Subgroups — C₁₁×#14523610 #37528513

Order 23100.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₇⋊#1043	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	C₁₁×#1043⋊C₃	—	7	1	no	maximal, Hall
6	#14523610	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅²×C₇×C₁₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₁₁×(C₅⋊D₅)⋊C₃	D₇	1	1	yes	characteristic
9	C₁₁×C₇⋊AGL(1,𝔽₅)	—	15	2	no	—
10	C₁₁×#1043	—	7	1	no	Hall
11	C₇×(C₅⋊D₅)⋊C₃	C₂×C₁₁	1	1	yes	characteristic
12	C₃×C₁₁×Dic₇	—	25	1	no	maximal, Hall
13	C₁₁×C₅²⋊C₃	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₇×D₅×C₁₁	—	15	2	no	—
15	C₇⋊#1043	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₁₁×C₅⋊D₅	C₃×D₇	1	1	yes	characteristic
17	C₇×C₅²⋊C₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₇×C₁₁	—	25	1	no	—
19	C₅×C₇×C₁₁	—	3	2	no	—
20	C₇×C₅⋊D₅	C₂×C₃×C₁₁	1	1	yes	characteristic
21	C₁₁×Dic₇	—	25	1	no	Hall
22	#1043⋊C₃	—	7	1	no	Hall
23	C₅²×C₁₁	C₃×Dic₇	1	1	yes	characteristic, complemented, Hall
24	C₃×C₇×C₁₁	—	25	1	no	Hall
25	C₁₁×AGL(1,𝔽₅)	—	105	2	no	—
26	C₅²×C₇	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
27	C₂×C₇×C₁₁	—	25	1	no	—
28	(C₅⋊D₅)⋊C₃	C₁₁×D₇	1	1	yes	characteristic
29	C₇⋊AGL(1,𝔽₅)	—	15	2	no	—
30	C₃×C₄×C₁₁	—	175	1	no	Hall
31	D₅×C₁₁	—	15	2	no	—
32	#1043	—	7	1	no	Hall
33	C₃×Dic₇	—	25	1	no	Hall
34	C₇×C₁₁	#1043⋊C₃	1	1	yes	characteristic, complemented, Hall
35	C₅²⋊C₃	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Hall
36	C₇×D₅	—	15	2	no	—
37	C₂×C₃×C₁₁	—	25	1	no	—
38	C₅×C₁₁	—	3	2	no	—
39	C₅⋊D₅	C₃×C₁₁×D₇	1	1	yes	characteristic
40	C₄×C₁₁	—	175	1	no	Hall
41	C₂×C₃×C₇	—	25	1	no	—
42	C₅×C₇	—	3	2	no	—
43	C₃×C₁₁	—	25	1	no	Hall
44	Dic₇	—	25	1	no	Hall
45	C₅²	C₃×C₁₁×Dic₇	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₁₁	—	25	1	no	—
47	C₃×C₇	—	25	1	no	Hall
48	AGL(1,𝔽₅)	—	105	2	no	—
49	C₂×C₇	—	25	1	no	—
50	C₃×C₄	—	175	1	no	Hall
51	C₁₁	#14523610	1	1	yes	characteristic, direct product factor, Sylow
52	D₅	—	15	2	no	—
53	C₇	C₁₁×#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃	—	25	1	no	—
55	C₅	—	3	2	no	—
56	C₄	—	175	1	no	Sylow
57	C₃	—	25	1	no	Sylow
58	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	#14523610
commutator, hypocenter	C₅²×C₇	C₃×C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₁	C₃×C₄
prime radical	C₇×C₁₁×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₇×C₅⋊D₅	C₂×C₃×C₁₁
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₇⋊#1043	C₃	semidirect
3. C₇×C₁₁×C₅²⋊C₃	C₄	semidirect
6. #14523610	C₁₁	direct (N × H)
7. C₅²×C₇×C₁₁	C₃×C₄	semidirect
13. C₁₁×C₅²⋊C₃	Dic₇	semidirect
15. C₇⋊#1043	C₃×C₁₁	semidirect
17. C₇×C₅²⋊C₃	C₄×C₁₁	semidirect
23. C₅²×C₁₁	C₃×Dic₇	semidirect
26. C₅²×C₇	C₃×C₄×C₁₁	semidirect
34. C₇×C₁₁	#1043⋊C₃	semidirect
35. C₅²⋊C₃	C₁₁×Dic₇	semidirect
45. C₅²	C₃×C₁₁×Dic₇	semidirect
51. C₁₁	#14523610	direct (N × H)
53. C₇	C₁₁×#1043⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₁₁×(C₅⋊D₅)⋊C₃	2
C₁₁×C₇⋊#1043	3
C₁₁×#1043⋊C₃	7
#14523610	11
C₃×C₁₁×Dic₇	25

Subgroups — C11×#14523610 #37528513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#14523610 #37528513