Subgroups — C₈×Q₁₆ #1577

Order 128.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈	C₂	1	2	yes	maximal
2	C₄×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	#335	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊C₈	C₂	1	2	yes	maximal
5	C₈²	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆	C₄	1	1	yes	characteristic
7	C₄×Q₈	C₂²	1	2	yes	—
8	#107	C₄	1	1	yes	characteristic
9	C₄⋊C₈	—	2	2	no	—
10	C₄⋊C₈	C₂²	1	2	yes	—
11	#103	C₄	1	2	yes	—
12	C₄×C₈	—	2	2	no	—
13	C₄×C₈	C₂²	1	1	yes	characteristic
14	C₄×C₈	C₂²	1	1	yes	characteristic
15	C₄×C₈	C₂²	1	1	yes	characteristic
16	C₂×Q₈	C₂×C₄	1	2	yes	—
17	Q₁₆	C₈	1	4	yes	direct product factor
18	C₂×C₈	—	2	1	no	—
19	C₂×C₈	—	2	2	no	—
20	C₂×C₈	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈	D₄	1	1	yes	characteristic
23	C₂×C₈	D₄	1	1	yes	characteristic
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	C₂×C₄	1	2	yes	—
26	C₄²	—	2	2	no	—
27	C₄²	C₂³	1	1	yes	characteristic
28	Q₈	—	2	2	no	—
29	Q₈	C₂×C₈	1	4	yes	—
30	C₂×C₄	—	2	2	no	—
31	C₂×C₄	—	2	2	no	—
32	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
33	C₂×C₄	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄	#41	1	1	yes	characteristic
35	C₈	—	2	2	no	—
36	C₈	—	2	1	no	—
37	C₈	—	2	1	no	—
38	C₈	—	4	2	no	—
39	C₈	C₂×C₈	1	2	yes	—
40	C₈	Q₁₆	1	2	yes	direct product factor
41	C₂²	C₄×D₄	1	1	yes	characteristic
42	C₄	—	2	4	no	—
43	C₄	—	2	1	no	—
44	C₄	—	4	2	no	—
45	C₄	C₂²×C₈	1	1	yes	characteristic
46	C₄	#131	1	1	yes	characteristic
47	C₄	C₂×Q₁₆	1	1	yes	characteristic
48	C₄	#135	1	1	yes	characteristic
49	C₂	C₈×D₄	1	1	yes	characteristic
50	C₂	C₄×Q₁₆	1	1	yes	characteristic
51	C₂	#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄
commutator	C₄	C₂²×C₈
Frattini, cosocle	C₄²	C₂³
socle, prime radical	C₂²	C₄×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
17. Q₁₆	C₈	direct (N × H)
40. C₈	Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×Q₈	2
C₄×Q₁₆	2
#335	2
Q₈⋊C₈	2
C₈²	2

Subgroups — C8×Q16 #1577

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×Q₁₆ #1577