Subgroups — #49089902

Order 35868.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁×#3862	C₂	1	1	yes	maximal, characteristic
2	C₇⋊(C₇⋊#6923)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₆₁×#3862	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇²×D₆₁	C₂×C₃	1	1	yes	characteristic
5	ΓL(1,𝔽₈)⋊#6923	—	7	2	no	maximal
6	C₇²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	ΓL(1,𝔽₈)×D₆₁	—	7	2	no	—
8	C₇⋊#6923	—	7	2	no	—
9	C₇⋊#6923	—	21	2	no	—
10	ΓL(1,𝔽₈)×C₆₁	—	7	2	no	—
11	C₇×D₆₁	—	3	2	no	—
12	C₇×D₆₁	AGL(1,𝔽₇)	1	2	yes	—
13	C₃×#6923	—	49	1	no	Hall
14	#10596875	—	61	1	no	maximal, Hall
15	C₇×C₆₁	—	3	2	no	—
16	C₇×C₆₁	ΓL(1,𝔽₈)⋊C₄	1	2	yes	complemented
17	C₃×D₆₁	—	49	1	no	—
18	C₂×#3862	—	61	1	no	—
19	#6923	—	49	1	no	Hall
20	C₇⋊Dic₇	—	61	1	no	Hall
21	C₃×C₆₁	—	49	1	no	Hall
22	#3862	#6923	1	1	yes	characteristic, complemented, Hall
23	D₆₁	#64425	1	1	yes	characteristic
24	C₂×C₇²	—	61	1	no	—
25	ΓL(1,𝔽₈)⋊C₄	—	427	2	no	—
26	C₆₁	#10596875	1	1	yes	characteristic, complemented, Sylow
27	C₇²	C₃×#6923	1	1	yes	characteristic, complemented, Sylow
28	C₂×ΓL(1,𝔽₈)	—	427	2	no	—
29	Dic₇	—	1281	2	no	—
30	Dic₇	—	427	2	no	—
31	ΓL(1,𝔽₈)	—	7	2	no	—
32	C₂×C₇	—	61	2	no	—
33	C₂×C₇	—	183	2	no	—
34	C₃×C₄	—	2989	1	no	Hall
35	C₇	—	3	2	no	—
36	C₇	ΓL(1,𝔽₈)⋊#6923	1	2	yes	complemented
37	C₂×C₃	—	2989	1	no	—
38	C₄	—	2989	1	no	Sylow
39	C₃	—	49	1	no	Sylow
40	C₂	—	61	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₆₁	C₃×C₄
prime radical	D₆₁×#3862	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.