Subgroups — C₂×C₉⋊S₄ #88889

Order 432.

139 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×A₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉⋊S₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊S₄	—	3	1	no	maximal
4	C₂×(C₂²⋊C₉)⋊C₂	—	3	2	no	maximal
5	C₂×#611	—	3	1	no	maximal
6	C₂×C₃⋊D₉	—	4	1	no	maximal
7	C₉×A₄	C₂²	1	1	yes	characteristic, complemented
8	C₂×C₃×A₄	D₃	1	1	yes	characteristic
9	C₃⋊S₄	—	3	2	no	—
10	C₂³×C₉	D₃	1	1	yes	characteristic, complemented
11	C₂²×D₉	—	3	1	no	—
12	C₂×C₂²⋊C₉	D₃	1	2	yes	complemented
13	(C₂²⋊C₉)⋊C₂	—	3	4	no	—
14	#611	—	3	2	no	—
15	#611	—	3	2	no	—
16	C₂×Dic₉	—	3	1	no	—
17	C₂×C₃×C₉	—	4	1	no	—
18	C₃⋊D₉	—	4	2	no	—
19	C₂×S₄	—	9	3	no	—
20	C₂×#67	—	9	1	no	—
21	C₂×C₃⋊D₃	—	12	1	no	—
22	C₃×A₄	C₂×D₃	1	1	yes	characteristic
23	C₂²×C₉	—	3	1	no	—
24	C₂²×C₉	—	3	1	no	—
25	C₂²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
26	C₂×D₉	—	3	2	no	—
27	C₂×D₉	—	6	1	no	—
28	C₂×D₉	—	6	1	no	—
29	C₂×D₉	—	12	2	no	—
30	C₂²⋊C₉	C₂×D₃	1	2	yes	complemented
31	Dic₉	—	3	2	no	—
32	C₃×C₉	—	4	1	no	Sylow
33	C₂³×C₃	C₃⋊D₃	1	1	yes	characteristic
34	C₂²×D₃	—	9	1	no	—
35	C₂×A₄	D₉	1	3	yes	complemented
36	S₄	—	9	6	no	—
37	#67	—	9	2	no	—
38	#67	—	9	2	no	—
39	C₂×Dic₃	—	9	1	no	—
40	C₂×C₃²	—	4	1	no	—
41	C₃⋊D₃	—	12	2	no	—
42	C₂×C₉	—	3	1	no	—
43	C₂×C₉	—	3	1	no	—
44	C₂×C₉	—	4	2	no	—
45	C₂×C₉	S₄	1	1	yes	characteristic, complemented
46	D₉	—	6	2	no	—
47	D₉	—	12	4	no	—
48	C₂×D₄	—	27	1	no	Sylow
49	C₂²×C₃	—	3	1	no	—
50	C₂²×C₃	—	3	1	no	—
51	C₂²×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
52	C₂×D₃	—	9	2	no	—
53	C₂×D₃	—	18	1	no	—
54	C₂×D₃	—	18	1	no	—
55	C₂×D₃	—	36	3	no	—
56	A₄	C₂×D₉	1	3	yes	complemented
57	Dic₃	—	9	2	no	—
58	C₃²	—	4	1	no	—
59	C₉	—	4	2	no	—
60	C₉	C₂×S₄	1	1	yes	characteristic, complemented
61	C₂³	—	27	1	no	—
62	C₂³	C₃⋊D₉	1	1	yes	characteristic, complemented
63	D₄	—	27	2	no	—
64	D₄	—	27	2	no	—
65	C₂×C₄	—	27	1	no	—
66	C₂×C₃	—	3	1	no	—
67	C₂×C₃	—	3	1	no	—
68	C₂×C₃	—	4	3	no	—
69	C₂×C₃	C₃⋊S₄	1	1	yes	characteristic
70	D₃	—	18	2	no	—
71	D₃	—	36	6	no	—
72	C₂²	—	3	1	no	—
73	C₂²	—	3	1	no	—
74	C₂²	—	27	2	no	—
75	C₂²	—	54	1	no	—
76	C₂²	—	54	1	no	—
77	C₂²	C₂×C₃⋊D₉	1	1	yes	characteristic, complemented
78	C₄	—	27	2	no	—
79	C₃	—	4	3	no	—
80	C₃	C₂×C₃⋊S₄	1	1	yes	characteristic
81	C₂	—	3	1	no	—
82	C₂	—	3	1	no	—
83	C₂	—	54	2	no	—
84	C₂	C₉⋊S₄	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₉⋊S₄
commutator, cosocle, hypocenter	C₉×A₄	C₂²
Frattini	C₃	C₂×C₃⋊S₄
Fitting	C₂³×C₉	D₃
socle	C₂³×C₃	C₃⋊D₃
LCS	G ▷ C₉×A₄
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₉×A₄	C₂	semidirect
2. C₉⋊S₄	C₂	direct (N × H)
7. C₉×A₄	C₂²	semidirect
10. C₂³×C₉	D₃	semidirect
12. C₂×C₂²⋊C₉	D₃	semidirect
25. C₂²×C₉	C₂×D₃	semidirect
30. C₂²⋊C₉	C₂×D₃	semidirect
35. C₂×A₄	D₉	semidirect
45. C₂×C₉	S₄	semidirect
56. A₄	C₂×D₉	semidirect
60. C₉	C₂×S₄	semidirect
62. C₂³	C₃⋊D₉	semidirect
77. C₂²	C₂×C₃⋊D₉	semidirect
84. C₂	C₉⋊S₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉×A₄	2
C₉⋊S₄	2
C₂×C₃⋊S₄	3
C₂×(C₂²⋊C₉)⋊C₂	3
C₂×#611	3
C₂×C₃⋊D₉	4

Subgroups — C2×C9⋊S4 #88889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉⋊S₄ #88889