Subgroups — Q₈⋊C₈×C₁₀₁ #20264635

Order 6464.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₁₀₁	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₀₁	—	2	1	no	—
6	C₂×C₈×C₁₀₁	—	2	1	no	—
7	C₄⋊C₄×C₁₀₁	—	2	1	no	—
8	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
9	C₄²×C₁₀₁	—	2	1	no	—
10	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
11	Q₈×C₁₀₁	—	2	1	no	—
12	Q₈×C₁₀₁	C₈	1	2	yes	complemented
13	C₂×C₄×C₁₀₁	—	2	1	no	—
14	C₂×C₄×C₁₀₁	—	2	1	no	—
15	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
18	C₈×C₁₀₁	—	2	2	no	—
19	C₈×C₁₀₁	—	4	1	no	—
20	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₁₀₁	—	2	2	no	—
22	C₄×C₁₀₁	—	2	1	no	—
23	C₄×C₁₀₁	—	4	1	no	—
24	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
26	C₄×C₁₀₁	SD₁₆	1	1	yes	characteristic
27	C₄×C₁₀₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₁₀₁	#103	1	1	yes	characteristic
30	C₂×C₁₀₁	#104	1	1	yes	characteristic
31	C₁₀₁	Q₈⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
32	Q₈⋊C₈	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₄×Q₈	C₂×C₁₀₁	1	1	yes	characteristic
34	C₄⋊C₈	C₂×C₁₀₁	1	1	yes	characteristic
35	C₄×C₈	C₂×C₁₀₁	1	1	yes	characteristic
36	C₂×Q₈	C₄×C₁₀₁	1	1	yes	characteristic
37	C₂×C₈	—	2	1	no	—
38	C₂×C₈	—	2	1	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	C₄×C₁₀₁	1	1	yes	characteristic
41	C₄²	—	2	1	no	—
42	C₄²	C₂²×C₁₀₁	1	1	yes	characteristic
43	Q₈	—	2	1	no	—
44	Q₈	C₈×C₁₀₁	1	2	yes	complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	C₂×C₄×C₁₀₁	1	1	yes	characteristic
48	C₂×C₄	D₄×C₁₀₁	1	1	yes	characteristic
49	C₂×C₄	D₄×C₁₀₁	1	1	yes	characteristic
50	C₈	—	2	2	no	—
51	C₈	—	4	1	no	—
52	C₂²	C₂²⋊C₄×C₁₀₁	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	2	1	no	—
55	C₄	—	4	1	no	—
56	C₄	C₂×C₈×C₁₀₁	1	1	yes	characteristic
57	C₄	M₁₆×C₁₀₁	1	1	yes	characteristic
58	C₄	SD₁₆×C₁₀₁	1	1	yes	characteristic
59	C₄	Q₁₆×C₁₀₁	1	1	yes	characteristic
60	C₂	C₂²⋊C₈×C₁₀₁	1	1	yes	characteristic
61	C₂	#103×C₁₀₁	1	1	yes	characteristic
62	C₂	#104×C₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₀₁	D₄
commutator	C₄	C₂×C₈×C₁₀₁
Frattini, cosocle	C₄²	C₂²×C₁₀₁
socle, prime radical	C₂²×C₁₀₁	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₁ ◁ C₄²×C₁₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
12. Q₈×C₁₀₁	C₈	semidirect
31. C₁₀₁	Q₈⋊C₈	direct (N × H)
32. Q₈⋊C₈	C₁₀₁	direct (N × H)
44. Q₈	C₈×C₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₄×Q₈×C₁₀₁	2
C₄⋊C₈×C₁₀₁	2
C₄×C₈×C₁₀₁	2
Q₈⋊C₈	101

Subgroups — Q8⋊C8×C101 #20264635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊C₈×C₁₀₁ #20264635