Subgroups — #37551139

Order 23226.

80 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	C₇₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15693302	—	7	3	no	maximal
5	#15693302	—	7	2	no	maximal
6	#15693302	—	7	3	no	maximal
7	#13110305	—	7	3	no	—
8	#13110305	—	7	2	no	—
9	#13110305	—	7	3	no	—
10	D₇×C₇₉	—	7	3	no	—
11	D₇×C₇₉	—	21	2	no	—
12	D₇×C₇₉	—	21	3	no	—
13	C₇×C₇₉	AGL(1,𝔽₇)	1	3	yes	complemented
14	C₇×C₇₉	AGL(1,𝔽₇)	1	2	yes	complemented
15	C₇×C₇₉	AGL(1,𝔽₇)	1	3	yes	complemented
16	C₂×C₇₉⋊C₃	—	49	1	no	Hall
17	#64424	—	79	1	no	maximal, Hall
18	C₇₉⋊C₃	—	49	1	no	Hall
19	C₂×C₇₉	—	147	1	no	Hall
20	#3861	—	79	1	no	Hall
21	C₇⋊D₇	C₇₉⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₇₉	#64424	1	1	yes	characteristic, complemented, Sylow
23	C₇²	C₂×C₇₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	AGL(1,𝔽₇)	—	553	2	no	—
25	AGL(1,𝔽₇)	—	553	3	no	—
26	AGL(1,𝔽₇)	—	553	3	no	—
27	ΓL(1,𝔽₈)	—	553	2	no	—
28	ΓL(1,𝔽₈)	—	553	3	no	—
29	ΓL(1,𝔽₈)	—	553	3	no	—
30	D₇	—	7	2	no	—
31	D₇	—	21	3	no	—
32	D₇	—	21	3	no	—
33	C₇	#15693302	1	2	yes	complemented
34	C₇	#15693302	1	3	yes	complemented
35	C₇	#15693302	1	3	yes	complemented
36	C₂×C₃	—	3871	1	no	Hall
37	C₃	—	3871	1	no	Sylow
38	C₂	—	147	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.