Subgroups — #44567124

Order 32193.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₉×C₇₃	C₃	1	1	yes	maximal, characteristic
2	#17987160	—	7	1	no	maximal
3	C₄₉×C₇₃	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₇₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
5	#10620321	—	49	1	no	Hall
6	C₇×C₇₃	C₇⋊C₉	1	1	yes	characteristic
7	C₄₉⋊C₉	—	73	1	no	maximal, Hall
8	C₃×C₇₃	C₄₉⋊C₃	1	1	yes	characteristic
9	C₃×C₄₉	C₇₃⋊C₃	1	1	yes	characteristic
10	C₇₃	C₄₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
11	C₇⋊C₉	—	511	1	no	—
12	C₄₉	#10620321	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₇	#13095276	1	1	yes	characteristic
14	C₉	—	3577	1	no	Sylow
15	C₇	#17987160	1	1	yes	characteristic
16	C₃	#24924355	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.