Subgroups — 3₋¹⁺²⋊D₃₇ #14522011

Order 1998.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	3₋¹⁺²×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₁₁	—	3	1	no	maximal
3	D₃₃₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₃₇	D₃	1	1	yes	characteristic
5	C₉×C₃₇	—	2	1	no	—
6	C₉×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
7	D₁₁₁	—	3	1	no	—
8	C₃×D₃₇	—	9	1	no	—
9	C₃×C₃₇	—	3	1	no	—
10	C₃×C₃₇	C₃×D₃	1	1	yes	characteristic
11	D₃₇	—	9	1	no	Hall
12	AGL(1,ℤ/9)	—	37	1	no	maximal, Hall
13	C₃₇	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented, Sylow
14	3₋¹⁺²	D₃₇	1	1	yes	characteristic, complemented, Sylow
15	C₃×D₃	—	111	1	no	—
16	D₉	—	37	1	no	—
17	C₃²	D₁₁₁	1	1	yes	characteristic
18	C₉	—	2	1	no	—
19	C₉	C₃×D₃₇	1	1	yes	characteristic, complemented
20	C₂×C₃	—	333	1	no	—
21	D₃	—	111	1	no	—
22	C₃	—	3	1	no	—
23	C₃	C₃×D₁₁₁	1	1	yes	characteristic
24	C₂	—	333	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₉×C₃₇	C₂×C₃
Frattini	C₃	C₃×D₁₁₁
Fitting	3₋¹⁺²×C₃₇	C₂
socle	C₃×C₃₇	C₃×D₃
LCS	G ▷ C₉×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.