Subgroups — #37551151

Order 23226.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉⋊#3862	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	#15693303	—	7	1	no	maximal
5	C₂×#13110305	—	7	1	no	maximal
6	#13110306	—	7	1	no	—
7	#13110305	—	7	1	no	—
8	C₂×C₇×C₇₉	—	21	1	no	—
9	D₇×C₇₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
10	C₇×C₇₉	—	6	1	no	—
11	C₇×C₇₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
12	C₇×C₇₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₂×C₇₉⋊C₃	—	49	1	no	Hall
14	#64422	—	79	1	no	maximal, Hall
15	C₇₉⋊C₃	—	49	1	no	Hall
16	C₂×C₇₉	—	21	1	no	Hall
17	#3862	—	79	1	no	Hall
18	C₇×D₇	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₇₉	#64422	1	1	yes	characteristic, complemented, Sylow
20	C₇²	C₂×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×ΓL(1,𝔽₈)	—	553	1	no	—
22	AGL(1,𝔽₇)	—	553	1	no	—
23	ΓL(1,𝔽₈)	—	553	1	no	—
24	ΓL(1,𝔽₈)	—	553	1	no	—
25	C₂×C₇	—	21	1	no	—
26	D₇	#13110305	1	1	yes	characteristic, complemented
27	C₇	—	6	1	no	—
28	C₇	C₂×#13110305	1	1	yes	characteristic, complemented
29	C₇	#15693303	1	1	yes	characteristic, complemented
30	C₂×C₃	—	3871	1	no	Hall
31	C₃	—	3871	1	no	Sylow
32	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.