Subgroups — Q₈⋊#10596842 #17989675

Order 4672.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596842	C₂	1	1	yes	maximal, characteristic
2	C₄×#10596842	C₂	1	1	yes	maximal, characteristic
3	Q₈×#64408	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596842	—	2	1	no	—
5	C₂×#10596842	—	2	1	no	—
6	C₄⋊#64408	—	2	1	no	—
7	C₄⋊#64408	C₄	1	1	yes	characteristic
8	C₄×#64408	—	2	1	no	—
9	C₄×#64408	C₂²	1	1	yes	characteristic
10	Q₈×D₇₃	C₄	1	1	yes	characteristic
11	C₂×#64408	—	2	1	no	—
12	C₂×#64408	D₄	1	1	yes	characteristic
13	C₂×#64408	D₄	1	1	yes	characteristic
14	#10596842	—	2	2	no	—
15	#10596842	—	4	1	no	—
16	Q₈×C₇₃	C₈	1	1	yes	characteristic, complemented
17	C₄×D₇₃	—	2	1	no	—
18	C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	Dic₁₄₆	—	2	1	no	—
20	Dic₁₄₆	C₈	1	1	yes	characteristic, complemented
21	C₂×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	#64408	—	2	1	no	—
23	#64408	—	4	1	no	—
24	#64408	SD₁₆	1	1	yes	characteristic
25	#64408	Q₁₆	1	1	yes	characteristic
26	C₄×C₇₃	—	2	1	no	—
27	C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
28	Dic₇₃	—	2	1	no	—
29	Dic₇₃	M₁₆	1	1	yes	characteristic
30	C₂×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
31	D₇₃	#103	1	1	yes	characteristic
32	D₇₃	#104	1	1	yes	characteristic
33	C₇₃	Q₈⋊C₈	1	1	yes	characteristic, complemented, Sylow
34	Q₈⋊C₈	—	73	1	no	maximal, Sylow
35	C₄×Q₈	—	73	1	no	—
36	C₄⋊C₈	—	73	1	no	—
37	C₄×C₈	—	73	1	no	—
38	C₂×Q₈	—	73	1	no	—
39	C₂×C₈	—	146	1	no	—
40	C₂×C₈	—	146	1	no	—
41	C₄⋊C₄	—	73	1	no	—
42	C₄⋊C₄	—	146	1	no	—
43	C₄²	—	73	1	no	—
44	C₄²	—	146	1	no	—
45	Q₈	—	73	1	no	—
46	Q₈	—	146	1	no	—
47	Q₈	#10596842	1	1	yes	characteristic, complemented
48	C₂×C₄	—	73	1	no	—
49	C₂×C₄	—	73	1	no	—
50	C₂×C₄	—	73	1	no	—
51	C₂×C₄	—	146	1	no	—
52	C₂×C₄	—	146	1	no	—
53	C₈	—	292	1	no	—
54	C₈	—	146	2	no	—
55	C₂²	—	73	1	no	—
56	C₄	—	2	1	no	—
57	C₄	—	292	1	no	—
58	C₄	—	73	1	no	—
59	C₄	—	73	1	no	—
60	C₄	—	73	1	no	—
61	C₄	—	146	1	no	—
62	C₄	—	146	1	no	—
63	C₄	C₂×#10596842	1	1	yes	characteristic
64	C₂	—	73	1	no	—
65	C₂	—	73	1	no	—
66	C₂	C₂²⋊#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#10596842
commutator	C₄×C₇₃	C₂×C₈
Frattini	C₄	C₂×#10596842
Fitting	Q₈×C₇₃	C₈
socle	C₂×C₇₃	C₂²⋊C₈
prime radical	C₂×D₇₃	C₂²⋊C₄
cosocle	C₄×#64408	C₂²
hypercenter	Q₈	#10596842
hypocenter	C₇₃	Q₈⋊C₈
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
16. Q₈×C₇₃	C₈	semidirect
20. Dic₁₄₆	C₈	semidirect
33. C₇₃	Q₈⋊C₈	semidirect
47. Q₈	#10596842	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#10596842	2
C₄×#10596842	2
Q₈×#64408	2
Q₈⋊C₈	73

Subgroups — Q8⋊#10596842 #17989675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈⋊#10596842 #17989675