Subgroups — C₉×#1313 #11766034

Order 1152.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#346	C₂	1	1	yes	maximal, characteristic
2	C₉×#346	C₂	1	1	yes	maximal, characteristic
3	C₉×#322	C₂	1	1	yes	maximal, characteristic
4	C₃×#1313	C₃	1	1	yes	maximal, characteristic
5	C₂×C₉×C₁₆	C₄	1	2	yes	—
6	C₂×C₉×C₁₆	C₄	1	2	yes	—
7	C₄×C₈×C₉	C₄	1	2	yes	—
8	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₃×#346	C₂×C₃	1	1	yes	characteristic
10	C₃×#346	C₂×C₃	1	1	yes	characteristic
11	C₃×#322	C₂×C₃	1	1	yes	characteristic
12	C₂×C₈×C₉	—	2	2	no	—
13	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₉	C₂×C₄	1	1	yes	characteristic
15	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×C₁₆	—	2	2	no	—
17	C₉×C₁₆	C₈	1	4	yes	complemented
18	#1313	C₉	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃×C₁₆	C₃×C₄	1	2	yes	—
20	C₂×C₃×C₁₆	C₃×C₄	1	2	yes	—
21	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
22	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
23	C₂×C₄×C₉	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₉	M₁₆	1	2	yes	—
25	C₈×C₉	—	4	2	no	—
26	C₈×C₉	C₂×C₈	1	2	yes	—
27	C₈×C₉	M₁₆	1	2	yes	—
28	#346	C₂×C₉	1	1	yes	characteristic
29	#346	C₂×C₉	1	1	yes	characteristic
30	#322	C₂×C₉	1	1	yes	characteristic
31	C₂×C₃×C₈	—	2	2	no	—
32	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
33	C₂×C₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
34	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
35	C₃×C₁₆	—	2	2	no	—
36	C₃×C₁₆	C₃×C₈	1	4	yes	—
37	C₂²×C₉	#97	1	1	yes	characteristic
38	C₄×C₉	—	2	2	no	—
39	C₄×C₉	C₄×C₈	1	1	yes	characteristic
40	C₄×C₉	#97	1	1	yes	characteristic
41	C₂×C₁₆	C₄×C₉	1	2	yes	—
42	C₂×C₁₆	C₄×C₉	1	2	yes	—
43	C₄×C₈	C₄×C₉	1	2	yes	—
44	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
45	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
46	C₂×C₃×C₄	C₃×M₁₆	1	2	yes	—
47	C₃×C₈	—	4	2	no	—
48	C₃×C₈	C₂×C₃×C₈	1	2	yes	—
49	C₃×C₈	C₃×M₁₆	1	2	yes	—
50	C₂×C₉	#322	1	1	yes	characteristic
51	C₂×C₉	#347	1	2	yes	—
52	C₂×C₈	—	2	2	no	—
53	C₂×C₈	C₂×C₄×C₉	1	1	yes	characteristic
54	C₂×C₈	C₂×C₄×C₉	1	1	yes	characteristic
55	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
56	C₁₆	—	2	2	no	—
57	C₁₆	C₈×C₉	1	4	yes	complemented
58	C₂²×C₃	C₃×#97	1	1	yes	characteristic
59	C₃×C₄	—	2	2	no	—
60	C₃×C₄	C₃×C₄×C₈	1	1	yes	characteristic
61	C₃×C₄	C₃×#97	1	1	yes	characteristic
62	C₉	#1313	1	1	yes	characteristic, direct product factor, Sylow
63	C₂×C₄	C₄²×C₉	1	1	yes	characteristic
64	C₂×C₄	C₉×M₁₆	1	2	yes	—
65	C₈	—	4	2	no	—
66	C₈	C₂×C₈×C₉	1	2	yes	—
67	C₈	C₉×M₁₆	1	2	yes	—
68	C₂×C₃	C₃×#322	1	1	yes	characteristic
69	C₂×C₃	C₃×#347	1	2	yes	—
70	C₂²	C₉×#97	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	C₄×C₈×C₉	1	1	yes	characteristic
73	C₄	C₉×#97	1	1	yes	characteristic
74	C₃	C₃×#1313	1	1	yes	characteristic
75	C₂	C₉×#322	1	1	yes	characteristic
76	C₂	C₉×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₉	C₄²
commutator	C₄	C₄×C₈×C₉
Frattini, cosocle	C₃×C₄×C₈	C₂²×C₃
socle, prime radical	C₂²×C₃	C₃×#97
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
17. C₉×C₁₆	C₈	semidirect
18. #1313	C₉	direct (N × H)
57. C₁₆	C₈×C₉	semidirect
62. C₉	#1313	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×#346	2
C₉×#322	2
C₃×#1313	3

Subgroups — C9×#1313 #11766034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1313 #11766034