Subgroups — #23780573

Order 10374.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19104440	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#13093366	—	7	1	no	maximal, Hall
5	#11716321	—	13	1	no	maximal, Hall
6	#10625202	—	7	1	no	Hall
7	#10587716	—	19	1	no	maximal, Hall
8	D₂₄₇	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
9	#87704	—	13	1	no	Hall
10	#63270	—	19	1	no	Hall
11	C₇×D₁₉	—	13	1	no	Hall
12	C₁₃×C₁₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
13	C₇×D₁₃	—	19	1	no	Hall
14	C₇×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
15	D₁₉⋊C₃	—	91	1	no	Hall
16	C₇×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
17	D₁₃⋊C₃	—	133	1	no	Hall
18	C₁₉⋊C₃	—	91	1	no	Hall
19	C₂×ΓL(1,𝔽₈)	—	247	1	no	Hall
20	C₁₃⋊C₃	—	133	1	no	Hall
21	D₁₉	—	13	1	no	Hall
22	D₁₃	—	19	1	no	Hall
23	ΓL(1,𝔽₈)	—	247	1	no	Hall
24	C₁₉	#10587716	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₇	—	247	1	no	Hall
26	C₁₃	#11716321	1	1	yes	characteristic, complemented, Sylow
27	C₇	#13093366	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	1729	1	no	Hall
29	C₃	—	1729	1	no	Sylow
30	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₃×C₁₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.