Subgroups — #37551134

Order 23226.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042479	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₇₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15693299	—	7	8	no	maximal
5	#13110306	—	7	8	no	—
6	C₇×D₇₉	ΓL(1,𝔽₈)	1	8	yes	complemented
7	C₇×C₇₉	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
8	D₇₉⋊C₃	—	49	1	no	Hall
9	C₂×#3861	—	79	1	no	maximal, Hall
10	C₇₉⋊C₃	—	49	1	no	Hall
11	D₇₉	#3861	1	1	yes	characteristic, complemented, Hall
12	#3861	—	79	1	no	Hall
13	C₂×C₇²	—	237	1	no	Hall
14	C₇₉	C₂×#3861	1	1	yes	characteristic, complemented, Sylow
15	C₇²	D₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
16	C₂×ΓL(1,𝔽₈)	—	553	8	no	—
17	ΓL(1,𝔽₈)	—	553	8	no	—
18	C₂×C₇	—	237	8	no	—
19	C₇	#15693299	1	8	yes	complemented
20	C₂×C₃	—	3871	1	no	Hall
21	C₃	—	3871	1	no	Sylow
22	C₂	—	237	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.