Subgroups — C₃₇×C₂²⋊(C₃₇⋊C₃) #30656113

Order 16428.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₇²	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₃₇⋊C₃	—	4	1	no	maximal, Hall
3	C₂×C₃₇²	—	3	1	no	—
4	C₃₇²	A₄	1	1	yes	characteristic, complemented, Sylow
5	C₂²⋊(C₃₇⋊C₃)	C₃₇	1	1	yes	maximal, characteristic, direct product factor
6	A₄×C₃₇	—	37	1	no	maximal
7	C₂²×C₃₇	—	3	12	no	—
8	C₂²×C₃₇	C₃₇⋊C₃	1	1	yes	characteristic, complemented
9	C₂²×C₃₇	C₃×C₃₇	1	1	yes	characteristic, complemented
10	C₃×C₃₇	—	148	1	no	—
11	C₃₇⋊C₃	—	4	1	no	—
12	C₂×C₃₇	—	3	36	no	—
13	C₂×C₃₇	—	3	1	no	—
14	C₂×C₃₇	—	3	1	no	—
15	C₃₇	—	3	12	no	—
16	C₃₇	A₄×C₃₇	1	1	yes	characteristic, complemented
17	C₃₇	C₂²⋊(C₃₇⋊C₃)	1	1	yes	characteristic, direct product factor
18	A₄	—	37	1	no	Hall
19	C₂²	C₃₇×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₃	—	148	1	no	Sylow
21	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃₇	C₂²⋊(C₃₇⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₃₇	C₃×C₃₇
Frattini	C₁	G
Fitting, socle	C₂²×C₃₇²	C₃
LCS	G ▷ C₂²×C₃₇
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.