Subgroups — C₃₇×D₄₉⋊C₃ #24925916

Order 10878.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₄₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃₇×AGL(1,𝔽₇)	—	7	1	no	maximal
5	ΓL(1,𝔽₈)×C₃₇	—	7	1	no	—
6	D₇×C₃₇	—	7	1	no	—
7	D₄₉⋊C₃	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic
9	C₂×C₃×C₃₇	—	49	1	no	Hall
10	C₄₉⋊C₃	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
11	C₃×C₃₇	—	49	1	no	Hall
12	D₄₉	C₃×C₃₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₃₇	—	49	1	no	Hall
14	C₄₉	C₂×C₃×C₃₇	1	1	yes	characteristic, complemented, Sylow
15	AGL(1,𝔽₇)	—	7	1	no	—
16	C₃₇	D₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
17	ΓL(1,𝔽₈)	—	7	1	no	—
18	D₇	—	7	1	no	—
19	C₇	C₃₇×AGL(1,𝔽₇)	1	1	yes	characteristic
20	C₂×C₃	—	49	1	no	Hall
21	C₃	—	49	1	no	Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	D₄₉⋊C₃
commutator, cosocle, hypocenter	C₄₉	C₂×C₃×C₃₇
Frattini	C₇	C₃₇×AGL(1,𝔽₇)
Fitting	C₃₇×C₄₉	C₂×C₃
socle	C₇×C₃₇	AGL(1,𝔽₇)
LCS	G ▷ C₄₉
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.