Subgroups — Q₈×Q₁₆ #3382

Order 128.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈²	C₂	1	2	yes	maximal
2	#500	C₂	1	3	yes	maximal
3	#477	C₂	1	6	yes	maximal
4	C₈×Q₈	C₂	1	1	yes	maximal, characteristic
5	C₄×Q₁₆	C₂	1	3	yes	maximal
6	C₂×Q₁₆	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈	—	2	6	no	—
8	C₄⋊Q₈	C₂²	1	6	yes	—
9	C₄×Q₈	—	2	2	no	—
10	C₄×Q₈	C₂²	1	6	yes	—
11	C₄×Q₈	C₂²	1	1	yes	characteristic
12	#107	C₂²	1	3	yes	—
13	#107	C₂²	1	6	yes	—
14	C₄⋊C₈	C₂²	1	3	yes	—
15	#103	C₂²	1	6	yes	—
16	C₄×C₈	C₂²	1	3	yes	—
17	C₂×Q₈	—	2	6	no	—
18	C₂×Q₈	D₄	1	1	yes	characteristic
19	C₂×Q₈	C₂³	1	2	yes	—
20	Q₁₆	Q₈	1	4	yes	direct product factor
21	C₂×C₈	C₂³	1	3	yes	—
22	C₂×C₈	C₂³	1	1	yes	characteristic
23	C₄⋊C₄	—	2	6	no	—
24	C₄⋊C₄	—	2	6	no	—
25	C₄⋊C₄	D₄	1	3	yes	—
26	C₄⋊C₄	C₂³	1	6	yes	—
27	C₄²	—	2	6	no	—
28	C₄²	C₂³	1	3	yes	—
29	Q₈	—	2	2	no	—
30	Q₈	—	8	6	no	—
31	Q₈	Q₁₆	1	4	yes	direct product factor
32	Q₈	C₂×Q₈	1	4	yes	—
33	C₂×C₄	—	2	2	no	—
34	C₂×C₄	—	2	6	no	—
35	C₂×C₄	C₂×D₄	1	3	yes	—
36	C₂×C₄	C₂×D₄	1	3	yes	—
37	C₂×C₄	C₂⁴	1	1	yes	characteristic
38	C₈	—	2	3	no	—
39	C₈	C₂×Q₈	1	2	yes	—
40	C₂²	C₂²×D₄	1	1	yes	characteristic
41	C₄	—	2	4	no	—
42	C₄	—	2	3	no	—
43	C₄	—	4	6	no	—
44	C₄	C₂×Q₁₆	1	6	yes	—
45	C₄	C₂²×Q₈	1	1	yes	characteristic
46	C₄	2₋¹⁺⁴	1	1	yes	characteristic
47	C₂	D₄×Q₈	1	1	yes	characteristic
48	C₂	C₂²×Q₁₆	1	1	yes	characteristic
49	C₂	#576	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

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

N	H ≅ G/N	type
20. Q₁₆	Q₈	direct (N × H)
31. Q₈	Q₁₆	direct (N × H)

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