Subgroups — C₉×#1273 #11765994

Order 1152.

318 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₉	C₂	1	3	yes	maximal
2	C₃×#1273	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₉	C₄	1	6	yes	—
4	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₉	—	2	6	no	—
6	C₂×C₃×C₄×C₈	C₂×C₃	1	3	yes	—
7	C₂²×C₄×C₉	C₂×C₄	1	3	yes	—
8	C₂×C₈×C₉	—	2	6	no	—
9	C₂×C₈×C₉	—	2	6	no	—
10	C₂×C₈×C₉	C₈	1	12	yes	complemented
11	C₄²×C₉	D₄	1	3	yes	—
12	C₄²×C₉	Q₈	1	1	yes	characteristic
13	#1273	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂²×C₃×C₈	C₃×C₄	1	6	yes	—
15	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
16	C₃×C₄×C₈	—	2	6	no	—
17	C₂³×C₉	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₉	C₂²⋊C₄	1	3	yes	—
19	C₂×C₄×C₉	C₄⋊C₄	1	3	yes	—
20	C₂×C₄×C₉	C₂×C₈	1	6	yes	—
21	C₂×C₄×C₉	M₁₆	1	6	yes	—
22	C₈×C₉	—	2	12	no	—
23	C₂×C₄×C₈	C₂×C₉	1	3	yes	—
24	C₂²×C₃×C₄	C₂×C₃×C₄	1	3	yes	—
25	C₂×C₃×C₈	—	2	6	no	—
26	C₂×C₃×C₈	—	2	6	no	—
27	C₂×C₃×C₈	C₃×C₈	1	12	yes	—
28	C₃×C₄²	C₃×D₄	1	3	yes	—
29	C₃×C₄²	C₃×Q₈	1	1	yes	characteristic
30	C₂²×C₉	#95	1	1	yes	characteristic
31	C₂²×C₉	C₄×C₈	1	3	yes	—
32	C₂²×C₉	#97	1	3	yes	—
33	C₄×C₉	C₂²⋊C₈	1	6	yes	—
34	C₄×C₉	C₄⋊C₈	1	6	yes	—
35	C₂²×C₈	C₄×C₉	1	6	yes	—
36	C₂×C₄²	C₂²×C₉	1	1	yes	characteristic
37	C₄×C₈	—	2	6	no	—
38	C₂³×C₃	C₃×C₄²	1	1	yes	characteristic
39	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	3	yes	—
40	C₂×C₃×C₄	C₃×C₄⋊C₄	1	3	yes	—
41	C₂×C₃×C₄	C₂×C₃×C₈	1	6	yes	—
42	C₂×C₃×C₄	C₃×M₁₆	1	6	yes	—
43	C₃×C₈	—	2	12	no	—
44	C₂×C₉	C₈²	1	1	yes	characteristic
45	C₂×C₉	#322	1	3	yes	—
46	C₂×C₉	#336	1	3	yes	—
47	C₂²×C₄	C₂×C₄×C₉	1	3	yes	—
48	C₂×C₈	—	2	6	no	—
49	C₂×C₈	—	2	6	no	—
50	C₂×C₈	C₈×C₉	1	12	yes	complemented
51	C₄²	D₄×C₉	1	3	yes	—
52	C₄²	Q₈×C₉	1	1	yes	characteristic
53	C₂²×C₃	C₃×#95	1	1	yes	characteristic
54	C₂²×C₃	C₃×C₄×C₈	1	3	yes	—
55	C₂²×C₃	C₃×#97	1	3	yes	—
56	C₃×C₄	C₃×C₂²⋊C₈	1	6	yes	—
57	C₃×C₄	C₃×C₄⋊C₈	1	6	yes	—
58	C₉	#1273	1	1	yes	characteristic, direct product factor, Sylow
59	C₂³	C₄²×C₉	1	1	yes	characteristic
60	C₂×C₄	C₉×C₂²⋊C₄	1	3	yes	—
61	C₂×C₄	C₉×C₄⋊C₄	1	3	yes	—
62	C₂×C₄	C₂×C₈×C₉	1	6	yes	—
63	C₂×C₄	C₉×M₁₆	1	6	yes	—
64	C₈	—	2	12	no	—
65	C₂×C₃	C₃×C₈²	1	1	yes	characteristic
66	C₂×C₃	C₃×#322	1	3	yes	—
67	C₂×C₃	C₃×#336	1	3	yes	—
68	C₂²	C₉×#95	1	1	yes	characteristic
69	C₂²	C₄×C₈×C₉	1	3	yes	—
70	C₂²	C₉×#97	1	3	yes	—
71	C₄	C₉×C₂²⋊C₈	1	6	yes	—
72	C₄	C₉×C₄⋊C₈	1	6	yes	—
73	C₃	C₃×#1273	1	1	yes	characteristic
74	C₂	C₈²×C₉	1	1	yes	characteristic
75	C₂	C₉×#322	1	3	yes	—
76	C₂	C₉×#336	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₉	C₂²
commutator	C₂	C₈²×C₉
Frattini, cosocle	C₂×C₃×C₄²	C₂²×C₃
socle, prime radical	C₂³×C₃	C₃×C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₂×C₈×C₉	C₈	semidirect
13. #1273	C₉	direct (N × H)
50. C₂×C₈	C₈×C₉	semidirect
58. C₉	#1273	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×C₉	2
C₃×#1273	3

Subgroups — C9×#1273 #11765994

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#1273 #11765994