Subgroups — C₉×#819 #11720414

Order 864.

112 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×#208	C₂	1	2	yes	maximal
3	C₃×#819	C₃	1	1	yes	maximal, characteristic
4	C₉×#108	—	3	1	no	maximal
5	C₂×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₃×C₈×C₉	C₄	1	2	yes	—
7	C₉×C₃⋊C₈	—	2	2	no	—
8	C₂×C₃²×C₈	C₂×C₃	1	1	yes	characteristic
9	C₃×#208	C₂×C₃	1	2	yes	—
10	C₉×M₁₆	—	3	2	no	—
11	C₂×C₈×C₉	—	2	1	no	—
12	C₂×C₈×C₉	D₃	1	1	yes	characteristic
13	C₂²×C₃×C₉	Q₈	1	1	yes	characteristic
14	C₃×C₄×C₉	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₉	D₄	1	1	yes	characteristic
16	C₃×#108	—	3	1	no	—
17	#819	C₉	1	1	yes	characteristic, direct product factor
18	C₂×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
19	C₃²×C₈	C₃×C₄	1	2	yes	—
20	C₃×C₃⋊C₈	—	2	2	no	—
21	C₂×C₄×C₉	—	2	1	no	—
22	C₂×C₄×C₉	C₂×D₃	1	1	yes	characteristic
23	C₈×C₉	—	2	2	no	—
24	C₈×C₉	—	6	2	no	—
25	C₈×C₉	Dic₃	1	2	yes	—
26	C₂×C₃×C₉	—	2	1	no	—
27	C₂×C₃×C₉	C₄⋊C₄	1	1	yes	characteristic
28	C₃×M₁₆	—	3	2	no	—
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	#208	C₂×C₉	1	2	yes	—
33	C₂²×C₃²	C₃×Q₈	1	1	yes	characteristic
34	C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
35	C₃²×C₄	C₃×D₄	1	1	yes	characteristic
36	C₂²×C₉	—	2	1	no	—
37	C₂²×C₉	Dic₆	1	1	yes	characteristic
38	C₄×C₉	—	2	1	no	—
39	C₄×C₉	—	2	1	no	—
40	C₄×C₉	D₁₂	1	1	yes	characteristic
41	C₄×C₉	C₂×Dic₃	1	1	yes	characteristic
42	#108	—	3	1	no	Sylow
43	C₃×C₉	#108	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₃×C₄	—	2	1	no	—
45	C₂×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
46	C₂×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
47	C₃×C₈	—	2	2	no	—
48	C₃×C₈	—	6	2	no	—
49	C₃×C₈	C₄×C₉	1	2	yes	—
50	C₃×C₈	C₃×Dic₃	1	2	yes	—
51	C₃⋊C₈	—	2	2	no	—
52	C₂×C₃²	—	2	1	no	—
53	C₂×C₃²	C₃×C₄⋊C₄	1	1	yes	characteristic
54	C₂×C₉	—	2	2	no	—
55	C₂×C₉	—	2	1	no	—
56	C₂×C₉	—	2	1	no	—
57	C₂×C₉	C₄⋊Dic₃	1	1	yes	characteristic
58	M₁₆	—	3	2	no	—
59	C₂×C₈	D₃×C₉	1	1	yes	characteristic
60	C₂²×C₃	—	2	1	no	—
61	C₂²×C₃	Q₈×C₉	1	1	yes	characteristic
62	C₂²×C₃	C₃×Dic₆	1	1	yes	characteristic
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	2	1	no	—
65	C₃×C₄	C₂×C₄×C₉	1	1	yes	characteristic
66	C₃×C₄	D₄×C₉	1	1	yes	characteristic
67	C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
68	C₃×C₄	C₂×C₃×Dic₃	1	1	yes	characteristic
69	C₃²	C₃×#108	1	1	yes	characteristic
70	C₉	—	2	1	no	—
71	C₉	#819	1	1	yes	characteristic, direct product factor
72	C₂×C₄	C₂×D₃×C₉	1	1	yes	characteristic
73	C₈	—	6	2	no	—
74	C₈	C₉×Dic₃	1	2	yes	—
75	C₂×C₃	—	2	2	no	—
76	C₂×C₃	—	2	1	no	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	2	1	no	—
79	C₂×C₃	C₉×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₃	C₃×C₄⋊Dic₃	1	1	yes	characteristic
81	C₂²	C₉×Dic₆	1	1	yes	characteristic
82	C₄	C₉×D₁₂	1	1	yes	characteristic
83	C₄	C₂×C₉×Dic₃	1	1	yes	characteristic
84	C₃	—	2	1	no	—
85	C₃	C₉×#108	1	1	yes	characteristic, complemented
86	C₃	C₃×#819	1	1	yes	characteristic
87	C₂	—	2	1	no	—
88	C₂	C₉×C₄⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₉	D₁₂
commutator	C₃×C₄	C₂×C₄×C₉
Frattini	C₂×C₃×C₄	C₂×C₃×D₃
Fitting	C₂×C₃×C₈×C₉	C₂
socle	C₂×C₃²	C₃×C₄⋊C₄
prime radical	C₂²×C₃²	C₃×Q₈
cosocle	C₂×C₃²×C₄	C₂²×C₃
hypercenter	C₂×C₈×C₉	D₃
hypocenter	C₃	C₉×#108
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₈×C₉

Complements

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

N	H ≅ G/N	type
17. #819	C₉	direct (N × H)
43. C₃×C₉	#108	semidirect
71. C₉	#819	direct (N × H)
85. C₃	C₉×#108	semidirect

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×#208	2
C₃×#819	3
C₉×#108	3

Subgroups — C9×#819 #11720414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#819 #11720414