	9	8	no	—
14	C₉⋊S₄	—	9	36	no	—
15	#6233	—	9	4	no	—
16	C₃⋊(C₃⋊D₉)	—	12	4	no	—
17	C₂×C₉²	—	3	1	no	—
18	C₉⋊D₉	—	6	1	no	—
19	C₉⋊D₉	—	12	8	no	—
20	C₃²×A₄	C₃⋊D₃	1	1	yes	characteristic
21	C₂²×C₃×C₉	C₃⋊D₃	1	4	yes	—
22	C₂×C₃⋊D₉	—	9	4	no	—
23	C₃×C₂²⋊C₉	C₃⋊D₃	1	8	yes	—
24	C₉×A₄	D₉	1	36	yes	complemented
25	C₃⋊Dic₉	—	9	4	no	—
26	C₃²×C₉	—	4	4	no	—
27	C₉²	—	4	8	no	—
28	C₉²	S₄	1	1	yes	characteristic, complemented
29	C₃⋊S₄	—	27	12	no	—
30	#638	—	27	1	no	—
31	(C₂²⋊C₉)⋊C₂	—	27	24	no	—
32	#611	—	27	12	no	—
33	C₃⋊(C₃⋊D₃)	—	36	1	no	—
34	C₂×C₃×C₉	—	3	4	no	—
35	C₃⋊D₉	—	18	4	no	—
36	C₃⋊D₉	—	36	36	no	—
37	C₃⋊D₉	—	36	8	no	—
38	C₂²×C₃²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
39	C₂×C₃⋊D₃	—	27	1	no	—
40	C₃×A₄	C₃⋊D₉	1	12	yes	—
41	C₃⋊Dic₃	—	27	1	no	—
42	C₂²×C₉	C₃⋊D₉	1	12	yes	complemented
43	C₂×D₉	—	27	12	no	—
44	C₂²⋊C₉	C₃⋊D₉	1	24	yes	complemented
45	Dic₉	—	27	12	no	—
46	C₃³	—	4	1	no	—
47	C₃×C₉	—	4	8	no	—
48	C₃×C₉	—	4	36	no	—
49	C₃×C₉	C₃⋊S₄	1	4	yes	—
50	S₄	—	81	9	no	—
51	#67	—	81	4	no	—
52	C₂×C₃²	—	3	1	no	—
53	C₃⋊D₃	—	54	1	no	—
54	C₃⋊D₃	—	108	12	no	—
55	C₂×C₉	—	3	12	no	—
56	D₉	—	54	12	no	—
57	D₉	—	108	24	no	—
58	C₂²×C₃	C₃⋊(C₃⋊D₉)	1	4	yes	—
59	C₂×D₃	—	81	4	no	—
60	A₄	C₉⋊D₉	1	9	yes	complemented
61	Dic₃	—	81	4	no	—
62	C₃²	—	4	12	no	—
63	C₃²	C₃⋊(C₃⋊S₄)	1	1	yes	characteristic
64	C₉	—	4	24	no	—
65	C₉	C₉⋊S₄	1	12	yes	complemented
66	D₄	—	243	1	no	Sylow
67	C₂×C₃	—	3	4	no	—
68	D₃	—	324	9	no	—
69	D₃	—	162	4	no	—
70	C₂²	—	243	1	no	—
71	C₂²	C₃⋊(C₉⋊D₉)	1	1	yes	characteristic, complemented
72	C₄	—	243	1	no	—
73	C₃	—	4	9	no	—
74	C₃	C₃⋊(C₉⋊S₄)	1	4	yes	—
75	C₂	—	3	1	no	—
76	C₂	—	486	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉²×A₄	C₂
Frattini	C₃²	C₃⋊(C₃⋊S₄)
Fitting	C₂²×C₉²	D₃
socle	C₂²×C₃²	C₃⋊(C₃⋊D₃)
LCS	G ▷ C₉²×A₄
UCS	C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₉²×A₄	C₂	semidirect
7. C₂²×C₉²	D₃	semidirect
9. C₉×C₂²⋊C₉	D₃	semidirect
24. C₉×A₄	D₉	semidirect
28. C₉²	S₄	semidirect
42. C₂²×C₉	C₃⋊D₉	semidirect
44. C₂²⋊C₉	C₃⋊D₉	semidirect
60. A₄	C₉⋊D₉	semidirect
65. C₉	C₉⋊S₄	semidirect
71. C₂²	C₃⋊(C₉⋊D₉)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₉²×A₄	2
C₃⋊(C₉⋊S₄)	3
C₉⋊((C₂²⋊C₉)⋊C₂)	3
#10619673	3
C₃⋊(C₉⋊D₉)	4

Subgroups — C9⋊(C9⋊S4) #14518095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉⋊(C₉⋊S₄) #14518095