Subgroups — C₃₇⋊H(5,𝔽₃) #22582676

Order 8991.

586 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₃₇⋊C₃)	C₃	1	12	yes	maximal, complemented
2	H(3,𝔽₃)×C₃₇⋊C₃	C₃	1	27	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₃₇	C₃²	1	4	yes	complemented
5	C₃²×C₃₇⋊C₃	C₃²	1	36	yes	complemented
6	H(3,𝔽₃)×C₃₇	C₃²	1	9	yes	complemented
7	C₃²⋊(C₃₇⋊C₃)	C₃²	1	72	yes	complemented
8	C₃²⋊(C₃₇⋊C₃)	C₃²	1	9	yes	complemented
9	C₃²×C₃₇	—	9	4	no	—
10	C₃²×C₃₇	C₃³	1	1	yes	characteristic
11	C₃²×C₃₇	C₃³	1	12	yes	—
12	C₃×C₃₇⋊C₃	—	9	36	no	—
13	C₃×C₃₇⋊C₃	C₃³	1	27	yes	—
14	H(5,𝔽₃)	—	37	1	no	maximal, Sylow
15	C₃×C₃₇	—	3	12	no	—
16	C₃×C₃₇	—	3	1	no	—
17	C₃×C₃₇	C₃⁴	1	1	yes	characteristic
18	C₃₇⋊C₃	—	3	27	no	—
19	C₃×H(3,𝔽₃)	—	37	12	no	—
20	C₃×H(3,𝔽₃)	—	37	27	no	—
21	C₃×H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
22	C₃₇	H(5,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
23	C₃³	—	37	36	no	—
24	C₃³	C₃×C₃₇⋊C₃	1	4	yes	complemented
25	H(3,𝔽₃)	—	37	9	no	—
26	H(3,𝔽₃)	—	37	72	no	—
27	H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	9	yes	complemented
28	C₃²	—	9	4	no	—
29	C₃²	—	37	27	no	—
30	C₃²	—	333	36	no	—
31	C₃²	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
32	C₃²	C₃²×C₃₇⋊C₃	1	12	yes	—
33	C₃	—	3	1	no	—
34	C₃	—	3	12	no	—
35	C₃	—	111	27	no	—
36	C₃	C₃³×C₃₇⋊C₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.