Subgroups — C₃×C₆₁×C₄₉⋊C₃ #41002004

Order 26901.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₄₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₄₉×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×ΓL(1,𝔽₈)×C₆₁	—	7	1	no	maximal
4	C₄₉×C₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₆₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
6	ΓL(1,𝔽₈)×C₆₁	—	7	3	no	—
7	C₃²×C₆₁	—	49	1	no	Hall
8	C₃×C₄₉⋊C₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₇×C₆₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
10	C₃×C₆₁	—	49	3	no	—
11	C₃×C₆₁	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
12	C₃×C₄₉	C₃×C₆₁	1	1	yes	characteristic, complemented
13	C₄₉⋊C₃	C₃×C₆₁	1	3	yes	direct product factor
14	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
15	C₆₁	C₃×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₄₉	C₃²×C₆₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₇	ΓL(1,𝔽₈)×C₆₁	1	1	yes	characteristic
18	ΓL(1,𝔽₈)	—	7	3	no	—
19	C₃²	—	49	1	no	Sylow
20	C₇	C₃×ΓL(1,𝔽₈)×C₆₁	1	1	yes	characteristic
21	C₃	—	49	3	no	—
22	C₃	C₆₁×C₄₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₆₁	C₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₃²×C₆₁
Frattini	C₇	C₃×ΓL(1,𝔽₈)×C₆₁
Fitting	C₃×C₄₉×C₆₁	C₃
socle	C₃×C₇×C₆₁	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₃×C₆₁

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.