Subgroups — D₁₁×Q₁₂₈ #14674821

Order 2816.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×Q₆₄	C₂	1	2	yes	maximal
2	Dic₃₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#13066833	C₂	1	2	yes	maximal, complemented
4	D₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
5	C₁₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₁×Q₃₂	—	2	2	no	—
7	C₁₁×Q₆₄	C₂²	1	2	yes	—
8	#10622160	—	2	2	no	—
9	Dic₁₇₆	C₂²	1	2	yes	—
10	D₁₁×C₃₂	C₂²	1	1	yes	characteristic
11	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
12	C₁₁⋊C₆₄	C₂²	1	1	yes	characteristic
13	Q₁₆×D₁₁	—	4	2	no	—
14	C₁₁×Q₃₂	—	2	2	no	—
15	#66893	—	4	2	no	—
16	Dic₈₈	—	2	2	no	—
17	C₁₆×D₁₁	D₄	1	1	yes	characteristic
18	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
19	C₁₁⋊C₃₂	D₄	1	1	yes	characteristic
20	C₂×Q₁₂₈	—	11	1	no	maximal, Sylow
21	Q₈×D₁₁	—	8	2	no	—
22	C₁₁×Q₁₆	—	4	2	no	—
23	#4326	—	8	2	no	—
24	Dic₄₄	—	4	2	no	—
25	C₈×D₁₁	D₈	1	1	yes	characteristic
26	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
27	C₁₁⋊C₁₆	D₈	1	1	yes	characteristic
28	C₂×Q₆₄	—	11	2	no	—
29	Q₁₂₈	—	11	2	no	—
30	Q₁₂₈	—	11	1	no	—
31	Q₁₂₈	D₁₁	1	1	yes	characteristic, direct product factor
32	C₂×C₆₄	—	11	1	no	—
33	Q₈×C₁₁	—	8	2	no	—
34	C₄×D₁₁	—	16	2	no	—
35	C₄×D₁₁	D₁₆	1	1	yes	characteristic
36	Dic₂₂	—	8	2	no	—
37	Dic₂₂	—	16	2	no	—
38	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
39	C₁₁⋊C₈	D₁₆	1	1	yes	characteristic
40	C₂×Q₃₂	—	22	2	no	—
41	Q₆₄	—	11	2	no	—
42	Q₆₄	—	22	2	no	—
43	Q₆₄	C₂×D₁₁	1	2	yes	—
44	C₂×C₃₂	—	11	1	no	—
45	C₆₄	—	11	1	no	—
46	C₆₄	C₂×D₁₁	1	1	yes	characteristic
47	C₂×D₁₁	D₃₂	1	1	yes	characteristic
48	C₄×C₁₁	—	16	2	no	—
49	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
50	Dic₁₁	—	16	2	no	—
51	Dic₁₁	D₃₂	1	1	yes	characteristic
52	C₂×Q₁₆	—	44	2	no	—
53	Q₃₂	—	2	2	no	—
54	Q₃₂	—	22	2	no	—
55	Q₃₂	—	44	2	no	—
56	C₂×C₁₆	—	11	1	no	—
57	C₃₂	—	11	1	no	—
58	C₃₂	C₂²×D₁₁	1	1	yes	characteristic
59	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
60	D₁₁	Q₁₂₈	1	2	yes	direct product factor
61	C₂×Q₈	—	88	2	no	—
62	Q₁₆	—	4	2	no	—
63	Q₁₆	—	44	2	no	—
64	Q₁₆	—	88	2	no	—
65	C₂×C₈	—	11	1	no	—
66	C₁₆	—	11	1	no	—
67	C₁₆	D₄×D₁₁	1	1	yes	characteristic
68	C₁₁	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
69	Q₈	—	8	2	no	—
70	Q₈	—	88	2	no	—
71	Q₈	—	176	2	no	—
72	C₂×C₄	—	11	1	no	—
73	C₂×C₄	—	176	2	no	—
74	C₈	—	11	1	no	—
75	C₈	D₈×D₁₁	1	1	yes	characteristic
76	C₂²	—	11	1	no	—
77	C₄	—	11	1	no	—
78	C₄	—	16	2	no	—
79	C₄	—	176	2	no	—
80	C₄	D₁₁×D₁₆	1	1	yes	characteristic
81	C₂	—	11	2	no	—
82	C₂	D₁₁×D₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₁×D₃₂
commutator, cosocle	C₁₁×C₃₂	C₂³
Frattini	C₃₂	C₂²×D₁₁
Fitting	C₁₁×Q₁₂₈	C₂
socle	C₂×C₁₁	C₂×D₃₂
prime radical	C₂×D₁₁	D₃₂
hypercenter	Q₁₂₈	D₁₁
hypocenter	C₁₁	C₂×Q₁₂₈
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ Q₁₂₈

Complements

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

N	H ≅ G/N	type
2. Dic₃₅₂	C₂	semidirect
3. #13066833	C₂	semidirect
5. C₁₁×Q₁₂₈	C₂	semidirect
31. Q₁₂₈	D₁₁	direct (N × H)
60. D₁₁	Q₁₂₈	direct (N × H)
68. C₁₁	C₂×Q₁₂₈	semidirect

Maximal subgroups

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

subgroup	index
D₁₁×Q₆₄	2
Dic₃₅₂	2
#13066833	2
D₁₁×C₆₄	2
C₁₁×Q₁₂₈	2
C₂×Q₁₂₈	11

Subgroups — D11×Q128 #14674821

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×Q₁₂₈ #14674821