Subgroups — C₇×D₇×C₃₇⋊C₃ #24925945

Order 10878.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₃₇⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×C₃₇⋊C₃	—	7	1	no	maximal
5	D₇×C₃₇⋊C₃	C₇	1	1	yes	maximal, characteristic, direct product factor
6	C₇×C₃₇⋊C₃	—	2	3	no	—
7	C₇×C₃₇⋊C₃	D₇	1	1	yes	characteristic, direct product factor
8	C₇×C₃₇⋊C₃	C₂×C₇	1	1	yes	characteristic, complemented
9	C₂×C₇×C₃₇	—	7	1	no	—
10	D₇×C₃₇	C₃×C₇	1	1	yes	characteristic, complemented
11	C₃×C₇×D₇	—	37	1	no	maximal, Hall
12	C₇×C₃₇	—	2	3	no	—
13	C₇×C₃₇	C₃×D₇	1	1	yes	characteristic, complemented
14	C₇×C₃₇	C₂×C₃×C₇	1	1	yes	characteristic, complemented
15	C₂×C₃₇⋊C₃	—	7	1	no	Hall
16	C₃×C₇²	—	37	1	no	Hall
17	C₃₇⋊C₃	C₇×D₇	1	1	yes	characteristic, direct product factor, Hall
18	C₇×D₇	C₃₇⋊C₃	1	1	yes	characteristic, direct product factor, Hall
19	C₂×C₃₇	—	7	1	no	Hall
20	C₇²	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃×C₇	—	259	1	no	—
22	C₃×D₇	—	37	1	no	—
23	C₃₇	C₃×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
24	C₃×C₇	—	37	1	no	—
25	C₃×C₇	—	37	1	no	—
26	C₃×C₇	—	74	3	no	—
27	C₂×C₇	—	7	1	no	—
28	D₇	C₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
29	C₇	—	2	3	no	—
30	C₇	D₇×C₃₇⋊C₃	1	1	yes	characteristic, direct product factor
31	C₇	C₂×C₇×C₃₇⋊C₃	1	1	yes	characteristic, complemented
32	C₂×C₃	—	259	1	no	Hall
33	C₃	—	37	1	no	Sylow
34	C₂	—	7	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇	D₇×C₃₇⋊C₃
commutator, cosocle, hypocenter	C₇×C₃₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₃₇	C₂×C₃
LCS	G ▷ C₇×C₃₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×C₃₇⋊C₃	C₂	semidirect
2. C₇×D₇×C₃₇	C₃	semidirect
3. C₇²×C₃₇	C₂×C₃	semidirect
5. D₇×C₃₇⋊C₃	C₇	direct (N × H)
7. C₇×C₃₇⋊C₃	D₇	direct (N × H)
8. C₇×C₃₇⋊C₃	C₂×C₇	semidirect
10. D₇×C₃₇	C₃×C₇	semidirect
13. C₇×C₃₇	C₃×D₇	semidirect
14. C₇×C₃₇	C₂×C₃×C₇	semidirect
17. C₃₇⋊C₃	C₇×D₇	direct (N × H)
18. C₇×D₇	C₃₇⋊C₃	direct (N × H)
20. C₇²	C₂×C₃₇⋊C₃	semidirect
23. C₃₇	C₃×C₇×D₇	semidirect
28. D₇	C₇×C₃₇⋊C₃	direct (N × H)
30. C₇	D₇×C₃₇⋊C₃	direct (N × H)
31. C₇	C₂×C₇×C₃₇⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₇²×C₃₇⋊C₃	2
C₇×D₇×C₃₇	3
C₂×C₇×C₃₇⋊C₃	7
D₇×C₃₇⋊C₃	7
C₃×C₇×D₇	37

Subgroups — C7×D7×C37⋊C3 #24925945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×C₃₇⋊C₃ #24925945