Subgroups — Q₈×Dic₁₁⋊C₅ #13182543

Order 1760.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(Dic₁₁⋊C₅)	C₂	1	3	yes	maximal
3	C₄×Dic₁₁⋊C₅	C₂	1	3	yes	maximal
4	Q₈×C₁₁⋊C₅	C₄	1	4	yes	complemented
5	C₂×C₄×C₁₁⋊C₅	C₂²	1	3	yes	—
6	C₂×Dic₁₁⋊C₅	C₂²	1	3	yes	—
7	C₂×Dic₁₁⋊C₅	C₂²	1	1	yes	characteristic
8	Q₈×Dic₁₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
9	C₂²×C₁₁⋊C₅	C₂³	1	1	yes	characteristic
10	C₄×C₁₁⋊C₅	C₂×C₄	1	6	yes	—
11	Dic₁₁⋊C₅	—	2	3	no	—
12	Dic₁₁⋊C₅	Q₈	1	2	yes	direct product factor
13	C₂×Q₈×C₁₁	C₂×C₅	1	1	yes	characteristic
14	C₄⋊Dic₁₁	C₂×C₅	1	3	yes	—
15	C₄×Dic₁₁	C₂×C₅	1	3	yes	—
16	C₄×C₅×Q₈	—	11	1	no	maximal, Hall
17	C₂×C₁₁⋊C₅	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₁₁⋊C₅	C₂×Q₈	1	1	yes	characteristic
19	C₂×C₁₁⋊C₅	#41	1	1	yes	characteristic
20	Q₈×C₁₁	C₄×C₅	1	4	yes	complemented
21	C₂×C₄×C₁₁	C₂²×C₅	1	3	yes	—
22	C₂×Dic₁₁	C₂²×C₅	1	3	yes	—
23	C₂×Dic₁₁	C₂²×C₅	1	1	yes	characteristic
24	C₂×C₅×Q₈	—	11	1	no	—
25	C₅×C₄⋊C₄	—	11	3	no	—
26	C₄²×C₅	—	11	3	no	—
27	C₁₁⋊C₅	C₄×Q₈	1	1	yes	characteristic, complemented, Hall
28	C₂²×C₁₁	C₂³×C₅	1	1	yes	characteristic
29	C₄×C₁₁	C₂×C₄×C₅	1	6	yes	—
30	Dic₁₁	—	2	3	no	—
31	Dic₁₁	C₅×Q₈	1	2	yes	complemented
32	C₅×Q₈	—	11	4	no	—
33	C₂×C₄×C₅	—	11	1	no	—
34	C₂×C₄×C₅	—	11	3	no	—
35	C₂×C₄×C₅	—	11	3	no	—
36	C₄×Q₈	—	11	1	no	Sylow
37	C₂×C₁₁	C₂²×C₄×C₅	1	1	yes	characteristic
38	C₂×C₁₁	C₂×C₅×Q₈	1	1	yes	characteristic
39	C₂×C₁₁	C₅×#41	1	1	yes	characteristic
40	C₂²×C₅	—	11	1	no	—
41	C₄×C₅	—	11	2	no	—
42	C₄×C₅	—	11	6	no	—
43	C₄×C₅	—	22	3	no	—
44	C₂×Q₈	AGL(1,𝔽₁₁)	1	1	yes	characteristic
45	C₄⋊C₄	—	11	3	no	—
46	C₄²	—	11	3	no	—
47	C₁₁	C₄×C₅×Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₅	—	11	1	no	—
49	C₂×C₅	—	11	1	no	—
50	C₂×C₅	—	11	1	no	—
51	Q₈	Dic₁₁⋊C₅	1	4	yes	direct product factor
52	C₂×C₄	—	11	1	no	—
53	C₂×C₄	—	11	3	no	—
54	C₂×C₄	C₂×AGL(1,𝔽₁₁)	1	3	yes	—
55	C₅	—	11	1	no	Sylow
56	C₂²	C₂²×AGL(1,𝔽₁₁)	1	1	yes	characteristic
57	C₄	—	11	2	no	—
58	C₄	—	22	3	no	—
59	C₄	C₂×Dic₁₁⋊C₅	1	6	yes	—
60	C₂	Q₈×AGL(1,𝔽₁₁)	1	1	yes	characteristic
61	C₂	#4343⋊C₅	1	1	yes	characteristic
62	C₂	C₂²×Dic₁₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×AGL(1,𝔽₁₁)
commutator	C₂×C₁₁	C₂²×C₄×C₅
Fitting	C₂×Q₈×C₁₁	C₂×C₅
socle, cosocle	C₂²×C₁₁	C₂³×C₅
prime radical	C₂²×C₁₁⋊C₅	C₂³
hypercenter	C₂×Q₈	AGL(1,𝔽₁₁)
hypocenter	C₁₁	C₄×C₅×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
4. Q₈×C₁₁⋊C₅	C₄	semidirect
8. Q₈×Dic₁₁	C₅	semidirect
12. Dic₁₁⋊C₅	Q₈	direct (N × H)
20. Q₈×C₁₁	C₄×C₅	semidirect
27. C₁₁⋊C₅	C₄×Q₈	semidirect
31. Dic₁₁	C₅×Q₈	semidirect
47. C₁₁	C₄×C₅×Q₈	semidirect
51. Q₈	Dic₁₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₁⋊C₅	2
C₄⋊(Dic₁₁⋊C₅)	2
C₄×Dic₁₁⋊C₅	2
Q₈×Dic₁₁	5
C₄×C₅×Q₈	11

Subgroups — Q8×Dic11⋊C5 #13182543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×Dic₁₁⋊C₅ #13182543