Subgroups — #13133514

Order 1701.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#733	C₃	1	1	yes	maximal, characteristic, complemented
2	#10588039	C₃	1	1	yes	maximal, characteristic, complemented
3	#10588038	C₃	1	1	yes	maximal, characteristic
4	#10588035	C₃	1	1	yes	maximal, characteristic, complemented
5	#6883	—	7	1	no	maximal, Sylow
6	C₇×3₋¹⁺²	—	3	1	no	—
7	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
8	C₇⋊H(3,𝔽₃)	—	3	1	no	—
9	#4430	—	3	1	no	—
10	C₃×C₇⋊C₉	—	3	1	no	—
11	#733	—	7	1	no	—
12	#733	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	#732	—	7	1	no	—
14	C₉⋊C₉	—	7	1	no	—
15	C₃²×C₇	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃×ΓL(1,𝔽₈)	—	9	1	no	—
17	C₇×C₉	—	3	1	no	—
18	C₇×C₉	—	9	1	no	—
19	C₇⋊C₉	—	9	1	no	—
20	C₇⋊C₉	—	9	1	no	—
21	3₋¹⁺²	—	3	1	no	—
22	3₋¹⁺²	—	21	1	no	—
23	H(3,𝔽₃)	—	21	1	no	—
24	C₃×C₉	—	21	1	no	—
25	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	C₃×C₇	—	3	1	no	—
27	C₃×C₇	#732	1	1	yes	characteristic
28	ΓL(1,𝔽₈)	—	27	1	no	—
29	C₃²	—	63	1	no	—
30	C₃²	C₇⋊H(3,𝔽₃)	1	1	yes	characteristic
31	C₉	—	3	1	no	—
32	C₉	—	9	1	no	—
33	C₉	—	63	1	no	—
34	C₉	—	63	1	no	—
35	C₇	#6883	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	3	1	no	—
37	C₃	—	189	1	no	—
38	C₃	#10588042	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.