Subgroups — D₇×D₃₁₉ #22582017

Order 8932.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₂₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₇×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₃₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₁×C₂₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₃₁₉	—	7	1	no	maximal, Hall
6	D₇×D₂₉	—	11	1	no	maximal, Hall
7	C₂×C₁₁×C₂₉	—	7	1	no	—
8	D₃₁₉	—	7	1	no	—
9	D₃₁₉	D₇	1	1	yes	characteristic, direct product factor
10	D₂₀₃	—	11	1	no	—
11	C₇×D₂₉	—	11	1	no	—
12	D₇×C₂₉	D₁₁	1	1	yes	characteristic, complemented
13	C₁₁×C₂₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
14	D₇×D₁₁	—	29	1	no	maximal, Hall
15	C₇×C₂₉	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
16	D₇₇	—	29	1	no	—
17	C₇×D₁₁	—	29	1	no	—
18	C₁₁×D₇	D₂₉	1	1	yes	characteristic, complemented
19	C₂×D₂₉	—	77	1	no	Hall
20	C₇×C₁₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₂₉	—	7	1	no	—
22	D₂₉	—	11	1	no	—
23	D₂₉	—	77	1	no	—
24	C₂×D₁₁	—	203	1	no	Hall
25	C₂₉	D₇×D₁₁	1	1	yes	characteristic, complemented, Sylow
26	C₂×D₇	—	319	1	no	Hall
27	C₂×C₁₁	—	7	1	no	—
28	D₁₁	—	29	1	no	—
29	D₁₁	—	203	1	no	—
30	C₂×C₇	—	319	1	no	—
31	D₇	—	319	1	no	—
32	D₇	D₃₁₉	1	1	yes	characteristic, direct product factor
33	C₁₁	D₇×D₂₉	1	1	yes	characteristic, complemented, Sylow
34	C₇	C₂×D₃₁₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2233	1	no	Sylow
36	C₂	—	7	1	no	—
37	C₂	—	319	1	no	—
38	C₂	—	2233	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₁×C₂₉	C₂²
LCS	G ▷ C₇×C₁₁×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₂₂₃₃	C₂	semidirect
2. C₁₁×D₇×C₂₉	C₂	semidirect
3. C₇×D₃₁₉	C₂	semidirect
4. C₇×C₁₁×C₂₉	C₂²	semidirect
9. D₃₁₉	D₇	direct (N × H)
12. D₇×C₂₉	D₁₁	semidirect
13. C₁₁×C₂₉	C₂×D₇	semidirect
15. C₇×C₂₉	C₂×D₁₁	semidirect
18. C₁₁×D₇	D₂₉	semidirect
20. C₇×C₁₁	C₂×D₂₉	semidirect
25. C₂₉	D₇×D₁₁	semidirect
32. D₇	D₃₁₉	direct (N × H)
33. C₁₁	D₇×D₂₉	semidirect
34. C₇	C₂×D₃₁₉	semidirect

Subgroups — D7×D319 #22582017

Conjugacy classes of subgroups

Complements

Subgroups — D₇×D₃₁₉ #22582017