Subgroups — C₃₇×C₃⋊D₉ #14522012

Order 1998.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊D₃×C₃₇	—	3	1	no	maximal
3	D₉×C₃₇	—	3	3	no	maximal
4	C₃²×C₃₇	D₃	1	1	yes	characteristic
5	C₉×C₃₇	D₃	1	3	yes	complemented
6	D₃×C₃₇	—	9	3	no	—
7	D₃×C₃₇	—	9	1	no	—
8	C₃×C₃₇	D₉	1	3	yes	complemented
9	C₃×C₃₇	C₃⋊D₃	1	1	yes	characteristic
10	C₂×C₃₇	—	27	1	no	Hall
11	C₃⋊D₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃₇	C₃⋊D₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Sylow
14	C₃⋊D₃	—	3	1	no	—
15	D₉	—	3	3	no	—
16	C₃²	D₃×C₃₇	1	1	yes	characteristic
17	C₉	D₃×C₃₇	1	3	yes	complemented
18	D₃	—	9	3	no	—
19	D₃	—	9	1	no	—
20	C₃	D₉×C₃₇	1	3	yes	complemented
21	C₃	C₃⋊D₃×C₃₇	1	1	yes	characteristic
22	C₂	—	27	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	C₃⋊D₉
commutator, cosocle, hypocenter	C₃×C₉	C₂×C₃₇
Frattini	C₃	C₃⋊D₃×C₃₇
Fitting	C₃×C₉×C₃₇	C₂
socle	C₃²×C₃₇	D₃
LCS	G ▷ C₃×C₉
UCS	C₁ ◁ C₃₇

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.