Subgroups — C₉×#829 #11720468

Order 864.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₁₂	C₂	1	1	yes	maximal, characteristic
3	C₉×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#829	C₃	1	1	yes	maximal, characteristic
5	C₉×Q₃₂	—	3	1	no	maximal
6	C₃×Q₈×C₉	—	2	1	no	—
7	C₉×Dic₆	—	2	1	no	—
8	C₃×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₃²×Q₁₆	C₂×C₃	1	1	yes	characteristic
10	C₃×Dic₁₂	C₂×C₃	1	1	yes	characteristic
11	C₃×C₃⋊C₁₆	C₂×C₃	1	1	yes	characteristic
12	C₉×Q₁₆	—	2	1	no	—
13	C₉×Q₁₆	—	3	1	no	—
14	C₉×Q₁₆	D₃	1	1	yes	characteristic
15	C₉×C₁₆	—	3	1	no	—
16	C₃×C₄×C₉	—	4	1	no	—
17	C₃×C₄×C₉	D₄	1	1	yes	characteristic
18	C₉×Dic₃	—	4	1	no	—
19	C₃×Q₃₂	—	3	1	no	—
20	#829	C₉	1	1	yes	characteristic, direct product factor
21	C₃²×Q₈	—	2	1	no	—
22	C₃×Dic₆	—	2	1	no	—
23	C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
24	Q₈×C₉	—	2	2	no	—
25	Q₈×C₉	—	2	1	no	—
26	Q₈×C₉	—	6	1	no	—
27	C₈×C₉	—	2	1	no	—
28	C₈×C₉	C₂×D₃	1	1	yes	characteristic
29	C₂×C₃×C₉	D₈	1	1	yes	characteristic
30	C₃×Q₁₆	—	2	1	no	—
31	C₃×Q₁₆	—	3	1	no	—
32	C₃×Q₁₆	C₂×C₉	1	1	yes	characteristic
33	C₃×Q₁₆	C₃×D₃	1	1	yes	characteristic
34	Dic₁₂	C₂×C₉	1	1	yes	characteristic
35	C₃×C₁₆	—	3	1	no	—
36	C₃⋊C₁₆	C₂×C₉	1	1	yes	characteristic
37	C₃²×C₄	—	4	1	no	—
38	C₃²×C₄	C₃×D₄	1	1	yes	characteristic
39	C₃×Dic₃	—	4	1	no	—
40	C₄×C₉	—	2	1	no	—
41	C₄×C₉	—	4	2	no	—
42	C₄×C₉	—	4	1	no	—
43	C₄×C₉	—	12	1	no	—
44	C₄×C₉	#67	1	1	yes	characteristic
45	Q₃₂	—	3	1	no	Sylow
46	C₃×C₉	Q₃₂	1	1	yes	characteristic, complemented, Sylow
47	C₃×Q₈	—	2	2	no	—
48	C₃×Q₈	—	2	1	no	—
49	C₃×Q₈	—	2	1	no	—
50	C₃×Q₈	—	6	1	no	—
51	Dic₆	—	2	1	no	—
52	C₃×C₈	—	2	1	no	—
53	C₃×C₈	C₂²×C₉	1	1	yes	characteristic
54	C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
55	C₂×C₃²	C₃×D₈	1	1	yes	characteristic
56	C₂×C₉	—	2	1	no	—
57	C₂×C₉	#213	1	1	yes	characteristic
58	Q₁₆	—	3	1	no	—
59	Q₁₆	D₃×C₉	1	1	yes	characteristic
60	C₁₆	—	3	1	no	—
61	C₃×C₄	—	2	1	no	—
62	C₃×C₄	—	4	2	no	—
63	C₃×C₄	—	4	1	no	—
64	C₃×C₄	—	4	1	no	—
65	C₃×C₄	—	12	1	no	—
66	C₃×C₄	D₄×C₉	1	1	yes	characteristic
67	C₃×C₄	C₃×#67	1	1	yes	characteristic
68	Dic₃	—	4	1	no	—
69	C₃²	C₃×Q₃₂	1	1	yes	characteristic
70	C₉	—	2	1	no	—
71	C₉	#829	1	1	yes	characteristic, direct product factor
72	Q₈	—	2	1	no	—
73	Q₈	—	6	1	no	—
74	C₈	C₂×D₃×C₉	1	1	yes	characteristic
75	C₂×C₃	—	2	1	no	—
76	C₂×C₃	C₉×D₈	1	1	yes	characteristic
77	C₂×C₃	C₃×#213	1	1	yes	characteristic
78	C₄	—	4	1	no	—
79	C₄	—	12	1	no	—
80	C₄	C₉×#67	1	1	yes	characteristic
81	C₃	—	2	1	no	—
82	C₃	C₉×Q₃₂	1	1	yes	characteristic, complemented
83	C₃	C₃×#829	1	1	yes	characteristic
84	C₂	C₉×#213	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#213
commutator	C₃×C₈	C₂²×C₉
Frattini	C₃×C₈	C₂×C₃×D₃
Fitting	C₃×C₉×Q₁₆	C₂
socle, prime radical	C₂×C₃²	C₃×D₈
cosocle	C₃²×C₈	C₂²×C₃
hypercenter	C₉×Q₁₆	D₃
hypocenter	C₃	C₉×Q₃₂
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉ ◁ C₈×C₉ ◁ C₉×Q₁₆

Complements

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

N	H ≅ G/N	type
20. #829	C₉	direct (N × H)
46. C₃×C₉	Q₃₂	semidirect
71. C₉	#829	direct (N × H)
82. C₃	C₉×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×Q₁₆	2
C₉×Dic₁₂	2
C₉×C₃⋊C₁₆	2
C₃×#829	3
C₉×Q₃₂	3

Subgroups — C9×#829 #11720468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#829 #11720468