Subgroups — #335

Order 64.

27 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	—	2	2	no	—
4	C₂×C₈	C₄	1	1	yes	characteristic
5	C₂×C₈	C₄	1	1	yes	characteristic
6	C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₄	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄	D₄	1	1	yes	characteristic
9	C₂×C₄	Q₈	1	1	yes	characteristic
10	C₈	—	2	1	no	—
11	C₈	—	4	2	no	—
12	C₈	C₈	1	2	yes	complemented
13	C₂²	C₄⋊C₄	1	1	yes	characteristic
14	C₄	—	2	1	no	—
15	C₄	C₂×C₈	1	1	yes	characteristic
16	C₄	M₁₆	1	1	yes	characteristic
17	C₄	D₈	1	1	yes	characteristic
18	C₄	Q₁₆	1	1	yes	characteristic
19	C₂	C₄⋊C₈	1	1	yes	characteristic
20	C₂	#107	1	1	yes	characteristic
21	C₂	#108	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. 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
C₄×C₈	2