Subgroups — #13133587

Order 1701.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#4428	C₃	1	1	yes	maximal, characteristic
2	C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₃×ΓL(1,𝔽₈))⋊C₉	C₃	1	3	yes	maximal
4	#10588036	C₃	1	2	yes	maximal, complemented
5	(C₇⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
6	#6899	—	7	1	no	maximal, Sylow
7	C₃²×ΓL(1,𝔽₈)	C₃²	1	1	yes	characteristic
8	C₃×C₇×C₉	C₃²	1	3	yes	—
9	C₃×C₇×C₉	C₃²	1	1	yes	characteristic
10	C₃×C₇⋊C₉	C₃²	1	2	yes	—
11	C₃×C₇⋊C₉	C₃²	1	6	yes	—
12	#4428	—	3	3	no	—
13	C₃×3₋¹⁺²	—	7	1	no	—
14	C₉⋊C₉	—	7	6	no	—
15	C₉⋊C₉	—	7	2	no	—
16	C₃²⋊C₉	—	7	3	no	—
17	C₉²	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
18	C₃²×C₇	C₃³	1	1	yes	characteristic
19	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
20	C₃×ΓL(1,𝔽₈)	—	3	3	no	—
21	C₇×C₉	—	3	3	no	—
22	C₇×C₉	3₋¹⁺²	1	3	yes	—
23	C₇⋊C₉	—	3	2	no	—
24	C₇⋊C₉	—	3	6	no	—
25	C₃³	—	7	1	no	—
26	3₋¹⁺²	—	21	3	no	—
27	C₃×C₉	—	7	6	no	—
28	C₃×C₉	—	7	2	no	—
29	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
30	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃×C₇	C₃×3₋¹⁺²	1	1	yes	characteristic
32	C₃×C₇	#737	1	3	yes	—
33	ΓL(1,𝔽₈)	—	9	1	no	—
34	C₃²	—	21	1	no	—
35	C₃²	—	21	3	no	—
36	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	21	2	no	—
39	C₉	—	21	6	no	—
40	C₉	#4428	1	3	yes	—
41	C₇	#6899	1	1	yes	characteristic, complemented, Sylow
42	C₃	—	63	1	no	—
43	C₃	C₃×#4428	1	1	yes	characteristic
44	C₃	#10588061	1	3	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.