Subgroups — #16838457

Order 3822.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14274262	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₉₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#10587723	—	7	1	no	maximal
5	#10587717	—	7	1	no	maximal
6	#64423	—	13	1	no	maximal, Hall
7	#63271	—	7	1	no	—
8	#63271	—	7	1	no	—
9	#63271	—	14	3	no	—
10	D₉₁	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₇×D₁₃	—	7	1	no	—
12	#3861	—	13	1	no	Hall
13	C₇×D₇	—	13	1	no	Hall
14	C₇×C₁₃	—	2	3	no	—
15	C₇×C₁₃	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
16	C₇×C₁₃	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
17	D₁₃⋊C₃	—	49	1	no	Hall
18	C₇²	D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₂×ΓL(1,𝔽₈)	—	91	1	no	—
20	AGL(1,𝔽₇)	—	91	1	no	—
21	C₁₃⋊C₃	—	49	1	no	Hall
22	D₁₃	—	7	1	no	Hall
23	ΓL(1,𝔽₈)	—	91	1	no	—
24	ΓL(1,𝔽₈)	—	91	1	no	—
25	ΓL(1,𝔽₈)	—	182	3	no	—
26	C₂×C₇	—	91	1	no	—
27	D₇	—	13	1	no	—
28	C₁₃	#64423	1	1	yes	characteristic, complemented, Sylow
29	C₇	—	2	3	no	—
30	C₇	#10587717	1	1	yes	characteristic, complemented
31	C₇	#10587723	1	1	yes	characteristic, complemented
32	C₂×C₃	—	637	1	no	Hall
33	C₃	—	637	1	no	Sylow
34	C₂	—	91	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇²×C₁₃	C₂×C₃
LCS	G ▷ C₇²×C₁₃
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.