Subgroups — C₃⋊#20293709 #35207608

Order 20646.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812216	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#20293709	—	3	1	no	maximal
3	C₃₁×D₁₁₁	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
5	#16812216	—	2	1	no	—
6	#16812216	D₃	1	1	yes	characteristic, complemented
7	C₃₁×D₃₇	—	3	1	no	Hall
8	C₃₁×C₃₇	C₃×D₃	1	1	yes	characteristic, complemented, Hall
9	C₃⋊(D₃₇⋊C₃)	—	31	1	no	maximal, Hall
10	D₃×C₃₁⋊C₃	—	37	1	no	maximal, Hall
11	C₃×C₃₇⋊C₃	—	31	1	no	Hall
12	C₃×C₃₁⋊C₃	—	37	1	no	Hall
13	D₁₁₁	C₃₁⋊C₃	1	1	yes	characteristic, complemented
14	D₃₇⋊C₃	—	93	1	no	—
15	D₃×C₃₁	—	37	1	no	—
16	C₂×C₃₁⋊C₃	—	111	1	no	—
17	C₃×C₃₇	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
18	C₃₇⋊C₃	—	31	1	no	—
19	C₃₇⋊C₃	—	62	1	no	—
20	C₃×C₃₁	D₃₇⋊C₃	1	1	yes	characteristic, complemented
21	C₃₁⋊C₃	—	37	1	no	—
22	C₃₁⋊C₃	—	74	1	no	—
23	D₃₇	—	3	1	no	Hall
24	C₂×C₃₁	—	111	1	no	Hall
25	C₃₇	D₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₃₁	C₃⋊(D₃₇⋊C₃)	1	1	yes	characteristic, complemented, Sylow
27	C₃×D₃	—	1147	1	no	Hall
28	C₃²	—	1147	1	no	Sylow
29	C₂×C₃	—	3441	1	no	—
30	D₃	—	37	1	no	—
31	C₃	—	1147	1	no	—
32	C₃	—	2294	1	no	—
33	C₃	#20293709	1	1	yes	characteristic, complemented
34	C₂	—	111	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₃₇	C₂×C₃
LCS	G ▷ C₃×C₃₁×C₃₇
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.