Subgroups — #1372

Order 128.

35 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
2	#335	C₂	1	2	yes	maximal
3	C₂×C₁₆	C₄	1	1	yes	characteristic
4	C₂×C₁₆	C₄	1	1	yes	characteristic
5	C₄⋊C₈	—	2	2	no	—
6	C₄×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₈	—	4	2	no	—
8	C₂×C₈	C₂×C₄	1	1	yes	characteristic
9	C₂×C₈	Q₈	1	1	yes	characteristic
10	C₄²	D₄	1	1	yes	characteristic
11	C₁₆	—	2	1	no	—
12	C₁₆	C₈	1	2	yes	complemented
13	C₂×C₄	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄	D₈	1	1	yes	characteristic
15	C₂×C₄	Q₁₆	1	1	yes	characteristic
16	C₈	—	2	1	no	—
17	C₈	—	8	2	no	—
18	C₈	C₂×C₈	1	1	yes	characteristic
19	C₈	M₁₆	1	1	yes	characteristic
20	C₂²	#107	1	1	yes	characteristic
21	C₄	—	2	1	no	—
22	C₄	C₄⋊C₈	1	1	yes	characteristic
23	C₄	#108	1	1	yes	characteristic
24	C₄	SD₃₂	1	2	yes	—
25	C₂	#335	1	1	yes	characteristic
26	C₂	#367	1	1	yes	characteristic
27	C₂	#368	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. 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
#335	2