Subgroups — C₄×C₁₉×#3861 #26013863

Order 11172.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#3861	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×#3861	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	8	no	maximal
6	C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₂×C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
8	C₄×#3861	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
10	C₁₉×ΓL(1,𝔽₈)	—	7	8	no	—
11	C₂×#3861	C₂×C₁₉	1	1	yes	characteristic
12	C₂×C₇×C₁₉	C₂×ΓL(1,𝔽₈)	1	8	yes	—
13	C₃×C₄×C₁₉	—	49	1	no	Hall
14	C₄×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
15	#3861	C₄×C₁₉	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₁₉	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
17	C₂×C₃×C₁₉	—	49	1	no	—
18	C₂×C₇²	C₂×C₃×C₁₉	1	1	yes	characteristic
19	C₄×ΓL(1,𝔽₈)	—	7	8	no	—
20	C₄×C₁₉	#3861	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₁₉	—	49	1	no	Hall
22	C₇²	C₃×C₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
23	C₂×ΓL(1,𝔽₈)	—	7	8	no	—
24	C₂×C₁₉	C₂×#3861	1	1	yes	characteristic
25	C₄×C₇	C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
26	ΓL(1,𝔽₈)	—	7	8	no	—
27	C₁₉	C₄×#3861	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₇	C₂×C₁₉×ΓL(1,𝔽₈)	1	8	yes	—
29	C₃×C₄	—	49	1	no	Hall
30	C₇	C₄×C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
31	C₂×C₃	—	49	1	no	—
32	C₄	C₁₉×#3861	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	—	49	1	no	Sylow
34	C₂	C₂×C₁₉×#3861	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₁₉	#3861
commutator, hypocenter	C₇²	C₃×C₄×C₁₉
Frattini	C₂	C₂×C₁₉×#3861
Fitting	C₄×C₇²×C₁₉	C₃
socle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×#3861	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×#3861	C₄	direct (N × H)
6. C₇²×C₁₉	C₃×C₄	semidirect
8. C₄×#3861	C₁₉	direct (N × H)
9. C₄×C₇×C₁₉	ΓL(1,𝔽₈)	semidirect
14. C₄×C₇²	C₃×C₁₉	semidirect
15. #3861	C₄×C₁₉	direct (N × H)
16. C₇×C₁₉	C₄×ΓL(1,𝔽₈)	semidirect
20. C₄×C₁₉	#3861	direct (N × H)
22. C₇²	C₃×C₄×C₁₉	semidirect
25. C₄×C₇	C₁₉×ΓL(1,𝔽₈)	semidirect
27. C₁₉	C₄×#3861	direct (N × H)
30. C₇	C₄×C₁₉×ΓL(1,𝔽₈)	semidirect
32. C₄	C₁₉×#3861	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×#3861	2
C₄×C₇²×C₁₉	3
C₄×C₁₉×ΓL(1,𝔽₈)	7
C₄×#3861	19

Subgroups — C4×C19×#3861 #26013863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₉×#3861 #26013863