Subgroups — C₂²×D₂₀₈ #13127942

Order 1664.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₀₄	C₂	1	2	yes	maximal, complemented
2	C₂²×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₀₈	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₅₂	—	2	2	no	—
5	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×D₁₀₄	—	2	6	no	—
7	C₂×D₁₀₄	C₂²	1	12	yes	complemented
8	C₂×C₁₃×C₁₆	C₂²	1	6	yes	complemented
9	D₂₀₈	C₂²	1	16	yes	direct product factor
10	C₂³×D₁₃	—	4	2	no	—
11	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
12	C₂×D₅₂	—	2	12	no	—
13	C₂×D₅₂	—	4	6	no	—
14	C₂×C₈×C₁₃	D₄	1	3	yes	—
15	C₂×C₈×C₁₃	C₂³	1	3	yes	—
16	D₁₀₄	—	2	12	no	—
17	D₁₀₄	C₂³	1	8	yes	complemented
18	C₁₃×C₁₆	C₂³	1	4	yes	complemented
19	C₂²×D₁₆	—	13	1	no	maximal, Sylow
20	C₂³×C₁₃	D₈	1	1	yes	characteristic
21	C₂²×D₁₃	—	4	12	no	—
22	C₂²×D₁₃	—	8	8	no	—
23	C₂×C₄×C₁₃	D₈	1	3	yes	—
24	C₂×C₄×C₁₃	C₂×D₄	1	3	yes	—
25	D₅₂	—	2	8	no	—
26	D₅₂	—	4	12	no	—
27	C₈×C₁₃	C₂×D₄	1	3	yes	—
28	C₈×C₁₃	C₂⁴	1	1	yes	characteristic
29	C₂²×D₈	—	13	2	no	—
30	C₂×D₁₆	—	13	12	no	—
31	C₂²×C₁₆	D₁₃	1	1	yes	characteristic, complemented
32	C₂²×C₁₃	D₁₆	1	4	yes	complemented
33	C₂²×C₁₃	C₂×D₈	1	3	yes	—
34	C₂×D₁₃	—	4	8	no	—
35	C₂×D₁₃	—	8	24	no	—
36	C₄×C₁₃	C₂×D₈	1	3	yes	—
37	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
38	C₂²×D₄	—	26	2	no	—
39	C₂×D₈	—	13	12	no	—
40	C₂×D₈	—	26	6	no	—
41	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
42	D₁₆	—	13	16	no	—
43	C₂×C₁₆	C₂×D₁₃	1	6	yes	complemented
44	C₂×C₁₃	C₂×D₁₆	1	6	yes	complemented
45	C₂×C₁₃	C₂²×D₈	1	1	yes	characteristic
46	D₁₃	—	8	8	no	—
47	C₂⁴	—	52	2	no	—
48	C₂×D₄	—	26	12	no	—
49	C₂×D₄	—	52	6	no	—
50	C₂²×C₄	D₅₂	1	1	yes	characteristic
51	D₈	—	13	8	no	—
52	D₈	—	26	12	no	—
53	C₂×C₈	D₅₂	1	3	yes	—
54	C₂×C₈	C₂²×D₁₃	1	3	yes	—
55	C₁₆	C₂²×D₁₃	1	4	yes	complemented
56	C₁₃	C₂²×D₁₆	1	1	yes	characteristic, complemented, Sylow
57	C₂³	—	52	12	no	—
58	C₂³	—	104	8	no	—
59	C₂³	D₁₀₄	1	1	yes	characteristic
60	D₄	—	26	8	no	—
61	D₄	—	52	12	no	—
62	C₂×C₄	D₁₀₄	1	3	yes	—
63	C₂×C₄	C₂×D₅₂	1	3	yes	—
64	C₈	C₂×D₅₂	1	3	yes	—
65	C₈	C₂³×D₁₃	1	1	yes	characteristic
66	C₂²	—	52	8	no	—
67	C₂²	—	104	24	no	—
68	C₂²	D₂₀₈	1	4	yes	direct product factor
69	C₂²	C₂×D₁₀₄	1	3	yes	—
70	C₄	C₂×D₁₀₄	1	3	yes	—
71	C₄	C₂²×D₅₂	1	1	yes	characteristic
72	C₂	—	104	8	no	—
73	C₂	C₂×D₂₀₈	1	6	yes	direct product factor
74	C₂	C₂²×D₁₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₀₄
commutator, cosocle	C₈×C₁₃	C₂⁴
Frattini	C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	D₈
hypercenter	C₂²×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×D₁₆
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×D₁₀₄	C₂	semidirect
2. C₂²×C₁₃×C₁₆	C₂	semidirect
3. C₂×D₂₀₈	C₂	direct (N × H)
7. C₂×D₁₀₄	C₂²	semidirect
8. C₂×C₁₃×C₁₆	C₂²	semidirect
9. D₂₀₈	C₂²	direct (N × H)
17. D₁₀₄	C₂³	semidirect
18. C₁₃×C₁₆	C₂³	semidirect
31. C₂²×C₁₆	D₁₃	semidirect
32. C₂²×C₁₃	D₁₆	semidirect
43. C₂×C₁₆	C₂×D₁₃	semidirect
44. C₂×C₁₃	C₂×D₁₆	semidirect
55. C₁₆	C₂²×D₁₃	semidirect
56. C₁₃	C₂²×D₁₆	semidirect
68. C₂²	D₂₀₈	direct (N × H)
73. C₂	C₂×D₂₀₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×D₁₀₄	2
C₂²×C₁₃×C₁₆	2
C₂×D₂₀₈	2
C₂²×D₁₆	13

Subgroups — C22×D208 #13127942

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₂₀₈ #13127942