Subgroups — D₄×D₉ #3698

Order 144.

81 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₉	C₂	1	2	yes	maximal, complemented
2	D₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#611	C₂	1	2	yes	maximal, complemented
4	D₃₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×D₄	—	3	1	no	maximal
7	C₂²×C₉	C₂²	1	2	yes	complemented
8	C₂×D₉	—	2	4	no	—
9	C₂×D₉	C₂²	1	1	yes	characteristic
10	C₂×D₉	C₂²	1	2	yes	complemented
11	C₄×C₉	C₂²	1	1	yes	characteristic, complemented
12	Dic₉	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₃	—	3	2	no	—
14	C₃×D₄	D₃	1	1	yes	characteristic
15	#67	—	3	2	no	—
16	D₁₂	—	3	1	no	—
17	C₄×D₃	—	3	1	no	—
18	C₂×C₉	—	2	2	no	—
19	C₂×C₉	C₂³	1	1	yes	characteristic
20	D₉	—	2	2	no	—
21	D₉	D₄	1	2	yes	direct product factor
22	C₂×D₄	—	9	1	no	Sylow
23	C₂²×C₃	C₂×D₃	1	2	yes	—
24	C₂×D₃	—	3	1	no	—
25	C₂×D₃	—	3	2	no	—
26	C₂×D₃	—	6	4	no	—
27	C₃×C₄	C₂×D₃	1	1	yes	characteristic
28	Dic₃	—	3	1	no	—
29	C₉	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	9	2	no	—
31	D₄	—	9	2	no	—
32	D₄	—	9	1	no	—
33	D₄	D₉	1	1	yes	characteristic, direct product factor
34	C₂×C₄	—	9	1	no	—
35	C₂×C₃	—	2	2	no	—
36	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
37	D₃	—	3	2	no	—
38	D₃	—	6	2	no	—
39	C₂²	—	9	1	no	—
40	C₂²	—	9	2	no	—
41	C₂²	—	18	4	no	—
42	C₂²	C₂×D₉	1	2	yes	complemented
43	C₄	—	9	1	no	—
44	C₄	C₂×D₉	1	1	yes	characteristic, complemented
45	C₃	D₃×D₄	1	1	yes	characteristic
46	C₂	—	2	2	no	—
47	C₂	—	9	2	no	—
48	C₂	—	18	2	no	—
49	C₂	C₂²×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₉
commutator, cosocle	C₂×C₉	C₂³
Frattini, socle	C₂×C₃	C₂²×D₃
Fitting	D₄×C₉	C₂
hypercenter	D₄	D₉
hypocenter	C₉	C₂×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₉	C₂	semidirect
2. D₄×C₉	C₂	semidirect
3. #611	C₂	semidirect
4. D₃₆	C₂	semidirect
5. C₄×D₉	C₂	semidirect
7. C₂²×C₉	C₂²	semidirect
10. C₂×D₉	C₂²	semidirect
11. C₄×C₉	C₂²	semidirect
12. Dic₉	C₂²	semidirect
21. D₉	D₄	direct (N × H)
29. C₉	C₂×D₄	semidirect
33. D₄	D₉	direct (N × H)
42. C₂²	C₂×D₉	semidirect
44. C₄	C₂×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₉	2
D₄×C₉	2
#611	2
D₃₆	2
C₄×D₉	2
D₃×D₄	3

Subgroups — D4×D9 #3698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₉ #3698