Subgroups — C₉×#1309 #11766030

Order 1152.

219 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#423	C₂	1	3	yes	maximal
2	C₃×#1309	C₃	1	1	yes	maximal, characteristic
3	C₂×C₉×M₁₆	C₄	1	6	yes	—
4	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
5	C₉×C₄⋊C₈	—	2	6	no	—
6	C₃×#423	C₂×C₃	1	3	yes	—
7	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
8	C₉×M₁₆	—	4	6	no	—
9	C₂×C₈×C₉	—	2	6	no	—
10	C₄²×C₉	D₄	1	3	yes	—
11	C₄²×C₉	Q₈	1	1	yes	characteristic
12	#1309	C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×M₁₆	C₃×C₄	1	6	yes	—
14	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
15	C₃×C₄⋊C₈	—	2	6	no	—
16	C₂³×C₉	C₄²	1	1	yes	characteristic
17	C₂×C₄×C₉	—	2	3	no	—
18	C₂×C₄×C₉	—	2	3	no	—
19	C₂×C₄×C₉	C₂²⋊C₄	1	3	yes	—
20	C₂×C₄×C₉	C₄⋊C₄	1	3	yes	—
21	C₈×C₉	—	4	6	no	—
22	#423	C₂×C₉	1	3	yes	—
23	C₂²×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
24	C₃×M₁₆	—	4	6	no	—
25	C₂×C₃×C₈	—	2	6	no	—
26	C₃×C₄²	C₃×D₄	1	3	yes	—
27	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
28	C₂²×C₉	—	2	3	no	—
29	C₂²×C₉	#95	1	1	yes	characteristic
30	C₄×C₉	—	2	3	no	—
31	C₄×C₉	#100	1	3	yes	—
32	C₄×C₉	#101	1	3	yes	—
33	C₂×M₁₆	C₄×C₉	1	6	yes	—
34	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
35	C₄⋊C₈	—	2	6	no	—
36	C₂³×C₃	C₃×C₄²	1	1	yes	characteristic
37	C₂×C₃×C₄	—	2	3	no	—
38	C₂×C₃×C₄	—	2	3	no	—
39	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	3	yes	—
40	C₂×C₃×C₄	C₃×C₄⋊C₄	1	3	yes	—
41	C₃×C₈	—	4	6	no	—
42	C₂×C₉	—	4	1	no	—
43	C₂×C₉	#343	1	3	yes	—
44	C₂²×C₄	C₂×C₄×C₉	1	3	yes	—
45	M₁₆	—	4	6	no	—
46	C₂×C₈	—	2	6	no	—
47	C₄²	D₄×C₉	1	3	yes	—
48	C₄²	Q₈×C₉	1	1	yes	characteristic
49	C₂²×C₃	—	2	3	no	—
50	C₂²×C₃	C₃×#95	1	1	yes	characteristic
51	C₃×C₄	—	2	3	no	—
52	C₃×C₄	C₃×#100	1	3	yes	—
53	C₃×C₄	C₃×#101	1	3	yes	—
54	C₉	#1309	1	1	yes	characteristic, direct product factor, Sylow
55	C₂³	C₄²×C₉	1	1	yes	characteristic
56	C₂×C₄	—	2	3	no	—
57	C₂×C₄	—	2	3	no	—
58	C₂×C₄	C₉×C₂²⋊C₄	1	3	yes	—
59	C₂×C₄	C₉×C₄⋊C₄	1	3	yes	—
60	C₈	—	4	6	no	—
61	C₂×C₃	—	4	1	no	—
62	C₂×C₃	C₃×#343	1	3	yes	—
63	C₂²	—	2	3	no	—
64	C₂²	C₉×#95	1	1	yes	characteristic
65	C₄	—	2	3	no	—
66	C₄	C₉×#100	1	3	yes	—
67	C₄	C₉×#101	1	3	yes	—
68	C₃	C₃×#1309	1	1	yes	characteristic
69	C₂	—	4	1	no	—
70	C₂	C₉×#343	1	3	yes	—

	subgroup	G/H
center	C₂²×C₉	#95
commutator	C₂³	C₄²×C₉
Frattini, cosocle	C₂×C₃×C₄²	C₂²×C₃
socle	C₂²×C₃	C₃×#95
prime radical	C₂³×C₃	C₃×C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
12. #1309	C₉	direct (N × H)
54. C₉	#1309	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×#423	2
C₃×#1309	3

Subgroups — C9×#1309 #11766030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1309 #11766030