Subgroups — C₃⋊#26015425 #46801413

Order 34038.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#19150898	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#26015425	—	3	1	no	maximal
3	C₆₁×D₉₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented
5	#19150898	—	2	1	no	—
6	#19150898	D₃	1	1	yes	characteristic, complemented
7	C₆₁×D₃₁	—	3	1	no	Hall
8	C₃₁×C₆₁	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	D₃×C₆₁⋊C₃	—	31	1	no	maximal, Hall
10	C₃⋊(D₃₁⋊C₃)	—	61	1	no	maximal, Hall
11	C₃×C₆₁⋊C₃	—	31	1	no	Hall
12	D₃×C₆₁	—	31	1	no	—
13	C₂×C₆₁⋊C₃	—	93	1	no	—
14	C₃×C₃₁⋊C₃	—	61	1	no	Hall
15	D₉₃	C₆₁⋊C₃	1	1	yes	characteristic, complemented
16	D₃₁⋊C₃	—	183	1	no	—
17	C₃×C₆₁	D₃₁⋊C₃	1	1	yes	characteristic, complemented
18	C₆₁⋊C₃	—	31	1	no	—
19	C₆₁⋊C₃	—	62	1	no	—
20	C₂×C₆₁	—	93	1	no	Hall
21	C₃×C₃₁	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented
22	C₃₁⋊C₃	—	61	1	no	—
23	C₃₁⋊C₃	—	122	1	no	—
24	D₃₁	—	3	1	no	Hall
25	C₆₁	C₃⋊(D₃₁⋊C₃)	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	D₃×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1891	1	no	Hall
28	C₃²	—	1891	1	no	Sylow
29	C₂×C₃	—	5673	1	no	—
30	D₃	—	31	1	no	—
31	C₃	—	1891	1	no	—
32	C₃	—	3782	1	no	—
33	C₃	#26015425	1	1	yes	characteristic, complemented
34	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₆₁	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₆₁
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.