Subgroups — C₁₁⋊#15690920 #46803159

Order 34188.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#11715913	C₂	1	1	yes	maximal, characteristic
2	C₇×Dic₄₀₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×#11715913	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₁₁⋊(Dic₃₇⋊C₃)	—	7	1	no	maximal, Hall
6	#15690920	—	11	1	no	maximal, Hall
7	C₇×C₁₁×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₁₁×C₃₇⋊C₃	—	7	1	no	—
9	Dic₄₀₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂×#11715913	D₁₁	1	1	yes	characteristic
11	C₁₁×C₃₇⋊C₃	—	7	1	no	Hall
12	C₇×Dic₃₇	—	11	1	no	Hall
13	ΓL(1,𝔽₈)×Dic₁₁	—	37	1	no	maximal, Hall
14	C₂×C₁₁×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	#11715913	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₃₇	C₃×D₁₁	1	1	yes	characteristic
17	C₂×C₁₁×ΓL(1,𝔽₈)	—	37	1	no	—
18	Dic₃₇⋊C₃	—	77	1	no	Hall
19	C₁₁×C₃₇	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
20	C₇×Dic₁₁	—	37	1	no	Hall
21	C₇×C₃₇	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×ΓL(1,𝔽₈)	—	37	1	no	Hall
23	C₂×C₃₇⋊C₃	—	7	1	no	—
24	C₂×C₇×C₁₁	D₃₇⋊C₃	1	1	yes	characteristic
25	Dic₃₇	—	11	1	no	Hall
26	C₃×Dic₁₁	—	259	1	no	Hall
27	C₃₇⋊C₃	—	7	1	no	Hall
28	C₄×ΓL(1,𝔽₈)	—	407	1	no	Hall
29	C₇×C₁₁	Dic₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₇	ΓL(1,𝔽₈)×D₁₁	1	1	yes	characteristic
31	C₂×C₃×C₁₁	—	259	1	no	—
32	Dic₁₁	—	37	1	no	Hall
33	C₂×ΓL(1,𝔽₈)	—	37	1	no	—
34	C₃₇	ΓL(1,𝔽₈)×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₁₁	—	259	1	no	Hall
36	C₄×C₇	—	407	1	no	Hall
37	C₂×C₁₁	#13095531	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	—	37	1	no	Hall
39	C₂×C₇	C₁₁⋊(D₃₇⋊C₃)	1	1	yes	characteristic
40	C₃×C₄	—	2849	1	no	Hall
41	C₁₁	#15690920	1	1	yes	characteristic, complemented, Sylow
42	C₇	C₁₁⋊(Dic₃₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	259	1	no	—
44	C₄	—	407	1	no	Sylow
45	C₃	—	259	1	no	Sylow
46	C₂	C₁₁⋊#13095531	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₁₁⋊#13095531
commutator, hypocenter	C₇×C₁₁×C₃₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₇×C₁₁×C₃₇	C₂×C₃
prime radical	C₂×C₁₁×#11715913	C₂
LCS	G ▷ C₇×C₁₁×C₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₇×Dic₄₀₇	C₃	semidirect
3. C₁₁×#11715913	C₄	semidirect
7. C₇×C₁₁×C₃₇	C₃×C₄	semidirect
9. Dic₄₀₇	ΓL(1,𝔽₈)	semidirect
15. #11715913	Dic₁₁	semidirect
19. C₁₁×C₃₇	C₄×ΓL(1,𝔽₈)	semidirect
21. C₇×C₃₇	C₃×Dic₁₁	semidirect
29. C₇×C₁₁	Dic₃₇⋊C₃	semidirect
34. C₃₇	ΓL(1,𝔽₈)×Dic₁₁	semidirect
41. C₁₁	#15690920	semidirect
42. C₇	C₁₁⋊(Dic₃₇⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#11715913	2
C₇×Dic₄₀₇	3
C₁₁⋊(Dic₃₇⋊C₃)	7
#15690920	11
ΓL(1,𝔽₈)×Dic₁₁	37

Subgroups — C11⋊#15690920 #46803159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁⋊#15690920 #46803159