Subgroups — C₄×SD₁₆ #438

Order 64.

61 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄	C₂	1	1	yes	maximal, characteristic
4	#106	C₂	1	1	yes	maximal, characteristic, complemented
5	#103	C₂	1	1	yes	maximal, characteristic, complemented
6	#102	C₂	1	1	yes	maximal, characteristic
7	C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈	C₂²	1	1	yes	characteristic
9	C₂×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₄	—	2	1	no	—
11	SD₁₆	C₄	1	4	yes	direct product factor
12	C₂×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₈	C₂²	1	1	yes	characteristic
14	C₄⋊C₄	—	2	1	no	—
15	C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²⋊C₄	—	2	1	no	—
18	C₄²	—	2	1	no	—
19	C₄²	C₂²	1	1	yes	characteristic
20	C₂³	—	2	1	no	—
21	Q₈	—	2	1	no	—
22	Q₈	C₂×C₄	1	2	yes	complemented
23	D₄	—	2	1	no	—
24	D₄	C₂×C₄	1	2	yes	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	—	2	1	no	—
28	C₂×C₄	—	4	2	no	—
29	C₂×C₄	D₄	1	1	yes	characteristic
30	C₂×C₄	D₄	1	1	yes	characteristic
31	C₂×C₄	C₂³	1	1	yes	characteristic
32	C₈	—	2	1	no	—
33	C₈	C₂×C₄	1	2	yes	complemented
34	C₂²	—	2	2	no	—
35	C₂²	—	4	1	no	—
36	C₂²	—	4	1	no	—
37	C₂²	C₂×D₄	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	2	1	no	—
40	C₄	—	4	1	no	—
41	C₄	—	4	1	no	—
42	C₄	SD₁₆	1	2	yes	direct product factor
43	C₄	C₂²×C₄	1	1	yes	characteristic
44	C₄	#41	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	C₄×D₄	1	1	yes	characteristic
47	C₂	C₂×SD₁₆	1	1	yes	characteristic
48	C₂	#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄
commutator	C₄	C₂²×C₄
Frattini, cosocle	C₂×C₄	C₂³
socle	C₂²	C₂×D₄
prime radical	C₂×D₄	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈	C₂	semidirect
4. #106	C₂	semidirect
5. #103	C₂	semidirect
7. C₄×C₈	C₂	semidirect
11. SD₁₆	C₄	direct (N × H)
22. Q₈	C₂×C₄	semidirect
33. C₈	C₂×C₄	semidirect
42. C₄	SD₁₆	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×SD₁₆	2
C₄×Q₈	2
C₄×D₄	2
#106	2
#103	2
#102	2
C₄×C₈	2

Subgroups — C4×SD16 #438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆ #438