Subgroups — C₆₁×#89205 #41002008

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	C₆₁×C₇⋊C₉	—	7	2	no	maximal
3	C₇²×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×C₆₁	—	3	2	no	—
5	C₃×C₇×C₆₁	ΓL(1,𝔽₈)	1	2	yes	—
6	C₉×C₆₁	—	49	1	no	Hall
7	#89205	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₆₁	—	3	2	no	—
9	C₇×C₆₁	C₇⋊C₉	1	2	yes	complemented
10	C₃×C₆₁	#3862	1	1	yes	characteristic
11	C₃×C₇²	C₃×C₆₁	1	1	yes	characteristic
12	C₇⋊C₉	—	7	2	no	—
13	C₆₁	#89205	1	1	yes	characteristic, direct product factor, Sylow
14	C₇²	C₉×C₆₁	1	1	yes	characteristic, complemented, Sylow
15	C₃×C₇	—	3	2	no	—
16	C₃×C₇	ΓL(1,𝔽₈)×C₆₁	1	2	yes	—
17	C₉	—	49	1	no	Sylow
18	C₇	—	3	2	no	—
19	C₇	C₆₁×C₇⋊C₉	1	2	yes	complemented
20	C₃	C₆₁×#3862	1	1	yes	characteristic

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.