Subgroups — D₄×C₁₆ #2167

Order 128.

87 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆	C₂	1	2	yes	maximal, complemented
2	C₈×D₄	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊C₁₆	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈	C₂²	1	2	yes	—
7	C₄×D₄	C₄	1	1	yes	characteristic
8	C₂×C₁₆	—	2	4	no	—
9	C₂×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₆	C₂²	1	2	yes	—
11	C₂×C₁₆	C₂²	1	1	yes	characteristic
12	C₄⋊C₈	C₄	1	1	yes	characteristic
13	C₂²⋊C₈	C₄	1	2	yes	—
14	C₄×C₈	C₂²	1	1	yes	characteristic
15	C₂×D₄	C₈	1	1	yes	characteristic
16	C₂²×C₄	C₂×C₄	1	2	yes	—
17	C₂×C₈	—	2	2	no	—
18	C₂×C₈	—	2	2	no	—
19	C₂×C₈	C₂×C₄	1	1	yes	characteristic
20	C₂×C₈	C₂×C₄	1	2	yes	—
21	C₂×C₈	C₂³	1	1	yes	characteristic
22	C₄⋊C₄	C₈	1	1	yes	characteristic
23	C₂²⋊C₄	C₈	1	2	yes	—
24	C₄²	C₂×C₄	1	1	yes	characteristic
25	C₁₆	—	2	2	no	—
26	C₁₆	—	2	1	no	—
27	C₁₆	D₄	1	2	yes	direct product factor
28	C₂³	C₂×C₈	1	2	yes	—
29	D₄	C₁₆	1	4	yes	direct product factor
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	—	2	2	no	—
32	C₂×C₄	C₂×C₈	1	1	yes	characteristic
33	C₂×C₄	C₂×C₈	1	2	yes	—
34	C₂×C₄	C₂×C₈	1	1	yes	characteristic
35	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
36	C₈	—	2	2	no	—
37	C₈	—	2	1	no	—
38	C₈	C₂×D₄	1	1	yes	characteristic
39	C₈	#41	1	1	yes	characteristic
40	C₂²	—	2	2	no	—
41	C₂²	—	2	2	no	—
42	C₂²	C₂×C₁₆	1	4	yes	complemented
43	C₂²	C₂²×C₈	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	—	2	1	no	—
46	C₄	C₂×C₁₆	1	2	yes	complemented
47	C₄	C₄×D₄	1	1	yes	characteristic
48	C₄	#131	1	1	yes	characteristic
49	C₂	—	2	4	no	—
50	C₂	C₈×D₄	1	1	yes	characteristic
51	C₂	C₂²×C₁₆	1	1	yes	characteristic
52	C₂	#504	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₆	C₂	semidirect
3. C₄⋊C₁₆	C₂	semidirect
4. C₂²⋊C₁₆	C₂	semidirect
5. C₄×C₁₆	C₂	semidirect
27. C₁₆	D₄	direct (N × H)
29. D₄	C₁₆	direct (N × H)
42. C₂²	C₂×C₁₆	semidirect
46. C₄	C₂×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₆	2
C₈×D₄	2
C₄⋊C₁₆	2
C₂²⋊C₁₆	2
C₄×C₁₆	2

Subgroups — D4×C16 #2167

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₆ #2167