Subgroups — C₂×C₁₁×Q₁₂₈ #14590933

Order 2816.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×Q₆₄	C₂	1	2	yes	maximal
2	C₁₁×Q₁₂₈	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×Q₃₂	—	2	2	no	—
5	C₁₁×Q₆₄	—	2	2	no	—
6	C₁₁×Q₆₄	C₂²	1	4	yes	—
7	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
8	C₁₁×C₆₄	C₂²	1	2	yes	—
9	C₂×C₁₁×Q₁₆	—	4	2	no	—
10	C₁₁×Q₃₂	—	2	4	no	—
11	C₁₁×Q₃₂	—	4	2	no	—
12	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
13	C₁₁×C₃₂	D₄	1	1	yes	characteristic
14	C₁₁×C₃₂	C₂³	1	1	yes	characteristic
15	C₂×Q₁₂₈	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂×Q₈×C₁₁	—	8	2	no	—
17	C₁₁×Q₁₆	—	4	4	no	—
18	C₁₁×Q₁₆	—	8	2	no	—
19	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
20	C₁₁×C₁₆	D₈	1	1	yes	characteristic
21	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
22	C₂×Q₆₄	C₂×C₁₁	1	2	yes	—
23	Q₁₂₈	C₂×C₁₁	1	4	yes	direct product factor
24	C₂×C₆₄	C₂×C₁₁	1	1	yes	characteristic
25	Q₈×C₁₁	—	8	4	no	—
26	Q₈×C₁₁	—	16	2	no	—
27	C₂×C₄×C₁₁	—	16	2	no	—
28	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
29	C₈×C₁₁	D₁₆	1	1	yes	characteristic
30	C₈×C₁₁	C₂×D₈	1	1	yes	characteristic
31	C₂×Q₃₂	—	2	2	no	—
32	Q₆₄	—	2	2	no	—
33	Q₆₄	C₂²×C₁₁	1	4	yes	—
34	C₂×C₃₂	C₂²×C₁₁	1	1	yes	characteristic
35	C₆₄	C₂²×C₁₁	1	2	yes	—
36	C₂²×C₁₁	D₃₂	1	1	yes	characteristic
37	C₄×C₁₁	—	16	4	no	—
38	C₄×C₁₁	D₃₂	1	1	yes	characteristic
39	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
40	C₂×Q₁₆	—	4	2	no	—
41	Q₃₂	—	2	4	no	—
42	Q₃₂	—	4	2	no	—
43	C₂×C₁₆	D₄×C₁₁	1	1	yes	characteristic
44	C₃₂	D₄×C₁₁	1	1	yes	characteristic
45	C₃₂	C₂³×C₁₁	1	1	yes	characteristic
46	C₂×C₁₁	Q₁₂₈	1	2	yes	direct product factor
47	C₂×C₁₁	C₂×D₃₂	1	1	yes	characteristic
48	C₂×Q₈	—	8	2	no	—
49	Q₁₆	—	4	4	no	—
50	Q₁₆	—	8	2	no	—
51	C₂×C₈	C₁₁×D₈	1	1	yes	characteristic
52	C₁₆	C₁₁×D₈	1	1	yes	characteristic
53	C₁₆	C₂×D₄×C₁₁	1	1	yes	characteristic
54	C₁₁	C₂×Q₁₂₈	1	1	yes	characteristic, direct product factor, Sylow
55	Q₈	—	8	4	no	—
56	Q₈	—	16	2	no	—
57	C₂×C₄	—	16	2	no	—
58	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
59	C₈	C₁₁×D₁₆	1	1	yes	characteristic
60	C₈	C₂×C₁₁×D₈	1	1	yes	characteristic
61	C₂²	C₁₁×D₃₂	1	1	yes	characteristic
62	C₄	—	16	4	no	—
63	C₄	C₁₁×D₃₂	1	1	yes	characteristic
64	C₄	C₂×C₁₁×D₁₆	1	1	yes	characteristic
65	C₂	C₁₁×Q₁₂₈	1	2	yes	direct product factor
66	C₂	C₂×C₁₁×D₃₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×Q₁₂₈	C₂	direct (N × H)
15. C₂×Q₁₂₈	C₁₁	direct (N × H)
23. Q₁₂₈	C₂×C₁₁	direct (N × H)
46. C₂×C₁₁	Q₁₂₈	direct (N × H)
54. C₁₁	C₂×Q₁₂₈	direct (N × H)
65. C₂	C₁₁×Q₁₂₈	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×C₁₁×Q₆₄	2
C₁₁×Q₁₂₈	2
C₂×C₁₁×C₆₄	2
C₂×Q₁₂₈	11

Subgroups — C2×C11×Q128 #14590933

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×Q₁₂₈ #14590933