Subgroups — C₂×Q₈×C₁₆ #33472

Order 256.

291 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₆	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₁₆	C₂	1	3	yes	maximal
4	C₂×C₄×C₁₆	C₂	1	3	yes	maximal
5	C₂×C₄×Q₈	C₄	1	1	yes	characteristic
6	C₂²×C₁₆	C₂²	1	3	yes	—
7	C₂²×C₁₆	C₂²	1	1	yes	characteristic
8	C₈×Q₈	C₄	1	4	yes	—
9	C₈×Q₈	C₂²	1	4	yes	—
10	C₂×C₄⋊C₈	C₄	1	3	yes	—
11	C₂×C₄×C₈	C₂²	1	3	yes	—
12	C₄⋊C₁₆	C₂²	1	12	yes	—
13	C₄×C₁₆	C₂²	1	12	yes	—
14	C₂²×Q₈	C₈	1	1	yes	characteristic
15	C₂²×C₈	C₂×C₄	1	3	yes	—
16	C₂²×C₈	C₂³	1	1	yes	characteristic
17	C₄×Q₈	C₈	1	4	yes	—
18	C₄×Q₈	C₂×C₄	1	4	yes	—
19	C₂×C₄⋊C₄	C₈	1	3	yes	—
20	C₂×C₄²	C₂×C₄	1	3	yes	—
21	C₂×C₁₆	—	2	6	no	—
22	C₂×C₁₆	Q₈	1	4	yes	direct product factor
23	C₂×C₁₆	C₂³	1	6	yes	—
24	C₂×C₁₆	C₂³	1	2	yes	—
25	C₄⋊C₈	C₂×C₄	1	12	yes	—
26	C₄×C₈	C₂×C₄	1	6	yes	—
27	C₄×C₈	C₂³	1	6	yes	—
28	C₂×Q₈	C₁₆	1	8	yes	direct product factor
29	C₂×Q₈	C₂×C₈	1	4	yes	—
30	C₂²×C₄	C₂×C₈	1	3	yes	—
31	C₂²×C₄	C₂×C₈	1	3	yes	—
32	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₈	—	2	6	no	—
34	C₂×C₈	C₂²×C₄	1	6	yes	—
35	C₂×C₈	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈	C₂×Q₈	1	2	yes	—
37	C₂×C₈	#41	1	2	yes	—
38	C₂×C₈	C₂⁴	1	1	yes	characteristic
39	C₄⋊C₄	C₂×C₈	1	12	yes	—
40	C₄²	C₂×C₈	1	6	yes	—
41	C₄²	C₂²×C₄	1	6	yes	—
42	C₁₆	—	2	6	no	—
43	C₁₆	C₂×Q₈	1	4	yes	direct product factor
44	C₂³	C₂²×C₈	1	1	yes	characteristic
45	Q₈	C₂×C₁₆	1	16	yes	direct product factor
46	C₂×C₄	—	2	6	no	—
47	C₂×C₄	C₂×C₁₆	1	12	yes	—
48	C₂×C₄	C₄×Q₈	1	2	yes	—
49	C₂×C₄	C₂²×C₈	1	6	yes	—
50	C₂×C₄	C₂²×C₈	1	1	yes	characteristic
51	C₂×C₄	C₂²×C₈	1	6	yes	—
52	C₂×C₄	#131	1	2	yes	—
53	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
54	C₈	—	2	6	no	—
55	C₈	C₄×Q₈	1	2	yes	—
56	C₈	C₂²×Q₈	1	1	yes	characteristic
57	C₈	C₂×#41	1	1	yes	characteristic
58	C₂²	C₈×Q₈	1	2	yes	—
59	C₂²	C₂²×C₁₆	1	2	yes	—
60	C₂²	#504	1	2	yes	—
61	C₂²	C₂³×C₈	1	1	yes	characteristic
62	C₄	—	2	6	no	—
63	C₄	C₈×Q₈	1	2	yes	—
64	C₄	C₂²×C₁₆	1	12	yes	—
65	C₄	C₂×C₄×Q₈	1	1	yes	characteristic
66	C₄	C₂×#131	1	1	yes	characteristic
67	C₂	Q₈×C₁₆	1	4	yes	direct product factor
68	C₂	C₂×C₈×Q₈	1	1	yes	characteristic
69	C₂	C₂³×C₁₆	1	1	yes	characteristic
70	C₂	C₂×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂²
commutator	C₂	C₂³×C₁₆
Frattini, cosocle	C₂×C₈	C₂⁴
socle, prime radical	C₂³	C₂²×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₆ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₆	C₂	direct (N × H)
22. C₂×C₁₆	Q₈	direct (N × H)
28. C₂×Q₈	C₁₆	direct (N × H)
43. C₁₆	C₂×Q₈	direct (N × H)
45. Q₈	C₂×C₁₆	direct (N × H)
67. C₂	Q₈×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
C₂×C₈×Q₈	2
Q₈×C₁₆	2
C₂×C₄⋊C₁₆	2
C₂×C₄×C₁₆	2

Subgroups — C2×Q8×C16 #33472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₁₆ #33472