Subgroups — #49089859

Order 35868.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#31822467	C₂	1	1	yes	maximal, characteristic
2	C₇²×#6923	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	#22582225	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₆₁	C₂×C₃	1	1	yes	characteristic
5	#19103986	—	7	8	no	maximal
6	C₇²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	#14579420	—	7	8	no	—
8	C₇×#6923	ΓL(1,𝔽₈)	1	8	yes	complemented
9	#13046197	—	7	8	no	—
10	C₇×D₆₁	C₂×ΓL(1,𝔽₈)	1	8	yes	—
11	#6923⋊C₃	—	49	1	no	Hall
12	C₄×#3861	—	61	1	no	maximal, Hall
13	C₇×C₆₁	C₄×ΓL(1,𝔽₈)	1	8	yes	complemented
14	D₆₁⋊C₃	—	49	1	no	—
15	C₂×#3861	—	61	1	no	—
16	#6923	#3861	1	1	yes	characteristic, complemented, Hall
17	C₄×C₇²	—	61	1	no	Hall
18	C₆₁⋊C₃	—	49	1	no	Hall
19	#3861	—	61	1	no	Hall
20	D₆₁	C₂×#3861	1	1	yes	characteristic
21	C₂×C₇²	—	61	1	no	—
22	C₄×ΓL(1,𝔽₈)	—	427	8	no	—
23	C₆₁	C₄×#3861	1	1	yes	characteristic, complemented, Sylow
24	C₇²	#6923⋊C₃	1	1	yes	characteristic, complemented, Sylow
25	C₂×ΓL(1,𝔽₈)	—	427	8	no	—
26	C₄×C₇	—	61	8	no	—
27	ΓL(1,𝔽₈)	—	427	8	no	—
28	C₂×C₇	—	61	8	no	—
29	C₃×C₄	—	2989	1	no	Hall
30	C₇	#19103986	1	8	yes	complemented
31	C₂×C₃	—	2989	1	no	—
32	C₄	—	61	1	no	Sylow
33	C₃	—	2989	1	no	Sylow
34	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₆₁	C₃×C₄
prime radical	#31822467	C₂
cosocle	C₇²×D₆₁	C₂×C₃
LCS	G ▷ C₇²×C₆₁
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.