Subgroups — Q₈×M₁₆ #2963

Order 128.

194 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	#446	C₂	1	6	yes	maximal, complemented
3	C₈×Q₈	C₂	1	2	yes	maximal, complemented
4	#423	C₂	1	3	yes	maximal
5	C₄×M₁₆	C₂	1	3	yes	maximal
6	C₂²×Q₈	C₄	1	1	yes	characteristic
7	C₂×M₁₆	C₂²	1	3	yes	—
8	C₂×M₁₆	C₂²	1	1	yes	characteristic
9	C₄×Q₈	C₄	1	3	yes	—
10	C₄×Q₈	C₄	1	1	yes	characteristic
11	C₄×Q₈	C₂²	1	1	yes	characteristic
12	C₄×Q₈	C₂²	1	3	yes	—
13	C₂×C₄⋊C₄	C₄	1	3	yes	—
14	C₂×C₄²	C₂²	1	3	yes	—
15	C₄⋊C₈	C₂²	1	6	yes	—
16	C₄⋊C₈	C₂²	1	6	yes	—
17	#97	C₂²	1	6	yes	—
18	C₄×C₈	C₂²	1	6	yes	—
19	C₂×Q₈	—	2	4	no	—
20	C₂×Q₈	C₂×C₄	1	3	yes	—
21	C₂×Q₈	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₄	C₂×C₄	1	3	yes	—
23	C₂²×C₄	C₂×C₄	1	3	yes	—
24	C₂²×C₄	C₂³	1	1	yes	characteristic
25	M₁₆	—	2	6	no	—
26	M₁₆	Q₈	1	4	yes	direct product factor
27	C₂×C₈	C₂³	1	6	yes	—
28	C₂×C₈	C₂³	1	2	yes	—
29	C₄⋊C₄	C₂×C₄	1	6	yes	—
30	C₄⋊C₄	C₂×C₄	1	3	yes	—
31	C₄⋊C₄	C₂×C₄	1	3	yes	—
32	C₄²	C₂×C₄	1	3	yes	—
33	C₄²	C₂×C₄	1	3	yes	—
34	C₄²	C₂³	1	3	yes	—
35	C₄²	C₂³	1	3	yes	—
36	C₂³	C₂²×C₄	1	1	yes	characteristic
37	Q₈	—	2	6	no	—
38	Q₈	M₁₆	1	4	yes	direct product factor
39	C₂×C₄	—	2	6	no	—
40	C₂×C₄	—	4	3	no	—
41	C₂×C₄	C₂²×C₄	1	3	yes	—
42	C₂×C₄	C₂²×C₄	1	3	yes	—
43	C₂×C₄	C₂²×C₄	1	3	yes	—
44	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₄	C₂²×C₄	1	3	yes	—
46	C₂×C₄	C₂×Q₈	1	2	yes	—
47	C₂×C₄	#41	1	2	yes	—
48	C₂×C₄	C₂⁴	1	1	yes	characteristic
49	C₈	—	2	6	no	—
50	C₈	C₂×Q₈	1	4	yes	complemented
51	C₂²	—	2	1	no	—
52	C₂²	—	2	1	no	—
53	C₂²	C₄×Q₈	1	2	yes	—
54	C₂²	C₂³×C₄	1	1	yes	characteristic
55	C₄	—	2	3	no	—
56	C₄	—	2	3	no	—
57	C₄	—	2	3	no	—
58	C₄	C₄×Q₈	1	2	yes	—
59	C₄	C₂×M₁₆	1	6	yes	—
60	C₄	C₂²×Q₈	1	1	yes	characteristic
61	C₄	C₂×#41	1	1	yes	characteristic
62	C₂	—	2	2	no	—
63	C₂	C₂×C₄×Q₈	1	1	yes	characteristic
64	C₂	C₂²×M₁₆	1	1	yes	characteristic
65	C₂	#568	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #446	C₂	semidirect
3. C₈×Q₈	C₂	semidirect
26. M₁₆	Q₈	direct (N × H)
38. Q₈	M₁₆	direct (N × H)
50. C₈	C₂×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₈	2
#446	2
C₈×Q₈	2
#423	2
C₄×M₁₆	2

Subgroups — Q8×M16 #2963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×M₁₆ #2963