Subgroups — #41001998

Order 26901.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₆₁	C₃	1	1	yes	maximal, characteristic
2	#16838635	—	7	1	no	maximal
3	C₄₉×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₆₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	C₆₁⋊C₉	—	49	1	no	Hall
6	C₄₉⋊C₉	—	61	1	no	maximal, Hall
7	C₇×C₆₁	C₇⋊C₉	1	1	yes	characteristic
8	C₃×C₆₁	C₄₉⋊C₃	1	1	yes	characteristic
9	C₃×C₄₉	C₆₁⋊C₃	1	1	yes	characteristic
10	C₇⋊C₉	—	427	1	no	—
11	C₆₁	C₄₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
12	C₄₉	C₆₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₇	#13046196	1	1	yes	characteristic
14	C₉	—	2989	1	no	Sylow
15	C₇	#16838635	1	1	yes	characteristic
16	C₃	#22582217	1	1	yes	characteristic

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.