Subgroups — Q₈×C₁₆ #2182

Order 128.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆	C₂	1	3	yes	maximal
3	C₄×C₁₆	C₂	1	3	yes	maximal
4	C₄×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₁₆	C₂²	1	3	yes	—
6	C₂×C₁₆	C₂²	1	1	yes	characteristic
7	C₄⋊C₈	C₄	1	3	yes	—
8	C₄×C₈	C₂²	1	3	yes	—
9	C₂×Q₈	C₈	1	1	yes	characteristic
10	C₂×C₈	C₂×C₄	1	3	yes	—
11	C₂×C₈	C₂³	1	1	yes	characteristic
12	C₄⋊C₄	C₈	1	3	yes	—
13	C₄²	C₂×C₄	1	3	yes	—
14	C₁₆	—	2	3	no	—
15	C₁₆	Q₈	1	2	yes	direct product factor
16	Q₈	C₁₆	1	4	yes	direct product factor
17	C₂×C₄	C₂×C₈	1	3	yes	—
18	C₂×C₄	C₂×C₈	1	3	yes	—
19	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
20	C₈	—	2	3	no	—
21	C₈	C₂×Q₈	1	1	yes	characteristic
22	C₈	#41	1	1	yes	characteristic
23	C₂²	C₂²×C₈	1	1	yes	characteristic
24	C₄	—	2	3	no	—
25	C₄	C₂×C₁₆	1	6	yes	—
26	C₄	C₄×Q₈	1	1	yes	characteristic
27	C₄	#131	1	1	yes	characteristic
28	C₂	C₈×Q₈	1	1	yes	characteristic
29	C₂	C₂²×C₁₆	1	1	yes	characteristic
30	C₂	#504	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₁₆	Q₈	direct (N × H)
16. Q₈	C₁₆	direct (N × H)

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