Subgroups — #13133578

Order 1701.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
2	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃	1	4	yes	maximal
3	(C₇⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
4	#6897	—	7	1	no	maximal, Sylow
5	C₃²×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
6	C₃×C₇×C₉	C₃²	1	4	yes	—
7	C₃×C₇⋊C₉	C₃²	1	8	yes	—
8	C₉⋊C₉	—	7	8	no	—
9	C₃²⋊C₉	—	7	4	no	—
10	C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
11	C₃²×C₇	C₃³	1	1	yes	characteristic
12	C₃×ΓL(1,𝔽₈)	—	3	4	no	—
13	C₇×C₉	—	3	4	no	—
14	C₇⋊C₉	—	3	8	no	—
15	C₃³	—	7	1	no	—
16	C₃×C₉	—	7	8	no	—
17	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	4	yes	—
18	C₃×C₇	#737	1	4	yes	—
19	ΓL(1,𝔽₈)	—	9	1	no	—
20	C₃²	—	21	4	no	—
21	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
22	C₉	—	3	4	no	—
23	C₉	—	21	8	no	—
24	C₇	#6897	1	1	yes	characteristic, complemented, Sylow
25	C₃	—	63	1	no	—
26	C₃	#10588061	1	4	yes	—

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.