Subgroups — C₂²⋊#19104440 #35209180

Order 20748.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	#19104440	—	4	1	no	maximal, Hall
3	C₂×C₇×C₁₃×C₁₉	—	3	1	no	—
4	C₂²⋊#10625202	—	7	1	no	maximal, Hall
5	C₇×C₁₃×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²⋊#87704	—	13	1	no	maximal, Hall
7	C₂²⋊#63270	—	19	1	no	maximal, Hall
8	C₂²×C₁₃×C₁₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	#10625202	—	28	1	no	Hall
10	C₂²×C₇×C₁₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₁₃×C₁₉	—	3	1	no	—
12	#87704	—	52	1	no	Hall
13	C₂²×C₇×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
14	#63270	—	76	1	no	Hall
15	C₂×C₇×C₁₉	—	3	1	no	—
16	C₁₃×C₁₉	C₂²⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
17	C₂²⋊(C₁₉⋊C₃)	—	91	1	no	Hall
18	C₂×C₇×C₁₃	—	3	1	no	—
19	C₂²⋊(C₁₃⋊C₃)	—	133	1	no	Hall
20	C₇×C₁₉	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, complemented, Hall
21	C₇×C₁₃	C₂²⋊(C₁₉⋊C₃)	1	1	yes	characteristic, complemented, Hall
22	C₂²⋊ΓL(1,𝔽₈)	—	247	1	no	Hall
23	C₂²×C₁₉	#63270	1	1	yes	characteristic, complemented, Hall
24	C₁₉⋊C₃	—	364	1	no	Hall
25	C₂²×C₁₃	#87704	1	1	yes	characteristic, complemented, Hall
26	C₁₃⋊C₃	—	532	1	no	Hall
27	C₂×C₁₉	—	3	1	no	—
28	C₂²×C₇	#10625202	1	1	yes	characteristic, complemented, Hall
29	C₂×C₁₃	—	3	1	no	—
30	ΓL(1,𝔽₈)	—	988	1	no	Hall
31	C₁₉	C₂²⋊#63270	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₇	—	3	1	no	—
33	C₁₃	C₂²⋊#87704	1	1	yes	characteristic, complemented, Sylow
34	A₄	—	1729	1	no	Hall
35	C₇	C₂²⋊#10625202	1	1	yes	characteristic, complemented, Sylow
36	C₂²	#19104440	1	1	yes	characteristic, complemented, Sylow
37	C₃	—	6916	1	no	Sylow
38	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₇×C₁₃×C₁₉	C₃
LCS	G ▷ C₂²×C₇×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂²×C₇×C₁₃×C₁₉	C₃	semidirect
5. C₇×C₁₃×C₁₉	A₄	semidirect
8. C₂²×C₁₃×C₁₉	ΓL(1,𝔽₈)	semidirect
10. C₂²×C₇×C₁₉	C₁₃⋊C₃	semidirect
13. C₂²×C₇×C₁₃	C₁₉⋊C₃	semidirect
16. C₁₃×C₁₉	C₂²⋊ΓL(1,𝔽₈)	semidirect
20. C₇×C₁₉	C₂²⋊(C₁₃⋊C₃)	semidirect
21. C₇×C₁₃	C₂²⋊(C₁₉⋊C₃)	semidirect
23. C₂²×C₁₉	#63270	semidirect
25. C₂²×C₁₃	#87704	semidirect
28. C₂²×C₇	#10625202	semidirect
31. C₁₉	C₂²⋊#63270	semidirect
33. C₁₃	C₂²⋊#87704	semidirect
35. C₇	C₂²⋊#10625202	semidirect
36. C₂²	#19104440	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₇×C₁₃×C₁₉	3
#19104440	4
C₂²⋊#10625202	7
C₂²⋊#87704	13
C₂²⋊#63270	19

Subgroups — C22⋊#19104440 #35209180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19104440 #35209180