Subgroups — C₉×#876 #11721378

Order 864.

210 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×(C₂×D₃)⋊C₄	C₂	1	3	yes	maximal
3	C₉×Dic₃⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₃×#876	C₃	1	1	yes	maximal, characteristic
5	C₉×#126	—	3	1	no	maximal
6	C₂²×D₃×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₂×C₉×Dic₃	C₂²	1	3	yes	—
9	C₃²×C₄²	C₂×C₃	1	1	yes	characteristic
10	C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	3	yes	—
11	C₃×Dic₃⋊C₄	C₂×C₃	1	3	yes	—
12	C₉×C₄⋊C₄	—	3	3	no	—
13	C₉×C₂²⋊C₄	—	3	3	no	—
14	C₄²×C₉	—	2	1	no	—
15	C₄²×C₉	D₃	1	1	yes	characteristic, complemented
16	C₂²×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₂×D₃×C₉	—	2	3	no	—
18	C₃×C₄×C₉	—	2	3	no	—
19	C₉×Dic₃	—	2	3	no	—
20	C₃×#126	—	3	1	no	—
21	#876	C₉	1	1	yes	characteristic, direct product factor
22	C₂²×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₄	C₂²×C₃	1	3	yes	—
24	C₂×C₃×Dic₃	C₂²×C₃	1	3	yes	—
25	C₂³×C₉	—	3	1	no	—
26	C₂×C₄×C₉	—	2	3	no	—
27	C₂×C₄×C₉	—	3	3	no	—
28	C₂×C₄×C₉	C₂×D₃	1	3	yes	—
29	C₂×C₃×C₉	#41	1	3	yes	—
30	D₃×C₉	—	4	1	no	—
31	C₃×C₄⋊C₄	—	3	3	no	—
32	C₃×C₂²⋊C₄	—	3	3	no	—
33	C₃×C₄²	—	2	1	no	—
34	C₃×C₄²	C₂×C₉	1	1	yes	characteristic, complemented
35	C₃×C₄²	C₃×D₃	1	1	yes	characteristic
36	(C₂×D₃)⋊C₄	C₂×C₉	1	3	yes	—
37	Dic₃⋊C₄	C₂×C₉	1	3	yes	complemented
38	C₂²×C₃²	C₂³×C₃	1	1	yes	characteristic
39	C₂×C₃×D₃	—	2	3	no	—
40	C₃²×C₄	—	2	3	no	—
41	C₃×Dic₃	—	2	3	no	—
42	C₂²×C₉	—	2	1	no	—
43	C₂²×C₉	—	6	3	no	—
44	C₂²×C₉	C₂²×D₃	1	1	yes	characteristic
45	C₄×C₉	—	2	6	no	—
46	C₄×C₉	—	2	3	no	—
47	C₄×C₉	—	6	3	no	—
48	#126	—	3	1	no	Sylow
49	C₃×C₉	#126	1	1	yes	characteristic, complemented, Sylow
50	C₂³×C₃	—	3	1	no	—
51	C₂²×D₃	C₂²×C₉	1	1	yes	characteristic
52	C₂×C₃×C₄	—	2	3	no	—
53	C₂×C₃×C₄	—	3	3	no	—
54	C₂×C₃×C₄	C₂²×C₉	1	3	yes	—
55	C₂×C₃×C₄	C₂×C₃×D₃	1	3	yes	—
56	C₂×Dic₃	C₂²×C₉	1	3	yes	—
57	C₂×C₃²	C₃×#41	1	3	yes	—
58	C₃×D₃	—	4	1	no	—
59	C₂×C₉	—	2	3	no	—
60	C₂×C₉	—	12	1	no	—
61	C₂×C₉	#235	1	3	yes	—
62	C₄⋊C₄	—	3	3	no	—
63	C₂²⋊C₄	—	3	3	no	—
64	C₄²	D₃×C₉	1	1	yes	characteristic, complemented
65	C₂²×C₃	—	2	1	no	—
66	C₂²×C₃	—	6	3	no	—
67	C₂²×C₃	C₂³×C₉	1	1	yes	characteristic
68	C₂²×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
69	C₂×D₃	—	2	3	no	—
70	C₃×C₄	—	2	6	no	—
71	C₃×C₄	—	2	3	no	—
72	C₃×C₄	—	2	3	no	—
73	C₃×C₄	—	6	3	no	—
74	Dic₃	—	2	3	no	—
75	C₃²	C₃×#126	1	1	yes	characteristic
76	C₉	—	2	1	no	—
77	C₉	#876	1	1	yes	characteristic, direct product factor
78	C₂³	—	3	1	no	—
79	C₂×C₄	—	3	3	no	—
80	C₂×C₄	C₂×D₃×C₉	1	3	yes	—
81	C₂×C₃	—	2	3	no	—
82	C₂×C₃	—	12	1	no	—
83	C₂×C₃	C₉×#41	1	3	yes	—
84	C₂×C₃	C₃×#235	1	3	yes	—
85	D₃	—	4	1	no	—
86	C₂²	—	6	3	no	—
87	C₂²	C₂²×D₃×C₉	1	1	yes	characteristic
88	C₄	—	2	3	no	—
89	C₄	—	6	3	no	—
90	C₃	—	2	1	no	—
91	C₃	C₉×#126	1	1	yes	characteristic, complemented
92	C₃	C₃×#876	1	1	yes	characteristic
93	C₂	—	12	1	no	—
94	C₂	C₉×#235	1	3	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₉
Frattini	C₂²×C₃	C₂²×C₃×D₃
Fitting	C₃×C₄²×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂³×C₃
prime radical	C₂²×C₃×D₃	C₂²×C₃
hypercenter	C₄²×C₉	D₃
hypocenter	C₃	C₉×#126
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₉	C₂	semidirect
3. C₉×Dic₃⋊C₄	C₂	semidirect
15. C₄²×C₉	D₃	semidirect
21. #876	C₉	direct (N × H)
34. C₃×C₄²	C₂×C₉	semidirect
37. Dic₃⋊C₄	C₂×C₉	semidirect
49. C₃×C₉	#126	semidirect
64. C₄²	D₃×C₉	semidirect
77. C₉	#876	direct (N × H)
91. C₃	C₉×#126	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₉	2
C₉×(C₂×D₃)⋊C₄	2
C₉×Dic₃⋊C₄	2
C₃×#876	3
C₉×#126	3

Subgroups — C9×#876 #11721378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#876 #11721378