Subgroups — C₂×C₃×#19154120 #46853549

Order 34914.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19154120	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#19154120	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	#19154120	C₂×C₃	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₂₃²	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₂₃⋊C₁₁	—	23	24	no	maximal
7	C₂×C₂₃²	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×C₂₃⋊C₁₁	—	23	24	no	—
9	C₂₃²	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
10	C₂×C₂₃⋊C₁₁	—	23	24	no	—
11	C₂₃⋊C₁₁	—	23	24	no	—
12	C₂×C₃×C₂₃	C₂₃⋊C₁₁	1	24	yes	complemented
13	C₃×C₂₃	C₂×C₂₃⋊C₁₁	1	24	yes	complemented
14	C₂×C₃×C₁₁	—	529	1	no	Hall
15	C₂×C₂₃	C₃×C₂₃⋊C₁₁	1	24	yes	complemented
16	C₃×C₁₁	—	529	1	no	Hall
17	C₂₃	C₂×C₃×C₂₃⋊C₁₁	1	24	yes	complemented
18	C₂×C₁₁	—	529	1	no	Hall
19	C₁₁	—	529	1	no	Sylow
20	C₂×C₃	#19154120	1	1	yes	characteristic, direct product factor, Hall
21	C₃	C₂×#19154120	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₃×#19154120	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#19154120
commutator, cosocle, hypocenter	C₂₃²	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₂₃²	C₁₁
LCS	G ▷ C₂₃²
UCS	C₁ ◁ C₂×C₃

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.