Subgroups — Q₈×C₄₁₉⋊C₈ #41000487

Order 26816.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₄₁₉⋊C₈)	C₂	1	3	yes	maximal
2	C₄×C₄₁₉⋊C₈	C₂	1	3	yes	maximal
3	C₄×Q₈×C₄₁₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₁₉⋊C₈	C₂²	1	3	yes	—
5	C₂×C₄₁₉⋊C₈	C₂²	1	1	yes	characteristic
6	C₂×Q₈×C₄₁₉	C₄	1	1	yes	characteristic
7	C₄⋊C₄×C₄₁₉	C₄	1	3	yes	—
8	C₄²×C₄₁₉	C₂²	1	3	yes	—
9	C₄₁₉⋊C₈	—	2	3	no	—
10	C₄₁₉⋊C₈	Q₈	1	2	yes	direct product factor
11	Q₈×C₄₁₉	C₈	1	4	yes	complemented
12	C₂×C₄×C₄₁₉	C₂×C₄	1	3	yes	—
13	C₂×C₄×C₄₁₉	C₂×C₄	1	3	yes	—
14	C₂×C₄×C₄₁₉	C₂³	1	1	yes	characteristic
15	C₂²×C₄₁₉	C₂²×C₄	1	1	yes	characteristic
16	C₄×C₄₁₉	—	2	3	no	—
17	C₄×C₄₁₉	C₂×C₈	1	6	yes	—
18	C₄×C₄₁₉	C₂×Q₈	1	1	yes	characteristic
19	C₄×C₄₁₉	#41	1	1	yes	characteristic
20	C₂×C₄₁₉	C₄×Q₈	1	1	yes	characteristic
21	C₂×C₄₁₉	C₂²×C₈	1	1	yes	characteristic
22	C₂×C₄₁₉	#131	1	1	yes	characteristic
23	C₄₁₉	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
24	C₈×Q₈	—	419	1	no	maximal, Sylow
25	C₄×Q₈	D₄₁₉	1	1	yes	characteristic
26	C₄⋊C₈	—	419	3	no	—
27	C₄×C₈	—	419	3	no	—
28	C₂×Q₈	Dic₄₁₉	1	1	yes	characteristic
29	C₂×C₈	—	419	3	no	—
30	C₂×C₈	—	419	1	no	—
31	C₄⋊C₄	Dic₄₁₉	1	3	yes	—
32	C₄²	C₂×D₄₁₉	1	3	yes	—
33	Q₈	C₄₁₉⋊C₈	1	4	yes	direct product factor
34	C₂×C₄	C₂×Dic₄₁₉	1	3	yes	—
35	C₂×C₄	C₂×Dic₄₁₉	1	3	yes	—
36	C₂×C₄	C₂²×D₄₁₉	1	1	yes	characteristic
37	C₈	—	838	3	no	—
38	C₈	—	419	2	no	—
39	C₂²	C₂²×Dic₄₁₉	1	1	yes	characteristic
40	C₄	—	2	3	no	—
41	C₄	C₂×C₄₁₉⋊C₈	1	6	yes	—
42	C₄	Q₈×D₄₁₉	1	1	yes	characteristic
43	C₄	#20269412	1	1	yes	characteristic
44	C₂	Q₈×Dic₄₁₉	1	1	yes	characteristic
45	C₂	C₂²×C₄₁₉⋊C₈	1	1	yes	characteristic
46	C₂	#27211725	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁₉
commutator	C₂×C₄₁₉	C₂²×C₈
Fitting	C₄×Q₈×C₄₁₉	C₂
socle, prime radical	C₂²×C₄₁₉	C₂²×C₄
cosocle	C₂×C₄×C₄₁₉	C₂³
hypercenter	C₄×Q₈	D₄₁₉
hypocenter	C₄₁₉	C₈×Q₈
LCS	G ▷ C₂×C₄₁₉ ▷ C₄₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. C₄₁₉⋊C₈	Q₈	direct (N × H)
11. Q₈×C₄₁₉	C₈	semidirect
23. C₄₁₉	C₈×Q₈	semidirect
33. Q₈	C₄₁₉⋊C₈	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⋊(C₄₁₉⋊C₈)	2
C₄×C₄₁₉⋊C₈	2
C₄×Q₈×C₄₁₉	2
C₈×Q₈	419

Subgroups — Q8×C419⋊C8 #41000487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₄₁₉⋊C₈ #41000487