Subgroups — C₂×C₁₁×#688 #13183156

Order 1760.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×D₂₀	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#688	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₅×C₁₁	—	2	1	no	—
6	C₅×Q₈×C₁₁	—	2	1	no	—
7	C₅×Q₈×C₁₁	C₂²	1	2	yes	complemented
8	C₂×C₄×C₅×C₁₁	—	2	1	no	—
9	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×D₂₀	—	2	1	no	—
11	C₁₁×D₂₀	C₂²	1	2	yes	—
12	C₁₁×#168	C₂²	1	2	yes	complemented
13	C₂×C₁₁×SD₁₆	—	5	1	no	maximal, Hall
14	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
15	C₂×D₅×C₁₁	—	2	2	no	—
16	C₂×D₅×C₁₁	—	4	2	no	—
17	C₄×C₅×C₁₁	—	2	2	no	—
18	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
19	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×Q₈×C₁₁	D₅	1	1	yes	characteristic, complemented
21	C₂×D₄×C₁₁	—	5	1	no	—
22	C₁₁×SD₁₆	—	5	4	no	—
23	C₂×C₈×C₁₁	—	5	1	no	—
24	C₂×#688	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂×C₅×C₁₁	SD₁₆	1	2	yes	complemented
26	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
27	D₅×C₁₁	—	4	2	no	—
28	C₂³×C₁₁	—	10	1	no	—
29	Q₈×C₁₁	—	2	1	no	—
30	Q₈×C₁₁	C₂×D₅	1	2	yes	complemented
31	D₄×C₁₁	—	5	2	no	—
32	D₄×C₁₁	—	10	1	no	—
33	C₂×C₄×C₁₁	—	2	1	no	—
34	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
35	C₈×C₁₁	—	5	2	no	—
36	C₂×C₅×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
37	C₂×D₂₀	C₂×C₁₁	1	1	yes	characteristic
38	#688	C₂×C₁₁	1	4	yes	direct product factor
39	C₂×#168	C₂×C₁₁	1	1	yes	characteristic, complemented
40	C₅×C₁₁	C₂×SD₁₆	1	1	yes	characteristic, complemented, Hall
41	C₂²×C₁₁	—	10	2	no	—
42	C₂²×C₁₁	—	20	2	no	—
43	C₂²×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
44	C₄×C₁₁	—	2	2	no	—
45	C₄×C₁₁	C₂²⋊D₅	1	1	yes	characteristic
46	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
47	C₂²×D₅	—	2	1	no	—
48	C₅×Q₈	—	2	1	no	—
49	C₅×Q₈	C₂²×C₁₁	1	2	yes	complemented
50	C₂×C₄×C₅	—	2	1	no	—
51	C₂×C₄×C₅	C₂²×C₁₁	1	1	yes	characteristic
52	D₂₀	—	2	1	no	—
53	D₂₀	C₂²×C₁₁	1	2	yes	—
54	#168	C₂²×C₁₁	1	2	yes	complemented
55	C₂×SD₁₆	—	5	1	no	Sylow
56	C₂×C₁₁	—	20	2	no	—
57	C₂×C₁₁	#688	1	2	yes	direct product factor
58	C₂×C₁₁	C₂×C₂²⋊D₅	1	1	yes	characteristic
59	C₂²×C₅	D₄×C₁₁	1	1	yes	characteristic
60	C₂×D₅	—	2	2	no	—
61	C₂×D₅	—	4	2	no	—
62	C₄×C₅	—	2	2	no	—
63	C₄×C₅	D₄×C₁₁	1	1	yes	characteristic
64	C₄×C₅	C₂³×C₁₁	1	1	yes	characteristic
65	C₂×Q₈	D₅×C₁₁	1	1	yes	characteristic, complemented
66	C₂×D₄	—	5	1	no	—
67	SD₁₆	—	5	4	no	—
68	C₂×C₈	—	5	1	no	—
69	C₁₁	C₂×#688	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×C₅	C₁₁×SD₁₆	1	2	yes	complemented
71	C₂×C₅	C₂×D₄×C₁₁	1	1	yes	characteristic
72	D₅	—	4	2	no	—
73	C₂³	—	10	1	no	—
74	Q₈	—	2	1	no	—
75	Q₈	C₂×D₅×C₁₁	1	2	yes	complemented
76	D₄	—	5	2	no	—
77	D₄	—	10	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	C₂×D₅×C₁₁	1	1	yes	characteristic
80	C₈	—	5	2	no	—
81	C₅	C₂×C₁₁×SD₁₆	1	1	yes	characteristic, complemented, Sylow
82	C₂²	—	10	2	no	—
83	C₂²	—	20	2	no	—
84	C₂²	C₁₁×C₂²⋊D₅	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	C₁₁×C₂²⋊D₅	1	1	yes	characteristic
87	C₄	C₂²×D₅×C₁₁	1	1	yes	characteristic
88	C₂	—	20	2	no	—
89	C₂	C₁₁×#688	1	2	yes	direct product factor
90	C₂	C₂×C₁₁×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₁	C₂²⋊D₅
commutator, cosocle	C₄×C₅	C₂³×C₁₁
Frattini	C₄	C₂²×D₅×C₁₁
Fitting	C₂×C₅×Q₈×C₁₁	C₂
socle	C₂²×C₅×C₁₁	D₄
prime radical	C₂×C₁₁×D₂₀	C₂
hypercenter	C₂×Q₈×C₁₁	D₅
hypocenter	C₅	C₂×C₁₁×SD₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄×C₁₁ ◁ C₂×Q₈×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×Q₈×C₁₁	C₂	semidirect
3. C₁₁×#688	C₂	direct (N × H)
4. C₂×C₁₁×#168	C₂	semidirect
7. C₅×Q₈×C₁₁	C₂²	semidirect
12. C₁₁×#168	C₂²	semidirect
20. C₂×Q₈×C₁₁	D₅	semidirect
24. C₂×#688	C₁₁	direct (N × H)
25. C₂×C₅×C₁₁	SD₁₆	semidirect
30. Q₈×C₁₁	C₂×D₅	semidirect
36. C₂×C₅×Q₈	C₂×C₁₁	semidirect
38. #688	C₂×C₁₁	direct (N × H)
39. C₂×#168	C₂×C₁₁	semidirect
40. C₅×C₁₁	C₂×SD₁₆	semidirect
49. C₅×Q₈	C₂²×C₁₁	semidirect
54. #168	C₂²×C₁₁	semidirect
57. C₂×C₁₁	#688	direct (N × H)
65. C₂×Q₈	D₅×C₁₁	semidirect
69. C₁₁	C₂×#688	direct (N × H)
70. C₂×C₅	C₁₁×SD₁₆	semidirect
75. Q₈	C₂×D₅×C₁₁	semidirect
81. C₅	C₂×C₁₁×SD₁₆	semidirect
89. C₂	C₁₁×#688	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×C₅×Q₈×C₁₁	2
C₂×C₁₁×D₂₀	2
C₁₁×#688	2
C₂×C₁₁×#168	2
C₂×C₁₁×SD₁₆	5
C₂×#688	11

Subgroups — C2×C11×#688 #13183156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#688 #13183156