Subgroups — C₄×C₁₉×#3862 #26013866

Order 11172.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#3862	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×#3862	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	maximal
6	C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
8	C₄×#3862	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₁₉	—	3	2	no	—
10	C₄×C₇×C₁₉	ΓL(1,𝔽₈)	1	2	yes	complemented
11	C₁₉×ΓL(1,𝔽₈)	—	7	2	no	—
12	C₂×#3862	C₂×C₁₉	1	1	yes	characteristic
13	C₂×C₇×C₁₉	—	3	2	no	—
14	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	2	yes	—
15	C₃×C₄×C₁₉	—	49	1	no	Hall
16	C₄×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
17	#3862	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₇×C₁₉	—	3	2	no	—
19	C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	2	yes	complemented
20	C₂×C₃×C₁₉	—	49	1	no	—
21	C₂×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
22	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
23	C₄×C₁₉	#3862	1	1	yes	characteristic, direct product factor, Hall
24	C₃×C₁₉	—	49	1	no	Hall
25	C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
26	C₂×ΓL(1,𝔽₈)	—	7	2	no	—
27	C₂×C₁₉	C₂×#3862	1	1	yes	characteristic
28	C₄×C₇	—	3	2	no	—
29	C₄×C₇	C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
30	ΓL(1,𝔽₈)	—	7	2	no	—
31	C₁₉	C₄×#3862	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₇	—	3	2	no	—
33	C₂×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	2	yes	—
34	C₃×C₄	—	49	1	no	Hall
35	C₇	—	3	2	no	—
36	C₇	C₄×C₁₉×ΓL(1,𝔽₈)	1	2	yes	complemented
37	C₂×C₃	—	49	1	no	—
38	C₄	C₁₉×#3862	1	1	yes	characteristic, direct product factor, Sylow
39	C₃	—	49	1	no	Sylow
40	C₂	C₂×C₁₉×#3862	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₉	#3862
commutator, hypocenter	C₇²	C₃×C₄×C₁₉
Frattini	C₂	C₂×C₁₉×#3862
Fitting	C₄×C₇²×C₁₉	C₃
socle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×#3862	C₂
cosocle	C₂×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₄×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₄×C₇²×C₁₉	C₃	semidirect
3. C₁₉×#3862	C₄	direct (N × H)
6. C₇²×C₁₉	C₃×C₄	semidirect
8. C₄×#3862	C₁₉	direct (N × H)
10. C₄×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
16. C₄×C₇²	C₃×C₁₉	semidirect
17. #3862	C₄×C₁₉	direct (N × H)
19. C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
23. C₄×C₁₉	#3862	direct (N × H)
25. C₇²	C₃×C₄×C₁₉	semidirect
29. C₄×C₇	C₁₉×ΓL(1,𝔽₈)	semidirect
31. C₁₉	C₄×#3862	direct (N × H)
36. C₇	C₄×C₁₉×ΓL(1,𝔽₈)	semidirect
38. C₄	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
C₄×C₇²×C₁₉	3
C₄×C₁₉×ΓL(1,𝔽₈)	7
C₄×#3862	19

Subgroups — C4×C19×#3862 #26013866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#3862 #26013866