Subgroups — C₃⋊#26042790 #46853545

Order 34914.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19154124	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26042790	—	3	1	no	maximal, Hall
3	#19154124	D₃	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	—	3	1	no	Hall
8	C₃×C₂₃⋊C₁₁	—	23	2	no	—
9	C₂₃²	D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
10	AGL(1,𝔽₂₃)	—	69	2	no	—
11	C₂₃⋊C₁₁	—	23	2	no	—
12	D₆₉	—	23	2	no	—
13	D₆₉	—	253	2	no	—
14	C₃×C₂₃	—	11	2	no	—
15	C₃×C₂₃	AGL(1,𝔽₂₃)	1	2	yes	complemented
16	D₃×C₁₁	—	529	1	no	Hall
17	D₂₃	—	69	2	no	—
18	D₂₃	—	759	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	—	1587	1	no	Hall
23	C₁₁	—	529	1	no	Sylow
24	D₃	—	529	1	no	Hall
25	C₃	#26042790	1	1	yes	characteristic, complemented, Sylow
26	C₂	—	1587	1	no	Sylow

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