Subgroups — C₂×C₁₆×D₉ #10588579

Order 576.

147 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×D₃×C₁₆	—	3	1	no	maximal
6	C₂×C₄×D₉	C₄	1	1	yes	characteristic
7	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉⋊C₈	C₄	1	1	yes	characteristic
9	C₈×D₉	C₄	1	2	yes	—
10	C₈×D₉	C₂²	1	2	yes	—
11	C₉×C₁₆	C₂²	1	2	yes	complemented
12	C₉⋊C₁₆	C₂²	1	2	yes	complemented
13	C₂×D₃×C₈	—	3	1	no	—
14	C₂×C₃×C₁₆	D₃	1	1	yes	characteristic
15	C₂×C₃⋊C₁₆	—	3	1	no	—
16	D₃×C₁₆	—	3	4	no	—
17	C₂²×D₉	C₈	1	1	yes	characteristic
18	C₂×C₄×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₉	C₈	1	1	yes	characteristic
20	C₄×D₉	C₈	1	2	yes	—
21	C₄×D₉	C₂×C₄	1	2	yes	—
22	C₈×C₉	C₂×C₄	1	1	yes	characteristic
23	C₈×C₉	C₂³	1	1	yes	characteristic
24	C₉⋊C₈	C₂×C₄	1	2	yes	—
25	C₂²×C₁₆	—	9	1	no	Sylow
26	C₂×C₄×D₃	—	3	1	no	—
27	C₂×C₃×C₈	C₂×D₃	1	1	yes	characteristic
28	C₂×C₃⋊C₈	—	3	1	no	—
29	D₃×C₈	—	3	2	no	—
30	D₃×C₈	—	3	2	no	—
31	C₃×C₁₆	C₂×D₃	1	2	yes	—
32	C₃⋊C₁₆	—	3	2	no	—
33	C₂²×C₉	C₂×C₈	1	1	yes	characteristic
34	C₂×D₉	C₁₆	1	4	yes	direct product factor
35	C₂×D₉	C₂×C₈	1	2	yes	—
36	C₄×C₉	C₂×C₈	1	1	yes	characteristic
37	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
38	Dic₉	C₂×C₈	1	2	yes	—
39	C₂²×C₈	—	9	1	no	—
40	C₂×C₁₆	—	9	1	no	—
41	C₂×C₁₆	—	9	4	no	—
42	C₂×C₁₆	D₉	1	1	yes	characteristic, direct product factor
43	C₂²×D₃	—	3	1	no	—
44	C₂×C₃×C₄	C₄×D₃	1	1	yes	characteristic
45	C₂×Dic₃	—	3	1	no	—
46	C₄×D₃	—	3	2	no	—
47	C₄×D₃	—	3	2	no	—
48	C₃×C₈	C₄×D₃	1	1	yes	characteristic
49	C₃×C₈	C₂²×D₃	1	1	yes	characteristic
50	C₃⋊C₈	—	3	2	no	—
51	C₂×C₉	C₂×C₁₆	1	2	yes	complemented
52	C₂×C₉	C₂²×C₈	1	1	yes	characteristic
53	D₉	C₂×C₁₆	1	4	yes	direct product factor
54	C₂²×C₄	—	9	1	no	—
55	C₂×C₈	—	9	1	no	—
56	C₂×C₈	—	9	2	no	—
57	C₂×C₈	—	9	2	no	—
58	C₂×C₈	C₂×D₉	1	1	yes	characteristic
59	C₁₆	—	9	2	no	—
60	C₁₆	C₂×D₉	1	2	yes	direct product factor
61	C₂²×C₃	D₃×C₈	1	1	yes	characteristic
62	C₂×D₃	—	3	4	no	—
63	C₂×D₃	—	3	2	no	—
64	C₃×C₄	D₃×C₈	1	1	yes	characteristic
65	C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
66	Dic₃	—	3	2	no	—
67	C₉	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
68	C₂³	—	9	1	no	—
69	C₂×C₄	—	9	1	no	—
70	C₂×C₄	—	9	2	no	—
71	C₂×C₄	—	9	2	no	—
72	C₂×C₄	C₄×D₉	1	1	yes	characteristic
73	C₈	—	9	2	no	—
74	C₈	C₄×D₉	1	1	yes	characteristic
75	C₈	C₂²×D₉	1	1	yes	characteristic
76	C₂×C₃	D₃×C₁₆	1	2	yes	—
77	C₂×C₃	C₂×D₃×C₈	1	1	yes	characteristic
78	D₃	—	3	4	no	—
79	C₂²	—	9	4	no	—
80	C₂²	—	9	2	no	—
81	C₂²	C₈×D₉	1	1	yes	characteristic
82	C₄	—	9	2	no	—
83	C₄	C₈×D₉	1	1	yes	characteristic
84	C₄	C₂×C₄×D₉	1	1	yes	characteristic
85	C₃	C₂×D₃×C₁₆	1	1	yes	characteristic
86	C₂	—	9	4	no	—
87	C₂	C₁₆×D₉	1	2	yes	direct product factor
88	C₂	C₂×C₈×D₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₆	D₉
commutator, hypocenter	C₉	C₂²×C₁₆
Frattini	C₃×C₈	C₂²×D₃
Fitting	C₂×C₉×C₁₆	C₂
socle	C₂²×C₃	D₃×C₈
prime radical	C₂²×D₉	C₈
cosocle	C₈×C₉	C₂³
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₉×C₁₆	C₂	semidirect
3. C₂×C₉⋊C₁₆	C₂	semidirect
4. C₁₆×D₉	C₂	direct (N × H)
11. C₉×C₁₆	C₂²	semidirect
12. C₉⋊C₁₆	C₂²	semidirect
34. C₂×D₉	C₁₆	direct (N × H)
42. C₂×C₁₆	D₉	direct (N × H)
51. C₂×C₉	C₂×C₁₆	semidirect
53. D₉	C₂×C₁₆	direct (N × H)
60. C₁₆	C₂×D₉	direct (N × H)
67. C₉	C₂²×C₁₆	semidirect
87. C₂	C₁₆×D₉	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×C₈×D₉	2
C₂×C₉×C₁₆	2
C₂×C₉⋊C₁₆	2
C₁₆×D₉	2
C₂×D₃×C₁₆	3

Subgroups — C2×C16×D9 #10588579

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×D₉ #10588579