Subgroups — #1312

Order 128.

46 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	1	yes	characteristic
5	C₄×C₈	C₄	1	1	yes	characteristic
6	C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₈	C₈	1	2	yes	—
8	C₂×C₈	C₈	1	2	yes	—
9	C₂×C₈	C₂×C₄	1	2	yes	—
10	C₄²	C₂×C₄	1	1	yes	characteristic
11	C₁₆	—	2	4	no	—
12	C₂×C₄	C₄²	1	1	yes	characteristic
13	C₂×C₄	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄	C₂×C₈	1	1	yes	characteristic
15	C₈	—	2	2	no	—
16	C₈	C₁₆	1	4	yes	complemented
17	C₈	M₁₆	1	4	yes	—
18	C₂²	C₄×C₈	1	1	yes	characteristic
19	C₄	#97	1	2	yes	—
20	C₄	C₂×C₁₆	1	2	yes	—
21	C₄	M₃₂	1	2	yes	—
22	C₂	#322	1	1	yes	characteristic
23	C₂	C₄×C₁₆	1	1	yes	characteristic
24	C₂	#346	1	1	yes	characteristic

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

N	H ≅ G/N	type
16. C₈	C₁₆	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