Subgroups — #13133507

Order 1701.

42 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	#10588038	C₃	1	2	yes	maximal, complemented
3	#10588035	C₃	1	1	yes	maximal, characteristic, complemented
4	#6881	—	7	1	no	maximal, Sylow
5	C₇×3₋¹⁺²	—	3	1	no	—
6	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
7	C₇⋊H(3,𝔽₃)	—	3	2	no	—
8	C₃×C₇⋊C₉	—	3	1	no	—
9	#733	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
10	#732	—	7	2	no	—
11	C₉⋊C₉	—	7	1	no	—
12	C₃²×C₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×ΓL(1,𝔽₈)	—	9	2	no	—
14	C₇×C₉	—	3	1	no	—
15	C₇×C₉	—	9	1	no	—
16	C₇⋊C₉	—	9	1	no	—
17	3₋¹⁺²	—	3	1	no	—
18	H(3,𝔽₃)	—	21	2	no	—
19	C₃×C₉	—	21	1	no	—
20	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	C₃×C₇	—	3	1	no	—
22	C₃×C₇	#732	1	1	yes	characteristic
23	ΓL(1,𝔽₈)	—	27	2	no	—
24	C₃²	—	63	2	no	—
25	C₃²	C₇⋊H(3,𝔽₃)	1	1	yes	characteristic
26	C₉	—	3	1	no	—
27	C₉	—	9	1	no	—
28	C₉	—	63	1	no	—
29	C₇	#6881	1	1	yes	characteristic, complemented, Sylow
30	C₃	—	3	1	no	—
31	C₃	—	189	2	no	—
32	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.