Subgroups — D₇×C₃₁×D₃₁ #41002064

Order 26908.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃₁×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×C₃₁²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×D₂₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₃₁²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃₁×D₃₁	—	7	1	no	maximal, Hall
6	C₂×C₃₁²	—	7	1	no	—
7	C₃₁×D₃₁	—	7	1	no	—
8	C₃₁×D₃₁	D₇	1	1	yes	characteristic, direct product factor
9	C₃₁²	C₂×D₇	1	1	yes	characteristic, complemented, Sylow
10	C₂×D₇×C₃₁	—	31	1	no	maximal
11	D₇×D₃₁	C₃₁	1	1	yes	maximal, characteristic, direct product factor
12	C₂×C₇×C₃₁	—	31	1	no	—
13	D₂₁₇	C₂×C₃₁	1	1	yes	characteristic, complemented
14	C₇×D₃₁	C₂×C₃₁	1	1	yes	characteristic, complemented
15	D₇×C₃₁	—	2	15	no	—
16	D₇×C₃₁	—	31	1	no	—
17	D₇×C₃₁	D₃₁	1	1	yes	characteristic, direct product factor
18	D₇×C₃₁	C₂×C₃₁	1	1	yes	characteristic, complemented
19	C₇×C₃₁	—	2	15	no	—
20	C₇×C₃₁	C₂×D₃₁	1	1	yes	characteristic, complemented
21	C₇×C₃₁	C₂²×C₃₁	1	1	yes	characteristic, complemented
22	C₂²×C₃₁	—	217	1	no	—
23	C₂×D₃₁	—	7	1	no	—
24	C₂×C₃₁	—	7	1	no	—
25	C₂×C₃₁	—	7	1	no	—
26	C₂×C₃₁	—	14	15	no	—
27	C₂×C₃₁	—	31	1	no	—
28	C₂×C₃₁	—	217	1	no	—
29	D₃₁	—	7	1	no	—
30	D₃₁	D₇×C₃₁	1	1	yes	characteristic, direct product factor
31	C₃₁	—	2	15	no	—
32	C₃₁	D₇×D₃₁	1	1	yes	characteristic, direct product factor
33	C₃₁	C₂×D₇×C₃₁	1	1	yes	characteristic, complemented
34	C₂×D₇	—	31	1	no	Hall
35	C₂×C₇	—	31	1	no	—
36	D₇	—	31	1	no	—
37	D₇	C₃₁×D₃₁	1	1	yes	characteristic, direct product factor
38	C₇	C₂×C₃₁×D₃₁	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	217	1	no	Sylow
40	C₂	—	7	1	no	—
41	C₂	—	31	1	no	—
42	C₂	—	217	1	no	—

	subgroup	G/H
center, hypercenter	C₃₁	D₇×D₃₁
commutator, cosocle, hypocenter	C₇×C₃₁	C₂²×C₃₁
Frattini	C₁	G
Fitting, socle	C₇×C₃₁²	C₂²
LCS	G ▷ C₇×C₃₁
UCS	C₁ ◁ C₃₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₃₁×D₃₁	C₂	semidirect
2. D₇×C₃₁²	C₂	semidirect
3. C₃₁×D₂₁₇	C₂	semidirect
4. C₇×C₃₁²	C₂²	semidirect
8. C₃₁×D₃₁	D₇	direct (N × H)
9. C₃₁²	C₂×D₇	semidirect
11. D₇×D₃₁	C₃₁	direct (N × H)
13. D₂₁₇	C₂×C₃₁	semidirect
14. C₇×D₃₁	C₂×C₃₁	semidirect
17. D₇×C₃₁	D₃₁	direct (N × H)
18. D₇×C₃₁	C₂×C₃₁	semidirect
20. C₇×C₃₁	C₂×D₃₁	semidirect
21. C₇×C₃₁	C₂²×C₃₁	semidirect
30. D₃₁	D₇×C₃₁	direct (N × H)
32. C₃₁	D₇×D₃₁	direct (N × H)
33. C₃₁	C₂×D₇×C₃₁	semidirect
37. D₇	C₃₁×D₃₁	direct (N × H)
38. C₇	C₂×C₃₁×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₃₁×D₃₁	2
D₇×C₃₁²	2
C₃₁×D₂₁₇	2
C₂×C₃₁×D₃₁	7
C₂×D₇×C₃₁	31
D₇×D₃₁	31

Subgroups — D7×C31×D31 #41002064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×C₃₁×D₃₁ #41002064