Subgroups — SD₁₆×D₉ #63475

Order 288.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×D₉	C₂	1	1	yes	maximal, characteristic
3	C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#3675	C₂	1	1	yes	maximal, characteristic, complemented
5	#3672	C₂	1	1	yes	maximal, characteristic, complemented
6	#3664	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×D₉	C₂	1	1	yes	maximal, characteristic, complemented
8	D₃×SD₁₆	—	3	1	no	maximal
9	C₂²×D₉	—	2	1	no	—
10	Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
11	D₄×C₉	C₂²	1	1	yes	characteristic
12	#611	—	2	1	no	—
13	D₃₆	C₂²	1	1	yes	characteristic
14	C₄×D₉	—	2	1	no	—
15	C₄×D₉	C₂²	1	1	yes	characteristic
16	Dic₁₈	—	2	1	no	—
17	Dic₁₈	C₂²	1	1	yes	characteristic, complemented
18	C₈×C₉	C₂²	1	1	yes	characteristic, complemented
19	C₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
20	D₃×Q₈	—	3	1	no	—
21	D₃×D₄	—	3	1	no	—
22	C₃×SD₁₆	D₃	1	1	yes	characteristic
23	#215	—	3	1	no	—
24	#214	—	3	1	no	—
25	#204	—	3	1	no	—
26	D₃×C₈	—	3	1	no	—
27	C₂²×C₉	—	2	1	no	—
28	C₂×D₉	—	2	1	no	—
29	C₂×D₉	—	4	2	no	—
30	C₂×D₉	D₄	1	1	yes	characteristic
31	C₄×C₉	—	2	1	no	—
32	C₄×C₉	C₂³	1	1	yes	characteristic
33	Dic₉	—	2	1	no	—
34	Dic₉	D₄	1	1	yes	characteristic
35	C₂×SD₁₆	—	9	1	no	Sylow
36	C₂²×D₃	—	6	1	no	—
37	C₃×Q₈	C₂×D₃	1	1	yes	characteristic
38	C₃×D₄	C₂×D₃	1	1	yes	characteristic
39	#67	—	6	1	no	—
40	D₁₂	—	3	1	no	—
41	C₄×D₃	—	3	1	no	—
42	C₄×D₃	—	6	1	no	—
43	Dic₆	—	3	1	no	—
44	Dic₆	—	6	1	no	—
45	C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₃⋊C₈	—	3	1	no	—
47	C₂×C₉	—	4	1	no	—
48	C₂×C₉	C₂×D₄	1	1	yes	characteristic
49	D₉	—	4	1	no	—
50	D₉	SD₁₆	1	2	yes	direct product factor
51	C₂×Q₈	—	9	1	no	—
52	C₂×D₄	—	9	1	no	—
53	SD₁₆	—	9	1	no	—
54	SD₁₆	—	9	1	no	—
55	SD₁₆	—	9	1	no	—
56	SD₁₆	D₉	1	1	yes	characteristic, direct product factor
57	C₂×C₈	—	9	1	no	—
58	C₂²×C₃	—	2	1	no	—
59	C₂×D₃	—	3	1	no	—
60	C₂×D₃	—	6	1	no	—
61	C₂×D₃	—	12	2	no	—
62	C₃×C₄	—	2	1	no	—
63	C₃×C₄	C₂²×D₃	1	1	yes	characteristic
64	Dic₃	—	3	1	no	—
65	Dic₃	—	6	1	no	—
66	C₉	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
67	C₂³	—	18	1	no	—
68	Q₈	—	9	1	no	—
69	Q₈	—	18	1	no	—
70	Q₈	C₂×D₉	1	1	yes	characteristic, complemented
71	D₄	—	9	1	no	—
72	D₄	—	18	1	no	—
73	D₄	C₂×D₉	1	1	yes	characteristic
74	C₂×C₄	—	9	1	no	—
75	C₂×C₄	—	18	1	no	—
76	C₈	—	9	1	no	—
77	C₈	C₂×D₉	1	1	yes	characteristic, complemented
78	C₂×C₃	—	4	1	no	—
79	C₂×C₃	D₃×D₄	1	1	yes	characteristic
80	D₃	—	3	2	no	—
81	D₃	—	12	1	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	9	1	no	—
84	C₂²	—	18	1	no	—
85	C₂²	—	36	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	9	1	no	—
88	C₄	—	18	1	no	—
89	C₄	C₂²×D₉	1	1	yes	characteristic
90	C₃	D₃×SD₁₆	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	9	2	no	—
93	C₂	—	36	1	no	—
94	C₂	D₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₉
commutator, cosocle	C₄×C₉	C₂³
Frattini	C₃×C₄	C₂²×D₃
Fitting	C₉×SD₁₆	C₂
socle	C₂×C₃	D₃×D₄
prime radical	D₄×D₉	C₂
hypercenter	SD₁₆	D₉
hypocenter	C₉	C₂×SD₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×D₉	C₂	semidirect
3. C₉×SD₁₆	C₂	semidirect
4. #3675	C₂	semidirect
5. #3672	C₂	semidirect
6. #3664	C₂	semidirect
7. C₈×D₉	C₂	semidirect
10. Q₈×C₉	C₂²	semidirect
17. Dic₁₈	C₂²	semidirect
18. C₈×C₉	C₂²	semidirect
19. C₉⋊C₈	C₂²	semidirect
50. D₉	SD₁₆	direct (N × H)
56. SD₁₆	D₉	direct (N × H)
66. C₉	C₂×SD₁₆	semidirect
70. Q₈	C₂×D₉	semidirect
77. C₈	C₂×D₉	semidirect

Maximal subgroups

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

subgroup	index
Q₈×D₉	2
D₄×D₉	2
C₉×SD₁₆	2
#3675	2
#3672	2
#3664	2
C₈×D₉	2
D₃×SD₁₆	3

Subgroups — SD16×D9 #63475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×D₉ #63475