Subgroups — C₂×#72218858 #72244635

Order 46080.

At least 8571 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has at least 8571 conjugacy classes of subgroups — too many to draw. Only its 23 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#72218849	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#72218850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#72218848	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#72209614	C₂²	1	1	yes	characteristic, complemented
5	#72218858	C₂	1	4	yes	maximal, direct product factor
6	#72218850	C₂²	1	2	yes	complemented
7	#72218849	C₂²	1	2	yes	complemented
8	#72218848	C₂²	1	2	yes	complemented
9	#72209614	C₂³	1	1	yes	characteristic, complemented
10	C₂⁶	S₆	1	1	yes	characteristic, complemented
11	C₂⁵	C₂×S₆	1	1	yes	characteristic
12	C₂⁵	C₂×S₆	1	2	yes	complemented
13	C₂⁴	C₂²×S₆	1	1	yes	characteristic
14	C₂	#72218858	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	#72218858
commutator, cosocle, hypocenter	#72209614	C₂³
Frattini	C₂⁴	C₂²×S₆
Fitting	C₂⁶	S₆
socle	C₂⁵	C₂×S₆
LCS	G ▷ #72209614
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.