Subgroups — #7462

Order 256.

39 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	#1373	C₂	1	2	yes	maximal
3	C₂×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₃₂	C₄	1	1	yes	characteristic
5	#364	—	2	2	no	—
6	C₄×C₁₆	C₂²	1	1	yes	characteristic
7	M₃₂	—	4	2	no	—
8	C₂×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₆	Q₈	1	1	yes	characteristic
10	C₄×C₈	D₄	1	1	yes	characteristic
11	C₃₂	—	2	1	no	—
12	C₃₂	C₈	1	2	yes	—
13	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₈	D₈	1	1	yes	characteristic
15	C₄²	Q₁₆	1	1	yes	characteristic
16	C₁₆	—	2	1	no	—
17	C₁₆	—	8	2	no	—
18	C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₆	M₁₆	1	1	yes	characteristic
20	C₂×C₄	—	2	1	no	—
21	C₂×C₄	#107	1	1	yes	characteristic
22	C₈	C₄⋊C₈	1	1	yes	characteristic
23	C₈	#108	1	1	yes	characteristic
24	C₈	D₁₆	1	1	yes	characteristic
25	C₈	Q₃₂	1	1	yes	characteristic
26	C₂²	#368	1	1	yes	characteristic
27	C₄	—	2	2	no	—
28	C₄	#335	1	1	yes	characteristic
29	C₄	#366	1	1	yes	characteristic
30	C₂	—	2	1	no	—
31	C₂	#1371	1	1	yes	characteristic

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

subgroup	index
C₄×C₃₂	2
#1373	2