Subgroups — C₄₉⋊C₃×C₆₁⋊C₃ #41002001

Order 26901.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582218	C₃	1	1	yes	maximal, characteristic, complemented
2	#22582217	C₃	1	1	yes	maximal, characteristic, complemented
3	C₄₉×C₆₁⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₆₁×C₄₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	ΓL(1,𝔽₈)×C₆₁⋊C₃	—	7	1	no	maximal
6	C₄₉×C₆₁	C₃²	1	1	yes	characteristic, complemented, Hall
7	#13046197	—	7	1	no	—
8	#13046196	—	7	1	no	—
9	C₇×C₆₁⋊C₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
10	ΓL(1,𝔽₈)×C₆₁	—	7	1	no	—
11	C₃×C₆₁⋊C₃	—	49	1	no	Hall
12	C₃×C₄₉⋊C₃	—	61	1	no	maximal, Hall
13	C₇×C₆₁	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₆₁	—	49	1	no	—
15	C₆₁⋊C₃	—	49	1	no	—
16	C₆₁⋊C₃	—	49	1	no	—
17	C₆₁⋊C₃	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor
18	C₃×C₄₉	—	61	1	no	—
19	C₄₉⋊C₃	—	61	1	no	—
20	C₄₉⋊C₃	—	61	1	no	—
21	C₄₉⋊C₃	C₆₁⋊C₃	1	1	yes	characteristic, direct product factor
22	C₃×ΓL(1,𝔽₈)	—	427	1	no	—
23	C₆₁	C₃×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₄₉	C₃×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₇	—	61	1	no	—
26	ΓL(1,𝔽₈)	—	7	1	no	—
27	ΓL(1,𝔽₈)	—	427	1	no	—
28	ΓL(1,𝔽₈)	—	427	1	no	—
29	C₃²	—	2989	1	no	Sylow
30	C₇	ΓL(1,𝔽₈)×C₆₁⋊C₃	1	1	yes	characteristic
31	C₃	—	49	1	no	—
32	C₃	—	61	1	no	—
33	C₃	—	2989	1	no	—
34	C₃	—	2989	1	no	—

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

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.