Subgroups — C₁₆×#6090 #15749532

Order 3328.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#6090	C₂	1	2	yes	maximal
2	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
4	C₈²×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×#6090	C₄	1	4	yes	—
6	C₂×C₁₃×C₁₆	C₈	1	4	yes	—
7	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
8	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₂×#6090	C₈	1	8	yes	—
10	C₁₆²	—	13	1	no	maximal, Sylow
11	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
12	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
13	C₄²×C₁₃	C₄²	1	1	yes	characteristic
14	C₁₃×C₁₆	C₁₆	1	8	yes	complemented
15	#6090	C₁₆	1	16	yes	direct product factor
16	C₈×C₁₆	—	13	2	no	—
17	C₈×C₁₆	D₁₃	1	1	yes	characteristic
18	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
19	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
20	C₈×C₁₃	C₂×C₁₆	1	8	yes	—
21	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
22	C₄×C₁₆	—	13	4	no	—
23	C₄×C₁₆	Dic₁₃	1	2	yes	—
24	C₈²	C₂×D₁₃	1	1	yes	characteristic
25	C₂²×C₁₃	C₈²	1	1	yes	characteristic
26	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
27	C₄×C₁₃	C₄×C₁₆	1	4	yes	—
28	C₂×C₁₆	—	13	8	no	—
29	C₂×C₁₆	#1055	1	4	yes	—
30	C₄×C₈	C₄×D₁₃	1	2	yes	—
31	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
32	C₂×C₁₃	C₈×C₁₆	1	2	yes	—
33	C₂×C₁₃	C₈×C₁₆	1	1	yes	characteristic
34	C₂×C₈	C₈×D₁₃	1	4	yes	—
35	C₂×C₈	C₂×#1055	1	2	yes	—
36	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
37	C₁₆	—	13	16	no	—
38	C₁₆	#6090	1	8	yes	direct product factor
39	C₁₃	C₁₆²	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₄	C₄×#1055	1	1	yes	characteristic
41	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
42	C₈	C₁₆×D₁₃	1	8	yes	—
43	C₈	C₂×#6090	1	4	yes	—
44	C₂²	C₈×#1055	1	1	yes	characteristic
45	C₄	C₄×#6090	1	2	yes	—
46	C₄	C₁₆×Dic₁₃	1	4	yes	—
47	C₂	C₁₆×#1055	1	2	yes	—
48	C₂	C₈×#6090	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₈×C₁₆	D₁₃
commutator, hypocenter	C₁₃	C₁₆²
Frattini	C₈²	C₂×D₁₃
Fitting	C₈×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	C₈²
cosocle	C₈²×C₁₃	C₂²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
14. C₁₃×C₁₆	C₁₆	semidirect
15. #6090	C₁₆	direct (N × H)
38. C₁₆	#6090	direct (N × H)
39. C₁₃	C₁₆²	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6090	2
C₈×C₁₃×C₁₆	2
C₁₆²	13

Subgroups — C16×#6090 #15749532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×#6090 #15749532