Subgroups — #24925921

Order 10878.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19129580	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₈₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₃₇×C₄₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#13095538	—	7	1	no	maximal
5	#11715912	—	7	1	no	—
6	D₂₅₉	—	7	1	no	—
7	D₄₉⋊C₃	—	37	1	no	maximal, Hall
8	C₇×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic
9	D₃₇⋊C₃	—	49	1	no	Hall
10	C₄₉⋊C₃	—	37	1	no	Hall
11	C₃₇⋊C₃	—	49	1	no	Hall
12	D₄₉	—	37	1	no	Hall
13	D₃₇	—	49	1	no	Hall
14	C₄₉	D₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	AGL(1,𝔽₇)	—	259	1	no	—
16	C₃₇	D₄₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	ΓL(1,𝔽₈)	—	259	1	no	—
18	D₇	—	259	1	no	—
19	C₇	#13095538	1	1	yes	characteristic
20	C₂×C₃	—	1813	1	no	Hall
21	C₃	—	1813	1	no	Sylow
22	C₂	—	1813	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃₇×C₄₉	C₂×C₃
Frattini	C₇	#13095538
socle	C₇×C₃₇	AGL(1,𝔽₇)
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.