Subgroups — C₃×C₇×#6897 #19100283

Order 5103.

692 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#6897	C₃	1	27	yes	maximal, direct product factor
2	C₃×C₇×C₉⋊C₉	C₃	1	8	yes	maximal, complemented
3	C₃×C₇×C₃²⋊C₉	C₃	1	4	yes	maximal
4	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#6897	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₃⁴×C₇	C₃²	1	1	yes	characteristic
7	C₃²×C₇×C₉	C₃²	1	4	yes	—
8	C₃²×C₇×C₉	C₃²	1	8	yes	—
9	C₇×C₉⋊C₉	C₃²	1	72	yes	complemented
10	C₇×C₃²⋊C₉	C₃²	1	36	yes	—
11	C₇×C₉²	C₃²	1	9	yes	complemented
12	#6897	C₃×C₇	1	27	yes	direct product factor
13	C₃×C₉⋊C₉	C₃×C₇	1	8	yes	complemented
14	C₃×C₃²⋊C₉	C₃×C₇	1	4	yes	—
15	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
16	C₃³×C₇	—	3	12	no	—
17	C₃³×C₇	C₃³	1	3	yes	—
18	C₃³×C₇	C₃³	1	1	yes	characteristic
19	C₃×C₇×C₉	—	3	12	no	—
20	C₃×C₇×C₉	—	3	24	no	—
21	C₃×C₇×C₉	C₃³	1	12	yes	—
22	C₃×C₇×C₉	C₃³	1	24	yes	—
23	C₃⁴	C₃²×C₇	1	1	yes	characteristic
24	C₃²×C₉	C₃²×C₇	1	4	yes	—
25	C₃²×C₉	C₃²×C₇	1	8	yes	—
26	C₉⋊C₉	C₃²×C₇	1	72	yes	complemented
27	C₃²⋊C₉	C₃²×C₇	1	36	yes	—
28	C₉²	C₃²×C₇	1	9	yes	complemented
29	C₃²×C₇	—	3	12	no	—
30	C₃²×C₇	—	9	9	no	—
31	C₃²×C₇	#737	1	12	yes	—
32	C₃²×C₇	C₃⁴	1	1	yes	characteristic
33	C₇×C₉	—	3	12	no	—
34	C₇×C₉	—	3	24	no	—
35	C₃³	—	3	12	no	—
36	C₃³	C₃³×C₇	1	3	yes	—
37	C₃³	C₃³×C₇	1	1	yes	characteristic
38	C₃×C₉	—	3	12	no	—
39	C₃×C₉	—	3	24	no	—
40	C₃×C₉	C₃³×C₇	1	12	yes	—
41	C₃×C₉	C₃³×C₇	1	24	yes	—
42	C₃×C₇	—	9	3	no	—
43	C₃×C₇	#6897	1	9	yes	direct product factor
44	C₃×C₇	C₃×#737	1	4	yes	—
45	C₃²	—	3	12	no	—
46	C₃²	—	9	9	no	—
47	C₃²	C₇×#737	1	12	yes	—
48	C₃²	C₃⁴×C₇	1	1	yes	characteristic
49	C₉	—	3	12	no	—
50	C₉	—	3	24	no	—
51	C₇	C₃×#6897	1	1	yes	characteristic, direct product factor, Sylow
52	C₃	—	9	3	no	—
53	C₃	C₇×#6897	1	9	yes	direct product factor
54	C₃	C₃×C₇×#737	1	4	yes	—

	subgroup	G/H
center, socle	C₃³×C₇	C₃³
commutator, Frattini	C₃²	C₃⁴×C₇
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#6897	C₃	direct (N × H)
2. C₃×C₇×C₉⋊C₉	C₃	semidirect
4. C₃×C₇×C₉²	C₃	semidirect
5. C₃×#6897	C₇	direct (N × H)
9. C₇×C₉⋊C₉	C₃²	semidirect
11. C₇×C₉²	C₃²	semidirect
12. #6897	C₃×C₇	direct (N × H)
13. C₃×C₉⋊C₉	C₃×C₇	semidirect
15. C₃×C₉²	C₃×C₇	semidirect
26. C₉⋊C₉	C₃²×C₇	semidirect
28. C₉²	C₃²×C₇	semidirect
43. C₃×C₇	#6897	direct (N × H)
51. C₇	C₃×#6897	direct (N × H)
53. C₃	C₇×#6897	direct (N × H)

Subgroups — C3×C7×#6897 #19100283

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6897 #19100283