Subgroups — #13133595

Order 1701.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#4428	C₃	1	4	yes	maximal
2	C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	#10588036	C₃	1	8	yes	maximal, complemented
4	#6900	—	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	#4428	—	3	12	no	—
9	C₃×3₋¹⁺²	—	7	4	no	—
10	C₉⋊C₉	—	7	8	no	—
11	C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
12	C₃²×C₇	C₃³	1	1	yes	characteristic
13	C₃×ΓL(1,𝔽₈)	—	3	4	no	—
14	C₇×C₉	3₋¹⁺²	1	12	yes	complemented
15	C₇⋊C₉	—	3	8	no	—
16	C₃³	—	7	1	no	—
17	3₋¹⁺²	—	21	12	no	—
18	C₃×C₉	—	7	8	no	—
19	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	4	yes	—
20	C₃×C₇	C₃×3₋¹⁺²	1	4	yes	—
21	ΓL(1,𝔽₈)	—	9	1	no	—
22	C₃²	—	21	4	no	—
23	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
24	C₉	—	21	8	no	—
25	C₉	#4428	1	12	yes	complemented
26	C₇	#6900	1	1	yes	characteristic, complemented, Sylow
27	C₃	—	63	1	no	—
28	C₃	C₃×#4428	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.