Subgroups — C₂²×C₁₉×#3862 #26014040

Order 11172.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#3862	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×#3862	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	3	yes	complemented
5	C₂²×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	maximal
6	C₇²×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	6	no	—
8	C₂²×#3862	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₇×C₁₉	—	3	2	no	—
10	C₂²×C₇×C₁₉	ΓL(1,𝔽₈)	1	2	yes	complemented
11	C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
12	C₂×#3862	C₂×C₁₉	1	3	yes	direct product factor
13	C₂×C₇×C₁₉	—	3	6	no	—
14	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	6	yes	complemented
15	C₂²×C₃×C₁₉	—	49	1	no	Hall
16	C₂²×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	#3862	C₂²×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₉	—	3	2	no	—
19	C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	1	2	yes	complemented
20	C₂×C₃×C₁₉	—	49	3	no	—
21	C₂×C₇²	C₂×C₃×C₁₉	1	3	yes	complemented
22	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
23	C₂²×C₁₉	#3862	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₉	—	49	1	no	Hall
25	C₇²	C₂²×C₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×ΓL(1,𝔽₈)	—	7	6	no	—
27	C₂×C₁₉	C₂×#3862	1	3	yes	direct product factor
28	C₂²×C₇	—	3	2	no	—
29	C₂²×C₇	C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
30	ΓL(1,𝔽₈)	—	7	2	no	—
31	C₁₉	C₂²×#3862	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₇	—	3	6	no	—
33	C₂×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	6	yes	complemented
34	C₂²×C₃	—	49	1	no	Hall
35	C₇	—	3	2	no	—
36	C₇	C₂²×C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
37	C₂×C₃	—	49	3	no	—
38	C₂²	C₁₉×#3862	1	1	yes	characteristic, direct product factor, Sylow
39	C₃	—	49	1	no	Sylow
40	C₂	C₂×C₁₉×#3862	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₉	#3862
commutator, cosocle, hypocenter	C₇²	C₂²×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₉	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#3862	C₂	direct (N × H)
2. C₂²×C₇²×C₁₉	C₃	semidirect
3. C₁₉×#3862	C₂²	direct (N × H)
4. C₂×C₇²×C₁₉	C₂×C₃	semidirect
6. C₇²×C₁₉	C₂²×C₃	semidirect
8. C₂²×#3862	C₁₉	direct (N × H)
10. C₂²×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
12. C₂×#3862	C₂×C₁₉	direct (N × H)
14. C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	semidirect
16. C₂²×C₇²	C₃×C₁₉	semidirect
17. #3862	C₂²×C₁₉	direct (N × H)
19. C₇×C₁₉	C₂²×ΓL(1,𝔽₈)	semidirect
21. C₂×C₇²	C₂×C₃×C₁₉	semidirect
23. C₂²×C₁₉	#3862	direct (N × H)
25. C₇²	C₂²×C₃×C₁₉	semidirect
27. C₂×C₁₉	C₂×#3862	direct (N × H)
29. C₂²×C₇	C₁₉×ΓL(1,𝔽₈)	semidirect
31. C₁₉	C₂²×#3862	direct (N × H)
33. C₂×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	semidirect
36. C₇	C₂²×C₁₉×ΓL(1,𝔽₈)	semidirect
38. C₂²	C₁₉×#3862	direct (N × H)
40. C₂	C₂×C₁₉×#3862	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#3862	2
C₂²×C₇²×C₁₉	3
C₂²×C₁₉×ΓL(1,𝔽₈)	7
C₂²×#3862	19

Subgroups — C22×C19×#3862 #26014040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₉×#3862 #26014040