Subgroups — C₆₁⋊#89205 #41002007

Order 26901.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₆₁	C₃	1	1	yes	maximal, characteristic
2	#16838636	—	7	1	no	maximal
3	#16838635	—	7	1	no	maximal
4	C₇²×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇×C₆₁	—	3	2	no	—
6	C₃×C₇×C₆₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₃×C₇×C₆₁	ΓL(1,𝔽₈)	1	1	yes	characteristic
8	C₆₁⋊C₉	—	49	1	no	Hall
9	#89205	—	61	1	no	maximal, Hall
10	C₇×C₆₁	—	3	2	no	—
11	C₇×C₆₁	C₇⋊C₉	1	1	yes	characteristic, complemented
12	C₇×C₆₁	C₇⋊C₉	1	1	yes	characteristic, complemented
13	C₃×C₆₁	#3862	1	1	yes	characteristic
14	C₃×C₇²	C₆₁⋊C₃	1	1	yes	characteristic
15	C₇⋊C₉	—	427	1	no	—
16	C₇⋊C₉	—	427	1	no	—
17	C₆₁	#89205	1	1	yes	characteristic, complemented, Sylow
18	C₇²	C₆₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₇	—	3	2	no	—
20	C₃×C₇	#13046196	1	1	yes	characteristic
21	C₃×C₇	#13046197	1	1	yes	characteristic
22	C₉	—	2989	1	no	Sylow
23	C₇	—	3	2	no	—
24	C₇	#16838635	1	1	yes	characteristic, complemented
25	C₇	#16838636	1	1	yes	characteristic, complemented
26	C₃	C₆₁⋊#3862	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₆₁⋊#3862
commutator, hypocenter	C₇²×C₆₁	C₉
Fitting, socle, prime radical, cosocle	C₃×C₇²×C₆₁	C₃
LCS	G ▷ C₇²×C₆₁
UCS	C₁ ◁ C₃

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.