Subgroups — Q₈×#14268661 #28407864

Order 14464.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268661	C₂	1	3	yes	maximal
2	C₄×#14268661	C₂	1	3	yes	maximal
3	Q₈×#11744762	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268661	C₂²	1	3	yes	—
5	C₂×#14268661	C₂²	1	1	yes	characteristic
6	C₄⋊#11744762	C₄	1	3	yes	—
7	C₄×#11744762	C₂²	1	3	yes	—
8	Q₈×#90673	C₄	1	1	yes	characteristic
9	#14268661	—	2	3	no	—
10	#14268661	Q₈	1	2	yes	direct product factor
11	C₂×#11744762	C₂×C₄	1	3	yes	—
12	C₂×#11744762	C₂³	1	1	yes	characteristic
13	C₄⋊#90673	C₈	1	3	yes	—
14	C₄×#90673	C₂×C₄	1	3	yes	—
15	Q₈×D₁₁₃	C₈	1	1	yes	characteristic
16	C₂×#90673	C₂×C₈	1	3	yes	—
17	C₂×#90673	C₂²×C₄	1	1	yes	characteristic
18	#11744762	—	2	3	no	—
19	#11744762	C₂×Q₈	1	1	yes	characteristic
20	#11744762	#41	1	1	yes	characteristic
21	Q₈×C₁₁₃	C₁₆	1	1	yes	characteristic, complemented
22	C₄×D₁₁₃	C₂×C₈	1	3	yes	—
23	Dic₂₂₆	C₁₆	1	3	yes	complemented
24	C₂×D₁₁₃	C₂²×C₈	1	1	yes	characteristic
25	#90673	—	2	3	no	—
26	#90673	C₄×Q₈	1	1	yes	characteristic
27	#90673	#131	1	1	yes	characteristic
28	C₄×C₁₁₃	C₂×C₁₆	1	3	yes	—
29	Dic₁₁₃	C₂×C₁₆	1	3	yes	—
30	C₂×C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic
31	D₁₁₃	C₈×Q₈	1	1	yes	characteristic
32	D₁₁₃	#504	1	1	yes	characteristic
33	Q₈×C₁₆	—	113	1	no	maximal, Sylow
34	C₁₁₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
35	C₈×Q₈	—	113	1	no	—
36	C₄⋊C₁₆	—	113	3	no	—
37	C₄×C₁₆	—	113	3	no	—
38	C₄×Q₈	—	113	1	no	—
39	C₂×C₁₆	—	113	1	no	—
40	C₂×C₁₆	—	113	3	no	—
41	C₄⋊C₈	—	113	3	no	—
42	C₄×C₈	—	113	3	no	—
43	C₂×Q₈	—	113	1	no	—
44	C₂×C₈	—	113	1	no	—
45	C₂×C₈	—	113	3	no	—
46	C₄⋊C₄	—	113	3	no	—
47	C₄²	—	113	3	no	—
48	C₁₆	—	113	2	no	—
49	C₁₆	—	226	3	no	—
50	Q₈	—	113	3	no	—
51	Q₈	#14268661	1	1	yes	characteristic, direct product factor
52	C₂×C₄	—	113	1	no	—
53	C₂×C₄	—	113	3	no	—
54	C₂×C₄	—	113	3	no	—
55	C₈	—	113	1	no	—
56	C₈	—	113	1	no	—
57	C₈	—	226	3	no	—
58	C₂²	—	113	1	no	—
59	C₄	—	113	1	no	—
60	C₄	—	113	1	no	—
61	C₄	—	113	3	no	—
62	C₄	—	226	3	no	—
63	C₄	C₂×#14268661	1	3	yes	—
64	C₂	—	113	1	no	—
65	C₂	—	113	1	no	—
66	C₂	C₂²×#14268661	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#14268661
commutator, socle	C₂×C₁₁₃	C₂²×C₁₆
Fitting	Q₈×C₁₁₃	C₁₆
prime radical	C₂×D₁₁₃	C₂²×C₈
cosocle	C₂×#11744762	C₂³
hypercenter	Q₈	#14268661
hypocenter	C₁₁₃	Q₈×C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
10. #14268661	Q₈	direct (N × H)
21. Q₈×C₁₁₃	C₁₆	semidirect
23. Dic₂₂₆	C₁₆	semidirect
34. C₁₁₃	Q₈×C₁₆	semidirect
51. Q₈	#14268661	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⋊#14268661	2
C₄×#14268661	2
Q₈×#11744762	2
Q₈×C₁₆	113

Subgroups — Q8×#14268661 #28407864

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#14268661 #28407864