Subgroups — C₄⋊C₁₂₈ #94838

Order 512.

43 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₂₈	C₂	1	2	yes	maximal
2	C₄×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₄	C₄	1	1	yes	characteristic
4	C₂×C₆₄	C₂²	1	1	yes	characteristic
5	C₄×C₃₂	C₄	1	1	yes	characteristic
6	C₁₂₈	—	2	2	no	—
7	C₂×C₃₂	C₈	1	1	yes	characteristic
8	C₂×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₆	C₈	1	1	yes	characteristic
10	C₆₄	—	2	1	no	—
11	C₆₄	D₄	1	1	yes	characteristic
12	C₆₄	Q₈	1	1	yes	characteristic
13	C₂×C₁₆	C₁₆	1	1	yes	characteristic
14	C₂×C₁₆	C₂×C₈	1	1	yes	characteristic
15	C₄×C₈	C₁₆	1	1	yes	characteristic
16	C₃₂	—	2	1	no	—
17	C₃₂	C₄⋊C₄	1	1	yes	characteristic
18	C₃₂	M₁₆	1	1	yes	characteristic
19	C₂×C₈	C₃₂	1	1	yes	characteristic
20	C₂×C₈	C₂×C₁₆	1	1	yes	characteristic
21	C₄²	C₃₂	1	1	yes	characteristic
22	C₁₆	—	2	1	no	—
23	C₁₆	C₄⋊C₈	1	1	yes	characteristic
24	C₁₆	M₃₂	1	1	yes	characteristic
25	C₂×C₄	C₆₄	1	1	yes	characteristic
26	C₂×C₄	C₆₄	1	1	yes	characteristic
27	C₂×C₄	C₂×C₃₂	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₈	C₄⋊C₁₆	1	1	yes	characteristic
30	C₈	M₆₄	1	1	yes	characteristic
31	C₂²	C₂×C₆₄	1	1	yes	characteristic
32	C₄	—	2	1	no	—
33	C₄	C₁₂₈	1	2	yes	complemented
34	C₄	C₄⋊C₃₂	1	1	yes	characteristic
35	C₄	M₁₂₈	1	1	yes	characteristic
36	C₂	C₄⋊C₆₄	1	1	yes	characteristic
37	C₂	C₂×C₁₂₈	1	1	yes	characteristic
38	C₂	M₂₅₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₄	C₁₂₈	semidirect

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

subgroup	index
C₂×C₁₂₈	2
C₄×C₆₄	2