Subgroups — C₃×C₇×#6879 #19100244

Order 5103.

260 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#732	C₃	1	3	yes	maximal, complemented
2	C₃×C₇×C₉²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₇×#6879	C₃	1	9	yes	maximal, direct product factor
4	C₃×#6879	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
5	C₃×C₇×H(3,𝔽₃)	—	3	3	no	—
6	C₃²×C₇×C₉	—	3	1	no	—
7	C₃²×C₇×C₉	C₃²	1	1	yes	characteristic
8	C₇×#732	—	3	6	no	—
9	C₇×#732	C₃²	1	9	yes	complemented
10	C₇×C₉²	—	3	2	no	—
11	C₇×C₉²	C₃²	1	3	yes	complemented
12	C₃×#732	C₃×C₇	1	3	yes	complemented
13	C₃×C₉²	C₃×C₇	1	1	yes	characteristic, complemented
14	#6879	C₃×C₇	1	9	yes	direct product factor
15	C₃³×C₇	—	9	3	no	—
16	C₃³×C₇	H(3,𝔽₃)	1	1	yes	characteristic
17	C₇×H(3,𝔽₃)	—	3	9	no	—
18	C₇×H(3,𝔽₃)	—	9	6	no	—
19	C₃×C₇×C₉	—	3	9	no	—
20	C₃×C₇×C₉	—	3	2	no	—
21	C₃×C₇×C₉	—	3	1	no	—
22	C₃×C₇×C₉	—	3	3	no	—
23	C₃×C₇×C₉	H(3,𝔽₃)	1	2	yes	—
24	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
25	C₃×H(3,𝔽₃)	—	3	3	no	—
26	C₃²×C₉	—	3	1	no	—
27	C₃²×C₉	C₃²×C₇	1	1	yes	characteristic
28	#732	—	3	6	no	—
29	#732	C₃²×C₇	1	9	yes	complemented
30	C₉²	—	3	2	no	—
31	C₉²	C₃²×C₇	1	3	yes	complemented
32	C₃²×C₇	—	3	3	no	—
33	C₃²×C₇	—	9	9	no	—
34	C₃²×C₇	—	27	9	no	—
35	C₃²×C₇	#732	1	2	yes	—
36	C₃²×C₇	#732	1	1	yes	characteristic
37	C₃²×C₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₇×C₉	—	3	9	no	—
39	C₇×C₉	—	3	2	no	—
40	C₇×C₉	—	3	1	no	—
41	C₃³	—	9	3	no	—
42	C₃³	C₇×H(3,𝔽₃)	1	1	yes	characteristic
43	H(3,𝔽₃)	—	3	9	no	—
44	H(3,𝔽₃)	—	9	6	no	—
45	C₃×C₉	—	3	9	no	—
46	C₃×C₉	—	3	2	no	—
47	C₃×C₉	—	3	1	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	C₇×H(3,𝔽₃)	1	2	yes	—
50	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
51	C₃×C₇	—	3	1	no	—
52	C₃×C₇	—	3	2	no	—
53	C₃×C₇	—	27	9	no	—
54	C₃×C₇	#6879	1	3	yes	direct product factor
55	C₃×C₇	C₃×#732	1	1	yes	characteristic
56	C₃²	—	3	3	no	—
57	C₃²	—	9	9	no	—
58	C₃²	—	27	9	no	—
59	C₃²	C₇×#732	1	2	yes	—
60	C₃²	C₇×#732	1	1	yes	characteristic
61	C₃²	C₃×C₇×H(3,𝔽₃)	1	1	yes	characteristic
62	C₉	—	3	9	no	—
63	C₉	—	3	2	no	—
64	C₉	—	3	1	no	—
65	C₇	C₃×#6879	1	1	yes	characteristic, direct product factor, Sylow
66	C₃	—	3	1	no	—
67	C₃	—	3	2	no	—
68	C₃	—	27	9	no	—
69	C₃	C₇×#6879	1	3	yes	direct product factor
70	C₃	C₃×C₇×#732	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃²×C₇	#732
commutator, Frattini	C₃×C₉	C₃³×C₇
LCS	G ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃²×C₇ ◁ C₃³×C₇ ◁ C₃²×C₇×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×#732	C₃	semidirect
2. C₃×C₇×C₉²	C₃	semidirect
3. C₇×#6879	C₃	direct (N × H)
4. C₃×#6879	C₇	direct (N × H)
9. C₇×#732	C₃²	semidirect
11. C₇×C₉²	C₃²	semidirect
12. C₃×#732	C₃×C₇	semidirect
13. C₃×C₉²	C₃×C₇	semidirect
14. #6879	C₃×C₇	direct (N × H)
29. #732	C₃²×C₇	semidirect
31. C₉²	C₃²×C₇	semidirect
54. C₃×C₇	#6879	direct (N × H)
65. C₇	C₃×#6879	direct (N × H)
69. C₃	C₇×#6879	direct (N × H)

Subgroups — C3×C7×#6879 #19100244

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₇×#6879 #19100244