Subgroups — C₂²×D₄₁₆ #16021035

Order 3328.

542 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₀₈	C₂	1	2	yes	maximal, complemented
2	C₂×D₄₁₆	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₀₄	—	2	2	no	—
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×D₂₀₈	—	2	6	no	—
7	C₂×D₂₀₈	C₂²	1	12	yes	complemented
8	C₂×C₁₃×C₃₂	C₂²	1	6	yes	complemented
9	D₄₁₆	C₂²	1	16	yes	direct product factor
10	C₂²×D₅₂	—	4	2	no	—
11	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
12	C₂×D₁₀₄	—	2	12	no	—
13	C₂×D₁₀₄	—	4	6	no	—
14	C₂×C₁₃×C₁₆	D₄	1	3	yes	—
15	C₂×C₁₃×C₁₆	C₂³	1	3	yes	—
16	D₂₀₈	—	2	12	no	—
17	D₂₀₈	C₂³	1	8	yes	complemented
18	C₁₃×C₃₂	C₂³	1	4	yes	complemented
19	C₂²×D₃₂	—	13	1	no	maximal, Sylow
20	C₂³×D₁₃	—	8	2	no	—
21	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
22	C₂×D₅₂	—	4	12	no	—
23	C₂×D₅₂	—	8	6	no	—
24	C₂×C₈×C₁₃	D₈	1	3	yes	—
25	C₂×C₈×C₁₃	C₂×D₄	1	3	yes	—
26	D₁₀₄	—	2	8	no	—
27	D₁₀₄	—	4	12	no	—
28	C₁₃×C₁₆	C₂×D₄	1	3	yes	—
29	C₁₃×C₁₆	C₂⁴	1	1	yes	characteristic
30	C₂²×D₁₆	—	13	2	no	—
31	C₂×D₃₂	—	13	12	no	—
32	C₂²×C₃₂	D₁₃	1	1	yes	characteristic, complemented
33	C₂³×C₁₃	D₁₆	1	1	yes	characteristic
34	C₂²×D₁₃	—	8	12	no	—
35	C₂²×D₁₃	—	16	8	no	—
36	C₂×C₄×C₁₃	D₁₆	1	3	yes	—
37	C₂×C₄×C₁₃	C₂×D₈	1	3	yes	—
38	D₅₂	—	4	8	no	—
39	D₅₂	—	8	12	no	—
40	C₈×C₁₃	C₂×D₈	1	3	yes	—
41	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
42	C₂²×D₈	—	26	2	no	—
43	C₂×D₁₆	—	13	12	no	—
44	C₂×D₁₆	—	26	6	no	—
45	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
46	D₃₂	—	13	16	no	—
47	C₂×C₃₂	C₂×D₁₃	1	6	yes	complemented
48	C₂²×C₁₃	D₃₂	1	4	yes	complemented
49	C₂²×C₁₃	C₂×D₁₆	1	3	yes	—
50	C₂×D₁₃	—	8	8	no	—
51	C₂×D₁₃	—	16	24	no	—
52	C₄×C₁₃	C₂×D₁₆	1	3	yes	—
53	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
54	C₂²×D₄	—	52	2	no	—
55	C₂×D₈	—	26	12	no	—
56	C₂×D₈	—	52	6	no	—
57	C₂²×C₈	D₅₂	1	1	yes	characteristic
58	D₁₆	—	13	8	no	—
59	D₁₆	—	26	12	no	—
60	C₂×C₁₆	D₅₂	1	3	yes	—
61	C₂×C₁₆	C₂²×D₁₃	1	3	yes	—
62	C₃₂	C₂²×D₁₃	1	4	yes	complemented
63	C₂×C₁₃	C₂×D₃₂	1	6	yes	complemented
64	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
65	D₁₃	—	16	8	no	—
66	C₂⁴	—	104	2	no	—
67	C₂×D₄	—	52	12	no	—
68	C₂×D₄	—	104	6	no	—
69	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
70	D₈	—	26	8	no	—
71	D₈	—	52	12	no	—
72	C₂×C₈	D₁₀₄	1	3	yes	—
73	C₂×C₈	C₂×D₅₂	1	3	yes	—
74	C₁₆	C₂×D₅₂	1	3	yes	—
75	C₁₆	C₂³×D₁₃	1	1	yes	characteristic
76	C₁₃	C₂²×D₃₂	1	1	yes	characteristic, complemented, Sylow
77	C₂³	—	104	12	no	—
78	C₂³	—	208	8	no	—
79	C₂³	D₂₀₈	1	1	yes	characteristic
80	D₄	—	52	8	no	—
81	D₄	—	104	12	no	—
82	C₂×C₄	D₂₀₈	1	3	yes	—
83	C₂×C₄	C₂×D₁₀₄	1	3	yes	—
84	C₈	C₂×D₁₀₄	1	3	yes	—
85	C₈	C₂²×D₅₂	1	1	yes	characteristic
86	C₂²	—	104	8	no	—
87	C₂²	—	208	24	no	—
88	C₂²	D₄₁₆	1	4	yes	direct product factor
89	C₂²	C₂×D₂₀₈	1	3	yes	—
90	C₄	C₂×D₂₀₈	1	3	yes	—
91	C₄	C₂²×D₁₀₄	1	1	yes	characteristic
92	C₂	—	208	8	no	—
93	C₂	C₂×D₄₁₆	1	6	yes	direct product factor
94	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	C₂³×C₁₃	D₁₆
hypercenter	C₂²×C₃₂	D₁₃
hypocenter	C₁₃	C₂²×D₃₂
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
1. C₂²×D₂₀₈	C₂	semidirect
2. C₂×D₄₁₆	C₂	direct (N × H)
3. C₂²×C₁₃×C₃₂	C₂	semidirect
7. C₂×D₂₀₈	C₂²	semidirect
8. C₂×C₁₃×C₃₂	C₂²	semidirect
9. D₄₁₆	C₂²	direct (N × H)
17. D₂₀₈	C₂³	semidirect
18. C₁₃×C₃₂	C₂³	semidirect
32. C₂²×C₃₂	D₁₃	semidirect
47. C₂×C₃₂	C₂×D₁₃	semidirect
48. C₂²×C₁₃	D₃₂	semidirect
62. C₃₂	C₂²×D₁₃	semidirect
63. C₂×C₁₃	C₂×D₃₂	semidirect
76. C₁₃	C₂²×D₃₂	semidirect
88. C₂²	D₄₁₆	direct (N × H)
93. C₂	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
C₂²×D₂₀₈	2
C₂×D₄₁₆	2
C₂²×C₁₃×C₃₂	2
C₂²×D₃₂	13

Subgroups — C22×D416 #16021035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₄₁₆ #16021035