Subgroups — C₂²×C₄×C₁₆ #33320

Order 256.

511 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₆	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₆	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₈	C₄	1	1	yes	characteristic
5	C₂³×C₈	C₂²	1	1	yes	characteristic
6	C₂²×C₄²	C₄	1	1	yes	characteristic
7	C₂²×C₁₆	C₄	1	16	yes	direct product factor
8	C₂²×C₁₆	C₂²	1	12	yes	—
9	C₂×C₄×C₈	C₄	1	6	yes	—
10	C₂×C₄×C₈	C₂²	1	6	yes	—
11	C₄×C₁₆	C₂²	1	16	yes	direct product factor
12	C₂³×C₄	C₈	1	2	yes	—
13	C₂³×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈	C₈	1	8	yes	—
15	C₂²×C₈	C₂×C₄	1	3	yes	—
16	C₂²×C₈	C₂×C₄	1	6	yes	—
17	C₂²×C₈	C₂×C₄	1	8	yes	—
18	C₂²×C₈	C₂³	1	3	yes	—
19	C₂×C₄²	C₈	1	6	yes	—
20	C₂×C₄²	C₂×C₄	1	6	yes	—
21	C₂×C₁₆	C₂×C₄	1	48	yes	direct product factor
22	C₂×C₁₆	C₂³	1	8	yes	—
23	C₄×C₈	C₂×C₄	1	12	yes	—
24	C₄×C₈	C₂³	1	4	yes	—
25	C₂⁴	C₂×C₈	1	1	yes	characteristic
26	C₂²×C₄	C₁₆	1	16	yes	direct product factor
27	C₂²×C₄	C₄²	1	4	yes	—
28	C₂²×C₄	C₂×C₈	1	3	yes	—
29	C₂²×C₄	C₂×C₈	1	4	yes	—
30	C₂²×C₄	C₂×C₈	1	12	yes	—
31	C₂²×C₄	C₂²×C₄	1	3	yes	—
32	C₂×C₈	C₄²	1	12	yes	—
33	C₂×C₈	C₂×C₈	1	24	yes	—
34	C₂×C₈	C₂²×C₄	1	3	yes	—
35	C₂×C₈	C₂²×C₄	1	4	yes	—
36	C₂×C₈	C₂²×C₄	1	12	yes	—
37	C₂×C₈	C₂⁴	1	1	yes	characteristic
38	C₄²	C₂×C₈	1	12	yes	—
39	C₄²	C₂²×C₄	1	4	yes	—
40	C₁₆	C₂²×C₄	1	16	yes	direct product factor
41	C₂³	C₄×C₈	1	4	yes	—
42	C₂³	C₂×C₁₆	1	8	yes	—
43	C₂³	C₂²×C₈	1	3	yes	—
44	C₂×C₄	C₄×C₈	1	12	yes	—
45	C₂×C₄	C₂×C₁₆	1	48	yes	direct product factor
46	C₂×C₄	C₂×C₄²	1	6	yes	—
47	C₂×C₄	C₂²×C₈	1	3	yes	—
48	C₂×C₄	C₂²×C₈	1	6	yes	—
49	C₂×C₄	C₂²×C₈	1	8	yes	—
50	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
51	C₈	C₂×C₄²	1	6	yes	—
52	C₈	C₂²×C₈	1	8	yes	—
53	C₈	C₂³×C₄	1	2	yes	—
54	C₂²	C₄×C₁₆	1	16	yes	direct product factor
55	C₂²	C₂×C₄×C₈	1	6	yes	—
56	C₂²	C₂²×C₁₆	1	12	yes	—
57	C₂²	C₂³×C₈	1	1	yes	characteristic
58	C₄	C₂×C₄×C₈	1	6	yes	—
59	C₄	C₂²×C₁₆	1	16	yes	direct product factor
60	C₄	C₂²×C₄²	1	1	yes	characteristic
61	C₄	C₂³×C₈	1	1	yes	characteristic
62	C₂	C₂×C₄×C₁₆	1	12	yes	direct product factor
63	C₂	C₂²×C₄×C₈	1	1	yes	characteristic
64	C₂	C₂³×C₁₆	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂⁴
socle, prime radical	C₂⁴	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₁₆	C₂	direct (N × H)
7. C₂²×C₁₆	C₄	direct (N × H)
11. C₄×C₁₆	C₂²	direct (N × H)
21. C₂×C₁₆	C₂×C₄	direct (N × H)
26. C₂²×C₄	C₁₆	direct (N × H)
40. C₁₆	C₂²×C₄	direct (N × H)
45. C₂×C₄	C₂×C₁₆	direct (N × H)
54. C₂²	C₄×C₁₆	direct (N × H)
59. C₄	C₂²×C₁₆	direct (N × H)
62. C₂	C₂×C₄×C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₆	2
C₂²×C₄×C₈	2
C₂×C₄×C₁₆	2

Subgroups — C22×C4×C16 #33320

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₁₆ #33320