Subgroups — D₁₁×Q₆₄ #13070919

Order 1408.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×Q₃₂	C₂	1	2	yes	maximal
2	C₁₁×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#10622160	C₂	1	2	yes	maximal, complemented
4	Dic₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
6	Q₁₆×D₁₁	—	2	2	no	—
7	C₁₁×Q₃₂	C₂²	1	2	yes	—
8	#66893	—	2	2	no	—
9	Dic₈₈	C₂²	1	2	yes	—
10	C₁₆×D₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×C₃₂	C₂²	1	1	yes	characteristic
12	C₁₁⋊C₃₂	C₂²	1	1	yes	characteristic
13	Q₈×D₁₁	—	4	2	no	—
14	C₁₁×Q₁₆	—	2	2	no	—
15	#4326	—	4	2	no	—
16	Dic₄₄	—	2	2	no	—
17	C₈×D₁₁	D₄	1	1	yes	characteristic
18	C₁₁×C₁₆	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₁₆	D₄	1	1	yes	characteristic
20	C₂×Q₆₄	—	11	1	no	maximal, Sylow
21	Q₈×C₁₁	—	4	2	no	—
22	C₄×D₁₁	—	8	2	no	—
23	C₄×D₁₁	D₈	1	1	yes	characteristic
24	Dic₂₂	—	4	2	no	—
25	Dic₂₂	—	8	2	no	—
26	C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
27	C₁₁⋊C₈	D₈	1	1	yes	characteristic
28	C₂×Q₃₂	—	11	2	no	—
29	Q₆₄	—	11	2	no	—
30	Q₆₄	—	11	1	no	—
31	Q₆₄	D₁₁	1	1	yes	characteristic, direct product factor
32	C₂×C₃₂	—	11	1	no	—
33	C₂×D₁₁	D₁₆	1	1	yes	characteristic
34	C₄×C₁₁	—	8	2	no	—
35	C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
36	Dic₁₁	—	8	2	no	—
37	Dic₁₁	D₁₆	1	1	yes	characteristic
38	C₂×Q₁₆	—	22	2	no	—
39	Q₃₂	—	11	2	no	—
40	Q₃₂	—	22	2	no	—
41	Q₃₂	C₂×D₁₁	1	2	yes	—
42	C₂×C₁₆	—	11	1	no	—
43	C₃₂	—	11	1	no	—
44	C₃₂	C₂×D₁₁	1	1	yes	characteristic
45	C₂×C₁₁	C₂×D₁₆	1	1	yes	characteristic
46	D₁₁	Q₆₄	1	2	yes	direct product factor
47	C₂×Q₈	—	44	2	no	—
48	Q₁₆	—	2	2	no	—
49	Q₁₆	—	22	2	no	—
50	Q₁₆	—	44	2	no	—
51	C₂×C₈	—	11	1	no	—
52	C₁₆	—	11	1	no	—
53	C₁₆	C₂²×D₁₁	1	1	yes	characteristic
54	C₁₁	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
55	Q₈	—	4	2	no	—
56	Q₈	—	44	2	no	—
57	Q₈	—	88	2	no	—
58	C₂×C₄	—	11	1	no	—
59	C₂×C₄	—	88	2	no	—
60	C₈	—	11	1	no	—
61	C₈	D₄×D₁₁	1	1	yes	characteristic
62	C₂²	—	11	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	11	1	no	—
65	C₄	—	88	2	no	—
66	C₄	D₈×D₁₁	1	1	yes	characteristic
67	C₂	—	11	2	no	—
68	C₂	D₁₁×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₁×D₁₆
commutator, cosocle	C₁₁×C₁₆	C₂³
Frattini	C₁₆	C₂²×D₁₁
Fitting	C₁₁×Q₆₄	C₂
socle	C₂×C₁₁	C₂×D₁₆
prime radical	C₂×D₁₁	D₁₆
hypercenter	Q₆₄	D₁₁
hypocenter	C₁₁	C₂×Q₆₄
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. C₁₁×Q₆₄	C₂	semidirect
3. #10622160	C₂	semidirect
4. Dic₁₇₆	C₂	semidirect
31. Q₆₄	D₁₁	direct (N × H)
46. D₁₁	Q₆₄	direct (N × H)
54. C₁₁	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×Q₃₂	2
C₁₁×Q₆₄	2
#10622160	2
Dic₁₇₆	2
D₁₁×C₃₂	2
C₂×Q₆₄	11

Subgroups — D11×Q64 #13070919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×Q₆₄ #13070919