Subgroups — #322

Order 64.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈	C₂	1	2	yes	maximal
2	C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈	C₄	1	4	yes	—
4	C₂×C₈	C₄	1	2	yes	—
5	C₄²	C₂²	1	1	yes	characteristic
6	C₂×C₄	C₂×C₄	1	1	yes	characteristic
7	C₂×C₄	C₂×C₄	1	2	yes	—
8	C₈	—	2	4	no	—
9	C₈	C₈	1	4	yes	complemented
10	C₂²	C₄²	1	1	yes	characteristic
11	C₄	C₂×C₈	1	2	yes	—
12	C₄	M₁₆	1	4	yes	—
13	C₂	C₄×C₈	1	1	yes	characteristic
14	C₂	#97	1	2	yes	—

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

N	H ≅ G/N	type
9. C₈	C₈	semidirect

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

subgroup	index
C₄×C₈	2