Subgroups — #37551145

Order 23226.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042478	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15693302	—	7	1	no	maximal
5	C₂×#13110305	—	7	1	no	maximal
6	#13110305	—	7	1	no	—
7	#13110305	—	7	1	no	—
8	#13110305	—	14	3	no	—
9	C₂×C₇×C₇₉	—	21	1	no	—
10	D₇×C₇₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₇×C₇₉	—	2	3	no	—
12	C₇×C₇₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
13	C₇×C₇₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
14	C₂×C₇₉⋊C₃	—	49	1	no	Hall
15	#64423	—	79	1	no	maximal, Hall
16	C₇₉⋊C₃	—	49	1	no	Hall
17	C₂×C₇₉	—	21	1	no	Hall
18	#3861	—	79	1	no	Hall
19	C₇×D₇	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₇₉	#64423	1	1	yes	characteristic, complemented, Sylow
21	C₇²	C₂×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₂×ΓL(1,𝔽₈)	—	553	1	no	—
23	AGL(1,𝔽₇)	—	553	1	no	—
24	ΓL(1,𝔽₈)	—	553	1	no	—
25	ΓL(1,𝔽₈)	—	553	1	no	—
26	ΓL(1,𝔽₈)	—	1106	3	no	—
27	C₂×C₇	—	21	1	no	—
28	D₇	#13110305	1	1	yes	characteristic, complemented
29	C₇	—	2	3	no	—
30	C₇	C₂×#13110305	1	1	yes	characteristic, complemented
31	C₇	#15693302	1	1	yes	characteristic, complemented
32	C₂×C₃	—	3871	1	no	Hall
33	C₃	—	3871	1	no	Sylow
34	C₂	—	21	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₇₉	C₂×C₃
LCS	G ▷ C₇²×C₇₉
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.