Subgroups — #1311

Order 128.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆	C₂	1	2	yes	maximal
2	C₈²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆	C₄	1	4	yes	—
4	C₄×C₈	C₄	1	2	yes	—
5	C₄×C₈	C₂²	1	1	yes	characteristic
6	C₂×C₈	C₈	1	4	yes	—
7	C₂×C₈	C₂×C₄	1	2	yes	—
8	C₄²	C₂×C₄	1	1	yes	characteristic
9	C₁₆	C₈	1	8	yes	complemented
10	C₂×C₄	C₄²	1	1	yes	characteristic
11	C₂×C₄	C₂×C₈	1	2	yes	—
12	C₈	—	2	4	no	—
13	C₈	C₂×C₈	1	4	yes	—
14	C₂²	C₄×C₈	1	1	yes	characteristic
15	C₄	C₄×C₈	1	2	yes	—
16	C₄	M₃₂	1	4	yes	—
17	C₂	C₈²	1	1	yes	characteristic
18	C₂	#346	1	2	yes	—

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

N	H ≅ G/N	type
9. C₁₆	C₈	semidirect

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

subgroup	index
C₄×C₁₆	2
C₈²	2