Subgroups — C₇×C₁₁×#90865 #49114879

Order 36036.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×C₁₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₁₁×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₁₁×C₁₃	—	6	2	no	—
4	C₁₁×#90865	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₁×Dic₁₃	—	9	1	no	maximal, Hall
6	C₇×#90865	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₇×C₁₁×C₁₃	—	2	2	no	—
8	C₇×C₁₁×#157	—	13	1	no	maximal, Hall
9	C₁₁×C₁₃×C₃⋊D₃	C₂×C₇	1	1	yes	characteristic
10	C₂×C₇×C₁₁×C₁₃	—	9	1	no	—
11	C₇×C₁₃×C₃⋊D₃	C₂×C₁₁	1	1	yes	characteristic
12	C₇×C₁₁×C₃⋊D₃	D₁₃	1	1	yes	characteristic
13	C₃²×C₁₁×C₁₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×C₁₁×C₁₃	#157	1	1	yes	characteristic, complemented, Hall
15	D₃×C₁₁×C₁₃	—	6	2	no	—
16	C₃²×C₇×C₁₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
17	C₃²×C₇×C₁₁	Dic₁₃	1	1	yes	characteristic, complemented, Hall
18	C₁₁×Dic₁₃	—	9	1	no	Hall
19	D₃×C₇×C₁₃	—	6	2	no	—
20	#90865	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	D₃×C₇×C₁₁	—	6	2	no	—
22	C₃×C₁₁×C₁₃	—	2	2	no	—
23	C₁₁×#157	—	13	1	no	Hall
24	C₇×Dic₁₃	—	9	1	no	Hall
25	C₄×C₇×C₁₁	—	117	1	no	Hall
26	C₂×C₁₁×C₁₃	—	9	1	no	—
27	C₃×C₇×C₁₃	—	2	2	no	—
28	C₇×#157	—	13	1	no	Hall
29	C₁₃×C₃⋊D₃	C₂×C₇×C₁₁	1	1	yes	characteristic
30	C₃×C₇×C₁₁	—	2	2	no	—
31	C₁₁×C₃⋊D₃	C₇×D₁₃	1	1	yes	characteristic
32	C₂×C₇×C₁₃	—	9	1	no	—
33	C₂×C₇×C₁₁	—	9	1	no	—
34	C₁₁×C₁₃	C₇×#157	1	1	yes	characteristic, complemented, Hall
35	C₇×C₃⋊D₃	C₁₁×D₁₃	1	1	yes	characteristic
36	C₃²×C₁₃	C₄×C₇×C₁₁	1	1	yes	characteristic, complemented, Hall
37	C₃²×C₁₁	C₇×Dic₁₃	1	1	yes	characteristic, complemented, Hall
38	C₇×C₁₃	C₁₁×#157	1	1	yes	characteristic, complemented, Hall
39	D₃×C₁₃	—	6	2	no	—
40	C₇×C₁₁	#90865	1	1	yes	characteristic, direct product factor, Hall
41	D₃×C₁₁	—	6	2	no	—
42	C₃²×C₇	C₁₁×Dic₁₃	1	1	yes	characteristic, complemented, Hall
43	Dic₁₃	—	9	1	no	Hall
44	C₄×C₁₁	—	117	1	no	Hall
45	D₃×C₇	—	6	2	no	—
46	C₃×C₁₃	—	2	2	no	—
47	#157	—	13	1	no	Hall
48	C₃×C₁₁	—	2	2	no	—
49	C₄×C₇	—	117	1	no	Hall
50	C₂×C₁₃	—	9	1	no	—
51	C₂×C₁₁	—	9	1	no	—
52	C₃×C₇	—	2	2	no	—
53	C₃⋊D₃	C₇×C₁₁×D₁₃	1	1	yes	characteristic
54	C₂×C₇	—	9	1	no	—
55	C₁₃	C₇×C₁₁×#157	1	1	yes	characteristic, complemented, Sylow
56	C₁₁	C₇×#90865	1	1	yes	characteristic, direct product factor, Sylow
57	C₃²	C₇×C₁₁×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
58	C₇	C₁₁×#90865	1	1	yes	characteristic, direct product factor, Sylow
59	D₃	—	6	2	no	—
60	C₄	—	117	1	no	Sylow
61	C₃	—	2	2	no	—
62	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₁	#90865
commutator, hypocenter	C₃²×C₁₃	C₄×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₁₁×C₁₃	C₄
prime radical	C₇×C₁₁×C₁₃×C₃⋊D₃	C₂
cosocle	C₁₃×C₃⋊D₃	C₂×C₇×C₁₁
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₇×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₇×C₁₁×C₁₃	C₄	semidirect
4. C₁₁×#90865	C₇	direct (N × H)
6. C₇×#90865	C₁₁	direct (N × H)
13. C₃²×C₁₁×C₁₃	C₄×C₇	semidirect
14. C₇×C₁₁×C₁₃	#157	semidirect
16. C₃²×C₇×C₁₃	C₄×C₁₁	semidirect
17. C₃²×C₇×C₁₁	Dic₁₃	semidirect
20. #90865	C₇×C₁₁	direct (N × H)
34. C₁₁×C₁₃	C₇×#157	semidirect
36. C₃²×C₁₃	C₄×C₇×C₁₁	semidirect
37. C₃²×C₁₁	C₇×Dic₁₃	semidirect
38. C₇×C₁₃	C₁₁×#157	semidirect
40. C₇×C₁₁	#90865	direct (N × H)
42. C₃²×C₇	C₁₁×Dic₁₃	semidirect
55. C₁₃	C₇×C₁₁×#157	semidirect
56. C₁₁	C₇×#90865	direct (N × H)
57. C₃²	C₇×C₁₁×Dic₁₃	semidirect
58. C₇	C₁₁×#90865	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₁₁×C₁₃×C₃⋊D₃	2
C₁₁×#90865	7
C₇×C₁₁×Dic₁₃	9
C₇×#90865	11
C₇×C₁₁×#157	13

Subgroups — C7×C11×#90865 #49114879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₁₁×#90865 #49114879