Subgroups — C₃×#22582217 #41002002

Order 26901.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582217	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₄₉×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#13046196	—	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	#13046196	—	7	3	no	—
7	C₃×C₆₁⋊C₃	—	49	1	no	Hall
8	C₃×C₄₉⋊C₃	—	61	1	no	maximal, Hall
9	C₇×C₆₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
10	C₃×C₆₁	C₄₉⋊C₃	1	1	yes	characteristic, complemented
11	C₆₁⋊C₃	—	49	3	no	—
12	C₃×C₄₉	C₆₁⋊C₃	1	1	yes	characteristic, complemented
13	C₄₉⋊C₃	—	61	3	no	—
14	C₃×ΓL(1,𝔽₈)	—	427	1	no	—
15	C₆₁	C₃×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₄₉	C₃×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₇	#13046196	1	1	yes	characteristic
18	ΓL(1,𝔽₈)	—	427	3	no	—
19	C₃²	—	2989	1	no	Sylow
20	C₇	C₃×#13046196	1	1	yes	characteristic
21	C₃	—	2989	3	no	—
22	C₃	#22582217	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	#22582217
commutator, cosocle, hypocenter	C₄₉×C₆₁	C₃²
Frattini	C₇	C₃×#13046196
Fitting	C₃×C₄₉×C₆₁	C₃
socle	C₃×C₇×C₆₁	ΓL(1,𝔽₈)
LCS	G ▷ C₄₉×C₆₁
UCS	C₁ ◁ C₃

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.