Subgroups — C₄₉⋊C₃×D₁₁₃ #45684792

Order 33222.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁₃×C₄₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₉×D₁₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₉×C₁₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	ΓL(1,𝔽₈)×D₁₁₃	—	7	1	no	maximal
5	ΓL(1,𝔽₈)×C₁₁₃	—	7	1	no	—
6	C₇×D₁₁₃	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₇×C₁₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
8	C₃×D₁₁₃	—	49	1	no	Hall
9	C₃×C₁₁₃	—	49	1	no	Hall
10	C₂×C₄₉⋊C₃	—	113	1	no	maximal, Hall
11	D₁₁₃	C₄₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
12	C₄₉⋊C₃	D₁₁₃	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁₃	C₂×C₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₄₉	—	113	1	no	Hall
15	C₄₉	C₃×D₁₁₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×ΓL(1,𝔽₈)	—	791	1	no	—
17	ΓL(1,𝔽₈)	—	7	1	no	—
18	C₂×C₇	—	113	1	no	—
19	C₇	ΓL(1,𝔽₈)×D₁₁₃	1	1	yes	characteristic
20	C₂×C₃	—	5537	1	no	Hall
21	C₃	—	49	1	no	Sylow
22	C₂	—	113	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₄₉×C₁₁₃	C₂×C₃
Frattini	C₇	ΓL(1,𝔽₈)×D₁₁₃
socle	C₇×C₁₁₃	C₂×ΓL(1,𝔽₈)
LCS	G ▷ C₄₉×C₁₁₃
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.