Subgroups — C₂×SD₂₅₆ #153703

Order 512.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₆₄	C₂	1	1	yes	maximal, characteristic
3	SD₂₅₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₆₄	—	2	1	no	—
6	C₂×D₃₂	—	2	1	no	—
7	Q₁₂₈	—	2	1	no	—
8	Q₁₂₈	C₂²	1	2	yes	complemented
9	D₆₄	—	2	1	no	—
10	D₆₄	C₂²	1	2	yes	—
11	C₂×C₆₄	C₂²	1	1	yes	characteristic
12	C₁₂₈	C₂²	1	2	yes	complemented
13	C₂×Q₃₂	—	4	1	no	—
14	C₂×D₁₆	—	4	1	no	—
15	Q₆₄	—	2	2	no	—
16	Q₆₄	—	4	1	no	—
17	D₃₂	—	2	2	no	—
18	D₃₂	—	4	1	no	—
19	C₂×C₃₂	D₄	1	1	yes	characteristic
20	C₆₄	D₄	1	1	yes	characteristic
21	C₆₄	C₂³	1	1	yes	characteristic
22	C₂×Q₁₆	—	8	1	no	—
23	C₂×D₈	—	8	1	no	—
24	Q₃₂	—	4	2	no	—
25	Q₃₂	—	8	1	no	—
26	D₁₆	—	4	2	no	—
27	D₁₆	—	8	1	no	—
28	C₂×C₁₆	D₈	1	1	yes	characteristic
29	C₃₂	D₈	1	1	yes	characteristic
30	C₃₂	C₂×D₄	1	1	yes	characteristic
31	C₂×Q₈	—	16	1	no	—
32	C₂×D₄	—	16	1	no	—
33	Q₁₆	—	8	2	no	—
34	Q₁₆	—	16	1	no	—
35	D₈	—	8	2	no	—
36	D₈	—	16	1	no	—
37	C₂×C₈	D₁₆	1	1	yes	characteristic
38	C₁₆	D₁₆	1	1	yes	characteristic
39	C₁₆	C₂×D₈	1	1	yes	characteristic
40	C₂³	—	32	1	no	—
41	Q₈	—	16	2	no	—
42	Q₈	—	32	1	no	—
43	D₄	—	16	2	no	—
44	D₄	—	32	1	no	—
45	C₂×C₄	—	32	1	no	—
46	C₂×C₄	D₃₂	1	1	yes	characteristic
47	C₈	D₃₂	1	1	yes	characteristic
48	C₈	C₂×D₁₆	1	1	yes	characteristic
49	C₂²	—	32	2	no	—
50	C₂²	—	64	2	no	—
51	C₂²	D₆₄	1	1	yes	characteristic
52	C₄	—	32	2	no	—
53	C₄	D₆₄	1	1	yes	characteristic
54	C₄	C₂×D₃₂	1	1	yes	characteristic
55	C₂	—	64	2	no	—
56	C₂	SD₂₅₆	1	2	yes	direct product factor
57	C₂	C₂×D₆₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	D₆₄
commutator, Frattini, cosocle	C₆₄	C₂³
prime radical	C₂×D₆₄	C₂
LCS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄ ◁ G
LECS	G ▷ C₆₄ ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₂₈	C₂	semidirect
3. SD₂₅₆	C₂	direct (N × H)
4. C₂×C₁₂₈	C₂	semidirect
8. Q₁₂₈	C₂²	semidirect
12. C₁₂₈	C₂²	semidirect
56. C₂	SD₂₅₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₁₂₈	2
C₂×D₆₄	2
SD₂₅₆	2
C₂×C₁₂₈	2

Subgroups — C2×SD256 #153703

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×SD₂₅₆ #153703