Subgroups — C₁₁×C₁₃×C₃⋊Dic₂₁ #49114597

Order 36036.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇×C₁₁×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₁₃×Dic₂₁	—	3	4	no	maximal
3	C₃²×C₇×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇×C₁₁×C₁₃	D₃	1	4	yes	—
5	C₁₁×C₁₃×C₃⋊Dic₃	—	7	1	no	maximal, Hall
6	C₁₁×C₁₃×Dic₇	—	9	1	no	Hall
7	C₁₃×C₃⋊Dic₂₁	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₇×C₁₁×C₁₃	Dic₃	1	4	yes	complemented
9	C₁₁×C₃⋊Dic₂₁	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃²×C₁₁×C₁₃	D₇	1	1	yes	characteristic
11	C₂×C₇×C₁₁×C₁₃	C₃⋊D₃	1	1	yes	characteristic
12	C₁₁×Dic₃×C₁₃	—	21	4	no	—
13	C₂×C₃²×C₇×C₁₃	C₂×C₁₁	1	1	yes	characteristic
14	C₂×C₃²×C₇×C₁₁	C₂×C₁₃	1	1	yes	characteristic
15	C₃²×C₁₁×C₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₁₃×Dic₂₁	—	3	4	no	—
17	C₇×C₁₁×C₁₃	C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
18	C₁₁×Dic₂₁	—	3	4	no	—
19	C₂×C₃×C₁₁×C₁₃	D₂₁	1	4	yes	—
20	C₃²×C₇×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
21	C₃²×C₇×C₁₁	C₄×C₁₃	1	1	yes	characteristic, complemented, Hall
22	C₄×C₁₁×C₁₃	—	63	1	no	Hall
23	C₂×C₃×C₇×C₁₃	D₃×C₁₁	1	4	yes	—
24	C₁₃×C₃⋊Dic₃	—	7	1	no	Hall
25	C₂×C₃×C₇×C₁₁	D₃×C₁₃	1	4	yes	—
26	C₃×C₁₁×C₁₃	Dic₂₁	1	4	yes	complemented
27	C₁₁×C₃⋊Dic₃	—	7	1	no	Hall
28	C₁₃×Dic₇	—	9	1	no	Hall
29	C₁₁×Dic₇	—	9	1	no	Hall
30	C₂×C₁₁×C₁₃	C₃⋊D₂₁	1	1	yes	characteristic
31	C₃×C₇×C₁₃	C₁₁×Dic₃	1	4	yes	complemented
32	C₃⋊Dic₂₁	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₃²×C₁₃	C₁₁×D₇	1	1	yes	characteristic
34	C₃×C₇×C₁₁	Dic₃×C₁₃	1	4	yes	complemented
35	C₂×C₃²×C₁₁	C₁₃×D₇	1	1	yes	characteristic
36	C₂×C₇×C₁₃	C₁₁×C₃⋊D₃	1	1	yes	characteristic
37	Dic₃×C₁₃	—	21	4	no	—
38	C₂×C₇×C₁₁	C₁₃×C₃⋊D₃	1	1	yes	characteristic
39	C₁₁×C₁₃	C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Hall
40	C₁₁×Dic₃	—	21	4	no	—
41	C₂×C₃²×C₇	C₂×C₁₁×C₁₃	1	1	yes	characteristic
42	C₃²×C₁₃	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Hall
43	C₃²×C₁₁	C₁₃×Dic₇	1	1	yes	characteristic, complemented, Hall
44	C₇×C₁₃	C₁₁×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
45	Dic₂₁	—	3	4	no	—
46	C₂×C₃×C₁₃	C₁₁×D₂₁	1	4	yes	—
47	C₇×C₁₁	C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Hall
48	C₂×C₃×C₁₁	C₁₃×D₂₁	1	4	yes	—
49	C₃²×C₇	C₄×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Hall
50	C₄×C₁₃	—	63	1	no	Hall
51	C₄×C₁₁	—	63	1	no	Hall
52	C₂×C₃×C₇	D₃×C₁₁×C₁₃	1	4	yes	—
53	C₃×C₁₃	C₁₁×Dic₂₁	1	4	yes	complemented
54	C₃⋊Dic₃	—	7	1	no	Hall
55	C₃×C₁₁	C₁₃×Dic₂₁	1	4	yes	complemented
56	Dic₇	—	9	1	no	Hall
57	C₂×C₁₃	C₁₁×C₃⋊D₂₁	1	1	yes	characteristic
58	C₂×C₁₁	C₁₃×C₃⋊D₂₁	1	1	yes	characteristic
59	C₃×C₇	C₁₁×Dic₃×C₁₃	1	4	yes	complemented
60	C₂×C₃²	C₁₁×C₁₃×D₇	1	1	yes	characteristic
61	C₂×C₇	C₁₁×C₁₃×C₃⋊D₃	1	1	yes	characteristic
62	C₁₃	C₁₁×C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
63	Dic₃	—	21	4	no	—
64	C₁₁	C₁₃×C₃⋊Dic₂₁	1	1	yes	characteristic, direct product factor, Sylow
65	C₃²	C₁₁×C₁₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
66	C₇	C₁₁×C₁₃×C₃⋊Dic₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₃	C₁₁×C₁₃×D₂₁	1	4	yes	—
68	C₄	—	63	1	no	Sylow
69	C₃	C₁₁×C₁₃×Dic₂₁	1	4	yes	complemented
70	C₂	C₁₁×C₁₃×C₃⋊D₂₁	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁×C₁₃	C₃⋊D₂₁
commutator, hypocenter	C₃²×C₇	C₄×C₁₁×C₁₃
Frattini	C₂	C₁₁×C₁₃×C₃⋊D₂₁
Fitting, socle, prime radical	C₂×C₃²×C₇×C₁₁×C₁₃	C₂
cosocle	C₂×C₃²×C₇	C₂×C₁₁×C₁₃
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₁₁×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₃²×C₇×C₁₁×C₁₃	C₄	semidirect
7. C₁₃×C₃⋊Dic₂₁	C₁₁	direct (N × H)
8. C₃×C₇×C₁₁×C₁₃	Dic₃	semidirect
9. C₁₁×C₃⋊Dic₂₁	C₁₃	direct (N × H)
15. C₃²×C₁₁×C₁₃	Dic₇	semidirect
17. C₇×C₁₁×C₁₃	C₃⋊Dic₃	semidirect
20. C₃²×C₇×C₁₃	C₄×C₁₁	semidirect
21. C₃²×C₇×C₁₁	C₄×C₁₃	semidirect
26. C₃×C₁₁×C₁₃	Dic₂₁	semidirect
31. C₃×C₇×C₁₃	C₁₁×Dic₃	semidirect
32. C₃⋊Dic₂₁	C₁₁×C₁₃	direct (N × H)
34. C₃×C₇×C₁₁	Dic₃×C₁₃	semidirect
39. C₁₁×C₁₃	C₃⋊Dic₂₁	direct (N × H)
42. C₃²×C₁₃	C₁₁×Dic₇	semidirect
43. C₃²×C₁₁	C₁₃×Dic₇	semidirect
44. C₇×C₁₃	C₁₁×C₃⋊Dic₃	semidirect
47. C₇×C₁₁	C₁₃×C₃⋊Dic₃	semidirect
49. C₃²×C₇	C₄×C₁₁×C₁₃	semidirect
53. C₃×C₁₃	C₁₁×Dic₂₁	semidirect
55. C₃×C₁₁	C₁₃×Dic₂₁	semidirect
59. C₃×C₇	C₁₁×Dic₃×C₁₃	semidirect
62. C₁₃	C₁₁×C₃⋊Dic₂₁	direct (N × H)
64. C₁₁	C₁₃×C₃⋊Dic₂₁	direct (N × H)
65. C₃²	C₁₁×C₁₃×Dic₇	semidirect
66. C₇	C₁₁×C₁₃×C₃⋊Dic₃	semidirect
69. C₃	C₁₁×C₁₃×Dic₂₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇×C₁₁×C₁₃	2
C₁₁×C₁₃×Dic₂₁	3
C₁₁×C₁₃×C₃⋊Dic₃	7
C₁₃×C₃⋊Dic₂₁	11
C₁₁×C₃⋊Dic₂₁	13

Subgroups — C11×C13×C3⋊Dic21 #49114597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₁₃×C₃⋊Dic₂₁ #49114597