Subgroups — #1370

Order 128.

38 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	—	2	2	no	—
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	—	2	1	no	—
8	C₂×C₈	C₈	1	1	yes	characteristic
9	C₂×C₈	C₈	1	1	yes	characteristic
10	C₂×C₈	D₄	1	1	yes	characteristic
11	C₂×C₈	Q₈	1	1	yes	characteristic
12	C₄²	C₂×C₄	1	1	yes	characteristic
13	C₁₆	—	4	2	no	—
14	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄	M₁₆	1	1	yes	characteristic
17	C₈	—	2	2	no	—
18	C₈	—	2	1	no	—
19	C₈	—	2	1	no	—
20	C₈	C₁₆	1	2	yes	complemented
21	C₈	D₈	1	1	yes	characteristic
22	C₈	Q₁₆	1	1	yes	characteristic
23	C₂²	C₄⋊C₈	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	#107	1	1	yes	characteristic
26	C₄	#108	1	1	yes	characteristic
27	C₄	C₂×C₁₆	1	1	yes	characteristic
28	C₄	M₃₂	1	1	yes	characteristic
29	C₂	#335	1	1	yes	characteristic
30	C₂	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂	#364	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. 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