Subgroups — C₉×#1357 #11766078

Order 1152.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#493	C₂	1	1	yes	maximal, characteristic
2	C₉×#364	C₂	1	2	yes	maximal, complemented
3	C₃×#1357	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×D₈	—	2	2	no	—
5	C₉×#127	C₄	1	2	yes	—
6	C₉×M₃₂	—	2	2	no	—
7	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
8	C₃×#493	C₂×C₃	1	1	yes	characteristic
9	C₃×#364	C₂×C₃	1	2	yes	—
10	C₂×D₄×C₉	—	2	2	no	—
11	C₂×D₄×C₉	—	4	2	no	—
12	C₉×D₈	—	4	2	no	—
13	C₉×D₈	—	4	2	no	—
14	C₂×C₈×C₉	D₄	1	2	yes	—
15	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
16	C₉×C₁₆	—	4	2	no	—
17	#1357	C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×D₈	—	2	2	no	—
19	C₃×#127	C₃×C₄	1	2	yes	—
20	C₃×M₃₂	—	2	2	no	—
21	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
22	C₂³×C₉	—	4	2	no	—
23	D₄×C₉	—	4	4	no	—
24	D₄×C₉	—	8	4	no	—
25	C₂×C₄×C₉	—	2	1	no	—
26	C₂×C₄×C₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₈×C₉	D₈	1	2	yes	—
28	C₈×C₉	SD₁₆	1	2	yes	—
29	#493	C₂×C₉	1	1	yes	characteristic
30	#364	C₂×C₉	1	2	yes	complemented
31	C₂×C₃×D₄	—	2	2	no	—
32	C₂×C₃×D₄	—	4	2	no	—
33	C₃×D₈	—	4	2	no	—
34	C₃×D₈	—	4	2	no	—
35	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
36	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
37	C₃×C₁₆	—	4	2	no	—
38	C₂²×C₉	—	8	4	no	—
39	C₂²×C₉	—	8	2	no	—
40	C₂²×C₉	#100	1	1	yes	characteristic
41	C₄×C₉	—	2	2	no	—
42	C₄×C₉	#102	1	2	yes	—
43	C₂×D₈	—	2	2	no	—
44	#127	C₄×C₉	1	2	yes	—
45	M₃₂	—	2	2	no	—
46	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
47	C₂³×C₃	—	4	2	no	—
48	C₃×D₄	—	4	4	no	—
49	C₃×D₄	—	8	4	no	—
50	C₂×C₃×C₄	—	2	1	no	—
51	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
52	C₃×C₈	C₃×D₈	1	2	yes	—
53	C₃×C₈	C₃×SD₁₆	1	2	yes	—
54	C₂×C₉	—	2	1	no	—
55	C₂×C₉	—	16	2	no	—
56	C₂×C₉	#331	1	1	yes	characteristic
57	C₂×D₄	—	2	2	no	—
58	C₂×D₄	—	4	2	no	—
59	D₈	—	4	2	no	—
60	D₈	—	4	2	no	—
61	C₂×C₈	D₄×C₉	1	2	yes	—
62	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
63	C₁₆	—	4	2	no	—
64	C₂²×C₃	—	8	4	no	—
65	C₂²×C₃	—	8	2	no	—
66	C₂²×C₃	C₃×#100	1	1	yes	characteristic
67	C₃×C₄	—	2	2	no	—
68	C₃×C₄	C₃×#102	1	2	yes	—
69	C₉	#1357	1	1	yes	characteristic, direct product factor, Sylow
70	C₂³	—	4	2	no	—
71	D₄	—	4	4	no	—
72	D₄	—	8	4	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	C₉×C₂²⋊C₄	1	1	yes	characteristic
75	C₈	C₉×D₈	1	2	yes	—
76	C₈	C₉×SD₁₆	1	2	yes	—
77	C₂×C₃	—	2	1	no	—
78	C₂×C₃	—	16	2	no	—
79	C₂×C₃	C₃×#331	1	1	yes	characteristic
80	C₂²	—	8	4	no	—
81	C₂²	—	8	2	no	—
82	C₂²	C₉×#100	1	1	yes	characteristic
83	C₄	—	2	2	no	—
84	C₄	C₉×#102	1	2	yes	—
85	C₃	C₃×#1357	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	16	2	no	—
88	C₂	C₉×#331	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	#331
commutator	C₄²	C₂×C₄×C₉
Frattini, cosocle	C₃×C₄×C₈	C₂²×C₃
socle	C₂×C₃	C₃×#331
prime radical	C₃×#493	C₂×C₃
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₄×C₈×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₉×#364	C₂	semidirect
17. #1357	C₉	direct (N × H)
30. #364	C₂×C₉	semidirect
69. C₉	#1357	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×#493	2
C₉×#364	2
C₃×#1357	3

Subgroups — C9×#1357 #11766078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1357 #11766078