Subgroups — C₁₁×ΓL(1,𝔽₈)⋊Dic₃₇ #46803166

Order 34188.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×ΓL(1,𝔽₈)×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×Dic₂₅₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×ΓL(1,𝔽₈)×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₁₁×C₃₇	C₂×C₃	1	1	yes	characteristic
5	C₃×C₁₁×Dic₃₇	—	7	1	no	maximal, Hall
6	ΓL(1,𝔽₈)⋊Dic₃₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₁×C₃₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₁×C₃₇	—	7	1	no	—
9	C₁₁×Dic₃₇	—	7	1	no	Hall
10	C₂×ΓL(1,𝔽₈)×C₃₇	C₂×C₁₁	1	1	yes	characteristic
11	C₃×C₁₁×C₃₇	—	7	1	no	Hall
12	Dic₂₅₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
13	C₁₁×ΓL(1,𝔽₈)⋊C₄	—	37	1	no	maximal, Hall
14	C₂×C₁₁×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic
15	ΓL(1,𝔽₈)×C₃₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₃₇	C₂×C₃×C₁₁	1	1	yes	characteristic
17	C₂×C₁₁×ΓL(1,𝔽₈)	D₃₇	1	1	yes	characteristic
18	C₃×Dic₃₇	—	7	1	no	Hall
19	C₁₁×C₃₇	ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Hall
20	C₁₁×Dic₇	—	37	1	no	Hall
21	C₇×C₃₇	C₃×C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
22	C₁₁×ΓL(1,𝔽₈)	Dic₃₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₃₇	—	7	1	no	—
24	C₂×C₇×C₁₁	C₃×D₃₇	1	1	yes	characteristic
25	Dic₃₇	—	7	1	no	Hall
26	C₃×C₄×C₁₁	—	259	1	no	Hall
27	C₃×C₃₇	—	7	1	no	Hall
28	ΓL(1,𝔽₈)⋊C₄	—	37	1	no	Hall
29	C₇×C₁₁	C₃×Dic₃₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₃₇	C₁₁×AGL(1,𝔽₇)	1	1	yes	characteristic
31	C₂×C₃×C₁₁	—	7	1	no	—
32	C₄×C₁₁	—	259	1	no	Hall
33	C₂×ΓL(1,𝔽₈)	C₁₁×D₃₇	1	1	yes	characteristic
34	C₃₇	C₁₁×ΓL(1,𝔽₈)⋊C₄	1	1	yes	characteristic, complemented, Sylow
35	C₃×C₁₁	—	7	1	no	Hall
36	Dic₇	—	37	1	no	Hall
37	C₂×C₁₁	ΓL(1,𝔽₈)⋊D₃₇	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	C₁₁×Dic₃₇	1	1	yes	characteristic, complemented, Hall
39	C₂×C₇	C₃×C₁₁×D₃₇	1	1	yes	characteristic
40	C₃×C₄	—	259	1	no	Hall
41	C₁₁	ΓL(1,𝔽₈)⋊Dic₃₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃×C₁₁×Dic₃₇	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	7	1	no	—
44	C₄	—	259	1	no	Sylow
45	C₃	—	7	1	no	Sylow
46	C₂	C₁₁×ΓL(1,𝔽₈)⋊D₃₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₁₁	ΓL(1,𝔽₈)⋊D₃₇
commutator, hypocenter	C₇×C₃₇	C₃×C₄×C₁₁
Frattini	C₂	C₁₁×ΓL(1,𝔽₈)⋊D₃₇
Fitting, socle	C₂×C₇×C₁₁×C₃₇	C₂×C₃
prime radical	C₂×C₁₁×ΓL(1,𝔽₈)×C₃₇	C₂
cosocle	C₂×C₇×C₃₇	C₂×C₃×C₁₁
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₂×C₁₁

Complements

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

N	H ≅ G/N	type
2. C₁₁×Dic₂₅₉	C₃	semidirect
3. C₁₁×ΓL(1,𝔽₈)×C₃₇	C₄	semidirect
6. ΓL(1,𝔽₈)⋊Dic₃₇	C₁₁	direct (N × H)
7. C₇×C₁₁×C₃₇	C₃×C₄	semidirect
12. Dic₂₅₉	C₃×C₁₁	semidirect
15. ΓL(1,𝔽₈)×C₃₇	C₄×C₁₁	semidirect
19. C₁₁×C₃₇	ΓL(1,𝔽₈)⋊C₄	semidirect
21. C₇×C₃₇	C₃×C₄×C₁₁	semidirect
22. C₁₁×ΓL(1,𝔽₈)	Dic₃₇	semidirect
29. C₇×C₁₁	C₃×Dic₃₇	semidirect
34. C₃₇	C₁₁×ΓL(1,𝔽₈)⋊C₄	semidirect
38. ΓL(1,𝔽₈)	C₁₁×Dic₃₇	semidirect
41. C₁₁	ΓL(1,𝔽₈)⋊Dic₃₇	direct (N × H)
42. C₇	C₃×C₁₁×Dic₃₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×ΓL(1,𝔽₈)×C₃₇	2
C₁₁×Dic₂₅₉	3
C₃×C₁₁×Dic₃₇	7
ΓL(1,𝔽₈)⋊Dic₃₇	11
C₁₁×ΓL(1,𝔽₈)⋊C₄	37

Subgroups — C11×ΓL(1,𝔽8)⋊Dic37 #46803166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×ΓL(1,𝔽₈)⋊Dic₃₇ #46803166