Subgroups — C₂×#30630501 #44544255

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, direct product factor, Hall
2	C₂×C₇₃²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇₃²	C₂×C₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₇₃⋊C₃	—	73	2	no	maximal
5	C₇₃⋊C₃	—	73	2	no	—
6	C₂×C₇₃	—	3	24	no	—
7	C₂×C₇₃	C₇₃⋊C₃	1	2	yes	complemented
8	C₇₃	—	3	24	no	—
9	C₇₃	C₂×C₇₃⋊C₃	1	2	yes	complemented
10	C₂×C₃	—	5329	1	no	Hall
11	C₃	—	5329	1	no	Sylow
12	C₂	#30630501	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	#30630501
commutator, cosocle, hypocenter	C₇₃²	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇₃²	C₃
LCS	G ▷ C₇₃²
UCS	C₁ ◁ C₂

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.