Subgroups — Q₈⋊#14523348 #30657825

Order 16448.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14523348	C₂	1	1	yes	maximal, characteristic
2	C₄×#14523348	C₂	1	1	yes	maximal, characteristic
3	Q₈×#11759967	C₂	1	1	yes	maximal, characteristic
4	C₂×#14523348	—	2	1	no	—
5	C₂×#14523348	—	2	1	no	—
6	C₄⋊#11759967	—	2	1	no	—
7	C₄⋊#11759967	C₄	1	1	yes	characteristic
8	C₄×#11759967	—	2	1	no	—
9	C₄×#11759967	C₂²	1	1	yes	characteristic
10	Q₈×D₂₅₇	C₄	1	1	yes	characteristic
11	#14523348	—	2	2	no	—
12	#14523348	—	4	1	no	—
13	C₂×#11759967	—	2	1	no	—
14	C₂×#11759967	D₄	1	1	yes	characteristic
15	C₂×#11759967	D₄	1	1	yes	characteristic
16	Dic₅₁₄	—	2	1	no	—
17	Dic₅₁₄	C₈	1	1	yes	characteristic, complemented
18	C₄×D₂₅₇	—	2	1	no	—
19	C₄×D₂₅₇	C₂×C₄	1	1	yes	characteristic
20	Q₈×C₂₅₇	C₈	1	1	yes	characteristic, complemented
21	C₂×D₂₅₇	C₂²⋊C₄	1	1	yes	characteristic
22	#11759967	—	2	1	no	—
23	#11759967	—	4	1	no	—
24	#11759967	SD₁₆	1	1	yes	characteristic
25	#11759967	Q₁₆	1	1	yes	characteristic
26	C₄×C₂₅₇	—	2	1	no	—
27	C₄×C₂₅₇	C₂×C₈	1	1	yes	characteristic
28	Dic₂₅₇	—	2	1	no	—
29	Dic₂₅₇	M₁₆	1	1	yes	characteristic
30	C₂×C₂₅₇	C₂²⋊C₈	1	1	yes	characteristic
31	D₂₅₇	#103	1	1	yes	characteristic
32	D₂₅₇	#104	1	1	yes	characteristic
33	C₂₅₇	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	Q₈⋊C₈	—	257	1	no	maximal, Sylow
35	C₄×Q₈	—	257	1	no	—
36	C₄⋊C₈	—	257	1	no	—
37	C₄×C₈	—	257	1	no	—
38	C₂×Q₈	—	257	1	no	—
39	C₂×C₈	—	514	1	no	—
40	C₂×C₈	—	514	1	no	—
41	C₄⋊C₄	—	257	1	no	—
42	C₄⋊C₄	—	514	1	no	—
43	C₄²	—	257	1	no	—
44	C₄²	—	514	1	no	—
45	Q₈	—	257	1	no	—
46	Q₈	—	514	1	no	—
47	Q₈	#14523348	1	1	yes	characteristic, complemented
48	C₂×C₄	—	257	1	no	—
49	C₂×C₄	—	257	1	no	—
50	C₂×C₄	—	257	1	no	—
51	C₂×C₄	—	514	1	no	—
52	C₂×C₄	—	514	1	no	—
53	C₈	—	514	2	no	—
54	C₈	—	1028	1	no	—
55	C₂²	—	257	1	no	—
56	C₄	—	257	1	no	—
57	C₄	—	257	1	no	—
58	C₄	—	257	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	514	1	no	—
61	C₄	—	514	1	no	—
62	C₄	—	1028	1	no	—
63	C₄	C₂×#14523348	1	1	yes	characteristic
64	C₂	—	257	1	no	—
65	C₂	—	257	1	no	—
66	C₂	C₂²⋊#14523348	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14523348
commutator	C₄×C₂₅₇	C₂×C₈
Frattini	C₄	C₂×#14523348
Fitting	Q₈×C₂₅₇	C₈
socle	C₂×C₂₅₇	C₂²⋊C₈
prime radical	C₂×D₂₅₇	C₂²⋊C₄
cosocle	C₄×#11759967	C₂²
hypercenter	Q₈	#14523348
hypocenter	C₂₅₇	Q₈⋊C₈
LCS	G ▷ C₄×C₂₅₇ ▷ C₂×C₂₅₇ ▷ C₂₅₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
17. Dic₅₁₄	C₈	semidirect
20. Q₈×C₂₅₇	C₈	semidirect
33. C₂₅₇	Q₈⋊C₈	semidirect
47. Q₈	#14523348	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14523348	2
C₄×#14523348	2
Q₈×#11759967	2
Q₈⋊C₈	257

Subgroups — Q8⋊#14523348 #30657825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#14523348 #30657825