Subgroups — #7460

Order 256.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#1371	C₂	1	2	yes	maximal
3	C₂×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₃₂	C₄	1	1	yes	characteristic
5	C₄×C₁₆	C₂²	1	1	yes	characteristic
6	#335	—	2	2	no	—
7	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆	Q₈	1	1	yes	characteristic
9	C₄⋊C₈	—	4	2	no	—
10	C₄×C₈	D₄	1	1	yes	characteristic
11	C₃₂	—	2	1	no	—
12	C₃₂	C₈	1	2	yes	complemented
13	C₂×C₈	—	8	2	no	—
14	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈	Q₁₆	1	1	yes	characteristic
16	C₄²	D₈	1	1	yes	characteristic
17	C₁₆	—	2	1	no	—
18	C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₆	M₁₆	1	1	yes	characteristic
20	C₂×C₄	#107	1	1	yes	characteristic
21	C₂×C₄	D₁₆	1	1	yes	characteristic
22	C₂×C₄	Q₃₂	1	1	yes	characteristic
23	C₈	—	2	1	no	—
24	C₈	—	16	2	no	—
25	C₈	C₄⋊C₈	1	1	yes	characteristic
26	C₈	#108	1	1	yes	characteristic
27	C₂²	#366	1	1	yes	characteristic
28	C₄	—	2	1	no	—
29	C₄	#335	1	1	yes	characteristic
30	C₄	#368	1	1	yes	characteristic
31	C₄	D₃₂	1	1	yes	characteristic
32	C₄	Q₆₄	1	1	yes	characteristic
33	C₂	#1371	1	1	yes	characteristic
34	C₂	#1423	1	1	yes	characteristic
35	C₂	#1425	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₃₂	C₈	semidirect

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

subgroup	index
C₄×C₃₂	2
#1371	2