Subgroups — C₁₆×Q₁₆ #12052

Order 256.

109 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₆	C₂	1	2	yes	maximal
2	C₈×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	#1370	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊C₁₆	C₂	1	2	yes	maximal
5	C₈×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₈×Q₈	C₂²	1	2	yes	—
7	C₄×Q₁₆	C₄	1	1	yes	characteristic
8	C₄⋊C₁₆	—	2	2	no	—
9	C₄⋊C₁₆	C₂²	1	2	yes	—
10	C₄×C₁₆	—	2	2	no	—
11	C₄×C₁₆	C₂²	1	1	yes	characteristic
12	C₄×C₁₆	C₂²	1	1	yes	characteristic
13	#335	C₄	1	1	yes	characteristic
14	Q₈⋊C₈	C₄	1	2	yes	—
15	C₈²	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆	C₈	1	1	yes	characteristic
17	C₄×Q₈	C₂×C₄	1	2	yes	—
18	C₂×C₁₆	—	2	1	no	—
19	C₂×C₁₆	—	2	2	no	—
20	C₂×C₁₆	D₄	1	1	yes	characteristic
21	C₂×C₁₆	D₄	1	1	yes	characteristic
22	#107	C₈	1	1	yes	characteristic
23	C₄⋊C₈	—	2	2	no	—
24	C₄⋊C₈	C₂×C₄	1	2	yes	—
25	#103	C₈	1	2	yes	—
26	C₄×C₈	—	2	2	no	—
27	C₄×C₈	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈	C₂×C₄	1	1	yes	characteristic
29	C₄×C₈	C₂³	1	1	yes	characteristic
30	C₂×Q₈	C₂×C₈	1	2	yes	—
31	Q₁₆	C₁₆	1	4	yes	direct product factor
32	C₂×C₈	—	2	1	no	—
33	C₂×C₈	—	2	2	no	—
34	C₂×C₈	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈	C₂×D₄	1	1	yes	characteristic
37	C₂×C₈	#41	1	1	yes	characteristic
38	C₄⋊C₄	—	2	2	no	—
39	C₄⋊C₄	C₂×C₈	1	2	yes	—
40	C₄²	—	2	2	no	—
41	C₄²	C₂²×C₄	1	1	yes	characteristic
42	C₁₆	—	2	2	no	—
43	C₁₆	—	2	1	no	—
44	C₁₆	—	4	2	no	—
45	C₁₆	Q₁₆	1	2	yes	direct product factor
46	Q₈	—	2	2	no	—
47	Q₈	C₂×C₁₆	1	4	yes	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	C₄×D₄	1	1	yes	characteristic
51	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄	#131	1	1	yes	characteristic
53	C₈	—	2	2	no	—
54	C₈	—	2	1	no	—
55	C₈	—	2	1	no	—
56	C₈	—	4	2	no	—
57	C₈	C₂×C₁₆	1	2	yes	—
58	C₈	C₂×Q₁₆	1	1	yes	characteristic
59	C₈	#135	1	1	yes	characteristic
60	C₂²	C₈×D₄	1	1	yes	characteristic
61	C₄	—	2	4	no	—
62	C₄	—	2	1	no	—
63	C₄	—	4	2	no	—
64	C₄	C₄×Q₁₆	1	1	yes	characteristic
65	C₄	#443	1	1	yes	characteristic
66	C₄	C₂²×C₁₆	1	1	yes	characteristic
67	C₄	#504	1	1	yes	characteristic
68	C₂	C₈×Q₁₆	1	1	yes	characteristic
69	C₂	D₄×C₁₆	1	1	yes	characteristic
70	C₂	#2170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	D₄
commutator	C₄	C₂²×C₁₆
Frattini, cosocle	C₄×C₈	C₂³
socle, prime radical	C₂²	C₈×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
31. Q₁₆	C₁₆	direct (N × H)
45. C₁₆	Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×C₁₆	2
C₈×Q₁₆	2
#1370	2
Q₈⋊C₁₆	2
C₈×C₁₆	2

Subgroups — C16×Q16 #12052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₆×Q₁₆ #12052