Subgroups — C₃×#26042788 #46853508

Order 34914.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19154121	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26042788	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	#19154121	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₂₃⋊D₂₃	C₁₁	1	1	yes	maximal, characteristic, complemented, Hall
5	C₃×C₂₃²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
6	C₃×AGL(1,𝔽₂₃)	—	23	2	no	maximal
7	C₂₃⋊D₂₃	C₃×C₁₁	1	1	yes	characteristic, complemented, Hall
8	C₃×C₂₃⋊C₁₁	—	23	2	no	—
9	C₂₃²	C₂×C₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
10	AGL(1,𝔽₂₃)	—	23	2	no	—
11	C₂₃⋊C₁₁	—	23	2	no	—
12	C₃×D₂₃	—	23	2	no	—
13	C₃×D₂₃	—	253	2	no	—
14	C₃×C₂₃	—	11	2	no	—
15	C₃×C₂₃	AGL(1,𝔽₂₃)	1	2	yes	complemented
16	C₂×C₃×C₁₁	—	529	1	no	Hall
17	D₂₃	—	23	2	no	—
18	D₂₃	—	253	2	no	—
19	C₃×C₁₁	—	529	1	no	Hall
20	C₂₃	—	11	2	no	—
21	C₂₃	C₃×AGL(1,𝔽₂₃)	1	2	yes	complemented
22	C₂×C₁₁	—	529	1	no	Hall
23	C₁₁	—	529	1	no	Sylow
24	C₂×C₃	—	529	1	no	Hall
25	C₃	#26042788	1	1	yes	characteristic, direct product factor, Sylow
26	C₂	—	529	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#26042788
commutator, cosocle, hypocenter	C₂₃²	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₂₃²	C₂×C₁₁
LCS	G ▷ C₂₃²
UCS	C₁ ◁ 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.