Subgroups — C₇²×A₄×C₁₁⋊C₅ #44568611

Order 32340.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₁⋊C₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₇²×C₁₁⋊C₅	—	4	1	no	maximal, Hall
3	C₇²×C₁₁×A₄	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₇²×C₁₁⋊C₅	—	3	1	no	—
5	C₇×A₄×C₁₁⋊C₅	C₇	1	8	yes	maximal, direct product factor
6	C₅×C₇²×A₄	—	11	1	no	maximal, Hall
7	C₇²×C₁₁⋊C₅	A₄	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₇²×C₁₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₇²×C₁₁	—	4	1	no	Hall
10	C₂²×C₇×C₁₁⋊C₅	C₃×C₇	1	8	yes	complemented
11	C₃×C₇×C₁₁⋊C₅	—	4	8	no	—
12	C₂×C₇²×C₁₁	—	3	1	no	—
13	C₂²×C₅×C₇²	—	11	1	no	Hall
14	C₇×C₁₁×A₄	C₅×C₇	1	8	yes	complemented
15	C₂×C₇×C₁₁⋊C₅	—	3	8	no	—
16	C₃×C₅×C₇²	—	44	1	no	Hall
17	A₄×C₁₁⋊C₅	C₇²	1	1	yes	characteristic, direct product factor, Hall
18	C₇²×A₄	C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
19	C₇²×C₁₁	C₅×A₄	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇²	—	33	1	no	—
21	C₅×C₇×A₄	—	11	8	no	—
22	C₇×C₁₁⋊C₅	C₇×A₄	1	8	yes	direct product factor
23	C₂²×C₇×C₁₁	C₃×C₅×C₇	1	8	yes	complemented
24	C₅×C₇²	—	11	1	no	Hall
25	C₃×C₇×C₁₁	—	4	8	no	—
26	C₂²×C₁₁⋊C₅	C₃×C₇²	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₇²	C₃×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₁₁⋊C₅	—	4	1	no	Hall
29	C₂×C₇×C₁₁	—	3	8	no	—
30	C₃×C₇²	—	4	1	no	Hall
31	C₂²×C₅×C₇	—	11	8	no	—
32	C₁₁×A₄	C₅×C₇²	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₁⋊C₅	—	3	1	no	—
34	C₃×C₅×C₇	—	44	8	no	—
35	C₂×C₇²	—	3	1	no	—
36	C₇×A₄	C₇×C₁₁⋊C₅	1	8	yes	direct product factor
37	C₇×C₁₁	C₅×C₇×A₄	1	8	yes	complemented
38	C₂×C₅×C₇	—	33	8	no	—
39	C₅×A₄	—	11	1	no	Hall
40	C₁₁⋊C₅	C₇²×A₄	1	1	yes	characteristic, direct product factor, Hall
41	C₇²	A₄×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²×C₁₁	C₃×C₅×C₇²	1	1	yes	characteristic, complemented, Hall
43	C₅×C₇	—	11	8	no	—
44	C₃×C₁₁	—	4	1	no	Hall
45	C₂²×C₇	C₃×C₇×C₁₁⋊C₅	1	8	yes	complemented
46	C₂×C₁₁	—	3	1	no	—
47	C₃×C₇	—	4	8	no	—
48	C₂²×C₅	—	11	1	no	Hall
49	C₃×C₅	—	44	1	no	Hall
50	C₂×C₇	—	3	8	no	—
51	A₄	C₇²×C₁₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
52	C₁₁	C₅×C₇²×A₄	1	1	yes	characteristic, complemented, Sylow
53	C₂×C₅	—	33	1	no	—
54	C₇	C₇×A₄×C₁₁⋊C₅	1	8	yes	direct product factor
55	C₅	—	11	1	no	Sylow
56	C₂²	C₃×C₇²×C₁₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
57	C₃	—	4	1	no	Sylow
58	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₇²	A₄×C₁₁⋊C₅
commutator, cosocle, hypocenter	C₂²×C₁₁	C₃×C₅×C₇²
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₁	C₃×C₅
LCS	G ▷ C₂²×C₁₁
UCS	C₁ ◁ C₇²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇²×C₁₁⋊C₅	C₃	semidirect
3. C₇²×C₁₁×A₄	C₅	semidirect
5. C₇×A₄×C₁₁⋊C₅	C₇	direct (N × H)
7. C₇²×C₁₁⋊C₅	A₄	direct (N × H)
8. C₂²×C₇²×C₁₁	C₃×C₅	semidirect
10. C₂²×C₇×C₁₁⋊C₅	C₃×C₇	semidirect
14. C₇×C₁₁×A₄	C₅×C₇	semidirect
17. A₄×C₁₁⋊C₅	C₇²	direct (N × H)
18. C₇²×A₄	C₁₁⋊C₅	direct (N × H)
19. C₇²×C₁₁	C₅×A₄	semidirect
22. C₇×C₁₁⋊C₅	C₇×A₄	direct (N × H)
23. C₂²×C₇×C₁₁	C₃×C₅×C₇	semidirect
26. C₂²×C₁₁⋊C₅	C₃×C₇²	semidirect
27. C₂²×C₇²	C₃×C₁₁⋊C₅	semidirect
32. C₁₁×A₄	C₅×C₇²	semidirect
36. C₇×A₄	C₇×C₁₁⋊C₅	direct (N × H)
37. C₇×C₁₁	C₅×C₇×A₄	semidirect
40. C₁₁⋊C₅	C₇²×A₄	direct (N × H)
41. C₇²	A₄×C₁₁⋊C₅	direct (N × H)
42. C₂²×C₁₁	C₃×C₅×C₇²	semidirect
45. C₂²×C₇	C₃×C₇×C₁₁⋊C₅	semidirect
51. A₄	C₇²×C₁₁⋊C₅	direct (N × H)
52. C₁₁	C₅×C₇²×A₄	semidirect
54. C₇	C₇×A₄×C₁₁⋊C₅	direct (N × H)
56. C₂²	C₃×C₇²×C₁₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇²×C₁₁⋊C₅	3
C₃×C₇²×C₁₁⋊C₅	4
C₇²×C₁₁×A₄	5
C₇×A₄×C₁₁⋊C₅	7
C₅×C₇²×A₄	11

Subgroups — C72×A4×C11⋊C5 #44568611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇²×A₄×C₁₁⋊C₅ #44568611