Subgroups — C₇×#10624900 #19100309

Order 5103.

730 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×#737	C₃	1	1	yes	maximal, characteristic
2	C₇×#6895	C₃	1	8	yes	maximal, complemented
3	C₇×#6894	C₃	1	8	yes	maximal, complemented
4	C₇×#6894	C₃	1	16	yes	maximal, complemented
5	C₇×C₉×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	C₇×C₉×H(3,𝔽₃)	C₃	1	2	yes	maximal
7	C₃×C₇×C₉⋊C₉	C₃	1	4	yes	maximal, complemented
8	#10624900	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₇×#737	—	3	9	no	—
10	C₃×C₇×3₋¹⁺²	C₃²	1	8	yes	—
11	C₃×C₇×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
12	C₃²×C₇×C₉	C₃²	1	4	yes	—
13	C₃²×C₇×C₉	C₃²	1	4	yes	—
14	C₃²×C₇×C₉	C₃²	1	8	yes	—
15	C₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
16	C₇×C₉⋊C₉	C₃²	1	16	yes	—
17	C₇×C₉⋊C₉	C₃²	1	8	yes	—
18	C₇×C₉⋊C₉	C₃²	1	8	yes	—
19	C₇×C₉⋊C₉	C₃²	1	48	yes	—
20	C₇×C₃²⋊C₉	C₃²	1	8	yes	—
21	C₇×C₃²⋊C₉	C₃²	1	16	yes	—
22	C₃×#737	C₃×C₇	1	1	yes	characteristic
23	#6895	C₃×C₇	1	8	yes	complemented
24	#6894	C₃×C₇	1	8	yes	complemented
25	#6894	C₃×C₇	1	16	yes	complemented
26	C₉×H(3,𝔽₃)	C₃×C₇	1	1	yes	characteristic
27	C₉×H(3,𝔽₃)	C₃×C₇	1	2	yes	—
28	C₃×C₉⋊C₉	C₃×C₇	1	4	yes	complemented
29	C₃³×C₇	C₃³	1	4	yes	—
30	C₇×3₋¹⁺²	—	3	24	no	—
31	C₇×H(3,𝔽₃)	3₋¹⁺²	1	9	yes	—
32	C₃×C₇×C₉	—	3	12	no	—
33	C₃×C₇×C₉	—	3	12	no	—
34	C₃×C₇×C₉	—	9	8	no	—
35	C₃×C₇×C₉	C₃³	1	8	yes	—
36	C₃×C₇×C₉	C₃³	1	16	yes	—
37	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
38	C₃×C₇×C₉	C₃³	1	2	yes	—
39	C₃×C₇×C₉	C₃³	1	8	yes	—
40	C₃×C₇×C₉	C₃³	1	1	yes	characteristic
41	#737	—	3	9	no	—
42	C₃×3₋¹⁺²	C₃²×C₇	1	8	yes	—
43	C₃×H(3,𝔽₃)	C₃²×C₇	1	1	yes	characteristic
44	C₃²×C₉	C₃²×C₇	1	4	yes	—
45	C₃²×C₉	C₃²×C₇	1	4	yes	—
46	C₃²×C₉	C₃²×C₇	1	8	yes	—
47	C₉⋊C₉	C₃²×C₇	1	1	yes	characteristic
48	C₉⋊C₉	C₃²×C₇	1	16	yes	—
49	C₉⋊C₉	C₃²×C₇	1	8	yes	—
50	C₉⋊C₉	C₃²×C₇	1	8	yes	—
51	C₉⋊C₉	C₃²×C₇	1	48	yes	—
52	C₃²⋊C₉	C₃²×C₇	1	8	yes	—
53	C₃²⋊C₉	C₃²×C₇	1	16	yes	—
54	C₃²×C₇	—	3	4	no	—
55	C₃²×C₇	—	3	8	no	—
56	C₃²×C₇	C₃×3₋¹⁺²	1	12	yes	—
57	C₃²×C₇	C₃⁴	1	1	yes	characteristic
58	C₇×C₉	—	3	1	no	—
59	C₇×C₉	—	3	8	no	—
60	C₇×C₉	—	3	8	no	—
61	C₇×C₉	—	3	2	no	—
62	C₇×C₉	—	3	16	no	—
63	C₇×C₉	#737	1	3	yes	complemented
64	C₃³	C₃³×C₇	1	4	yes	—
65	3₋¹⁺²	—	3	24	no	—
66	H(3,𝔽₃)	C₇×3₋¹⁺²	1	9	yes	—
67	C₃×C₉	—	3	12	no	—
68	C₃×C₉	—	3	12	no	—
69	C₃×C₉	—	9	8	no	—
70	C₃×C₉	C₃³×C₇	1	8	yes	—
71	C₃×C₉	C₃³×C₇	1	16	yes	—
72	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
73	C₃×C₉	C₃³×C₇	1	2	yes	—
74	C₃×C₉	C₃³×C₇	1	8	yes	—
75	C₃×C₉	C₃³×C₇	1	1	yes	characteristic
76	C₃×C₇	—	3	12	no	—
77	C₃×C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
78	C₃×C₇	C₃×#737	1	1	yes	characteristic
79	C₃×C₇	3₋¹⁺⁴	1	2	yes	—
80	C₃²	—	3	4	no	—
81	C₃²	—	3	8	no	—
82	C₃²	C₃×C₇×3₋¹⁺²	1	12	yes	—
83	C₃²	C₃⁴×C₇	1	1	yes	characteristic
84	C₉	—	3	1	no	—
85	C₉	—	3	8	no	—
86	C₉	—	3	8	no	—
87	C₉	—	3	2	no	—
88	C₉	—	3	16	no	—
89	C₉	C₇×#737	1	3	yes	complemented
90	C₇	#10624900	1	1	yes	characteristic, direct product factor, Sylow
91	C₃	—	3	12	no	—
92	C₃	C₃²×C₇×3₋¹⁺²	1	1	yes	characteristic
93	C₃	C₃×C₇×#737	1	1	yes	characteristic
94	C₃	C₇×3₋¹⁺⁴	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₇×#6895	C₃	semidirect
3. C₇×#6894	C₃	semidirect
4. C₇×#6894	C₃	semidirect
7. C₃×C₇×C₉⋊C₉	C₃	semidirect
8. #10624900	C₇	direct (N × H)
23. #6895	C₃×C₇	semidirect
24. #6894	C₃×C₇	semidirect
25. #6894	C₃×C₇	semidirect
28. C₃×C₉⋊C₉	C₃×C₇	semidirect
63. C₇×C₉	#737	semidirect
89. C₉	C₇×#737	semidirect
90. C₇	#10624900	direct (N × H)

Subgroups — C7×#10624900 #19100309

Conjugacy classes of subgroups

Complements

Subgroups — C₇×#10624900 #19100309