Subgroups — C₂×Dic₄₁₆ #15783969

Order 3328.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀₈	C₂	1	2	yes	maximal
2	Dic₄₁₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₃×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₄	—	2	2	no	—
5	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
6	Dic₂₀₈	—	2	2	no	—
7	Dic₂₀₈	C₂²	1	4	yes	—
8	C₁₃×C₆₄	C₂²	1	2	yes	—
9	C₂×Dic₅₂	—	4	2	no	—
10	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
11	Dic₁₀₄	—	2	4	no	—
12	Dic₁₀₄	—	4	2	no	—
13	C₁₃×C₃₂	D₄	1	1	yes	characteristic
14	C₁₃×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×Q₁₂₈	—	13	1	no	maximal, Sylow
16	C₂×Dic₂₆	—	8	2	no	—
17	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
18	Dic₅₂	—	4	4	no	—
19	Dic₅₂	—	8	2	no	—
20	C₁₃×C₁₆	D₈	1	1	yes	characteristic
21	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
22	C₂×Q₆₄	—	13	2	no	—
23	Q₁₂₈	—	13	4	no	—
24	C₂×C₆₄	D₁₃	1	1	yes	characteristic
25	C₂×C₄×C₁₃	D₁₆	1	1	yes	characteristic
26	C₂×Dic₁₃	—	16	2	no	—
27	Dic₂₆	—	8	4	no	—
28	Dic₂₆	—	16	2	no	—
29	C₈×C₁₃	D₁₆	1	1	yes	characteristic
30	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
31	C₂×Q₃₂	—	26	2	no	—
32	Q₆₄	—	13	4	no	—
33	Q₆₄	—	26	2	no	—
34	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
35	C₆₄	C₂×D₁₃	1	2	yes	—
36	C₂²×C₁₃	D₃₂	1	1	yes	characteristic
37	C₄×C₁₃	D₃₂	1	1	yes	characteristic
38	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
39	Dic₁₃	—	16	4	no	—
40	C₂×Q₁₆	—	52	2	no	—
41	Q₃₂	—	26	4	no	—
42	Q₃₂	—	52	2	no	—
43	C₂×C₁₆	D₅₂	1	1	yes	characteristic
44	C₃₂	D₅₂	1	1	yes	characteristic
45	C₃₂	C₂²×D₁₃	1	1	yes	characteristic
46	C₂×C₁₃	Q₁₂₈	1	2	yes	complemented
47	C₂×C₁₃	C₂×D₃₂	1	1	yes	characteristic
48	C₂×Q₈	—	104	2	no	—
49	Q₁₆	—	52	4	no	—
50	Q₁₆	—	104	2	no	—
51	C₂×C₈	D₁₀₄	1	1	yes	characteristic
52	C₁₆	D₁₀₄	1	1	yes	characteristic
53	C₁₆	C₂×D₅₂	1	1	yes	characteristic
54	C₁₃	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	104	4	no	—
56	Q₈	—	208	2	no	—
57	C₂×C₄	—	208	2	no	—
58	C₂×C₄	D₂₀₈	1	1	yes	characteristic
59	C₈	D₂₀₈	1	1	yes	characteristic
60	C₈	C₂×D₁₀₄	1	1	yes	characteristic
61	C₂²	D₄₁₆	1	1	yes	characteristic
62	C₄	—	208	4	no	—
63	C₄	D₄₁₆	1	1	yes	characteristic
64	C₄	C₂×D₂₀₈	1	1	yes	characteristic
65	C₂	Dic₄₁₆	1	2	yes	direct product factor
66	C₂	C₂×D₄₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄₁₆
commutator, cosocle	C₁₃×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₃
Fitting	C₂×C₁₃×C₆₄	C₂
socle, prime radical	C₂²×C₁₃	D₃₂
hypercenter	C₂×C₆₄	D₁₃
hypocenter	C₁₃	C₂×Q₁₂₈
LCS	G ▷ C₁₃×C₃₂ ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×C₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₄₁₆	C₂	direct (N × H)
46. C₂×C₁₃	Q₁₂₈	semidirect
54. C₁₃	C₂×Q₁₂₈	semidirect
65. C₂	Dic₄₁₆	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×Dic₂₀₈	2
Dic₄₁₆	2
C₂×C₁₃×C₆₄	2
C₂×Q₁₂₈	13

Subgroups — C2×Dic416 #15783969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₄₁₆ #15783969