Subgroups — C₅×C₁₁×C₂²⋊#3862 #44568928

Order 32340.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₇²×C₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₁₁×#3862	—	4	1	no	maximal, Hall
3	C₁₁×C₂²⋊#3862	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₅×C₇²×C₁₁	—	3	1	no	—
5	C₅×C₁₁×C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	maximal
6	C₅×C₂²⋊#3862	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₇²×C₁₁	A₄	1	1	yes	characteristic, complemented, Hall
8	C₂²×C₇²×C₁₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
9	C₁₁×#3862	—	4	1	no	Hall
10	C₂²×C₅×C₇×C₁₁	—	3	2	no	—
11	C₂²×C₅×C₇×C₁₁	ΓL(1,𝔽₈)	1	2	yes	complemented
12	C₅×C₁₁×ΓL(1,𝔽₈)	—	28	2	no	—
13	C₂×C₇²×C₁₁	—	3	1	no	—
14	C₂²×C₅×C₇²	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	—
16	C₂×C₅×C₇×C₁₁	—	3	6	no	—
17	C₂×C₅×C₇×C₁₁	—	3	2	no	—
18	C₅×#3862	—	4	1	no	Hall
19	C₅×C₁₁×A₄	—	49	1	no	Hall
20	C₂²⋊#3862	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₇²×C₁₁	C₅×A₄	1	1	yes	characteristic, complemented, Hall
22	C₂×C₅×C₇²	—	3	1	no	—
23	C₅×C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	—
24	C₅×C₇×C₁₁	—	3	2	no	—
25	C₅×C₇×C₁₁	C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
26	C₂²×C₇×C₁₁	—	3	2	no	—
27	C₂²×C₇×C₁₁	C₅×ΓL(1,𝔽₈)	1	2	yes	complemented
28	C₅×C₇²	C₁₁×A₄	1	1	yes	characteristic, complemented, Hall
29	C₁₁×ΓL(1,𝔽₈)	—	28	2	no	—
30	C₂²×C₅×C₁₁	#3862	1	1	yes	characteristic, complemented, Hall
31	C₂²×C₇²	C₃×C₅×C₁₁	1	1	yes	characteristic, complemented, Hall
32	C₃×C₅×C₁₁	—	196	1	no	Hall
33	C₂×C₇×C₁₁	—	3	6	no	—
34	C₂×C₇×C₁₁	—	3	2	no	—
35	#3862	—	4	1	no	Hall
36	C₂²×C₅×C₇	—	3	2	no	—
37	C₂²×C₅×C₇	C₁₁×ΓL(1,𝔽₈)	1	2	yes	complemented
38	C₁₁×A₄	—	49	1	no	Hall
39	C₂×C₅×C₁₁	—	3	1	no	—
40	C₅×ΓL(1,𝔽₈)	—	28	2	no	—
41	C₂×C₇²	—	3	1	no	—
42	C₂²⋊ΓL(1,𝔽₈)	—	7	2	no	—
43	C₇×C₁₁	—	3	2	no	—
44	C₇×C₁₁	C₅×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
45	C₂×C₅×C₇	—	3	6	no	—
46	C₂×C₅×C₇	—	3	2	no	—
47	C₅×A₄	—	49	1	no	Hall
48	C₅×C₁₁	C₂²⋊#3862	1	1	yes	characteristic, direct product factor, Hall
49	C₇²	C₅×C₁₁×A₄	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₁₁	C₅×#3862	1	1	yes	characteristic, complemented, Hall
51	C₅×C₇	—	3	2	no	—
52	C₅×C₇	C₁₁×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
53	C₃×C₁₁	—	196	1	no	Hall
54	C₂²×C₇	—	3	2	no	—
55	C₂²×C₇	C₅×C₁₁×ΓL(1,𝔽₈)	1	2	yes	complemented
56	C₂×C₁₁	—	3	1	no	—
57	ΓL(1,𝔽₈)	—	28	2	no	—
58	C₂²×C₅	C₁₁×#3862	1	1	yes	characteristic, complemented, Hall
59	C₃×C₅	—	196	1	no	Hall
60	C₂×C₇	—	3	6	no	—
61	C₂×C₇	—	3	2	no	—
62	A₄	—	49	1	no	Hall
63	C₁₁	C₅×C₂²⋊#3862	1	1	yes	characteristic, direct product factor, Sylow
64	C₂×C₅	—	3	1	no	—
65	C₇	—	3	2	no	—
66	C₇	C₅×C₁₁×C₂²⋊ΓL(1,𝔽₈)	1	2	yes	complemented
67	C₅	C₁₁×C₂²⋊#3862	1	1	yes	characteristic, direct product factor, Sylow
68	C₂²	C₅×C₁₁×#3862	1	1	yes	characteristic, complemented, Sylow
69	C₃	—	196	1	no	Sylow
70	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₅×C₁₁	C₂²⋊#3862
commutator, cosocle, hypocenter	C₂²×C₇²	C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₂²×C₅×C₇²×C₁₁	C₃
LCS	G ▷ C₂²×C₇²
UCS	C₁ ◁ C₅×C₁₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×C₇²×C₁₁	C₃	semidirect
3. C₁₁×C₂²⋊#3862	C₅	direct (N × H)
6. C₅×C₂²⋊#3862	C₁₁	direct (N × H)
7. C₅×C₇²×C₁₁	A₄	semidirect
8. C₂²×C₇²×C₁₁	C₃×C₅	semidirect
11. C₂²×C₅×C₇×C₁₁	ΓL(1,𝔽₈)	semidirect
14. C₂²×C₅×C₇²	C₃×C₁₁	semidirect
20. C₂²⋊#3862	C₅×C₁₁	direct (N × H)
21. C₇²×C₁₁	C₅×A₄	semidirect
25. C₅×C₇×C₁₁	C₂²⋊ΓL(1,𝔽₈)	semidirect
27. C₂²×C₇×C₁₁	C₅×ΓL(1,𝔽₈)	semidirect
28. C₅×C₇²	C₁₁×A₄	semidirect
30. C₂²×C₅×C₁₁	#3862	semidirect
31. C₂²×C₇²	C₃×C₅×C₁₁	semidirect
37. C₂²×C₅×C₇	C₁₁×ΓL(1,𝔽₈)	semidirect
44. C₇×C₁₁	C₅×C₂²⋊ΓL(1,𝔽₈)	semidirect
48. C₅×C₁₁	C₂²⋊#3862	direct (N × H)
49. C₇²	C₅×C₁₁×A₄	semidirect
50. C₂²×C₁₁	C₅×#3862	semidirect
52. C₅×C₇	C₁₁×C₂²⋊ΓL(1,𝔽₈)	semidirect
55. C₂²×C₇	C₅×C₁₁×ΓL(1,𝔽₈)	semidirect
58. C₂²×C₅	C₁₁×#3862	semidirect
63. C₁₁	C₅×C₂²⋊#3862	direct (N × H)
66. C₇	C₅×C₁₁×C₂²⋊ΓL(1,𝔽₈)	semidirect
67. C₅	C₁₁×C₂²⋊#3862	direct (N × H)
68. C₂²	C₅×C₁₁×#3862	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×C₇²×C₁₁	3
C₅×C₁₁×#3862	4
C₁₁×C₂²⋊#3862	5
C₅×C₁₁×C₂²⋊ΓL(1,𝔽₈)	7
C₅×C₂²⋊#3862	11

Subgroups — C5×C11×C22⋊#3862 #44568928

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₁×C₂²⋊#3862 #44568928