Subgroups — C₈×Q₈ #445

Order 64.

51 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
9. Q₈	C₈	direct (N × H)
14. C₈	Q₈	direct (N × H)

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