Subgroups — #7456

Order 256.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1422	C₂	1	2	yes	maximal
2	#1311	C₂	1	1	yes	maximal, characteristic
3	M₆₄	—	2	2	no	—
4	C₄×C₁₆	C₄	1	1	yes	characteristic
5	C₄×C₁₆	C₂²	1	1	yes	characteristic
6	C₈²	C₄	1	1	yes	characteristic
7	C₂×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₆	C₈	1	1	yes	characteristic
9	C₂×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈	—	2	1	no	—
12	C₄×C₈	C₂×C₄	1	1	yes	characteristic
13	C₃₂	—	4	2	no	—
14	C₂×C₈	—	2	2	no	—
15	C₂×C₈	C₄⋊C₄	1	1	yes	characteristic
16	C₂×C₈	C₂×C₈	1	1	yes	characteristic
17	C₄²	M₁₆	1	1	yes	characteristic
18	C₁₆	—	2	1	no	—
19	C₁₆	—	2	1	no	—
20	C₁₆	C₁₆	1	2	yes	—
21	C₁₆	SD₁₆	1	2	yes	—
22	C₂×C₄	—	2	1	no	—
23	C₂×C₄	C₄⋊C₈	1	1	yes	characteristic
24	C₈	—	4	2	no	—
25	C₈	#106	1	1	yes	characteristic
26	C₈	#108	1	1	yes	characteristic
27	C₈	C₂×C₁₆	1	1	yes	characteristic
28	C₈	M₃₂	1	1	yes	characteristic
29	C₂²	#364	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	#334	1	1	yes	characteristic
32	C₄	C₄⋊C₁₆	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#1367	1	1	yes	characteristic

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

subgroup	index
#1422	2
#1311	2