Subgroups — D₃₇×C₄₉⋊C₃ #24925913

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	C₄₉×D₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)×D₃₇	—	7	1	no	maximal
5	ΓL(1,𝔽₈)×C₃₇	—	7	1	no	—
6	C₇×D₃₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₂×C₄₉⋊C₃	—	37	1	no	maximal, Hall
8	C₇×C₃₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
9	C₃×D₃₇	—	49	1	no	Hall
10	C₄₉⋊C₃	D₃₇	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₃₇	—	49	1	no	Hall
12	C₂×C₄₉	—	37	1	no	Hall
13	D₃₇	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₄₉	C₃×D₃₇	1	1	yes	characteristic, complemented, Sylow
15	C₂×ΓL(1,𝔽₈)	—	259	1	no	—
16	C₃₇	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	ΓL(1,𝔽₈)	—	7	1	no	—
18	C₂×C₇	—	37	1	no	—
19	C₇	ΓL(1,𝔽₈)×D₃₇	1	1	yes	characteristic
20	C₂×C₃	—	1813	1	no	Hall
21	C₃	—	49	1	no	Sylow
22	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃₇×C₄₉	C₂×C₃
Frattini	C₇	ΓL(1,𝔽₈)×D₃₇
socle	C₇×C₃₇	C₂×ΓL(1,𝔽₈)
LCS	G ▷ C₃₇×C₄₉
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.