Subgroups — H(3,𝔽₃)×C₇⋊C₉ #13133533

Order 1701.

202 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	C₃²×C₇⋊C₉	C₃	1	4	yes	maximal, complemented
3	C₃²⋊(C₇⋊C₉)	C₃	1	8	yes	maximal, complemented
4	C₉×H(3,𝔽₃)	—	7	1	no	maximal, Sylow
5	C₃³×C₇	C₃²	1	4	yes	—
6	C₇×H(3,𝔽₃)	C₉	1	9	yes	complemented
7	C₃×C₇⋊C₉	—	3	12	no	—
8	C₃×C₇⋊C₉	C₃²	1	8	yes	—
9	C₃×C₇⋊C₉	C₃²	1	1	yes	characteristic
10	C₃×H(3,𝔽₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃²×C₉	—	7	4	no	—
12	C₃²⋊C₉	—	7	8	no	—
13	C₃²×C₇	—	3	4	no	—
14	C₃²×C₇	—	3	8	no	—
15	C₃²×C₇	C₃×C₉	1	12	yes	complemented
16	C₃²×C₇	C₃³	1	1	yes	characteristic
17	C₇⋊C₉	—	3	8	no	—
18	C₇⋊C₉	H(3,𝔽₃)	1	3	yes	direct product factor
19	C₃³	C₃×ΓL(1,𝔽₈)	1	4	yes	—
20	H(3,𝔽₃)	C₇⋊C₉	1	9	yes	direct product factor
21	C₃×C₉	—	7	1	no	—
22	C₃×C₉	—	7	8	no	—
23	C₃×C₉	—	21	12	no	—
24	C₃×C₇	—	3	12	no	—
25	C₃×C₇	C₃²×C₉	1	1	yes	characteristic
26	C₃×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
27	C₃×C₇	#737	1	2	yes	—
28	C₃²	—	3	8	no	—
29	C₃²	—	3	4	no	—
30	C₃²	C₃×C₇⋊C₉	1	12	yes	complemented
31	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
32	C₉	—	7	3	no	—
33	C₉	—	21	8	no	—
34	C₇	C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
35	C₃	—	3	12	no	—
36	C₃	#10588062	1	2	yes	—
37	C₃	ΓL(1,𝔽₈)×H(3,𝔽₃)	1	1	yes	characteristic
38	C₃	C₃²×C₇⋊C₉	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.