Subgroups — Q₈⋊#16861967 #45688281

Order 33344.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#16861967	C₂	1	1	yes	maximal, characteristic
2	C₄×#16861967	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₅₂₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#16861967	—	2	1	no	—
5	C₂×#16861967	—	2	1	no	—
6	C₄⋊Dic₅₂₁	—	2	1	no	—
7	C₄⋊Dic₅₂₁	C₄	1	1	yes	characteristic
8	C₄×Dic₅₂₁	—	2	1	no	—
9	C₄×Dic₅₂₁	C₂²	1	1	yes	characteristic
10	C₂×Q₈×C₅₂₁	C₄	1	1	yes	characteristic
11	#16861967	—	2	2	no	—
12	#16861967	—	4	1	no	—
13	C₂×Dic₅₂₁	—	2	1	no	—
14	C₂×Dic₅₂₁	D₄	1	1	yes	characteristic
15	C₂×Dic₅₂₁	D₄	1	1	yes	characteristic
16	Q₈×C₅₂₁	—	2	1	no	—
17	Q₈×C₅₂₁	C₈	1	2	yes	complemented
18	C₂×C₄×C₅₂₁	—	2	1	no	—
19	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₅₂₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₅₂₁	—	2	2	no	—
22	C₄×C₅₂₁	C₂×C₈	1	1	yes	characteristic
23	C₄×C₅₂₁	M₁₆	1	1	yes	characteristic
24	Dic₅₂₁	—	2	1	no	—
25	Dic₅₂₁	—	4	1	no	—
26	Dic₅₂₁	SD₁₆	1	1	yes	characteristic
27	Dic₅₂₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₅₂₁	C₂²⋊C₈	1	1	yes	characteristic
29	C₂×C₅₂₁	#103	1	1	yes	characteristic
30	C₂×C₅₂₁	#104	1	1	yes	characteristic
31	C₅₂₁	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
32	Q₈⋊C₈	—	521	1	no	maximal, Sylow
33	C₄×Q₈	—	521	1	no	—
34	C₄⋊C₈	—	521	1	no	—
35	C₄×C₈	—	521	1	no	—
36	C₂×Q₈	#14523438	1	1	yes	characteristic
37	C₂×C₈	—	1042	1	no	—
38	C₂×C₈	—	1042	1	no	—
39	C₄⋊C₄	—	521	1	no	—
40	C₄⋊C₄	—	1042	1	no	—
41	C₄²	—	521	1	no	—
42	C₄²	—	1042	1	no	—
43	Q₈	—	2	1	no	—
44	Q₈	#16861967	1	2	yes	complemented
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	521	1	no	—
47	C₂×C₄	—	521	1	no	—
48	C₂×C₄	—	1042	1	no	—
49	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
50	C₈	—	1042	2	no	—
51	C₈	—	2084	1	no	—
52	C₂²	C₂²⋊#14523438	1	1	yes	characteristic
53	C₄	—	2	2	no	—
54	C₄	—	521	1	no	—
55	C₄	—	521	1	no	—
56	C₄	—	1042	1	no	—
57	C₄	—	2084	1	no	—
58	C₄	C₂×#16861967	1	1	yes	characteristic
59	C₄	#22552373	1	1	yes	characteristic
60	C₂	C₂²⋊#16861967	1	1	yes	characteristic
61	C₂	#30659771	1	1	yes	characteristic
62	C₂	#30659773	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14523438
commutator	C₄×C₅₂₁	C₂×C₈
Frattini	C₂×C₄	C₂×#14523438
Fitting	C₂×Q₈×C₅₂₁	C₄
socle, prime radical	C₂²×C₅₂₁	C₂²⋊C₄
cosocle	C₄×Dic₅₂₁	C₂²
hypercenter	C₂×Q₈	#14523438
hypocenter	C₅₂₁	Q₈⋊C₈
LCS	G ▷ C₄×C₅₂₁ ▷ C₂×C₅₂₁ ▷ C₅₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
17. Q₈×C₅₂₁	C₈	semidirect
31. C₅₂₁	Q₈⋊C₈	semidirect
44. Q₈	#16861967	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#16861967	2
C₄×#16861967	2
Q₈×Dic₅₂₁	2
Q₈⋊C₈	521

Subgroups — Q8⋊#16861967 #45688281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#16861967 #45688281