Subgroups — C₇×C₆₁×C₇⋊C₉ #41002011

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	C₇	1	1	yes	maximal, characteristic, direct product factor
3	C₇×C₉×C₆₁	—	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	C₃×C₇	1	1	yes	characteristic
8	C₉×C₆₁	—	7	1	no	Hall
9	C₇×C₇⋊C₉	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₆₁	—	3	2	no	—
11	C₇×C₆₁	C₇⋊C₉	1	1	yes	characteristic, direct product factor
12	C₇×C₆₁	C₇×C₉	1	1	yes	characteristic, complemented
13	C₃×C₆₁	C₇×ΓL(1,𝔽₈)	1	1	yes	characteristic
14	C₃×C₇²	C₃×C₆₁	1	1	yes	characteristic
15	C₇×C₉	—	7	1	no	—
16	C₇⋊C₉	C₇×C₆₁	1	1	yes	characteristic, direct product factor
17	C₆₁	C₇×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₇²	C₉×C₆₁	1	1	yes	characteristic, complemented, Sylow
19	C₃×C₇	—	3	2	no	—
20	C₃×C₇	ΓL(1,𝔽₈)×C₆₁	1	1	yes	characteristic
21	C₃×C₇	C₃×C₇×C₆₁	1	1	yes	characteristic
22	C₉	—	7	1	no	Sylow
23	C₇	—	3	2	no	—
24	C₇	C₇×C₉×C₆₁	1	1	yes	characteristic, complemented
25	C₇	C₆₁×C₇⋊C₉	1	1	yes	characteristic, direct product factor
26	C₃	C₇×ΓL(1,𝔽₈)×C₆₁	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.