Subgroups — C₇×D₇×D₁₂₇ #38733539

Order 24892.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₇×C₁₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₈₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇²×C₁₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×D₁₂₇	—	7	1	no	maximal
6	D₇×D₁₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₇×C₁₂₇	—	7	1	no	—
8	D₈₈₉	C₂×C₇	1	1	yes	characteristic, complemented
9	C₇×D₁₂₇	—	2	3	no	—
10	C₇×D₁₂₇	—	7	1	no	—
11	C₇×D₁₂₇	D₇	1	1	yes	characteristic, direct product factor
12	C₇×D₁₂₇	C₂×C₇	1	1	yes	characteristic, complemented
13	D₇×C₁₂₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₇×C₁₂₇	—	2	3	no	—
15	C₇×C₁₂₇	C₂×D₇	1	1	yes	characteristic, complemented
16	C₇×C₁₂₇	C₂²×C₇	1	1	yes	characteristic, complemented
17	C₂×D₁₂₇	—	7	1	no	Hall
18	C₂×C₁₂₇	—	7	1	no	—
19	D₁₂₇	—	7	1	no	—
20	D₁₂₇	C₇×D₇	1	1	yes	characteristic, direct product factor
21	C₂×C₇×D₇	—	127	1	no	maximal, Hall
22	C₁₂₇	C₂×C₇×D₇	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₇²	—	127	1	no	—
24	C₇×D₇	—	127	1	no	—
25	C₇×D₇	D₁₂₇	1	1	yes	characteristic, direct product factor
26	C₇²	C₂×D₁₂₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₇	—	889	1	no	—
28	C₂×D₇	—	127	1	no	—
29	C₂×C₇	—	7	1	no	—
30	C₂×C₇	—	889	1	no	—
31	C₂×C₇	—	127	1	no	—
32	C₂×C₇	—	127	1	no	—
33	C₂×C₇	—	254	3	no	—
34	D₇	—	127	1	no	—
35	D₇	C₇×D₁₂₇	1	1	yes	characteristic, direct product factor
36	C₇	—	2	3	no	—
37	C₇	D₇×D₁₂₇	1	1	yes	characteristic, direct product factor
38	C₇	C₂×C₇×D₁₂₇	1	1	yes	characteristic, complemented
39	C₂²	—	889	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	889	1	no	—
42	C₂	—	127	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₇×D₁₂₇
commutator, cosocle, hypocenter	C₇×C₁₂₇	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₇²×C₁₂₇	C₂²
LCS	G ▷ C₇×C₁₂₇
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇²×D₁₂₇	C₂	semidirect
2. C₇×D₇×C₁₂₇	C₂	semidirect
3. C₇×D₈₈₉	C₂	semidirect
4. C₇²×C₁₂₇	C₂²	semidirect
6. D₇×D₁₂₇	C₇	direct (N × H)
8. D₈₈₉	C₂×C₇	semidirect
11. C₇×D₁₂₇	D₇	direct (N × H)
12. C₇×D₁₂₇	C₂×C₇	semidirect
13. D₇×C₁₂₇	C₂×C₇	semidirect
15. C₇×C₁₂₇	C₂×D₇	semidirect
16. C₇×C₁₂₇	C₂²×C₇	semidirect
20. D₁₂₇	C₇×D₇	direct (N × H)
22. C₁₂₇	C₂×C₇×D₇	semidirect
25. C₇×D₇	D₁₂₇	direct (N × H)
26. C₇²	C₂×D₁₂₇	semidirect
35. D₇	C₇×D₁₂₇	direct (N × H)
37. C₇	D₇×D₁₂₇	direct (N × H)
38. C₇	C₂×C₇×D₁₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₇²×D₁₂₇	2
C₇×D₇×C₁₂₇	2
C₇×D₈₈₉	2
C₂×C₇×D₁₂₇	7
D₇×D₁₂₇	7
C₂×C₇×D₇	127

Subgroups — C7×D7×D127 #38733539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₇×D₁₂₇ #38733539