Subgroups — Q₈×#17985113 #49097207

Order 35968.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#17985113	C₂	1	3	yes	maximal
2	C₄×#17985113	C₂	1	3	yes	maximal
3	C₈×Q₈×C₂₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#17985113	C₂²	1	3	yes	—
5	C₂×#17985113	C₂²	1	1	yes	characteristic
6	C₄×Q₈×C₂₈₁	C₄	1	1	yes	characteristic
7	C₄⋊C₈×C₂₈₁	C₄	1	3	yes	—
8	C₄×C₈×C₂₈₁	C₂²	1	3	yes	—
9	#17985113	—	2	3	no	—
10	#17985113	Q₈	1	2	yes	direct product factor
11	C₂×Q₈×C₂₈₁	C₈	1	1	yes	characteristic
12	C₂×C₈×C₂₈₁	C₂×C₄	1	3	yes	—
13	C₂×C₈×C₂₈₁	C₂³	1	1	yes	characteristic
14	C₄⋊C₄×C₂₈₁	C₈	1	3	yes	—
15	C₄²×C₂₈₁	C₂×C₄	1	3	yes	—
16	Q₈×C₂₈₁	C₁₆	1	4	yes	complemented
17	C₂×C₄×C₂₈₁	C₂×C₈	1	3	yes	—
18	C₂×C₄×C₂₈₁	C₂×C₈	1	3	yes	—
19	C₂×C₄×C₂₈₁	C₂²×C₄	1	1	yes	characteristic
20	C₈×C₂₈₁	—	2	3	no	—
21	C₈×C₂₈₁	C₂×Q₈	1	1	yes	characteristic
22	C₈×C₂₈₁	#41	1	1	yes	characteristic
23	C₂²×C₂₈₁	C₂²×C₈	1	1	yes	characteristic
24	C₄×C₂₈₁	—	2	3	no	—
25	C₄×C₂₈₁	C₂×C₁₆	1	6	yes	—
26	C₄×C₂₈₁	C₄×Q₈	1	1	yes	characteristic
27	C₄×C₂₈₁	#131	1	1	yes	characteristic
28	C₂×C₂₈₁	C₈×Q₈	1	1	yes	characteristic
29	C₂×C₂₈₁	C₂²×C₁₆	1	1	yes	characteristic
30	C₂×C₂₈₁	#504	1	1	yes	characteristic
31	C₂₈₁	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
32	Q₈×C₁₆	—	281	1	no	maximal, Sylow
33	C₈×Q₈	D₂₈₁	1	1	yes	characteristic
34	C₄⋊C₁₆	—	281	3	no	—
35	C₄×C₁₆	—	281	3	no	—
36	C₄×Q₈	Dic₂₈₁	1	1	yes	characteristic
37	C₂×C₁₆	—	281	1	no	—
38	C₂×C₁₆	—	281	3	no	—
39	C₄⋊C₈	Dic₂₈₁	1	3	yes	—
40	C₄×C₈	C₂×D₂₈₁	1	3	yes	—
41	C₂×Q₈	#14555886	1	1	yes	characteristic
42	C₂×C₈	C₂×Dic₂₈₁	1	3	yes	—
43	C₂×C₈	C₂²×D₂₈₁	1	1	yes	characteristic
44	C₄⋊C₄	#14555886	1	3	yes	—
45	C₄²	C₂×Dic₂₈₁	1	3	yes	—
46	C₁₆	—	281	2	no	—
47	C₁₆	—	562	3	no	—
48	Q₈	#17985113	1	4	yes	direct product factor
49	C₂×C₄	C₂×#14555886	1	3	yes	—
50	C₂×C₄	C₂×#14555886	1	3	yes	—
51	C₂×C₄	C₂²×Dic₂₈₁	1	1	yes	characteristic
52	C₈	—	2	3	no	—
53	C₈	Q₈×D₂₈₁	1	1	yes	characteristic
54	C₈	#17985139	1	1	yes	characteristic
55	C₂²	C₂²×#14555886	1	1	yes	characteristic
56	C₄	—	2	3	no	—
57	C₄	C₂×#17985113	1	6	yes	—
58	C₄	Q₈×Dic₂₈₁	1	1	yes	characteristic
59	C₄	#22582886	1	1	yes	characteristic
60	C₂	Q₈×#14555886	1	1	yes	characteristic
61	C₂	C₂²×#17985113	1	1	yes	characteristic
62	C₂	#31823880	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₈₁
commutator	C₂×C₂₈₁	C₂²×C₁₆
Fitting	C₈×Q₈×C₂₈₁	C₂
socle, prime radical	C₂²×C₂₈₁	C₂²×C₈
cosocle	C₂×C₈×C₂₈₁	C₂³
hypercenter	C₈×Q₈	D₂₈₁
hypocenter	C₂₈₁	Q₈×C₁₆
LCS	G ▷ C₂×C₂₈₁ ▷ C₂₈₁
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

Complements

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

N	H ≅ G/N	type
10. #17985113	Q₈	direct (N × H)
16. Q₈×C₂₈₁	C₁₆	semidirect
31. C₂₈₁	Q₈×C₁₆	semidirect
48. Q₈	#17985113	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄⋊#17985113	2
C₄×#17985113	2
C₈×Q₈×C₂₈₁	2
Q₈×C₁₆	281

Subgroups — Q8×#17985113 #49097207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#17985113 #49097207