Subgroups — Q₈×C₃₂ #13659

Order 256.

83 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₃₂	C₂	1	3	yes	maximal
3	C₄×C₃₂	C₂	1	3	yes	maximal
4	C₈×Q₈	C₄	1	1	yes	characteristic
5	C₂×C₃₂	C₂²	1	3	yes	—
6	C₂×C₃₂	C₂²	1	1	yes	characteristic
7	C₄⋊C₁₆	C₄	1	3	yes	—
8	C₄×C₁₆	C₂²	1	3	yes	—
9	C₄×Q₈	C₈	1	1	yes	characteristic
10	C₂×C₁₆	C₂×C₄	1	3	yes	—
11	C₂×C₁₆	C₂³	1	1	yes	characteristic
12	C₄⋊C₈	C₈	1	3	yes	—
13	C₄×C₈	C₂×C₄	1	3	yes	—
14	C₃₂	—	2	3	no	—
15	C₃₂	Q₈	1	2	yes	direct product factor
16	C₂×Q₈	C₁₆	1	1	yes	characteristic
17	C₂×C₈	C₂×C₈	1	3	yes	—
18	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
19	C₄⋊C₄	C₁₆	1	3	yes	—
20	C₄²	C₂×C₈	1	3	yes	—
21	C₁₆	—	2	3	no	—
22	C₁₆	C₂×Q₈	1	1	yes	characteristic
23	C₁₆	#41	1	1	yes	characteristic
24	Q₈	C₃₂	1	4	yes	direct product factor
25	C₂×C₄	C₂×C₁₆	1	3	yes	—
26	C₂×C₄	C₂×C₁₆	1	3	yes	—
27	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
28	C₈	—	2	3	no	—
29	C₈	C₄×Q₈	1	1	yes	characteristic
30	C₈	#131	1	1	yes	characteristic
31	C₂²	C₂²×C₁₆	1	1	yes	characteristic
32	C₄	—	2	3	no	—
33	C₄	C₂×C₃₂	1	6	yes	—
34	C₄	C₈×Q₈	1	1	yes	characteristic
35	C₄	#504	1	1	yes	characteristic
36	C₂	Q₈×C₁₆	1	1	yes	characteristic
37	C₂	C₂²×C₃₂	1	1	yes	characteristic
38	C₂	#2258	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₃₂	Q₈	direct (N × H)
24. Q₈	C₃₂	direct (N × H)

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