Subgroups — D₄×Dic₉ #63496

Order 288.

141 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₉	C₂	1	2	yes	maximal, complemented
3	#3676	C₂	1	2	yes	maximal, complemented
4	C₄⋊Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×Dic₃	—	3	1	no	maximal
7	C₂³×C₉	C₂²	1	2	yes	—
8	D₄×C₉	C₄	1	4	yes	complemented
9	C₂×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₉	—	2	4	no	—
11	C₂×Dic₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₉	C₂²	1	2	yes	—
13	C₂×Dic₉	C₂²	1	1	yes	characteristic
14	C₂×C₃×D₄	D₃	1	1	yes	characteristic
15	C₂²×Dic₃	—	3	2	no	—
16	#217	—	3	2	no	—
17	C₄⋊Dic₃	—	3	1	no	—
18	C₄×Dic₃	—	3	1	no	—
19	C₂²×C₉	—	2	2	no	—
20	C₂²×C₉	—	2	2	no	—
21	C₂²×C₉	C₂×C₄	1	4	yes	complemented
22	C₂²×C₉	C₂³	1	1	yes	characteristic
23	C₄×C₉	C₂×C₄	1	2	yes	complemented
24	Dic₉	—	2	2	no	—
25	Dic₉	—	2	1	no	—
26	Dic₉	D₄	1	2	yes	direct product factor
27	C₄×D₄	—	9	1	no	Sylow
28	C₂³×C₃	C₂×D₃	1	2	yes	—
29	C₃×D₄	Dic₃	1	4	yes	—
30	C₂×C₃×C₄	C₂×D₃	1	1	yes	characteristic
31	C₂×Dic₃	—	3	1	no	—
32	C₂×Dic₃	—	3	1	no	—
33	C₂×Dic₃	—	3	2	no	—
34	C₂×Dic₃	—	6	4	no	—
35	C₂×C₉	—	2	4	no	—
36	C₂×C₉	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₉	#41	1	1	yes	characteristic
39	C₂×D₄	D₉	1	1	yes	characteristic
40	C₂²×C₄	—	9	2	no	—
41	C₄⋊C₄	—	9	1	no	—
42	C₂²⋊C₄	—	9	2	no	—
43	C₄²	—	9	1	no	—
44	C₂²×C₃	—	2	2	no	—
45	C₂²×C₃	—	2	2	no	—
46	C₂²×C₃	C₂×Dic₃	1	4	yes	—
47	C₂²×C₃	C₂²×D₃	1	1	yes	characteristic
48	C₃×C₄	C₂×Dic₃	1	2	yes	—
49	Dic₃	—	3	2	no	—
50	Dic₃	—	6	2	no	—
51	Dic₃	—	6	1	no	—
52	C₉	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
53	C₂³	C₂×D₉	1	2	yes	—
54	D₄	Dic₉	1	4	yes	direct product factor
55	C₂×C₄	—	9	1	no	—
56	C₂×C₄	—	9	1	no	—
57	C₂×C₄	—	9	2	no	—
58	C₂×C₄	—	18	4	no	—
59	C₂×C₄	C₂×D₉	1	1	yes	characteristic
60	C₂×C₃	—	2	4	no	—
61	C₂×C₃	D₃×D₄	1	1	yes	characteristic
62	C₂×C₃	#237	1	1	yes	characteristic
63	C₂×C₃	C₂²×Dic₃	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	C₂×Dic₉	1	4	yes	complemented
67	C₂²	C₂²×D₉	1	1	yes	characteristic
68	C₄	—	9	2	no	—
69	C₄	—	18	2	no	—
70	C₄	—	18	1	no	—
71	C₄	C₂×Dic₉	1	2	yes	complemented
72	C₃	D₄×Dic₃	1	1	yes	characteristic
73	C₂	—	2	4	no	—
74	C₂	D₄×D₉	1	1	yes	characteristic
75	C₂	#3699	1	1	yes	characteristic
76	C₂	C₂²×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₉
commutator	C₂×C₉	C₂²×C₄
Frattini, socle	C₂²×C₃	C₂²×D₃
Fitting	C₂×D₄×C₉	C₂
prime radical	C₂×C₃×D₄	D₃
cosocle	C₂²×C₉	C₂³
hypercenter	C₂×D₄	D₉
hypocenter	C₉	C₄×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₉	C₂	semidirect
3. #3676	C₂	semidirect
4. C₄⋊Dic₉	C₂	semidirect
5. C₄×Dic₉	C₂	semidirect
8. D₄×C₉	C₄	semidirect
21. C₂²×C₉	C₂×C₄	semidirect
23. C₄×C₉	C₂×C₄	semidirect
26. Dic₉	D₄	direct (N × H)
52. C₉	C₄×D₄	semidirect
54. D₄	Dic₉	direct (N × H)
66. C₂²	C₂×Dic₉	semidirect
71. C₄	C₂×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×C₉	2
C₂²×Dic₉	2
#3676	2
C₄⋊Dic₉	2
C₄×Dic₉	2
D₄×Dic₃	3

Subgroups — D4×Dic9 #63496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×Dic₉ #63496