Subgroups — #94841

Order 512.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₈	C₂	1	1	yes	maximal, characteristic
2	#7545	C₂	1	2	yes	maximal
3	C₂×C₆₄	C₂²	1	1	yes	characteristic
4	#1423	—	2	2	no	—
5	C₁₂₈	C₄	1	2	yes	complemented
6	C₂×C₃₂	D₄	1	1	yes	characteristic
7	#366	—	4	2	no	—
8	C₆₄	C₂×C₄	1	1	yes	characteristic
9	C₆₄	Q₈	1	1	yes	characteristic
10	C₂×C₁₆	D₈	1	1	yes	characteristic
11	#107	—	8	2	no	—
12	C₃₂	C₄⋊C₄	1	1	yes	characteristic
13	C₃₂	Q₁₆	1	1	yes	characteristic
14	C₂×C₈	D₁₆	1	1	yes	characteristic
15	C₄⋊C₄	—	16	2	no	—
16	C₁₆	#107	1	1	yes	characteristic
17	C₁₆	Q₃₂	1	1	yes	characteristic
18	C₂×C₄	—	32	2	no	—
19	C₂×C₄	D₃₂	1	1	yes	characteristic
20	C₈	#366	1	1	yes	characteristic
21	C₈	Q₆₄	1	1	yes	characteristic
22	C₂²	D₆₄	1	1	yes	characteristic
23	C₄	—	64	2	no	—
24	C₄	#1423	1	1	yes	characteristic
25	C₄	Q₁₂₈	1	1	yes	characteristic
26	C₂	#7545	1	1	yes	characteristic
27	C₂	SD₂₅₆	1	2	yes	—

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

N	H ≅ G/N	type
5. C₁₂₈	C₄	semidirect

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

subgroup	index
C₂×C₁₂₈	2
#7545	2