Subgroups — C₂×D₆₀₈ #14565933

Order 2432.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₀₄	C₂	1	2	yes	maximal, complemented
2	D₆₀₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₉×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅₂	—	2	2	no	—
5	C₂×C₁₆×C₁₉	C₂²	1	1	yes	characteristic
6	D₃₀₄	—	2	2	no	—
7	D₃₀₄	C₂²	1	4	yes	complemented
8	C₁₉×C₃₂	C₂²	1	2	yes	complemented
9	C₂×D₇₆	—	4	2	no	—
10	C₂×C₈×C₁₉	D₄	1	1	yes	characteristic
11	D₁₅₂	—	2	4	no	—
12	D₁₅₂	—	4	2	no	—
13	C₁₆×C₁₉	D₄	1	1	yes	characteristic
14	C₁₆×C₁₉	C₂³	1	1	yes	characteristic
15	C₂²×D₁₉	—	8	2	no	—
16	C₂×C₄×C₁₉	D₈	1	1	yes	characteristic
17	D₇₆	—	4	4	no	—
18	D₇₆	—	8	2	no	—
19	C₈×C₁₉	D₈	1	1	yes	characteristic
20	C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
21	C₂×D₃₂	—	19	1	no	maximal, Sylow
22	C₂²×C₁₉	D₁₆	1	1	yes	characteristic
23	C₂×D₁₉	—	8	4	no	—
24	C₂×D₁₉	—	16	4	no	—
25	C₄×C₁₉	D₁₆	1	1	yes	characteristic
26	C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
27	C₂×D₁₆	—	19	2	no	—
28	D₃₂	—	19	4	no	—
29	C₂×C₃₂	D₁₉	1	1	yes	characteristic, complemented
30	C₂×C₁₉	D₃₂	1	2	yes	complemented
31	C₂×C₁₉	C₂×D₁₆	1	1	yes	characteristic
32	D₁₉	—	16	4	no	—
33	C₂×D₈	—	38	2	no	—
34	D₁₆	—	19	4	no	—
35	D₁₆	—	38	2	no	—
36	C₂×C₁₆	C₂×D₁₉	1	1	yes	characteristic
37	C₃₂	C₂×D₁₉	1	2	yes	complemented
38	C₁₉	C₂×D₃₂	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₄	—	76	2	no	—
40	D₈	—	38	4	no	—
41	D₈	—	76	2	no	—
42	C₂×C₈	D₇₆	1	1	yes	characteristic
43	C₁₆	D₇₆	1	1	yes	characteristic
44	C₁₆	C₂²×D₁₉	1	1	yes	characteristic
45	C₂³	—	152	2	no	—
46	D₄	—	76	4	no	—
47	D₄	—	152	2	no	—
48	C₂×C₄	D₁₅₂	1	1	yes	characteristic
49	C₈	D₁₅₂	1	1	yes	characteristic
50	C₈	C₂×D₇₆	1	1	yes	characteristic
51	C₂²	—	304	4	no	—
52	C₂²	—	152	4	no	—
53	C₂²	D₃₀₄	1	1	yes	characteristic
54	C₄	D₃₀₄	1	1	yes	characteristic
55	C₄	C₂×D₁₅₂	1	1	yes	characteristic
56	C₂	—	304	4	no	—
57	C₂	D₆₀₈	1	2	yes	direct product factor
58	C₂	C₂×D₃₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₀₄
commutator, cosocle	C₁₆×C₁₉	C₂³
Frattini	C₁₆	C₂²×D₁₉
Fitting	C₂×C₁₉×C₃₂	C₂
socle	C₂²×C₁₉	D₁₆
hypercenter	C₂×C₃₂	D₁₉
hypocenter	C₁₉	C₂×D₃₂
LCS	G ▷ C₁₆×C₁₉ ▷ C₈×C₁₉ ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
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×D₃₀₄	C₂	semidirect
2. D₆₀₈	C₂	direct (N × H)
3. C₂×C₁₉×C₃₂	C₂	semidirect
7. D₃₀₄	C₂²	semidirect
8. C₁₉×C₃₂	C₂²	semidirect
29. C₂×C₃₂	D₁₉	semidirect
30. C₂×C₁₉	D₃₂	semidirect
37. C₃₂	C₂×D₁₉	semidirect
38. C₁₉	C₂×D₃₂	semidirect
57. C₂	D₆₀₈	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×D₃₀₄	2
D₆₀₈	2
C₂×C₁₉×C₃₂	2
C₂×D₃₂	19

Subgroups — C2×D608 #14565933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₆₀₈ #14565933