Subgroups — C₂×D₄₆₄ #14271584

Order 1856.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₃₂	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₆₄	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₁₆	—	2	2	no	—
5	C₂×C₈×C₂₉	C₂²	1	1	yes	characteristic
6	D₂₃₂	—	2	2	no	—
7	D₂₃₂	C₂²	1	4	yes	complemented
8	C₁₆×C₂₉	C₂²	1	2	yes	complemented
9	C₂²×D₂₉	—	4	2	no	—
10	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
11	D₁₁₆	—	2	4	no	—
12	D₁₁₆	—	4	2	no	—
13	C₈×C₂₉	D₄	1	1	yes	characteristic
14	C₈×C₂₉	C₂³	1	1	yes	characteristic
15	C₂²×C₂₉	D₈	1	1	yes	characteristic
16	C₂×D₂₉	—	4	4	no	—
17	C₂×D₂₉	—	8	4	no	—
18	C₄×C₂₉	D₈	1	1	yes	characteristic
19	C₄×C₂₉	C₂×D₄	1	1	yes	characteristic
20	C₂×D₁₆	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	D₁₆	1	2	yes	complemented
22	C₂×C₂₉	C₂×D₈	1	1	yes	characteristic
23	D₂₉	—	8	4	no	—
24	C₂×D₈	—	29	2	no	—
25	D₁₆	—	29	4	no	—
26	C₂×C₁₆	D₂₉	1	1	yes	characteristic, complemented
27	C₂₉	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂×D₄	—	58	2	no	—
29	D₈	—	29	4	no	—
30	D₈	—	58	2	no	—
31	C₂×C₈	C₂×D₂₉	1	1	yes	characteristic
32	C₁₆	C₂×D₂₉	1	2	yes	complemented
33	C₂³	—	116	2	no	—
34	D₄	—	58	4	no	—
35	D₄	—	116	2	no	—
36	C₂×C₄	D₁₁₆	1	1	yes	characteristic
37	C₈	D₁₁₆	1	1	yes	characteristic
38	C₈	C₂²×D₂₉	1	1	yes	characteristic
39	C₂²	—	116	4	no	—
40	C₂²	—	232	4	no	—
41	C₂²	D₂₃₂	1	1	yes	characteristic
42	C₄	D₂₃₂	1	1	yes	characteristic
43	C₄	C₂×D₁₁₆	1	1	yes	characteristic
44	C₂	—	232	4	no	—
45	C₂	D₄₆₄	1	2	yes	direct product factor
46	C₂	C₂×D₂₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₃₂
commutator, cosocle	C₈×C₂₉	C₂³
Frattini	C₈	C₂²×D₂₉
Fitting	C₂×C₁₆×C₂₉	C₂
socle	C₂²×C₂₉	D₈
hypercenter	C₂×C₁₆	D₂₉
hypocenter	C₂₉	C₂×D₁₆
LCS	G ▷ C₈×C₂₉ ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₃₂	C₂	semidirect
2. C₂×C₁₆×C₂₉	C₂	semidirect
3. D₄₆₄	C₂	direct (N × H)
7. D₂₃₂	C₂²	semidirect
8. C₁₆×C₂₉	C₂²	semidirect
21. C₂×C₂₉	D₁₆	semidirect
26. C₂×C₁₆	D₂₉	semidirect
27. C₂₉	C₂×D₁₆	semidirect
32. C₁₆	C₂×D₂₉	semidirect
45. C₂	D₄₆₄	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×D₂₃₂	2
C₂×C₁₆×C₂₉	2
D₄₆₄	2
C₂×D₁₆	29

Subgroups — C2×D464 #14271584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₆₄ #14271584