Subgroups — C₇⋊H(5,𝔽₃) #13133668

Order 1701.

586 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, complemented
2	C₃×C₇⋊H(3,𝔽₃)	C₃	1	12	yes	maximal, complemented
3	ΓL(1,𝔽₈)×H(3,𝔽₃)	C₃	1	27	yes	maximal, complemented
4	H(5,𝔽₃)	—	7	1	no	maximal, Sylow
5	C₃³×C₇	C₃²	1	4	yes	complemented
6	C₃²×ΓL(1,𝔽₈)	C₃²	1	36	yes	complemented
7	C₇×H(3,𝔽₃)	C₃²	1	9	yes	complemented
8	C₇⋊H(3,𝔽₃)	C₃²	1	72	yes	complemented
9	C₇⋊H(3,𝔽₃)	C₃²	1	9	yes	complemented
10	C₃×H(3,𝔽₃)	—	7	12	no	—
11	C₃×H(3,𝔽₃)	—	7	27	no	—
12	C₃×H(3,𝔽₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
13	C₃²×C₇	—	9	4	no	—
14	C₃²×C₇	C₃³	1	1	yes	characteristic
15	C₃²×C₇	C₃³	1	12	yes	—
16	C₃×ΓL(1,𝔽₈)	—	9	36	no	—
17	C₃×ΓL(1,𝔽₈)	C₃³	1	27	yes	—
18	C₃³	—	7	36	no	—
19	C₃³	C₃×ΓL(1,𝔽₈)	1	4	yes	complemented
20	H(3,𝔽₃)	—	7	9	no	—
21	H(3,𝔽₃)	—	7	72	no	—
22	H(3,𝔽₃)	C₃×ΓL(1,𝔽₈)	1	9	yes	complemented
23	C₃×C₇	—	3	12	no	—
24	C₃×C₇	—	3	1	no	—
25	C₃×C₇	C₃⁴	1	1	yes	characteristic
26	ΓL(1,𝔽₈)	—	3	27	no	—
27	C₃²	—	7	27	no	—
28	C₃²	—	9	4	no	—
29	C₃²	—	63	36	no	—
30	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
31	C₃²	C₃²×ΓL(1,𝔽₈)	1	12	yes	—
32	C₇	H(5,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
33	C₃	—	3	1	no	—
34	C₃	—	3	12	no	—
35	C₃	—	21	27	no	—
36	C₃	C₃³×ΓL(1,𝔽₈)	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.