Subgroups — Q₈×#66491 #14580462

Order 2624.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#66491	C₂	1	3	yes	maximal
2	C₄×#66491	C₂	1	3	yes	maximal
3	C₄×Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₄₁	C₄	1	1	yes	characteristic
5	C₄⋊C₄×C₄₁	C₄	1	3	yes	—
6	C₄²×C₄₁	C₂²	1	3	yes	—
7	C₂×#66491	C₂²	1	3	yes	—
8	C₂×#66491	C₂²	1	1	yes	characteristic
9	Q₈×C₄₁	C₈	1	4	yes	complemented
10	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
11	C₂×C₄×C₄₁	C₂×C₄	1	3	yes	—
12	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
13	#66491	—	2	3	no	—
14	#66491	Q₈	1	2	yes	direct product factor
15	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₄₁	—	2	3	no	—
17	C₄×C₄₁	C₂×C₈	1	6	yes	—
18	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₄₁	#41	1	1	yes	characteristic
20	C₂×C₄₁	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₄₁	#131	1	1	yes	characteristic
23	C₈×Q₈	—	41	1	no	maximal, Sylow
24	C₄₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
25	C₄×Q₈	D₄₁	1	1	yes	characteristic
26	C₄⋊C₈	—	41	3	no	—
27	C₄×C₈	—	41	3	no	—
28	C₂×Q₈	Dic₄₁	1	1	yes	characteristic
29	C₂×C₈	—	41	1	no	—
30	C₂×C₈	—	41	3	no	—
31	C₄⋊C₄	Dic₄₁	1	3	yes	—
32	C₄²	C₂×D₄₁	1	3	yes	—
33	Q₈	#66491	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₄₁	1	3	yes	—
35	C₂×C₄	C₂×Dic₄₁	1	3	yes	—
36	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
37	C₈	—	41	2	no	—
38	C₈	—	82	3	no	—
39	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×#66491	1	6	yes	—
42	C₄	Q₈×D₄₁	1	1	yes	characteristic
43	C₄	#10620310	1	1	yes	characteristic
44	C₂	Q₈×Dic₄₁	1	1	yes	characteristic
45	C₂	C₂²×#66491	1	1	yes	characteristic
46	C₂	#13050171	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator	C₂×C₄₁	C₂²×C₈
Fitting	C₄×Q₈×C₄₁	C₂
socle, prime radical	C₂²×C₄₁	C₂²×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄×Q₈	D₄₁
hypocenter	C₄₁	C₈×Q₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. Q₈×C₄₁	C₈	semidirect
14. #66491	Q₈	direct (N × H)
24. C₄₁	C₈×Q₈	semidirect
33. Q₈	#66491	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⋊#66491	2
C₄×#66491	2
C₄×Q₈×C₄₁	2
C₈×Q₈	41

Subgroups — Q8×#66491 #14580462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#66491 #14580462