Subgroups — C₉×#857 #11720713

Order 864.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#857	C₃	1	1	yes	maximal, characteristic
3	C₉×#104	—	3	1	no	maximal
4	C₉×S₄	—	4	1	no	maximal
5	C₃×C₄²⋊C₃	C₂×C₃	1	1	yes	characteristic
6	C₉×#41	—	3	1	no	—
7	C₉×M₁₆	—	3	1	no	—
8	C₄²×C₉	D₃	1	1	yes	characteristic, complemented
9	C₄²⋊C₉	—	2	1	no	—
10	C₉×A₄	—	4	1	no	—
11	#857	C₉	1	1	yes	characteristic, direct product factor
12	C₃×#104	—	3	1	no	—
13	C₃×S₄	—	4	1	no	—
14	Q₈×C₉	—	3	1	no	—
15	D₄×C₉	—	3	1	no	—
16	D₄×C₉	—	6	1	no	—
17	C₂×C₄×C₉	—	3	1	no	—
18	C₂×C₄×C₉	—	6	1	no	—
19	C₈×C₉	—	6	1	no	—
20	D₃×C₉	—	16	1	no	—
21	C₃×#41	—	3	1	no	—
22	C₃×M₁₆	—	3	1	no	—
23	C₃×C₄²	C₃×D₃	1	1	yes	characteristic
24	C₄²⋊C₃	—	2	1	no	—
25	C₄²⋊C₃	C₂×C₉	1	1	yes	characteristic, complemented
26	C₃×A₄	—	4	1	no	—
27	C₂²×C₉	—	6	1	no	—
28	C₂²×C₉	S₄	1	1	yes	characteristic
29	C₂²⋊C₉	—	8	1	no	—
30	C₄×C₉	—	3	1	no	—
31	C₄×C₉	—	3	1	no	—
32	C₄×C₉	—	6	1	no	—
33	#104	—	3	1	no	Sylow
34	C₃×C₉	—	16	1	no	Sylow
35	S₄	—	4	1	no	—
36	C₃×Q₈	—	3	1	no	—
37	C₃×D₄	—	3	1	no	—
38	C₃×D₄	—	6	1	no	—
39	C₂×C₃×C₄	—	3	1	no	—
40	C₂×C₃×C₄	—	6	1	no	—
41	C₃×C₈	—	6	1	no	—
42	C₃×D₃	—	16	1	no	—
43	C₂×C₉	—	3	1	no	—
44	C₂×C₉	—	12	1	no	—
45	#41	—	3	1	no	—
46	M₁₆	—	3	1	no	—
47	C₄²	D₃×C₉	1	1	yes	characteristic, complemented
48	C₂²×C₃	—	6	1	no	—
49	C₂²×C₃	C₃×S₄	1	1	yes	characteristic
50	A₄	—	4	1	no	—
51	A₄	—	8	1	no	—
52	C₃×C₄	—	3	1	no	—
53	C₃×C₄	—	3	1	no	—
54	C₃×C₄	—	6	1	no	—
55	C₃²	—	16	1	no	—
56	C₉	—	32	1	no	—
57	C₉	#857	1	1	yes	characteristic, direct product factor
58	Q₈	—	3	1	no	—
59	D₄	—	3	1	no	—
60	D₄	—	6	1	no	—
61	C₂×C₄	—	3	1	no	—
62	C₂×C₄	—	6	1	no	—
63	C₈	—	6	1	no	—
64	C₂×C₃	—	3	1	no	—
65	C₂×C₃	—	12	1	no	—
66	D₃	—	16	1	no	—
67	C₂²	—	6	1	no	—
68	C₂²	C₉×S₄	1	1	yes	characteristic
69	C₄	—	3	1	no	—
70	C₄	—	3	1	no	—
71	C₄	—	6	1	no	—
72	C₃	—	16	1	no	—
73	C₃	—	32	1	no	—
74	C₃	C₃×#857	1	1	yes	characteristic
75	C₂	—	3	1	no	—
76	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₉	#857
commutator, hypocenter	C₄²⋊C₃	C₂×C₉
Frattini, socle	C₂²×C₃	C₃×S₄
Fitting	C₄²×C₉	D₃
prime radical	C₃×#857	C₃
cosocle	C₃×C₄²⋊C₃	C₂×C₃
LCS	G ▷ C₄²⋊C₃
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₄²⋊C₃	C₂	semidirect
8. C₄²×C₉	D₃	semidirect
11. #857	C₉	direct (N × H)
25. C₄²⋊C₃	C₂×C₉	semidirect
47. C₄²	D₃×C₉	semidirect
57. C₉	#857	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×C₄²⋊C₃	2
C₃×#857	3
C₉×#104	3
C₉×S₄	4

Subgroups — C9×#857 #11720713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#857 #11720713