Subgroups — C₈×C₉×C₁₆ #11766031

Order 1152.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₉×C₁₆	C₂	1	2	yes	maximal
2	C₈²×C₉	C₂	1	1	yes	maximal, characteristic
3	C₃×C₈×C₁₆	C₃	1	1	yes	maximal, characteristic
4	C₂×C₉×C₁₆	C₄	1	4	yes	—
5	C₄×C₈×C₉	C₄	1	2	yes	—
6	C₄×C₈×C₉	C₂²	1	1	yes	characteristic
7	C₃×C₄×C₁₆	C₂×C₃	1	2	yes	—
8	C₃×C₈²	C₂×C₃	1	1	yes	characteristic
9	C₂×C₈×C₉	C₈	1	4	yes	—
10	C₂×C₈×C₉	C₂×C₄	1	2	yes	—
11	C₄²×C₉	C₂×C₄	1	1	yes	characteristic
12	C₉×C₁₆	C₈	1	8	yes	direct product factor
13	C₈×C₁₆	C₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₃×C₁₆	C₃×C₄	1	4	yes	—
15	C₃×C₄×C₈	C₃×C₄	1	2	yes	—
16	C₃×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
17	C₂×C₄×C₉	C₄²	1	1	yes	characteristic
18	C₂×C₄×C₉	C₂×C₈	1	2	yes	—
19	C₈×C₉	C₁₆	1	8	yes	direct product factor
20	C₈×C₉	C₂×C₈	1	4	yes	—
21	C₄×C₁₆	C₂×C₉	1	2	yes	—
22	C₈²	C₂×C₉	1	1	yes	characteristic
23	C₂×C₃×C₈	C₃×C₈	1	4	yes	—
24	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
25	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
26	C₃×C₁₆	C₃×C₈	1	8	yes	—
27	C₂²×C₉	C₄×C₈	1	1	yes	characteristic
28	C₄×C₉	C₄×C₈	1	2	yes	—
29	C₄×C₉	C₂×C₁₆	1	4	yes	—
30	C₂×C₁₆	C₄×C₉	1	4	yes	—
31	C₄×C₈	C₄×C₉	1	2	yes	—
32	C₄×C₈	C₂²×C₉	1	1	yes	characteristic
33	C₂×C₃×C₄	C₃×C₄²	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂×C₃×C₈	1	2	yes	—
35	C₃×C₈	C₃×C₁₆	1	8	yes	—
36	C₃×C₈	C₂×C₃×C₈	1	4	yes	—
37	C₂×C₉	C₈²	1	1	yes	characteristic
38	C₂×C₉	C₄×C₁₆	1	2	yes	—
39	C₂×C₈	C₈×C₉	1	4	yes	—
40	C₂×C₈	C₂×C₄×C₉	1	2	yes	—
41	C₄²	C₂×C₄×C₉	1	1	yes	characteristic
42	C₁₆	C₈×C₉	1	8	yes	direct product factor
43	C₂²×C₃	C₃×C₄×C₈	1	1	yes	characteristic
44	C₃×C₄	C₃×C₄×C₈	1	2	yes	—
45	C₃×C₄	C₂×C₃×C₁₆	1	4	yes	—
46	C₉	C₈×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×C₄	C₄²×C₉	1	1	yes	characteristic
48	C₂×C₄	C₂×C₈×C₉	1	2	yes	—
49	C₈	C₉×C₁₆	1	8	yes	direct product factor
50	C₈	C₂×C₈×C₉	1	4	yes	—
51	C₂×C₃	C₃×C₈²	1	1	yes	characteristic
52	C₂×C₃	C₃×C₄×C₁₆	1	2	yes	—
53	C₂²	C₄×C₈×C₉	1	1	yes	characteristic
54	C₄	C₄×C₈×C₉	1	2	yes	—
55	C₄	C₂×C₉×C₁₆	1	4	yes	—
56	C₃	C₃×C₈×C₁₆	1	1	yes	characteristic
57	C₂	C₈²×C₉	1	1	yes	characteristic
58	C₂	C₄×C₉×C₁₆	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
12. C₉×C₁₆	C₈	direct (N × H)
13. C₈×C₁₆	C₉	direct (N × H)
19. C₈×C₉	C₁₆	direct (N × H)
42. C₁₆	C₈×C₉	direct (N × H)
46. C₉	C₈×C₁₆	direct (N × H)
49. C₈	C₉×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₉×C₁₆	2
C₈²×C₉	2
C₃×C₈×C₁₆	3

Subgroups — C8×C9×C16 #11766031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₉×C₁₆ #11766031