Subgroups — #7545

Order 256.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic
2	#1423	C₂	1	2	yes	maximal
3	C₂×C₃₂	C₂²	1	1	yes	characteristic
4	#366	—	2	2	no	—
5	C₆₄	C₄	1	2	yes	complemented
6	C₂×C₁₆	D₄	1	1	yes	characteristic
7	#107	—	4	2	no	—
8	C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₃₂	Q₈	1	1	yes	characteristic
10	C₂×C₈	D₈	1	1	yes	characteristic
11	C₄⋊C₄	—	8	2	no	—
12	C₁₆	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆	Q₁₆	1	1	yes	characteristic
14	C₂×C₄	—	16	2	no	—
15	C₂×C₄	D₁₆	1	1	yes	characteristic
16	C₈	#107	1	1	yes	characteristic
17	C₈	Q₃₂	1	1	yes	characteristic
18	C₂²	D₃₂	1	1	yes	characteristic
19	C₄	—	32	2	no	—
20	C₄	#366	1	1	yes	characteristic
21	C₄	Q₆₄	1	1	yes	characteristic
22	C₂	#1423	1	1	yes	characteristic
23	C₂	D₆₄	1	1	yes	characteristic
24	C₂	Q₁₂₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. C₆₄	C₄	semidirect

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

subgroup	index
C₂×C₆₄	2
#1423	2