Subgroups — C₂×C₉×C₃⋊C₁₆ #11720399

Order 864.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃⋊C₁₆	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₃⋊C₁₆	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₁₆	—	3	1	no	maximal
5	C₂×C₃×C₄×C₉	C₄	1	1	yes	characteristic
6	C₃×C₈×C₉	C₄	1	1	yes	characteristic
7	C₃×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₃²×C₈	C₂×C₃	1	1	yes	characteristic
9	C₃×C₃⋊C₁₆	C₂×C₃	1	2	yes	—
10	C₂×C₈×C₉	—	2	1	no	—
11	C₂×C₈×C₉	D₃	1	1	yes	characteristic
12	C₉×C₁₆	—	3	2	no	—
13	C₂²×C₃×C₉	C₈	1	1	yes	characteristic
14	C₃×C₄×C₉	C₈	1	1	yes	characteristic
15	C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₃×C₁₆	—	3	1	no	—
17	C₂×C₃⋊C₁₆	C₉	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₄	C₃×C₄	1	1	yes	characteristic
19	C₃²×C₈	C₃×C₄	1	1	yes	characteristic
20	C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
21	C₂×C₄×C₉	—	2	1	no	—
22	C₂×C₄×C₉	Dic₃	1	1	yes	characteristic
23	C₈×C₉	—	2	1	no	—
24	C₈×C₉	—	2	1	no	—
25	C₈×C₉	Dic₃	1	1	yes	characteristic
26	C₈×C₉	C₂×D₃	1	1	yes	characteristic
27	C₂×C₃×C₉	C₁₆	1	2	yes	complemented
28	C₂×C₃×C₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₃×C₈	—	2	1	no	—
30	C₂×C₃×C₈	C₂×C₉	1	1	yes	characteristic
31	C₂×C₃×C₈	C₃×D₃	1	1	yes	characteristic
32	C₃×C₁₆	—	3	2	no	—
33	C₃⋊C₁₆	C₂×C₉	1	2	yes	direct product factor
34	C₂²×C₃²	C₃×C₈	1	1	yes	characteristic
35	C₃²×C₄	C₃×C₈	1	1	yes	characteristic
36	C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
37	C₂²×C₉	—	2	1	no	—
38	C₂²×C₉	C₃⋊C₈	1	1	yes	characteristic
39	C₄×C₉	—	2	1	no	—
40	C₄×C₉	—	2	1	no	—
41	C₄×C₉	C₃⋊C₈	1	1	yes	characteristic
42	C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
43	C₂×C₁₆	—	3	1	no	Sylow
44	C₃×C₉	C₂×C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃×C₄	—	2	1	no	—
46	C₂×C₃×C₄	C₄×C₉	1	1	yes	characteristic
47	C₂×C₃×C₄	C₃×Dic₃	1	1	yes	characteristic
48	C₃×C₈	—	2	1	no	—
49	C₃×C₈	—	2	1	no	—
50	C₃×C₈	C₄×C₉	1	1	yes	characteristic
51	C₃×C₈	C₂²×C₉	1	1	yes	characteristic
52	C₃×C₈	C₃×Dic₃	1	1	yes	characteristic
53	C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
54	C₂×C₃²	C₃×C₁₆	1	2	yes	—
55	C₂×C₃²	C₂×C₃×C₈	1	1	yes	characteristic
56	C₂×C₉	—	2	2	no	—
57	C₂×C₉	—	2	1	no	—
58	C₂×C₉	C₃⋊C₁₆	1	2	yes	direct product factor
59	C₂×C₉	C₂×C₃⋊C₈	1	1	yes	characteristic
60	C₂×C₈	D₃×C₉	1	1	yes	characteristic
61	C₁₆	—	3	2	no	—
62	C₂²×C₃	—	2	1	no	—
63	C₂²×C₃	C₈×C₉	1	1	yes	characteristic
64	C₂²×C₃	C₃×C₃⋊C₈	1	1	yes	characteristic
65	C₃×C₄	—	2	1	no	—
66	C₃×C₄	—	2	1	no	—
67	C₃×C₄	C₈×C₉	1	1	yes	characteristic
68	C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
69	C₃×C₄	C₃×C₃⋊C₈	1	1	yes	characteristic
70	C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
71	C₃²	C₂×C₃×C₁₆	1	1	yes	characteristic
72	C₉	—	2	1	no	—
73	C₉	C₂×C₃⋊C₁₆	1	1	yes	characteristic, direct product factor
74	C₂×C₄	C₉×Dic₃	1	1	yes	characteristic
75	C₈	C₉×Dic₃	1	1	yes	characteristic
76	C₈	C₂×D₃×C₉	1	1	yes	characteristic
77	C₂×C₃	—	2	2	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	C₉×C₁₆	1	2	yes	complemented
80	C₂×C₃	C₂×C₈×C₉	1	1	yes	characteristic
81	C₂×C₃	C₃×C₃⋊C₁₆	1	2	yes	—
82	C₂×C₃	C₂×C₃×C₃⋊C₈	1	1	yes	characteristic
83	C₂²	C₉×C₃⋊C₈	1	1	yes	characteristic
84	C₄	C₉×C₃⋊C₈	1	1	yes	characteristic
85	C₄	C₂×C₉×Dic₃	1	1	yes	characteristic
86	C₃	—	2	1	no	—
87	C₃	C₂×C₉×C₁₆	1	1	yes	characteristic, complemented
88	C₃	C₂×C₃×C₃⋊C₁₆	1	1	yes	characteristic
89	C₂	C₉×C₃⋊C₁₆	1	2	yes	direct product factor
90	C₂	C₂×C₉×C₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈×C₉	D₃
commutator, hypocenter	C₃	C₂×C₉×C₁₆
Frattini	C₃×C₈	C₂×C₃×D₃
Fitting	C₂×C₃×C₈×C₉	C₂
socle, prime radical	C₂²×C₃²	C₃×C₈
cosocle	C₃²×C₈	C₂²×C₃
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₈×C₉

Complements

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

N	H ≅ G/N	type
2. C₉×C₃⋊C₁₆	C₂	direct (N × H)
17. C₂×C₃⋊C₁₆	C₉	direct (N × H)
27. C₂×C₃×C₉	C₁₆	semidirect
33. C₃⋊C₁₆	C₂×C₉	direct (N × H)
44. C₃×C₉	C₂×C₁₆	semidirect
58. C₂×C₉	C₃⋊C₁₆	direct (N × H)
73. C₉	C₂×C₃⋊C₁₆	direct (N × H)
79. C₂×C₃	C₉×C₁₆	semidirect
87. C₃	C₂×C₉×C₁₆	semidirect
89. C₂	C₉×C₃⋊C₁₆	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×C₃×C₈×C₉	2
C₉×C₃⋊C₁₆	2
C₂×C₃×C₃⋊C₁₆	3
C₂×C₉×C₁₆	3

Subgroups — C2×C9×C3⋊C16 #11720399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₃⋊C₁₆ #11720399