Subgroups — C₉×#499 #10589053

Order 576.

129 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#125	C₂	1	2	yes	maximal
2	C₉×#107	C₂	1	2	yes	maximal
3	C₉×#106	C₂	1	2	yes	maximal
4	C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
5	C₃×#499	C₃	1	1	yes	maximal, characteristic
6	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₉×C₄⋊C₄	—	2	4	no	—
9	C₉×C₄⋊C₄	C₂²	1	4	yes	—
10	C₄²×C₉	C₂²	1	1	yes	characteristic
11	C₃×#125	C₂×C₃	1	2	yes	—
12	C₃×#107	C₂×C₃	1	2	yes	—
13	C₃×#106	C₂×C₃	1	2	yes	—
14	C₃×C₄×C₈	C₂×C₃	1	1	yes	characteristic
15	C₂×C₄×C₉	—	2	4	no	—
16	C₂×C₄×C₉	D₄	1	2	yes	—
17	C₂×C₄×C₉	C₂³	1	1	yes	characteristic
18	C₈×C₉	Q₈	1	2	yes	—
19	C₈×C₉	Q₈	1	2	yes	—
20	#499	C₉	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₃×C₄⋊C₄	—	2	4	no	—
24	C₃×C₄⋊C₄	C₂²×C₃	1	4	yes	—
25	C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
26	C₂²×C₉	C₂×D₄	1	1	yes	characteristic
27	C₄×C₉	—	2	2	no	—
28	C₄×C₉	—	4	4	no	—
29	C₄×C₉	C₂×Q₈	1	1	yes	characteristic
30	C₄×C₉	C₂×Q₈	1	1	yes	characteristic
31	#125	C₂×C₉	1	2	yes	—
32	#107	C₂×C₉	1	2	yes	—
33	#106	C₂×C₉	1	2	yes	—
34	C₄×C₈	C₂×C₉	1	1	yes	characteristic
35	C₂×C₃×C₄	—	2	4	no	—
36	C₂×C₃×C₄	C₃×D₄	1	2	yes	—
37	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
38	C₃×C₈	C₃×Q₈	1	2	yes	—
39	C₃×C₈	C₃×Q₈	1	2	yes	—
40	C₂×C₉	C₄⋊Q₈	1	1	yes	characteristic
41	C₂×C₉	#135	1	2	yes	—
42	C₂×C₈	C₂²×C₉	1	1	yes	characteristic
43	C₂×C₈	C₂²×C₉	1	1	yes	characteristic
44	C₄⋊C₄	—	2	4	no	—
45	C₄⋊C₄	C₂²×C₉	1	4	yes	—
46	C₄²	C₂²×C₉	1	1	yes	characteristic
47	C₂²×C₃	C₂×C₃×D₄	1	1	yes	characteristic
48	C₃×C₄	—	2	2	no	—
49	C₃×C₄	—	4	4	no	—
50	C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
51	C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
52	C₉	#499	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₄	—	2	4	no	—
54	C₂×C₄	D₄×C₉	1	2	yes	—
55	C₂×C₄	C₂³×C₉	1	1	yes	characteristic
56	C₈	Q₈×C₉	1	2	yes	—
57	C₈	Q₈×C₉	1	2	yes	—
58	C₂×C₃	C₃×C₄⋊Q₈	1	1	yes	characteristic
59	C₂×C₃	C₃×#135	1	2	yes	—
60	C₂²	C₂×D₄×C₉	1	1	yes	characteristic
61	C₄	—	2	2	no	—
62	C₄	—	4	4	no	—
63	C₄	C₂×Q₈×C₉	1	1	yes	characteristic
64	C₄	C₂×Q₈×C₉	1	1	yes	characteristic
65	C₃	C₃×#499	1	1	yes	characteristic
66	C₂	C₉×C₄⋊Q₈	1	1	yes	characteristic
67	C₂	C₉×#135	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂³×C₃
socle, prime radical	C₂²×C₃	C₂×C₃×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
20. #499	C₉	direct (N × H)
52. C₉	#499	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×#125	2
C₉×#107	2
C₉×#106	2
C₄×C₈×C₉	2
C₃×#499	3

Subgroups — C9×#499 #10589053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#499 #10589053