Subgroups — C₂×D₄₁₆ #13117134

Order 1664.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₀₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₀₄	—	2	2	no	—
5	C₂×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	D₂₀₈	—	2	2	no	—
7	D₂₀₈	C₂²	1	4	yes	complemented
8	C₁₃×C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₅₂	—	4	2	no	—
10	C₂×C₈×C₁₃	D₄	1	1	yes	characteristic
11	D₁₀₄	—	2	4	no	—
12	D₁₀₄	—	4	2	no	—
13	C₁₃×C₁₆	D₄	1	1	yes	characteristic
14	C₁₃×C₁₆	C₂³	1	1	yes	characteristic
15	C₂×D₃₂	—	13	1	no	maximal, Sylow
16	C₂²×D₁₃	—	8	2	no	—
17	C₂×C₄×C₁₃	D₈	1	1	yes	characteristic
18	D₅₂	—	4	4	no	—
19	D₅₂	—	8	2	no	—
20	C₈×C₁₃	D₈	1	1	yes	characteristic
21	C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
22	C₂×D₁₆	—	13	2	no	—
23	D₃₂	—	13	4	no	—
24	C₂×C₃₂	D₁₃	1	1	yes	characteristic, complemented
25	C₂²×C₁₃	D₁₆	1	1	yes	characteristic
26	C₂×D₁₃	—	8	4	no	—
27	C₂×D₁₃	—	16	4	no	—
28	C₄×C₁₃	D₁₆	1	1	yes	characteristic
29	C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
30	C₂×D₈	—	26	2	no	—
31	D₁₆	—	13	4	no	—
32	D₁₆	—	26	2	no	—
33	C₂×C₁₆	C₂×D₁₃	1	1	yes	characteristic
34	C₃₂	C₂×D₁₃	1	2	yes	complemented
35	C₂×C₁₃	D₃₂	1	2	yes	complemented
36	C₂×C₁₃	C₂×D₁₆	1	1	yes	characteristic
37	D₁₃	—	16	4	no	—
38	C₂×D₄	—	52	2	no	—
39	D₈	—	26	4	no	—
40	D₈	—	52	2	no	—
41	C₂×C₈	D₅₂	1	1	yes	characteristic
42	C₁₆	D₅₂	1	1	yes	characteristic
43	C₁₆	C₂²×D₁₃	1	1	yes	characteristic
44	C₁₃	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
45	C₂³	—	104	2	no	—
46	D₄	—	52	4	no	—
47	D₄	—	104	2	no	—
48	C₂×C₄	D₁₀₄	1	1	yes	characteristic
49	C₈	D₁₀₄	1	1	yes	characteristic
50	C₈	C₂×D₅₂	1	1	yes	characteristic
51	C₂²	—	104	4	no	—
52	C₂²	—	208	4	no	—
53	C₂²	D₂₀₈	1	1	yes	characteristic
54	C₄	D₂₀₈	1	1	yes	characteristic
55	C₄	C₂×D₁₀₄	1	1	yes	characteristic
56	C₂	—	208	4	no	—
57	C₂	D₄₁₆	1	2	yes	direct product factor
58	C₂	C₂×D₂₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₀₈
commutator, cosocle	C₁₃×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×C₃₂	C₂
socle	C₂²×C₁₃	D₁₆
hypercenter	C₂×C₃₂	D₁₃
hypocenter	C₁₃	C₂×D₃₂
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×D₂₀₈	C₂	semidirect
2. C₂×C₁₃×C₃₂	C₂	semidirect
3. D₄₁₆	C₂	direct (N × H)
7. D₂₀₈	C₂²	semidirect
8. C₁₃×C₃₂	C₂²	semidirect
24. C₂×C₃₂	D₁₃	semidirect
34. C₃₂	C₂×D₁₃	semidirect
35. C₂×C₁₃	D₃₂	semidirect
44. C₁₃	C₂×D₃₂	semidirect
57. C₂	D₄₁₆	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×D₂₀₈	2
C₂×C₁₃×C₃₂	2
D₄₁₆	2
C₂×D₃₂	13

Subgroups — C2×D416 #13117134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄₁₆ #13117134