Subgroups — C₁₁×C₁₃×C₄₉⋊C₃ #35230815

Order 21021.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×C₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×C₁₃×ΓL(1,𝔽₈)	—	7	1	no	maximal
3	C₁₃×C₄₉⋊C₃	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₁×C₄₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₇×C₁₁×C₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	C₁₃×C₄₉	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₁₁×C₄₉	C₃×C₁₃	1	1	yes	characteristic, complemented, Hall
8	C₃×C₁₁×C₁₃	—	49	1	no	Hall
9	C₁₃×ΓL(1,𝔽₈)	—	7	1	no	—
10	C₁₁×ΓL(1,𝔽₈)	—	7	1	no	—
11	C₄₉⋊C₃	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₁₁×C₁₃	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
13	C₇×C₁₃	C₁₁×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₇×C₁₁	C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₄₉	C₃×C₁₁×C₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₁₃	—	49	1	no	Hall
17	C₃×C₁₁	—	49	1	no	Hall
18	ΓL(1,𝔽₈)	—	7	1	no	—
19	C₁₃	C₁₁×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
20	C₁₁	C₁₃×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
21	C₇	C₁₁×C₁₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₃	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₃	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₃×C₁₁×C₁₃
Frattini	C₇	C₁₁×C₁₃×ΓL(1,𝔽₈)
Fitting	C₁₁×C₁₃×C₄₉	C₃
socle	C₇×C₁₁×C₁₃	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₁₁×C₁₃

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.