Subgroups — C₃⋊#26042798 #46853539

Order 34914.

34 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	#26042798	—	3	1	no	maximal, Hall
3	#19154121	D₃	1	1	yes	characteristic, complemented, Hall
4	C₂₃×D₆₉	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	1	no	maximal
7	D₃×C₂₃⋊C₁₁	—	23	1	no	maximal
8	C₂₃×D₂₃	—	3	1	no	Hall
9	C₃×C₂₃⋊C₁₁	—	23	1	no	—
10	C₃×C₂₃⋊C₁₁	—	23	1	no	—
11	C₂₃²	D₃×C₁₁	1	1	yes	characteristic, complemented, Sylow
12	C₂×C₂₃⋊C₁₁	—	69	1	no	—
13	AGL(1,𝔽₂₃)	—	69	1	no	—
14	C₂₃⋊C₁₁	—	23	1	no	—
15	C₂₃⋊C₁₁	—	23	1	no	—
16	D₆₉	C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
17	D₃×C₂₃	—	23	1	no	—
18	C₃×C₂₃	—	22	1	no	—
19	C₃×C₂₃	AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
20	C₃×C₂₃	C₂×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
21	D₃×C₁₁	—	529	1	no	Hall
22	C₂×C₂₃	—	69	1	no	—
23	D₂₃	—	3	1	no	—
24	C₃×C₁₁	—	529	1	no	Hall
25	C₂₃	—	22	1	no	—
26	C₂₃	D₃×C₂₃⋊C₁₁	1	1	yes	characteristic, complemented
27	C₂₃	C₃⋊AGL(1,𝔽₂₃)	1	1	yes	characteristic, complemented
28	C₂×C₁₁	—	1587	1	no	Hall
29	C₁₁	—	529	1	no	Sylow
30	D₃	—	23	1	no	Hall
31	C₃	#26042798	1	1	yes	characteristic, complemented, Sylow
32	C₂	—	69	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.