Subgroups — #13133554

Order 1701.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃×#4430	C₃	1	2	yes	maximal, complemented
3	C₃²×C₇⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊(C₇⋊C₉)	C₃	1	9	yes	maximal, complemented
5	#6893	—	7	1	no	maximal, Sylow
6	C₃³×C₇	C₃²	1	3	yes	—
7	C₃³×C₇	C₃²	1	1	yes	characteristic
8	C₇×H(3,𝔽₃)	—	3	3	no	—
9	#4430	—	3	6	no	—
10	C₃×C₇⋊C₉	—	3	3	no	—
11	C₃×C₇⋊C₉	C₃²	1	3	yes	—
12	C₃×C₇⋊C₉	C₃²	1	6	yes	—
13	C₃×3₋¹⁺²	—	7	2	no	—
14	C₃×H(3,𝔽₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃²×C₉	—	7	1	no	—
16	C₃²⋊C₉	—	7	9	no	—
17	C₃²×C₇	—	3	3	no	—
18	C₃²×C₇	—	3	3	no	—
19	C₃²×C₇	—	3	9	no	—
20	C₃²×C₇	H(3,𝔽₃)	1	3	yes	—
21	C₃²×C₇	C₃³	1	1	yes	characteristic
22	C₇⋊C₉	—	3	3	no	—
23	C₇⋊C₉	—	3	6	no	—
24	C₃³	C₃×ΓL(1,𝔽₈)	1	3	yes	—
25	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
26	3₋¹⁺²	—	21	6	no	—
27	H(3,𝔽₃)	—	3	3	no	—
28	C₃×C₉	—	7	3	no	—
29	C₃×C₉	—	7	6	no	—
30	C₃×C₉	—	21	3	no	—
31	C₃×C₇	—	3	3	no	—
32	C₃×C₇	—	9	3	no	—
33	C₃×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
34	C₃×C₇	#737	1	3	yes	—
35	C₃²	—	3	3	no	—
36	C₃²	—	3	9	no	—
37	C₃²	—	3	3	no	—
38	C₃²	C₇⋊H(3,𝔽₃)	1	3	yes	—
39	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
40	C₉	—	21	3	no	—
41	C₉	—	21	6	no	—
42	C₇	#6893	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	3	3	no	—
44	C₃	—	9	3	no	—
45	C₃	#10588062	1	3	yes	—
46	C₃	C₃×C₇⋊H(3,𝔽₃)	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.