Subgroups — C₂×SD₆₄ #2260

Order 128.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₆	C₂	1	1	yes	maximal, characteristic
3	SD₆₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₁₆	—	2	1	no	—
6	C₂×D₈	—	2	1	no	—
7	Q₃₂	—	2	1	no	—
8	Q₃₂	C₂²	1	2	yes	complemented
9	D₁₆	—	2	1	no	—
10	D₁₆	C₂²	1	2	yes	—
11	C₂×C₁₆	C₂²	1	1	yes	characteristic
12	C₃₂	C₂²	1	2	yes	complemented
13	C₂×Q₈	—	4	1	no	—
14	C₂×D₄	—	4	1	no	—
15	Q₁₆	—	2	2	no	—
16	Q₁₆	—	4	1	no	—
17	D₈	—	2	2	no	—
18	D₈	—	4	1	no	—
19	C₂×C₈	D₄	1	1	yes	characteristic
20	C₁₆	D₄	1	1	yes	characteristic
21	C₁₆	C₂³	1	1	yes	characteristic
22	C₂³	—	8	1	no	—
23	Q₈	—	4	2	no	—
24	Q₈	—	8	1	no	—
25	D₄	—	4	2	no	—
26	D₄	—	8	1	no	—
27	C₂×C₄	—	8	1	no	—
28	C₂×C₄	D₈	1	1	yes	characteristic
29	C₈	D₈	1	1	yes	characteristic
30	C₈	C₂×D₄	1	1	yes	characteristic
31	C₂²	—	8	2	no	—
32	C₂²	—	16	2	no	—
33	C₂²	D₁₆	1	1	yes	characteristic
34	C₄	—	8	2	no	—
35	C₄	D₁₆	1	1	yes	characteristic
36	C₄	C₂×D₈	1	1	yes	characteristic
37	C₂	—	16	2	no	—
38	C₂	SD₆₄	1	2	yes	direct product factor
39	C₂	C₂×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³
prime radical	C₂×D₁₆	C₂
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ G
LECS	G ▷ 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.