Subgroups — Q₈×#10596842 #17989702

Order 4672.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#10596842	C₂	1	3	yes	maximal
2	C₄×#10596842	C₂	1	3	yes	maximal
3	Q₈×#64408	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596842	C₂²	1	3	yes	—
5	C₂×#10596842	C₂²	1	1	yes	characteristic
6	C₄⋊#64408	C₄	1	3	yes	—
7	C₄×#64408	C₂²	1	3	yes	—
8	Q₈×D₇₃	C₄	1	1	yes	characteristic
9	C₂×#64408	C₂×C₄	1	3	yes	—
10	C₂×#64408	C₂³	1	1	yes	characteristic
11	#10596842	—	2	3	no	—
12	#10596842	Q₈	1	2	yes	direct product factor
13	Q₈×C₇₃	C₈	1	1	yes	characteristic, complemented
14	C₄×D₇₃	C₂×C₄	1	3	yes	—
15	Dic₁₄₆	C₈	1	3	yes	complemented
16	C₂×D₇₃	C₂²×C₄	1	1	yes	characteristic
17	#64408	—	2	3	no	—
18	#64408	C₂×Q₈	1	1	yes	characteristic
19	#64408	#41	1	1	yes	characteristic
20	C₄×C₇₃	C₂×C₈	1	3	yes	—
21	Dic₇₃	C₂×C₈	1	3	yes	—
22	C₂×C₇₃	C₂²×C₈	1	1	yes	characteristic
23	D₇₃	C₄×Q₈	1	1	yes	characteristic
24	D₇₃	#131	1	1	yes	characteristic
25	C₇₃	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
26	C₈×Q₈	—	73	1	no	maximal, Sylow
27	C₄×Q₈	—	73	1	no	—
28	C₄⋊C₈	—	73	3	no	—
29	C₄×C₈	—	73	3	no	—
30	C₂×Q₈	—	73	1	no	—
31	C₂×C₈	—	73	1	no	—
32	C₂×C₈	—	73	3	no	—
33	C₄⋊C₄	—	73	3	no	—
34	C₄²	—	73	3	no	—
35	Q₈	—	73	3	no	—
36	Q₈	#10596842	1	1	yes	characteristic, direct product factor
37	C₂×C₄	—	73	1	no	—
38	C₂×C₄	—	73	3	no	—
39	C₂×C₄	—	73	3	no	—
40	C₈	—	73	2	no	—
41	C₈	—	146	3	no	—
42	C₂²	—	73	1	no	—
43	C₄	—	73	1	no	—
44	C₄	—	73	1	no	—
45	C₄	—	73	3	no	—
46	C₄	—	146	3	no	—
47	C₄	C₂×#10596842	1	3	yes	—
48	C₂	—	73	1	no	—
49	C₂	—	73	1	no	—
50	C₂	C₂²×#10596842	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#10596842
commutator, socle	C₂×C₇₃	C₂²×C₈
Fitting	Q₈×C₇₃	C₈
prime radical	C₂×D₇₃	C₂²×C₄
cosocle	C₂×#64408	C₂³
hypercenter	Q₈	#10596842
hypocenter	C₇₃	C₈×Q₈
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ Q₈

Complements

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

N	H ≅ G/N	type
12. #10596842	Q₈	direct (N × H)
13. Q₈×C₇₃	C₈	semidirect
15. Dic₁₄₆	C₈	semidirect
25. C₇₃	C₈×Q₈	semidirect
36. Q₈	#10596842	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⋊#10596842	2
C₄×#10596842	2
Q₈×#64408	2
C₈×Q₈	73

Subgroups — Q8×#10596842 #17989702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#10596842 #17989702