Subgroups — C₂²×Dic₂₀₈ #16021042

Order 3328.

462 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₄	C₂	1	2	yes	maximal
2	C₂×Dic₂₀₈	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₅₂	—	2	2	no	—
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×Dic₁₀₄	—	2	6	no	—
7	C₂×Dic₁₀₄	C₂²	1	12	yes	—
8	C₂×C₁₃×C₃₂	C₂²	1	6	yes	—
9	Dic₂₀₈	C₂²	1	16	yes	direct product factor
10	C₂²×Dic₂₆	—	4	2	no	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×Dic₅₂	—	2	12	no	—
13	C₂×Dic₅₂	—	4	6	no	—
14	C₂×C₁₃×C₁₆	D₄	1	3	yes	—
15	C₂×C₁₃×C₁₆	C₂³	1	3	yes	—
16	Dic₁₀₄	—	2	12	no	—
17	Dic₁₀₄	C₂³	1	8	yes	—
18	C₁₃×C₃₂	C₂³	1	4	yes	—
19	C₂²×Q₆₄	—	13	1	no	maximal, Sylow
20	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
21	C₂²×Dic₁₃	—	8	2	no	—
22	C₂×Dic₂₆	—	4	12	no	—
23	C₂×Dic₂₆	—	8	6	no	—
24	C₂×C₈×C₁₃	D₈	1	3	yes	—
25	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
26	Dic₅₂	—	2	8	no	—
27	Dic₅₂	—	4	12	no	—
28	C₁₃×C₁₆	C₂×D₄	1	3	yes	—
29	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
30	C₂²×Q₃₂	—	13	2	no	—
31	C₂×Q₆₄	—	13	12	no	—
32	C₂²×C₃₂	D₁₃	1	1	yes	characteristic
33	C₂³×C₁₃	D₁₆	1	1	yes	characteristic
34	C₂×C₄×C₁₃	D₁₆	1	3	yes	—
35	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
36	C₂×Dic₁₃	—	8	12	no	—
37	Dic₂₆	—	4	8	no	—
38	Dic₂₆	—	8	12	no	—
39	C₈×C₁₃	C₂×D₈	1	3	yes	—
40	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²×Q₁₆	—	26	2	no	—
42	C₂×Q₃₂	—	13	12	no	—
43	C₂×Q₃₂	—	26	6	no	—
44	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
45	Q₆₄	—	13	16	no	—
46	C₂×C₃₂	C₂×D₁₃	1	6	yes	—
47	C₂²×C₁₃	Q₆₄	1	4	yes	complemented
48	C₂²×C₁₃	C₂×D₁₆	1	3	yes	—
49	C₄×C₁₃	C₂×D₁₆	1	3	yes	—
50	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
51	Dic₁₃	—	8	8	no	—
52	C₂²×Q₈	—	52	2	no	—
53	C₂×Q₁₆	—	26	12	no	—
54	C₂×Q₁₆	—	52	6	no	—
55	C₂²×C₈	D₅₂	1	1	yes	characteristic
56	Q₃₂	—	13	8	no	—
57	Q₃₂	—	26	12	no	—
58	C₂×C₁₆	D₅₂	1	3	yes	—
59	C₂×C₁₆	C₂²×D₁₃	1	3	yes	—
60	C₃₂	C₂²×D₁₃	1	4	yes	—
61	C₂×C₁₃	C₂×Q₆₄	1	6	yes	complemented
62	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
63	C₂×Q₈	—	52	12	no	—
64	C₂×Q₈	—	104	6	no	—
65	C₂²×C₄	—	104	2	no	—
66	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
67	Q₁₆	—	26	8	no	—
68	Q₁₆	—	52	12	no	—
69	C₂×C₈	D₁₀₄	1	3	yes	—
70	C₂×C₈	C₂×D₅₂	1	3	yes	—
71	C₁₆	C₂×D₅₂	1	3	yes	—
72	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
73	C₁₃	C₂²×Q₆₄	1	1	yes	characteristic, complemented, Sylow
74	C₂³	D₂₀₈	1	1	yes	characteristic
75	Q₈	—	52	8	no	—
76	Q₈	—	104	12	no	—
77	C₂×C₄	—	104	12	no	—
78	C₂×C₄	D₂₀₈	1	3	yes	—
79	C₂×C₄	C₂×D₁₀₄	1	3	yes	—
80	C₈	C₂×D₁₀₄	1	3	yes	—
81	C₈	C₂²×D₅₂	1	1	yes	characteristic
82	C₂²	Dic₂₀₈	1	4	yes	direct product factor
83	C₂²	C₂×D₂₀₈	1	3	yes	—
84	C₄	—	104	8	no	—
85	C₄	C₂×D₂₀₈	1	3	yes	—
86	C₄	C₂²×D₁₀₄	1	1	yes	characteristic
87	C₂	C₂×Dic₂₀₈	1	6	yes	direct product factor
88	C₂	C₂²×D₂₀₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₀₈
commutator, cosocle	C₁₃×C₁₆	C₂⁴
Frattini	C₁₆	C₂³×D₁₃
Fitting	C₂²×C₁₃×C₃₂	C₂
socle, prime radical	C₂³×C₁₃	D₁₆
hypercenter	C₂²×C₃₂	D₁₃
hypocenter	C₁₃	C₂²×Q₆₄
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₀₈	C₂	direct (N × H)
9. Dic₂₀₈	C₂²	direct (N × H)
47. C₂²×C₁₃	Q₆₄	semidirect
61. C₂×C₁₃	C₂×Q₆₄	semidirect
73. C₁₃	C₂²×Q₆₄	semidirect
82. C₂²	Dic₂₀₈	direct (N × H)
87. C₂	C₂×Dic₂₀₈	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×Dic₁₀₄	2
C₂×Dic₂₀₈	2
C₂²×C₁₃×C₃₂	2
C₂²×Q₆₄	13

Subgroups — C22×Dic208 #16021042

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₂₀₈ #16021042