Subgroups — C₂²×C₄⋊C₁₆ #33394

Order 256.

431 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	—	2	8	no	—
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	1	yes	characteristic
13	C₂³×C₄	C₈	1	1	yes	characteristic
14	C₂³×C₄	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈	—	2	4	no	—
16	C₂²×C₈	C₂×C₄	1	6	yes	—
17	C₂²×C₈	C₂×C₄	1	3	yes	—
18	C₂²×C₈	D₄	1	4	yes	—
19	C₂²×C₈	Q₈	1	4	yes	—
20	C₂²×C₈	C₂³	1	3	yes	—
21	C₂×C₄²	C₈	1	6	yes	—
22	C₂×C₄²	C₂×C₄	1	6	yes	—
23	C₂×C₁₆	—	2	24	no	—
24	C₂×C₁₆	C₂³	1	8	yes	—
25	C₄×C₈	C₂×C₄	1	12	yes	—
26	C₄×C₈	C₂³	1	4	yes	—
27	C₂⁴	C₂×C₈	1	1	yes	characteristic
28	C₂²×C₄	—	2	4	no	—
29	C₂²×C₄	C₁₆	1	8	yes	complemented
30	C₂²×C₄	C₄⋊C₄	1	4	yes	—
31	C₂²×C₄	C₂×C₈	1	6	yes	—
32	C₂²×C₄	C₂×C₈	1	3	yes	—
33	C₂²×C₄	C₂×C₈	1	6	yes	—
34	C₂²×C₄	M₁₆	1	4	yes	—
35	C₂²×C₄	C₂²×C₄	1	3	yes	—
36	C₂×C₈	—	2	12	no	—
37	C₂×C₈	C₄⋊C₄	1	12	yes	—
38	C₂×C₈	C₂²×C₄	1	4	yes	—
39	C₂×C₈	C₂²×C₄	1	3	yes	—
40	C₂×C₈	C₂×D₄	1	6	yes	—
41	C₂×C₈	C₂×Q₈	1	6	yes	—
42	C₂×C₈	C₂⁴	1	1	yes	characteristic
43	C₄²	C₂×C₈	1	12	yes	—
44	C₄²	C₂²×C₄	1	4	yes	—
45	C₁₆	—	2	8	no	—
46	C₂³	C₄⋊C₈	1	4	yes	—
47	C₂³	C₂×C₁₆	1	4	yes	—
48	C₂³	M₃₂	1	4	yes	—
49	C₂³	C₂²×C₈	1	3	yes	—
50	C₂×C₄	—	2	12	no	—
51	C₂×C₄	C₄⋊C₈	1	12	yes	—
52	C₂×C₄	C₂×C₁₆	1	24	yes	complemented
53	C₂×C₄	C₂×C₄⋊C₄	1	6	yes	—
54	C₂×C₄	C₂²×C₈	1	4	yes	—
55	C₂×C₄	C₂²×C₈	1	3	yes	—
56	C₂×C₄	C₂²×C₈	1	4	yes	—
57	C₂×C₄	C₂×M₁₆	1	6	yes	—
58	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
59	C₈	—	2	4	no	—
60	C₈	C₂×C₄⋊C₄	1	6	yes	—
61	C₈	C₂²×D₄	1	1	yes	characteristic
62	C₈	C₂²×Q₈	1	1	yes	characteristic
63	C₂²	C₄⋊C₁₆	1	16	yes	direct product factor
64	C₂²	C₂×C₄⋊C₈	1	6	yes	—
65	C₂²	C₂²×C₁₆	1	6	yes	—
66	C₂²	C₂×M₃₂	1	6	yes	—
67	C₂²	C₂³×C₈	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	C₂×C₄⋊C₈	1	6	yes	—
70	C₄	C₂²×C₁₆	1	8	yes	complemented
71	C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
72	C₄	C₂²×M₁₆	1	1	yes	characteristic
73	C₂	C₂×C₄⋊C₁₆	1	12	yes	direct product factor
74	C₂	C₂²×C₄⋊C₈	1	1	yes	characteristic
75	C₂	C₂³×C₁₆	1	1	yes	characteristic
76	C₂	C₂²×M₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₈	C₂²
commutator	C₂	C₂³×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴
socle, prime radical	C₂⁴	C₂×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈ ◁ 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)
11. C₄⋊C₁₆	C₂²	direct (N × H)
29. C₂²×C₄	C₁₆	semidirect
52. C₂×C₄	C₂×C₁₆	semidirect
63. C₂²	C₄⋊C₁₆	direct (N × H)
70. C₄	C₂²×C₁₆	semidirect
73. 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 #33394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄⋊C₁₆ #33394