Subgroups — C₁₉×C₂²⋊#3861 #26014036

Order 11172.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇²×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×#3861	—	4	1	no	maximal, Hall
3	C₂×C₇²×C₁₉	—	3	1	no	—
4	C₁₉×C₂²⋊ΓL(1,𝔽₈)	—	7	8	no	maximal
5	C₇²×C₁₉	A₄	1	1	yes	characteristic, complemented, Hall
6	C₂²⋊#3861	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₇×C₁₉	ΓL(1,𝔽₈)	1	8	yes	complemented
8	C₁₉×ΓL(1,𝔽₈)	—	28	8	no	—
9	C₂×C₇×C₁₉	—	3	8	no	—
10	A₄×C₁₉	—	49	1	no	Hall
11	C₂²×C₇²	C₃×C₁₉	1	1	yes	characteristic, complemented, Hall
12	#3861	—	4	1	no	Hall
13	C₇×C₁₉	C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
14	C₂×C₇²	—	3	1	no	—
15	C₂²⋊ΓL(1,𝔽₈)	—	7	8	no	—
16	C₂²×C₁₉	#3861	1	1	yes	characteristic, complemented, Hall
17	C₃×C₁₉	—	196	1	no	Hall
18	C₇²	A₄×C₁₉	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₁₉	—	3	1	no	—
20	C₂²×C₇	C₁₉×ΓL(1,𝔽₈)	1	8	yes	complemented
21	ΓL(1,𝔽₈)	—	28	8	no	—
22	C₁₉	C₂²⋊#3861	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₇	—	3	8	no	—
24	A₄	—	49	1	no	Hall
25	C₇	C₁₉×C₂²⋊ΓL(1,𝔽₈)	1	8	yes	complemented
26	C₂²	C₁₉×#3861	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	196	1	no	Sylow
28	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₂²⋊#3861
commutator, cosocle, hypocenter	C₂²×C₇²	C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₇²×C₁₉	C₃
LCS	G ▷ C₂²×C₇²
UCS	C₁ ◁ C₁₉

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

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