Subgroups — C₂×D₆₄ #13738

Order 256.

71 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂	C₂	1	2	yes	maximal, complemented
2	D₆₄	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆	—	2	2	no	—
5	D₃₂	—	2	2	no	—
6	D₃₂	C₂²	1	4	yes	complemented
7	C₂×C₃₂	C₂²	1	1	yes	characteristic
8	C₆₄	C₂²	1	2	yes	complemented
9	C₂×D₈	—	4	2	no	—
10	D₁₆	—	2	4	no	—
11	D₁₆	—	4	2	no	—
12	C₂×C₁₆	D₄	1	1	yes	characteristic
13	C₃₂	D₄	1	1	yes	characteristic
14	C₃₂	C₂³	1	1	yes	characteristic
15	C₂×D₄	—	8	2	no	—
16	D₈	—	4	4	no	—
17	D₈	—	8	2	no	—
18	C₂×C₈	D₈	1	1	yes	characteristic
19	C₁₆	D₈	1	1	yes	characteristic
20	C₁₆	C₂×D₄	1	1	yes	characteristic
21	C₂³	—	16	2	no	—
22	D₄	—	8	4	no	—
23	D₄	—	16	2	no	—
24	C₂×C₄	D₁₆	1	1	yes	characteristic
25	C₈	D₁₆	1	1	yes	characteristic
26	C₈	C₂×D₈	1	1	yes	characteristic
27	C₂²	—	16	4	no	—
28	C₂²	—	32	4	no	—
29	C₂²	D₃₂	1	1	yes	characteristic
30	C₄	D₃₂	1	1	yes	characteristic
31	C₄	C₂×D₁₆	1	1	yes	characteristic
32	C₂	—	32	4	no	—
33	C₂	D₆₄	1	2	yes	direct product factor
34	C₂	C₂×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₃₂
commutator, Frattini, cosocle	C₃₂	C₂³
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ G
LECS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

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

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