Subgroups — C₁₁×#15668773 #44568643

Order 32340.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₁×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇×C₁₁×C₇⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₅×C₁₁×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×#10596868	—	5	1	no	maximal, Hall
5	C₇²×D₅×C₁₁	D₃	1	1	yes	characteristic
6	C₂×C₁₁×#3862	—	5	1	no	—
7	#15668773	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₇²×C₁₁	Dic₃	1	1	yes	characteristic, complemented, Hall
9	D₅×C₁₁×ΓL(1,𝔽₈)	—	14	1	no	—
10	C₇×C₁₁×Dic₇	—	15	1	no	Hall
11	C₁₁×#3862	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₁₁×C₇⋊AGL(1,𝔽₅)	—	3	1	no	—
13	C₇×C₁₁×AGL(1,𝔽₅)	—	21	1	no	—
14	D₅×#3862	C₂×C₁₁	1	1	yes	characteristic
15	C₅×C₁₁×ΓL(1,𝔽₈)	—	14	1	no	—
16	C₂×C₇²×C₁₁	—	5	1	no	—
17	C₇×C₇⋊AGL(1,𝔽₅)	—	3	1	no	Hall
18	C₇×D₅×C₁₁	—	2	1	no	—
19	C₇×D₅×C₁₁	—	3	1	no	—
20	C₇×D₅×C₁₁	—	3	1	no	—
21	C₅×#3862	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×ΓL(1,𝔽₁₆)	—	49	1	no	maximal, Hall
23	#10596868	—	5	1	no	Hall
24	C₇²×C₁₁	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
25	C₇²×D₅	D₃×C₁₁	1	1	yes	characteristic
26	C₂×C₁₁×ΓL(1,𝔽₈)	—	70	1	no	—
27	C₅×C₇×C₁₁	—	2	1	no	—
28	C₅×C₇×C₁₁	—	3	1	no	—
29	C₅×C₇×C₁₁	—	3	1	no	—
30	C₃×D₅×C₁₁	—	49	1	no	—
31	C₄×C₇×C₁₁	—	105	1	no	—
32	C₁₁×Dic₇	—	15	1	no	—
33	C₂×#3862	—	5	1	no	—
34	C₅×C₇²	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
35	C₁₁×ΓL(1,𝔽₈)	—	14	1	no	—
36	C₁₁×AGL(1,𝔽₅)	—	21	1	no	Hall
37	D₅×ΓL(1,𝔽₈)	—	14	1	no	—
38	C₇×Dic₇	—	15	1	no	Hall
39	C₃×C₅×C₁₁	—	49	1	no	Hall
40	C₂×C₇×C₁₁	—	10	1	no	—
41	C₂×C₇×C₁₁	—	15	1	no	—
42	C₂×C₇×C₁₁	—	15	1	no	—
43	#3862	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
44	C₇⋊AGL(1,𝔽₅)	—	3	1	no	—
45	C₇×AGL(1,𝔽₅)	—	21	1	no	—
46	C₁₁×Dic₃	—	245	1	no	Hall
47	D₅×C₁₁	#64418	1	1	yes	characteristic
48	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
49	C₂×C₇²	—	5	1	no	—
50	C₇×C₁₁	—	2	1	no	—
51	C₇×C₁₁	—	3	1	no	—
52	C₇×C₁₁	—	3	1	no	—
53	C₇×D₅	—	2	1	no	—
54	C₇×D₅	—	3	1	no	—
55	C₇×D₅	—	3	1	no	—
56	C₂×C₃×C₁₁	—	245	1	no	—
57	ΓL(1,𝔽₁₆)	—	49	1	no	Hall
58	C₅×C₁₁	#10596868	1	1	yes	characteristic, complemented, Hall
59	C₇²	C₁₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
60	C₄×C₁₁	—	105	1	no	Hall
61	C₂×ΓL(1,𝔽₈)	—	70	1	no	—
62	C₅×C₇	—	2	1	no	—
63	C₅×C₇	—	3	1	no	—
64	C₅×C₇	—	3	1	no	—
65	C₃×C₁₁	—	49	1	no	Hall
66	C₃×D₅	—	49	1	no	—
67	C₄×C₇	—	105	1	no	—
68	Dic₇	—	15	1	no	—
69	C₂×C₁₁	—	5	1	no	—
70	ΓL(1,𝔽₈)	—	14	1	no	—
71	AGL(1,𝔽₅)	—	21	1	no	Hall
72	C₃×C₅	—	49	1	no	Hall
73	C₂×C₇	—	10	1	no	—
74	C₂×C₇	—	15	1	no	—
75	C₂×C₇	—	15	1	no	—
76	Dic₃	—	245	1	no	Hall
77	C₁₁	#15668773	1	1	yes	characteristic, direct product factor, Sylow
78	D₅	C₁₁×#64418	1	1	yes	characteristic
79	C₇	—	2	1	no	—
80	C₇	—	3	1	no	—
81	C₇	—	3	1	no	—
82	C₂×C₃	—	245	1	no	—
83	C₅	C₁₁×#10596868	1	1	yes	characteristic, complemented, Sylow
84	C₄	—	105	1	no	Sylow
85	C₃	—	49	1	no	Sylow
86	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#15668773
commutator, hypocenter	C₅×#3862	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	Dic₃
prime radical	D₅×C₁₁×#3862	C₂
cosocle	D₅×#3862	C₂×C₁₁
LCS	G ▷ C₅×#3862
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₁₁×#3862	C₄	semidirect
7. #15668773	C₁₁	direct (N × H)
8. C₅×C₇²×C₁₁	Dic₃	semidirect
11. C₁₁×#3862	AGL(1,𝔽₅)	semidirect
21. C₅×#3862	C₄×C₁₁	semidirect
24. C₇²×C₁₁	ΓL(1,𝔽₁₆)	semidirect
34. C₅×C₇²	C₁₁×Dic₃	semidirect
43. #3862	C₁₁×AGL(1,𝔽₅)	semidirect
58. C₅×C₁₁	#10596868	semidirect
59. C₇²	C₁₁×ΓL(1,𝔽₁₆)	semidirect
77. C₁₁	#15668773	direct (N × H)
83. C₅	C₁₁×#10596868	semidirect

Maximal subgroups

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

subgroup	index
D₅×C₁₁×#3862	2
C₇×C₁₁×C₇⋊AGL(1,𝔽₅)	3
C₁₁×#10596868	5
#15668773	11
C₁₁×ΓL(1,𝔽₁₆)	49

Subgroups — C11×#15668773 #44568643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#15668773 #44568643