Subgroups — #44544252

Order 31974.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30630501	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₃⋊D₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₃²	C₂×C₃	1	1	yes	characteristic, complemented, Sylow
4	D₇₃⋊C₃	—	73	2	no	maximal
5	C₇₃⋊C₃	—	73	2	no	—
6	D₇₃	—	73	2	no	—
7	D₇₃	—	219	24	no	—
8	C₇₃	—	3	24	no	—
9	C₇₃	D₇₃⋊C₃	1	2	yes	complemented
10	C₂×C₃	—	5329	1	no	Hall
11	C₃	—	5329	1	no	Sylow
12	C₂	—	5329	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇₃²	C₂×C₃
LCS	G ▷ C₇₃²
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.