Subgroups — Q₈⋊#16861969 #45688520

Order 33344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16861969	C₂	1	1	yes	maximal, characteristic
2	C₄×#16861969	C₂	1	1	yes	maximal, characteristic
3	Q₈×#14523438	C₂	1	1	yes	maximal, characteristic
4	C₂×#16861969	—	2	1	no	—
5	C₂×#16861969	—	2	1	no	—
6	C₄⋊#14523438	—	2	1	no	—
7	C₄⋊#14523438	C₄	1	1	yes	characteristic
8	C₄×#14523438	—	2	1	no	—
9	C₄×#14523438	C₂²	1	1	yes	characteristic
10	Q₈×D₅₂₁	C₄	1	1	yes	characteristic
11	#16861969	—	2	2	no	—
12	#16861969	—	4	1	no	—
13	C₂×#14523438	—	2	1	no	—
14	C₂×#14523438	D₄	1	1	yes	characteristic
15	C₂×#14523438	D₄	1	1	yes	characteristic
16	Dic₁₀₄₂	—	2	1	no	—
17	Dic₁₀₄₂	C₈	1	1	yes	characteristic, complemented
18	C₄×D₅₂₁	—	2	1	no	—
19	C₄×D₅₂₁	C₂×C₄	1	1	yes	characteristic
20	Q₈×C₅₂₁	C₈	1	1	yes	characteristic, complemented
21	C₂×D₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
22	#14523438	—	2	1	no	—
23	#14523438	—	4	1	no	—
24	#14523438	SD₁₆	1	1	yes	characteristic
25	#14523438	Q₁₆	1	1	yes	characteristic
26	C₄×C₅₂₁	—	2	1	no	—
27	C₄×C₅₂₁	C₂×C₈	1	1	yes	characteristic
28	Dic₅₂₁	—	2	1	no	—
29	Dic₅₂₁	M₁₆	1	1	yes	characteristic
30	C₂×C₅₂₁	C₂²⋊C₈	1	1	yes	characteristic
31	D₅₂₁	#103	1	1	yes	characteristic
32	D₅₂₁	#104	1	1	yes	characteristic
33	C₅₂₁	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	Q₈⋊C₈	—	521	1	no	maximal, Sylow
35	C₄×Q₈	—	521	1	no	—
36	C₄⋊C₈	—	521	1	no	—
37	C₄×C₈	—	521	1	no	—
38	C₂×Q₈	—	521	1	no	—
39	C₂×C₈	—	1042	1	no	—
40	C₂×C₈	—	1042	1	no	—
41	C₄⋊C₄	—	521	1	no	—
42	C₄⋊C₄	—	1042	1	no	—
43	C₄²	—	521	1	no	—
44	C₄²	—	1042	1	no	—
45	Q₈	—	521	1	no	—
46	Q₈	—	1042	1	no	—
47	Q₈	#16861969	1	1	yes	characteristic, complemented
48	C₂×C₄	—	521	1	no	—
49	C₂×C₄	—	521	1	no	—
50	C₂×C₄	—	521	1	no	—
51	C₂×C₄	—	1042	1	no	—
52	C₂×C₄	—	1042	1	no	—
53	C₈	—	1042	2	no	—
54	C₈	—	2084	1	no	—
55	C₂²	—	521	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	521	1	no	—
58	C₄	—	521	1	no	—
59	C₄	—	521	1	no	—
60	C₄	—	1042	1	no	—
61	C₄	—	1042	1	no	—
62	C₄	—	2084	1	no	—
63	C₄	C₂×#16861969	1	1	yes	characteristic
64	C₂	—	521	1	no	—
65	C₂	—	521	1	no	—
66	C₂	C₂²⋊#16861969	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#16861969
commutator	C₄×C₅₂₁	C₂×C₈
Frattini	C₄	C₂×#16861969
Fitting	Q₈×C₅₂₁	C₈
socle	C₂×C₅₂₁	C₂²⋊C₈
prime radical	C₂×D₅₂₁	C₂²⋊C₄
cosocle	C₄×#14523438	C₂²
hypercenter	Q₈	#16861969
hypocenter	C₅₂₁	Q₈⋊C₈
LCS	G ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
17. Dic₁₀₄₂	C₈	semidirect
20. Q₈×C₅₂₁	C₈	semidirect
33. C₅₂₁	Q₈⋊C₈	semidirect
47. Q₈	#16861969	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#16861969	2
C₄×#16861969	2
Q₈×#14523438	2
Q₈⋊C₈	521

Subgroups — Q8⋊#16861969 #45688520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#16861969 #45688520