Subgroups — C₇×C₃⋊D₃×C₂₉⋊C₇ #38784669

Order 25578.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃×C₇×C₂₉⋊C₇	—	3	4	no	maximal
3	C₃×C₇×C₂₉⋊C₇	D₃	1	4	yes	complemented
4	C₇×C₃⋊D₃×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented
5	C₃⋊D₃×C₂₉⋊C₇	C₇	1	7	yes	maximal, direct product factor
6	C₂×C₇×C₂₉⋊C₇	—	9	1	no	Hall
7	C₃²×C₇×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented
8	C₃²×C₂₉⋊C₇	C₂×C₇	1	7	yes	complemented
9	C₇×C₂₉⋊C₇	C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
10	D₃×C₇×C₂₉	—	3	4	no	—
11	D₃×C₂₉⋊C₇	—	3	28	no	—
12	C₇²×C₃⋊D₃	—	29	1	no	maximal, Hall
13	C₃×C₇×C₂₉	D₃×C₇	1	4	yes	complemented
14	C₃×C₂₉⋊C₇	D₃×C₇	1	28	yes	complemented
15	C₃⋊D₃×C₂₉	C₇²	1	1	yes	characteristic, complemented, Hall
16	C₃²×C₇²	—	29	1	no	Hall
17	C₂×C₇×C₂₉	—	9	1	no	—
18	C₂×C₂₉⋊C₇	—	9	7	no	—
19	D₃×C₇²	—	87	4	no	—
20	C₃²×C₂₉	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
21	C₇×C₂₉	C₇×C₃⋊D₃	1	1	yes	characteristic, complemented
22	C₂₉⋊C₇	C₇×C₃⋊D₃	1	7	yes	direct product factor
23	D₃×C₂₉	—	3	4	no	—
24	C₃×C₇²	—	29	4	no	—
25	C₇×C₃⋊D₃	—	29	7	no	—
26	C₇×C₃⋊D₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
27	C₂×C₇²	—	261	1	no	Hall
28	C₃×C₂₉	D₃×C₇²	1	4	yes	complemented
29	C₃²×C₇	—	29	7	no	—
30	C₃²×C₇	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented
31	C₂×C₂₉	—	9	1	no	Hall
32	C₇²	—	29	1	no	Sylow
33	D₃×C₇	—	3	4	no	—
34	D₃×C₇	—	87	28	no	—
35	C₂₉	C₇²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
36	C₃×C₇	—	29	28	no	—
37	C₃×C₇	D₃×C₂₉⋊C₇	1	4	yes	complemented
38	C₃⋊D₃	C₇×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
39	C₂×C₇	—	261	7	no	—
40	C₂×C₇	—	9	1	no	—
41	C₃²	C₂×C₇×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
42	C₇	—	29	7	no	—
43	C₇	C₃⋊D₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
44	D₃	—	3	4	no	—
45	C₃	D₃×C₇×C₂₉⋊C₇	1	4	yes	complemented
46	C₂	—	9	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	C₃⋊D₃×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₃²×C₂₉	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂×C₇
LCS	G ▷ C₃²×C₂₉
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₃²×C₇×C₂₉⋊C₇	C₂	semidirect
3. C₃×C₇×C₂₉⋊C₇	D₃	semidirect
4. C₇×C₃⋊D₃×C₂₉	C₇	semidirect
5. C₃⋊D₃×C₂₉⋊C₇	C₇	direct (N × H)
7. C₃²×C₇×C₂₉	C₂×C₇	semidirect
8. C₃²×C₂₉⋊C₇	C₂×C₇	semidirect
9. C₇×C₂₉⋊C₇	C₃⋊D₃	direct (N × H)
13. C₃×C₇×C₂₉	D₃×C₇	semidirect
14. C₃×C₂₉⋊C₇	D₃×C₇	semidirect
15. C₃⋊D₃×C₂₉	C₇²	semidirect
20. C₃²×C₂₉	C₂×C₇²	semidirect
21. C₇×C₂₉	C₇×C₃⋊D₃	semidirect
22. C₂₉⋊C₇	C₇×C₃⋊D₃	direct (N × H)
26. C₇×C₃⋊D₃	C₂₉⋊C₇	direct (N × H)
28. C₃×C₂₉	D₃×C₇²	semidirect
30. C₃²×C₇	C₂×C₂₉⋊C₇	semidirect
35. C₂₉	C₇²×C₃⋊D₃	semidirect
37. C₃×C₇	D₃×C₂₉⋊C₇	semidirect
38. C₃⋊D₃	C₇×C₂₉⋊C₇	direct (N × H)
41. C₃²	C₂×C₇×C₂₉⋊C₇	semidirect
43. C₇	C₃⋊D₃×C₂₉⋊C₇	direct (N × H)
45. C₃	D₃×C₇×C₂₉⋊C₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃²×C₇×C₂₉⋊C₇	2
D₃×C₇×C₂₉⋊C₇	3
C₇×C₃⋊D₃×C₂₉	7
C₃⋊D₃×C₂₉⋊C₇	7
C₇²×C₃⋊D₃	29

Subgroups — C7×C3⋊D3×C29⋊C7 #38784669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₃⋊D₃×C₂₉⋊C₇ #38784669